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formula: 2256
omitted: 1062
the: 743
and: 469
is: 267
of: 265
#: 220
for: 209
acad: 203
a: 158
2018: 155
in: 143
to: 140
j: 108
as: 104
that: 103
are: 94
by: 86
we: 83
physics: 70
with: 69
statistical: 68
then: 65
where: 57
at: 54
c: 53
see: 51
if: 51
on: 50
#formula: 49
from: 43
pdf: 43
be: 43
given: 41
omittedformula: 40
omittedwhere: 38
european: 36
data: 36
this: 35
physical: 35
computational: 35
mechanics: 31
which: 31
all: 31
2019: 29
have: 27
or: 27
such: 26
science: 26
eq: 24
let: 24
probability: 23
both: 23
it: 23
case: 22
can: 22
values: 21
hence: 20
asformula: 20
thatformula: 19
an: 18
vector: 18
respectively: 18
": 18
other: 18
function: 17
each: 16
parameters: 16
ie: 16
byformula: 16
d: 15
n: 15
when: 15
set: 15
epj: 15
has: 14
matrix: 14
thus: 14
proof: 14
factor: 14
obtained: 14
#omitted: 13
value: 13
gang: 13
note: 13
scale: 13
two: 13
positive: 13
gauge: 13
into: 13
so: 12
will: 12
m: 12
due: 12
since: 12
fig: 12
weight: 12
3: 11
meteorology: 11
denote: 11
distribution: 11
equation: 11
configuration: 11
energy: 11
one: 11
state: 11
over: 11
omittedthe: 11
1: 10
4: 10
above: 10
continuity: 10
chosen: 10
below: 10
terms: 10
constant: 10
space: 10
boundary: 10
vertices: 10
provided: 10
three: 10
reference: 10
threshold: 9
namelyformula: 9
limit: 9
well: 9
size: 9
model: 9
different: 9
average: 9
electromagnetic: 9
k: 9
obtain: 9
large: 9
online: 9
length: 9
not: 9
diagonal: 9
i: 9
general: 9
2017: 8
henceformula: 8
here: 8
independent: 8
quantitative: 8
risk: 8
therefore: 8
conditions: 8
#the: 8
change: 8
term: 8
image: 8
following: 8
also: 8
there: 8
hand: 8
fraction: 8
final: 8
<sec>: 8
coupling: 8
rate: 8
s: 8
same: 8
dimers: 8
consider: 8
small: 8
between: 8
fitness: 8
finally: 8
=: 8
only: 8
0: 7
2: 7
shape: 7
corresponding: 7
omittedby: 7
calculated: 7
us: 7
but: 7
real: 7
defined: 7
region: 7
materials: 7
expression: 7
coefficients: 7
free: 7
integral: 7
engineering: 7
though: 7
boundary-layer: 7
biomedical: 7
choice: 7
dimer: 7
horizontal: 7
zero: 7
theory: 7
any: 7
time: 7
number: 7
some: 7
rational: 7
posterior: 7
numerical: 7
constants: 7
b: 7
leads: 7
using: 7
local: 7
7: 6
genotype: 6
scales: 6
velocity: 6
assume: 6
random: 6
ncertainty: 6
respect: 6
t: 6
element: 6
sequence: 6
#and: 6
scaling: 6
charge: 6
input: 6
than: 6
follows: 6
denotes: 6
total: 6
e: 6
discontinuity: 6
map: 6
fixed: 6
##: 6
radius: 6
findformula: 6
become: 6
shows: 6
unit: 6
high: 6
correlation: 6
density: 6
resp: 6
maximum: 6
law: 6
satisfy: 6
segment: 6
gb: 6
493: 5
roots: 5
either: 5
linearly: 5
etc: 5
initial: 5
implies: 5
was: 5
sites: 5
get: 5
states: 5
volume: 5
displacement: 5
corresponds: 5
score: 5
order: 5
splitting: 5
reduces: 5
feature: 5
expressed: 5
null: 5
effect: 5
measurable: 5
shift: 5
proves: 5
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reduced: 5
another: 5
whereas: 5
points: 5
holds: 5
line: 5
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orthogonal: 5
strength: 5
product: 5
hoc: 5
landscapes: 5
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dominant: 5
parameter: 5
non-zero: 5
readsformula: 5
bound: 5
need: 5
f: 5
abelian: 5
sign: 5
horizon: 5
material: 5
target: 5
whole: 5
quantity: 5
difference: 5
under: 5

 

 
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1    2018    ACAD    ...ional Journal of Computer Vision      #all shape vectors Formula omitted with a squared norm Formula omitted above a threshold Formula omitted. This threshold is selected so that Formula omitted
2    2018    ACAD    European Physical J C      #, hence simple roots have either Formula omitted or Formula omitted. # We introduce a chemical potential for the Cartan, as in the
3    2019    ACAD    EPJ Data Science      #, and thus our model specifies that the outcome Formula omitted will occur with probability Formula omitted. By choosing an appropriate discrimination threshold theta
4    2018    ACAD    Boundary-Layer Meteorology      #yield values of Formula omitted, Formula omitted, Formula omitted, corresponding to 1.1, 0.2, and 0.7 times their respective reported values
5    2018    ACAD    European Physical J C      #to the beta function of Formula omitted linearly in Formula omitted, Formula omitted, Formula omitted, etc, namelyFormula omittedwhere Formula omitted means
6    2018    ACAD    Hydrobiologia      #et al., 2015). Wind stress (Formula omitted) from remote sensing were considered. These quantities are derived from ocean surface
7    2017    ACAD    American Economist      #two. (V.1, p. 261) # Formula Omitted: See PDF # Exceptionalism has three determinants as stated in Equation 3a.
8    2018    ACAD    J Statistical Physics      #3), in this case Formula omitted, Formula omitted, henceFormula omittedBy continuity, Formula omitted for the chosen Formula omitted, Formula
9    2018    ACAD    J Statistical Physics      #Fitness Landscapes # A fitness landscape is a mapping Formula omitted assigning each genotype a real-valued fitness. Starting from an initial genotype Formula omitted
10    2018    ACAD    J Statistical Physics      #omitted of Formula omitted such that Formula omitted, Formula omitted and Formula omitted. Here, we denote A as the cardinality of a
11    2018    ACAD    J Statistical Physics      #, if Formula omitted, Formula omitted, and Formula omitted, then Formula omitted. This implies that Formula omitted, hence from (
12    2017    ACAD    American Economist      #constraint states that the accumulation of commodity stocks, Formula Omitted: See PDF, equals the net purchases of commodity stocks plus the excess
13    2018    ACAD    European Physical J C      #is, we proceed to compare Formula omitted and Formula omitted at scales parametrically below the quantum gravity scale and derive the consequences of certain
14    2018    ACAD    Computational Mechanics      #boundary conditions does not affect the limit value of Formula omitted is attributed to the extent of the plastic zone size in the specific problem
15    2018    ACAD    Computational Mechanics      #Formula omitted matrix. Each column of the matrix Formula omitted can be calculated by running a linear elastic or plastic DNS with a perturbation
16    2018    ACAD    Boundary-Layer Meteorology      #(roughness) parameters d, Formula omitted and Formula omitted from the mean velocity profile. # Background # Knowledge of the flow over
17    2018    ACAD    ...ncertainty and Quantitative Risk      #n greater than or equal to0, the equations Formula omitted have unique solutions by Theorem 3.1. In general, the coefficients in (
18    2018    ACAD    J Statistical Physics      #A similar but not identical transfer matrix technique for Formula omitted was originally introduced by Evans and Steinsaltz 20. # Finding eigenvalues of arbitrary integral
19    2019    ACAD    Crime Science      #on, through to the sites held by gang Formula omitted, the gang immediately above Formula omitted in the hierarchy. Gang Formula omitted
20    2018    ACAD    European Physical J C      #of the highest derivative terms (of the type Formula omitted) quadratic in curvature, which result from the UV behaviour of the form-factor
21    2018    ACAD    J Statistical Physics      ## Random utility Here we assume the random errors Formula omitted and Formula omitted are independent and extreme-value distributed, such that Formula omitted #
22    2018    ACAD    ...ncertainty and Quantitative Risk      #from barX (omega). We denote by Formula omitted the completion with respect to Formula omitted. For t element of0, T
23    2018    ACAD    ...ncertainty and Quantitative Risk      #sub-subsequence Formula omitted we get the a.s. convergence Formula omitted # Thus, for the original sequence, a.s. Formula omitted and therefore
24    2018    ACAD    J Statistical Physics      #Formula omitted. Note from the above conditions on Formula omitted, Formula omitted and Formula omitted, and (2.2) thatFormula omittedLet us
25    2018    ACAD    Computational Mechanics      #, during the analysis, a constant axial load Formula omitted is applied at the end of the component to simulate the constant centrifugal load
26    2018    ACAD    ...ional Journal of Computer Vision      #on the model subspace by finding the shape vector Formula omitted that generates a shape instance Eq. (1) that is as close
27    2018    ACAD    J Statistical Physics      #Formula omitted, Formula omitted as Formula omitted and Formula omitted as Formula omitted. Formula omitted # Proof of Corollary 4.2 # Proof #
28    2018    ACAD    Computational Mechanics      #the specific heat Formula omitted and change in enthalpy Formula omitted for a stainless steel SS316L between handbook properties (H.B) and a CALPHAD-based
29    2018    ACAD    J Statistical Physics      #numerically through a standard algorithm. The behaviors of Formula omitted for the gamma distribution and the negative gamma distribution are illustrated in Fig. 4
30    2018    ACAD    J Statistical Physics      #subsequent two sections by showing that Formula omitted and Formula omitted, respectively. # Identities Formula omitted, Formula omitted for Odd n #
31    2018    ACAD    European Physical J C      #(there are no charged particles), but Formula omitted, so the matching begins near the compactification scale, exactly where we expect
32    2018    ACAD    European Physical J C      #The virtual and real corrections, Formula omitted and Formula omitted, as well as the collinear counter term, Formula omitted, are defined
33    2018    ACAD    European Physical J C      #we have the inverse situation when Formula omitted and Formula omitted. # At this point we can write down the area per unit length
34    2018    ACAD    J Statistical Physics      #and external field Formula omitted. The scaling factor Formula omitted is the limiting effective size of the set of sites Formula omitted. Notice
35    2018    ACAD    European Physical J C      #charged particles, and the tower of states above Formula omitted may be very subextremal with respect to Formula omitted as a result. Nonetheless
36    2018    ACAD    Computational Mechanics      #. For example, if a Kriging surrogate model Formula omitted is used to replace Formula omitted, then the prediction of the surrogate model
37    2018    ACAD    European Physical J C      #cast by five-dimensional EMCS black hole with inclination angle Formula omitted for different values of charge q and the spin a with the case Formula
38    2019    ACAD    Progress Earth Planetary Sci      #a sustained forcing of superposed sinusoidal meridional modes as Formula omitted # where W m is amplitude of the m th meridional mode of w
39    2018    ACAD    J Materials Science      #distribution law, respectively. In both cases, Formula omitted is the average volume occupied by each microcrack. In other words, Formula
40    2018    ACAD    EPJ Data Science      #to the state if the input gate vector (Formula omitted) is larger than the forget gate vector (Formula omitted), Formula
41    2018    ACAD    J Statistical Physics      #holds for Formula omitted, with Formula omitted and Formula omitted. # The proof for the case Formula omitted follows from arguments similar to
42    2018    ACAD    Computational Mechanics      #omitted belongs to the space of admissible displacement fluctuation Formula omitted. # The goal is to find the displacement fluctuation field Formula omitted that
43    2018    ACAD    J Materials Science      #simplest maximum principal stress criterion for microscopic fracture, Formula omitted. Due to Formula omitted, the resultant formulation of Formula omitted is given
44    2018    ACAD    European Physical J C      #summation can the limit Formula omitted be taken. Formula omitted and Formula omitted are the four and d dimensional phase space element. As
45    2018    ACAD    J Statistical Physics      #the sr -plane. The shaded region corresponds to Formula omitted such that Formula omitted or Formula omitted with Formula omitted see PDF for image
46    2018    ACAD    ...ional Journal of Computer Vision      #the tracking process. We set the stability threshold Formula omitted to 0.38 to conservatively update the filter Formula omitted for maintaining the long-term memory
47    2016    ACAD    Computers Biology Medicine      #entropy EL is formulated by the following equation: Formula omitted. See PDF where m denotes the number of flowline segments, Dj is
48    2018    ACAD    J Materials Science      #omittedandFormula omittedwhere Formula omitted is the position vector and Formula omitted is the center of the grains. The grain advection velocity corresponding to each
49    2018    ACAD    European Physical J C      #are the metric Formula omitted, the electromagnetic four-potential Formula omitted, and the scale field k (x). The effective action for
50    2019    ACAD    EPJ Data Science      #the binning Formula omitted of Formula omitted with splits Formula omitted, the total score Formula omitted can be calculated from Eq. (2
51    2018    ACAD    European Physical J C      #omitted the underlying Born configuration and its order, Formula omitted in case of a QCD splitting function and Formula omitted in case of a
52    2018    ACAD    J Statistical Physics      #omitted, is the following expression: Formula omittedwhere Formula omitted is given by (2.1). Having (2.14), the Pfaffian
53    2018    ACAD    ...ional Journal of Computer Vision      #contain the shape eigenvectors Formula omitted. Also, Formula omitted is the shape vector that contains the parameters (coefficients) Formula omitted that
54    2018    ACAD    Computational Mechanics      #for drawing a definite conclusion regarding the value of Formula omitted for infinitesimal Formula omitted, see Sect. 5.2.2. # Unlike the example of the
55    2018    ACAD    Computational Mechanics      #12f, for " free " boundary conditions, Formula omitted. As was also observed in Fig. 11f, the global response of the
56    2018    ACAD    European Physical J C      #constant and we obtain Formula omitted. Even if Formula omitted grows asymptotically the large E part of the integral is enhanced and Formula omitted
57    2018    ACAD    European Physical J C      #1) compatible with unitarity the Wald entropy in Formula omitted is: Formula omittedFinally, at quantum level the form-factors receive corrections strictly related
58    2019    ACAD    BioMedical Engineering OnLine      #SC reduces formula omitted, formula omitted, and formula omitted by 20.25%, 8.37%, and 7.86%, respectively, compared to DLS. #
59    2018    ACAD    J Statistical Physics      #omitted, there is a discontinuity in the map Formula omitted, at Formula omitted, though both Formula omitted and Formula omitted will be
60    2018    ACAD    J Statistical Physics      #Formula omitted, Formula omitted and Formula omitted as Formula omitted. Formula omitted # Proof of Corollary 4.3 # Proof # As indicated in
61    2018    ACAD    Boundary-Layer Meteorology      #omittedabove the canopy in neutral stratification. Here, Formula omitted is the aerodynamic roughness length, Formula omitted is the friction velocity and Formula
62    2018    ACAD    European Physical J C      #an LWGC-saturating tower of extremal particles. For fixed Formula omitted there is an approximately extremal particle in the IR theory (i.e., with
63    2018    ACAD    J Statistical Physics      #is slightly different. If Formula omitted, then Formula omitted due to the factor Formula omitted, Formula omitted On the other hand,
64    2018    ACAD    J Statistical Physics      #Formula omitted, which contradicts (3). Formula omitted # Since Formula omitted is empty, let us considerFormula omittedAnalogous to the decomposition
65    2018    ACAD    Computational Mechanics      #, b for " hard " boundary conditions, Formula omitted, and " free " boundary conditions, Formula omitted, respectively. The
66    2018    ACAD    ...ional Journal of Computer Vision      #when the confidence score is below the re-detection threshold Formula omitted and avoid the computationally expensive search in sliding window. In terms of the
67    2018    ACAD    Computational Mechanics      #omitted where Formula omitted is the volumetric change, Formula omitted and Formula omitted are the bulk modulus and the derivative of the bulk modulus
68    2018    ACAD    J Statistical Physics      #In particular, the largest eigenvalue will correspond to Formula omitted in the limit Formula omitted. A similar but not identical transfer matrix technique
69    2019    ACAD    EPJ Data Science      #The method bins the values of each important feature Formula omitted to decompose the m -dimensional selected feature space into smaller non-overlapping blocks, such
70    2018    ACAD    Computational Mechanics      #Formula omitted is a vector of deterministic inputs, Formula omitted is a vector of aleatory inputs, Formula omitted is a vector of epistemic
71    2019    ACAD    BioMedical Engineering OnLine      #omitted tissues is obtained by combining initial fraction distribution formula omitted and formula omitted. The final formula omitted is obtained by adding the constraints
72    2018    ACAD    J Statistical Physics      ## If Formula omitted and Formula omitted, then Formula omitted, due to the factor Formula omitted, Formula omitted. On the other
73    2018    ACAD    J Materials Science      #structure oriented along the Formula omitted direction, the Formula omitted interplanar distance is found to be equal to 0.25 nm, and all the
74    2018    ACAD    ...ncertainty and Quantitative Risk      #measure associated with X n can be expressed as Formula omitted Let Formula omitted # <sec> # where Formula omitted stands for the null sets
75    2018    ACAD    European Physical J C      #which can be related with the gravitational coupling by Formula omitted), and (ii) the electromagnetic coupling Formula omitted. Furthermore,
76    2018    ACAD    European Physical J C      #integrated subtraction term and differentially subtracted real emission for Formula omitted at Formula omitted on the choice of recoil partner for the final state photon
77    2018    ACAD    EPJ Data Science      #, the 3-grams extracted were: Formula omitted, Formula omitted, Formula omitted, and Formula omitted. Each of the L unique 3-grams
78    2018    ACAD    J Family Violence      #variance in slopes must come from Formula omitted and Formula omitted; in effect, we are claiming that this earlier model was misspecified.
79    2018    ACAD    European Physical J C      #(6.4) implies that the particles lighter than Formula omitted are, on average, superextremal. # Comparisons at lower energies # We have
80    2018    ACAD    Computational Mechanics      #elastic potential energy Formula omitted and the regularization energy Formula omitted, Formula omitted. The elastic potential energy is given asFormula omittedwhere Formula omitted
81    2018    ACAD    J Statistical Physics      #. Because the exponential growth rate is rescaled by Formula omitted, the curve for BN is constant at 1. The results for the
82    2018    ACAD    Computational Mechanics      #), we also have the model discrepancy term Formula omitted of the physics-based structural model, and the stochastic residual term Formula omitted (
83    2018    ACAD    European Physical J C      #observable is independent of the choice of the technical Formula omitted and Formula omitted parameters as well as the choice Formula omitted of spectator for
84    2018    ACAD    J Family Violence      #level 2, and explained total variance. Unlike Formula omitted in standard regression, variance explained in MLM is not produced by estimation,
85    2019    ACAD    EPJ Data Science      #split Formula omitted as the split s that maximizes Formula omitted of Eq. (3). Choosing Formula omitted, and binning the
86    2018    ACAD    J Statistical Physics      #how small it is, that we make around Formula omitted will lead to a dramatic change in the macroscopic behaviour of the system.
87    2018    ACAD    European Physical J C      #parametrically favors Formula omitted, the same scaling as Formula omitted in the (most optimistic) SU(2) case. For instance, all benchmark
88    2018    ACAD    J Statistical Physics      #number of horizontal, vertical and diagonal dimers in Formula omitted by Formula omitted, Formula omitted and Formula omitted respectively, then the dimer
89    2019    ACAD    Earth, Planets and Space      #, Pederson current), where Formula omitted and Formula omitted are horizontal neutral wind velocity and geomagnetic field, respectively (Rishbeth 1997)
90    2018    ACAD    J Statistical Physics      #current reaches a maximum and decreases to zero at Formula omitted. # A detailed study of the diffusion and current in periodic one-dimensional discrete
91    2011    FIC    FantasySciFi      # 861627837 (ProQuest:... denotes formula omitted.) # THINGS HAD MOVED FAST on the Pacific coast. Harry Angleton
92    2018    ACAD    Computational Mechanics      #determined from the wallclock time for the multi-scale analysis Formula omitted measured on the previous macro-iteration, according to the number of slaves that were
93    2018    ACAD    J Statistical Physics      #is called a (mutational) path(-way). Here Formula omitted is the initial genotype and Formula omitted the final genotype, and n is
94    2019    ACAD    BioMedical Engineering OnLine      #omitted (formula omitted). Correspondingly, matrix formula omitted will change to formula omitted. The final objective is as follows: formula
95    2018    ACAD    European Physical J C      #the simple examples that we discussed above. While Formula omitted in KK theory, this continues below the compactification scale even though at low
96    2018    ACAD    ...ional Journal of Computer Vision      #the i -th triangle. Note that the indices Formula omitted correspond to vertices of the mesh. # Texture information is given as a
97    2018    ACAD    J Statistical Physics      #Formula omitted. On the other hand, if Formula omitted, then Formula omitted, hence Formula omitted. # Consider Formula omitted.
98    2018    ACAD    J Statistical Physics      #social utilities associated with a choice Formula omitted and Formula omitted is a random utility term. The latter part of the utility is unobserved
99    2016    ACAD    Computers Biology Medicine      #. It is described by the following formula: Formula omitted. See PDF where vsr→ is the separation velocity, vc→ is the velocity
100    2018    ACAD    J Statistical Physics      #likewise Formula omitted choices in placing each of the Formula omitted diagonal dimer pairs, hence Formula omitted. # For any given configuration Formula
101    2018    ACAD    J Statistical Physics      #for the process to travel from Formula omitted to Formula omitted (thereby allowing the process to go backwards and re-enter the interval Formula omitted
102    2018    ACAD    ...ncertainty and Quantitative Risk      #fields Formula omitted which are measurable with respect to Formula omitted (where Formula omitted denotes the predictable sigma -algebra on x0, T generated
103    2018    ACAD    J Statistical Physics      #omitted is occupied completely by horizontal dimers. Let Formula omitted and Formula omitted obtained from Formula omitted by the shift Formula omitted on the
104    2018    ACAD    J Statistical Physics      #henceFormula omittedBy continuity, Formula omitted for the chosen Formula omitted, Formula omitted, and small Formula omitted. This proves that Formula omitted
105    2019    ACAD    Crime Science      #node size scaled according to estimated gang territory size Formula omitted (Table 1). Edges are directed from the aggressor gang to the
106    2019    ACAD    BioMedical Engineering OnLine      #distribution formula omitted and formula omitted. The final formula omitted is obtained by adding the constraints of Eq. (13) to formula
107    2019    ACAD    BMC Evolutionary Biology      #known) is rewritten using a given reduced alphabet formula omitted, a 10-member subset of the 20 genetically coded amino acids, and formula
108    2019    ACAD    Crime Science      #for new gang activity at any one time is Formula omitted. At equilibrium, the proportions of space taken up by each gang are
109    2018    ACAD    Boundary-Layer Meteorology      #the ordinate see PDF for image # Formula omittedwhere Formula omitted is the ordinate, Formula omitted is the slope, Formula omitted is the
110    2018    ACAD    EPJ Data Science      #Formula omitted. Formula omitted, Formula omitted, Formula omitted, and Formula omitted denote the bias vectors. # BLSTM # An LSTM
111    2019    ACAD    Applied Network Science      #(i, j) element ofE C if Formula omitted # That is, vertex i has degree at least j if (11
112    2019    ACAD    BMC Evolutionary Biology      #to these informatic quantities. The optimal substitution rules formula omitted for the reduced alphabets formula omitted for five SCOP classes examined in this work
113    2019    ACAD    Crime Science      #the strict competitive hierarchy (Tilman 1994): Formula omitted # The first two terms on the right-hand side of Eq. 13 together
114    2018    ACAD    J Statistical Physics      #a current going to zero for large E provided Formula omitted. The physical reason is that as E increases the walker also goes to
115    2018    ACAD    European Physical J C      #omitted or for the case of Formula omitted, Formula omitted. In the absence of the charge q, the condition for the existence
116    2018    ACAD    ...ncertainty and Quantitative Risk      #indistinguishable. Hence, we find a null set Formula omitted, such that for omega outside this set and for all Formula omitted:
117    2018    ACAD    European Physical J C      #of the surface Formula omitted and a two-dimensional disk Formula omitted. On Formula omitted the time coordinate plays the role of an angular coordinate
118    2018    ACAD    J Statistical Physics      #, we may set up our starting equation for Formula omitted asFormula omittedHere, we introduced another theta function Formula omitted enforcing the condition Formula
119    2019    ACAD    EPJ Data Science      #maximum likelihood estimate of the probability of the outcome Formula omitted in the block Formula omitted, and thus our model specifies that the outcome
120    2018    ACAD    European Physical J C      #a heavy particle i, expanding in powers of Formula omitted to obtain a threshold correction to Formula omitted together with an infinite sum of
121    2018    ACAD    ...ncertainty and Quantitative Risk      #with radius Formula omitted in c 0 and let Formula omitted be the ball of radius N in Formula omitted. The balls Formula omitted
122    2018    ACAD    European Physical J C      #any Formula omitted (with Formula omitted) and Formula omitted (the sLWGC is approximately satisfied with sublattice index P). # Thus
123    2018    ACAD    European Physical J C      #. Asymptotically for large Formula omitted we findFormula omittedwhere Formula omitted is the number of positive roots and Formula omitted is an order-one function which
124    2018    ACAD    Computational Mechanics      #the i th experiment input setting Formula omitted and Formula omitted is the i th observation, Formula omitted is a realization of the observation
125    2018    ACAD    Computational Mechanics      #variation of Formula omitted, as the internal length Formula omitted tends to zero, is illustrated in Fig. 14a, b for " hard
126    2018    ACAD    European Physical J C      #the initial state momentum rescaling parameters Formula omitted, Formula omitted and Formula omitted, as well as the splitting variables Formula omitted, Formula
127    2018    ACAD    European Physical J C      #beta functions in Formula omitted are Formula omitted and Formula omitted, whereas Formula omitted. It is to be noticed that, as Formula
128    2018    ACAD    J Statistical Physics      #their journey. In other words, the points Formula omitted become traps when Formula omitted, and more so for large E. Trapping
129    2018    ACAD    European Physical J C      #that the black holes studied here are unstable (Formula omitted), both classically and in the scale dependent scenario. To conclude,
130    2018    ACAD    European Physical J C      #multiparticle state with charge Formula omitted for some rational Formula omitted. If Formula omitted is rational then so are Formula omitted and Formula omitted
131    2019    ACAD    Journal of Big Data      #the industries being studied. Next, for state Formula omitted and posterior draw Formula omitted, the benchmarked posterior state-level value is calculated as
132    2018    ACAD    ...ncertainty and Quantitative Risk      #that Formula omitted # Then, it holds that Formula omitted # for all t element of0, T such that Formula omitted Here Formula
133    2018    ACAD    European Physical J C      #may choose Formula omitted, Formula omitted such that Formula omitted to arbitrarily good precision. If the WGC is satisfied in the un-Higgsed theory
134    2018    ACAD    Computational Mechanics      #present, i.e. Formula omitted, and consequently, Formula omitted from Eq. (4), we obtain Formula omitted from Eq.
135    2018    ACAD    J Statistical Physics      #accessible path. # We say a path from Formula omitted to Formula omitted is direct if Formula omitted is the number of steps taken
136    2019    ACAD    EPJ Data Science      #, projected onto the space defined by two features Formula omitted and Formula omitted. As the first step, S3D bins the values of
137    2018    ACAD    J Statistical Physics      #not allow for a closed form solution for general Formula omitted. However, a straightforward calculation shows that the expected results can be recovered
138    2018    ACAD    J Statistical Physics      #, which was obtained by maximizing each of the Formula omitted ray locus contributions between the two possible states of that locus. Thus Formula
139    2018    ACAD    European Physical J C      #surface terms given by integrals over the entangling surface Formula omitted. The surface term for Formula omitted is just the area of the surface
140    2018    ACAD    J Statistical Physics      #. Let Formula omitted and Formula omitted obtained from Formula omitted by the shift Formula omitted on the line Formula omitted. Then again Formula
141    2019    ACAD    BMC Evolutionary Biology      #in a given protein, the equation becomes: formula omitted # The two component terms above are parameterized the same way as Eqs. (
142    2018    ACAD    European Physical J C      #the fit to inflationary phenomenology prefers Formula omitted and Formula omitted, this requires a large integer of order Formula omitted to appear in the
143    2018    ACAD    J Statistical Physics      #follows. Consider the lexicographic ordering of the vertices Formula omitted. Namely, Formula omittedThenFormula omittedObserve thatFormula omittedbecause Formula omitted and Formula omitted.
144    2018    ACAD    J Statistical Physics      #. # In the former case, we had Formula omitted. In the latter case, the particle jumped to Formula omitted after a
145    2018    ACAD    J Statistical Physics      #). # Fig. 5: a Plots of Formula omitted for various NK structures. The standard normal distribution is chosen as the base
146    2017    ACAD    American Economist      #deficits must be equal to nominal government debt: Formula Omitted: See PDF # It is the interaction of the supply and demand for
147    2018    ACAD    European Physical J C      #based on demanding that semiclassical black holes of radius Formula omitted not evaporate too quickly 49, 3.1. # Suppose now that we have a
148    2018    ACAD    J Materials Science      #steel punches of diameter d 0. The proportions Formula omitted are adopted. The applied load F induces an almost identical tensile stress over
149    2019    ACAD    Journal of Big Data      #to note that there is no variability in the Formula omitted values from posterior draw to draw. Therefore, the CV calculated using (
150    2018    ACAD    European Physical J C      #and Formula omitted on the one hand side and Formula omitted on the other are defined on phase spaces of different parton multiplicity, Eq
151    2019    ACAD    BMC Bioinformatics      #maxconc, so the dash lines end at around formula omitted # From Additional file 1: Figure S2, it can be observed that
152    2019    ACAD    EPJ Data Science      #feature Formula omitted has an Formula omitted improvement of Formula omitted. At the next stage of the algorithm, given Formula omitted has been
153    2018    ACAD    European Physical J C      #cosmic rays was reconstructed in the energy range from Formula omitted to Formula omitted from the data of the Grande extension 14. The spectrum
154    2018    ACAD    J Statistical Physics      #Formula omitted and consider the case Formula omitted, Formula omitted, and Formula omitted. By Proposition 3.1 (3), in this
155    2018    ACAD    Boundary-Layer Meteorology      #likely to be available, though the value of Formula omitted will have some variability. With three unknowns (d, Formula omitted,
156    2018    ACAD    European Physical J C      #, we obtainFormula omittedup to numerical factors, where Formula omitted is the rank plus half the number of roots, equal to Formula omitted
157    2018    ACAD    J Materials Science      #distribution as below: Formula omittedwhere Formula omitted and Formula omitted are constants with Formula omitted. Formula omitted has the unit of Formula omitted
158    2018    ACAD    J Statistical Physics      #implies that only beneficial mutations that increase fitness (Formula omitted) have a chance of going to fixation in the population. Thus in
159    2018    ACAD    European Physical J C      #charge lattice Formula omitted intersects the plane orthogonal to Formula omitted in an Formula omitted dimensional sublattice generalizes the requirement that Formula omitted is rational
160    2018    ACAD    Boundary-Layer Meteorology      #logarithmic region occupies more than 50% of the depth Formula omitted of the boundary layer, and that the fraction is smaller (Formula omitted
161    2018    ACAD    Boundary-Layer Meteorology      #, respectively, the shaded areas Formula omitted, Formula omitted are the frontal and plan areas of the buildings, respectively, and Formula
162    2019    ACAD    BMC Evolutionary Biology      #points in the grid. # This algorithm yields formula omitted, the optimal discretization of the (gammai-1, gammai) space into k
163    2018    ACAD    J Materials Science      #omitted in a Cartesian coordinate system is expressed as Formula omitted. Here Formula omitted is a dimensionless function of coordinates Formula omitted. In
164    2018    ACAD    J Materials Science      #after the removal of an atomic row in the Formula omitted and Formula omitted planes. Finally, Fig. 11d shows one possible atomic structural
165    2018    ACAD    European Physical J C      #Formula omitted (each has finite coarseness). Formula omitted is Weyl-invariant by assumption, whereas since Formula omitted is Weyl-invariant, Formula omitted
166    2019    ACAD    BioMedical Engineering OnLine      #lesion of JPEG format and with the size of formula omitted and formula omitted. To have a dataset with equal-size images, the smaller
167    2018    ACAD    Computational Mechanics      #i is considered to vary linearly with pressureFormula omittedwhere Formula omitted is the reference elasticity tensor at 0 Pa and 300 K and Formula omitted
168    2019    ACAD    EPJ Data Science      #, and a high correlation (Formula omitted, Formula omitted). # The third example is Nepal and Qatar (NPLQAT) on
169    2018    ACAD    J Materials Science      #constant b being confined to the three cases: Formula omitted. As represented by line-1 in Fig. 2, per the foregoing introduction,
170    2018    ACAD    European Physical J C      #spectators for the final state photon splitting ocurring at Formula omitted. No dependence on this choice is observed. Please note that for this
171    2019    ACAD    Journal of Big Data      #CV equalsFormula omitted # Benchmarking # The state-level estimates Formula omitted are not guaranteed to sum to the published national MRTS estimate. This consistency
172    2018    ACAD    Oecologia      #disappeared through time (Latitude x Period interaction: Formula omitted = 12.23, P = 0.057). Belgian larvae tended to have a
173    2018    ACAD    Boundary-Layer Meteorology      #, the logarithmic law occupies a substantial fraction (Formula omitted) of the depth of the boundary layer. We also find the relevant
174    2018    ACAD    Computational Mechanics      ## 5 The symbol for the absolute/fixed configuration " Formula omitted " should not be confused with the respective symbol " Formula omitted " used
175    2019    ACAD    Crime Science      #. If the in-degree exceeds the out-degree, gang Formula omitted is a net importer of violence. If the out-degree exceeds the in-degree,
176    2018    ACAD    J Family Violence      #omitted # Assuming that Formula omitted is fixed (Formula omitted = Formula omitted) Eq. 7 can be substituted into Eq. 4
177    2019    ACAD    BMC Bioinformatics      #i, 1, y i, 2 with formula omitted and y i, 2 member of0,1 for survival outcomes, where y i
178    2018    ACAD    J Materials Science      #nominal strength Formula omitted and specimen size d (Formula omitted) at a given failure probability as shown in Fig. 8. For comparison
179    2018    ACAD    J Statistical Physics      #ThenFormula omittedHere there is a discontinuity in the map Formula omitted at Formula omitted for Formula omitted. This discontinuity is not followed by change
180    2018    ACAD    J Statistical Physics      #moment method Hegarty and Martinsson showed that 33Formula omittedas Formula omitted. Thus the probability of finding any direct accessible path to the global maximum
181    2018    ACAD    J Statistical Physics      #be a product of Formula omitted independent realizations of Formula omitted for HoC landscapes with k loci. # For the probability to find an accessible
182    2018    ACAD    European Physical J C      #and iron absorber sheets (Formula omitted Pb and Formula omitted Fe) underneath the Formula omitted detectors to measure the muonic shower component (
183    2018    ACAD    J Statistical Physics      #the following theorem: # Theorem 5.2 # Let Formula omitted. Then for all Formula omitted, Formula omitted # Numeric data for Pfaffians
184    2018    ACAD    European Physical J C      #unique weight which satisfies Formula omitted for all weights Formula omitted in R. A weight Formula omitted is dominant if Formula omitted for all
185    2018    ACAD    EPJ Data Science      #score. The f1 score is calculated as: Formula omitted, and is between 0 and 1, where 1 shows perfect precision and
186    2018    ACAD    Computational Mechanics      #set of parent nodes of node Formula omitted and Formula omitted is the conditional probability density function (PDF) of node Formula omitted for
187    2018    ACAD    Computational Mechanics      #omitted mm) and b the 5th increment (Formula omitted mm) of the multi-scale 3D uniaxial traction problem, using a different number
188    2018    ACAD    J Statistical Physics      #small in absolute terms, then the linear approximation Formula omitted can be employed and the transition probabilities become proportional to the (positive)
189    2018    ACAD    J Statistical Physics      #a The solid curve indicates the numerical solution for Formula omitted. The dashed curve shows the first order approximation Formula omitted in Eq.
190    2018    ACAD    Computational Mechanics      #Fig. 13b. # Fig. 19: Convergence error of Formula omitted with Formula omitted, for different values of Formula omitted. (a)
191    2018    ACAD    EPJ Data Science      #omitted, Formula omitted, Formula omitted, and Formula omitted denote the weight matrices of different gates for input Formula omitted, and Formula
192    2018    ACAD    Oecologia      #not influenced by the food treatment (GLMM, Formula omitted = 0.06, P = 0.81, Fig. 1a). While winter survival
193    2018    ACAD    European Physical J C      #flat spacetime metric and derivatives. Inverting the operator Formula omitted 52, 53 and making use of the form-factors (2) and (
194    2018    ACAD    European Physical J C      #Formula omitted, Formula omitted, Formula omitted, Formula omitted, Formula omitted, Formula omitted and Formula omitted are numerical constants depending only
195    2017    ACAD    Computers Biology Medicine      #is mathematically expressed as Formula omitted. See PDF Formula omitted. See PDF where xdisp and ydisp are the displaced coordinates from the adjacent
196    2018    ACAD    European Physical J C      #non-positive integer because Q is dominant and lies in Formula omitted. Since the graviton has spin 2, this state also has spin 2
197    2018    ACAD    European Physical J C      ## allow all particles as spectators. # The Formula omitted are set to the phase space point independent value Formula omitted, with Formula
198    2018    ACAD    ...ncertainty and Quantitative Risk      #Formula omitted, we cancel out terms and get Formula omitted # Bounding Formula omitted by Formula omitted, leads us to Formula omitted #
199    2019    ACAD    BioMedical Engineering OnLine      #4. When SNR is 80 dB, the formula omitted of the two algorithms is very small, and the main difference is that
200    2018    ACAD    J Statistical Physics      #spin value of Formula omitted and those labelled by Formula omitted are free to choose any of the two spin values. In this section
201    2018    ACAD    J Statistical Physics      #that field w, we introduce the driving parameter Formula omitted and we consider the discrete-time nearest-neighbor random walk Formula omitted on Formula omitted with
202    2018    ACAD    European Physical J C      #, then only the beta functions for the operators Formula omitted of dimension D are non-zero, namelyFormula omittedThis is due to the fact that
203    2018    ACAD    Computational Mechanics      #(a) Formula omitted. (b) Formula omitted see PDF for image # Rate-independent plasticity as a limit case of viscoplasticity #
204    2018    ACAD    J Statistical Physics      #the process to go backwards and re-enter the interval Formula omitted). Averaging only over the dynamics we have the following " Dynkin formula
205    2018    ACAD    European Physical J C      #short, the quadratic operator in the graviton fluctuation Formula omitted, including the gauge fixing, readsFormula omitted where all indices are neglected,
206    2018    ACAD    European Physical J C      #The impact parameters Formula omitted, Formula omitted and Formula omitted for the photon orbits around the five-dimensional EMCS black hole determine the contour of
207    2017    ACAD    American Economist      #of capital and labor determine the real wage, Formula Omitted: See PDF, and the real return on capital, Formula Omitted:
208    2019    ACAD    EPJ Data Science      #set of data points in Formula omitted for which Formula omitted (resp. Formula omitted). In general, given n splits and
209    2019    ACAD    Crime Science      #probability that gang 1 spreads to a site and Formula omitted is the probability that the site already hosts gang 2. # It is reasonable
210    2019    ACAD    BioMedical Engineering OnLine      ## formula omittedwhere formula omitted. The weighting value formula omitted is the volume fraction of the formula omitted tissue in the formula omitted element
211    2017    ACAD    American Economist      #withdrawal of money and debt from the economy: Formula Omitted: See PDF # In an environment with zero inflation, the budget constraint
212    2018    ACAD    J Materials Science      #specimen size is close to the maximum aggregate size Formula omitted, the size effect on strength can be well characterized by Eq. (
213    2019    ACAD    Crime Science      #omitted > 0 and isolating either Formula omitted or Formula omitted. The mathematical results are conceptually the same as for the two-gang asymmetrical case
214    2018    ACAD    Computational Mechanics      #drag through the hardening law 18 given asFormula omittedwhere Formula omitted and Formula omitted are the current and reference elastic shear modulus, respectively,
215    2018    ACAD    Boundary-Layer Meteorology      #i.e. Formula omitted) differ since negative values of Formula omitted occur below Formula omitted for the data of Macdonald et al. (2000
216    2018    ACAD    J Statistical Physics      #we might as well have changed Formula omitted into Formula omitted with Formula omitted: The essence is thatFormula omittedSuch behavior where the exponential decay
217    2018    ACAD    European Physical J C      #(32), the terms Formula omitted and Formula omitted are given byFormula omittedFormula omittedwhere Formula omitted is the Carter constant 48 andFormula omittedThese
218    2018    ACAD    Computational Mechanics      #we haveFormula omittedSimilarly, when the true posterior distribution Formula omitted is used for uncertainty quantification in the actual physics, we haveFormula omittedAccording to
219    2018    ACAD    European Physical J C      #in the last line we apply the species bound Formula omitted. Rearranging the last inequality, we have Formula omitted, which has the
220    2018    ACAD    European Physical J C      #and this always comes linearly in the front coefficients Formula omitted in the second variation. So in the expression for a divergent part of
221    2018    ACAD    Boundary-Layer Meteorology      #roughness parameters (d, Formula omitted, and Formula omitted) from samples of a mean velocity profile for boundary-layer flow over model urban
222    2018    ACAD    European Physical J C      #if we fix Formula omitted, then we need Formula omitted to generate significant screening, but then the species bound gives Formula omitted,
223    2018    ACAD    J Statistical Physics      #. # Fig. 4: a A plot of Formula omitted as a function of the shape parameter s for the gamma distribution (red
224    2018    ACAD    J Family Violence      #. Thus the variance in slopes must come from Formula omitted and Formula omitted; in effect, we are claiming that this earlier model
225    2018    ACAD    Boundary-Layer Meteorology      #lines mark the top of the roughness elements at Formula omitted and Formula omitted for the optimized, and Formula omitted and Formula omitted for
226    2018    ACAD    J Statistical Physics      #can decompose Formula omitted asFormula omittedwhere Formula omitted and Formula omitted can be further decomposed asFormula omittedHere Formula omitted is the number of diagonal dimers
227    2018    ACAD    J Statistical Physics      #previous example is a gamma distribution with shape parameter Formula omitted, and in fact gamma-distributed fitness values appear in several earlier studies where exact
228    2017    ACAD    Computers Biology Medicine      #omitted. See PDF Formula omitted. See PDF Formula omitted. See PDF Formula omitted. See PDF where is the predefined threshold distance
229    2018    ACAD    J Statistical Physics      #, the size of Formula omitted is given by Formula omitted unlike classical NK structures that satisfy Formula omitted. Because of this huge combinatorial
230    2018    ACAD    Oecologia      #Belgian larvae had overall the highest food intake (Formula omitted = 20.69, P < 0.001, Fig. 2e-h), differences among latitudes
231    2018    ACAD    J Statistical Physics      #contour. # Let us introduce a standard configuration Formula omitted as follows. Consider the lexicographic ordering of the vertices Formula omitted. Namely
232    2018    ACAD    J Statistical Physics      #Thus, Formula omitted will be a product of Formula omitted independent realizations of Formula omitted for HoC landscapes with k loci. # For the
233    2018    ACAD    J Statistical Physics      #the average time required for the particle to hit Formula omitted if it starts at Formula omitted. # It is therefore essential to compute
234    2019    ACAD    Crime Science      #At equilibrium, the superior gang holds a proportion Formula omitted of the sites and the inferior gang a proportion Formula omitted of the sites
235    2018    ACAD    J Statistical Physics      #, using the result for the HoC model that Formula omitted actually converges to a non-zero constant for Formula omitted, Formula omitted also converges
236    2018    ACAD    European Physical J C      #number of phase space points in the computation of Formula omitted is kept constant for each process, such that the indicated statistical uncertainty can
237    2018    ACAD    European Physical J C      #significantly larger: Formula omitted. Such a large Formula omitted is in clear tension with sLWGC constraints on even mildly small gauge couplings.
238    2018    ACAD    ...analytical and Nuclear Chemistry      #enthalpy change of reaction R1 is calculated as: Formula omitted # The separation factor for the isotope exchange reaction R2 is simply its equilibrium
239    2019    ACAD    Environmental Systems Research      #adsorptive capacity was calculated using Eq. 6. Formula omitted # General Langmuir isotherm equation was indicated in Eq. 7. Formula omittedwhere
240    2018    ACAD    Computational Mechanics      #(d) Formula omitted. (e) Formula omitted. (f) Formula omitted see PDF for image # Fig. 18:
241    2017    ACAD    Computers Biology Medicine      #set of corrected boundary contour coordinates, expressed as Formula omitted. See PDF # Thus, the corrected boundary contour is given by Formula
242    2018    ACAD    J Statistical Physics      #in the map Formula omitted at Formula omitted for Formula omitted and for choices of (s, r) from the shaded region in
243    2018    ACAD    European Physical J C      #Formula omitted with gauge couplings Formula omitted and an Formula omitted abelian gauge kinetic matrix Formula omitted (generalizing Formula omitted for a single Formula
244    2018    ACAD    J Statistical Physics      #that Formula omitted. # For the scaling limit Formula omitted at constant k, we can find bounds on the probability that the candidates
245    2016    ACAD    Clinical Therapeutics      #al, 11 the relationship was reformulated as: Formula omitted. See PDF # Thus: Formula omitted. See PDF # This was
246    2018    ACAD    J Statistical Physics      #Formula omitted is a set of two neighboring vertices Formula omitted connected by an edge. A dimer configuration Formula omitted on Formula omitted is
247    2017    ACAD    Forensic Science Intl      #in the form of Euler-Lagrange differential equation as: Formula omitted. See PDF # Thus, Eq. (19) can be re-written
248    2018    ACAD    J Statistical Physics      #the square lattice, which corresponds to the weight Formula omitted. He showed that in this case Formula omitted and he assumed that Formula
249    2018    ACAD    European Physical J C      #not change the conclusion. # More generally, Formula omitted when Formula omitted is not too sharply peaked at Formula omitted. For instance
250    2018    ACAD    J Statistical Physics      #the case Formula omitted, Formula omitted, and Formula omitted. Since n is even, then by Proposition 3.1 (1),
251    2018    ACAD    Computational Mechanics      #omitted see PDF for image # The variation of Formula omitted, as Formula omitted tends to zero, is illustrated in Fig. 20a,
252    2018    ACAD    J Statistical Physics      #for which Formula omitted has the same sign as Formula omitted. On the other hand, there is zero net magnetization as h goes
253    2018    ACAD    J Statistical Physics      #Formula omitted. If exactly one of the vertices Formula omitted, Formula omitted is covered by a diagonal dimer, then the superposition Formula
254    2018    ACAD    ...ncertainty and Quantitative Risk      #respect to Formula omitted. The same holds for Formula omitted # and Formula omitted # Hence, for delta n defined in (33
255    2018    ACAD    Computational Mechanics      #the regularization flux drives Formula omitted to zero for Formula omitted 31. This affects the evolution of the LSP, and hence, the
256    2018    ACAD    Computational Mechanics      #number of load cycles, and Formula omitted and Formula omitted are two parameters estimated based on experimental data. # Due to the uncertainty
257    2018    ACAD    Computational Mechanics      #Recovery of nodal value of the plastic strain, Formula omitted, from values of Formula omitted at the integration points, over a patch
258    2018    ACAD    European Physical J C      #Q is the largest charge in the tower, Formula omitted. Again, this leads to the conclusionFormula omittedThus we see that a tower
259    2018    ACAD    ...ional Journal of Computer Vision      #determining the tracking failures. We learn the filter Formula omitted using both HOG and HOI features. # Online Detector # A robust tracking
260    2018    ACAD    Computational Mechanics      #, after observing data D), and " Formula omitted " stands for " proportional to ". Methods for computing Formula omitted are
261    2018    ACAD    European Physical J C      #can be visualized by plotting Formula omitted vs. Formula omitted for different values of the rotation parameter (a) and the charge (
262    2018    ACAD    J Statistical Physics      #row, so thatFormula omittedSimilarly, the sign function Formula omitted is obtained from Formula omitted by the reversal of the horizontal and diagonal arrows
263    2019    ACAD    Earth, Planets and Space      #1224 sites report k values (while 7479 report Formula omitted values). k > 50 has been taken as a parameter for some
264    2018    ACAD    J Statistical Physics      #again Formula omitted. Finally, if both vertices Formula omitted, Formula omitted are covered by diagonal dimers, then Formula omitted, because
265    2019    ACAD    Earth, Planets and Space      #direction at the AF step which produces the smallest Formula omitted is selected). # Palaeointensity data and metadata # These fields include data
266    2018    ACAD    J Statistical Physics      #, Formula omitted be the Borel Formula omitted-algebra of Formula omitted, and Formula omitted a sequence of probability measures on Formula omitted. Assume
267    2019    ACAD    BMC Bioinformatics      #1,..., w N as follows: formula omitted # formula omitted # where formula omitted and formula omitted are parameters of the
268    2018    ACAD    European Physical J C      #the following conditions has to be met: # Formula omitted, with Formula omitted # Formula omitted or Formula omitted, with Formula omitted
269    2018    ACAD    J Statistical Physics      #comparison with simulation results obtained for the sequence length Formula omitted (black dashed line of Fig. 4a), that a very precise estimate
270    2017    ACAD    Public Administration Q      #Indirect Cost Measurement # (ProQuest:... denotes formula omitted.) # The statistical model is a hierarchical logistic regression to fit the probability
271    2018    ACAD    Computational Mechanics      #For a given realization of the epistemic uncertainty sources Formula omitted is given byFormula omittedin which Formula omitted is the CDF of the life distribution
272    2018    ACAD    J Statistical Physics      #. Now, since the sign of the superpositions Formula omitted and Formula omitted is Formula omitted, we obtain that Formula omitted, hence
273    2019    ACAD    EPJ Data Science      #learns an ordered set of important, orthogonal features Formula omitted, a partitioning Formula omitted of the selected feature space with corresponding Formula omitted
274    2018    ACAD    J Statistical Physics      #. (6). However each fitness contribution Formula omitted is now not only dependent on Formula omitted, but also on the states
275    2018    ACAD    J Statistical Physics      ## If Formula omitted, Formula omitted, and Formula omitted, then Formula omitted # Proof # (1) Assume that Formula omitted
276    2018    ACAD    J Statistical Physics      #of center loci, there can be at most Formula omitted local maxima on the star neighborhood. This by itself already proves that Formula
277    2018    ACAD    Computational Mechanics      #CDF over Formula omitted as Formula omitted, if Formula omitted experiment data are observed in the segment Formula omitted, the probability of observing
278    2016    ACAD    Computers Biology Medicine      #better quality if CEn has lower value 63. Formula omitted. See PDF # Correlation coefficient # The correlation coefficient (CCR) represents
279    2018    ACAD    European Physical J C      #containing the explicit Laurent expansion in Formula omitted as Formula omitted needs to reproduce the correct Formula omitted and Formula omitted coefficients in order to
280    2018    ACAD    Computational Mechanics      #We may reformulate Eq. (8) as Formula omitted, whereby it appears that Formula omitted plays the role of back-stress in kinematic
281    2018    ACAD    J Statistical Physics      #total number of elements (multiplicities included) of Formula omitted and we index the NK edges (in some fixed manner) by natural
282    2018    ACAD    J Statistical Physics      #Formula omitted as shown in Fig. 5, hence Formula omitted. This shows that for any Formula omitted, Formula omitted. The proof
283    2019    ACAD    BMC Bioinformatics      #example y i member of0,1 for binary outcomes or formula omitted for metric outcomes. They may, however, also take the form of
284    2018    ACAD    European Physical J C      #22 When the UV WGC scales Formula omitted and Formula omitted are both below Formula omitted, the UV theory enforces the stronger constraint Formula
285    2018    ACAD    European Physical J C      #omitted. If Formula omitted then the WGC scale Formula omitted for the second gauge theory lies above Formula omitted, so there is no
286    2018    ACAD    European Physical J C      #, with Formula omitted # Formula omitted, with Formula omitted. # A positive energy density in a region that rests outside the horizon
287    2018    ACAD    EPJ Data Science      #of h consecutive POIs in the trajectory and obtained Formula omitted. The trajectory representation is computed in the max pooling layer, Formula omitted
288    2018    ACAD    European Physical J C      #omitted or-with the help of the timelike Killing vector Formula omitted that exhibits a Killing horizon at Formula omitted - by Formula omitted. In
289    2018    ACAD    Computational Mechanics      #micro-stress. # 6 The material time derivative is denoted Formula omitted. # 7 The number of independent, non-zero components in the plastic strain
290    2018    ACAD    European Physical J C      #the mass of the scale-dependent black hole. The Formula omitted identification is made when we take the limit Formula omitted, since the scale-dependent
291    2018    ACAD    European Physical J C      #Formula omitted, Formula omitted, Formula omitted and Formula omitted are numerical constants depending only on the non-running coupling constants in front of the
292    2018    ACAD    European Physical J C      #omitted abelian gauge kinetic matrix Formula omitted (generalizing Formula omitted for a single Formula omitted). Irreps are labeled by Formula omitted for
293    2018    ACAD    Computational Mechanics      #spaces with gradients and divergence, respectively, in Formula omitted. The mixed-dual weak form of the time-discrete problem can now be stated as
294    2018    ACAD    ...ncertainty and Quantitative Risk      #object (Y, Z, U) in Formula omitted. # Step 4: # In the final step, we want to
295    2019    ACAD    Crime Science      #that are currently unoccupied, captured by the term Formula omitted. If the availability of sites were the only constraint, then gang activity
296    2019    ACAD    EPJ Data Science      #(Formula omitted) and a high synchronicity (Formula omitted). The seasonal pattern of country pairs falling into this category appears to
297    2018    ACAD    J Statistical Physics      #with an index describing the model. There are Formula omitted genotypes and thus the fraction of genotypes expected to be local maxima can be
298    2018    ACAD    Computational Mechanics      #variance of the prediction is given by 38Formula omittedwhere Formula omitted is a parameter estimated during the surrogate modeling. # Based on the above
299    2018    ACAD    European Physical J C      #production of at least two jets at a hypothetical Formula omitted collider at a centre-of-mass energy of 1 TeV and inclusive single jet production in
300    2018    ACAD    European Physical J C      #of the strong coupling in the Born process and Formula omitted, i.e. it takes the values 2 in the gg channel, 1 in
301    2018    ACAD    European Physical J C      #the same time the NLO QCD correction to the Formula omitted process and will in general exhibit the corresponding infrared singularities. Further, matters
302    2018    ACAD    Computational Mechanics      #prediction model, and not simply the posterior distribution Formula omitted. If the probability that the likelihood function is accurate is high, this
303    2018    ACAD    ...ncertainty and Quantitative Risk      #to Formula omitted # We split up the set Formula omitted into Formula omitted # Taking into account that less than or equal to'
304    2018    ACAD    European Physical J C      #SUSY-breaking scale Formula omitted, which is larger than Formula omitted if we demand that gravitinos decay before BBN (and can be even larger
305    2018    ACAD    J Statistical Physics      #and Formula omitted, we have Formula omitted, Formula omitted, Formula omitted and Formula omitted. The expression for the average current Formula
306    2018    ACAD    European Physical J C      #It also defines the initial state momentum rescaling parameters Formula omitted, Formula omitted and Formula omitted, as well as the splitting variables Formula
307    2018    ACAD    Computational Mechanics      #in the material domain, i.e. Formula omitted and Formula omitted are unaffected by the configurational velocity Formula omitted, cf. Runesson et al.
308    2018    ACAD    European Physical J C      #overcompensated by the decrease in the black hole horizon Formula omitted as it can be appreciated from e.g. (57). In the lower
309    2017    ACAD    American Economist      #the Constitution (Tocqueville, 1963). # Formula Omitted: See PDF # Interest group activities appear in a conflict in relation with
310    2018    ACAD    Computational Mechanics      #In the second case, only the components of Formula omitted parallel to the outward pointing unit normal Formula omitted on the boundary vanish,
311    2018    ACAD    J Statistical Physics      #Appendix B we present numerical data for the Pfaffians Formula omitted for different dimensions m and n. # Dimer Model and Kasteleyn Matrices #
312    2018    ACAD    European Physical J C      #that the entropy function has positive values only when Formula omitted or the power k is a negative, even integer. # The purpose
313    2018    ACAD    ...ional Journal of Computer Vision      #Formula omitted is the average of the response maps Formula omitted and Formula omitted. We locate the target object based on the maximum value
314    2019    ACAD    ... of the National Research Centre      #the following equation: Formula omitted # Where: Formula omitted # Where: Formula omitted # Biochemical analysis # Sample extraction # One hundred
315    2018    ACAD    J Statistical Physics      #results can be recovered in the two limiting cases Formula omitted (for linear landscapes) and Formula omitted (for HoC landscapes).
316    2018    ACAD    Computational Mechanics      #omitted, and " free " boundary conditions, Formula omitted, respectively. In the latter figures, the relative error in Formula omitted
317    2018    ACAD    J Statistical Physics      #, Formula omitted and Formula omitted. Then, Formula omitted is a local maximum if Formula omitted or Formula omitted for all Formula omitted
318    2018    ACAD    European Physical J C      #of the charged particles. The angular resolution is Formula omitted with a small dependence on the shower size Formula omitted. The reconstruction algorithm
319    2018    ACAD    ...ional Journal of Computer Vision      #7) as Formula omitted. The optimal scale Formula omitted can then be inferred by: Formula omittedIn Fig. 6, we compare four
320    2018    ACAD    European Physical J C      #integral can be evaluated in four dimensions. The Formula omitted and Formula omitted operators are infrared finite by construction and, thus, evaluation
321    2018    ACAD    J Statistical Physics      #denote the fitness values of genotypes Formula omitted and Formula omitted, respectively, i.e., Formula omitted and Formula omitted. Then, Formula
322    2018    ACAD    Computational Mechanics      #convergence behavior for fixed values of the internal length Formula omitted irrespective of the value of the relaxation time Formula omitted. # Next,
323    2018    ACAD    Boundary-Layer Meteorology      #omitted in heterogeneous urban areas, the constraint of Formula omitted may need to be relaxed to account for, e.g., the tallest building
324    2018    ACAD    European Physical J C      #Formula omitted is chosen to satisfy Formula omitted and Formula omitted. The superextremality conditions before and after Higgsing areFormula omittedrespectively, where Formula omitted
325    2018    ACAD    J Statistical Physics      #can not be smaller than 1, the bounds Formula omitted apply. # In order to minimize the notational burden unavoidable for the large
326    2018    ACAD    ...ional Journal of Computer Vision      #top (bottom) row corresponds to deviating from Formula omitted in the direction of the corresponding texture eigenvector, with a weight of 3Formula
327    2018    ACAD    EPJ Data Science      #from the t th POI outputs a scalar feature Formula omitted where Formula omitted is a POI sequence matrix whose i th column is Formula
328    2018    ACAD    J Statistical Physics      #Formula omitted, we need thatFormula omittedWe have that Formula omitted, provided Formula omitted, due to the factor Formula omitted, Formula omitted
329    2018    ACAD    Computational Mechanics      #QOI) Formula omitted; the simulation model output Formula omitted, which is the prediction of Formula omitted, is given byFormula omittedwhere Formula
330    2018    ACAD    European Physical J C      #the ab channel. The sums run over all Formula omitted flavours of mass Formula omitted that are part of the Formula omitted-flavour PDF parametrisation
331    2016    ACAD    Computers Biology Medicine      #its feature vector f is then obtained by: Formula omitted. See PDF where the set of i are the Lagrangian multipliers of the
332    2019    ACAD    BMC Evolutionary Biology      #a particular reduced alphabet formula omitted and substitution rule formula omitted. For S loc, we considered the trimer sequence, known to carry
333    2018    ACAD    ...ncertainty and Quantitative Risk      #X n can be expressed as Formula omitted Let Formula omitted # <sec> # where Formula omitted stands for the null sets of Formula omitted
334    2018    ACAD    Computational Mechanics      #of observing Formula omitted experiment data in the segment Formula omitted becomesFormula omittedThe Bayes factor of the predicted CDF over Formula omitted after considering epistemic
335    2018    ACAD    J Materials Science      #Eq. (9) 46; Formula omittedwhere Formula omitted and Formula omitted denote the weight and volume of the substrate coated by PyC
336    2018    ACAD    Computational Mechanics      #is the speed of sound for the material, Formula omitted and Formula omitted are dimensionless constants 23. # For the regularization energy functional Formula
337    2018    ACAD    European Physical J C      #in Formula omitted, roughly Formula omitted, where Formula omitted is the gravitational coupling. # 25 If G is simply laced, we
338    2018    ACAD    European Physical J C      #, Formula omitted is the electromagnetic Lagrangian density, Formula omitted is a proportionality constant, F is the Maxwell invariant previously defined, and
339    2018    ACAD    Computational Mechanics      #Formula omitted-RDX Formula omitted are Formula omitted 14 and Formula omitted 17, respectively. The reference densities for Formula omitted- and Formula omitted-phases are
340    2018    ACAD    J Statistical Physics      #This proves that Formula omitted in the whole region Formula omitted. Formula omitted # The positivity of Formula omitted in the case Formula omitted
341    2018    ACAD    Boundary-Layer Meteorology      #omitted of the rough-plate boundary layer is small (Formula omitted, see the reviews of Jimenez 2004; Flack et al. 2005)
342    2018    ACAD    European Physical J C      #omitted (Formula omitted) and Formula omitted (Formula omitted). The most general condition for a naked singularity in the five-dimensional Myers-Perry
343    2018    ACAD    European Physical J C      #forces, gravitational forces, and other interactions; Formula omitted and Formula omitted as we have defined them become meaningless. Whether some improved
344    2018    ACAD    European Physical J C      #Formula omitted is the number of positive roots and Formula omitted is an order-one function which depends only on the direction of Formula omitted within
345    2018    ACAD    ...ional Journal of Computer Vision      #the multi-scale representation of the target. # Let Formula omitted denote the target features in the s th scale. We assign Formula omitted
346    2018    ACAD    ...ncertainty and Quantitative Risk      #as the space of all Formula omitted-progressively measurable processes Formula omitted such that Formula omitted # Let Formula omitted. We define Formula omitted as
347    2018    ACAD    European Physical J C      #omitted is the volume of the fundamental domain of Formula omitted. We can assume that the Higgs charge Formula omitted is primitive - i.e.
348    2018    ACAD    European Physical J C      #Formula omitted for Formula omitted charges Formula omitted and Formula omitted representation Formula omitted, corresponding to the highest weight vector Formula omitted. Superextremal
349    2019    ACAD    Crime Science      #al. 2017). We assume that both Formula omitted and Formula omitted are intrinsic traits that do not vary through time, but
350    2019    ACAD    Earth, Planets and Space      #depending on the research purpose, values up to Formula omitted could be considered acceptable (see Butler 1992). Fig. 9 # Histogram
351    2018    ACAD    J Statistical Physics      #and Formula omitted, then Formula omitted # If Formula omitted, Formula omitted, and Formula omitted, then Formula omitted # If Formula
352    2018    ACAD    J Statistical Physics      #of the exponential growth rate of the partition function Formula omitted. To investigate this growth rate, let us first of all note the
353    2018    ACAD    European Physical J C      #group G, there is a finite-index Weyl-invariant sublattice Formula omitted of the weight lattice Formula omitted such that for every dominant weight Formula omitted
354    2018    ACAD    J Statistical Physics      #the probability measure Formula omitted. As long as Formula omitted is a typical realization, this claim must be true. However, we
355    2018    ACAD    Computational Mechanics      #entropy. Considering the specific Helmholtz free energy, Formula omitted, and Eq. (7), we obtain the dissipation inequalityFormula omittedUsing
356    2018    ACAD    J Statistical Physics      #get a current we choose Formula omitted and let Formula omitted at rate Formula omitted, Formula omitted at rate Formula omitted for all Formula
357    2018    ACAD    Computational Mechanics      #approximate the unknown statistical model of the actual physics Formula omitted given in Eq. (14) using the BN built based on the
358    2018    ACAD    European Physical J C      #, it reduces toFormula omittedThe Komar integral readsFormula omittedwhere Formula omitted or Formula omitted, yieldingFormula omittedThe electric charge can be calculated by the Gaussian
359    2018    ACAD    J Materials Science      #(V). Particularly, the mean (Formula omitted) of the nominal strength Formula omitted as a function of specimen volume V
360    2018    ACAD    J Family Violence      #us Eq. 8 (and rearranging): Formula omitted # Note that both Formula omitted and Formula omitted have average sample-wide effects,
361    2018    ACAD    ...ncertainty and Quantitative Risk      #Another example for a function rho is given by Formula omitted # <sec> # Remark 3.2 # white. # Condition (A2) implies
362    2018    ACAD    J Family Violence      #estimation of Formula omitted by substituting Formula omitted and Formula omitted into Eq. 4: Formula omitted # Rearranging terms into fixed and random
363    2018    ACAD    European Physical J C      #, the gauge coupling Formula omitted at a scale Formula omitted is related to the low-energy gauge coupling e according to: Formula omittedwith Formula
364    2018    ACAD    J Statistical Physics      #follows: For any positive integer N, let Formula omitted, Formula omitted and Formula omitted be positive real numbers such that Formula omitted
365    2018    ACAD    Computational Mechanics      #, the minimal kinematical admissible constraint arises, where Formula omitted denotes the outward unit reference vector: Formula omittedThe space of admissible displacement fluctuations
366    2018    ACAD    ...ional Journal of Computer Vision      #three important thresholds: (1) re-detection threshold Formula omitted for activating the detection module; (2) acceptance threshold Formula omitted for
367    2018    ACAD    ...ncertainty and Quantitative Risk      #, u) is a jointly measurable version of Formula omitted which is Formula omitted-optional, so especially it is progressively measurable. # <sec>
368    2018    ACAD    EPJ Data Science      #for input Formula omitted, and Formula omitted, Formula omitted, Formula omitted, and Formula omitted are the weight matrices for the hidden
369    2018    ACAD    Computational Mechanics      #is a scalar Grneisen parameter and the initial temperature Formula omitted is 300 K. The material parameters for the temperature-volume equation of state, slip
370    2018    ACAD    Computational Mechanics      #omitted is the shape function of node I, Formula omitted is the nodal displacement, and Formula omitted is the nodal level set parameter
371    2018    ACAD    European Physical J C      #now details Formula omitted for all three setups. Formula omitted production, detailed in the left hand side plot, comprises only FF dipoles
372    2018    ACAD    J Materials Science      #the GB mobility (M GB) asFormula omittedwith Formula omitted being the GB thickness. The GB mobility is calculated asFormula omittedwhere M GB0
373    2019    ACAD    BMC Bioinformatics      #formula omitted for one epoch, and it becomes formula omitted in the next phase. The CRF layer is attached to the final output
374    2018    ACAD    J Statistical Physics      #be the number of intersections of the vertical line Formula omitted with the dimers in Formula omitted. ThenFormula omittedObviously, Formula omittedwhere Formula omitted
375    2018    ACAD    Computational Mechanics      #, Formula omitted, respectively. The value of Formula omitted from local theory is also marked with dashed line. The depicted curves pertain
376    2018    ACAD    Computational Mechanics      #contain the delta function which is non-zero only for Formula omitted, we restrict our attention of the level set evolution to a narrowband around
377    2018    ACAD    J Statistical Physics      #of locus 3, i.e. the pattern in the Formula omitted plane is simply translated along the 3-direction. Note that the direction of arrows
378    2019    ACAD    BMC Evolutionary Biology      #this I total with the fitness of the particular formula omitted. # The fitness of the prebiotic alphabet in preserving fold information is evaluated
379    2018    ACAD    J Statistical Physics      #with respect to the disorder): Formula omittedwhere Formula omitted is the time required for the walker to reach the site (1,
380    2018    ACAD    Computational Mechanics      #Formula omitted is the slip resistance on the' Formula omitted' slip system. The resolved shear stress on slip system is given asFormula
381    2019    ACAD    Applied Network Science      #, in the large-network limit N right arrowinfinity, Formula omitted # <sec> # We define the random variable D 0 with the limiting distribution
382    2019    ACAD    EPJ Data Science      #to an answer and contains a binary outcome variable Formula omitted (one indicates the answer was accepted, and zero otherwise), along
383    2018    ACAD    J Statistical Physics      #Formula omitted be such that there is a partition Formula omitted, Formula omitted and Formula omitted of Formula omitted such that Formula omitted,
384    2018    ACAD    Boundary-Layer Meteorology      #robust determination of the roughness parameters (d, Formula omitted, Formula omitted) for complex three-dimensional flow of model urban canopies. A
385    2018    ACAD    Boundary-Layer Meteorology      #is 10 m sFormula omitted, and the velocity Formula omitted at the top of the model urban canopy is 1.58 m sFormula omitted,
386    2017    ACAD    American Economist      #in which a representative agent receives an endowment, Formula Omitted: See PDF, each period. The individual transforms the endowment into a
387    2018    ACAD    J Statistical Physics      #both sides yields Formula omitted. Hence (since Formula omitted is a positive random variable), Formula omittedWe conclude thatFormula omittedTo see where
388    2018    ACAD    European Physical J C      #(3) is independent of the coordinates (Formula omitted), and hence it admits three Killing vectors, given byFormula omittedand these
389    2019    ACAD    EPJ Data Science      #from Italy to Spain) are perfectly aligned (Formula omitted, Formula omitted) without having to shift one time series by one or
390    2019    ACAD    Crime Science      #by gang Formula omitted replaces the activity of gang Formula omitted (i.e., a top-down instance of a superior gang replacing and inferior one
391    2019    ACAD    Earth, Planets and Space      #overlaid as each reference. We chose the simultaneous Formula omitted index as the input of HWM14, and called the model every 0.5 h
392    2018    ACAD    Boundary-Layer Meteorology      #Values of the areal parameters are 0.25 for both Formula omitted and Formula omitted, the aspect ratio of height to width Formula omitted is
393    2018    ACAD    European Physical J C      #only be positive in the subsets Formula omitted and Formula omitted given that the radius is again greater than Formula omitted. It is also
394    2018    ACAD    J Statistical Physics      #vertical dimers are not on the same horizontal line Formula omitted apply sequence of swaps on one of them until Formula omitted Note that in
395    2017    ACAD    Computers Biology Medicine      #the need for re-initialization of the level set: Formula omitted. See PDF where p′ (s) is the derivative of the double
396    2018    ACAD    J Statistical Physics      #with probability Formula omitted for Formula omitted. When Formula omitted we associate to it a length Formula omitted which is drawn with probability densityFormula
397    2019    ACAD    BioMedical Engineering OnLine      #the phantom study # The results of comparison of formula omitted between the two algorithms are shown in Fig. 7. The results show the
398    2018    ACAD    J Statistical Physics      #n, m) to Formula omitted (provided Formula omitted); # All other inter-site jumps are forbidden. # We then define
399    2018    ACAD    EPJ Data Science      #(2) Formula omitted, (3) Formula omitted, 4) Formula omitted, and finally, Formula omitted. The Cohen
400    2019    ACAD    Crime Science      #) has the second largest equilibrium territory proportion (Formula omitted), and so on (see Fig. 3a). Figure 5 is
401    2018    ACAD    J Statistical Physics      #omitted, respectively, i.e., Formula omitted and Formula omitted. Then, Formula omitted is a local maximum if Formula omitted or Formula
402    2018    ACAD    European Physical J C      #constant Formula omitted in front of the horizon radius Formula omitted assumes values in the segment (1, e) as k varies from
403    2018    ACAD    J Family Violence      #of variability is Formula omitted (the variance of Formula omitted). Note that the variability in the slope for sibling bullying must come
404    2016    ACAD    Computers Biology Medicine      #. It is described by the following formula: Formula omitted. See PDF where var→ is the velocity driven by the alignment rule,
405    2018    ACAD    J Materials Science      #microcracks on the volume of a material: a Formula omitted, b Formula omitted see PDF for image # Formula omitted. According to
406    2017    ACAD    American Economist      #start out with the following identical relationship. # Formula Omitted: See PDF # We focus first on the nature of the identity between
407    2018    ACAD    J Statistical Physics      #keep away from zero, uniformly in any cut-off Formula omitted. # Conclusion # We have presented mathematically fully treatable models of phase transitions
408    2018    ACAD    J Statistical Physics      #omitted, Formula omitted to produce a new configuration Formula omitted in which the vertical dimer is now above the diagonal dimer. The superposition
409    2019    ACAD    Crime Science      #. In general, the equilibrium proportion of gang Formula omitted is reduced by the total proportion of space occupied by superior gangs, scaled
410    2018    ACAD    J Statistical Physics      #In locally bounded NK structures at constant k as Formula omitted, the probability for existence of a GRSE pair of loci approaches unity exponentially
411    2018    ACAD    European Physical J C      #Fig. 2. Fig. 3 # The Hawking temperature Formula omitted and Bekenstein Hawking entropy S versus the classical mass Formula omitted for three cases
412    2019    ACAD    EPJ Data Science      #in Formula omitted as given by Formula omitted where Formula omitted in Eq. (4) is the bin in Formula omitted that contains
413    2018    ACAD    J Statistical Physics      #and diagonal dimers are pairwise placed on horizontal lines Formula omitted and Formula omitted, Formula omitted for Formula omitted or 1. We again
414    2018    ACAD    ...ional Journal of Computer Vision      #vertical directions) as training data. Each example Formula omitted, Formula omitted corresponds to a target score Formula omitted, where (m
415    2018    ACAD    J Materials Science      #. Formula omitted; and (3). Formula omitted. # Formula omitted. Equation (18) reduces to Eq. (
416    2018    ACAD    European Physical J C      #By (5.33) this implies Formula omitted for Formula omitted, and in particular gauge theory and gravitational loop corrections become large at parametrically
417    2018    ACAD    J Statistical Physics      #contours, one nontrivial positive square-shaped contour, and Formula omitted negative contours as shown in Fig. 9b. Hence, Formula omittedFormula omitted #
418    2018    ACAD    ...ional Journal of Computer Vision      #model. Then, we use the squared norm Formula omitted as the criterion to detect failures of the dense correspondence estimation. This is
419    2018    ACAD    European Physical J C      #coupling. At one loop, the gauge coupling Formula omitted at a scale Formula omitted is related to the low-energy gauge coupling e according
420    2018    ACAD    Computational Mechanics      #is available, the uncertainty regarding the unknown quantity Formula omitted can be updated using Bayes' theorem as 21Formula omittedwhere Formula omitted is the
421    2018    ACAD    J Statistical Physics      #, e.g. one could require Formula omitted for some Formula omitted as to limit the definition to more selectively robust maxima. Since one can
422    2019    ACAD    BioMedical Engineering OnLine      #DLS, which sets formula omitted in SC and formula omitted in DLS. # To satisfy the constraint formula omitted, a substitution is made
423    2018    ACAD    J Materials Science      #of a master curve to correlate the compound parameter Formula omitted and the nominal strength sigma N, rather than to find the best fitting
424    2018    ACAD    J Statistical Physics      #2), in this case Formula omitted, Formula omitted, henceFormula omittedBy continuity, Formula omitted for the chosen Formula omitted, Formula
425    2019    ACAD    Applied Network Science      #) In the subcritical (and critical) case Formula omitted, all components of the RIGC are sublinear in the network size N.
426    2018    ACAD    J Family Violence      #is multiplied by Formula omitted; commutative multiplication of Formula omitted by the terms in the parentheses and rearranging into fixed and random terms we
427    2018    ACAD    Computational Mechanics      #the internal length to the characteristic element length, Formula omitted, is depicted in logarithmic scale for both axes, in Fig. 13a,
428    2018    ACAD    ...ncertainty and Quantitative Risk      #' (s) 2 and the fact that Formula omitted a.s. leads to Formula omitted since rho is a concave function. #
429    2019    ACAD    EPJ Data Science      #omitted) is the set of data points in Formula omitted for which Formula omitted (resp. Formula omitted). In general,
430    2018    ACAD    J Statistical Physics      #field on some (random) stretches of length Formula omitted during their journey. In other words, the points Formula omitted become traps
431    2018    ACAD    European Physical J C      #, we findFormula omittedNote that in the weak regime Formula omitted we have approximated the total mass as the classical one. This should be
432    2018    ACAD    European Physical J C      #coupling constant, R is the Ricci scalar, Formula omitted is the electromagnetic Lagrangian density, Formula omitted is a proportionality constant, F
433    2019    ACAD    BMC Bioinformatics      #Through this step, the matrices X I and formula omitted are uniquely mapped to their respective time-series z t and epsilon t. #
434    2019    ACAD    BioMedical Engineering OnLine      #first derivative of formula omitted to zero 36: formula omitted # The temporary fraction vector formula omitted of formula omitted tissues is obtained by
435    2019    ACAD    EPJ Data Science      #of Formula omitted is the difference between these two Formula omitted: Formula omitted The coefficients Formula omitted facilitate our analysis of (a)
436    2018    ACAD    J Statistical Physics      #chosen i.i.d. from a continuous probability distribution, then Formula omitted is effectively a HoC landscape over one locus. This linear model is the
437    2018    ACAD    J Statistical Physics      #number by 2. # Fix Formula omitted and let Formula omitted be arbitrary. Consider, again, the elementary move described in Step 1
438    2018    ACAD    EPJ Data Science      #weight matrices for the hidden state Formula omitted. Formula omitted, Formula omitted, Formula omitted, and Formula omitted denote the bias vectors
439    2019    ACAD    Crime Science      #one another (Formula omitted, Formula omitted, Formula omitted). Fig. 8 # The in-degree and out-degree for the Hollenbeck gang homicide
440    2018    ACAD    J Statistical Physics      #let Formula omitted be the law of empirical average Formula omitted (2.11) under the product law Formula omitted on Formula omitted. Then
441    2018    ACAD    European Physical J C      #in (56) is negative in the region Formula omitted and when Formula omitted or Formula omitted, which are the roots of the
442    2018    ACAD    J Statistical Physics      #omitted, i.e. such that Formula omitted for all Formula omitted. Thus a local maximum is a sink in the fitness graph. Different
443    2018    ACAD    J Statistical Physics      #in the reference group is given byFormula omittedNote that Formula omitted Therefore it follows from (3.9) and the strong law of large numbers
444    2018    ACAD    J Statistical Physics      #, we have Formula omitted, Formula omitted, Formula omitted and Formula omitted. The expression for the average current Formula omitted reduces toFormula
445    2018    ACAD    ...ncertainty and Quantitative Risk      #, k =1,2,3 are the components of a in Formula omitted, Formula omitted and L 2 (). The space c 0 is
446    2018    ACAD    European Physical J C      #Sect. 3.1, this is the scale at which Formula omitted. We findFormula omittedwhere we use the Dynkin index I (j) of
447    2018    ACAD    European Physical J C      #for each PDF choice. In each case, Formula omitted is found to be stable under the variation of Formula omitted. Finally,
448    2018    ACAD    J Materials Science      #The expected " master curve " characteristic for the Formula omitted correlation defined by Eq. (15) has been validated by the strength
449    2018    ACAD    J Statistical Physics      #, this integral only depends on the two quantities Formula omitted and Formula omitted. Using the cumulant expansion Eq. (68),
450    2018    ACAD    J Statistical Physics      #that is, the change of Formula omitted to Formula omitted where a diagonal dimer Formula omitted is shifted to Formula omitted for some Formula
451    2018    ACAD    J Statistical Physics      #, i.e. Formula omitted for all Formula omitted and Formula omitted. Then the fitness graph is well-defined and acyclic (see Fig. 8 for
452    2018    ACAD    J Statistical Physics      #Formula omitted and Formula omitted as Formula omitted. Formula omitted # Proof of Corollary 4.3 # Proof # As indicated in the proof of
453    2018    ACAD    J Statistical Physics      #Formula omitted is invariant under the dynamics, where Formula omitted is defined asFormula omittedNote however that that is ill-defined unless Formula omitted for all
454    2018    ACAD    J Family Violence      #good enough reason to remove Formula omitted and treat Formula omitted as fixed. In other words, the within-family association of sibling bullying and
455    2019    ACAD    BMC Bioinformatics      #from marker data. # The pedigree-based native contribution formula omitted of individual i is the sum of the genetic contributions individual i has from
456    2018    ACAD    Computational Mechanics      #first discretize the performance prediction domain into several segments Formula omitted, where Formula omitted is the lower bound of the i th segment,
457    2018    ACAD    ...ncertainty and Quantitative Risk      #satisfies for all t element of0, T: Formula omitted # The BSDE (7) itself will be denoted by (, f
458    2019    ACAD    Progress Earth Planetary Sci      #wind stress (eta) is estimated to be Formula omitted # where rho 0 is set to 1025 kg m-3. Using the hydrostatic
459    2018    ACAD    Computational Mechanics      #the plausibility of two hypotheses: the null hypothesis Formula omitted and the alternative hypothesis Formula omitted. For given observation data Formula omitted,
460    2018    ACAD    BMC Bioinformatics      #1, 2 and 4. The C and formula omitted values were 0.1, 1, 10 and 100. For each combination of
461    2018    ACAD    European Physical J C      #omittedwhere Formula omitted is a Ricci-flat compact manifold, Formula omitted acts freely and transitively on Formula omitted, and Formula omitted is a finite
462    2018    ACAD    J Statistical Physics      #. Thus # Formula omitted for Formula omitted and Formula omitted, though # Formula omitted Similarly, Formula omitted, for Formula omitted and
463    2018    ACAD    J Statistical Physics      #split the full set of dimers in a configuration Formula omitted into three classes: horizontal, vertical, and diagonal with respective weights Formula
464    2019    ACAD    EPJ Data Science      #. The correlation is high (Formula omitted, Formula omitted) and synchronous (Formula omitted). The peak season takes place during
465    2018    ACAD    European Physical J C      #a general argument for why we consistently find that Formula omitted and Formula omitted become Formula omitted at parametrically the same energy. We focus
466    2018    ACAD    ...ional Journal of Computer Vision      #reasons. First, we learn the translation filter Formula omitted over a complementary set of features: HOG and HOI. Our tracker is
467    2019    ACAD    BMC Evolutionary Biology      #estimated as a sum of mutual information terms: formula omitted # where I bb (S, C bb formula omitted) refers to
468    2018    ACAD    European Physical J C      #there is now a clear evidence that just above Formula omitted the spectrum shows a significant' concave' behavior. A further feature in
469    2018    ACAD    J Statistical Physics      #Formula omitted, but discards all other loci in Formula omitted. The orthogonal projection Formula omitted yields those alleles that have been discarded by
470    2018    ACAD    J Statistical Physics      #the expectation over the disorder, Formula omittedTo determine Formula omitted, note thatFormula omittedwhere Formula omitted and Formula omitted are iid, and Formula
471    2018    ACAD    European Physical J C      #E is at leastFormula omittedusing an integral approximation for Formula omitted and Formula omitted. Thus, applying the species bound, we obtainFormula omittedup
472    2018    ACAD    J Statistical Physics      #continuous time random walk on the comb-like configuration space Formula omitted where a stands for " active " and s for " sleeping " (
473    2018    ACAD    J Statistical Physics      #omitted for Odd n # Lemma 5.1 # Let Formula omitted. Then Formula omitted and Formula omitted. # Proof # Recall that Formula
474    2018    ACAD    J Statistical Physics      #(generalized) NK model over a locus set Formula omitted is parametrized by a multiset Formula omitted containing subsets of Formula omitted. This
475    2018    ACAD    J Statistical Physics      #Formula omitted. On the other hand, if Formula omitted, then Formula omitted, hence Formula omitted. If Formula omitted, then
476    2018    ACAD    J Statistical Physics      #6.10), we have Formula omitted choices for Formula omitted. Therefore, Formula omittedhenceFormula omittedThe higher excited states have at least Formula omitted
477    2019    ACAD    BMC Evolutionary Biology      #of all individual contacts within a cut-off distance: formula omitted # where d c is the distance (nearest atom approach) between two
478    2018    ACAD    ...ncertainty and Quantitative Risk      #. It follows that Formula omitted # Note that Formula omitted # Hence, by (20) and Formula omitted a.s., we have
479    2018    ACAD    ...ional Journal of Computer Vision      #total number of channels. The kernel correlation matrix Formula omitted can be computed by a summation of the element-wise products over each feature channel
480    2018    ACAD    J Statistical Physics      #define the total fitness asFormula omittedIf the values of Formula omitted are chosen i.i.d. from a continuous probability distribution, then Formula omitted is effectively
481    2018    ACAD    J Statistical Physics      #integrate over the contour in Fig. 10 for some Formula omitted. By the Cauchy integral formula and the periodicity of f (x,
482    2018    ACAD    J Statistical Physics      #Formula omitted (provided Formula omitted); # Formula omitted for jumps from site (n, m) to Formula omitted (provided
483    2018    ACAD    ...ncertainty and Quantitative Risk      ## where Formula omitted. By the monotonicity of Formula omitted and Jensen's inequality, we get that Formula omitted # Doob's martingale
484    2017    ACAD    American Economist      #fixed coupon of $1 and a corresponding yield, Formula Omitted: See PDF. The quantity of bonds can be either positive or negative
485    2018    ACAD    European Physical J C      #four-potential Formula omitted taking into account the running of Formula omitted areFormula omittedIt is important to note that, in any quantum field theory the
486    2018    ACAD    J Statistical Physics      #up of N individuals labelled by the indexed set Formula omitted. The reference group is divided into three non-overlapping subgroups with Formula omitted,
487    2018    ACAD    Computational Mechanics      #CDF computation over segment Formula omitted is accurate and Formula omitted is the probability operator. # Equations (32) and (34)
488    2019    ACAD    Earth, Planets and Space      #omittedwhere Formula omitted is the ion-neutral collision frequency, Formula omitted is the ion cyclotron frequency, Formula omitted is the electric field. The
489    2018    ACAD    J Statistical Physics      #Formula omitted. Then for all Formula omitted, Formula omitted # Numeric data for Pfaffians Formula omitted in Appendix B illustrate the identities Formula
490    2018    ACAD    J Statistical Physics      #it is sufficient to pick an arbitrary reference genotype Formula omitted and focus on the problem of finding the probability Formula omitted for Formula omitted
491    2018    ACAD    European Physical J C      #function f (r) and the electromagnetic coupling Formula omitted versus radial coordinate r for three cases. The first line correspond to the
492    2018    ACAD    ...ional Journal of Computer Vision      #feature vector Formula omitted, the output cell state Formula omitted and hidden state Formula omitted are: Formula omittedFormula omittedFormula omittedFormula omittedFormula omittedFormula omittedFormula
493    2019    ACAD    Earth, Planets and Space      #by applying the same equation. Then the difference Formula omitted between Formula omitted and Formula omitted can be written asFormula omitted # This difference
494    2018    ACAD    J Statistical Physics      #functionFormula omittedAll the three components of the utility function Formula omitted are subject to the assumption of Sect. 2.1. Here the subscript c of
495    2019    ACAD    Crime Science      #slows as the environment fills up, but eventually Formula omitted. # Equation (1) goes one step further to assume that gang
496    2018    ACAD    European Physical J C      #scales. # 22 When the UV WGC scales Formula omitted and Formula omitted are both below Formula omitted, the UV theory enforces the
497    2018    ACAD    J Statistical Physics      #is given by the probability measure Formula omitted on Formula omitted given byFormula omittedThe quantity Formula omitted is a normalization term called the partition function
498    2018    ACAD    European Physical J C      #(Formula omitted), namelyFormula omittedFormula omittedThe form-factor Formula omitted stays arbitrary, but is constrained by renormalizability to have the same (or
499    2018    ACAD    J Statistical Physics      #chosen Formula omitted, Formula omitted, and small Formula omitted. This proves that Formula omitted in the whole region Formula omitted. The
500    2018    ACAD    Computational Mechanics      #estimated as Formula omitted and Formula omitted, where Formula omitted represents a normal distribution with mean Formula omitted and standard deviation Formula omitted.
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