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1  yet to be quantified empirically or modeled mathematically.
2 as been well studied both experimentally and mathematically.
3 ationally expensive and difficult to analyse mathematically.
4 late to other analyses both conceptually and mathematically.
5 are monitored systematically and deconvolved mathematically.
6 ed a simplified matK gene expression network mathematically.
7  and could be modeled both statistically and mathematically.
8  data to model individual acquisition curves mathematically.
9 shown to be bistable both experimentally and mathematically.
10 xG), and S(MaxG_root), which we demonstrated mathematically.
11 and different origin samples can be compared mathematically.
12                                           We mathematically account for the temporal response of the
13 oice and exchange that is neurally detailed, mathematically accurate, and behaviorally relevant.
14 The best level of predictability (99.6%) was mathematically achieved when severe centrilobular NIA an
15                   Here, we observe and model mathematically an unexpected fundamental mechanism by wh
16 -peptide association within the membrane are mathematically analogous to the adsorption discussed her
17 e patterning of haemocyte movements, we have mathematically analysed and simulated their contact repu
18                  We address this question by mathematically analyzing the nonlinear dynamics of learn
19 Additionally, we suggest several methods for mathematically analyzing these data to best utilize the
20 , so that the entire forest can be described mathematically and behaves structurally and functionally
21 e model for steady-state solutions to find a mathematically and biologically relevant stable steady-s
22 iations on this morphology have been modeled mathematically and computationally but the developmental
23                                Here, we show mathematically and empirically that cell-type-specific m
24           Here, we analysed seizure dynamics mathematically and established a taxonomy of seizures ba
25 by anaerobic ethylbenzene hydroxylation both mathematically and experimentally, develops alternative
26                                We show, both mathematically and experimentally, that the single nucle
27                                 We examined, mathematically and graphically, the relationship of PaO2
28 rify this question, we modelled this process mathematically and performed extensive deterministic and
29                   We solve the kinetic model mathematically and use it to analyze kinetic data from f
30 due to anemia is prevalent, can be corrected mathematically, and correction uncovers occult hypoglyce
31                       We verify our analysis mathematically, and show it reproduces (a) the time-depe
32           We formalized the sushi belt model mathematically, and show that it can achieve arbitrarily
33 show that inclusion of processes represented mathematically as density-dependent regulation of either
34 erials, and how materials can be represented mathematically as genomes, describes fitness landscapes
35                   Historically, stylized and mathematically based models have been used for establish
36  design and construction can be derived from mathematically based structures.
37                                              Mathematically, based on non-singular transformation, we
38 se-generating and analysis equations matched mathematically, bias in some parameters arose when sampl
39 unconstrained parameters and can be analyzed mathematically both at neuronal and cognitive levels.
40               Stomata have long been modeled mathematically, but until now, no systems analysis of a
41 g a Pt-Ir/H(2)O/DCE boundary that is defined mathematically by a line around the surface of the wire.
42      The dynamics of the system is described mathematically by a target-mediated drug disposition mod
43                       We address the problem mathematically by adopting the framework of the phenomen
44 by cooperative interactions and is described mathematically by the slope parameter or Hill coefficien
45 and, if possible, their results are combined mathematically by using a process known as meta-analysis
46             We formally define multiplexing, mathematically characterise which systems can multiplex
47                                           To mathematically characterize the organization of inputs w
48                            First, we seek to mathematically characterize the quality of the profile b
49                              Identifying and mathematically characterizing these algorithms has led t
50 (TCGA) and in-house patient databases can be mathematically classified into high miR-21/low Sox2 (Cla
51 ould brain signals be spatially selected and mathematically combined to ensure that decoding reflects
52 enged due to the use of highly-parameterized mathematically complex structures to capture the release
53 ure, which has long been sought and has been mathematically computed and known to exist in the resear
54 he conservativeness of our approach has been mathematically confirmed in this study.
55 ional approach to dissipative systems allows mathematically consistent treatment of the bio-ions Na(+
56 R(2) = 0.94-0.99), which were observed to be mathematically consistent with classic DLVO theory.
57 intuition about this system can be gained by mathematically constructing a single gene with effective
58 antifying the effect size of cis-eQTLs and a mathematically convenient approach for systematic modeli
59 any other basic population models, makes the mathematically convenient assumption that populations ar
60  such regressions by studying artificial but mathematically convenient fitness landscapes.
61 es a composite fluorescent contour, which is mathematically converted to a sequence-specific fluoresc
62 may lead to invalid results even if they are mathematically correct.
63 r and the local sample polarizability can be mathematically correlated, enabling quantitative analysi
64 ents in our ability to characterize the data mathematically could enable much more powerful statistic
65 Na(+), K(+), Rb(+), or Cs(+) counterions, we mathematically decompose the scattering profiles into co
66    Recently, we resolved individual CnClm by mathematically deconvolving soft ionization high-resolut
67 e entropic measures are nonadditive, and are mathematically deduced from a series of natural axioms.
68                                           We mathematically define a higher-order GSVD (HO GSVD) for
69  metabolism of E.coli into elementary modes (mathematically defined biochemical pathways) and assessi
70                                      Here we mathematically demonstrate how partitioning errors arise
71                                      Here we mathematically demonstrate how stochastic partitioning c
72                                      Here we mathematically demonstrate how two identical and indepen
73 r the capacity for multistationarity, and we mathematically demonstrate that shuttling confers flexib
74                                           We mathematically demonstrate that T6SS-mediated killing sh
75 ch as the brain, amplitude and frequency are mathematically dependent.
76             The combined dataset was used to mathematically derive a 3D quantitative map of frequency
77                                           We mathematically derive an observer structure for cells gr
78                                           We mathematically derive the expected statistics for any se
79 ptic plasticity termed the "Convallis rule", mathematically derived from a principle of unsupervised
80              We demonstrate that FRVs can be mathematically derived from coast down coefficients in t
81  We introduce here the use of a portfolio of mathematically derived immittance functions and related
82                                          The mathematically derived risk score model proposed by the
83 we developed a chemomechanical growth law to mathematically describe growth of the neuroepithelium.
84 p (EcCrp, also CAP) and DNA were analyzed to mathematically describe, and make human-readable, the re
85 dynamical systems, by virtue of a phenomenon mathematically described as bifurcation.
86 ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-St
87 ween retina and primary visual cortex can be mathematically described by the log-polar transform.
88                  The extraction kinetics was mathematically described using the first order kinetic m
89         Reaction progress experiments may be mathematically designed to elucidate catalytic rate laws
90              The purpose of this study is to mathematically determine local and regional patterns of
91 n solution with the concentrations that were mathematically determined from the measured in the gas-p
92  that survived the double interrogation were mathematically different but schematically identical and
93                          Models involved are mathematically difficult and computationally challenging
94                                         This mathematically diminishes the surface plasmon resonance
95 es of a gene in a population of cells can be mathematically dissected into two contributing component
96 erlapping in a chromatographic separation by mathematically dissecting the NMR spectra obtained from
97                Recent studies have used four mathematically distinct definitions of genetic interacti
98 al identifications necessary to move primary mathematically driven LC-EC biomarker discovery into bio
99 rrence of a cross-frequency arrangement that mathematically enables coupling between alpha and theta
100 , and it was presumed that these methods are mathematically equatable.
101 arch results from these methods could not be mathematically equated to the USDA Starch Research metho
102 he initial bolus and ion current models give mathematically equivalent predictions for length control
103 reated with a classical (non quantum) model, mathematically equivalent to a Nernst distribution for o
104            We developed a motor task that is mathematically equivalent to choosing between lotteries
105                             The parameter is mathematically equivalent to FST and we show how existin
106                             These models are mathematically equivalent to generalized linear models o
107                             These models are mathematically equivalent to statistical physics models
108            Our collaborative EM algorithm is mathematically equivalent to the original EM algorithm c
109 e vertical shifts of neighbouring chains-are mathematically equivalent to the phase angles of rotatin
110 adeoff between probability and numerosity is mathematically equivalent to the relationship between en
111 information within experimental units and is mathematically equivalent to the treatment level in a ne
112    In addition, we use a binding isotherm to mathematically estimate the loading capacity of the dend
113 inciple, implement any behaviour that can be mathematically expressed as such.
114  hydrodynamic volume of the attached entity, mathematically expressed by its intrinsic viscosity [eta
115                                              Mathematically, extending from 2D to 3D requires higher
116                     With these data, we also mathematically extrapolate the number of HIV-1 particles
117                                           By mathematically fitting the data, important biological pa
118 is has led to a reliance on metrics that are mathematically flawed and insufficiently diverse to acco
119               Here, we analyze this scenario mathematically, focusing on the evolution of a Dobzhansk
120                                   Correcting mathematically for the dose dependence of induction/reso
121 of different cognitive processes that can be mathematically formalised as dissociable computational m
122                                           We mathematically formulate the problem as one of optimally
123 states of polarization (SOP) has always been mathematically formulated by a series of linear transfor
124                                           We mathematically formulated our goal as a constrained opti
125 ped a physics model for the TIMES signal and mathematically formulated the problem to attain physical
126                                              Mathematically, Fourier ptychographic (FP) reconstructio
127 e initialized using empirically generated or mathematically generated pure component spectra.
128 eraction profiles, which we biologically and mathematically grouped into five positive and five negat
129  believe is the first such a design that has mathematically guaranteed properties of stability and au
130 result and computational efficiency are both mathematically guaranteed.
131  first show experimentally, and then explain mathematically, how even in the simplest signaling syste
132 tative approach to modeling behavior that is mathematically identical across species, and accruing ev
133  for Saito's 3-step mechanism is shown to be mathematically identical to the earlier, 1997 2-step F-W
134 a nonlinear classical-field equation that is mathematically identical to the Landau model and provide
135 imple "parsimonious" rabbit AP model that is mathematically identifiable (i.e., not over parameterize
136  from 72 immunogen-parasite combinations, we mathematically identified 13 amino acid polymorphic site
137 on-electron resonance (DEER) experiment is a mathematically ill-posed problem.
138 artial differential equation, and that it is mathematically impossible to do this using inclusive fit
139      We use OMPBioM to assess OMP biogenesis mathematically in a global manner.
140                   We have accounted for this mathematically in determining the concentration dispersi
141  varying-effectiveness (VE) model is studied mathematically in the context of HCV infection.
142 perty because it means that the inference is mathematically incorrect and formally illogical, and the
143                              This measure is mathematically independent from expression level and all
144                                            A mathematically independent phase-amplitude model reprodu
145  CD4 T-cell responses to vaccinia virus were mathematically indistinguishable for antigen breadth and
146              This hybrid behavior leads to a mathematically infinite number of crossover points in th
147                                              Mathematically integrating the mutation model with backg
148 disease map development is the generation of mathematically interpretable representations to predict
149 or 11 generic consumer strategies that group mathematically into predators, parasites, and micropreda
150 etrospectively or prospectively according to mathematically intractable genetic models, and to assist
151 n infusion pump into the hepatic artery were mathematically investigated.
152                               Modelling this mathematically is problematic since strains within a fun
153                                              Mathematically it explains how myofibers are bundled in
154 f whether such actuarial methods are in fact mathematically justified, even under the most idealized
155 certain successive steps together to yield a mathematically less complex representation that is able
156            As models become more complex and mathematically less tractable, the need for an integrate
157 le to infrared radiation that can be used to mathematically model and predict selectivity trends for
158  we present an intervention-free approach to mathematically model basal ECM turnover during embryogen
159 bfemtoliter nuclear volumes and used this to mathematically model DSB response kinetics of MDC1 and o
160 the detailed inhibition kinetics required to mathematically model HCV RNA decline have been lacking.
161 atic functions and differential equations to mathematically model molecular and cellular interactions
162 ues, including a novel MP grammars method to mathematically model putative regulatory interactions am
163                                     Here, we mathematically model the coevolution of sex-specific hel
164                              In this work we mathematically model the dynamics of CML response to com
165                                   Efforts to mathematically model the LuxR-LuxI system are providing
166 tions of these phototactic cells in order to mathematically model this quasi-random motion.
167                                           We mathematically model this transmission by a diffusive me
168  of eukaryotic mRNA from total RNA was first mathematically modeled and then achieved using PPM in ca
169            Real-world complex systems may be mathematically modeled as graphs, revealing properties o
170                       These responses can be mathematically modeled by assuming an internal state tha
171                       The physical system is mathematically modeled by time-dependent Schrodinger equ
172                                      Here we mathematically modeled hemifusion of synthetic vesicles,
173  delta's roles in inflammatory signaling, we mathematically modeled the 4-IkappaB-containing NF-kappa
174                          To address this, we mathematically modeled the effect of dedifferentiation o
175 vical cancer cells and, based on these data, mathematically modeled the proapoptotic TRAIL signaling
176                                           We mathematically modeled the steady-state PM distributions
177 o understand the basis for this reversal, we mathematically modeled these T(CD8+) responses and used
178                              Lung injury was mathematically modeled to define the military standard 1
179  and NIK with NF-kappaB2/p100 processing, we mathematically modeled TRAF1.NIK as a coupling signaling
180                                           We mathematically modeled transcriptional regulation of the
181        Bacterial burden observed at 24 h was mathematically modeled using a 3-dimensional response su
182 otemporal distribution of Abeta in AD can be mathematically modeled using a logistic growth model in
183 c flow, and their shapes both evaluated, and mathematically modeled, before subsequent shell solidifi
184  displacement-weighted velocity analysis and mathematically modeling the results, we found that K40 a
185 dently of one another, this behaviour can be mathematically modelled as a random process based on the
186                                           We mathematically modelled stress on individual bees which
187 they traverse incarceration and release, (2) mathematically models the impact of prison-based interve
188 icated profiles recorded in field nests plus mathematically-modified profiles of similar shape but wi
189 r students may easily follow by omitting the mathematically more elaborate parts.
190                   Based on our analysis, the mathematically most likely explanation for the renewed g
191 , we scanned professional mathematicians and mathematically naive subjects of equal academic standing
192  neurons on very short timescales, which are mathematically nearly independent of neuronal interactio
193                                              Mathematically, new loops are shown to form through a sa
194                            In this paper, we mathematically operationalize a widely used conceptual f
195 evelopmental enhancers closely approximate a mathematically optimal decoding strategy.
196    Here, the bang-bang control estimates the mathematically optimal dose and duration of the interven
197 models, we develop a new methodology to find mathematically optimal schedules of light exposure and a
198  faster, and in restricted cases, provides a mathematically optimal solution.
199 ise constant protocols are compared with the mathematically optimal solutions.
200                                            A mathematically optimal strategy would be "square-root bi
201 unction, suffer from a clear guidance either mathematically or biologically.
202 n illustrative clinical vignette through the mathematically permissible possibilities to account for
203                               Of the 216,739 mathematically possible cages for 60 < n <or= 84, just t
204                                      This is mathematically possible due to the existence of a unique
205 ptor responses by manipulating mixtures in a mathematically predictable manner.
206 ipulating these parameters directed cells in mathematically predictable ways; specific combinations c
207   CT image quality and radiation dose can be mathematically predicted and optimized on the basis of p
208                                          Our mathematically predicted cell division process will need
209                                        It is mathematically predicted that a highly variable surface
210 behavior: growth-defective cells exhibited a mathematically predicted transient increase in membrane
211 why our experimental results support what is mathematically predicted while previous experiments have
212                             We show that AIM mathematically preserves the asymmetric nature of mainta
213 q experiments necessitate scalable, fast and mathematically principled analysis software.
214 ommunity detection in networks and develop a mathematically principled approach that combines a netwo
215          Our method is a high-performing and mathematically principled framework for learning similar
216 do is always superior to that which would be mathematically propagated assuming independent measureme
217                                           We mathematically prove that any embedding (that uses dot p
218                    Within this framework, we mathematically prove that seeking rewards is equivalent
219                                           We mathematically proved the null independence of existent
220  date, only a few attempts have been made to mathematically quantify the probability of jamming, or i
221 ax, we used a machine-learning model [13] to mathematically quantify the uncertainty and surprise of
222                     This approach appears to mathematically reflect the linear relation of ferritin c
223 ty and fractional coverage, were found to be mathematically related.
224                          This approach, that mathematically relies on network paths of length three (
225 N, can be used and the associated dispersion mathematically removed.
226 uicides and daily duration of sunshine after mathematically removing the effects of season.
227                           These regions were mathematically resolved using parallel factor analysis t
228 nger path cell and the effects of dispersion mathematically reversed without major loss of S/N.
229                                DP provides a mathematically rigorous approach to prevent the risk of
230               Metabolic modelling provides a mathematically rigorous basis for system-level analysis
231 by the multidimensional parameter space in a mathematically rigorous fashion.
232 robed with single-particle tracking and is a mathematically rigorous framework that can be further ex
233 l standards and clustered chromatograms in a mathematically rigorous framework.
234 eveals many features of this transition in a mathematically rigorous manner.
235                            We present here a mathematically rigorous model for conditioning inspired
236 atures, and constructs a precise, smooth and mathematically rigorous profile.
237 ave found a physical realization of the only mathematically rigorous route to a non-Fermi liquid, nam
238  activities interplay with each other can be mathematically shaped using techniques from statistical
239                                           We mathematically show that the velocities of all swarm mem
240                                      Here we mathematically show that under these conditions, biogeoc
241                                     Here, we mathematically show the asymptotic trajectory of tetrapl
242 ilm in a quartz tube with its shape modelled mathematically, showing good agreement between the model
243                        We model this process mathematically, showing that it produces 32 equivalence
244                      In particular, the more mathematically similar (less orthogonal) the molar absor
245                                              Mathematically similar energy functionals have been rela
246 rdependent events is ultimately reduced to a mathematically simple model, whose two parameters can be
247 out the imaged scene, despite relying on the mathematically simple processes of linear diffractive wa
248 eriority trial of LTBI treatment.Methods: We mathematically simulated a two-arm randomized clinical t
249 This temperature profile was compared with a mathematically simulated profile generated by a cold-cap
250                                              Mathematically speaking, bow-ties evolve when the rank o
251 ing angles, do not challenge the evidence of mathematically specific geometric structure.
252                                 We propose a mathematically straightforward method to infer the incid
253     Genome-scale metabolic models (GEMs) are mathematically structured knowledge bases of metabolism
254            Genome-scale metabolic models are mathematically-structured knowledge bases that can be us
255 n this paper we explore (computationally and mathematically) such situations with the goal of uncover
256                 In conclusion, the proposed, mathematically supported, methodology was proven to be h
257        Do gender differences exist among the mathematically talented?
258                                      We show mathematically that differences between competing ParA c
259                                      We show mathematically that donor ability can be selected when r
260                                    We proved mathematically that if the variance spectrum was to deca
261                          Here we demonstrate mathematically that many less well understood, larger-sc
262                                      We show mathematically that such arrays can distinguish between
263  from statistical physics as a tool, we show mathematically that the marine ice sheet instability gre
264                         We previously showed mathematically that there is a unique minimal pathway of
265 tive form of Rho to the active form, we show mathematically that this active regulation of cellular c
266                                      We show mathematically that trans-pairing and active separation
267 onitor disease progression; and 2) to assess mathematically the diagnostic power of potential biomark
268 al, and measurement fluctuations, we dissect mathematically the relevant sources of fluctuations that
269 al equations, we are also able to manipulate mathematically the spatial location of the ribosomes, th
270                      Specifically, we define mathematically the spectral consistency as an existence
271                                              Mathematically, the combined rate of formation of biomas
272                                              Mathematically, the dynamical process of resource alloca
273 mbe to characterize, both experimentally and mathematically, the in vivo contributions of Cdk1-mediat
274                                              Mathematically, the latter question amounts to identifyi
275                                              Mathematically, the model is described by a coupled syst
276                                              Mathematically, the optimal learning rule requires weigh
277                                              Mathematically, the sensitivity of FBA to these flux imb
278 ontains slopes larger than a critical value; mathematically they are traveling waves (shocks) that ha
279                                              Mathematically they require breaking of time-reversal sy
280                                              Mathematically this is an important example of graph opt
281                                              Mathematically this problem involves an underdetermined
282                                              Mathematically, this can be achieved if the optimally ef
283      The emergence of leak is closely mapped mathematically to the Ising model from statistical mecha
284 , we demonstrate that this model corresponds mathematically to the well-known Cahn-Hilliard equation
285        Individual assay values were combined mathematically to yield an MDDScore.
286                      These results provide a mathematically tractable example of how collective pheno
287 ree distributions are reproduced in a simple mathematically tractable model introduced and analyzed i
288        These isolated flagella are a unique, mathematically tractable model system for the physics of
289                              Here a suite of mathematically tractable models with nontrivial eddy dif
290 c development of simple test models that are mathematically tractable yet capture key features of ani
291 ntial growth emerges in nonlinear systems is mathematically unclear.
292                We demonstrated this approach mathematically using stochastic modeling, and applied it
293 tally (using particle image velocimetry) and mathematically (using computational fluid dynamics and a
294                We demonstrate this principle mathematically, using stochastic modeling, and experimen
295 template" patterning mechanism we observe is mathematically very different from the well-known Turing
296                                              Mathematically, we count the number of mapped reads on e
297                                              Mathematically, we describe this type of learning as a d
298 being open curves in which the knots are not mathematically well defined; knotting can only be identi
299 hin the set of SNPs under investigation in a mathematically well-controlled manner into account.
300 ther, these results show that GNM provides a mathematically well-founded unified framework for modeli

 
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