579 research outputs found
On the biosynthesis of carnitine in Neurospora crassa lys-1 (33933)
On the biosynthesis of carnitine in lys-1 (33933
Rough stochastic differential equations
A hybrid theory of rough stochastic analysis is built. It seamlessly combines
the advantages of both It\^o's stochastic - and Lyons' rough differential
equations. Well-posedness of rough stochastic differential equation is
obtained, under natural assumptions and with precise estimates; many examples
and applications are mentioned. A major role is played by a new stochastic
variant of Gubinelli's controlled rough paths spaces, with norms that reflect
some generalized stochastic sewing lemma, and which may prove useful whenever
rough paths and It\^o integration meet
Stochastic sewing in Banach spaces
A stochastic sewing lemma which is applicable for processes taking values in Banach spaces is introduced. Applications to additive functionals of fractional Brownian motion of distributional type are discussed
Long-time limits and occupation times for stable FlemingâViot processes with decaying sampling rates
A class of Fleming-Viot processes with decaying sampling rates and a-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are developed, addressing the question of long-time population distribution for growing populations. Asymptotics in higher orders are investigated. Convergence of particle location occupation and inhabitation time processes are also addressed and related by way of the historical process. The basic results and techniques allow general Feller motion/mutation and may apply to other measure-valued Markov processes.
Dans cet article, nous introduisons et analysons une classe de processus de FlemingâViot, avec taux dâĂ©chantillonnage dĂ©croissant et dĂ©placement α-stable, correspondant Ă des distributions de populations croissantes. Les thĂ©orĂšmes limites en temps long presque-sĂ»r pour ces processus sont obtenus, rĂ©pondant ainsi Ă la question de la distribution en temps long de la population dans le cas de populations croissantes. Les asymptotiques dâordres supĂ©rieurs sont aussi obtenues. Les convergences des processus de temps dâoccupation et dâhabitation des particules sont considĂ©rĂ©es et reliĂ©es au moyen du processus historique. Les rĂ©sultats et techniques autorisent des processus de Feller de dĂ©placement/mutation gĂ©nĂ©raux et peuvent sâappliquer Ă dâautres processus de Markov Ă valeurs mesures
The AllenâCahn equation with generic initial datum
We consider the AllenâCahn equation âtuâÎu=uâu3 with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described by nodal sets of the BargmannâFock Gaussian field, which then evolve according to mean curvature flow
Sparse PLS discriminant analysis: biologically relevant feature selection and graphical displays for multiclass problems
Background: Variable selection on high throughput biological data, such as gene expression or single nucleotide polymorphisms (SNPs), becomes inevitable to select relevant information and, therefore, to better characterize diseases or assess genetic structure. There are different ways to perform variable selection in large data sets. Statistical tests are commonly used to identify differentially expressed features for explanatory purposes, whereas Machine Learning wrapper approaches can be used for predictive purposes. In the case of multiple highly correlated variables, another option is to use multivariate exploratory approaches to give more insight into cell biology, biological pathways or complex traits.Results: A simple extension of a sparse PLS exploratory approach is proposed to perform variable selection in a multiclass classification framework.Conclusions: sPLS-DA has a classification performance similar to other wrapper or sparse discriminant analysis approaches on public microarray and SNP data sets. More importantly, sPLS-DA is clearly competitive in terms of computational efficiency and superior in terms of interpretability of the results via valuable graphical outputs. sPLS-DA is available in the R package mixOmics, which is dedicated to the analysis of large biological data sets
Neural parameters estimation for brain tumor growth modeling
Understanding the dynamics of brain tumor progression is essential for
optimal treatment planning. Cast in a mathematical formulation, it is typically
viewed as evaluation of a system of partial differential equations, wherein the
physiological processes that govern the growth of the tumor are considered. To
personalize the model, i.e. find a relevant set of parameters, with respect to
the tumor dynamics of a particular patient, the model is informed from
empirical data, e.g., medical images obtained from diagnostic modalities, such
as magnetic-resonance imaging. Existing model-observation coupling schemes
require a large number of forward integrations of the biophysical model and
rely on simplifying assumption on the functional form, linking the output of
the model with the image information. In this work, we propose a learning-based
technique for the estimation of tumor growth model parameters from medical
scans. The technique allows for explicit evaluation of the posterior
distribution of the parameters by sequentially training a mixture-density
network, relaxing the constraint on the functional form and reducing the number
of samples necessary to propagate through the forward model for the estimation.
We test the method on synthetic and real scans of rats injected with brain
tumors to calibrate the model and to predict tumor progression
Feasible combinatorial matrix theory
We show that the well-known Konig's Min-Max Theorem (KMM), a fundamental
result in combinatorial matrix theory, can be proven in the first order theory
\LA with induction restricted to formulas. This is an
improvement over the standard textbook proof of KMM which requires
induction, and hence does not yield feasible proofs --- while our new approach
does. \LA is a weak theory that essentially captures the ring properties of
matrices; however, equipped with induction \LA is capable of
proving KMM, and a host of other combinatorial properties such as Menger's,
Hall's and Dilworth's Theorems. Therefore, our result formalizes Min-Max type
of reasoning within a feasible framework
Processing of the precursor of protamine P2 in mouse. Peptide mapping and N-terminal sequence analysis of intermediates
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