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 Fleming–Viot 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 Fleming–Viot, avec taux d’échantillonnage décroissant et déplacement α-stable, correspondant à des distributions de populations croissantes. Les théorèmes limites en temps long presque-sûr pour ces processus sont obtenus, répondant ainsi à la question de la distribution en temps long de la population dans le cas de populations croissantes. Les asymptotiques d’ordres supérieurs sont aussi obtenues. Les convergences des processus de temps d’occupation et d’habitation des particules sont considérées et reliées au moyen du processus historique. Les résultats et techniques autorisent des processus de Feller de déplacement/mutation généraux et peuvent s’appliquer à d’autres processus de Markov à valeurs mesures

The Allen–Cahn equation with generic initial datum

We consider the Allen–Cahn equation ∂tu−Δu=u−u3 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 Bargmann–Fock 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 $\Sigma_1^B$ formulas. This is an improvement over the standard textbook proof of KMM which requires $\Pi_2^B$ 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 $\Sigma_1^B$ 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