Introduction to vector quantization and its applications for numerics*

Proceedings of CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches. : T. Lelièvre et al. EditorsInternational audienceWe present an introductory survey to optimal vector quantization and its first applications to Numerical Probability and, to a lesser extent to Information Theory and Data Mining. Both theoretical results on the quantization rate of a random vector taking values in ℝd (equipped with the canonical Euclidean norm) and the learning procedures that allow to design optimal quantizers (CLVQ and Lloyd’s procedures) are presented. We also introduce and investigate the more recent notion of greedy quantization which may be seen as a sequential optimal quantization. A rate optimal result is established. A brief comparison with Quasi-Monte Carlo method is also carried out

Quadratic optimal functional quantization of stochastic processes and numerical applications

In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a Hilbert-valued random variable, using a nearest neighbour projection on a finite codebook. A special emphasis is made on the computational aspects and the numerical applications, in particular the pricing of some path-dependent European options.Comment: 41 page

Optimal quantization for the pricing of swing options

In this paper, we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in details and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff-Schwartz algorithm.Comment: 27

Mitochondrial fission as a driver of stemness in tumor cells : mDIVI1 inhibits mitochondrial function, cell migration and cancer stem cell (CSC) signalling

Mitochondria are dynamic organelles frequently undergoing fission and fusion events to maintain their integrity, bioenergetics and spatial distribution, which is fundamental to the processes of cell survival. Disruption in mitochondrial dynamics plays a role in cancer. Therefore, proteins involved in regulating mitochondrial dynamics are potential targets for treatment. mDIVI1 is an inhibitor of the mitochondrial fission protein DRP1, which induces i) mitochondrial oxidative stress and ii) effectively reduces mitochondrial metabolism. We show here that mDIVI1 is able to inhibit 3D tumorsphere forming capacity, cell migration and stemness-related signalling in breast cancer cells, indicating that mDIVI1 can potentially be used for the therapeutic elimination of cancer stem cells (CSCs)

Some recent developments in quantization of fractal measures

We give an overview on the quantization problem for fractal measures, including some related results and methods which have been developed in the last decades. Based on the work of Graf and Luschgy, we propose a three-step procedure to estimate the quantization errors. We survey some recent progress, which makes use of this procedure, including the quantization for self-affine measures, Markov-type measures on graph-directed fractals, and product measures on multiscale Moran sets. Several open problems are mentioned.Comment: 13 page

Dispersion and collapse in stochastic velocity fields on a cylinder

The dynamics of fluid particles on cylindrical manifolds is investigated. The velocity field is obtained by generalizing the isotropic Kraichnan ensemble, and is therefore Gaussian and decorrelated in time. The degree of compressibility is such that when the radius of the cylinder tends to infinity the fluid particles separate in an explosive way. Nevertheless, when the radius is finite the transition probability of the two-particle separation converges to an invariant measure. This behavior is due to the large-scale compressibility generated by the compactification of one dimension of the space

A multi-approach survey as the most reliable tool to accurately assess biodiversity: an example of thai murine rodents

Wildlife surveys rely on an accurate taxonomic framework. Identification tools used to reach this goal are not equivalent and may depend on several objectives and constraints, including sampling conservation difficulties, the invasiveness of the sampling techniques, sampling capacity, the relevance of the results, materials needed, the cost and the user time required in the field and laboratory. This article presents and discusses the advantages and limits of each identification tool used in the Ceropath (Community ecology of rodents and their pathogens in South East Asia) program to reach a fast and relevant identification of the rodents sampled. It is concluded that there needs to be a combination of the results from different methods, including the most recent ones, to achieve an improvement in taxonomic identification

Bergamot natural products eradicate cancer stem cells (CSCs) by targeting mevalonate, Rho-GDI-signalling and mitochondrial metabolism

Here, we show that a 2:1 mixture of Brutieridin and Melitidin, termed “BMF”, has a statin-like properties, which blocks the action of the rate-limiting enzyme for mevalonate biosynthesis, namely HMGR (3-hydroxy-3-methylglutaryl- CoA-reductase). Moreover, our results indicate that BMF functionally inhibits several key characteristics of CSCs. More specifically, BMF effectively i) reduced ALDH activity, ii) blocked mammosphere formation and iii) inhibited the activation of CSC-associated signalling pathways (STAT1/3, Notch and Wnt/ beta-catenin) targeting Rho-GDI-signalling. In addition, BMF metabolically inhibited mitochondrial respiration (OXPHOS) and fatty acid oxidation (FAO). Importantly, BMF did not show the same toxic side-effects in normal fibroblasts that were observed with statins. Lastly, we show that high expression of the mRNA species encoding HMGR is associated with poor clinical outcome in breast cancer patients, providing a potential companion diagnostic for BMF-directed personalized therapy

The porin and the permeating antibiotic: A selective diffusion barrier in gram-negative bacteria

Gram-negative bacteria are responsible for a large proportion of antibiotic resistant bacterial diseases. These bacteria have a complex cell envelope that comprises an outer membrane and an inner membrane that delimit the periplasm. The outer membrane contains various protein channels, called porins, which are involved in the influx of various compounds, including several classes of antibiotics. Bacterial adaptation to reduce influx through porins is an increasing problem worldwide that contributes, together with efflux systems, to the emergence and dissemination of antibiotic resistance. An exciting challenge is to decipher the genetic and molecular basis of membrane impermeability as a bacterial resistance mechanism. This Review outlines the bacterial response towards antibiotic stress on altered membrane permeability and discusses recent advances in molecular approaches that are improving our knowledge of the physico-chemical parameters that govern the translocation of antibiotics through porin channel