Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Context (language use) & Population. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

Homogenization and asymptotics for small transaction costs: the multidimensional case

Abstract: In the context of the multi-dimensional infinite horizon optimal consumption-investment problem with proportional transaction costs, we provide the first order expansion in small transact costs. Similar to the one-dimensional derivation in our accompanying paper [42], the asymptotic expansion is expressed in terms of a singular ergodic control problem, and our arguments are based on the theory of viscosity solutions, and the techniques of homogenization which leads to a system of corrector equations. In contrast with the one-dimensional case, no explicit solution of the first corrector equation is available anymore. Finally, we provide some numerical results which illustrate the structure of the first order optimal controls.

Local Profiles for Elliptic Problems at Different Scales: Defects in, and Interfaces between Periodic Structures

Abstract: Following-up on a previous work of ours, we present a general approach to approximate at the fine scale the solution to an elliptic equation with oscillatory coefficient when this coefficient consists of a “nice” (in the simplest possible case say periodic) function which is, in some sense to be made precise, perturbed. The approach is based on the determination of a local profile, solution to an equation similar to the corrector equation in classical homogenization. The well-posedness of that equation, in various functional settings depending upon the nature of the perturbation, is the purpose of this article. The case of a local perturbation is first addressed. The case of a more complex geometrical structure (such as the prototypical case of two different periodic structures separated by a common interface) is next discussed. Some related problems, and future directions of research are mentioned.

Thinking by classes in data science: the symbolic data analysis paradigm

Abstract: Data Science, considered as a science by itself, is in general terms, the extraction of knowledge from data. Symbolic data analysis SDA gives a new way of thinking in Data Science by extending the standard input to a set of classes of individual entities. Hence, classes of a given population are considered to be units of a higher level population to be studied. Such classes often represent the real units of interest. In order to take variability between the members of each class into account, classes are described by intervals, distributions, set of categories or numbers sometimes weighted and the like. In that way, we obtain new kinds of data, called 'symbolic' as they cannot be reduced to numbers without losing much information. The first step in SDA is to build the symbolic data table where the rows are classes and the variables can take symbolic values. The second step is to study and extract new knowledge from these new kinds of data by at least an extension of Computer Statistics and Data Mining to symbolic data. SDA is a new paradigm which opens up a vast domain of research and applications by giving complementary results to classical methods applied to standard data. SDA also gives answers to big data and complex data challenges as big data can be reduced and summarized by classes and as complex data with multiple unstructured data tables and unpaired variables can be transformed into a structured data table with paired symbolic-valued variables. WIREs Comput Stat 2016, 8:172-205. doi: 10.1002/wics.1384

Turnover Modulates the Need for a Cost of Resistance in Adaptive Therapy.

Abstract: Adaptive therapy seeks to exploit intratumoral competition to avoid, or at least delay, the emergence of therapy resistance in cancer. Motivated by promising results in prostate cancer, there is growing interest in extending this approach to other neoplasms. As such, it is urgent to understand the characteristics of a cancer that determine whether or not it will respond well to adaptive therapy. A plausible candidate for such a selection criterion is the fitness cost of resistance. In this article, we study a general, but simple, mathematical model to investigate whether the presence of a cost is necessary for adaptive therapy to extend the time to progression beyond that of a standard-of-care continuous therapy. Tumor cells were divided into sensitive and resistant populations and we model their competition using a system of two ordinary differential equations based on the Lotka-Volterra model. For tumors close to their environmental carrying capacity, a cost was not required. However, for tumors growing far from carrying capacity, a cost may be required to see meaningful gains. Notably, it is important to consider cell turnover in the tumor, and we discuss its role in modulating the impact of a resistance cost. To conclude, we present evidence for the predicted cost-turnover interplay in data from 67 patients with prostate cancer undergoing intermittent androgen deprivation therapy. Our work helps to clarify under which circumstances adaptive therapy may be beneficial and suggests that turnover may play an unexpectedly important role in the decision-making process. SIGNIFICANCE: Tumor cell turnover modulates the speed of selection against drug resistance by amplifying the effects of competition and resistance costs; as such, turnover is an important factor in resistance management via adaptive therapy.See related commentary by Strobl et al., p. 811.