Linear Quadratic Zero-Sum Two-Person Differential Games

International audienceAs in optimal control theory, linear quadratic (LQ) differential games (DG) can be solved, even in high dimension, via a Riccati equation. However, contrary to the control case, existence of the solution of the Riccati equation is not necessary for the existence of a closed-loop saddle point. One may " survive " a particular, non generic, type of conjugate point. An important application of LQDG's is the so-called H∞-optimal control, appearing in the theory of robust control

Formal asymptotic limit of a diffuse-interface tumor-growth model

We consider a diffuse-interface tumor-growth model which has the form of a phase-field system. We characterize the singular limit of this problem. More precisely, we formally prove that as the coefficient of the reaction term tends to infinity, the solution converges to the solution of a novel free boundary problem. We present numerical simulations which illustrate the convergence of the diffuse-interface model to the identified sharp-interface limit

Moving frames applied to shell elasticity

Exterior calculus and moving frames are used to describe curved elastic shells. The kinematics follow from the Lie-derivative on forms whereas the dynamics via stress-forms.Comment: 20 pages, 1 figur

hp-adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems

This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existence in the context of blow-up. The structure of the derived estimator leads naturally to the development of both h and hp versions of an adaptive algorithm designed to approximate the blow-up time. The adaptive algorithms are then applied in a series of numerical experiments, and the rate of convergence to the blow-up time is investigated

Maintaining RNA integrity in a homogeneous population of mammary epithelial cells isolated by Laser Capture Microdissection

Background: Laser-capture microdissection (LCM) that enables the isolation of specific cell populations from complex tissues under morphological control is increasingly used for subsequent gene expression studies in cell biology by methods such as real-time quantitative PCR (qPCR), microarrays and most recently by RNA-sequencing. Challenges are i) to select precisely and efficiently cells of interest and ii) to maintain RNA integrity. The mammary gland which is a complex and heterogeneous tissue, consists of multiple cell types, changing in relative proportion during its development and thus hampering gene expression profiling comparison on whole tissue between physiological stages. During lactation, mammary epithelial cells (MEC) are predominant. However several other cell types, including myoepithelial (MMC) and immune cells are present, making it difficult to precisely determine the specificity of gene expression to the cell type of origin. In this work, an optimized reliable procedure for producing RNA from alveolar epithelial cells isolated from frozen histological sections of lactating goat, sheep and cow mammary glands using an infrared-laser based Arcturus Veritas LCM (Applied Biosystems®) system has been developed. The following steps of the microdissection workflow: cryosectioning, staining, dehydration and harvesting of microdissected cells have been carefully considered and designed to ensure cell capture efficiency without compromising RNA integrity.[br/] Results: The best results were obtained when staining 8 μm-thick sections with Cresyl violet® (Ambion, Applied Biosystems®) and capturing microdissected cells during less than 2 hours before RNA extraction. In addition, particular attention was paid to animal preparation before biopsies or slaughtering (milking) and freezing of tissue blocks which were embedded in a cryoprotective compound before being immersed in isopentane. The amount of RNA thus obtained from ca.150 to 250 acini (300,000 to 600,000 μm2) ranges between 5 to 10 ng. RNA integrity number (RIN) was ca. 8.0 and selectivity of this LCM protocol was demonstrated through qPCR analyses for several alveolar cell specific genes, including LALBA (α-lactalbumin) and CSN1S2 (αs2-casein), as well as Krt14 (cytokeratin 14), CD3e and CD68 which are specific markers of MMC, lymphocytes and macrophages, respectively.[br/] Conclusions: RNAs isolated from MEC in this manner were of very good quality for subsequent linear amplification, thus making it possible to establish a referential gene expression profile of the healthy MEC, a useful platform for tumor biomarker discovery

Visual laterality in dolphins: importance of the familiarity of stimuli

<p>Abstract</p> <p>Background</p> <p>Many studies of cerebral asymmetries in different species lead, on the one hand, to a better understanding of the functions of each cerebral hemisphere and, on the other hand, to develop an evolutionary history of hemispheric laterality. Our animal model is particularly interesting because of its original evolutionary path, i.e. return to aquatic life after a terrestrial phase. The rare reports concerning visual laterality of marine mammals investigated mainly discrimination processes. As dolphins are migrant species they are confronted to a changing environment. Being able to categorize new versus familiar objects would allow dolphins a rapid adaptation to novel environments. Visual laterality could be a prerequisite to this adaptability. To date, no study, to our knowledge, has analyzed the environmental factors that could influence their visual laterality.</p> <p>Results</p> <p>We investigated visual laterality expressed spontaneously at the water surface by a group of five common bottlenose dolphins (<it>Tursiops truncatus</it>) in response to various stimuli. The stimuli presented ranged from very familiar objects (known and manipulated previously) to familiar objects (known but never manipulated) to unfamiliar objects (unknown, never seen previously). At the group level, dolphins used their left eye to observe very familiar objects and their right eye to observe unfamiliar objects. However, eyes are used indifferently to observe familiar objects with intermediate valence.</p> <p>Conclusion</p> <p>Our results suggest different visual cerebral processes based either on the global shape of well-known objects or on local details of unknown objects. Moreover, the manipulation of an object appears necessary for these dolphins to construct a global representation of an object enabling its immediate categorization for subsequent use. Our experimental results pointed out some cognitive capacities of dolphins which might be crucial for their wild life given their fission-fusion social system and migratory behaviour.</p