| Presentation hour: 2018-10-31-09:00-AM Presented by Hiroshi Matano (Meiji University) title: Front propagation in an epidemiological model with mutations abstract: We consider a reaction-diffusion system describing the propagation of disease that involves mutation of the pathogen. More precisely this is an S-I-S epidemic model with diffusion in which two types of pathogens appear (wild and mutant) that constantly mutate into the other type at a certain rate. The resulting reaction-diffusion system has a peculiar feature: it is of the cooperative type when the solutions are small, while it is of the competitive type in the region where the solutions are large. This model was introduced by Q.Griette and G.Raoul in 2016 for a spatially homogeneous environment. Similar systems were also studied more recently by L.Girardin and by E.Crooks et al, also for the spatially homogeneous case. In this talk, I will consider this system in spatially periodic environments and generalize the known results to the spatially periodic case. Some of the results I present here are new even in the spatially homogeneous case. This is joint work with Quentin Griette of Bordeaux. |
| Presentation hour: 2018-10-31-09:35-AM Presented by Benjamin Mauroy (Universite de Nice Cote d Azur / CNRS) title: About cliff-edge theory in evolution abstract: A genotype expresses into a phenotype through development. If a noise is affecting the developmental process, it may play a role on the selection by evolution of the optimal genotype: this is the cliff-edge theory, initially described with laboratory guinea pigs by Mountford in 1968. Evolution tends to maximize the fitness function which reflects the success of an individual into adapting to its environment. When the fitness function is not symmetrical near its maximum and when a noise is affecting development, the optimal genotype becomes not only correlated to the noise, but also to the way the fitness function is behaving in the vicinity of the maximum. The optimal genotype shifts away from the maximal fitness value, toward the side where the absolute value of the slope is lower. The larger the amplitude of the noise is, the higher the optimal genotype shifts away from the maximal fitness value. We analyze the model for cliff-edge theory developed by Vercken et al [1]. This model gives rise to non linear integro-differential equations on the distribution of phenotypes in a population and allow the authors to propose an alternative fitness function based on a convolution of a noise distribution kernel with the regular fitness. [1] E. Vercken, M. Wellenreuther, E. I. Svensson and B. Mauroy. Don’t fall off the adaptation cliff: when do asymmetrical fitness costs select for suboptimal traits? PLoS ONE 7(4): e34889, 2012. |
| Presentation hour: 2018-10-31-10:30-AM Presented by Thomas Giletti (University of Lorraine) title: Propagating terraces in one and multidimensional domains abstract: Travelling fronts typically connect two stationary states of a reaction-diffusion equation; and often accurately describe the large-time behavior of solutions. However, when many such steady states exist, a more complicated dynamics may appear involving a layer of several fronts, which we call a propagating terrace. In this talk, we will consider a multistable type equation in a periodically heterogeneous space of arbitrary dimension. In this rather general context, we will show that a propagating terrace exists in any direction. Surprisingly, due to the loss of symmetry induced by the heterogeneity, the shape of the propagating terrace may differ depending on the direction. In particular, travelling waves may exist only in some directions. The presented results come from a series of work with A. Ducrot, H. Matano and L. Rossi. |
| Presentation hour: 2018-10-31-11:05-AM Presented by Chueh-Hsin Chang (Tunghai University) title: Attractive Interaction between Traveling Waves in the Three-species Competition-diffusion Systems abstract: In this talk we consider the weak interaction between two traveling wave solutions of the three-species Lotka-Volterra competition-diffusion systems. Each of the two traveling wave solutions has one trivial component (called trivial waves). By the asymptotic behavior of the trivial waves and the existence results of the two-species traveling waves, we can prove that the two trivial waves interact attractively, and there exists an unstable three-species traveling wave solution which is close to the two trivial waves. This is a joint work with Prof. Chiun-Chuan Chen and Prof. Shin-Ichiro Ei. |
| Presentation hour: 2018-10-31-12:00-AM Presented by Inkyung Ahn (Korea University) title: Non-uniform dispersal of logistic population models with free boundaries in a spatially heterogeneous environment abstract: In many cases, the movement of species within a region depends on the availability of food and other resources necessary for its survival. Starvation driven diffusion (SDD) is a dispersal strategy that increases the motility of biological organisms in unfavorable environments i.e., a species moves more frequently in search of food if resources are insufficient (Cho and Kim, 2013). In this study, the proposed model represents the dispersion of an invasive species undergoing SDD, where the free boundary represents the expanding front. We observe that the spreading-vanishing dichotomy, which holds in the linear dispersal model (Zhou and Xiao, 2013), also holds in the model undergoing SDD. We also provide the estimates for the spreading speed of the free boundary during the spreading process. Finally, our results are compared with the results of the linear dispersal model to investigate the advantages of this strategic dispersal with respect to survival in new environments. This is a joint work with Wonhyung Choi. |
| Presentation hour: 2018-10-31-14:0-PM Presented by Chiun-Chuan Chen (National Taiwan University) title: Critical exponent of a simple model of spot replication abstract: We are concerned with a Henon type equation, which is introduced as a simple prototype of self-replication in more complex reaction–diffusion systems. When the exponent of x variable is super-critical, we prove a Liouville-type nonexistence theorem for positive solutions and study the oscillation property of radial solutions. |
| Presentation hour: 2018-10-31-14:35-PM Presented by Matthieu ALFARO (Univ. Montpellier) title: Population invasion with bistable dynamics and adaptive evolution: the evolutionary rescue abstract: We consider a system of reaction-diffusion equations as a population dynamics model. The first equation stands for the population density and models the ecological effects, namely dispersion and growth with a Allee effect (bistable nonlinearity). The second one stands for the Allee threshold, seen as a trait mean, and accounts for evolutionary effects. Precisely, the Allee threshold is submitted to three main effects: dispersion (mirroring ecology), asymmetrical gene ow and selection. The strength of the latter depends on the population density and is thus coupling ecology and evolution. Our main result is to mathematically prove evolutionary rescue: any small initial population, that would become extinct in the sole ecological context, will persist and spread thanks to evolutionary factors. This is a joint work with A. Ducrot. |
| Presentation hour: 2018-10-31-15:30-PM Presented by Hyowon Seo (Kyung Hee University) title: Anisotropic diffusion for the vineyard abstract: In this talk, we propose an anisotropic diffusion model for spreading pathogen in periodically fragmented environments such as a vineyard. To derive the anisotropic diffusion model we only consider two factors, namely, wind distribution and alternately arranged habitats. From this model, we can calculate the spreading speed and envelope of the leading edge of pathogen using traveling wave solutions for two different types of initial conditions. Also, if we consider pathogen as spore and fungus separately then we can observe the interesting phenomena which is called pushed front. This is joint work with Yong-Jung Kim. |
| Presentation hour: 2018-10-31-16:05-PM Presented by Lorenzo Contento (Meiji University) title: Outcome of ecological invasion for weak and strong exotic species abstract: Reaction–diffusion systems with a Lotka–Volterra-type reaction term, also known as competition–diffusion systems, have been used to investigate the dynamics of the competition among m ecological species for a limited resource necessary to their survival and growth. Notwithstanding their rather simple mathematical structure, such systems may display quite interesting behaviours. In particular, while for m=2 no coexistence of the two species is usually possible, if m≥3 we may observe coexistence of all or a subset of the species, sensitively depending on the parameter values. Such coexistence can take the form of very complex spatio-temporal patterns and oscillations. Unfortunately, at the moment there are no known tools for a complete analytical study of such systems for m≥3 . This means that establishing general criteria for the occurrence of coexistence appears to be very hard. In this paper we will instead give some criteria for the non-coexistence of species, motivated by the ecological problem of the invasion of an ecosystem by an exotic species. We will show that when the environment is very favourable to the invading species the invasion will always be successful and the native species will be driven to extinction. On the other hand, if the environment is not favourable enough, the invasion will always fail. |
| Presentation hour: 2018-10-31-17:00-PM Presented by Léo Girardin (Université Paris-Sud Paris-Saclay) title: Invasion of an empty habitat by two competitors: spreading properties of monostable two-species competition--diffusion systems abstract: In this talk, I will present results obtained in collaboration with Adrian Lam (Ohio State University) on some spreading properties of monostable Lotka–Volterra two-species competition–diffusion systems when the initial values are null or exponentially decaying in a right half-line. Thanks to a careful construction of super-solutions and sub-solutions, we improve previously known results and settle open questions. In particular, we show that if the weaker competitor is also the faster one, then it is able to evade the stronger and slower competitor by invading first into unoccupied territories. The pair of speeds depends on the initial values. If these are null in a right half-line, then the first speed is the KPP speed of the fastest competitor and the second speed is given by an exact formula depending on the first speed and on the minimal speed of traveling waves connecting the two semi-extinct equilibria. Furthermore, the unbounded set of pairs of speeds achievable with exponentially decaying initial values is characterized, up to a negligible set. |
| Presentation hour: 2018-10-31-17:35-PM Presented by Chang-Hong Wu (National University of Tainan) title: Traveling curved waves in two dimensional excitable media abstract: Wave propagation can occur in various area such as physics, biology, chemical kinetics, and so on. In particular, excitable media, which are often modeled by nonlinear PDEs, can support abundant spatiotemporal dynamics. In this talk, we focus on a free boundary problem in two-dimensional excitable media arising from a singular limiting problem of a FitzHugh-Nagumo-type reaction-diffusion system. The existence, uniqueness and stability of traveling curved waves will be discussed. This is a joint work with Hirokazu Ninomiya (Meiji University). |
| Presentation hour: 2018-11-01-09:00-AM Presented by Laurent Desvillettes (Université Paris Diderot) title: Some new results on cross diffusion equations abstract: Cross diffusion equations appearing in population dynamics have lately attracted a lot of interest. We present results on the existence, uniqueness, regularity and stability/linear instability of homogeneous steady states for cross diffusion equations naturally appearing in the theory of predator-prey models. The results that we present were obtained in collaboration with Fiammetta Conforto and Cinzia Soresina |
| Presentation hour: 2018-11-01-09:35-AM Presented by Toshiyuki Ogawa ( Meiji University) title: Oscillatory boundary dynamics coupled to a diffusive bulk abstract: Oscillatory dynamics coupled through membrane-bulk diffusion is observed in physiology, chemical reaction and so on. There are already several mathematical researches on this topic. Here, we consider the simplest cases: (1)two Van der Pol oscillators coupled by 1-D passive bulk diffusion and (2) oscillators on a circle coupled by the passive bulk disk inside. Depending on the diffusion and leakage constants we can observe both synchronized and a-synchronized oscillations. We are going to consider the linearized stability of the trivial state. |
| Presentation hour: 2018-11-01-10:30-AM Presented by LAURENCOT Philippe (CNRS & Universite Paul Sabatier) title: Global bounded and unbounded solutions to a chemotaxis system with indirect signal production abstract: Qualitative properties of a chemotaxis model describing the space and time evolution of the densities of two species and the concentration of a chemoattractant are studied. In contrast to the classical Keller-Segel chemotaxis system which involves only one species producing its own chemoattractant, the species which is influenced by the chemoattractant in the model under study is related to another species producing the chemoattractant. As already observed by Tao-Winkler (2017) in a particular case and for radially symmetric solutions, this process has far reaching consequences and shifts finite time blowup to infinite time blowup. The approach in Tao-Winkler (2017) relies on the reduction of the system to a single equation by exploiting both the structure of the equation and the radial symmetry of the solutions, this transformation allowing one to use comparison arguments. We here construct a Liapunov functional and exploit its properties to show the existence of global bounded and unbounded solutions. This construction does not require radial symmetry and extends to other models as well. |
| Presentation hour: 2018-11-01-11:05-AM Presented by Hirofumi Izuhara (University of Miyazaki) title: Time periodic coexistence in the cross-diffusion competition system abstract: We study a two component cross-diffusion competition system which describes the population dynamics between two biological species. Since the cross-diffusion competition system possesses the so-called population pressure effect, a variety of solution behaviors can be exhibited compared with the classical diffusion competition system. In particular, we discuss on the existence of spatially nonconstant time periodic solutions. Applying the center manifold theory and the standard normal form theory, the cross-diffusion competition system is reduced to a two dimensional dynamical system around a doubly degenerate point. It has a Hopf singularity on a nonconstant stationary solution branch which bifurcates from a constant solution branch. We show the existence of stable time periodic solutions which appears from the Hopf bifurcation point. This means spatiotemporal coexistence between two biological species. |
| Presentation hour: 2018-11-01-12:00-AM Presented by SALORT Delphine (SORBONNE UNIVERSITE) title: Qualitative properties of time elapsed and NLIF models for neural networks abstract: This talk is devoted to the study of two typical PDE models that describe the evolution of a network of neurons that interact via their common statistical distribution. In these two different models we will focus on the qualitative and asymptotic properties of solutions describing synchronization phenomena or convergence to a stationary state. Approach and technical difficulties differ for the two models: we will also discuss this aspect. This talk is based on collaborations with M. Caceres, J. A. Carrillo, K. Pakdaman, B. Perthame, P. Roux, R. Schneider and D. Smets. |
| Presentation hour: 2018-11-01-14:00-PM Presented by Tadahisa Funaki (Waseda University) title: Derivation of motion by mean curvature and Stefan problem from particle systems abstract: We discuss the derivation of motion by mean curvature and two-phase Stefan free boundary problem directly from particle systems called Glauber-Kawasaki dynamics. The derivation from reaction-diffusion systems was discussed by D. Hilhorst, M. Mimura, H. Matano and several other colleagues. Joint works with K. Tsunoda/A. De Masi, E. Presutti, M.E. Vares. |
| Presentation hour: 2018-11-01-14:35-PM Presented by Cédric Bernardin (University of Nice ) title: Fluctuations in a model of interacting active particles abstract: I will consider a model of interacting active particles. I will explain ho to derive heuristically fluctuating hydrodynamics equation for this model in the spirit of Chapman-Enskog expansion and I will propose a way to give a mathematical sense to this formal expansion. Work (in progres) with J. Barré, R. Chetrite, C. Nardini and F. Peruani |
| Presentation hour: 2018-11-01-15:30-PM Presented by Francesco RUSSO (ENSTA ParisTech) title: McKEAN stochastic differential equations and non-conservative PDEs abstract: Stochastic differential equations (SDEs) in the sense of McKean are stochastic differential equations whose coefficients do not only depend on time and on the position of the process solution but also on its marginal laws. Often they constitute probabilistic representation of conservative PDEs. The possibility of approaching them with particle systems provides a Monte-Carlo type approximation of the mentioned conservative PDEs. In this talk we will illustrate how the method can be adapted to the case of a class of non-conservative PDEs. The talk is based on recent work with A. Le Cavil, J. Lieber and N. Oudjane. |
| Presentation hour: 2018-11-01-16:05-PM Presented by Mayuko Iwamoto (Shimane University) title: Model for Dynamic Pattern Formation in Cuttlefish abstract: Different from some mechanism of pattern formation on animal skin, which has been understood by reaction diffusion equation such as Turing model, a body pattern of cephalopods changes instantaneously, and the time scale is fast compared with the Turing mechanism. In the case of cephalopods, the patterns are changed by muscle contraction around pigment cells through a control from nervous system. Most interest is that they can camouflage to fit their surroundings with their good eyesight. In this study, toward to understand pattern formation in cuttlefish, we classifiled the previous study about cuttlefish and try to build a mathematical model. |
| Presentation hour: 2018-11-01-17:00-PM Presented by Yu Uchiumi (Meiji University) title: Evolutionary maintenance of horizontally transmitted mutualism without frequent mutations abstract: Mutualism based on reciprocal exchange of costly services must avoid exploitation by “free-rides”. Accordingly, hosts discriminate against free-riding symbionts in many mutualistic relationships. However, as the selective advantage of discriminators comes from the presence of variability in symbiont quality that they eliminate, discrimination and thus mutualism have been considered to be not maintained unless free-riders are generated by frequent mutations. In this study, we tried to resolve the “paradoxical” coevolution of discrimination by hosts and cooperation by symbionts, by comparing two different types of discrimination: “one-shot” discrimination, where a host does not reacquire new symbionts after evicting free-riders, and “resampling” discrimination, where a host does from the environment. Our study shows that this apparently minor difference in discrimination types leads to qualitatively different evolutionary outcomes. First, although it has been usually considered that the benefit of discriminators is derived from the variability of symbiont quality, the benefit of a certain type of discriminators (e.g. one-shot discrimination) is proportional to the frequency of free-riders, which is in stark contrast to the case of resampling discrimination. As a result, one-shot discriminators can invade the free-rider/non-discriminator population, even if standing variation for symbiont quality is absent. Second, our one-shot discriminators can also be maintained without exogenous supply of free-riders and hence is free from the paradox of discrimination. Therefore, our result indicates that the paradox is not a common feature of evolution of discrimination but is a problem of specific types of discrimination. |
| Presentation hour: 2018-11-01-17:35-PM Presented by Jenn-Nan Wang (National Taiwan University) title: Quantitative uniqueness estimates for the fractional Schrodinger operator abstract: In this talk, I would like to discuss some quantitative uniqueness estimates related to the strong unique continuation property and the unique continuation at infinity for the fractional Schrodinger operator. These kinds of estimates are useful in understanding the local properties of the solution. For the classical Schrodinger operator, these estimates have been extensively studied and successfully applied to other problems. Recently, the study of the local properties of solutions to the fractional equation became possible thanks to the Caffarelli-Silvestre extension theorem. For the fractional Schr"odinger operator, we are especially interested in the dependence of the estimates on the size of the potential. Besides of mathematical interests, fractional equations arise naturally from superdiffusion and can be used in modeling a lot of physical phenomena involving long jumps. |
| Presentation hour: 2018-11-02-09:00-AM Presented by Jong-Shenq Guo (Tamkang University) title: The spreading speed of a predator-prey system with nonlocal dispersal abstract: We are concerned with the propagation dynamics of a predator-prey system with nonlocal dispersal. We obtain a threshold phenomenon for the invasion of the predator into the habitat of the aborigine prey. It turns out that this threshold is the so-called spreading speed of the predator. |
| Presentation hour: 2018-11-02-09:35-AM Presented by Changwook Yoon (Korea University) title: Predator–prey model with indirect prey(or antipredator)-taxis abstract: We analyze predator–prey models in which the movement of predator searching for prey is toward the gradient of concentration of some chemical released by prey (e.g. pheromone), or prey behaves as a chemo-repellent to chemical of predator. Global-in-time solutions are studied and stability of homogeneous steady states is shown by standard linearization technique. We also present results of numerical studies for this model. |
| Presentation hour: 2018-11-02-10:30-AM Presented by Feng-Bin Wang (Chang Gung University) title: A reaction-diffusion system modeling the intraguild predation and internal storage abstract: In this talk, I shall present a reaction-diffusion system modeling interactions of the intraguild predator and prey in an unstirred chemostat, in which the predator can also compete with its prey for one single nutrient resource that can be stored within individuals. Under suitable conditions, we first show that there are at least three steady-state solutions for the full system, a trivial steady-state solution with neither species present, and two semi-trivial steady-state solutions with just one of the species. Then we establish that coexistence of the intraguild predator and prey can occur if both of the semi-trivial steady-state solutions are invasible by the missing species. Comparing with the system without predation, our numerical simulations show that the introduction of predation in an ecosystem can enhance the coexistence of species. This talk is based on a joint work with Drs. Sze-Bi Hsu and Hua Nie. |
| Presentation hour: 2018-11-02-11:05-AM Presented by Kenji Handa (Saga University) title: Coagulation-fragmentation equations and underlying stochastic dynamics abstract: We consider stochastic dynamics of interval partitions evolving according to certain split-merge transformations. An asymptotic result for properly rescaled processes is shown to obtain a solution to a nonlinear equation called the coagulation-fragmentation equation. |
| Presentation hour: 2018-11-02-11:40-AM Presented by Frédérique NOEL (University of Nice) title: Oxygen and Carbon dioxide transport in the lung abstract: The human lung is a favorable site for the development of infections. That is why the lung has two types of protections: biological, thanks to the immune system, or mechanical, thanks to cilia cells and a mucus layer on the walls of the bronchi. But dysfunctions can affect these protections and infections can appear. Once in the lung, an infection needs oxygen to spread. In a first step to understand the development of infections, we need to understand how oxygen and carbon dioxide are transported in the lung. The lung can be modelled by a symmetric tree with 22 dichotomic bifurcations (23 generations). This tree can be divided in two parts: the bronchial tree (17 first generations) and the acini (6 last generations) where the exchange of gases with blood occurs. We developed a one dimension space model to study how oxygen and carbon dioxide transport is related to the characteristics of lungs and of the ventilation of lungs. In the physiological case, the molar flux of oxygen and carbon dioxide exchanged with blood predicted by our model are very close to the data from the literature [1]. Our model makes us able to explore how these exchanges are affected by several parameters such as ventilation rate, ventilation amplitude or the geometry of the lung. References: [1] Weibel E.R, The pathway for oxygen, Harvard University Press, 1984. |
| Presentation hour: 2018-11-02-11:42-AM Presented by HoYoun, Kim (KAIST) title: Convergence of discrete kinetic model to isotropic diffusion equation abstract: We consider one species discrete kinetic model with non-constant velocity and turning frequency. In this talk, we assume velocity and turning frequency have spatial heterogeneity or population dependency(non-linearity). In the bounded domain with periodic boundary condition, we will show that a weak solution of discrete kinetic model converges to a solution of isotropic diffusion equation. We will introduce an appropriate energy functional for discrete kinetic model and give mathematical insight about particle dynamics. |
| Presentation hour: 2018-11-02-11:44-AM Presented by HyunJin Lim (KAIST) title: Convergence of discrete kinetic model to isotropic diffusion equation abstract: We consider one species discrete kinetic model with non-constant velocity and turning frequency. In this talk, we assume velocity and turning frequency have spatial heterogeneity or population dependency(non-linearity). In the bounded domain with periodic boundary condition, we will show that a weak solution of discrete kinetic model converges to a solution of isotropic diffusion equation. We will introduce an appropriate energy functional for discrete kinetic model and give mathematical insight about particle dynamics. |
| Presentation hour: 2018-11-02-11:46-AM Presented by Pierre Roux (Université Paris-Saclay) title: The Nonlinear Noisy Leaky Integrate&Fire model for neurons with a transmission delay abstract: We derive mathematical results for the NNLIF model with a transmission delay. The model without synaptic delay was intensively studied. In particular, some solutions were proven to blow-up in finite time. With a synaptic delay, classical solutions globally exist and many results still hold. |
| Presentation hour: 2018-11-02-11:48-AM Presented by Wonhyung Choi (Korea University) title: A SIS epidemic reaction-diffusion model with risk-induced dispersal abstract: This study examined a spatial SIS (susceptible-infected-susceptible) epidemic model where the dispersal of the infected individuals was non-linear. Spatial heterogeneity and dispersal of individuals are important factors that influence the persistence and eradication of an infectious disease. Based on spatial SIS reaction- diffusion models, diseases have been known to be eradicated if the mobility of the infected individuals is above a certain value. Additionally, an area is categorized as high- or low-risk if the infection rate average is higher or lower than the recovery rate average, respectively. In this study, we promoted a risk-induced dispersal (RID) method of the infected individuals i.e., the mobility of the infected individuals was high in high-risk areas and low in low-risk areas. We also examined the effect of RID on the spatial SIS model by defining the basic reproduction number (R0) in the spatial SIS reaction-diffusion model and investigating its stability i.e., R0 < 1 represented a stable disease-free state and R0 > 1 represented an endemic state. By comparing the R0 of these models, RID of infected individuals proved to be a better strategy than random dispersal in obtaining a disease-free state. |
| Presentation hour: 2018-11-02-11:50-AM Presented by Yueyuan Gao (MathAM-OIL, AIST) title: Uniqueness result for a first order conservation law involving a Q-Brownian motion abstract: In this poster presentation, we prove the uniqueness of the entropy solution for a first order stochastic conservation law with a multiplicative source term involving a Q-Brownian motion. After having defined a measure-valued weak entropy solution of the stochastic conservation law, we present the Kato inequality and as a corollary we deduce the uniqueness of the measure-valued weak entropy solution which coincides with the unique weak entropy solution of the Problem. The Kato inequality is proved by a doubling of variables method; to that purpose, we also prove the existence and the uniqueness of the weak solution of an associated parabolic problem by means of an implicit time discretization. It is joint work with Prof. T. Funaki and Prof. D. Hilhorst. |
| Presentation hour: 2018-11-02-11:52-AM Presented by Hyunjoon Park (KAIST) title: Inside dynamics of a constant effect model abstract: In this poster session we give an inside dynamics of the species with constant Allee effect. The two main idea, the inside dynamics and constant Allee effect, were proposed by Jimmy Garnier and Jaywan Chung. After giving preliminary introduction of these two concepts, we give a properties of our main model and its proof. |
| Presentation hour: 2018-11-03-09:00-AM Presented by Kim, Yong Jung (KAIST) title: How to model biological reaction and diffusion abstract: The difference of biological dispersal over non-biological one is the adaptation ability to the environmental changes and differences. In the first part of this talk we will discuss how to give the adaptation ability to a dispersal model. In the second part, we discuss how to decide the coefficients of Lotka-Volterra type competition models. |
| Presentation hour: 2018-11-03-09:30-AM Presented by Yoshihisa Morita (Ryukoku University) title: Turing-type instability in coupled equations of bulk and lateral diffusions abstract: Motivated by cell polarity models we deal with a system of mass transport equations, that couples a diffusion equation in a bulk domain and a lateral diffusion on its boundary with mass transport. In the case that the bulk domain is a disk or a unit ball we perform the linearized stability analysis for a constant steady state and provide conditions under which a Turing-type instability takes place, namely, the constant state is stable for spatially uniform perturbations on the boundary while unstable for nonuniform perturbations as the lateral diffusion coefficient decreases. The talk is based on the recent joint work with K. Sakamoto (Hiroshima University). |
| Presentation hour: 2018-11-03-10:00-AM Presented by Sun-Ho Choi (Kyung Hee University) title: Food metric porous medium equation and chemotactic traveling waves with interface abstract: We present a chemotaxis model that has a traveling wave solution with interfaces. Our model is based on the food metric distance with slow diffusion. We considered a metric induced by the amount of resources such as food, and we derived a chemotaxis model from this metric and proved the existence of the traveling wave solution to the proposed model. The walk length of a random walk depending on this metric allowed the system in our previous paper to possess the chemotactic traveling wave phenomena without sensing the gradient of the chemical concentration. In this talk, we replace the linear diffusion with a slow diffusion in the derivation of the chemotactic system coming from the food metric. Then, we derive a slow diffusion model corresponding to the food metric. With the similar argument, we obtain a traveling wave solution and prove that its profile has interfaces. We provide numerical simulations to demonstrate our analytic results. |
| Presentation hour: 2018-11-03-11:00-AM Presented by Chih-Chiang Huang (National Center for Theoretical Sciences) title: A semi-wave for reaction-diffusion equations with a triple-well pontial abstract: In this talk, I would like to introduce a semi-wave arising from a free boundary problem. By a variational method, we can construct a semi-wave for such problems. In addition, reaction-diffusion equations with a triple-well potential are concerned. |
| Presentation hour: 2018-11-03-11:30-AM Presented by Danielle Hilhorst (CNRS and University Paris-Sud Paris-Saclay) title: On a nonlocal stochastic reaction-diffusion equation abstract: We first consider an initial value problem for a nonlocal stochastic reaction-diffusion equation with a nonlinear diffusion term and a homogenous Neumann boundary condition in arbitrary space dimension. We suppose that the noise is additive and induced by a Q-Wiener process. The deterministic problem with linear diffusion was introduced by Rubinstein and Sternberg to model phase separation in a binary mixture. We prove the existence and uniqueness of a weak solution. The proof of existence is based upon a change of function which involves the solution of the stochastic heat equation with a nonlinear diffusion term. We then obtain a problem without any noise term, which we discretize by means of the Galerkin method. The existence proof is based upon the monotonicity method, which we use to identify the limit of the nonlinear terms. This is joint work with Perla El Kettani and Kai Lee. We then study the stochastic nonlocal Allen-Cahn equation with linear diffusion in the more general case of a multiplicative noise. We prove the existence and the uniqueness of a pathwise solution in space dimension up to 6. The usual compactness methods for deterministic problems cannot be applied in a stochastic context because of the additional probability variable. This leads us to apply the stochastic compactness method in some fractional Sobolev spaces, and the Prokhorov and Skorokhod theorems to deduce the strong convergence of a subsequence of approximate solutions. This is joint work with Perla El Kettani. |
| Presentation hour: 2018-11-03-12:00-AM Presented by Masayasu Mimura (Musashino University) title: Expanding wave of sedentary farmer life in Neolithic transition abstract: Recently we have proposed a monostable reaction-diffusion system to explain the Neolithic transition from hunter-gatherer life to farmer life in Europe. The system is described by a three-component system for the populations of hunter-gatherer (H), sedentary farmer (F1), and migratory one (F2). The conversion between F1 and F2 is specified by such a way that if the total farmers F1 + F2 are over-crowded, F1 actively changes to F2, while if it is less crowded, the situation is vice versa. It looks population pressure effect for farmers. In this talk, we discuss analytically and complementarily numerically this system to investigate the development of farming technology on expanding waves of farmers into the region of hunter-gatherers in Europe. |
| Presentation hour: Not arranged. Presented by Byeon, Jaeyoung (KAIST) title: abstract: |
| Presentation hour: Talk is cancelled. Presented by Hyung Ju Hwang (POSTECH) title: Medical anomaly detection through neural density estimation abstract: A large amount of data is being collected recently. Such medical dataset shows a promising ability to leverage healthcare services. Based on the collected information, our main goal is to detect anomalies of patients. Such unsupervised analytics finds how much a subject is deviated from normal conditions. The difficulty of applying the anomaly detection on healthcare dataset lies on its sparsity and overdetermined structure. Medical records usually have the higher number of features than the number of patients due to the security issues among medical institutions. Furthermore, the data shows non-zero values on particular indices since a disease usually involves specific symptoms rather than shows entire malfunctioning on patient body. Therefore, a scalable anomaly detection methodology, which is robust to sparsity and overdetermined structure needs to be developed. We investigate many possibilities from machine learning and deep learning to properly estimate the density of anomaly and find how the medical anomaly detection algorithm can be efficiently developed. |
| Presentation hour: Talk is cancelled. Presented by Tai-Chia Lin (National Taiwan University) title: Analysis of ionic interactions and its applications abstract: The Lennard-Jones (LJ) potential, a well-known mathematical model for the interaction between a pair of ions, has important applications in many fields of biology, chemistry and physics. Using band-limited functions, we obtained a class of approximate LJ (LJ_a) potentials which can be used to derive PNP-steric equations as a model to describe the ion transport through (biological) channels (with B. Eisenberg, 2014). However, due to the strong singularities of LJ potentials, it is difficult to calculate the Fourier transform of LJ_a potentials. In this lecture, a new class of approximate LJ (LJ_na) potentials with precise formulas of Fourier transform will be introduced. Using techniques of complex analysis, we may prove that the energy of ions interacting by the LJ_na potential can approach to the energy of ions interacting by the LJ_a potential. This may provide a new PNP type model for the ion transport through channels. |