Abstract

Dynamic programming is an efficient technique to solve optimization problems.

Abstract

We establish a new oscillation estimate for solutions of nonlinear partial differential e

The time-dependent PDE system for mean field games is a coupled pair of parabolic equations, one forward in time and the other backward in time. The lecturer will demonstrate two techniques for proving existence and uniqueness of solutions for this system. The first of these techniques is inspired by work in fluid dynamics, as a similar forward-backward structure for vortex sheets was discovered by Duchon and Robert in the 1980s. Adapting the ideas of Duchon and Robert gives existence and uniqueness of solutions for the time-dependent mean field games system in function spaces based on the Wiener algebra. The second technique to be demonstrated by the speaker uses Sobolev spaces, and is an adaptation of the energy method to the forward-backward setting.

In this webinar we will give an overview of several key technologies related to our special issues in Frontiers of Communications and Networks; (1) visible light communications (VLC) and (2) applications of machine learning in optical and wireless communication systems. Firstly, several key research challenges have emerged within the VLC domain, including multi-technology network tenancy, high data rates, physical layer security, resource allocation, co-design of high-speed data rates and dimming capabilities, amongst others. Future networks are expected to support a wide range of heterogenous technologies beyond 5G and one of the most promising is VLC, which can support ultra-high data rates while providing illumination simultaneously. However, there are some key challenges that still remain and the vast majority of them concern real integration and some of these will be discussed in detail through the webinar. Secondly, artificial intelligence (AI) and machine learning (ML) have attracted increasing research interests and are ubiquitously emerging at different levels within optical communication systems and networks. From physical layer to subsystem layer, and to networking layer, we have observed the increasing complexity of optical communication systems due to higher-speed data transmission, more flexible networking and larger scale of connections under different use scenarios. The second part of this webinar will also discuss research on novel applications in optical and wireless communication systems and networks, including state-of-the-art developments from the respective laboratories.

Abstract

In statistical applications, there are often many competing models available, from which

The time-dependent PDE system for mean field games is a coupled pair of parabolic equations, one forward in time and the other backward in time. The lecturer will demonstrate two techniques for proving existence and uniqueness of solutions for this system. The first of these techniques is inspired by work in fluid dynamics, as a similar forward-backward structure for vortex sheets was discovered by Duchon and Robert in the 1980s. Adapting the ideas of Duchon and Robert gives existence and uniqueness of solutions for the time-dependent mean field games system in function spaces based on the Wiener algebra. The second technique to be demonstrated by the speaker uses Sobolev spaces, and is an adaptation of the energy method to the forward-backward setting.

Abstract

This session will help you to improve the efficiency of your literature searches.

The time-dependent PDE system for mean field games is a coupled pair of parabolic equations, one forward in time and the other backward in time. The lecturer will demonstrate two techniques for proving existence and uniqueness of solutions for this system. The first of these techniques is inspired by work in fluid dynamics, as a similar forward-backward structure for vortex sheets was discovered by Duchon and Robert in the 1980s. Adapting the ideas of Duchon and Robert gives existence and uniqueness of solutions for the time-dependent mean field games system in function spaces based on the Wiener algebra. The second technique to be demonstrated by the speaker uses Sobolev spaces, and is an adaptation of the energy method to the forward-backward setting.

In this course, we provide a brief introduction to fractional calculus with a view to applying it to the study of time fractional partial differential equations. We will introduce the definitions and main properties of  fractional integrals and derivatives, including those of Riemann-Liouville, Caputo and Grunwald-Letnikov. The previous results will serve as the main modeling tools for partial differential equations related to a class of non-Markovian stochastic processes, called subdiffusions. Then we will examine some results regarding time-fractional linear partial differential equations and conclude with a brief introduction to control problems and Mean Field Games for subdiffusion processes.

Computational mathematics has a millennium long history but its modern incarnation started after the advent of electronic computers about 80 years ago. Scientifically, it lies in the intersection between mathematics, a subject with a long history, and computer sciences, a relatively new discipline. Its motivations, approaches and practitioners have derived from different fields, and it has also had to evolve and adapt to new tools and opportunities. My own scientific career overlaps quite a bit with the field’s modern evolution and in this talk, I’ll give a personal, as well as a “historical” view of the field.

In this course, we provide a brief introduction to fractional calculus with a view to applying it to the study of time fractional partial differential equations. We will introduce the definitions and main properties of fractional integrals and derivatives, including those of Riemann-Liouville, Caputo and Grunwald-Letnikov. The previous results will serve as the main modeling tools for partial differential equations related to a class of non-Markovian stochastic processes, called subdiffusions. Then we will examine some results regarding time-fractional linear partial differential equations and conclude with a brief introduction to control problems and Mean Field Games for subdiffusion processes.

In this talk, I focus on the adoption of low latency persistent memory modules (PMMs). PMMs upend the long-established model of remote storage for distributed file systems. Instead, by colocating computation with PMM storage we can provide applications with much higher IO performance, sub-second application failover, and strong consistency. To demonstrate this, I present Assise, a new distributed file system, based on a persistent, replicated coherence protocol that manages client-local PMM as a linearizable and crash-recoverable cache between applications and slower (and possibly remote) storage.

In the first part of the talk, I will focus on ZygOS[SOSP 2017], a system optimized for μs-scale, in-memory computing on multicore servers. ZygOS implements a work-conserving scheduler within a specialized operating system designed for high request rates and a large number of network connections. ZygOS revealed the challenges associated with serving remote procedure calls (RPCs) on top of a byte-stream oriented protocol, such as TCP. In the second part of the talk, I will present R2P2[ATC 2019]. R2P2 is a transport protocol specifically designed for datacenter RPCs, that exposes the RPC abstraction to the endpoints and the network, making RPCs first-class datacenter citizens. R2P2 enables pushing functionality, such as scheduling, fault-tolerance, and tail-tolerance, inside the transport protocol, making it application-agnostic. I will show how using R2P2 allowed us to offload RPC scheduling to programmable switches that can schedule requests directly on individual cores.

Elliptic PDE are ubiquitous both in Mathematics and in the applications of Mathematics. The regularity of the generalized solutions is a very important issue that it is necessary to handle in proper way if one want to obtain useful information. The goal of my lectures is to introduce the audience to the topic of regularity for elliptic PDE under assumptions on the coefficients that are of minimal requirements.

Elliptic PDE are ubiquitous both in Mathematics and in the applications of Mathematics. The regularity of the generalized solutions is a very important issue that it is necessary to handle in proper way if one want to obtain useful information. The goal of my lectures is to introduce the audience to the topic of regularity for elliptic PDE under assumptions on the coefficients that are of minimal requirements.

This talk covers two research directions that address the shortcomings of existing network stacks. The first is on scalable software network stacks, solving problems in different components of operating systems and applications to allow a single server to handle data flows for tens of thousands of clients. The second is on Wide Area Network (WAN) congestion control, focusing on network-assisted congestion control schemes, where end-to-end solutions fail. The talk will conclude with a discussion of plans for future research in this area.

In this talk we prove that suitable deep neural network approximations do indeed overcome the curse of dimensionality in the case of a general class of semilinear parabolic PDEs and we thereby prove, for the first time, that a general semilinear parabolic PDE can be solved approximatively without the curse of dimensionality.

In this talk, several numerical methods will be presented and illustrated on examples. Borrowing tools from stochastic analysis, optimization, partial differential equations and machine learning, these methods enable us to solve mean field games with possibly complex sources of noise or high dimensional state variables.

What will it take for UAVs—and the associated ecosystem—to take off? Arguably, ubiquitous high-capacity links paired with hyper-reliable command and control all along. And indeed, meeting these aspirations may entail a full-blown mobile network support. While the understanding of UAV cellular communications has been advancing, many fundamental challenges remain to be addressed, with new applications demanding original solutions. In this talk, we blend academic and industrial views, navigating from 4G to 6G UAV use cases, requirements, and enabling technologies

Due to the increasing scarcity of RF spectrum and growing interference due to multiple users, deploying next generation high-speed wireless networks is becoming increasingly difficult. The use of unlicensed optical bands for wireless communications has been heralded as an exciting development for future broadband access for indoor, underwater and space communication links.

Geospatial health data are essential to inform public health and policy. These data can be used to quantify disease burden, understand geographic and temporal patterns, identify risk factors, and measure inequalities. In this talk, I will give an overview of my research which focuses on the development of geospatial methods and interactive visualization applications for health surveillance. I will present disease risk models where environmental, demographic and climatic data are used to predict the risk and identify targets for intervention of lymphatic filariasis in sub-Saharan Africa, and leptospirosis in a Brazilian urban slum. I will also show the R packages epiflows for risk assessment of travel-related spread of disease, and SpatialEpiApp for disease mapping and the detection of clusters. Finally, I will describe my future research and how it can inform better surveillance and improve population health globally.

A little more than half of the world’s population enjoy benefits of information technology which is enabled by complementary metal oxide semiconductor (CMOS) electronics. Going forward, we will enjoy further augmentation of quality of life through integrated CMOS electronic systems consisting of logic, memory, communication devices, energy storage and harvester, power management units, sensors and actuators. Their main attributes will include but not limited to high performance and storage capacity for data management; seamless connectivity; energy efficiency; hyper-scale integration density; appropriate functionalities based on their applications and operational environment; reliability and safety; and finally affordability and simplicity to expand their user base to include those who do not have any access to them today. Even using last fifty years’ wealth of knowledge and experience, such integrated electronic system development and deployment is a monumental engineering challenge. From that perspective, redesigning CMOS electronics might seem to be an overly ambitious goal specially, if that means transformation of such physically rigid complex electronic systems into a fully flexible one. To address this intriguing challenge, we have developed a unique coin like architecture based soft singular platform, which can be used as the building block of standalone fully flexible CMOS electronic system with all the aforementioned characteristics. We have devised an effective heterogeneous integration strategy based on mature and reliable CMOS technology only to integrate hybrid materials and diverse set of devices for multi-disciplinary applications. These will be the focus of this talk.

The theory of Mean Field Games (MFG) has been developed in the last two decades by economists, engineers, and mathematicians in order to study decision making in very large populations of “small" interacting agents. This short course will be focused on deterministic MFG, which are associated with a first order PDE system. We will address the problem assuming that agents are subject to state constraints, when classical PDE techniques are of little help. First, we will show how to prove the existence of solutions by the so-called Lagrangian approach, which interprets equilibria as certain measures on the space of paths that each agent can choose. Then, we will address regularity issues for such generalized solutions, deriving point-wise properties that allow to recover the typical MFG system. Finally, we will study the asymptotic behavior of solutions to the constrained MFG system as time goes to infinity, borrowing ideas from weak KAM theory.

Biological systems are distinguished by their enormous complexity and variability. That is why mathematical modeling and computational simulation of those systems is very difficult, in particular thinking of detailed models which are based on first principles. The difficulties start with geometric modeling which needs to extract basic structures from highly complex and variable phenotypes, on the other hand also has to take the statistic variability into account. Moreover, the models of the processes running on these geometries are not yet well established, since these are equally complex and often couple many scales in space and time. Thus, simulating such systems always means to put the whole frame to test, from modelling to the numerical methods and software tools used for simulation. These need to be advanced in connection with validating simulation results by comparing them to experiments.

The need for higher data-rates and more ubiquitous connectivity for an ever-increasing number of wirelessly connected devices motivates the exploration of uncharted spectral bands. In this context, Terahertz (THz)-band (0.1–10 THz) communication is envisioned as a key wireless technology of the next decade. The very large bandwidth available at THz frequencies (tens to hundreds of consecutive GHz) can alleviate the spectrum scarcity problem while enabling wireless Terabit-per-second (Tb/s) links in personal and local area networks, backhaul for urban and rural areas, and even space networks.