On the tractability of Nash equilibrium

In this paper, we propose a method for solving a PPAD-complete problem [Papadimitriou, 1994]. Given is the payoff matrix $C$ of a symmetric bimatrix game $(C, C^T)$ and our goal is to compute a Nash equilibrium of $(C, C^T)$. In this paper, we devise a nonlinear replicator dynamic (whose right-hand-side can be obtained by solving a pair of convex optimization problems) with the following property: Under any invertible $0 < C \leq 1$, every orbit of our dynamic starting at an interior strategy of the standard simplex approaches a set of strategies of $(C, C^T)$ such that, for each strategy in this set, a symmetric Nash equilibrium strategy can be computed by solving the aforementioned convex mathematical programs. We prove convergence using results in analysis (the analytic implicit function theorem), nonlinear optimization theory (duality theory, Berge's maximum principle, and a theorem of Robinson [1980] on the Lipschitz continuity of parametric nonlinear programs), and dynamical systems theory (such as the LaSalle invariance principle)

Genetics of Alzheimer's disease: recent advances

Alzheimer's disease is a progressive neurodegenerative disorder with high prevalence in old age. It is the most common cause of dementia, with a risk reaching 50% after the age of 85 years, and with the increasing age of the population it is one of the biggest healthcare challenges of the 21st century. Genetic variation is an important contributor to the risk for this disease, underlying an estimated heritability of about 70%. Alzheimer's genetics research in the 1990s was successful in identifying three genes accounting for most cases of early-onset disease with autosomal dominant inheritance, and one gene involved in the more common late-onset disease, which shows complex inheritance patterns. Despite the presence of significant remaining genetic contribution to the risk, the identification of genes since then has been elusive, reminiscent of most other complex disorders. In the past decade there have been significant efforts towards a systematic evaluation of the multiple genetic association studies for Alzheimer's disease, while the first genome-wide association studies are now being reported with promising results. As sample sizes grow through new collections and collaborative efforts, and as new technologies make it possible to test alternative hypotheses, it is expected that new genes involved in the disease will soon be identified and confirmed. The gene discoveries of the 1990s have taught us a lot about Alzheimer's disease pathogenesis, providing many therapeutic targets that are currently at various stages of testing for future clinical use. As new genes become known and the biological pathways leading to disease are further explored, the possibility of prevention and successful personalized treatment is becoming tangible, providing hope for the millions of patients with Alzheimer's disease and their caregivers

On algorithmically boosting fixed-point computations

This paper is a thought experiment on exponentiating algorithms. One of the main contributions of this paper is to show that this idea finds material implementation in exponentiating fixed-point computation algorithms. Various problems in computer science can be cast as instances of computing a fixed point of a map. In this paper, we present a general method of boosting the convergence of iterative fixed-point computations that we call algorithmic boosting, which is a (slight) generalization of algorithmic exponentiation. We first define our method in the general setting of nonlinear maps. Secondly, we restrict attention to convergent linear maps and show that our algorithmic boosting method can set in motion exponential speedups in the convergence rate. Thirdly, we show that algorithmic boosting can convert a (weak) non-convergent iterator to a (strong) convergent one. We then consider a variational approach to algorithmic boosting providing tools to convert a non-convergent continuous flow to a convergent one. We, finally, discuss implementations of the exponential function, an important issue even for the scalar case

Photonic integration enabling new multiplexing concepts in optical board-to-board and rack-to-rack interconnects

New broadband applications are causing the datacenters to proliferate, raising the bar for higher interconnection speeds. So far, optical board-to-board and rack-to-rack interconnects relied primarily on low-cost commodity optical components assembled in a single package. Although this concept proved successful in the first generations of optical-interconnect modules, scalability is a daunting issue as signaling rates extend beyond 25 Gb/s. In this paper we present our work towards the development of two technology platforms for migration beyond Infiniband enhanced data rate (EDR), introducing new concepts in board-to-board and rack-to-rack interconnects. The first platform is developed in the framework of MIRAGE European project and relies on proven VCSEL technology, exploiting the inherent cost, yield, reliability and power consumption advantages of VCSELs. Wavelength multiplexing, PAM-4 modulation and multi-core fiber (MCF) multiplexing are introduced by combining VCSELs with integrated Si and glass photonics as well as BiCMOS electronics. An in-plane MCF-to-SOI interface is demonstrated, allowing coupling from the MCF cores to 340x400 nm Si waveguides. Development of a low-power VCSEL driver with integrated feed-forward equalizer is reported, allowing PAM-4 modulation of a bandwidth-limited VCSEL beyond 25 Gbaud. The second platform, developed within the frames of the European project PHOXTROT, considers the use of modulation formats of increased complexity in the context of optical interconnects. Powered by the evolution of DSP technology and towards an integration path between inter and intra datacenter traffic, this platform investigates optical interconnection system concepts capable to support 16QAM 40GBd data traffic, exploiting the advancements of silicon and polymer technologies