On rationality of nonnegative matrix factorization

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. NMF has a wide variety of applications, including bioinformatics, chemometrics, communication complexity, machine learning, polyhedral combinatorics, among many others. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether every rational matrix M has an NMF with minimal d whose factors W and H are also rational. We answer this question negatively, by exhibiting a matrix M for which W and H require irrational entries. As an application of this result, we show that state minimization of labeled Markov chains can require the introduction of irrational transition probabilities. We complement these irrationality results with an NP- complete version of NMF for which rational numbers suffice

Synchronizing Objectives for Markov Decision Processes

We introduce synchronizing objectives for Markov decision processes (MDP). Intuitively, a synchronizing objective requires that eventually, at every step there is a state which concentrates almost all the probability mass. In particular, it implies that the probabilistic system behaves in the long run like a deterministic system: eventually, the current state of the MDP can be identified with almost certainty. We study the problem of deciding the existence of a strategy to enforce a synchronizing objective in MDPs. We show that the problem is decidable for general strategies, as well as for blind strategies where the player cannot observe the current state of the MDP. We also show that pure strategies are sufficient, but memory may be necessary.Comment: In Proceedings iWIGP 2011, arXiv:1102.374

Identification of biomolecule mass transport and binding rate parameters in living cells by inverse modeling

BACKGROUND: Quantification of in-vivo biomolecule mass transport and reaction rate parameters from experimental data obtained by Fluorescence Recovery after Photobleaching (FRAP) is becoming more important. METHODS AND RESULTS: The Osborne-Moré extended version of the Levenberg-Marquardt optimization algorithm was coupled with the experimental data obtained by the Fluorescence Recovery after Photobleaching (FRAP) protocol, and the numerical solution of a set of two partial differential equations governing macromolecule mass transport and reaction in living cells, to inversely estimate optimized values of the molecular diffusion coefficient and binding rate parameters of GFP-tagged glucocorticoid receptor. The results indicate that the FRAP protocol provides enough information to estimate one parameter uniquely using a nonlinear optimization technique. Coupling FRAP experimental data with the inverse modeling strategy, one can also uniquely estimate the individual values of the binding rate coefficients if the molecular diffusion coefficient is known. One can also simultaneously estimate the dissociation rate parameter and molecular diffusion coefficient given the pseudo-association rate parameter is known. However, the protocol provides insufficient information for unique simultaneous estimation of three parameters (diffusion coefficient and binding rate parameters) owing to the high intercorrelation between the molecular diffusion coefficient and pseudo-association rate parameter. Attempts to estimate macromolecule mass transport and binding rate parameters simultaneously from FRAP data result in misleading conclusions regarding concentrations of free macromolecule and bound complex inside the cell, average binding time per vacant site, average time for diffusion of macromolecules from one site to the next, and slow or rapid mobility of biomolecules in cells. CONCLUSION: To obtain unique values for molecular diffusion coefficient and binding rate parameters from FRAP data, we propose conducting two FRAP experiments on the same class of macromolecule and cell. One experiment should be used to measure the molecular diffusion coefficient independently of binding in an effective diffusion regime and the other should be conducted in a reaction dominant or reaction-diffusion regime to quantify binding rate parameters. The method described in this paper is likely to be widely used to estimate in-vivo biomolecule mass transport and binding rate parameters

An End-to-End Communication Architecture for Collaborative Virtual Environments

Synchronous collaboration in virtual reality spaces has specific requirements that differ from those of other application data, leading to a different communication approach. Update messages corresponding to the change in the state of a shared object must be communicated both reliably and in a timely manner among users. While a lot of research has been done in terms of transmission of update messages representing the motion of avatars and objects, very few works focus on collaboration itself. Here, we present an architecture that supports tightlycoupled collaborative tasks to be performed efficiently in virtual environments. The architecture consists of an application-general layer which is mapped into a communication protocol. An implementation is also presented as proof of concept

Parity objectives in countable MDPs

We study countably infinite MDPs with parity objectives, and special cases with a bounded number of colors in the Mostowski hierarchy (including reachability, safety, Büchi and co-Büchi). In finite MDPs there always exist optimal memoryless deterministic (MD) strategies for parity objectives, but this does not generally hold for countably infiniteMDPs. In particular, optimal strategies need not exist. For countable infinite MDPs, we provide a complete picture of the memory requirements of optimal (resp., ǫ-optimal) strategies for all objectives in the Mostowski hierarchy. In particular, there is a strong dichotomy between two different types of objectives. For the first type, optimal strategies, if they exist, can be chosen MD, while for the second type optimal strategies require infinite memory. (I.e., for all objectives in the Mostowski hierarchy, if finite-memory randomized strategies suffice then also MD-strategies suffice.) Similarly, some objectives admit ǫ-optimal MD-strategies, while for others ǫ-optimal strategies require infinite memory. Such a dichotomy also holds for the subclass of countably infinite MDPs that are finitely branching, though more objectives admit MD-strategies here.</p

A survey of application-layer multicast protocols

Abstract- In light of the slow deployment of IP Multicast technology on the global Internet and the explosive popularity of peer-to-peer file-sharing applications, there has been a flurry of research activities investigating the feasibility of implementing multicasting capability at the application layer, referred to as Application Layer Multicasting (ALM), and numerous algorithms and protocols have been proposed. This article aims to provide researchers in the field with an understanding of ALM protocols by identifying significant characteristics, from both application requirements and networking points of view, and by using those characteristics as a basis for organizing the protocols into an integrated and well-structured format. Current trends and directions for further research are also presented. This article surveys the literature over the period 1995-2005 on different application layer multicasting approaches