Modulated Branching Processes, Origins of Power Laws and Queueing Duality

Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas. In many of the observations, e.g., city populations and sizes of living organisms, the objects of interest evolve due to the replication of their many independent components, e.g., births-deaths of individuals and replications of cells. Furthermore, the rates of the replication are often controlled by exogenous parameters causing periods of expansion and contraction, e.g., baby booms and busts, economic booms and recessions, etc. In addition, the sizes of these objects often have reflective lower boundaries, e.g., cities do not fall bellow a certain size, low income individuals are subsidized by the government, companies are protected by bankruptcy laws, etc. Hence, it is natural to propose reflected modulated branching processes as generic models for many of the preceding observations. Indeed, our main results show that the proposed mathematical models result in power law distributions under quite general polynomial Gartner-Ellis conditions, the generality of which could explain the ubiquitous nature of power law distributions. In addition, on a logarithmic scale, we establish an asymptotic equivalence between the reflected branching processes and the corresponding multiplicative ones. The latter, as recognized by Goldie (1991), is known to be dual to queueing/additive processes. We emphasize this duality further in the generality of stationary and ergodic processes.Comment: 36 pages, 2 figures; added references; a new theorem in Subsection 4.

Q-CSMA: Queue-Length Based CSMA/CA Algorithms for Achieving Maximum Throughput and Low Delay in Wireless Networks

Recently, it has been shown that CSMA-type random access algorithms can achieve the maximum possible throughput in ad hoc wireless networks. However, these algorithms assume an idealized continuous-time CSMA protocol where collisions can never occur. In addition, simulation results indicate that the delay performance of these algorithms can be quite bad. On the other hand, although some simple heuristics (such as distributed approximations of greedy maximal scheduling) can yield much better delay performance for a large set of arrival rates, they may only achieve a fraction of the capacity region in general. In this paper, we propose a discrete-time version of the CSMA algorithm. Central to our results is a discrete-time distributed randomized algorithm which is based on a generalization of the so-called Glauber dynamics from statistical physics, where multiple links are allowed to update their states in a single time slot. The algorithm generates collision-free transmission schedules while explicitly taking collisions into account during the control phase of the protocol, thus relaxing the perfect CSMA assumption. More importantly, the algorithm allows us to incorporate mechanisms which lead to very good delay performance while retaining the throughput-optimality property. It also resolves the hidden and exposed terminal problems associated with wireless networks.Comment: 12 page

Maximizing sum rate and minimizing MSE on multiuser downlink: Optimality, fast algorithms and equivalence via max-min SIR

Maximizing the minimum weighted SIR, minimizing the weighted sum MSE and maximizing the weighted sum rate in a multiuser downlink system are three important performance objectives in joint transceiver and power optimization, where all the users have a total power constraint. We show that, through connections with the nonlinear Perron-Frobenius theory, jointly optimizing power and beamformers in the max-min weighted SIR problem can be solved optimally in a distributed fashion. Then, connecting these three performance objectives through the arithmetic-geometric mean inequality and nonnegative matrix theory, we solve the weighted sum MSE minimization and weighted sum rate maximization in the low to moderate interference regimes using fast algorithms

Elastic Deformation of Soft Coatings Due to Lubrication Forces

Elastic deformation of rigid materials with soft coatings (stratified materials) due to lubrication forces can also alter the interpretation of dynamic surface forces measurements and prevent contact formation between approaching surfaces. Understanding the role of elastic deformation on the process of fluid drainage is necessary, and the case where one (or both) of the interacting materials consists of a rigid substrate with a soft coating is still limited. We combine lubrication theory and solid linear elasticity to describe the dynamic of fluid drainage past a compliant stratified boundary. The analysis presented covers the full range of coating thicknesses, from an elastic foundation to a half-space for an incomressible coating. We decouple the individual contributions of the coating thickness and material properties on the elastic deformation, hydrodynamic forces, and fluid film thickness. We obtain a simple expression for the shift in contact position during force measurements that is valid for many experimental conditions. We compare directly the effect of stratification on the out-of-contact deformation to the well-known effect of stratification on indentation. We show that corrections developed for stratification in contact mechanics are not applicable to elastohydrodynamic deformation. Finally, we provide generalized contour maps that can be employed directly to estimate the elastic deformation present in most dynamic surface force measurements

A heterotic sigma model with novel target geometry

We construct a (1,2) heterotic sigma model whose target space geometry consists of a transitive Lie algebroid with complex structure on a Kaehler manifold. We show that, under certain geometrical and topological conditions, there are two distinguished topological half--twists of the heterotic sigma model leading to A and B type half--topological models. Each of these models is characterized by the usual topological BRST operator, stemming from the heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with the former, originating from the (1,0) supersymmetry. These BRST operators combined in a certain way provide each half--topological model with two inequivalent BRST structures and, correspondingly, two distinct perturbative chiral algebras and chiral rings. The latter are studied in detail and characterized geometrically in terms of Lie algebroid cohomology in the quasiclassical limit.Comment: 83 pages, no figures, 2 references adde

Achieving Effective Innovation Based On TRIZ Technological Evolution

Organised by: Cranfield UniversityThis paper outlines the conception of effective innovation and discusses the method to achieve it. Effective Innovation is constrained on the path of technological evolution so that the corresponding path must be detected before conceptual design of the product. The process of products technological evolution is a technical developing process that the products approach to Ideal Final Result (IFR). During the process, the sustaining innovation and disruptive innovation carry on alternately. By researching and forecasting potential techniques using TRIZ technological evolution theory, the effective innovation can be achieved finally.Mori Seiki – The Machine Tool Compan

Classification for the universal scaling of N\'eel temperature and staggered magnetization density of three-dimensional dimerized spin-1/2 antiferromagnets

Inspired by the recently theoretical development relevant to the experimental data of TlCuCl$_3$, particularly those associated with the universal scaling between the N\'eel temperature $T_N$ and the staggered magnetization density $M_s$, we carry a detailed investigation of 3-dimensional (3D) dimerized quantum antiferromagnets using the first principles quantum Monte Carlo calculations. The motivation behind our study is to better understand the microscopic effects on these scaling relations of $T_N$ and $M_s$, hence to shed some light on some of the observed inconsistency between the theoretical and the experimental results. Remarkably, for the considered 3D dimerized models, we find that the established universal scaling relations can indeed be categorized by the amount of stronger antiferromagnetic couplings connected to a lattice site. Convincing numerical evidence is provided to support this conjecture. The relevance of the outcomes presented here to the experiments of TlCuCl$_3$ is briefly discussed as well.Comment: 9 pages, 27 figure