Strong Stability of Nash Equilibria in Load Balancing Games

We study strong stability of Nash equilibria in load balancing games of m (m >= 2) identical servers, in which every job chooses one of the m servers and each job wishes to minimize its cost, given by the workload of the server it chooses. A Nash equilibrium (NE) is a strategy profile that is resilient to unilateral deviations. Finding an NE in such a game is simple. However, an NE assignment is not stable against coordinated deviations of several jobs, while a strong Nash equilibrium (SNE) is. We study how well an NE approximates an SNE. Given any job assignment in a load balancing game, the improvement ratio (IR) of a deviation of a job is defined as the ratio between the pre- and post-deviation costs. An NE is said to be a r-approximate SNE (r >= 1) if there is no coalition of jobs such that each job of the coalition will have an IR more than r from coordinated deviations of the coalition. While it is already known that NEs are the same as SNEs in the 2-server load balancing game, we prove that, in the m-server load balancing game for any given m >= 3, any NE is a (5/4)-approximate SNE, which together with the lower bound already established in the literature yields a tight approximation bound. This closes the final gap in the literature on the study of approximation of general NEs to SNEs in load balancing games. To establish our upper bound, we make a novel use of a graph-theoretic tool.Comment: 17 pages and 4 figure

A new potential radiosensitizer: ammonium persulfate modified WCNTs

Radiotherapy plays a very important role in cancer treatment. Radiosensitizers have been widely used to enhance the radiosensitivity of cancer cells at given radiations. Here we fabricate multi-walled carbon nanotubes with ammonium persulfate, and get very short samples with 30-50 nanometer length. Cell viability assay show that f-WCNTs induce cell death significantly. We hypothesize that free radicals originated from hydroxyl and carbonyl groups on the surface of f-WCNTs lead cell damage

Strong stability of Nash equilibria in load balancing games

We study strong stability of Nash equilibria in the load balancing games of m (m >= 2) identical servers, in which every job chooses one of the m servers and each job wishes to minimize its cost, given by the workload of the server it chooses. A Nash equilibrium (NE) is a strategy profile that is resilient to unilateral deviations. Finding an NE in such a game is simple. However, an NE assignment is not stable against coordinated deviations of several jobs, while a strong Nash equilibrium (SNE) is. We study how well an NE approximates an SNE. Given any job assignment in a load balancing game, the improvement ratio (IR) of a deviation of a job is defined as the ratio between the pre-and post-deviation costs. An NE is said to be a ρ-approximate SNE (ρ >= 1) if there is no coalition of jobs such that each job of the coalition will have an IR more than ρ from coordinated deviations of the coalition. While it is already known that NEs are the same as SNEs in the 2-server load balancing game, we prove that, in the m-server load balancing game for any given m >= 3, any NE is a (5=4)-approximate SNE, which together with the lower bound already established in the literature implies that the approximation bound is tight. This closes the final gap in the literature on the study of approximation of general NEs to SNEs in the load balancing games. To establish our upper bound, we apply with novelty a powerful graph-theoretic tool

Cooperation and Stability through Periodic Impulse

Basic games, where each individual chooses between two strategies, illustrate several issues that immediately emerge from the standard approach that applies strategic reasoning, based on rational decisions, to predict population behavior where no rationality is assumed. These include how mutual cooperation (which corresponds to the best outcome from the population perspective) can evolve when the only individually rational choice is to defect, illustrated by the Prisoner’s Dilemma (PD) game, and how individuals can randomize between two strategies when neither is individually rational, illustrated by the Battle of the Sexes (BS) game that models male-female conflict over parental investment in offspring. We examine these questions from an evolutionary perspective where the evolutionary dynamics includes an impulsive effect that models sudden changes in collective population behavior. For the PD game, we show analytically that cooperation can either coexist with defection or completely take over the population, depending on the strength of the impulse. By extending these results for the PD game, we also show that males and females each evolve to a single strategy in the BS game when the impulsive effect is strong and that weak impulses stabilize the randomized strategies of this game

FPGA-based ORB Feature Extraction for Real-Time Visual SLAM

Simultaneous Localization And Mapping (SLAM) is the problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it. How to enable SLAM robustly and durably on mobile, or even IoT grade devices, is the main challenge faced by the industry today. The main problems we need to address are: 1.) how to accelerate the SLAM pipeline to meet real-time requirements; and 2.) how to reduce SLAM energy consumption to extend battery life. After delving into the problem, we found out that feature extraction is indeed the bottleneck of performance and energy consumption. Hence, in this paper, we design, implement, and evaluate a hardware ORB feature extractor and prove that our design is a great balance between performance and energy consumption compared with ARM Krait and Intel Core i5