Optimal Resource Allocation in Random Networks with Transportation Bandwidths

We apply statistical physics to study the task of resource allocation in random sparse networks with limited bandwidths for the transportation of resources along the links. Useful algorithms are obtained from recursive relations. Bottlenecks emerge when the bandwidths are small, causing an increase in the fraction of idle links. For a given total bandwidth per node, the efficiency of allocation increases with the network connectivity. In the high connectivity limit, we find a phase transition at a critical bandwidth, above which clusters of balanced nodes appear, characterised by a profile of homogenized resource allocation similar to the Maxwell's construction.Comment: 28 pages, 11 figure

Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge-variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory.Comment: 21 pages, 10 figures, major changes: Sections IV to VII updated, Figs. 1 to 3 replace

Optimal Location of Sources in Transportation Networks

We consider the problem of optimizing the locations of source nodes in transportation networks. A reduction of the fraction of surplus nodes induces a glassy transition. In contrast to most constraint satisfaction problems involving discrete variables, our problem involves continuous variables which lead to cavity fields in the form of functions. The one-step replica symmetry breaking (1RSB) solution involves solving a stable distribution of functionals, which is in general infeasible. In this paper, we obtain small closed sets of functional cavity fields and demonstrate how functional recursions are converted to simple recursions of probabilities, which make the 1RSB solution feasible. The physical results in the replica symmetric (RS) and the 1RSB frameworks are thus derived and the stability of the RS and 1RSB solutions are examined.Comment: 38 pages, 18 figure

Local search heuristics for the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components

Goodyear Project - Mile Marker 0

This report offers recommendations and implementation methods of different modes of entry for Goodyear to enter into the last mile delivery market. Goodyear came to us with the prompt, pick a customer segment, build a strategy, frame how it works and pitch the idea, and this paper attempts to answer this prompt

High Throughput Microplate Respiratory Measurements Using Minimal Quantities Of Isolated Mitochondria

Recently developed technologies have enabled multi-well measurement of O2 consumption, facilitating the rate of mitochondrial research, particularly regarding the mechanism of action of drugs and proteins that modulate metabolism. Among these technologies, the Seahorse XF24 Analyzer was designed for use with intact cells attached in a monolayer to a multi-well tissue culture plate. In order to have a high throughput assay system in which both energy demand and substrate availability can be tightly controlled, we have developed a protocol to expand the application of the XF24 Analyzer to include isolated mitochondria. Acquisition of optimal rates requires assay conditions that are unexpectedly distinct from those of conventional polarography. The optimized conditions, derived from experiments with isolated mouse liver mitochondria, allow multi-well assessment of rates of respiration and proton production by mitochondria attached to the bottom of the XF assay plate, and require extremely small quantities of material (1–10 µg of mitochondrial protein per well). Sequential measurement of basal, State 3, State 4, and uncoupler-stimulated respiration can be made in each well through additions of reagents from the injection ports. We describe optimization and validation of this technique using isolated mouse liver and rat heart mitochondria, and apply the approach to discover that inclusion of phosphatase inhibitors in the preparation of the heart mitochondria results in a specific decrease in rates of Complex I-dependent respiration. We believe this new technique will be particularly useful for drug screening and for generating previously unobtainable respiratory data on small mitochondrial samples