Percolation-like Scaling Exponents for Minimal Paths and Trees in the Stochastic Mean Field Model

In the mean field (or random link) model there are $n$ points and inter-point distances are independent random variables. For $0 < \ell < \infty$ and in the $n \to \infty$ limit, let $\delta(\ell) = 1/n \times$ (maximum number of steps in a path whose average step-length is $\leq \ell$). The function $\delta(\ell)$ is analogous to the percolation function in percolation theory: there is a critical value $\ell_* = e^{-1}$ at which $\delta(\cdot)$ becomes non-zero, and (presumably) a scaling exponent $\beta$ in the sense $\delta(\ell) \asymp (\ell - \ell_*)^\beta$. Recently developed probabilistic methodology (in some sense a rephrasing of the cavity method of Mezard-Parisi) provides a simple albeit non-rigorous way of writing down such functions in terms of solutions of fixed-point equations for probability distributions. Solving numerically gives convincing evidence that $\beta = 3$. A parallel study with trees instead of paths gives scaling exponent $\beta = 2$. The new exponents coincide with those found in a different context (comparing optimal and near-optimal solutions of mean-field TSP and MST) and reinforce the suggestion that these scaling exponents determine universality classes for optimization problems on random points.Comment: 19 page

On the relationship between standard intersection cuts, lift-and-project cuts, and generalized intersection cuts

We examine the connections between the classes of cuts in the title. We show that lift-and-project (L&P) cuts from a given disjunction are equivalent to generalized intersection cuts from the family of polyhedra obtained by taking positive combinations of the complements of the inequalities of each term of the disjunction. While L&P cuts from split disjunctions are known to be equivalent to standard intersection cuts (SICs) from the strip obtained by complementing the terms of the split, we show that L&P cuts from more general disjunctions may not be equivalent to any SIC. In particular, we give easily verifiable necessary and sufficient conditions for a L&P cut from a given disjunction D to be equivalent to a SIC from the polyhedral counterpart of D. Irregular L&P cuts, i.e. those that violate these conditions, have interesting properties. For instance, unlike the regular ones, they may cut off part of the corner polyhedron associated with the LP solution from which they are derived. Furthermore, they are not exceptional: their frequency exceeds that of regular cuts. A numerical example illustrates some of the above properties. © 2016 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Societ

Iris Codes Classification Using Discriminant and Witness Directions

The main topic discussed in this paper is how to use intelligence for biometric decision defuzzification. A neural training model is proposed and tested here as a possible solution for dealing with natural fuzzification that appears between the intra- and inter-class distribution of scores computed during iris recognition tests. It is shown here that the use of proposed neural network support leads to an improvement in the artificial perception of the separation between the intra- and inter-class score distributions by moving them away from each other.Comment: 6 pages, 5 figures, Proc. 5th IEEE Int. Symp. on Computational Intelligence and Intelligent Informatics (Floriana, Malta, September 15-17), ISBN: 978-1-4577-1861-8 (electronic), 978-1-4577-1860-1 (print

Big Data and Analysis of Data Transfers for International Research Networks Using NetSage

Modern science is increasingly data-driven and collaborative in nature. Many scientific disciplines, including genomics, high-energy physics, astronomy, and atmospheric science, produce petabytes of data that must be shared with collaborators all over the world. The National Science Foundation-supported International Research Network Connection (IRNC) links have been essential to enabling this collaboration, but as data sharing has increased, so has the amount of information being collected to understand network performance. New capabilities to measure and analyze the performance of international wide-area networks are essential to ensure end-users are able to take full advantage of such infrastructure for their big data applications. NetSage is a project to develop a unified, open, privacy-aware network measurement, and visualization service to address the needs of monitoring today's high-speed international research networks. NetSage collects data on both backbone links and exchange points, which can be as much as 1Tb per month. This puts a significant strain on hardware, not only in terms storage needs to hold multi-year historical data, but also in terms of processor and memory needs to analyze the data to understand network behaviors. This paper addresses the basic NetSage architecture, its current data collection and archiving approach, and details the constraints of dealing with this big data problem of handling vast amounts of monitoring data, while providing useful, extensible visualization to end users

An analysis of mixed integer linear sets based on lattice point free convex sets

Split cuts are cutting planes for mixed integer programs whose validity is derived from maximal lattice point free polyhedra of the form $S:=\{x : \pi_0 \leq \pi^T x \leq \pi_0+1 \}$ called split sets. The set obtained by adding all split cuts is called the split closure, and the split closure is known to be a polyhedron. A split set $S$ has max-facet-width equal to one in the sense that $\max\{\pi^T x : x \in S \}-\min\{\pi^T x : x \in S \} \leq 1$. In this paper we consider using general lattice point free rational polyhedra to derive valid cuts for mixed integer linear sets. We say that lattice point free polyhedra with max-facet-width equal to $w$ have width size $w$. A split cut of width size $w$ is then a valid inequality whose validity follows from a lattice point free rational polyhedron of width size $w$. The $w$-th split closure is the set obtained by adding all valid inequalities of width size at most $w$. Our main result is a sufficient condition for the addition of a family of rational inequalities to result in a polyhedral relaxation. We then show that a corollary is that the $w$-th split closure is a polyhedron. Given this result, a natural question is which width size $w^*$ is required to design a finite cutting plane proof for the validity of an inequality. Specifically, for this value $w^*$, a finite cutting plane proof exists that uses lattice point free rational polyhedra of width size at most $w^*$, but no finite cutting plane proof that only uses lattice point free rational polyhedra of width size smaller than $w^*$. We characterize $w^*$ based on the faces of the linear relaxation

A decision-support system for the analysis of clinical practice patterns

pre-printSeveral studies documented substantial variation in medical practice patterns, but physicians often do not have adequate information on the cumulative clinical and financial effects of their decisions. The purpose of developing an expert system for the analysis of clinical practice patterns was to assist providers in analyzing and improving the process and outcome of patient care. The developed QFES (Quality Feedback Expert System) helps users in the definition and evaluation of measurable quality improvement objectives. Based on objectives and actual clinical data, several measures can be calculated (utilization of procedures, annualized cost effect of using a particular procedure, and expected utilization based on peer-comparison and case-mix adjustment). The quality management rules help to detect important discrepancies among members of the selected provider group and compare performance with objectives. The system incorporates a variety of data and knowledge bases: (i) clinical data on actual practice patterns, (ii) frames of quality parameters derived from clinical practice guidelines, and (iii) rules of quality management for data analysis. An analysis of practice patterns of 12 family physicians in the management of urinary tract infections illustrates the use of the system