The Lazy Flipper: MAP Inference in Higher-Order Graphical Models by Depth-limited Exhaustive Search

This article presents a new search algorithm for the NP-hard problem of optimizing functions of binary variables that decompose according to a graphical model. It can be applied to models of any order and structure. The main novelty is a technique to constrain the search space based on the topology of the model. When pursued to the full search depth, the algorithm is guaranteed to converge to a global optimum, passing through a series of monotonously improving local optima that are guaranteed to be optimal within a given and increasing Hamming distance. For a search depth of 1, it specializes to Iterated Conditional Modes. Between these extremes, a useful tradeoff between approximation quality and runtime is established. Experiments on models derived from both illustrative and real problems show that approximations found with limited search depth match or improve those obtained by state-of-the-art methods based on message passing and linear programming.Comment: C++ Source Code available from http://hci.iwr.uni-heidelberg.de/software.ph

On the probabilistic min spanning tree Problem

We study a probabilistic optimization model for min spanning tree, where any vertex vi of the input-graph G(V,E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Suppose that when this “real” instance G′ becomes known, a spanning tree T, called anticipatory or a priori spanning tree, has already been computed in G and one can run a quick algorithm (quicker than one that recomputes from scratch), called modification strategy, that modifies the anticipatory tree T in order to fit G ′. The goal is to compute an anticipatory spanning tree of G such that, its modification for any G ′ ⊆ G is optimal for G ′. This is what we call probabilistic min spanning tree problem. In this paper we study complexity and approximation of probabilistic min spanning tree in complete graphs under two distinct modification strategies leading to different complexity results for the problem. For the first of the strategies developed, we also study two natural subproblems of probabilistic min spanning tree, namely, the probabilistic metric min spanning tree and the probabilistic min spanning tree 1,2 that deal with metric complete graphs and complete graphs with edge-weights either 1, or 2, respectively

A fast ILP-based Heuristic for the robust design of Body Wireless Sensor Networks

We consider the problem of optimally designing a body wireless sensor network, while taking into account the uncertainty of data generation of biosensors. Since the related min-max robustness Integer Linear Programming (ILP) problem can be difficult to solve even for state-of-the-art commercial optimization solvers, we propose an original heuristic for its solution. The heuristic combines deterministic and probabilistic variable fixing strategies, guided by the information coming from strengthened linear relaxations of the ILP robust model, and includes a very large neighborhood search for reparation and improvement of generated solutions, formulated as an ILP problem solved exactly. Computational tests on realistic instances show that our heuristic finds solutions of much higher quality than a state-of-the-art solver and than an effective benchmark heuristic.Comment: This is the authors' final version of the paper published in G. Squillero and K. Sim (Eds.): EvoApplications 2017, Part I, LNCS 10199, pp. 1-17, 2017. DOI: 10.1007/978-3-319-55849-3\_16. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-55849-3_1

Towards three-loop QCD corrections to the time-like splitting functions

We report on the status of a direct computation of the time-like splitting functions at next-to-next-to-leading order in QCD. Time-like splitting functions govern the collinear kinematics of inclusive hadron production and the evolution of the parton fragmentation distributions. Current knowledge about them at three loops has been inferred by means of crossing symmetry from their related space-like counterparts, which has left certain parts of the off-diagonal quark-gluon splitting function undetermined. This motivates an independent calculation from first principles. We review the tools and methods which are applied to attack the problem.Comment: 11 pages, 5 figures; presented at the Epiphany Conference 2015 (Cracow, Poland); additional files: MassFactorization.n

On unique continuation for solutions of the Schr{\"o}dinger equation on trees

We prove that if a solution of the time-dependent Schr{\"o}dinger equation on an homogeneous tree with bounded potential decays fast at two distinct times then the solution is trivial. For the free Schr{\"o}dinger operator, we use the spectral theory of the Laplacian and complex analysis and obtain a characterization of the initial conditions that lead to a sharp decay at any time. We then use the recent spectral decomposition of the Schr{\"o}dinger operator with compactly supported potential due to Colin de Verdi{\`e}rre and Turc to extend our results in the presence of such potentials. Finally, we use real variable methods first introduced by Escauriaza, Kenig, Ponce and Vega to establish a general sharp result in the case of bounded potentials

An (MI)LP-based Primal Heuristic for 3-Architecture Connected Facility Location in Urban Access Network Design

We investigate the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks. We propose an original optimization model for the problem that includes additional variables and constraints to take into account wireless signal coverage. Since the problem can prove challenging even for modern state-of-the art optimization solvers, we propose to solve it by an original primal heuristic which combines a probabilistic fixing procedure, guided by peculiar Linear Programming relaxations, with an exact MIP heuristic, based on a very large neighborhood search. Computational experiments on a set of realistic instances show that our heuristic can find solutions associated with much lower optimality gaps than a state-of-the-art solver.Comment: This is the authors' final version of the paper published in: Squillero G., Burelli P. (eds), EvoApplications 2016: Applications of Evolutionary Computation, LNCS 9597, pp. 283-298, 2016. DOI: 10.1007/978-3-319-31204-0_19. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-31204-0_1

Physics of the Power Corrections in QCD

We review the physics of the power corrections to the parton model. In the first part, we consider the power corrections which characterize the infrared sensitivity of Feynman graphs when the contribution of short distances dominates. The second part is devoted to the hypothetical power corrections associated with nonperturbative effects at small distances.Comment: 35 pages, 6 figures. Lecture given by V.I.Zakharov at the Winter School of physics of ITEP, February 1999. Minor corrections, references adde

Water-soluble SOA from Alkene ozonolysis: composition and droplet activation kinetics inferences from analysis of CCN activity

Cloud formation characteristics of the water-soluble organic fraction (WSOC) of secondary organic aerosol (SOA) formed from the ozonolysis of alkene hydrocarbons (terpinolene, 1-methlycycloheptene and cycloheptene) are studied. Based on size-resolved measurements of CCN activity (of the pure and salted WSOC samples) we estimate the average molar volume and surface tension depression associated with the WSOC using Köhler Theory Analysis (KTA). Consistent with known speciation, the results suggest that the WSOC are composed of low molecular weight species, with an effective molar mass below 200 g mol^(−1). The water-soluble carbon is also surface-active, depressing surface tension 10–15% from that of pure water (at CCN-relevant concentrations). The inherent hygroscopicity parameter, κ, of the WSOC ranges between 0.17 and 0.25; if surface tension depression and molar volume effects are considered in κ, a remarkably constant "apparent" hygroscopicity ~0.3 emerges for all samples considered. This implies that the volume fraction of soluble material in the parent aerosol is the key composition parameter required for prediction of the SOA hygroscopicity, as shifts in molar volume across samples are compensated by changes in surface tension. Finally, using "threshold droplet growth analysis", the water-soluble organics in all samples considered do not affect CCN activation kinetics