An O(1)-Approximation for Minimum Spanning Tree Interdiction

Network interdiction problems are a natural way to study the sensitivity of a network optimization problem with respect to the removal of a limited set of edges or vertices. One of the oldest and best-studied interdiction problems is minimum spanning tree (MST) interdiction. Here, an undirected multigraph with nonnegative edge weights and positive interdiction costs on its edges is given, together with a positive budget B. The goal is to find a subset of edges R, whose total interdiction cost does not exceed B, such that removing R leads to a graph where the weight of an MST is as large as possible. Frederickson and Solis-Oba (SODA 1996) presented an O(log m)-approximation for MST interdiction, where m is the number of edges. Since then, no further progress has been made regarding approximations, and the question whether MST interdiction admits an O(1)-approximation remained open. We answer this question in the affirmative, by presenting a 14-approximation that overcomes two main hurdles that hindered further progress so far. Moreover, based on a well-known 2-approximation for the metric traveling salesman problem (TSP), we show that our O(1)-approximation for MST interdiction implies an O(1)-approximation for a natural interdiction version of metric TSP

Matroidal Degree-Bounded Minimum Spanning Trees

We consider the minimum spanning tree (MST) problem under the restriction that for every vertex v, the edges of the tree that are adjacent to v satisfy a given family of constraints. A famous example thereof is the classical degree-constrained MST problem, where for every vertex v, a simple upper bound on the degree is imposed. Iterative rounding/relaxation algorithms became the tool of choice for degree-bounded network design problems. A cornerstone for this development was the work of Singh and Lau, who showed for the degree-bounded MST problem how to find a spanning tree violating each degree bound by at most one unit and with cost at most the cost of an optimal solution that respects the degree bounds. However, current iterative rounding approaches face several limits when dealing with more general degree constraints. In particular, when several constraints are imposed on the edges adjacent to a vertex v, as for example when a partition of the edges adjacent to v is given and only a fixed number of elements can be chosen out of each set of the partition, current approaches might violate each of the constraints by a constant, instead of violating all constraints together by at most a constant number of edges. Furthermore, it is also not clear how previous iterative rounding approaches can be used for degree constraints where some edges are in a super-constant number of constraints. We extend iterative rounding/relaxation approaches both on a conceptual level as well as aspects involving their analysis to address these limitations. This leads to an efficient algorithm for the degree-constrained MST problem where for every vertex v, the edges adjacent to v have to be independent in a given matroid. The algorithm returns a spanning tree T of cost at most OPT, such that for every vertex v, it suffices to remove at most 8 edges from T to satisfy the matroidal degree constraint at v

Results from the ICARUS T600 module - A measurement of the muon decay spectrum

We have studied the muon decay energy spectrum from a sample of stopping muon events acquired during the test run of the ICARUS T600 prototype. This detector allows the spatial reconstruction of the events with fine granularity, hence the precise measurement of the muon range and dE/dx with high sampling rate. This information is used to compute the correction factors needed for the calorimetric reconstruction. The Michel rho parameter is then measured by comparison of the experimental and Monte Carlo simulated muon decay spectra, obtaining rho = 0.72 +/- 0.06 (stat) +/- 0.08 (syst).Comment: 3 pages. Proceedings for the International Europhysics Conference on High Energy Physics EPS (July 17th-23rd 2003) in Aachen, German

What is a Merciful Heart? Affective-Motivational Aspects of the Second Love Command

In this paper, I argue that Christ’s second love command implies not only that people’s volitions and actions be Christ-like, but also that their affective-motivational dispositions be Christ-like. More specifically, I argue that the command implies that people have aretaic obligations to strive to cultivate a merciful heart with the kind of affective depth described by St. Isaac of Syria in his 71st ascetical homily—i.e., one that is disposed to becoming inflamed, such that it is gripped by “strong and vehement mercy.

Gamma-Ray Dark Matter Searches in Milky Way Satellites -- A Comparative Review of Data Analysis Methods and Current Results

If dark matter is composed of weakly interacting particles with mass in the GeV-TeV range, their annihilation or decay may produce gamma rays that could be detected by gamma-ray telescopes. Observations of dwarf spheroidal satellite galaxies of the Milky Way (dSphs) benefit from the relatively accurate predictions of dSph dark matter content to produce robust constraints to the dark matter properties. The sensitivity of these observations for the search for dark matter signals can be optimized thanks to the use of advanced statistical techniques able to exploit the spectral and morphological peculiarities of the expected signal. In this paper, I review the status of the dark matter searches from observations of dSphs with the current generation of gamma-ray telescopes: Fermi-LAT, H.E.S.S, MAGIC, VERITAS and HAWC. I will describe in detail the general statistical analysis framework used by these instruments, putting in context the most recent experimental results and pointing out the most relevant differences among the different particular implementations. This~will facilitate the comparison of the current and future results, as well as their eventual integration in a multi-instrument and multi-target dark matter search.Comment: 27 pages, 7 figures. Invited review published by Galaxies, special issue "The Role of Halo Substructure in Gamma-Ray Dark Matter Searches

Book Review: The Human Icon: A Comparative Study of Hindu and Orthodox Christian Beliefs

Book review of The Human Icon: A Comparative Study of Hindu and Orthodox Christian Beliefs. By Christine Mangala Frost. Cambridge, UK: James Clarke & Co, 2017, xv + 368 pages

The Limits of Theodicy: An Eastern Orthodox Perspective on Evil and Interreligious Theology

This essay is written from the vantage point of a comparative theologian who is personally steeped in the Eastern Orthodox Christian tradition and who primarily specializes in Christian-Muslim comparative theology. It might seems curious, then, that the present essay employs the comparative theological method in order to focus on questions of theodicy in the Christian and Hindu traditions. Perhaps even more curious, however, is that I aim not at articulating a comparative Christian-Hindu theodicy, but rather at suggesting that the most productive path forward is a comparative theological rejection of theodicy as a productive enterprise. Drawing from resources within my own Orthodox Christian tradition, as well as from the thought of Paul Ricoeur, my essay will revolve around two primary arguments: first, theodicy functions primarily to reconcile human beings to evil’s existence, thus legitimizing it and reducing the need to counteract evil; and second, religious traditions more effectively encounter the question of evil by teaching a path by which practitioners can mourn, reject, combat, and transform evil. Accordingly, I will first briefly examine two salient instances of comparative Christian-Hindu theodicy in order to demonstrate how my approach differs. Next, I will engage with key critics of theodicy, some of whom are skeptical of religion (or even hostile to it), and some of whom are religious adherents who maintain theodicy is an inherently deleterious mode of thought. I will conclude by drawing from both Fyodor Dostoevsky and Paul Ricoeur in order to suggest a more productive trajectory for comparative theology and the challenges posed by the existence of evil and suffering

Extended soft wall model with background related to features of QCD thermodynamics

The soft wall model is extended to accommodate at the same time (i) approximately linear $\rho$ meson Regge trajectories at zero temperature $T$, (ii) various options for the thermodynamics with reference to QCD (cross over or second-order transition or first-order transition at $T_c$), and (iii) the appearance of vector meson states at $T \leq T_c$. While the vector meson masses display some modest model dependence very near to $T_c$, they stay below $T_c$ to good accuracy independent of the temperature, that is nearly as at $T=0$, thus being very consistent with the thermo-statistical models widely employed in analyses of the hadron yields in relativistic heavy-ion collisions in a region where baryon densitiy effects can be neglected and the vacuum hadron masses are used