Parallel Metric Tree Embedding based on an Algebraic View on Moore-Bellman-Ford

A \emph{metric tree embedding} of expected \emph{stretch~$\alpha \geq 1$} maps a weighted $n$-node graph $G = (V, E, \omega)$ to a weighted tree $T = (V_T, E_T, \omega_T)$ with $V \subseteq V_T$ such that, for all $v,w \in V$, $\operatorname{dist}(v, w, G) \leq \operatorname{dist}(v, w, T)$ and $operatorname{E}[\operatorname{dist}(v, w, T)] \leq \alpha \operatorname{dist}(v, w, G)$. Such embeddings are highly useful for designing fast approximation algorithms, as many hard problems are easy to solve on tree instances. However, to date the best parallel $(\operatorname{polylog} n)$-depth algorithm that achieves an asymptotically optimal expected stretch of $\alpha \in \operatorname{O}(\log n)$ requires $\operatorname{\Omega}(n^2)$ work and a metric as input. In this paper, we show how to achieve the same guarantees using $\operatorname{polylog} n$ depth and $\operatorname{\tilde{O}}(m^{1+\epsilon})$ work, where $m = |E|$ and $\epsilon > 0$ is an arbitrarily small constant. Moreover, one may further reduce the work to $\operatorname{\tilde{O}}(m + n^{1+\epsilon})$ at the expense of increasing the expected stretch to $\operatorname{O}(\epsilon^{-1} \log n)$. Our main tool in deriving these parallel algorithms is an algebraic characterization of a generalization of the classic Moore-Bellman-Ford algorithm. We consider this framework, which subsumes a variety of previous "Moore-Bellman-Ford-like" algorithms, to be of independent interest and discuss it in depth. In our tree embedding algorithm, we leverage it for providing efficient query access to an approximate metric that allows sampling the tree using $\operatorname{polylog} n$ depth and $\operatorname{\tilde{O}}(m)$ work. We illustrate the generality and versatility of our techniques by various examples and a number of additional results

Randomized Local Network Computing

International audienceIn this paper, we carry on investigating the line of research questioning the power of randomization for the design of distributed algorithms. In their seminal paper, Naor and Stockmeyer [STOC 1993] established that, in the context of network computing, in which all nodes execute the same algorithm in parallel, any construction task that can be solved locally by a randomized Monte-Carlo algorithm can also be solved locally by a deterministic algorithm. This result however holds in a specific context. In particular, it holds only for distributed tasks whose solutions that can be locally checked by a deterministic algorithm. In this paper, we extend the result of Naor and Stockmeyer to a wider class of tasks. Specifically, we prove that the same derandomization result holds for every task whose solutions can be locally checked using a 2-sided error randomized Monte-Carlo algorithm. This extension finds applications to, e.g., the design of lower bounds for construction tasks which tolerate that some nodes compute incorrect values. In a nutshell, we show that randomization does not help for solving such resilient tasks

A two-dimensional representation of four-dimensional gravitational waves

The Einstein equation in D dimensions, if restricted to the class of space-times possessing n = D - 2 commuting hypersurface-orthogonal Killing vectors, can be equivalently written as metric-dilaton gravity in 2 dimensions with n scalar fields. For n = 2, this results reduces to the known reduction of certain 4-dimensional metrics which include gravitational waves. Here, we give such a representation which leads to a new proof of the Birkhoff theorem for plane-symmetric space--times, and which leads to an explanation, in which sense two (spin zero-) scalar fields in 2 dimensions may incorporate the (spin two-) gravitational waves in 4 dimensions. (This result should not be mixed up with well--known analogous statements where, however, the 4-dimensional space-time is supposed to be spherically symmetric, and then, of course, the equivalent 2-dimensional picture cannot mimic any gravitational waves.) Finally, remarks on hidden symmetries in 2 dimensions are made.Comment: 12 pages, LaTeX, no figures, Int. J. Mod. Phys. D in prin

Anti-infective surface coatings: design and therapeutic promise against device-associated infections

Patient safety and well-being are under increasing threat from hospital-acquired infections [1]. The root cause of a large number of these infections arises from microbial biofilms that colonise on surfaces of medical devices such as the millions of catheters, endotracheal tubes, and prosthetics implanted every year [2]. Biofilm infections are accompanied by increased resistance to antimicrobial therapy and immune clearance, severely limiting treatment options and leading to life-threatening disease [3,4]. Device-associated infections are caused by both bacteria and fungi and, while most studies have focused on single-species biofilms, biofilm-related infections are often polymicrobial [5–8]. Multi-species biofilms, particularly those involving bacterial and fungal pathogens, are more challenging to treat, likely as a consequence of their combined architecture, protective extracellular matrix, and potential synergism in protecting against antimicrobials and host immunity [9–11]. Among the fungi, Candida species are the most important biofilm pathogens [12,13] and the fourth leading cause of blood-stream infections in United States hospitals [7]. Fungal diseases remain difficult to diagnose, mortality rates remain high, and antifungal drug resistance continues to limit therapeutic options [14,15]. We are in desperate need of innovative strategies that target the mechanisms of pathogenesis of polymicrobial biofilms on medical devices. This is a grand challenge because it requires multidisciplinary collaboration and breakthrough research involving physical chemistry, materials science, and microbiology. Communication between these disciplines has not been common, but recent advances show greater convergence in the development of anti-infective devices. At this nexus, we outline the therapeutic promise of anti-infective coatings for medical devices and discuss pitfalls and strategies for overcoming them.Bryan R. Coad, Hans J. Griesser, Anton Y. Peleg, Ana Trave

Computability of simple games: A complete investigation of the sixty-four possibilities

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier) and algorithmic computability. For each such class, we either show that it is empty or give an example of a game belonging to it. We observe that if a type contains an infinite game, then it contains both computable ones and noncomputable ones. This strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms.Comment: 25 page

An exact solution for 2+1 dimensional critical collapse

We find an exact solution in closed form for the critical collapse of a scalar field with cosmological constant in 2+1 dimensions. This solution agrees with the numerical simulation done by Pretorius and Choptuik of this system.Comment: 5 pages, 5 figures, Revtex. New comparison of analytic and numerical solutions beyond the past light cone of the singularity added. Two new references added. Error in equation (21) correcte

Normal scaling in globally conserved interface-controlled coarsening of fractal clusters

Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The sharp-interface limit of this equation is volume preserving motion by mean curvature. The scaled form of the correlation function has a power-law tail accommodating the fractal initial condition. The coarsening length exhibits normal scaling with time. Finally, shrinking of the fractal clusters with time is observed. The difference between global and local conservation is discussed.Comment: 4 pages, 3 eps figure

Publishing artificial intelligence research papers: A tale of three journals

With the growth in Artificial Intelligence in Medicine (AIM) research and the plethora of informatics journals, there is some confusion where to direct an AIM-related manuscript for peer review and possible pub- lication. As editors for three Elsevier biomedical informatics journals that publish AI-related papers, plus the publisher who oversees all three of these journals, we are aware of such confusion and felt it would be helpful to provide some guidance to prospective authors. Accordingly, we present this joint editorial that is being published in all three of our journals. Although there is some overlap among the types of papers that we publish, we offer here some advice on how best to select a preferred publication venue for your medical AI research papers

Publishing Artificial Intelligence Research Papers: A Tale of Three Journals

With the growth in Artificial Intelligence in Medicine (AIM) research and the plethora of informatics journals, there is some confusion where to direct an AIM-related manuscript for peer review and possible publication. As editors for three Elsevier biomedical informatics journals that publish AI-related papers, plus the publisher who oversees all three of these journals, we are aware of such confusion and felt it would be helpful to provide some guidance to prospective authors. Accordingly, we present this joint editorial that is being published in all three of our journals. Although there is some overlap among the types of papers that we publish, we offer here some advice on how best to select a preferred publication venue for your medical AI research papers