Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree

We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of $O(n\log \Delta)$ bits per node and $O(nD)$ respectively, where $\Delta$ is the highest degree of a node, $n$ is the number of nodes and $D$ is the diameter of the network. In contrast, our algorithm has a space complexity of $O(\log n)$ bits per node, which is optimal for silent-stabilizing spanning trees and runs in $O(n)$ time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a stand alone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, We also present a (non-sielnt) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones

On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

Self-Stabilizing Byzantine Asynchronous Unison

We explore asynchronous unison in the presence of systemic transient and permanent Byzantine faults in shared memory. We observe that the problem is not solvable under less than strongly fair scheduler or for system topologies with maximum node degree greater than two. We present a self-stabilizing Byzantine-tolerant solution to asynchronous unison for chain and ring topologies. Our algorithm has minimum possible containment radius and optimal stabilization time

El papel social del militar en el postconflicto colombiano

En el presente ensayo se pretende argumentar diferentes dinámicas del conflicto interno en Colombia que llevó a que de manera temprana las Fuerzas Militares del país asumieran funciones de seguridad civil, desarrollando su estructura y doctrina en torno a las necesidades de la lucha contra los grupos armados al margen de la ley y en defensa de la sociedad y las instituciones, de esta manera relegó a un segundo plano su rol clásico de defensa de las fronteras nacionales frente a potenciales amenazas externas. Así pues es necesario mirar en primera instancia como El ordenamiento constitucional, legal y jurídico del Estado moderno prevé y justifica la creación y existencia de las fuerzas militares FFMM- cuya misión fundamental es la defensa de la soberanía con respecto y frente a otras naciones del mundo (defensa nacional externa). Así mismo, la defensa nacional interna está asignada al cuerpo de policía, al margen y de manera totalmente separada de las FFMMPregrad

Scheduling Games with Machine-Dependent Priority Lists

We consider a scheduling game in which jobs try to minimize their completion time by choosing a machine to be processed on. Each machine uses an individual priority list to decide on the order according to which the jobs on the machine are processed. We characterize four classes of instances in which a pure Nash equilibrium (NE) is guaranteed to exist, and show, by means of an example, that none of these characterizations can be relaxed. We then bound the performance of Nash equilibria for each of these classes with respect to the makespan of the schedule and the sum of completion times. We also analyze the computational complexity of several problems arising in this model. For instance, we prove that it is NP-hard to decide whether a NE exists, and that even for instances with identical machines, for which a NE is guaranteed to exist, it is NP-hard to approximate the best NE within a factor of $2-\frac{1}{m}-\epsilon$ for all $\epsilon>0$. In addition, we study a generalized model in which players' strategies are subsets of resources, each having its own priority list over the players. We show that in this general model, even unweighted symmetric games may not have a pure NE, and we bound the price of anarchy with respect to the total players' costs.Comment: 19 pages, 2 figure

Sources of acoustic emission during fatigue of Ti-6Al-4V: effect of microstructure

The fundamentals of acoustic emission (AE) analysis of fatigue cracking were applied to Ti-6Al-4V. The effect of microstructure on the characteristics of the AE events generated and the failure mechanisms which produced AE in Ti-6Al-4V were established. Lamellar microstructures generated one to two orders of magnitude more emission than equiaxed microstructures. The combination of larger grain size, more continuous α/β interfaces, more tortuous crack-front geometry, cleavage and intergranular fracture in lamellar microstructures accounts for the greater amount of emission. For lamellar microstructures, most AE events were generated in the upper 20% of the stress range, whereas in equiaxed microstructures, most events were generated at lower stresses. Most AE events were generated during crack opening and also at low stresses. AE events having high level intensities were also generated at stresses other than the peak stress. This is because in titanium alloys, which have both high strength and toughness, AE events are generated from both plastic zone extension and crack extension.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44721/1/10853_2004_Article_BF00542927.pd

Online scheduling of bounded length jobs to maximize throughput

International audienceWe consider an online scheduling problem, motivated by the issues present at the joints of networks using ATM and TCP/IP. Namely, IP packets have to be broken down into small ATM cells and sent out before their deadlines, but cells corresponding to different packets can be interwoven. More formally, we consider the online scheduling problem with preemptions, where each job $j$ is revealed at release time $r_j$, and has processing time $p_j$, deadline $d_j$, and weight $w_j$. A preempted job can be resumed at any time. The goal is to maximize the total weight of all jobs completed on time. Our main results are as follows. Firstly, we prove that when the processing times of all jobs are at most $k$, the optimum deterministic competitive ratio is $\Theta(k /\log k)$. Secondly, we give a deterministic algorithm with competitive ratio depending on the ratio between the smallest and the largest processing time of all jobs. In particular, it attains competitive ratio 5 in the case when all jobs have identical processing times, for which we give a lower bound of 2.598. The latter upper bound also yields an $O(\log k)$-competitive randomized algorithm for the variant with processing times bounded by $k$

A prospective study of shoulder pain in primary care: Prevalence of imaged pathology and response to guided diagnostic blocks

<p>Abstract</p> <p>Background</p> <p>The prevalence of imaged pathology in primary care has received little attention and the relevance of identified pathology to symptoms remains unclear. This paper reports the prevalence of imaged pathology and the association between pathology and response to diagnostic blocks into the subacromial bursa (SAB), acromioclavicular joint (ACJ) and glenohumeral joint (GHJ).</p> <p>Methods</p> <p>Consecutive patients with shoulder pain recruited from primary care underwent standardised x-ray, diagnostic ultrasound scan and diagnostic injections of local anaesthetic into the SAB and ACJ. Subjects who reported less than 80% reduction in pain following either of these injections were referred for a magnetic resonance arthrogram (MRA) and GHJ diagnostic block. Differences in proportions of positive and negative imaging findings in the anaesthetic response groups were assessed using Fishers test and odds ratios were calculated a for positive anaesthetic response (PAR) to diagnostic blocks.</p> <p>Results</p> <p>In the 208 subjects recruited, the rotator cuff and SAB displayed the highest prevalence of pathology on both ultrasound (50% and 31% respectively) and MRA (65% and 76% respectively). The prevalence of PAR following SAB injection was 34% and ACJ injection 14%. Of the 59% reporting a negative anaesthetic response (NAR) for both of these injections, 16% demonstrated a PAR to GHJ injection. A full thickness tear of supraspinatus on ultrasound was associated with PAR to SAB injection (OR 5.02; <it>p </it>< 0.05). Ultrasound evidence of a biceps tendon sheath effusion (OR 8.0; <it>p </it>< 0.01) and an intact rotator cuff (OR 1.3; <it>p </it>< 0.05) were associated with PAR to GHJ injection. No imaging findings were strongly associated with PAR to ACJ injection (<it>p </it>≤ 0.05).</p> <p>Conclusions</p> <p>Rotator cuff and SAB pathology were the most common findings on ultrasound and MRA. Evidence of a full thickness supraspinatus tear was associated with symptoms arising from the subacromial region, and a biceps tendon sheath effusion and an intact rotator cuff were associated with an intra-articular GHJ pain source. When combined with clinical information, these results may help guide diagnostic decision making in primary care.</p