Vertex Stabilizers for Network Bargaining Games

Network bargaining games form a prominent class of examples of game theory problems defined on graphs, where vertices represent players, and edges represent their possible interactions. An instance of a \emph{network bargaining game} is given by a graph $G = (V, E)$ with edge weights $w \in \mathbb{R}^E_{+}$ and vertex capacities $c \in \mathbb{Z}^V_+$. A \emph{solution} to an instance $(G, w, c)$ of a network bargaining game is data $(M, z)$, where $M \subset E$ is a $c$-matching, and $z \in \mathbb{R}^{2E}_{\geq 0}$ is a vector which assigns each edge $uv \in E$ a pair of values $z_{uv}$ and $z_{vu}$, such that $z_{uv} + z_{vu} = w_{uv}$ if $uv \in M$, and $z_{uv} = z_{vu} = 0$ otherwise. An instance $(G, w, c)$ is said to be \emph{stable} if it admits a so-called `stable' solution, which represents a solution where a player has no incentive to deviate. Not all instances of a network bargaining game have a stable solution, and this naturally motivates the problem of how to modify the underlying graph such that the instance becomes stable. In recent years, researchers have investigated various modifications, typically by adding or removing edges or vertices. The natural algorithmic question which stems from this is whether these modifications can be performed efficiently. The answer varies, depending on the modification in question, and on whether the edges/vertices have been restricted to be unit weight/capacity. In this work, we consider the vertex-removal setting for a general instance $(G, w, c)$ of a network bargaining game. A set of vertices whose deletion from $G$ results in a stable instance of the induced network bargaining game is called a \emph{vertex stabilizer}. We demonstrate in this work that the algorithmic problem of finding a minimum cardinality vertex stabilizer is $NP$-complete, and give an efficient $2$-approximation algorithm. Further, we show that no efficient $(2 - \epsilon)$-approximation for this problem exists for any $\epsilon > 0$, assuming the Unique Games Conjecture holds. These results hold even in the case when all edges are of unit-weight. In contrast, if we are given an instance $(G, w, c)$ together with a maximum weight $c$-matching $M$, we show that the problem of finding a minimum cardinality vertex stabilizer that avoids $M$ can be solved efficiently. We provide a polynomial time algorithm for solving this problem

Stabilization of Capacitated Matching Games

An edge-weighted, vertex-capacitated graph G is called stable if the value of a maximum-weight capacity-matching equals the value of a maximum-weight fractional capacity-matching. Stable graphs play a key role in characterizing the existence of stable solutions for popular combinatorial games that involve the structure of matchings in graphs, such as network bargaining games and cooperative matching games. The vertex-stabilizer problem asks to compute a minimum number of players to block (i.e., vertices of G to remove) in order to ensure stability for such games. The problem has been shown to be solvable in polynomial-time, for unit-capacity graphs. This stays true also if we impose the restriction that the set of players to block must not intersect with a given specified maximum matching of G. In this work, we investigate these algorithmic problems in the more general setting of arbitrary capacities. We show that the vertex-stabilizer problem with the additional restriction of avoiding a given maximum matching remains polynomial-time solvable. Differently, without this restriction, the vertex-stabilizer problem becomes NP-hard and even hard to approximate, in contrast to the unit-capacity case. Finally, in unit-capacity graphs there is an equivalence between the stability of a graph, existence of a stable solution for network bargaining games, and existence of a stable solution for cooperative matching games. We show that this equivalence does not extend to the capacitated case.Comment: 14 pages, 3 figure

Dichtigkeitsuntersuchung von Wurzelkanalfüllungen nach verschiedenen medikamentösen Einlagen

The aim of this study was to investigate the influence of two different intracanal medications on the apical seal of root canal fillings. The endodontic sealers Tubli-Seal EWT and Apexit Plus as well as RelyX Unicem experimentally used as sealer were compared. Reasoning the results, intracanal medication is able to exert influence on the leak tightness of different sealers. A trend towards adhesive techniques can be observed. Because RelyX Unicem as a representative of composite based sealers achieved the best results compared to the other sealers.Ziel dieser Studie war es, den Einfluss von zwei verschiedenen medikamentösen Einlagen auf die apikale Dichtigkeit von Wurzelkanalfüllungen zu untersuchen. Dabei wurden die Sealer Tubli-Seal EWT und Apexit Plus sowie RelyX Unicem als experimenteller Sealer miteinander verglichen. Aus den Ergebnissen kann geschlussfolgert werden, dass die verwendete medikamentöse Einlage durchaus Einfluss auf das Abdichtungsverhalten verschiedener Sealer nehmen kann. So lässt sich sagen, dass der Weg der Weiterentwicklung in Richtung der Adhäsivtechnik begründet ist. Da RelyX Unicem als Vertreter der kunststoffbasierten Wurzelkanalfüllmaterialen im Vergleich zu den anderen Materialien bessere Ergebnisse erzielen konnte

Fatigue Strength of HFMI-treated High-strength Steel Joints under Constant and Variable Amplitude Block Loading

AbstractLightweight-design of welded high-strength steel structures in cyclic service necessitates the use of post-treatment methods like the high frequency mechanical impact treatment (HFMI). Service loads during operation mostly consist of variable amplitudes, whereat recommendations are only available for the as-welded condition. Therefore, this paper deals with the effect of variable amplitude block loading on the fatigue strength of HFMI-treated T-joints. An evaluation of the real damage sum exhibits characteristic distinctions to constant amplitude test results in regard to the base material strength. The application of an equivalent stress range method by nominal and effective notch stress approach is finally presented

In Caenorhabditis elegans Nanoparticle-Bio-Interactions Become Transparent: Silica-Nanoparticles Induce Reproductive Senescence

While expectations and applications of nanotechnologies grow exponentially, little is known about interactions of engineered nanoparticles with multicellular organisms. Here we propose the transparent roundworm Caenorhabditis elegans as a simple but anatomically and biologically well defined animal model that allows for whole organism analyses of nanoparticle-bio-interactions. Microscopic techniques showed that fluorescently labelled nanoparticles are efficiently taken up by the worms during feeding, and translocate to primary organs such as epithelial cells of the intestine, as well as secondary organs belonging to the reproductive tract. The life span of nanoparticle-fed Caenorhabditis elegans remained unchanged, whereas a reduction of progeny production was observed in silica-nanoparticle exposed worms versus untreated controls. This reduction was accompanied by a significant increase of the ‘bag of worms’ phenotype that is characterized by failed egg-laying and usually occurs in aged wild type worms. Experimental exclusion of developmental defects suggests that silica-nanoparticles induce an age-related degeneration of reproductive organs, and thus set a research platform for both, detailed elucidation of molecular mechanisms and high throughput screening of different nanomaterials by analyses of progeny production

Variable Pathogenicity Determines Individual Lifespan in Caenorhabditis elegans

A common property of aging in all animals is that chronologically and genetically identical individuals age at different rates. To unveil mechanisms that influence aging variability, we identified markers of remaining lifespan for Caenorhabditis elegans. In transgenic lines, we expressed fluorescent reporter constructs from promoters of C. elegans genes whose expression change with age. The expression levels of aging markers in individual worms from a young synchronous population correlated with their remaining lifespan. We identified eight aging markers, with the superoxide dismutase gene sod-3 expression being the best single predictor of remaining lifespan. Correlation with remaining lifespan became stronger if expression from two aging markers was monitored simultaneously, accounting for up to 49% of the variation in individual lifespan. Visualizing the physiological age of chronologically-identical individuals allowed us to show that a major source of lifespan variability is different pathogenicity from individual to individual and that the mechanism involves variable activation of the insulin-signaling pathway

Deletion of the Huntingtin Polyglutamine Stretch Enhances Neuronal Autophagy and Longevity in Mice

Expansion of a stretch of polyglutamine in huntingtin (htt), the protein product of the IT15 gene, causes Huntington's disease (HD). Previous investigations into the role of the polyglutamine stretch (polyQ) in htt function have suggested that its length may modulate a normal htt function involved in regulating energy homeostasis. Here we show that expression of full-length htt lacking its polyglutamine stretch (ΔQ-htt) in a knockin mouse model for HD (Hdh140Q/ΔQ), reduces significantly neuropil mutant htt aggregates, ameliorates motor/behavioral deficits, and extends lifespan in comparison to the HD model mice (Hdh140Q/+). The rescue of HD model phenotypes is accompanied by the normalization of lipofuscin levels in the brain and an increase in the steady-state levels of the mammalian autophagy marker microtubule-associate protein 1 light chain 3-II (LC3-II). We also find that ΔQ-htt expression in vitro increases autophagosome synthesis and stimulates the Atg5-dependent clearance of truncated N-terminal htt aggregates. ΔQ-htt's effect on autophagy most likely represents a gain-of-function, as overexpression of full-length wild-type htt in vitro does not increase autophagosome synthesis. Moreover, HdhΔQ/ΔQ mice live significantly longer than wild-type mice, suggesting that autophagy upregulation may be beneficial both in diseases caused by toxic intracellular aggregate-prone proteins and also as a lifespan extender in normal mammals

MicroRNA Predictors of Longevity in Caenorhabditis elegans

Neither genetic nor environmental factors fully account for variability in individual longevity: genetically identical invertebrates in homogenous environments often experience no less variability in lifespan than outbred human populations. Such variability is often assumed to result from stochasticity in damage accumulation over time; however, the identification of early-life gene expression states that predict future longevity would suggest that lifespan is least in part epigenetically determined. Such “biomarkers of aging,” genetic or otherwise, nevertheless remain rare. In this work, we sought early-life differences in organismal robustness in unperturbed individuals and examined the utility of microRNAs, known regulators of lifespan, development, and robustness, as aging biomarkers. We quantitatively examined Caenorhabditis elegans reared individually in a novel apparatus and observed throughout their lives. Early-to-mid–adulthood measures of homeostatic ability jointly predict 62% of longevity variability. Though correlated, markers of growth/muscle maintenance and of metabolic by-products (“age pigments”) report independently on lifespan, suggesting that graceful aging is not a single process. We further identified three microRNAs in which early-adulthood expression patterns individually predict up to 47% of lifespan differences. Though expression of each increases throughout this time, mir-71 and mir-246 correlate with lifespan, while mir-239 anti-correlates. Two of these three microRNA “biomarkers of aging” act upstream in insulin/IGF-1–like signaling (IIS) and other known longevity pathways, thus we infer that these microRNAs not only report on but also likely determine longevity. Thus, fluctuations in early-life IIS, due to variation in these microRNAs and from other causes, may determine individual lifespan

Mitochondrial Changes in Ageing Caenorhabditis elegans – What Do We Learn from Superoxide Dismutase Knockouts?

One of the most popular damage accumulation theories of ageing is the mitochondrial free radical theory of ageing (mFRTA). The mFRTA proposes that ageing is due to the accumulation of unrepaired oxidative damage, in particular damage to mitochondrial DNA (mtDNA). Within the mFRTA, the “vicious cycle” theory further proposes that reactive oxygen species (ROS) promote mtDNA mutations, which then lead to a further increase in ROS production. Recently, data have been published on Caenorhabditis elegans mutants deficient in one or both forms of mitochondrial superoxide dismutase (SOD). Surprisingly, even double mutants, lacking both mitochondrial forms of SOD, show no reduction in lifespan. This has been interpreted as evidence against the mFRTA because it is assumed that these mutants suffer from significantly elevated oxidative damage to their mitochondria. Here, using a novel mtDNA damage assay in conjunction with related, well established damage and metabolic markers, we first investigate the age-dependent mitochondrial decline in a cohort of ageing wild-type nematodes, in particular testing the plausibility of the “vicious cycle” theory. We then apply the methods and insights gained from this investigation to a mutant strain for C. elegans that lacks both forms of mitochondrial SOD. While we show a clear age-dependent, linear increase in oxidative damage in WT nematodes, we find no evidence for autocatalytic damage amplification as proposed by the “vicious cycle” theory. Comparing the SOD mutants with wild-type animals, we further show that oxidative damage levels in the mtDNA of SOD mutants are not significantly different from those in wild-type animals, i.e. even the total loss of mitochondrial SOD did not significantly increase oxidative damage to mtDNA. Possible reasons for this unexpected result and some implications for the mFRTA are discussed