Metastability of Logit Dynamics for Coordination Games

Logit Dynamics [Blume, Games and Economic Behavior, 1993] are randomized best response dynamics for strategic games: at every time step a player is selected uniformly at random and she chooses a new strategy according to a probability distribution biased toward strategies promising higher payoffs. This process defines an ergodic Markov chain, over the set of strategy profiles of the game, whose unique stationary distribution is the long-term equilibrium concept for the game. However, when the mixing time of the chain is large (e.g., exponential in the number of players), the stationary distribution loses its appeal as equilibrium concept, and the transient phase of the Markov chain becomes important. It can happen that the chain is "metastable", i.e., on a time-scale shorter than the mixing time, it stays close to some probability distribution over the state space, while in a time-scale multiple of the mixing time it jumps from one distribution to another. In this paper we give a quantitative definition of "metastable probability distributions" for a Markov chain and we study the metastability of the logit dynamics for some classes of coordination games. We first consider a pure $n$-player coordination game that highlights the distinctive features of our metastability notion based on distributions. Then, we study coordination games on the clique without a risk-dominant strategy (which are equivalent to the well-known Glauber dynamics for the Curie-Weiss model) and coordination games on a ring (both with and without risk-dominant strategy)

A survey of the follow-up studies carried out by recognized educational clinics in the United States.

Thesis (Ed.M.)--Boston Universit

Convergence to Equilibrium of Logit Dynamics for Strategic Games

We present the first general bounds on the mixing time of the Markov chain associated to the logit dynamics for wide classes of strategic games. The logit dynamics with inverse noise beta describes the behavior of a complex system whose individual components act selfishly and keep responding according to some partial ("noisy") knowledge of the system, where the capacity of the agent to know the system and compute her best move is measured by the inverse of the parameter beta. In particular, we prove nearly tight bounds for potential games and games with dominant strategies. Our results show that, for potential games, the mixing time is upper and lower bounded by an exponential in the inverse of the noise and in the maximum potential difference. Instead, for games with dominant strategies, the mixing time cannot grow arbitrarily with the inverse of the noise. Finally, we refine our analysis for a subclass of potential games called graphical coordination games, a class of games that have been previously studied in Physics and, more recently, in Computer Science in the context of diffusion of new technologies. We give evidence that the mixing time of the logit dynamics for these games strongly depends on the structure of the underlying graph. We prove that the mixing time of the logit dynamics for these games can be upper bounded by a function that is exponential in the cutwidth of the underlying graph and in the inverse of noise. Moreover, we consider two specific and popular network topologies, the clique and the ring. For games played on a clique we prove an almost matching lower bound on the mixing time of the logit dynamics that is exponential in the inverse of the noise and in the maximum potential difference, while for games played on a ring we prove that the time of convergence of the logit dynamics to its stationary distribution is significantly shorter

Assessment and relevance of the putative DNA/RNA helicase Schlafen-11 in ovarian and breast cancer

Abstract in English Schlafen 11 (SLFN11) is a putative DNA/RNA helicase, first described for its role in thymocyte development and differentiation in mouse models [1]. SLFN11 is part of a family of proteins with various degree of homology across species, but intriguingly being consistently present only in vertebrates and especially in mammals. Recently the role of this putative DNA/RNA helicase, SLFN11, was causal association with sensitivity to DNA damaging agents, such as platinum salts, topoisomerase I and II inhibitors, and other alkylators in the NCI-60 panel of cancer cell lines.13 In the first study, we validate an anti-SLFN11 antibody in formalin-fixed paraffin-embedded (FFPE) high-grade serous ovarian carcinoma (HGSOC) samples, developing a immunohistochemistry (IHC) protocol in order to determinate the expression of SLFN11 in our series of HGSOC. Indeed, we tested and validated a reliable SLFN 11 antibody (Ab) in IHC choosing between two anti-SLFN11 Ab used normally for Western Blot (WB) in culture cell block (CCB) of ovarian carcinoma and in an independent series of HGSOCs tissue micro-array (TMA). For each case, we evaluated both the Intensity Score (IS) and the Distribution Score (DS) evaluating at least 300 cells. A Histological Score (HS) was obtained as follow: HS=IS x DS. Successively, we applied our protocol to a large case series of HGSOC samples to confirm our preliminary results. We found one antibody to be reliable in CCB and TMA series allowing to determinate clearly IHC expression of SLFN11. These results were confirmed in our large case series of FFPE HGSOC samples. Briefly, as for TMA independent series, we found that the HS for SLFN11 expression presents a normal distribution with a prevalent ( 48 60%) intermediate expression. Parallel SLFN11 was not expressed in practically 40% of cases that clinically corresponded to the platinum resistant patients in about 60% of cases (16/27). So, we believe that low IHC expression of SLFN 11 should be correlated to response to the platinum based chemotherapy. In the second study, we investigate the transcriptional landscape of SLFN11 in breast cancer performing a gene expression microarray meta-analysis of more than 7000 cases from 35 publicly available data sets. By correlation analysis, we identified 537 transcripts in the top 95th percentile of Pearson\u2019s coef- ficients with SLFN11 identifying \u201cimmune response\u201d, \u201clymphocyte activation\u201dand \u201cT cell activation\u201d as top Gene Ontology enriched processes. Furthermore, we reported very strong association of SLFN11 with immune signatures in breast cancer through penalized maximum like-lihood lasso regression Finally, through multiple corresponde analysis we discovered a subgroup of patients, defined \u201cSLF11-hot cluster\u201d, characterized by high SLFN11 levels, estrogen receptor negativity, basal-like phenotype, elevated CD3D, STAT1 signature, and young age and using Cox proportional hazard regression, we characterized SLFN11 high levels, high proliferation index, and ER negativity as independent parameters for longer disease-free interval in patients undergoing chemotherapy. We believe that our work supports proof of concept that: i) A clear and specific role for SLFN11 in breast cancer, in likely connection with the immune system modulation in such disease entity, ii) a strong correlation between high SFLN 11 and specific molecular subtype of breast cancer (estrogen receptor negativity, basal-like phenotype)

Belief-Invariant and Quantum Equilibria in Games of Incomplete Information

Drawing on ideas from game theory and quantum physics, we investigate nonlocal correlations from the point of view of equilibria in games of incomplete information. These equilibria can be classified in decreasing power as general communication equilibria, belief-invariant equilibria and correlated equilibria, all of which contain the familiar Nash equilibria. The notion of belief-invariant equilibrium has appeared in game theory before, in the 1990s. However, the class of non-signalling correlations associated to belief-invariance arose naturally already in the 1980s in the foundations of quantum mechanics. Here, we explain and unify these two origins of the idea and study the above classes of equilibria, and furthermore quantum correlated equilibria, using tools from quantum information but the language of game theory. We present a general framework of belief-invariant communication equilibria, which contains (quantum) correlated equilibria as special cases. It also contains the theory of Bell inequalities, a question of intense interest in quantum mechanics, and quantum games where players have conflicting interests, a recent topic in physics. We then use our framework to show new results related to social welfare. Namely, we exhibit a game where belief-invariance is socially better than correlated equilibria, and one where all non-belief-invariant equilibria are socially suboptimal. Then, we show that in some cases optimal social welfare is achieved by quantum correlations, which do not need an informed mediator to be implemented. Furthermore, we illustrate potential practical applications: for instance, situations where competing companies can correlate without exposing their trade secrets, or where privacy-preserving advice reduces congestion in a network. Along the way, we highlight open questions on the interplay between quantum information, cryptography, and game theory

Applying the Automatic Stay to Non-Debtors

(Excerpt) The automatic stay provision of the Bankruptcy Code is regarded as one of the most essential protections the Code offers to debtors. Section 362(a) provides that the filing of a bankruptcy petition “operates as a stay [of] action[s] or proceeding[s] against the debtor.” Thus, when an entity files for bankruptcy, an automatic stay is created that prevents creditors from taking any action to collect or enforce a debt, including among other things, continuing ongoing litigation. Practically, the automatic stay enables all claims against a debtor to be brought in a single forum. Simultaneously, it also preserves “what remains of the debtor’s solvent estate and [provides] for a systematic and equitable liquidation procedure for all creditors.” Aside from its benefit to debtors, the automatic stay also incidentally benefits creditors by fostering an orderly and organized resolution of all pending claims against the debtor’s estate. Traditionally, courts have limited the application of the automatic stay to debtors and property of the estate, adhering to a strict interpretation of the language of section 362. Some courts, however, have expanded the application of the automatic stay to non-debtor entities under certain circumstances. This expansion is significant because it affords the protections of a bankruptcy to entities that have not filed and thus are not within the bankruptcy court’s jurisdiction. This Article will survey the different standards applied by circuit courts when determining whether the automatic stay should be expanded to cover non-debtor entities. Part I will analyze the “strict interpretation” of section 362, Part II will consider the “unusual circumstances” standard, Part III will evaluate the “immediate adverse economic consequence” standard, and Part IV will examine the nuances between the standards. Although two different models may justify expanding the application of the automatic stay provision to non-debtor entities, their nuances are important to note, especially when considering the implications that expansion will have on the debtor, its creditors, and the bankruptcy system as a whole. This is especially evident when compared to the strict interpretation of section 362. Moreover, while the expansion of section 362 may broaden its reach, non-debtor parties still must meet the stringent requirements of those standards in order to be afforded the protections of the automatic stay

Progressive Collapse Performance of Steel Beam-to-Column Connections: Critical Review of Experimental Results

Background: The steel beam-to-column connections are vulnerable structural elements when a building loses one or more of its vertical load-carrying components due to abnormal or accidental loading conditions. After a column is destroyed by abnormal loads, the tensile axial force of the beam gradually increased, while the bending moment decreased, and the load-resistance mechanism shifts from a flexural mechanism to a catenary mechanism, with the axial force becoming the prevailing factor. Aims: This paper investigates the progressive collapse performance of steel beam-to-column connections. While undergoing large deformation, the beamto- column connections are subjected to moment, shear, and tension in conjunction with high ductility demand. Their behavior under monotonic loading depends on the moment-axial tension interaction and greatly affects the progressive collapse resistance of the structure. This paper presents a critical review of experimental tests of different types of steel beam-column joints (flexible, rigid, and semi-rigid) under a central-columnremoval scenario. Methods: The experimental results, including load-deformation relationships, failure modes, and catenary effects, are described in detail. The findings are used to evaluate the rotation capacity of different types of steel beam-to-column connections. The results are compared to the acceptance criteria specified by the main progressive collapse guidelines for several beam-to-column connection categories. Results: In simple (flexible) joints, the stiffness and strength at higher drift angles essentially depend on the tensile capacity of the connection that prevents, in some cases, the full development of the catenary mechanism. The connection depth alone does not seem to be an effective parameter to predict the rotational capacity of beam-to-column connections, since different connections with similar values of the connection depth result in very different values of the maximum rotation capacity. In fully rigid and semi-rigid connections, after the column removal, the flexural resistance controls the behavior at the preliminary phase, and the tensile force is almost zero. With increased downward displacement, the axial tensile force also increases, developing a catenary mechanism. Although the stiffness of rigid and semi-rigid connections is higher than flexible connections, both categories result in similar rotation capacity. Conclusion: In all the simple connections herein considered, the plastic rotation capacity obtained by tests was found much higher than the code recommended values that are probably too conservative. On the contrary, for one rigid and two semi-rigid connections, the values of the plastic rotation capacity obtained by tests are lower than the corresponding recommended values. Thus, the suggested acceptance criteria proved to be out of the conservative side

Metastability of the Logit Dynamics for Asymptotically Well-Behaved Potential Games

Convergence rate and stability of a solution concept are classically measured in terms of “even- tually” and “forever”, respectively. In the wake of recent computational criticisms to this approach, we study whether these time frames can be updated to have states computed “quickly” and stable for “long enough”. Logit dynamics allows irrationality in players’ behavior, and may take time exponential in the number of players n to converge to a stable state (i.e., a certain distribution over pure strategy pro- files). We prove that every potential game, for which the behavior of the logit dynamics is not chaotic as n increases, admits distributions stable for a super-polynomial number of steps in n no matter the players’ irrationality, and the starting profile of the dynamics. The convergence rate to these metastable distributions is polynomial in n when the players are not too rational. Our proofs build upon the new concept of partitioned Markov chains, that might be of indepen- dent interest, and a number of involved technical contributions