Settling Some Open Problems on 2-Player Symmetric Nash Equilibria

Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the following; it was stated by Papadimitriou in 2007: find a non-symmetric Nash equilibrium (NE) in a symmetric game. We show that this problem is NP-complete and the problem of counting the number of non-symmetric NE in a symmetric game is #P-complete. In 2005, Kannan and Theobald defined the "rank of a bimatrix game" represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be computed in rank 1 games in polynomial time. Observe that the rank 0 case is precisely the zero sum case, for which a polynomial time algorithm follows from von Neumann's reduction of such games to linear programming. In 2011, Adsul et. al. obtained an algorithm for rank 1 games; however, it does not solve the case of symmetric rank 1 games. We resolve this problem

Holographic Renormalization of general dilaton-axion gravity

We consider a very general dilaton-axion system coupled to Einstein-Hilbert gravity in arbitrary dimension and we carry out holographic renormalization for any dimension up to and including five dimensions. This is achieved by developing a new systematic algorithm for iteratively solving the radial Hamilton-Jacobi equation in a derivative expansion. The boundary term derived is valid not only for asymptotically AdS backgrounds, but also for more general asymptotics, including non-conformal branes and Improved Holographic QCD. In the second half of the paper, we apply the general result to Improved Holographic QCD with arbitrary dilaton potential. In particular, we derive the generalized Fefferman-Graham asymptotic expansions and provide a proof of the holographic Ward identities.Comment: 42 pages. v2: two references added. Version published in JHEP. v3: fixed minor typos in eqs. (1.6), (2.3), (3.20), (A.3), (B.8), (B.12) and (B.22

Hitting Diamonds and Growing Cacti

We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the primal-dual method. Moreover, we show that the integrality gap of the natural LP relaxation of the problem is \Theta(\log n), where n denotes the number of vertices in the graph.Comment: v2: several minor changes

On kernels, defaults and even graphs

Extensions in prerequisite-free, disjunction-free default theories have been shown to be in direct correspondence with kernels of directed graphs; hence default theories without odd cycles always have a ``standard'' kind of an extension. We show that, although all ``standard'' extensions can be enumerated explicitly, several other problems remain intractable for such theories: Telling whether a non-standard extension exists, enumerating all extensions, and finding the minimal standard extension. We also present a new graph-theoretic algorithm, based on vertex feedback sets, for enumerating all extensions of a general prerequisite-free, disjunction-free default theory (possibly with odd cycles). The algorithm empirically performs well for quite large theories

A CROSS-CORRELATION TECHNIQUE FOR RELOCATION OF SEISMICITY IN THE WESTERN CORINTH RIFT

Local seismological networks provide data that allow the location of microearthquakes which otherwise would be dismissed due to low magnitudes and low signal-to-noise ratios of their seismic signals. The Corinth Rift Laboratory (CRL) network, installed in the western Corinth rift, has been providing digital waveform data since 2000. In this work, a semi-automatic picking technique has been applied which exploits the similarity between waveforms of events that have occurred in approximately the same area of an active fault. Similarity is measured by the crosscorrelation maxi-mum of full signals. Events with similar waveforms are grouped in multiplet clusters using the nearest-neighbour linkage algorithm. Manually located events act as masters, while automatically located events of each multiplet cluster act as slaves. By cross-correlating the P-wave or S-wave segments of a master event with the corresponding segments of each of its slave events, after appropriately aligning their offsets, the measured time-lag at the cross-correlation maximum can be subtracted from the arrival-time of the slave event. After the correction of the arrival-times, a double-difference technique is applied to the modified catalogue to further improve the locations of clusters and distinguish the active seismogenic structures in the tectonically complex Western Corinth rift

Reflective Relational Machines

AbstractWe propose a model of database programming withreflection(dynamic generation of queries within the host programming language), called thereflective relational machine, and characterize the power of this machine in terms of known complexity classes. In particular, the polynomial time restriction of the reflective relational machine is shown to express PSPACE, and to correspond precisely to uniform circuits of polynomial depth and exponential size. This provides an alternative, logic based formulation of the uniform circuit model, which may be more convenient for problems naturally formulated in logic terms, and establishes that reflection allows for more “intense” parallelism, which is not attainable otherwise (unless P=PSPACE). We also explore the power of the reflective relational machine subject to restrictions on the number of variables used, emphasizing the case of sublinear bounds

Anatomy of bubbling solutions

We present a comprehensive analysis of holography for the bubbling solutions of Lin-Lunin-Maldacena. These solutions are uniquely determined by a coloring of a 2-plane, which was argued to correspond to the phase space of free fermions. We show that in general this phase space distribution does not determine fully the 1/2 BPS state of N=4 SYM that the gravitational solution is dual to, but it does determine it enough so that vevs of all single trace 1/2 BPS operators in that state are uniquely determined to leading order in the large N limit. These are precisely the vevs encoded in the asymptotics of the LLM solutions. We extract these vevs for operators up to dimension 4 using holographic renormalization and KK holography and show exact agreement with the field theory expressions.Comment: 67 pages, 6 figures; v2: typos corrected, refs added; v3: expanded explanations, more typos correcte