First-order transition in small-world networks

The small-world transition is a first-order transition at zero density $p$ of shortcuts, whereby the normalized shortest-path distance undergoes a discontinuity in the thermodynamic limit. On finite systems the apparent transition is shifted by $\Delta p \sim L^{-d}$. Equivalently a ``persistence size'' $L^* \sim p^{-1/d}$ can be defined in connection with finite-size effects. Assuming $L^* \sim p^{-\tau}$, simple rescaling arguments imply that $\tau=1/d$. We confirm this result by extensive numerical simulation in one to four dimensions, and argue that $\tau=1/d$ implies that this transition is first-order.Comment: 4 pages, 3 figures, To appear in Europhysics Letter

Nuclear three-body problem in the complex energy plane: Complex-Scaling-Slater method

The physics of open quantum systems is an interdisciplinary area of research. The nuclear "openness" manifests itself through the presence of the many-body continuum representing various decay, scattering, and reaction channels. As the radioactive nuclear beam experimentation extends the known nuclear landscape towards the particle drip lines, the coupling to the continuum space becomes exceedingly more important. Of particular interest are weakly bound and unbound nuclear states appearing around particle thresholds. Theories of such nuclei must take into account their open quantum nature. To describe open quantum systems, we introduce a Complex Scaling (CS) approach in the Slater basis. We benchmark it with the complex-energy Gamow Shell Model (GSM) by studying energies and wave functions of the bound and unbound states of the two-neutron halo nucleus 6He viewed as an $\alpha$+ n + n cluster system. In the CS approach, we use the Slater basis, which exhibits the correct asymptotic behavior at large distances. To extract particle densities from the back-rotated CS solutions, we apply the Tikhonov regularization procedure, which minimizes the ultraviolet numerical noise. While standard applications of the inverse complex transformation to the complex-rotated solution provide unstable results, the stabilization method fully reproduces the GSM benchmark. We also propose a method to determine the smoothing parameter of the Tikhonov regularization. The combined suite of CS-Slater and GSM techniques has many attractive features when applied to nuclear problems involving weakly-bound and unbound states. While both methods can describe energies, total widths, and wave functions of nuclear states, the CS-Slater method, if it can be applied, can provide an additional information about partial energy widths associated with individual thresholds.Comment: 15 pages, 16 figure

Biased random satisfiability problems: From easy to hard instances

In this paper we study biased random K-SAT problems in which each logical variable is negated with probability $p$. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the typical complexity of random K-SAT problems. The exact solution of 1-SAT case is given. The critical point of K-SAT problems and results of replica method are derived in the replica symmetry framework. It is found that in this approximation $\alpha_c \propto p^{-(K-1)}$ for $p\to 0$. Solving numerically the survey propagation equations for K=3 we find that for $p<p^* \sim 0.17$ there is no replica symmetry breaking and still the SAT-UNSAT transition is discontinuous.Comment: 17 pages, 8 figure

Hamilton-Jacobi method for Domain Walls and Cosmologies

We use Hamiltonian methods to study curved domain walls and cosmologies. This leads naturally to first order equations for all domain walls and cosmologies foliated by slices of maximal symmetry. For Minkowski and AdS-sliced domain walls (flat and closed FLRW cosmologies) we recover a recent result concerning their (pseudo)supersymmetry. We show how domain-wall stability is consistent with the instability of adS vacua that violate the Breitenlohner-Freedman bound. We also explore the relationship to Hamilton-Jacobi theory and compute the wave-function of a 3-dimensional closed universe evolving towards de Sitter spacetime.Comment: 18 pages; v2: typos corrected, one ref added, version to appear in PR

Positivity of energy for asymptotically locally AdS spacetimes

We derive necessary conditions for the spinorial Witten-Nester energy to be well-defined for asymptotically locally AdS spacetimes. We find that the conformal boundary should admit a spinor satisfying certain differential conditions and in odd dimensions the boundary metric should be conformally Einstein. We show that these conditions are satisfied by asymptotically AdS spacetimes. The gravitational energy (obtained using the holographic stress energy tensor) and the spinorial energy are equal in even dimensions and differ by a bounded quantity related to the conformal anomaly in odd dimensions.Comment: 36 pages, 1 figure; minor corrections, JHEP versio

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

The computational difficulty of finding MPS ground states

We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians which are known to be Matrix Product States (MPS). To this end, we construct a class of 1D frustration free Hamiltonians with unique MPS ground states and a polynomial gap above, for which finding the ground state is at least as hard as factoring. By lifting the requirement of a unique ground state, we obtain a class for which finding the ground state solves an NP-complete problem. Therefore, for these Hamiltonians it is not even possible to certify that the ground state has been found. Our results thus imply that in order to prove convergence of variational methods over MPS, as the Density Matrix Renormalization Group, one has to put more requirements than just MPS ground states and a polynomial spectral gap.Comment: 5 pages. v2: accepted version, Journal-Ref adde

Bridging the gap between neurons and cognition through assemblies of neurons

During recent decades, our understanding of the brain has advanced dramatically at both the cellular and molecular levels and at the cognitive neurofunctional level; however, a huge gap remains between the microlevel of physiology and the macrolevel of cognition. We propose that computational models based on assemblies of neurons can serve as a blueprint for bridging these two scales. We discuss recently developed computational models of assemblies that have been demonstrated to mediate higher cognitive functions such as the processing of simple sentences, to be realistically realizable by neural activity, and to possess general computational power

LOCAL EARTHQUAKE TOMOGRAPHY IN THE BROADER AREA OF WESTERN CORINTH GULF

Η παρούσα εργασία περιγράφει τα αποτελέσματα της τρισδιάστατης τομογραφίας που πραγματοποιήθηκε στην ευρύτερη περιοχή του Δυτικού Κορινθιακού Κόλπου με σκοπό την χαρτογράφηση ενεργών τεκτονικών δομών. Για την πραγματοποίηση της παρούσης μελέτης χρησιμοποιήθηκαν δεδομένα από περισσότερους των 2,000 σεισμών οι οποίοι καταγράφηκαν από το Ενιαίο Σεισμολογικό Δίκτυο και το αντίστοιχο του Εργαστηρίου της Κορινθιακής Τάφρου (CRLN).Με την τομογραφική αντιστροφή παράγουμε και πραγματοποιούμε την ερμηνεία τρισδιάστατων μοντέλων κυμάτων χώρου (Vp, Vs) και του αντίστοιχου λόγου τους (Vp/Vs) για την περιοχή μελέτης. Τα τελικά αποτελέσματα καταδεικνύουν ορισμένες ενδιαφέρουσες δομές, κυρίως όσον αφορά τον λόγο Vp/Vs,που συσχετίζουν την κατανομή των προσδιορισθέντων υποκέντρων με διαφοροποιήσεις στη λιθολογία ή στο περιεχόμενο των γεωλογικών σχηματισμών σε ρευστά. Στην περιοχή του Πατραϊκού, ένας ανερχόμενος δόμος υψηλής ταχύτητας εντοπίστηκε, ο οποίος κάλλιστα μπορεί να συνδεθεί με την τεκτονική αλατούχων δόμων στο Αλπικό υπόβαθρο, γεγονός που επηρεάζει την κυκλοφορία των ρευστών καθώς και τη δράση των τοπικών ρηγμάτων.In this study, we applied Local Earthquake Tomography in order to investigate the detailed 3-D structure within and around the broader region of Western Corinth Gulf which is one of the most seismically active regions in the world. We use data from the 2012-2014 time-period, selecting about 2,000 seismic events recorded by the local seismic stations of Hellenic Unified Seismological Network (HUSN) and the Corinth Rift Laboratory Network (CRLN). Applying Tomographic Inversion, we produce and interpret 3-D models of Vp, Vs and Vp/Vs ratio in the study area. The obtained results shows several distinct structures, namely areas of high and low Vp/Vs ratio correlating the hypocenter distribution with changes in lithology or fluid concentration. In the area of Patraikos Gulf, an ascending velocity volume was traced that could possibly be connected to salt tectonics in the alpine basement, effecting the fluid circulation as well as the behavior of local faults