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

Ab-initio No-Core Gamow Shell Model calculations with realistic interactions

No-Core Gamow Shell Model (NCGSM) is applied for the first time to study selected well-bound and unbound states of helium isotopes. This model is formulated on the complex energy plane and, by using a complete Berggren ensemble, treats bound, resonant, and scattering states on equal footing. We use the Density Matrix Renormalization Group method to solve the many-body Schr\"{o}dinger equation. To test the validity of our approach, we benchmarked the NCGSM results against Faddeev and Faddeev-Yakubovsky exact calculations for $^3$H and $^4$He nuclei. We also performed {\textit ab initio} NCGSM calculations for the unstable nucleus $^5$He and determined the ground state energy and decay width, starting from a realistic N$^3$LO chiral interaction.Comment: 17 pages, 14 figures. Revised version. Discussion on microscopic overlap functions, SFs and ANCs is added. Added references. Accepted for publication at PR

Online Admission Control and Embedding of Service Chains

The virtualization and softwarization of modern computer networks enables the definition and fast deployment of novel network services called service chains: sequences of virtualized network functions (e.g., firewalls, caches, traffic optimizers) through which traffic is routed between source and destination. This paper attends to the problem of admitting and embedding a maximum number of service chains, i.e., a maximum number of source-destination pairs which are routed via a sequence of to-be-allocated, capacitated network functions. We consider an Online variant of this maximum Service Chain Embedding Problem, short OSCEP, where requests arrive over time, in a worst-case manner. Our main contribution is a deterministic O(log L)-competitive online algorithm, under the assumption that capacities are at least logarithmic in L. We show that this is asymptotically optimal within the class of deterministic and randomized online algorithms. We also explore lower bounds for offline approximation algorithms, and prove that the offline problem is APX-hard for unit capacities and small L > 2, and even Poly-APX-hard in general, when there is no bound on L. These approximation lower bounds may be of independent interest, as they also extend to other problems such as Virtual Circuit Routing. Finally, we present an exact algorithm based on 0-1 programming, implying that the general offline SCEP is in NP and by the above hardness results it is NP-complete for constant L.Comment: early version of SIROCCO 2015 pape

SEMI-MARKOV MODELS FOR SEISMIC HAZARD ASSESSMENT IN CERTAIN AREAS OF GREECE

The long-term probabilistic seismic hazard is studied through the application of semi-Markov model. In this model a sequence of earthquakes is considered as a Markov process and the waiting time distributions depend only on the type of the last and the next event. The principal hypothesis of the model is the property of one-step memory, according to which the probability of moving to any future state depends only on the present state. The model under consideration defines a continuous-time, discrete-state stationary process in which successive state occupancies are governed by the transition probabilities of the Markov process. The space of states is considered to be finite and the process started far in the past has achieved stationarity. Firstly, a non-parametric method is applied in order to determine the waiting times. Then, the waiting times derived by means of the exponential and Weibull distributions will be compared to each other, as well as with the actual waiting times. Thus, the probability of occurrence of the anticipated earthquakes of a specific magnitude scale is calculated. The models are applied to an historical catalogue for Northern Aegean Sea

A Markov model for seismic hazard analysis along the Hellenic subduction Zone (Greece)

Εφαρμόζεται  ένα  ομογενές  Μαρκοβιανό  μοντέλο  διακριτού  χρόνου  και  χώρου καταστάσεων για τη γένεση σεισμών στο Ελληνικό Τόξο, περιοχή υψηλής σεισμικής δραστηριότητας  και  ιδιαίτερης  σημασίας  από  σεισμοτεκτονική  άποψη.  Το  μοντέλο παρέχει μια στοχαστική αναπαράσταση της γένεσης των σεισμών συμβάλλοντας στην εκτίμηση της σεισμικής επικινδυνότητας για την περιοχή μελέτης. Τα δεδομένα που χρησιμοποιούνται  λήφθηκαν  από  τον  κατάλογο  του  Τομέα  Γεωφυσικής  του Αριστοτελείου  Πανεπιστημίου  Θεσσαλονίκης,  ο  οποίος  θεωρείται  ομογενής  και  πλήρης  για  σεισμούς  με  από  το  1911.  Ο  συνεχής  χώρος  καταστάσεων χωρίζεται  σε  κλάσεις  μεγεθών  καθορίζοντας  με  αυτό  τον  τρόπο  τον  χώρο καταστάσεων  του  μοντέλου.  Η  στοχαστική  συμπεριφορά  του  μοντέλου  καθορίζεται XLVII, No 3 - 1376από  τον  πίνακα  πιθανοτήτων  μετάβασής  του,  του  οποίου  υπολογίζεται  αρχικά ο εκτιμητής   μέγιστης   πιθανοφάνειας.   Στη  συνέχεια   εκτιμώνται   σημαντικά χαρακτηριστικά της Μαρκοβιανής αλυσίδας, παρέχοντας προγνωστικά αποτελέσματα σχετικά  με  την  πιθανότητα  γένεσης  ενός  επερχόμενου  ισχυρού  σεισμού.  Οι υπολογισμοί  περιλαμβάνουν  την  εκτίμηση  της  μέσης  τιμής,  της  διασποράς  και  του 95% διαστήματος εμπιστοσύνης του πλήθους των βημάτων που απαιτούνται ώστε η Μαρκοβιανή αλυσίδα να μεταβεί για πρώτη φορά σε μια ορισμένη κατάσταση (που σχετίζεται με τη γένεση ενός επερχόμενου ισχυρού σεισμού).A homogeneous finite–state discrete–time Markov model is applied for the earthquake occurrence in the Hellenic Subduction Zone (Greece), a region accommodating high seismic activity, being a key structure from a seismotectonic point of view. An attempt is made to provide a stochastic representation of the earthquake process and to assess the seismic hazard through the application of the Markov model. The model is applied on a complete data sample comprising strong () eart  h-quakes that occurred in the study area since 1911 up to present. The continuous magnitude scale is divided into appropriate intervals to specify discrete states of the model. As the stochastic behavior of the model is governed by its transition probability matrix, we firstly estimate its well–known maximum likelihood estimator. The estimation of the transition probability matrix leads to the estimation of important indicators of the Markov chain, including hitting times and failure rate functions. The   mean number of steps for the first occurrence of an anticipated earthquake (belonging to the class with the stronger events, which we are more interested in) is estimated along with its variance. In a next step, we calculate the confidence interval of the   aforementioned estimators

Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition

A geometric graph is angle-monotone if every pair of vertices has a path between them that---after some rotation---is $x$- and $y$-monotone. Angle-monotone graphs are $\sqrt 2$-spanners and they are increasing-chord graphs. Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in 2014 and proved that Gabriel triangulations are angle-monotone graphs. We give a polynomial time algorithm to recognize angle-monotone geometric graphs. We prove that every point set has a plane geometric graph that is generalized angle-monotone---specifically, we prove that the half-$\theta_6$-graph is generalized angle-monotone. We give a local routing algorithm for Gabriel triangulations that finds a path from any vertex $s$ to any vertex $t$ whose length is within $1 + \sqrt 2$ times the Euclidean distance from $s$ to $t$. Finally, we prove some lower bounds and limits on local routing algorithms on Gabriel triangulations.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

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

Phase transition for cutting-plane approach to vertex-cover problem

We study the vertex-cover problem which is an NP-hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, e.g., Erdoes-Renyi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g, for the ER ensemble at connectivity c=e=2.7183 from replica symmetric to replica-symmetry broken. For the vertex-cover problem, also the typical complexity of exact branch-and-bound algorithms, which proceed by exploring the landscape of feasible configurations, change close to this phase transition from "easy" to "hard". In this work, we consider an algorithm which has a completely different strategy: The problem is mapped onto a linear programming problem augmented by a cutting-plane approach, hence the algorithm operates in a space OUTSIDE the space of feasible configurations until the final step, where a solution is found. Here we show that this type of algorithm also exhibits an "easy-hard" transition around c=e, which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem.Comment: 4 pages, 3 figure

Charge radii and neutron correlations in helium halo nuclei

Within the complex-energy configuration interaction framework, we study correlations of valence neutrons to explain the behavior of charge radii in the neutron halo nuclei $^{6,8}$He. We find that the experimentally observed decrease of the charge radius between $^6$He and $^8$He is caused by a subtle interplay between three effects: dineutron correlations, a spin-orbit contribution to the charge radius, and a core swelling effect. We demonstrate that two-neutron angular correlations in the $2^+_1$ resonance of $^6$He differ markedly from the ground-state correlations in $^{6,8}$He.Comment: 5 pages, 5 figure