Optimal competitiveness for the Rectilinear Steiner Arborescence problem

We present optimal online algorithms for two related known problems involving Steiner Arborescence, improving both the lower and the upper bounds. One of them is the well studied continuous problem of the {\em Rectilinear Steiner Arborescence} ($RSA$). We improve the lower bound and the upper bound on the competitive ratio for $RSA$ from $O(\log N)$ and $\Omega(\sqrt{\log N})$ to $\Theta(\frac{\log N}{\log \log N})$, where $N$ is the number of Steiner points. This separates the competitive ratios of $RSA$ and the Symetric-$RSA$, two problems for which the bounds of Berman and Coulston is STOC 1997 were identical. The second problem is one of the Multimedia Content Distribution problems presented by Papadimitriou et al. in several papers and Charikar et al. SODA 1998. It can be viewed as the discrete counterparts (or a network counterpart) of $RSA$. For this second problem we present tight bounds also in terms of the network size, in addition to presenting tight bounds in terms of the number of Steiner points (the latter are similar to those we derived for $RSA$)

A Note on Scalar Field Theory in AdS_3/CFT_2

We consider a scalar field theory in AdS_{d+1}, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions \Delta_{-} and \Delta_{+}, respectively, where \Delta_{\pm} are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d=2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS_3/CFT_2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results.Comment: 24 pages. v2: added minor clarification. v3: added several comments and discussions, abstract sligthly changed. Version to be publishe

Kaluza-Klein Holography

We construct a holographic map between asymptotically AdS_5 x S^5 solutions of 10d supergravity and vacuum expectation values of gauge invariant operators of the dual QFT. The ingredients that enter in the construction are (i) gauge invariant variables so that the KK reduction is independent of any choice of gauge fixing; (ii) the non-linear KK reduction map from 10 to 5 dimensions (constructed perturbatively in the number of fields); (iii) application of holographic renormalization. A non-trivial role in the last step is played by extremal couplings. This map allows one to reliably compute vevs of operators dual to any KK fields. As an application we consider a Coulomb branch solution and compute the first two non-trivial vevs, involving operators of dimension 2 and 4, and reproduce the field theory result, in agreement with non-renormalization theorems. This constitutes the first quantitative test of the gravity/gauge theory duality away from the conformal point involving a vev of an operator dual to a KK field (which is not one of the gauged supergravity fields).Comment: 47 pages, v2: minor improvements, version to appear in JHE

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

Holographic Coulomb branch vevs

We compute holographically the vevs of all chiral primary operators for supergravity solutions corresponding to the Coulomb branch of N=4 SYM and find exact agreement with the corresponding field theory computation. Using the dictionary between 10d geometries and field theory developed to extract these vevs, we propose a gravity dual of a half supersymmetric deformation of N=4 SYM by certain irrelevant operators.Comment: 16 pages, v2 corrections in appendi

Seismic hazard assessment in the Northern Aegean Sea (Greece) through discrete Semi-Markov modeling.

Οι ημι-Μαρκοβιανές αλυσίδες χρησιμοποιούνται για τη μελέτη της σεισμικότητας στο Βόρειο  Αιγαίο.  Η  βασική  τους  διαφορά  από  τις  Μαρκοβιανές  αλυσίδες  είναι  ότι επιτρέπουν  μια  οποιαδήποτε  αυθαίρετη  κατανομή  για  τους  χρόνους  παραμονής (χρόνοι μεταξύ διαδοχικών σεισμών). Υποθέτουμε ότι η χρονοσειρά των σεισμών που έχουν  γίνει  στο  Βόρειο  Αιγαίο  αποτελεί  μια  διακριτή  ημι-Μαρκοβιανή  αλυσίδα. Θεωρείται ότι οι χρόνοι παραμονής ακολουθούν γεωμετρικές ή διακριτές κατανομές Weibull. Πρώτα ταξινομήθηκαν τα δεδομένα σε δυο κατηγορίες, όπου κατάσταση 1: Μέγεθος 6.5 -7 και κατάσταση 2 Μέγεθος>7, και στη συνέχεια σε τρεις κατηγορίες, όπου   κατάσταση 1: μέγεθος 6.5 -6.7,   κατάσταση 2 :   Μέγεθος 6.8 -7.1   και κατάσταση 3 : Μέγεθος 7.2 -7.4 . Εκτιμήθηκαν οι παράμετροι των συναρτήσεων πιθανότητας των χρόνων  παραμονής  και  υπολογίστηκαν  οι  πίνακες  πυρήνες  της  ημι-Μαρκοβιανής αλυσίδας για όλες τις παραπάνω περιπτώσεις. Έγινε σύγκριση των πινάκων πυρήνων και   προέκυψαν συμπεράσματα για  τη μελλοντική σεισμική επικινδυνότητα στην υπό μελέτη περιοχή.Semi-Markov  chains  are  used  for  studying  the  evolution  of  seismicity  in  the Northern Aegean Sea (Greece). Their main difference from the Markov chains is that   they  allow the sojourn times (i.e. the time between successive earthquakes), to follow any arbitrary distribution. It is assumed that the time series of earthquakes that  occurred  in  Northern  Aegean  Sea  form  a  discrete  semi-Markov  chain. The probability law of the sojourn times, is considered to be the geometric distribution or   the   discrete  Weibull  distribution. Firstly,  the  data  are  classified  into  two categories that is, state 1: Magnitude 6.5  -7 and state 2 Magnitude>7, and secondly into three categories , that is    state 1: Magnitude 6.5-6.7, state 2: Magnitude 6.8-7.1 and state 3: Magnitude 7.2-7.4 . This methodology is followed in order to obtain more accurate results and find out whether there exists an impact of the different classification on the results. The parameters of the probability laws of the sojourn times are estimated and the semi-Markov kernels are  evaluated for all the above cases  .  The  semi-Markov  kernels  are  compared and  the   conclusions  are  drawn relatively to future seismic hazard in the area under study

University Staff Teaching Allocation: Formulating and Optimising a Many-Objective Problem

This is the author accepted manuscript. The final version is available from ACM via the DOI in this record.The codebase for this paper is available at https://github.com/fieldsend/gecco_2017_staff_teaching_allocationThe allocation of university staff to teaching exhibits a range of often competing objectives. We illustrate the use of an augmented version of NSGA-III to undertake the seven-objective optimisation of this problem, to fi nd a trade-off front for a university department using real world data. We highlight its use in decision-making, and compare solutions identi fied to an actual allocation made prior to the availability of the optimisation tool. The criteria we consider include minimising the imbalance in workload distribution among staff; minimising the average load; minimising the maximum peak load; minimising the staff per module; minimising staff dissatisfaction with teaching allocations; and minimising the variation from the previous year’s allocation (allocation churn). We derive mathematical forms for these various criteria, and show we can determine the maximum possible values for all criteria and the minimum values for most exactly (with lower bounds on the remaining criteria). For many of the objectives, when considered in isolation, an optimal solution may be obtained rapidly. We demonstrate the advantage of utilising such extreme solutions to drastically improve the optimisation effi ciency in this many-objective optimisation problem. We also identify issues that NSGA-III can experience due to selection between generations

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

Scaling and Universality of the Complexity of Analog Computation

We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these ensembles, the probability distribution functions of certain quantities which measure the computational complexity, known as the convergence rate, the barrier and the computation time. We find that in the limit of very large problems these probability distributions are universal scaling functions. In other words, the probability distribution function for each of these three quantities becomes, in the limit of large problem size, a function of a single scaling variable, which is a certain composition of the quantity in question and the size of the system. Moreover, various ensembles studied seem to lead essentially to the same scaling functions, which depend only on the variance of the ensemble. These results extend analytical and numerical results obtained recently for the Gaussian ensemble, and support the conjecture that these scaling functions are universal.Comment: 22 pages, latex, 12 eps fig

Janus within Janus

We found a simple and interesting generalization of the non-supersymmetric Janus solution in type IIB string theory. The Janus solution can be thought of as a thick AdS_d-sliced domain wall in AdS_{d+1} space. It turns out that the AdS_d-sliced domain wall can support its own AdS_{d-1}-sliced domain wall within it. Indeed this pattern persists further until it reaches the AdS_2-slice of the domain wall within self-similar AdS_{p (2<p\le d)}-sliced domain walls. In other words the solution represents a sequence of little Janus nested in the interface of the parent Janus according to a remarkably simple ``nesting'' rule. Via the AdS/CFT duality, the dual gauge theory description is in general an interface CFT of higher codimensions.Comment: 15 pages, 6 figures, v2 references added. v3 eq.(3.33) correcte