A Study of the Complex Action Problem in a Simple Model for Dynamical Compactification in Superstring Theory Using the Factorization Method

The IIB matrix model proposes a mechanism for dynamically generating four dimensional space--time in string theory by spontaneous breaking of the ten dimensional rotational symmetry $\textrm{SO}(10)$. Calculations using the Gaussian expansion method (GEM) lend support to this conjecture. We study a simple $\textrm{SO}(4)$ invariant matrix model using Monte Carlo simulations and we confirm that its rotational symmetry breaks down, showing that lower dimensional configurations dominate the path integral. The model has a strong complex action problem and the calculations were made possible by the use of the factorization method on the density of states $\rho_n(x)$ of properly normalized eigenvalues $\tilde\lambda_n$ of the space--time moment of inertia tensor. We study scaling properties of the factorized terms of $\rho_n(x)$ and we find them in agreement with simple scaling arguments. These can be used in the finite size scaling extrapolation and in the study of the region of configuration space obscured by the large fluctuations of the phase. The computed values of $\tilde\lambda_n$ are in reasonable agreement with GEM calculations and a numerical method for comparing the free energy of the corresponding ansatze is proposed and tested.Comment: 7 pages, 4 figures, Talk presented at the XXVIII International Symposium on Lattice Field Theory, Lattice2010, Villasimius, Italy, June 201

A general approach to the sign problem - the factorization method with multiple observables

The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive. The basic idea of the factorization method applied on such a system is to control some observables in order to determine and sample efficiently the region of configuration space which gives important contribution to the partition function. We argue that it is crucial to choose appropriately the set of the observables to be controlled in order for the method to work successfully in a general system. This is demonstrated by an explicit example, in which it turns out to be necessary to control more than one observables. Extrapolation to large system size is possible due to the nice scaling properties of the factorized functions, and known results obtained by an analytic method are shown to be consistently reproduced.Comment: 6 pages, 3 figures, (v2) references added (v3) Sections IV, V and VI improved, final version accepted by PR

Training & acceleration of deep reinforcement learning agents

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) "Επιστήμη Δεδομένων και Μηχανική Μάθηση

Multi-criteria optimal task allocation at the edge

In Internet of Things (IoT), numerous nodes produce huge volumes of data that are subject of various processing tasks. Tasks execution on top of the collected data can be realized either at the edge of the network or at the Fog/Cloud. Their management at the network edge may limit the required time for concluding responses and return the final outcome/analytics to end-users or applications. IoT nodes, due to their limited computational and resource capabilities, can execute a limited number of tasks over the collected contextual data. A challenging decision is related to which tasks IoT nodes should execute locally. Each node should carefully select such tasks to maximize the performance based on the current contextual information, e.g., tasks’ characteristics, nodes’ load and energy capacity. In this paper, we propose an intelligent decision making scheme for selecting the tasks that will be locally executed. The remaining tasks will be transferred to peer nodes in the network or the Fog/Cloud. Our focus is to limit the time required for initiating the execution of each task by introducing a two-step decision process. The first step is to decide whether a task can be executed locally; if not, the second step involves the sophisticated selection of the most appropriate peer to allocate it. When, in the entire network, no node is capable of executing the task, it is, then, sent to the Fog/Cloud facing the maximum latency. We comprehensively evaluate the proposed scheme demonstrating its applicability and optimality at the network edge