Foundations & ICT & Physics  (FIP) Session 1

Abstract: Random matrix theory (RMT) is a tool to study complex quantum systems. In this talk I will present the basic idea of RMT, and how it can be used to study open quantum systems and present some of our results concerning decoherence. In particular, we shall show how purity decay can be predicted with this tool, show that generic quantum open systems display non-markovian behaviour and how this behaviour is smeared out when the coupling between the system of interest and the environment is weak. The transition from non-Markovian to Markovian dynamics for generic environments , Phys. Rev. A 93, 012113 (2016) Random density matrices versus random evolution of open systems, J. Phys. A: Math. Theor. 48 425005 (2015) A random matrix theory of decoherence, New J. Phys. 10, 115016 (2008) Close

Abstract: We discuss the average relaxation properties of the internal memory in models of pure memristive networks. We consider the simplest linear model of memristor unit and introduce a dynamical equation for the evolution of internal memory in terms of projection operators. We find that for the case of passive components the dynamics is described by an orthogonal projection operator and for the case of active elements by a non-orthogonal projector. We analyze the average properties of internal memory parameters for random projection operators, and find that this is well described by a slow relaxation evolution if no active components are present. We provide a simple explanation for the emerging slow relaxation as a superposition of exponential relaxations with broad time scales range. Close

Abstract: Many online collaboration networks struggle to gain user activity and become self-sustaining due to the ramp-up problem or dwindling activity within the system. Prominent examples include online encyclopedias such as (Semantic) MediaWikis, Question and Answering portals such as StackOverflow, online ontology editors and repositories, such as WebProtégé or BioPortal, and many others. Only a small fraction of these systems manage to reach self-sustaining activity, a level of activity that prevents the system from reverting to a non-active state. In this paper, we model and analyze activity dynamics in synthetic and empirical collaboration networks. Our approach is based on two opposing and well-studied principles: (i) without incentives, users tend to lose interest to contribute and thus, systems become inactive, and (ii) people are susceptible to actions taken by their peers (social or peer influence). With the activity dynamics model that we introduce in this paper we can represent typical situations of such collaboration networks. For example, activity in a collaborative network, without external impulses or investments, will vanish over time, eventually rendering the system inactive. However, by appropriately manipulating the activity dynamics and/or the underlying collaboration networks, we can jump-start a previously inactive system and advance it towards an active state. To be able to do so, we first describe our model and its underlying mechanisms. We then provide illustrative examples of empirical datasets and characterize the barrier that has to be breached by a system before it can become self-sustaining in terms of critical mass and activity dynamics. Additionally, we expand on this empirical illustration and introduce a new metric p—the Activity Momentum—to assess the activity robustness of collaboration networks. Full paper: http://dl.acm.org/citation.cfm?id=2873060 Close

Abstract: The competition for the attention of users is a central element of the Internet. Crucial issues are the origin and predictability of big hits, the few items that capture a big portion of the total attention. We address these issues analyzing 10 million time series of videos’ views from YouTube. We find that the average gain of views is linearly proportional to the number of views a video already has, in agreement with usual rich-get-richer mechanisms and Gibrat’s law, but this fails to explain the prevalence of big hits. The reason is that the fluctuations around the average views are themselves heavy tailed. Based on these empirical observations, we propose a stochastic differential equation with Lévy noise as a model of the dynamics of videos. We show how this model is substantially better in estimating the probability of an ordinary item becoming a big hit, which is considerably underestimated in the traditional proportional-growth models. Close

Abstract: At first, we say that a ego-community structure is a probability measure defined on the set of network nodes. Any subset of nodes may engender its own ego-community structure around. Many community detection algorithms can be modified to yield a result of this type, for instance, the personalized pagerank. Next, we present a continuous version of Viard-Latapy-Magnien link streams, that we call "temporal density". Classical kernel density estimation is used to move from discrete link streams to their continuous counterparts. Using matrix perturbation theory we can prove that ego-community structure changes smoothly when the network evolves smoothly. This is very important, for example, for visualization purposes. Combining the temporal density and personalized pagerank methods, we are able to visualize and study the evolution of the ego-community structures of complex networks with a large number of temporal links. We illustrate and validate our approach using "Primary school temporal network data" provided by sociopatterns.org, and we show how the temporal density can be applied to the study of very large datasets, such as a collection of tweets written by European Parliament candidates during European Parliament election in 2014. Main Topic: Foundations of Complex Systems Sub Topic: Social networks Close

Abstract: Many (experimental) sciences don't work or assume actual infinity. Finitely Supported Mathematics (FSM) is introduced as a mathematics dealing with a more relaxed notion of (in)finiteness. FSM has strong connections with the Fraenkel-Mostowski (FM) permutative model of Zermelo-Fraenkel set theory with atoms. However, FSM can characterize infinite algebraic structures using their finite supports. More exactly, FSM is ZF mathematics rephrased in terms of finitely supported structures by using an infinite set of atoms. In FSM, 'sets' are replaced either by `invariant sets' (sets endowed with some group actions satisfying a finite support requirement) or by `finitely supported sets' (finitely supported elements in the powerset of an invariant set), and developed a theory of `invariant algebraic structures'. We describe FSM by using principles (rather than axioms), and the principles of constructing FSM have historical roots both in the definition of Tarski `logical notions' and in the Erlangen Program of F.Klein for the classification of geometries according to invariants under suitable groups of transformations. There exist other connections between FSM, admissible sets and Gandy machines. The main principle of constructing FSM is that all the structures have to be invariant or finitely supported. As a consequence, we cannot obtain a property in FSM only by involving a ZF result without an appropriate proof reformulated according to the finite support requirement. Moreover, not every ZF result can be directly reformulated in terms of finitely supported objects because, given an invariant set, some of its subsets might be non-finitely supported (an example is given by a simultaneously infinite and coinfinite subset of the invariant set of all atoms). We have specific techniques of reformulating ZF properties of algebraic structures in FSM. More details are presented in the papers published by the authors in the last 2 years. Close