Epidemic Threshold in Continuous-Time Evolving Networks

Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We introduce the {\em weak commutation} condition allowing the interpretation of annealed networks, activity-driven networks, and time scale separation into one formalism. Our work provides a coherent connection between discrete and continuous time representations applicable to realistic scenarios.Comment: 13 pages, 2 figure

Transport equations for chiral fermions to order \hbar and electroweak baryogenesis: Part I

This is the first in a series of two papers. We use the Schwinger-Keldysh formalism to derive semiclassical Boltzmann transport equations for massive chiral fermions and scalar particles. Our considerations include complex mass terms and mixing fermion and scalar fields, such that CP-violation is naturally included, rendering the equations particularly suitable for studies of baryogenesis at a first order electroweak phase transition. In part II we discuss the collision terms.Comment: 58 pages, 5 figures; earlier version broken up into two parts, Part II is hep-ph/0406140; accepted for publication in Annals of Physic

The Linear Model under Mixed Gaussian Inputs: Designing the Transfer Matrix

Suppose a linear model y = Hx + n, where inputs x, n are independent Gaussian mixtures. The problem is to design the transfer matrix H so as to minimize the mean square error (MSE) when estimating x from y. This problem has important applications, but faces at least three hurdles. Firstly, even for a fixed H, the minimum MSE (MMSE) has no analytical form. Secondly, the MMSE is generally not convex in H. Thirdly, derivatives of the MMSE w.r.t. H are hard to obtain. This paper casts the problem as a stochastic program and invokes gradient methods. The study is motivated by two applications in signal processing. One concerns the choice of error-reducing precoders; the other deals with selection of pilot matrices for channel estimation. In either setting, our numerical results indicate improved estimation accuracy - markedly better than those obtained by optimal design based on standard linear estimators. Some implications of the non-convexities of the MMSE are noteworthy, yet, to our knowledge, not well known. For example, there are cases in which more pilot power is detrimental for channel estimation. This paper explains why

Tehokas sisäänpäindeterministisiin automaatteihin perustuva Constraint Grammar -jäsennin

Proceeding volume: 14 (2011)Pappret conceptualizes parsning med Constraint Grammar på ett nytt sätt som en process med två viktiga representationer. En representation innehåller lokala tvetydighet och den andra sammanfattar egenskaperna hos den lokala tvetydighet klasser. Båda representationer manipuleras med ren finite-state metoder, men deras samtrafik är en ad hoc -tillämpning av rationella potensserier. Den nya tolkningen av parsning systemet har flera praktiska fördelar, bland annat det inåt deterministiska sättet att beräkna, representera och räkna om alla potentiella tillämpningar av reglerna i meningen.Paperi uudelleenkonseptualisoi Constraint Grammarin sellaisena viitekehyksenä, jossa säännöt tarkentavat paikallisen ambiguiteetin tiivistä esitysmuotoa samalla kun sääntöjen ehdot sovitetaan piirrevektoreita vasten, jotka esittävät tiivistetyjen esitysmuotojen summia. Molemmat näkökulmat monitulkintaisuuteen käsitellään käyttäen puhtaita (pure) äärellistilaisia operaatioita. Tiivis esitysmuoto kuvataan piirrevektoreihin rationaalisten potenssisarjojen avulla. Tämä yhteys ei ole yhtään vähemmän puhdas kuin aikaisemmin vallalla ollut tulkinta, jonka edellyttää että leksikaalisen transduktorin tuottama sanan luentajoukko maagisesti linearisoidaan merkatuksi luentojen peräkkäinasetteluksi, joka syötetään puhtaille (äärellistilaisille) transduktoreille. Esitetyllä lähestymistavalla on useita käytännöllisiä etuja: mm. sisäänpäin deterministinen tapa laskea, esittää ja ylläpitää kaikki mahdolliset kohdat, joissa säännöt voivat soveltua virkkeeseen.The paper reconceptualizes Constraint Grammar as a framework where the rules refine the compact representations of local ambiguity while the rule conditions are matched against a string of feature vectors that summarize the compact representations. Both views to the ambiguity are processed with pure finite-state operations. The compact representations are mapped to feature vectors with the aid of a rational power series. This magical interconnection is not less pure than a prevalent interpretation that requires that the reading set provided by a lexical transducer is magically linearized to a marked concatenation of readings given to pure transducers. The current approach has several practical benefits, including the inward deterministic way to compute, represent and maintain all the applications of the rules in the sentence.Peer reviewe