Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for [formula]

"Vegeu el resum a l'inici del document del fitxer adjunt."

Forecasting volatility using a continuous time model

This paper evaluates the forecasting performance of a continuous stochastic volatility model with two factors of volatility (SV2F) and compares it to those of GARCH and ARFIMA models. The empirical results show that the volatility forecasting ability of the SV2F model is better than that of the GARCH and ARFIMA models, especially when volatility seems to change pattern. We use ex-post volatility as a proxy of the realized volatility obtained from intraday data and the forecasts from the SV2F are calculated using the reprojection technique proposed by Gallant and Tauchen (1998).

Commuters' valuation of travel time variability in Barcelona

The value given by commuters to the variability of travel times is empirically analysed using stated preference data from Barcelona (Spain). Respondents are asked to choose between alternatives that differ in terms of cost, average travel time, variability of travel times and departure time. Different specifications of a scheduling choice model are used to measure the influence of various socioeconomic characteristics. Our results show that travel time variability.

Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Planificación de aplicaciones best-effort y soft real-time en NOWs

La aparición de nuevos tipos de aplicaciones, como vídeo bajo demanda, realidad virtual y videoconferencias entre otras, caracterizadas por la necesidad de cumplir sus deadlines. Este tipo de aplicaciones, han sido denominadas en la literatura aplicaciones soft-real time (SRT) periódicas. Este trabajo se centra en el problema de la planificación temporal de este nuevo tipo de aplicaciones en clusters no dedicados.

Co-movements between US and UK stock prices: the roles of macroeconomic information and time-series varying conditional correlations

This paper provides evidence on the sources of co-movement in monthly US and UK stock price movements by investigating the role of macroeconomic and financial variables in a bivariate system with time-varying conditional correlations. Crosscountry communality in response is uncovered, with changes in the US Federal Funds rate, UK bond yields and oil prices having similar negative effects in both markets. Other variables also play a role, especially for the UK market. These effects do not, however, explain the marked increase in cross-market correlations observed from around 2000, which we attribute to time variation in the correlations of shocks to these markets. A regime-switching smooth transition model captures this time variation well and shows the correlations increase dramatically around 1999-2000. JEL classifications: C32, C51, G15 Keywords: international stock returns, DCC-GARCH model, smooth transition conditional correlation GARCH model, model evaluation.

Real time GPS precise positioning of LEO satellites

Report for the scientific sojourn at the German Aerospace Center (DLR) , Germany, during June and July 2006. The main objective of the two months stay has been to apply the techniques of LEO (Low Earth Orbiters) satellites GPS navigation which DLR currently uses in real time navigation. These techniques comprise the use of a dynamical model which takes into account the precise earth gravity field and models to account for the effects which perturb the LEO’s motion (such as drag forces due to earth’s atmosphere, solar pressure, due to the solar radiation impacting on the spacecraft, luni-solar gravity, due to the perturbation of the gravity field for the sun and moon attraction, and tidal forces, due to the ocean and solid tides). A high parameterized software was produced in the first part of work, which has been used to asses which accuracy could be reached exploring different models and complexities. The objective was to study the accuracy vs complexity, taking into account that LEOs at different heights have different behaviors. In this frame, several LEOs have been selected in a wide range of altitudes, and several approaches with different complexity have been chosen. Complexity is a very important issue, because processors onboard spacecrafts have very limited computing and memory resources, so it is mandatory to keep the algorithms simple enough to let the satellite process it by itself.

Sistema d'autenticació one-time password (OTP) per a mòbils

Aquest projecte consisteix en fer l’anàlisi, disseny i implementació d'un sistema d'autenticació a través de contrasenyes d’un sol ús (One Time Password ‐OTP‐) per a dispositius mòbils. Per evitar l’ús de contrasenyes estàtiques farem una aplicació per a telèfons mòbils capaç de generar contrasenyes aleatòries gràcies a uns paràmetres previs, així com de poder tenir un registre dels serveis on poden ser utilitzades. Partirem d’un protocol repte/resposta on l’usuari interactuarà amb el seu telèfon mòbil i un ordinador personal amb una connexió a Internet. Podrà registrar‐se i, introduint certes dades al mòbil que li proporciona el servidor, podrà fer el procés d’autenticar‐se per poder accedir a zones restringides del servei.

A first attempt of geographically-distributed Multi-scale integrated analysis of societal and ecosystem metabolism (MuSIASEM): mapping human time and energy throughput in metropolitan Barcelona

This study presents a first attempt to extend the “Multi-scale integrated analysis of societal and ecosystem metabolism (MuSIASEM)” approach to a spatial dimension using GIS techniques in the Metropolitan area of Barcelona. We use a combination of census and commercial databases along with a detailed land cover map to create a layer of Common Geographic Units that we populate with the local values of human time spent in different activities according to MuSIASEM hierarchical typology. In this way, we mapped the hours of available human time, in regards to the working hours spent in different locations, putting in evidence the gradients in spatial density between the residential location of workers (generating the work supply) and the places where the working hours are actually taking place. We found a strong three-modal pattern of clumps of areas with different combinations of values of time spent on household activities and on paid work. We also measured and mapped spatial segregation between these two activities and put forward the conjecture that this segregation increases with higher energy throughput, as the size of the functional units must be able to cope with the flow of exosomatic energy. Finally, we discuss the effectiveness of the approach by comparing our geographic representation of exosomatic throughput to the one issued from conventional methods.

Scene classifier for real time road detection

L’objectiu principal del projecte és el de classificar escenes de carretera en funció del contingut de les imatges per així poder fer un desglossament sobre quin tipus de situació tenim en el moment. És important que fixem els paràmetres necessaris en funció de l’escenari en què ens trobem per tal de treure el màxim rendiment possible a cada un dels algoritmes. La seva funcionalitat doncs, ha de ser la d’avís i suport davant els diferents escenaris de conducció. És a dir, el resultat final ha de contenir un algoritme o aplicació capaç de classificar les imatges d’entrada en diferents tipus amb la màxima eficiència espacial i temporal possible. L’algoritme haurà de classificar les imatges en diferents escenaris. Els algoritmes hauran de ser parametritzables i fàcilment manejables per l’usuari. L’eina utilitzada per aconseguir aquests objectius serà el MATLAB amb les toolboxs de visió i xarxes neuronals instal·lades.

A mixed splicing procedure for economic time series

This note develops a flexible methodology for splicing economic time series that avoids the extreme assumptions implicit in the procedures most commonly used in the literature. It allows the user to split the required correction to the older of the series being linked between its levels and growth rates on the basis what he knows or conjectures about the persistence of the factors that account for the discrepancy between the two series that emerges at their linking point. The time profile of the correction is derived from the assumption that the error in the older series reflects the inadequate coverage of emerging sectors or activities that grow faster than the aggregate.

Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

The Part-time pay penalty in a segmented labor market

This paper is the first to examine the implications of switching to PT work for women's subsequent earnings trajectories, distinguishing by their type of contract: permanent or fixedterm. Using a rich longitudinal Spanish data set from Social Security records of over 76,000 prime-aged women strongly attached to the Spanish labor market, we find that PT work aggravates the segmentation of the labor market insofar there is a PT pay penalty and this penalty is larger and more persistent in the case of women with fixed-term contracts. The paper discusses problems arising in empirical estimation (including a problem not discussed in the literature up to now: the differential measurement error of the LHS variable by PT status), and how to address them. It concludes with policy implications relevant for Continental Europe and its dual structure of employment protection.