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.

Toxic phytoplankton response to warming in two Mediterranean bays of the Ebro Delta

The analysis of the phytoplankton and environmental parameters of the time series in Alfacs and Fangar bays (north western Mediterranean) from 1990 to 2009 shows some trends. There is an increase in the average water column temperature, 0.11, 0.01, 0.80 and 0.23 ºC for spring, summer, fall and winter respectively in Alfacs Bay and 1.76, 0.71, 1.33, 0.89 ºC for spring, summer, fall and winter in Fangar Bay. The trends in phytoplankton populations show a shift in the timing of occurrence of Karlodinium spp. blooms and an increase of the Pseudo-nitzschia spp. abundances. There is a lack of correlation between the average seasonal temperatures and the toxic phytoplankton abundances.

Discovering similarities in the time use patterns of the Spanish Autonomous Communities by Fuzzy techniques

In 2000 the European Statistical Office published the guidelines for developing theHarmonized European Time Use Surveys system. Under such a unified framework,the first Time Use Survey of national scope was conducted in Spain during 2002–03. The aim of these surveys is to understand human behavior and the lifestyle ofpeople. Time allocation data are of compositional nature in origin, that is, they aresubject to non-negativity and constant-sum constraints. Thus, standard multivariatetechniques cannot be directly applied to analyze them. The goal of this work is toidentify homogeneous Spanish Autonomous Communities with regard to the typicalactivity pattern of their respective populations. To this end, fuzzy clustering approachis followed. Rather than the hard partitioning of classical clustering, where objects areallocated to only a single group, fuzzy method identify overlapping groups of objectsby allowing them to belong to more than one group. Concretely, the probabilistic fuzzyc-means algorithm is conveniently adapted to deal with the Spanish Time Use Surveymicrodata. As a result, a map distinguishing Autonomous Communities with similaractivity pattern is drawn.Key words: Time use data, Fuzzy clustering; FCM; simplex space; Aitchison distance

Theoretical study of the second-order vibrational Stark effect

The behaviour of the harmonic infrared frequency of diatomic molecules subjected to moderate static uniform electric fields is analysed. The potential energy expression has been developed as a function of a static uniform electric field, which brings about a formulation describing the frequency versus field strength curve. With the help of the first and second derivatives of the expressions obtained, which correspond to the first- and second-order Stark effects, it was possible to find the maxima of the frequency versus field strength curves for a series of molecules using a Newton-Raphson search. A method is proposed which requires only the calculation of a few energy derivatives at a particular value of the field strength. At the same time, the expression for the dependence of the interatomic distance on the electric field strength is derived and the minimum of this curve is found for the same species. Derived expressions and numerical results are discussed and compared with other studi

Time-Delayed Theory of the Neolithic Transition in Europe

The classical wave-of-advance model of the neolithic transition (i.e., the shift from hunter-gatherer to agricultural economies) is based on Fisher's reaction-diffusion equation. Here we present an extension of Einstein's approach to Fickian diffusion, incorporating reaction terms. On this basis we show that second-order terms in the reaction-diffusion equation, which have been neglected up to now, are not in fact negligible but can lead to important corrections. The resulting time-delayed model agrees quite well with observations

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

Initial convergence of the perturbation series expansion for vibrational nonlinear optical (NLO) properties was analyzed. The zero-point vibrational average (ZPVA) was obtained through first-order in mechanical plus electrical anharmonicity. Results indicated that higher-order terms in electrical and mechanical anharmonicity can make substantial contributions to the pure vibrational polarizibility of typical NLO molecules

A polynomial algorithm for special case of the one-machine scheduling problem with time-lags

The standard one-machine scheduling problem consists in schedulinga set of jobs in one machine which can handle only one job at atime, minimizing the maximum lateness. Each job is available forprocessing at its release date, requires a known processing timeand after finishing the processing, it is delivery after a certaintime. There also can exists precedence constraints between pairsof jobs, requiring that the first jobs must be completed beforethe second job can start. An extension of this problem consistsin assigning a time interval between the processing of the jobsassociated with the precedence constrains, known by finish-starttime-lags. In presence of this constraints, the problem is NP-hardeven if preemption is allowed. In this work, we consider a specialcase of the one-machine preemption scheduling problem with time-lags, where the time-lags have a chain form, and propose apolynomial algorithm to solve it. The algorithm consist in apolynomial number of calls of the preemption version of the LongestTail Heuristic. One of the applicability of the method is to obtainlower bounds for NP-hard one-machine and job-shop schedulingproblems. We present some computational results of thisapplication, followed by some conclusions.

A consistency test of the time trade-off

This paper tests the internal consistency of time trade-off utilities.We find significant violations of consistency in the direction predictedby loss aversion. The violations disappear for higher gauge durations.We show that loss aversion can also explain that for short gaugedurations time trade-off utilities exceed standard gamble utilities. Ourresults suggest that time trade-off measurements that use relativelyshort gauge durations, like the widely used EuroQol algorithm(Dolan 1997), are affected by loss aversion and lead to utilities thatare too high.

A test of the predictive validity of non-linear QALY models using time trade-off utilities

This paper presents a test of the predictive validity of various classes ofQALY models (i.e., linear, power and exponential models). We first estimatedTTO utilities for 43 EQ-5D chronic health states and next these states wereembedded in health profiles. The chronic TTO utilities were then used topredict the responses to TTO questions with health profiles. We find that thepower QALY model clearly outperforms linear and exponential QALY models.Optimal power coefficient is 0.65. Our results suggest that TTO-based QALYcalculations may be biased. This bias can be avoided using a power QALY model.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

Life-time redistribution effects of the Spanish public pension system

The paper analyses the inter and intragenerational redistribution effects ofthe public pensions system in Spain. This is achieved by first comparing the expected present value of life-time income transfers (PVT) and internalrates of return (IRR) of different population cohorts. Secondly, we study the intragenerational aspects of the Spanish public pensions by calculating PVTs the IRRs for workers of different categories, grouped by earnings, gender and marital status.The results obtained show the nature of the important intergenerational effects of the Social Security System in Spain. The oldest 1935 cohort clearlybenefits in relation to the youngest 1965 cohort. This is basically due to thegap between current wages and the contribution bases established in the 60s and 70s in Spain during the early stages of the Social Security System, and to the worsening shortfall in Social Security funding, combined with the longer of life expectancy.In addition, intragenerational effects exist by income levels. For contributors who pay between the minimum and the maximum allowable contribution bases, net transfers and rates of return are higher in actuarial terms for high incomecontributors. The social security `dealï is again more profitable for highincome individuals since they contribute at the maximum basis, with respect tolow income contributors at the minimum basis. This is due to the late entry and a higher survival rate for high income contributors.The system tends to favour women, given that they generally live longer than men and this factor is only partially offset by their lower wages. Married males, given the fact that they have longer life expectancy and leave a pension to their spouse, obtain higher present net transfers too than do single contributors.We close the paper with some comments on the slight impact and moderate effects of proposals for Social Security reform and on how these may change the previously observed redistribution effects.

Assessing the wellbeing of the Spanish elderly

In this paper we use a variety of data sources, both micro and macro, time series, crosssection, and panel data to provide an empirical evaluation of the current level of economicwellbeing of the Spanish elderly, and of its determinants. We focus, in particular on the role played by the pension system and its generosity in terms of minimum pension supplements and non-contributive pensions. In an IV context, we find that actual Social Security benefits contribute substantially to explain income and consumption poverty levels and trends of low income and consumption percentiles. Thus we offer support to previous evidence for Spain emphasizing the role of minimum benefit policies.

Death and resurrection of the human IRGM gene

Immunity-related GTPases (IRG) play an important role in defense against intracellular pathogens. One member of this gene family in humans, IRGM, has been recently implicated as a risk factor for Crohn's disease. We analyzed the detailed structure of this gene family among primates and showed that most of the IRG gene cluster was deleted early in primate evolution, after the divergence of the anthropoids from prosimians ( about 50 million years ago). Comparative sequence analysis of New World and Old World monkey species shows that the single-copy IRGM gene became pseudogenized as a result of an Alu retrotransposition event in the anthropoid common ancestor that disrupted the open reading frame (ORF). We find that the ORF was reestablished as a part of a polymorphic stop codon in the common ancestor of humans and great apes. Expression analysis suggests that this change occurred in conjunction with the insertion of an endogenous retrovirus, which altered the transcription initiation, splicing, and expression profile of IRGM. These data argue that the gene became pseudogenized and was then resurrected through a series of complex structural events and suggest remarkable functional plasticity where alleles experience diverse evolutionary pressures over time. Such dynamism in structure and evolution may be critical for a gene family locked in an arms race with an ever-changing repertoire of intracellular parasites.

Estimation of the extreme flash flood evolution in Barcelona county from 1351 to 2005

Every year, flash floods cause economic losses and major problems for undertaking daily activity in the Catalonia region (NE Spain). Sometimes catastrophic damage and casualties occur. When a long term analysis of floods is undertaken, a question arises regarding the changing role of the vulnerability and the hazard in risk evolution. This paper sets out to give some information to deal with this question, on the basis of analysis of all the floods that have occurred in Barcelona county (Catalonia) since the 14th century, as well as the flooded area, urban evolution, impacts and the weather conditions for any of most severe events. With this objective, the identification and classification of historical floods, and characterisation of flash-floods among these, have been undertaken. Besides this, the main meteorological factors associated with recent flash floods in this city and neighbouring regions are well-known. On the other hand, the identification of rainfall trends that could explain the historical evolution of flood hazard occurrence in this city has been analysed. Finally, identification of the influence of urban development on the vulnerability to floods has been carried out. Barcelona city has been selected thanks to its long continuous data series (daily rainfall data series, since 1854; one of the longest rainfall rate series of Europe, since 1921) and for the accurate historical archive information that is available (since the Roman Empire for the urban evolution). The evolution of flood occurrence shows the existence of oscillations in the earlier and later modern-age periods that can be attributed to climatic variability, evolution of the perception threshold and changes in vulnerability. A great increase of vulnerability can be assumed for the period 1850¿1900. The analysis of the time evolution for the Barcelona rainfall series (1854¿2000) shows that no trend exists, although, due to changes in urban planning, flash-floods impact has altered over this time. The number of catastrophic flash floods has diminished, although the extraordinary ones have increased.