Structured and unstructured continuous models for Wolbachia infections

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.

An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

Hypoxia and vasculature in models of lung cancer: implications for targeted therapeutics

Estudi realitzat a partir d’una estada a la Stanford University School of Medicine. Division of Radiation Oncology, Estats Units, entre 2010 i 2012. Durant els dos anys de beca postdoctoral he estat treballant en dos projectes diferents. En primer lloc, i com a continuació d'estudis previs del grup, volíem estudiar la causa de les diferències en nivells d'hipòxia que havíem observat en models de càncer de pulmó. La nostra hipòtesi es basava en el fet que aquestes diferències es devien a la funcionalitat de la vasculatura. Vam utilitzar dos models preclínics: un en què els tumors es formaven espontàniament als pulmons i l'altre on nosaltres injectàvem les cèl•lules de manera subcutània. Vam utilitzar tècniques com la ressonància magnètica dinàmica amb agent de contrast (DCE-MRI) i l'assaig de perfusió amb el Hoeschst 33342 i ambdues van demostrar que la funcionalitat de la vasculatura dels tumors espontanis era molt més elevada comparada amb la dels tumors subcutanis. D'aquest estudi, en podem concloure que les diferències en els nivells d'hipòxia en els diferents models tumorals de càncer de pulmó podrien ser deguts a la variació en la formació i funcionalitat de la vasculatura. Per tant, la selecció de models preclínics és essencial, tant pels estudi d'hipòxia i angiogènesi, com per a teràpies adreçades a aquests fenòmens. L'altre projecte que he estat desenvolupant es basa en l'estudi de la radioteràpia i els seus possibles efectes a l’hora de potenciar l'autoregeneració del tumor a partir de les cèl•lules tumorals circulants (CTC). Aquest efecte s'ha descrit en alguns models tumorals preclínics. Per tal de dur a terme els nostres estudis, vam utilitzar una línia tumoral de càncer de mama de ratolí, marcada permanentment amb el gen de Photinus pyralis o sense marcar i vam fer estudis in vitro i in vivo. Ambdós estudis han demostrat que la radiació tumoral promou la invasió cel•lular i l'autoregeneració del tumor per CTC. Aquest descobriment s'ha de considerar dins d'un context de radioteràpia clínica per tal d'aconseguir el millor tractament en pacients amb nivells de CTC elevats.

Money and prices in models of bounded rationality in high inflation economies

This paper studies the short run correlation of inflation and money growth. We study whether a model of learning can do better than a model of rational expectations, we focus our study on countries of high inflation. We take the money process as an exogenous variable, estimated from the data through a switching regime process. We findthat the rational expectations model and the model of learning both offer very good explanations for the joint behavior of money and prices.

Evaluating solutions to process, view and listen mathematical formula within an accessible context

Proves de conversió de fòrmules matemàtiques des d'editors de text ofimàtics i des de Làtex. Visionat en HTML i MathML. El millor resultat s'aconsegueix amb MSWord+MathType i IE+MathPlayer.

Language extinction and linguistic fronts

Language diversity has become greatly endangered in the past centuries owing to processes of language shift from indigenous languages to other languages that are seen as socially and economically more advantageous, resulting in the death or doom of minority languages. In this paper, we define a new language competition model that can describe the historical decline of minority languages in competition with more advantageous languages. We then implement this non-spatial model as an interaction term in a reactiondiffusion system to model the evolution of the two competing languages. We use the results to estimate the speed at which the more advantageous language spreads geographically, resulting in the shrinkage of the area of dominance of the minority language. We compare the results from our model with the observed retreat in the area of influence of the Welsh language in the UK, obtaining a good agreement between the model and the observed data

Effectiveness of early detection on breast cancer mortality reduction in Catalonia (Spain)

Background: At present, it is complicated to use screening trials to determine the optimal age intervals and periodicities of breast cancer early detection. Mathematical models are an alternative that has been widely used. The aim of this study was to estimate the effect of different breast cancer early detection strategies in Catalonia (Spain), in terms of breast cancer mortality reduction (MR) and years of life gained (YLG), using the stochastic models developed by Lee and Zelen (LZ). Methods: We used the LZ model to estimate the cumulative probability of death for a cohort exposed to different screening strategies after T years of follow-up. We also obtained the cumulative probability of death for a cohort with no screening. These probabilities were used to estimate the possible breast cancer MR and YLG by age, period and cohort of birth. The inputs of the model were: incidence of, mortality from and survival after breast cancer, mortality from other causes, distribution of breast cancer stages at diagnosis and sensitivity of mammography. The outputs were relative breast cancer MR and YLG. Results: Relative breast cancer MR varied from 20% for biennial exams in the 50 to 69 age interval to 30% for annual exams in the 40 to 74 age interval. When strategies differ in periodicity but not in the age interval of exams, biennial screening achieved almost 80% of the annual screening MR. In contrast to MR, the effect on YLG of extending screening from 69 to 74 years of age was smaller than the effect of extending the screening from 50 to 45 or 40 years. Conclusion: In this study we have obtained a measure of the effect of breast cancer screening in terms of mortality and years of life gained. The Lee and Zelen mathematical models have been very useful for assessing the impact of different modalities of early detection on MR and YLG in Catalonia (Spain).

Study and implementation of some quantitative trading models

Quantitative or algorithmic trading is the automatization of investments decisions obeying a fixed or dynamic sets of rules to determine trading orders. It has increasingly made its way up to 70% of the trading volume of one of the biggest financial markets such as the New York Stock Exchange (NYSE). However, there is not a signi cant amount of academic literature devoted to it due to the private nature of investment banks and hedge funds. This projects aims to review the literature and discuss the models available in a subject that publications are scarce and infrequently. We review the basic and fundamental mathematical concepts needed for modeling financial markets such as: stochastic processes, stochastic integration and basic models for prices and spreads dynamics necessary for building quantitative strategies. We also contrast these models with real market data with minutely sampling frequency from the Dow Jones Industrial Average (DJIA). Quantitative strategies try to exploit two types of behavior: trend following or mean reversion. The former is grouped in the so-called technical models and the later in the so-called pairs trading. Technical models have been discarded by financial theoreticians but we show that they can be properly cast into a well defined scientific predictor if the signal generated by them pass the test of being a Markov time. That is, we can tell if the signal has occurred or not by examining the information up to the current time; or more technically, if the event is F_t-measurable. On the other hand the concept of pairs trading or market neutral strategy is fairly simple. However it can be cast in a variety of mathematical models ranging from a method based on a simple euclidean distance, in a co-integration framework or involving stochastic differential equations such as the well-known Ornstein-Uhlenbeck mean reversal ODE and its variations. A model for forecasting any economic or financial magnitude could be properly defined with scientific rigor but it could also lack of any economical value and be considered useless from a practical point of view. This is why this project could not be complete without a backtesting of the mentioned strategies. Conducting a useful and realistic backtesting is by no means a trivial exercise since the \laws" that govern financial markets are constantly evolving in time. This is the reason because we make emphasis in the calibration process of the strategies' parameters to adapt the given market conditions. We find out that the parameters from technical models are more volatile than their counterpart form market neutral strategies and calibration must be done in a high-frequency sampling manner to constantly track the currently market situation. As a whole, the goal of this project is to provide an overview of a quantitative approach to investment reviewing basic strategies and illustrating them by means of a back-testing with real financial market data. The sources of the data used in this project are Bloomberg for intraday time series and Yahoo! for daily prices. All numeric computations and graphics used and shown in this project were implemented in MATLAB^R scratch from scratch as a part of this thesis. No other mathematical or statistical software was used.

A measure of stability as a criterion for the verification and analysis of simulation models

The aim of this study is to define a new statistic, PVL, based on the relative distance between the likelihood associated with the simulation replications and the likelihood of the conceptual model. Our results coming from several simulation experiments of a clinical trial show that the PVL statistic range can be a good measure of stability to establish when a computational model verifies the underlying conceptual model. PVL improves also the analysis of simulation replications because only one statistic is associated with all the simulation replications. As well it presents several verification scenarios, obtained by altering the simulation model, that show the usefulness of PVL. Further simulation experiments suggest that a 0 to 20 % range may define adequate limits for the verification problem, if considered from the viewpoint of an equivalence test.

Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.

Technology, business models and network structure in the airline industry

Network airlines have been increasingly focusing their operations on hub airports through the exploitation of connecting traffic, allowing them to take advantage of economies of traffic density, which are unequivocal in the airline industry. Less attention has been devoted to airlines? decisions on point-to-point thin routes, which could be served using different aircraft technologies and different business models. This paper examines, both theoretically and empirically, the impact on airlines ?networks of the two major innovations in the airline industry in the last two decades: the regional jet technology and the low-cost business model. We show that, under certain circumstances, direct services on point-to-point thin routes can be viable and thus airlines may be interested in deviating passengers out of the hub.

Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states

Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter.

Technology, business models and network structure in the airline industry

Network airlines have been increasingly focusing their operations on hub airports through the exploitation of connecting traffic, allowing them to take advantage of economies of traffic density, which are unequivocal in the airline industry. Less attention has been devoted to airlines' decisions on point-to-point thin routes, which could be served using different aircraft technologies and different business models. This paper examines, both theoretically and empirically, the impact on airlines' networks of the two major innovations in the airline industry in the last two decades: the regional jet technology and the low-cost business model. We show that, under certain circumstances, direct services on point-to-point thin routes can be viable and thus airlines may be interested in deviating passengers out of the hub. Keywords: regional jet technology; low-cost business model; point-to-point network; hub-and-spoke network JEL Classi…fication Numbers: L13; L2; L93

Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance

In this paper, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non-homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

Analysis and Monte Carlo simulations of a model for the spread of infectious diseases in heterogeneous metapopulations

We present a study of the continuous-time equations governing the dynamics of a susceptible infected-susceptible model on heterogeneous metapopulations. These equations have been recently proposed as an alternative formulation for the spread of infectious diseases in metapopulations in a continuous-time framework. Individual-based Monte Carlo simulations of epidemic spread in uncorrelated networks are also performed revealing a good agreement with analytical predictions under the assumption of simultaneous transmission or recovery and migration processes