Multiple target tracking using random sets

This paper presents several algorithms for joint estimation of the target number and state in a time-varying scenario. Building on the results presented in [1], which considers estimation of the target number only, we assume that not only the target number, but also their state evolution must be estimated. In this context, we extend to this new scenario the Rao-Blackwellization procedure of [1] to compute Bayes recursions, thus defining reduced-complexity solutions for the multi-target set estimator. A performance assessmentis finally given both in terms of Circular Position Error Probability - aimed at evaluating the accuracy of the estimated track - and in terms of Cardinality Error Probability, aimed at evaluating the reliability of the target number estimates.

Monetary policy with signal extraction from the bond market

Monetary policy is conducted in an environment of uncertainty. This paper sets upa model where the central bank uses real-time data from the bond market togetherwith standard macroeconomic indicators to estimate the current state of theeconomy more efficiently, while taking into account that its own actions influencewhat it observes. The timeliness of bond market data allows for quicker responsesof monetary policy to disturbances compared to the case when the central bankhas to rely solely on collected aggregate data. The information content of theterm structure creates a link between the bond market and the macroeconomythat is novel to the literature. To quantify the importance of the bond market asa source of information, the model is estimated on data for the United Statesand Australia using Bayesian methods. The empirical exercise suggests that thereis some information in the US term structure that helps the Federal Reserve toidentify shocks to the economy on a timely basis. Australian bond prices seemto be less informative than their US counterparts, perhaps because Australia is arelatively small and open economy.

Lipschitz harmonic capacity and Bilipschitz images of cantor sets

For bilipschitz images of Cantor sets in Rd we estimate the Lipschitz harmonic capacity and show this capacity is invariant under bilipschitz homeomorphisms.

Maximal operators and differentiation theorems for sparse sets

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Automatic DVB signal analyser

El problema de controlar les emissions de televisió digital a tota Europa pel desenvolupament de receptors robustos i fiables és cada vegada més significant, per això, sorgeix la necessitat d’automatitzar el procés d’anàlisi i control d’aquests senyals. Aquest projecte presenta el desenvolupament software d’una aplicació que vol solucionar una part d’aquest problema. L’aplicació s’encarrega d’analitzar, gestionar i capturar senyals de televisió digital. Aquest document fa una introducció a la matèria central que és la televisió digital i la informació que porten els senyals de televisió, concretament, la que es refereix a l’estàndard "Digital Video Broadcasting". A continuació d’aquesta part, l’escrit es concentra en l’explicació i descripció de les funcionalitats que necessita cobrir l'aplicació, així com introduir i explicar cada etapa d’un procés de desenvolupament software. Finalment, es resumeixen els avantatges de la creació d’aquest programa per l’automatització de l’anàlisi de senyal digital partint d’una optimització de recursos.

Calderón-Zygmund capacities and Wolff potentials on Cantor sets

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Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

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GNSS signal detection based on first-order absolute statistics

Aquest projecte es centra principalment en el detector no coherent d’un GPS. Per tal de caracteritzar el procés de detecció d’un receptor, es necessita conèixer l’estadística implicada. Pel cas dels detectors no coherents convencionals, l’estadística de segon ordre intervé plenament. Les prestacions que ens dóna l’estadística de segon ordre, plasmada en la ROC, són prou bons tot i que en diferents situacions poden no ser els millors. Aquest projecte intenta reproduir el procés de detecció mitjançant l’estadística de primer ordre com a alternativa a la ja coneguda i implementada estadística de segon ordre. Per tal d’aconseguir-ho, s’usen expressions basades en el Teorema Central del Límit i de les sèries Edgeworth com a bones aproximacions. Finalment, tant l’estadística convencional com l’estadística proposada són comparades, en termes de la ROC, per tal de determinar quin detector no coherent ofereix millor prestacions en cada situació.

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.

Internal test sets studies in a group of antimalarials

Topological indices have been applied to build QSAR models for a set of 20 antimalarial cyclic peroxy cetals. In order to evaluate the reliability of the proposed linear models leave-n-out and Internal Test Sets (ITS) approaches have been considered. The proposed procedure resulted in a robust and consensued prediction equation and here it is shown why it is superior to the employed standard cross-validation algorithms involving multilinear regression models

Involvement of the extracellular signal-regulated kinase cascade for cocaine-rewarding properties

A central feature of drugs of abuse is to induce gene expression in discrete brain structures that are critically involved in behavioral responses related to addictive processes. Although extracellular signal-regulated kinase (ERK) has been implicated in several neurobiological processes, including neuronal plasticity, its role in drug addiction remains poorly understood. This study was designed to analyze the activation of ERK by cocaine, its involvement in cocaine-induced early and long-term behavioral effects, as well as in gene expression. We show, by immunocytochemistry, that acute cocaine administration activates ERK throughout the striatum, rapidly but transiently. This activation was blocked when SCH 23390 [a specific dopamine (DA)-D1 antagonist] but not raclopride (a DA-D2 antagonist) was injected before cocaine. Glutamate receptors of NMDA subtypes also participated in ERK activation, as shown after injection of the NMDA receptor antagonist MK 801. The systemic injection of SL327, a selective inhibitor of the ERK kinase MEK, before cocaine, abolished the cocaine-induced ERK activation and decreased cocaine-induced hyperlocomotion, indicating a role of this pathway in events underlying early behavioral responses. Moreover, the rewarding effects of cocaine were abolished by SL327 in the place-conditioning paradigm. Because SL327 antagonized cocaine-induced c-fos expression and Elk-1 hyperphosphorylation, we suggest that the ERK intracellular signaling cascade is also involved in the prime burst of gene expression underlying long-term behavioral changes induced by cocaine. Altogether, these results reveal a new mechanism to explain behavioral responses of cocaine related to its addictive properties.

Minimizing recombinations in consensus networks for phylogeographic studies

Background: We address the problem of studying recombinational variations in (human) populations. In this paper, our focus is on one computational aspect of the general task: Given two networks G1 and G2, with both mutation and recombination events, defined on overlapping sets of extant units the objective is to compute a consensus network G3 with minimum number of additional recombinations. We describe a polynomial time algorithm with a guarantee that the number of computed new recombination events is within ϵ = sz(G1, G2) (function sz is a well-behaved function of the sizes and topologies of G1 and G2) of the optimal number of recombinations. To date, this is the best known result for a network consensus problem.Results: Although the network consensus problem can be applied to a variety of domains, here we focus on structure of human populations. With our preliminary analysis on a segment of the human Chromosome X data we are able to infer ancient recombinations, population-specific recombinations and more, which also support the widely accepted 'Out of Africa' model. These results have been verified independently using traditional manual procedures. To the best of our knowledge, this is the first recombinations-based characterization of human populations. Conclusion: We show that our mathematical model identifies recombination spots in the individual haplotypes; the aggregate of these spots over a set of haplotypes defines a recombinational landscape that has enough signal to detect continental as well as population divide based on a short segment of Chromosome X. In particular, we are able to infer ancient recombinations, population-specific recombinations and more, which also support the widely accepted 'Out of Africa' model. The agreement with mutation-based analysis can be viewed as an indirect validation of our results and the model. Since the model in principle gives us more information embedded in the networks, in our future work, we plan to investigate more non-traditional questions via these structures computed by our methodology.

Interplay of spectral efficiency, power and doppler spectrum for reference-signal-assisted wireless communication

Expressions relating spectral efficiency, power, and Doppler spectrum, are derived for Rayleigh-faded wireless channels with Gaussian signal transmission. No side information on the state of the channel is assumed at the receiver. Rather, periodic reference signals are postulated in accordance with the functioning of most wireless systems. The analysis relies on a well-established lower bound, generally tight and asymptotically exact at low SNR. In contrast with most previous studies, which relied on block-fading channel models, a continuous-fading model is adopted. This embeds the Doppler spectrum directly in the derived expressions, imbuing them with practical significance. Closed-form relationships are obtained for the popular Clarke-Jakes spectrum and informative expansions, valid for arbitrary spectra, are found for the low- and high-power regimes. While the paper focuses on scalar channels, the extension to multiantenna settings is also discussed.

Optimum power allocation for multiuser OFDM with arbitrary signal constellations

This paper formulates power allocation policies that maximize the region of mutual informationsachievable in multiuser downlink OFDM channels. Arbitrary partitioning ofthe available tones among users and arbitrary modulation formats, possibly different forevery user, are considered. Two distinct policies are derived, respectively for slow fadingchannels tracked instantaneously by the transmitter and for fast fading channels knownonly statistically thereby. With instantaneous channel tracking, the solution adopts theform of a multiuser mercury/waterfilling procedure that generalizes the single-user mercury/waterfilling introduced in [1, 2]. With only statistical channel information, in contrast,the mercury/waterfilling interpretation is lost. For both policies, a number of limitingregimes are explored and illustrative examples are provided.

Spectral efficiency in reference-signal-assisted low-power wireless communication

Expressions relating spectral efficiency, power and Doppler spectrum are derived for low-power Rayleighfaded wireless channels with proper complex signaling. Noside information on the state of the channel is assumed at the receiver. Rather, periodic reference signals are postulated inaccordance with the functioning of most wireless systems. In contrast with most previous studies, which relied on block-fading channel models, a continuous-fading model is adopted. This embeds the Doppler spectrum directly in thederived expressions thereby imbuing them with practical significance.