An algorithm for semi-infinite polynomial optimization

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

Non-characteristic half-lives in radioactive decay

Half-lives of radionuclides span more than 50 orders of magnitude. We characterize the probability distribution of this broad-range data set at the same time that explore a method for fitting power-laws and testing goodness-of-fit. It is found that the procedure proposed recently by Clauset et al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the power-law hypothesis even for power-law synthetic data. In contrast, we establish the existence of a power-law exponent with a value around 1.1 for the half-life density, which can be explained by the sharp relationship between decay rate and released energy, for different disintegration types. For the case of alpha emission, this relationship constitutes an original mechanism of power-law generation.

Krein's strings whose spectral functions are of polynomial growth

In case Krein's strings with spectral functions of polynomial growth a necessary and su fficient condition for the Krein's correspondence to be continuous is given.

Bernstein's problem on weighted polynomial approximation

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis].

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.

Adaptive sequence evolution in a color gene involved in the formation of the characteristic egg-dummies of male haplochromine cichlid fishes.

BACKGROUND: The exceptionally diverse species flocks of cichlid fishes in East Africa are prime examples of parallel adaptive radiations. About 80% of East Africa's more than 1 800 endemic cichlid species, and all species of the flocks of Lakes Victoria and Malawi, belong to a particularly rapidly evolving lineage, the haplochromines. One characteristic feature of the haplochromines is their possession of egg-dummies on the males' anal fins. These egg-spots mimic real eggs and play an important role in the mating system of these maternal mouthbrooding fish. RESULTS: Here, we show that the egg-spots of haplochromines are made up of yellow pigment cells, xanthophores, and that a gene coding for a type III receptor tyrosine kinase, colony-stimulating factor 1 receptor a (csf1ra), is expressed in egg-spot tissue. Molecular evolutionary analyses reveal that the extracellular ligand-binding and receptor-interacting domain of csf1ra underwent adaptive sequence evolution in the ancestral lineage of the haplochromines, coinciding with the emergence of egg-dummies. We also find that csf1ra is expressed in the egg-dummies of a distantly related cichlid species, the ectodine cichlid Ophthalmotilapia ventralis, in which markings with similar functions evolved on the pelvic fin in convergence to those of the haplochromines. CONCLUSION: We conclude that modifications of existing signal transduction mechanisms might have evolved in the haplochromine lineage in association with the origination of anal fin egg-dummies. That positive selection has acted during the evolution of a color gene that seems to be involved in the morphogenesis of a sexually selected trait, the egg-dummies, highlights the importance of further investigations of the comparative genomic basis of the phenotypic diversification of cichlid fishes.

Comparison of the polynomial model against explicit measurements of noise components for different mammography systems.

Given the adverse impact of image noise on the perception of important clinical details in digital mammography, routine quality control measurements should include an evaluation of noise. The European Guidelines, for example, employ a second-order polynomial fit of pixel variance as a function of detector air kerma (DAK) to decompose noise into quantum, electronic and fixed pattern (FP) components and assess the DAK range where quantum noise dominates. This work examines the robustness of the polynomial method against an explicit noise decomposition method. The two methods were applied to variance and noise power spectrum (NPS) data from six digital mammography units. Twenty homogeneously exposed images were acquired with PMMA blocks for target DAKs ranging from 6.25 to 1600 µGy. Both methods were explored for the effects of data weighting and squared fit coefficients during the curve fitting, the influence of the additional filter material (2 mm Al versus 40 mm PMMA) and noise de-trending. Finally, spatial stationarity of noise was assessed.Data weighting improved noise model fitting over large DAK ranges, especially at low detector exposures. The polynomial and explicit decompositions generally agreed for quantum and electronic noise but FP noise fraction was consistently underestimated by the polynomial method. Noise decomposition as a function of position in the image showed limited noise stationarity, especially for FP noise; thus the position of the region of interest (ROI) used for noise decomposition may influence fractional noise composition. The ROI area and position used in the Guidelines offer an acceptable estimation of noise components. While there are limitations to the polynomial model, when used with care and with appropriate data weighting, the method offers a simple and robust means of examining the detector noise components as a function of detector exposure.

On the Chern classes and the Euler characteristic for nonsingular complete intersections

It is shown that Hirzebruch's result on the Chern classes of a complete intersection of nonsingular hypersurfaces in general position in PN(C), is also valid for any nonsingular complete intersection. Then rela- tions between Euler characteristic, class and Milnor number are pointed out.

Genetic parameters for growth traits in pigs estimated using third degree polynomial functions

Selostus: Sian kasvuominaisuuksien perinnölliset tunnusluvut arvioituna kolmannen asteen polynomifunktion avulla

Characteristic of Dystrustepts in the Venezuelan Andes

The majority (60 %) of the soils in the Venezuelan Andes are Inceptisols, a large percentage of which are classified as Dystrustepts by the US Soil Taxonomy, Second Edition of 1999. Some of these soils were classified as Humitropepts (high organic - C-OC-soils) and Dystropepts by the Soil Taxonomy prior to 1999, but no equivalent large group was created for high-OC soils in the new Ustepts suborder. Dystrusepts developed on different materials, relief and vegetation. Their properties are closely related with the parent material. Soils developed on transported deposits or sediments have darker and thicker A horizons, a slightly acid reaction, greater CEC and OC contents than upland slope soils. Based on the previous classification into large groups (Humitropepts and Dystropepts) we found that: Humitropepts have a slightly less acid and higher values of CEC than Dystropepts. These properties or characteristics seem to be related to the fact that Humitropepts have a higher clay and OC content than the Dystropepts. Canonical discrimination analysis showed that the variables that discriminate the two great soil groups from each other are OC and silt. Data for Humitropepts are grouped around the OC vector (defining axis 3, principal component analysis), while Dystropepts are associated with the clay and sand vectors, with significant correlation. Given the importance of OC for soil properties, we propose the creation of a new large group named Humustepts for the order Inceptisol, suborder Ustepts.

Aggregate stability by the "high energy moisture characteristic" method in an oxisol under differentiated management

Studies testing the High Energy Moisture Characteristic (HEMC) technique in tropical soils are still incipient. By this method, the effects of different management systems can be evaluated. This study investigated the aggregation state of an Oxisol under coffee with Brachiaria between crop rows and surface-applied gypsum rates using HEMC. Soil in an experimental area in the Upper São Francisco region, Minas Gerais, was studied at depths of 0.05 and 0.20 m in coffee rows. The treatments consisted of 0, 7, and 28 Mg ha-1 of agricultural gypsum rates distributed on the soil surface of the coffee rows, between which Brachiaria was grown and periodically cut, and compared with a treatment without Brachiaria between coffee rows and no gypsum application. To determine the aggregation state using the HEMC method, soil aggregates were placed in a Büchner funnel (500 mL) and wetted using a peristaltic pump with a volumetric syringe. The wetting was applied increasingly at two pre-set speeds: slow (2 mm h-1) and fast (100 mm h-1). Once saturated, the aggregates were exposed to a gradually increasing tension by the displacement of a water column (varying from 0 to 30 cm) to obtain the moisture retention curve [M = f (Ψ) ], underlying the calculation of the stability parameters: modal suction, volume of drainable pores (VDP), stability index (slow and fast), VDP ratio, and stability ratio. The HEMC method conferred sensitivity in quantifying the aggregate stability parameters, and independent of whether gypsum was used, the soil managed with Brachiaria between the coffee rows, with regular cuts discharged in the crop row direction, exhibited a decreased susceptibility to disaggregation.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Proteomic analysis of membrane rafts of melanoma cells identifies protein patterns characteristic of the tumor progression stage.

The molecular mechanisms controlling the progression of melanoma from a localized tumor to an invasive and metastatic disease are poorly understood. In the attempt to start defining a functional protein profile of melanoma progression, we have analyzed by LC-MS/MS the proteins associated with detergent resistant membranes (DRMs), which are enriched in cholesterol/sphingolipids-containing membrane rafts, of melanoma cell lines derived from tumors at different stages of progression. Since membrane rafts are involved in several biological processes, including signal transduction and protein trafficking, we hypothesized that the association of proteins with rafts can be regulated during melanoma development and affect protein function and disease progression. We have identified a total of 177 proteins in the DRMs of the cell lines examined. Among these, we have found groups of proteins preferentially associated with DRMs of either less malignant radial growth phase/vertical growth phase (VGP) cells, or aggressive VGP and metastatic cells suggesting that melanoma cells with different degrees of malignancy have different DRM profiles. Moreover, some proteins were found in DRMs of only some cell lines despite being expressed at similar levels in all the cell lines examined, suggesting the existence of mechanisms controlling their association with DRMs. We expect that understanding the mechanisms regulating DRM targeting and the activity of the proteins differentially associated with DRMs in relation to cell malignancy will help identify new molecular determinants of melanoma progression.

Is it the grain size or the characteristic pore size that controls the induced polarization relaxation time of clean sands and sandstones?

There is a wide range of evidence to suggest that permeability can be constrained through of induced polarization measurements. For clean sands and sandstones, current mechanistic models of induced polarization predict a relationship between the low-frequency time constant inferred from induced polarization measurements and the grain diameter. A number of observations do, however, disagree with this and indicate that the observed relaxation behavior is rather governed by the so-called dynamic pore radius L. To test this hypothesis, we have developed a set of new scaling relationships, which allow the relaxation time to be computed from the pore size and the permeability to be computed from both the Cole-Cole time constant and the formation factor. Moreover, these new scaling relationships can be also used to predict the dependence of the Cole-Cole time constant as a function of the water saturation under unsaturated conditions. Comparative tests of the proposed new relationships with regard to various published experimental results for saturated clean sands and sandstones as well as for partially saturated clean sandstones, do indeed confirm that the dynamic pore radius L is a much more reliable indicator of the observed relaxation behavior than grain-size-based models.