On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<projections of P look like a scale mixture of spherically symmetric Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q . It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P ^ be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process n √ (P ^ −P) under random projections, conditional on P ^ .

Autenticação de vídeo H.264/AVC

Hoje em dia, há cada vez mais informação audiovisual e as transmissões ou ficheiros multimédia podem ser partilhadas com facilidade e eficiência. No entanto, a adulteração de conteúdos vídeo, como informação financeira, notícias ou sessões de videoconferência utilizadas num tribunal, pode ter graves consequências devido à importância desse tipo de informação. Surge então, a necessidade de assegurar a autenticidade e a integridade da informação audiovisual. Nesta dissertação é proposto um sistema de autenticação de vídeo H.264/Advanced Video Coding (AVC), denominado Autenticação de Fluxos utilizando Projecções Aleatórias (AFPA), cujos procedimentos de autenticação, são realizados ao nível de cada imagem do vídeo. Este esquema permite um tipo de autenticação mais flexível, pois permite definir um limite máximo de modificações entre duas imagens. Para efectuar autenticação é utilizada uma nova técnica de autenticação de imagens, que combina a utilização de projecções aleatórias com um mecanismo de correcção de erros nos dados. Assim é possível autenticar cada imagem do vídeo, com um conjunto reduzido de bits de paridade da respectiva projecção aleatória. Como a informação de vídeo é tipicamente, transportada por protocolos não fiáveis pode sofrer perdas de pacotes. De forma a reduzir o efeito das perdas de pacotes, na qualidade do vídeo e na taxa de autenticação, é utilizada Unequal Error Protection (UEP). Para validação e comparação dos resultados implementou-se um sistema clássico que autentica fluxos de vídeo de forma típica, ou seja, recorrendo a assinaturas digitais e códigos de hash. Ambos os esquemas foram avaliados, relativamente ao overhead introduzido e da taxa de autenticação. Os resultados mostram que o sistema AFPA, utilizando um vídeo com qualidade elevada, reduz o overhead de autenticação em quatro vezes relativamente ao esquema que utiliza assinaturas digitais e códigos de hash.

Approximate polytope ensemble for one-class classification

In this work, a new one-class classification ensemble strategy called approximate polytope ensemble is presented. The main contribution of the paper is threefold. First, the geometrical concept of convex hull is used to define the boundary of the target class defining the problem. Expansions and contractions of this geometrical structure are introduced in order to avoid over-fitting. Second, the decision whether a point belongs to the convex hull model in high dimensional spaces is approximated by means of random projections and an ensemble decision process. Finally, a tiling strategy is proposed in order to model non-convex structures. Experimental results show that the proposed strategy is significantly better than state of the art one-class classification methods on over 200 datasets.

Uncertainties In Future Projections Of Extreme Rainfall: The Role Of Climate Model, Emission Scenario And Randomness

Climate change has resulted in substantial variations in annual extreme rainfall quantiles in different durations and return periods. Predicting the future changes in extreme rainfall quantiles is essential for various water resources design, assessment, and decision making purposes. Current Predictions of future rainfall extremes, however, exhibit large uncertainties. According to extreme value theory, rainfall extremes are rather random variables, with changing distributions around different return periods; therefore there are uncertainties even under current climate conditions. Regarding future condition, our large-scale knowledge is obtained using global climate models, forced with certain emission scenarios. There are widely known deficiencies with climate models, particularly with respect to precipitation projections. There is also recognition of the limitations of emission scenarios in representing the future global change. Apart from these large-scale uncertainties, the downscaling methods also add uncertainty into estimates of future extreme rainfall when they convert the larger-scale projections into local scale. The aim of this research is to address these uncertainties in future projections of extreme rainfall of different durations and return periods. We plugged 3 emission scenarios with 2 global climate models and used LARS-WG, a well-known weather generator, to stochastically downscale daily climate models’ projections for the city of Saskatoon, Canada, by 2100. The downscaled projections were further disaggregated into hourly resolution using our new stochastic and non-parametric rainfall disaggregator. The extreme rainfall quantiles can be consequently identified for different durations (1-hour, 2-hour, 4-hour, 6-hour, 12-hour, 18-hour and 24-hour) and return periods (2-year, 10-year, 25-year, 50-year, 100-year) using Generalized Extreme Value (GEV) distribution. By providing multiple realizations of future rainfall, we attempt to measure the extent of total predictive uncertainty, which is contributed by climate models, emission scenarios, and downscaling/disaggregation procedures. The results show different proportions of these contributors in different durations and return periods.

On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

Biased Random-key Genetic Algorithms For The Winner Determination Problem In Combinatorial Auctions.

Abstract In this paper, we address the problem of picking a subset of bids in a general combinatorial auction so as to maximize the overall profit using the first-price model. This winner determination problem assumes that a single bidding round is held to determine both the winners and prices to be paid. We introduce six variants of biased random-key genetic algorithms for this problem. Three of them use a novel initialization technique that makes use of solutions of intermediate linear programming relaxations of an exact mixed integer-linear programming model as initial chromosomes of the population. An experimental evaluation compares the effectiveness of the proposed algorithms with the standard mixed linear integer programming formulation, a specialized exact algorithm, and the best-performing heuristics proposed for this problem. The proposed algorithms are competitive and offer strong results, mainly for large-scale auctions.

Synthesis and structural characterization of block and random low molecular weight copolymers composed of L-lactic acid and isosorbide succinate moieties

Isosorbide succinate moieties were incorporated into poly(L-lactide) (PLLA) backbone in order to obtain a new class of biodegradable polymer with enhanced properties. This paper describes the synthesis and characterization of four types of low molecular weight copolymers. Copolymer I was obtained from monomer mixtures of L-lactide, isosorbide, and succinic anhydride; II from oligo(L-lactide) (PLLA), isosorbide, and succinic anhydride; III from oligo(isosorbide succinate) (PIS) and L-lactide; and IV from transesterification reactions between PLLA and PIS. MALDI-TOFMS and 13C-NMR analyses gave evidence that co-oligomerization was successfully attained in all cases. The data suggested that the product I is a random co-oligomer and the products II-IV are block co-oligomers.

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Effect of Low-Level Laser Therapy on Malondialdehyde Concentration in Random Cutaneous Flap Viability

Objective: The aim of this study was to assess the effects of 830 and 670 nm laser on malondialdehyde (MDA) concentration in random skin-flap survival. Background Data: Low-level laser therapy (LLLT) has been reported to be successful in stimulating the formation of new blood vessels and activating superoxide-dismutase delivery, thus helping the inhibition of free-radical action and consequently reducing necrosis. Materials and Methods: Thirty Wistar rats were used and divided into three groups, with 10 rats in each one. A random skin flap was raised on the dorsum of each animal. Group 1 was the control group; group 2 received 830 nm laser radiation; and group 3 was submitted to 670 nm laser radiation. The animals underwent laser therapy with 36 J/cm(2) energy density immediately after surgery and on the 4 days subsequent to surgery. The application site of the laser radiation was 1 point, 2.5 cm from the flap's cranial base. The percentage of the skin-flap necrosis area was calculated 7 days postoperative using the paper-template method, and a skin sample was collected immediately after as a way of determining the MDA concentration. Results: Statistically significant differences were found between the necrosis percentages, with higher values seen in group 1 compared with groups 2 and 3. Groups 2 and 3 did not present statistically significant differences (p > 0.05). Group 3 had a lower concentration of MDA values compared to the control group (p < 0.05). Conclusion: LLLT was effective in increasing the random skin-flap viability in rats, and the 670 nm laser was efficient in reducing the MDA concentration.

Multi-trait and random regression mature weight heritability and breeding value estimates in Nelore cattle

Mature weight breeding values were estimated using a multi-trait animal model (MM) and a random regression animal model (RRM). Data consisted of 82 064 weight records from 8 145 animals, recorded from birth to eight years of age. Weights at standard ages were considered in the MM. All models included contemporary groups as fixed effects, and age of dam (linear and quadratic effects) and animal age as covariates. In the RRM, mean trends were modelled through a cubic regression on orthogonal polynomials of animal age and genetic maternal and direct and maternal permanent environmental effects were also included as random. Legendre polynomials of orders 4, 3, 6 and 3 were used for animal and maternal genetic and permanent environmental effects, respectively, considering five classes of residual variances. Mature weight (five years) direct heritability estimates were 0.35 (MM) and 0.38 (RRM). Rank correlation between sires' breeding values estimated by MM and RRM was 0.82. However, selecting the top 2% (12) or 10% (62) of the young sires based on the MM predicted breeding values, respectively 71% and 80% of the same sires would be selected if RRM estimates were used instead. The RRM modelled the changes in the (co) variances with age adequately and larger breeding value accuracies can be expected using this model.

Random X Inactivation and Extensive Mosaicism in Human Placenta Revealed by Analysis of Allele-Specific Gene Expression along the X Chromosome

Imprinted inactivation of the paternal X chromosome in marsupials is the primordial mechanism of dosage compensation for X-linked genes between females and males in Therians. In Eutherian mammals, X chromosome inactivation (XCI) evolved into a random process in cells from the embryo proper, where either the maternal or paternal X can be inactivated. However, species like mouse and bovine maintained imprinted XCI exclusively in extraembryonic tissues. The existence of imprinted XCI in humans remains controversial, with studies based on the analyses of only one or two X-linked genes in different extraembryonic tissues. Here we readdress this issue in human term placenta by performing a robust analysis of allele-specific expression of 22 X-linked genes, including XIST, using 27 SNPs in transcribed regions. We show that XCI is random in human placenta, and that this organ is arranged in relatively large patches of cells with either maternal or paternal inactive X. In addition, this analysis indicated heterogeneous maintenance of gene silencing along the inactive X, which combined with the extensive mosaicism found in placenta, can explain the lack of agreement among previous studies. Our results illustrate the differences of XCI mechanism between humans and mice, and highlight the importance of addressing the issue of imprinted XCI in other species in order to understand the evolution of dosage compensation in placental mammals.

Disordered ensembles of random matrices

It is shown that the families of generalized matrix ensembles recently considered which give rise to an orthogonal invariant stable Levy ensemble can be generated by the simple procedure of dividing Gaussian matrices by a random variable. The nonergodicity of this kind of disordered ensembles is investigated. It is shown that the same procedure applied to random graphs gives rise to a family that interpolates between the Erdos-Renyi and the scale free models.

A study of disorder effects in random (Al(x)Ga(1-x)As)(n)(Al(y)Ga(1-y)As)(m) superlattices embedded in a wide parabolic potential

A photoluminescence (PL) study of the individual electron states localized in a random potential is performed in artificially disordered superlattices embedded in a wide parabolic well. The valence band bowing of the parabolic potential provides a variation of the emission energies which splits the optical transitions corresponding to different wells within the random potential. The blueshift of the PL lines emitted by individual random wells, observed with increasing disorder strength, is demonstrated. The variation of temperature and magnetic field allowed for the behavior of the electrons localized in individual wells of the random potential to be distinguished.

Delocalization-localization transition of plasmons in random (GaAs)(m)(Al(0.3)Ga(0.7)As)(6) superlattices

The transition of plasmons from propagating to localized state was studied in disordered systems formed in GaAs/AlGaAs superlattices by impurities and by artificial random potential. Both the localization length and the linewidth of plasmons were measured by Raman scattering. The vanishing dependence of the plasmon linewidth on the disorder strength was shown to be a manifestation of the strong plasmon localization. The theoretical approach based on representation of the plasmon wave function in a Gaussian form well accounted for by the obtained experimental data.

On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.