Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Joint Densities of Correlation Coefficients for Samples from Multivariate Standard Normal Distribution

2000 Mathematics Subject Classification: 62H10.

Comparison of Multivariate and Univariate Models for Genetic Evaluation of Milk Yield based on Test Day Data

2000 Mathematics Subject Classification: 62H12, 62P99

Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences

ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2.

Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’S)

Given the polynomials f, g ∈ Z[x] of degrees n, m, respectively, with n > m, three new, and easy to understand methods — along with the more efficient variants of the last two of them — are presented for the computation of their subresultant polynomial remainder sequence (prs). All three methods evaluate a single determinant (subresultant) of an appropriate sub-matrix of sylvester1, Sylvester’s widely known and used matrix of 1840 of dimension (m + n) × (m + n), in order to compute the correct sign of each polynomial in the sequence and — except for the second method — to force its coefficients to become subresultants. Of interest is the fact that only the first method uses pseudo remainders. The second method uses regular remainders and performs operations in Q[x], whereas the third one triangularizes sylvester2, Sylvester’s little known and hardly ever used matrix of 1853 of dimension 2n × 2n. All methods mentioned in this paper (along with their supporting functions) have been implemented in Sympy and can be downloaded from the link http://inf-server.inf.uth.gr/~akritas/publications/subresultants.py

Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

2000 Mathematics Subject Classification: 62G07, 60F10.

Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.

The development and testing of a multivariate model of differentiation of self among Hispanics

Individuals of Hispanic origin are the nation's largest minority (13.4%). Therefore, there is a need for models and methods that are culturally appropriate for mental health research with this burgeoning population. This is an especially salient issue when applying family systems theories to Hispanics, who are heavily influenced by family bonds in a way that appears to be different from the more individualistic non-Hispanic White culture. Bowen asserted that his family systems' concept of differentiation of self, which values both individuality and connectedness, could be universally applied. However, there is a paucity of research systematically assessing the applicability of the differentiation of self construct in ethnic minority populations. ^ This dissertation tested a multivariate model of differentiation of self with a Hispanic sample. The manner in which the construct of differentiation of self was being assessed and how accurately it represented this particular ethnic minority group's functioning was examined. Additionally, the proposed model included key contextual variables (e.g., anxiety, relationship satisfaction, attachment and acculturation related variables) which have been shown to be related to the differentiation process. ^ The results from structural equation modeling (SEM) analyses confirmed and extended previous research, and helped to illuminate the complex relationships between key factors that need to be considered in order to better understand individuals with this cultural background. Overall results indicated that the manner in which Hispanic individuals negotiate the boundaries of interconnectedness with a sense of individual expression appears to be different from their non-Hispanic White counterparts in some important ways. These findings illustrate the need for research on Hispanic individuals that provides a more culturally sensitive framework. ^

Space time coding for polynomial phase modulated signals

Polynomial phase modulated (PPM) signals have been shown to provide improved error rate performance with respect to conventional modulation formats under additive white Gaussian noise and fading channels in single-input single-output (SISO) communication systems. In this dissertation, systems with two and four transmit antennas using PPM signals were presented. In both cases we employed full-rate space-time block codes in order to take advantage of the multipath channel. For two transmit antennas, we used the orthogonal space-time block code (OSTBC) proposed by Alamouti and performed symbol-wise decoding by estimating the phase coefficients of the PPM signal using three different methods: maximum-likelihood (ML), sub-optimal ML (S-ML) and the high-order ambiguity function (HAF). In the case of four transmit antennas, we used the full-rate quasi-OSTBC (QOSTBC) proposed by Jafarkhani. However, in order to ensure the best error rate performance, PPM signals were selected such as to maximize the QOSTBC’s minimum coding gain distance (CGD). Since this method does not always provide a unique solution, an additional criterion known as maximum channel interference coefficient (CIC) was proposed. Through Monte Carlo simulations it was shown that by using QOSTBCs along with the properly selected PPM constellations based on the CGD and CIC criteria, full diversity in flat fading channels and thus, low BER at high signal-to-noise ratios (SNR) can be ensured. Lastly, the performance of symbol-wise decoding for QOSTBCs was evaluated. In this case a quasi zero-forcing method was used to decouple the received signal and it was shown that although this technique reduces the decoding complexity of the system, there is a penalty to be paid in terms of error rate performance at high SNRs.

Comparative study of dissolved organic matter from groundwater and surface water in the Florida coastal Everglades using multi-dimensional spectrofluorometry combined with multivariate statistics

Dissolved organic matter (DOM) in groundwater and surface water samples from the Florida coastal Everglades were studied using excitation–emission matrix fluorescence modeled through parallel factor analysis (EEM-PARAFAC). DOM in both surface and groundwater from the eastern Everglades S332 basin reflected a terrestrial-derived fingerprint through dominantly higher abundances of humic-like PARAFAC components. In contrast, surface water DOM from northeastern Florida Bay featured a microbial-derived DOM signature based on the higher abundance of microbial humic-like and protein-like components consistent with its marine source. Surprisingly, groundwater DOM from northeastern Florida Bay reflected a terrestrial-derived source except for samples from central Florida Bay well, which mirrored a combination of terrestrial and marine end-member origin. Furthermore, surface water and groundwater displayed effects of different degradation pathways such as photodegradation and biodegradation as exemplified by two PARAFAC components seemingly indicative of such degradation processes. Finally, Principal Component Analysis of the EEM-PARAFAC data was able to distinguish and classify most of the samples according to DOM origins and degradation processes experienced, except for a small overlap of S332 surface water and groundwater, implying rather active surface-to-ground water interaction in some sites particularly during the rainy season. This study highlights that EEM-PARAFAC could be used successfully to trace and differentiate DOM from diverse sources across both horizontal and vertical flow profiles, and as such could be a convenient and useful tool for the better understanding of hydrological interactions and carbon biogeochemical cycling.

Quasi-Orthogonal Space-Time Block Coding Using Polynomial Phase Modulation

Recently, polynomial phase modulation (PPM) was shown to be a power- and bandwidth-efficient modulation format. These two characteristics are in high demand nowadays specially in mobile applications, where devices with size, weight, and power (SWaP) constraints are common. In this paper, we propose implementing a full-diversity quasiorthogonal space-time block code (QOSTBC) using polynomial phase signals as modulation format. QOSTBCs along with PPM are used in order to improve the power efficiency of communication systems with four transmit antennas. We obtain the optimal PPM constellations that ensure full diversity and maximize the QOSTBC's minimum coding gain distance. Simulation results show that by using QOSTBCs along with a properly selected PPM constellation, full diversity in flat fading channels and thus low BER at high signal-to-noise ratios (SNR) can be ensured. More importantly, it is also shown that QOSTBCs using PPM achieve a better error performance than those using conventional modulation formats.

Sea surface and the sea floor regionalization of the Southern Ocean by multivariate cluster analysis, links to ArcGIS project files

This study subdivides the Weddell Sea, Antarctica, into seafloor regions using multivariate statistical methods. These regions are categories used for comparing, contrasting and quantifying biogeochemical processes and biodiversity between ocean regions geographically but also regions under development within the scope of global change. The division obtained is characterized by the dominating components and interpreted in terms of ruling environmental conditions. The analysis uses 28 environmental variables for the sea surface, 25 variables for the seabed and 9 variables for the analysis between surface and bottom variables. The data were taken during the years 1983-2013. Some data were interpolated. The statistical errors of several interpolation methods (e.g. IDW, Indicator, Ordinary and Co-Kriging) with changing settings have been compared for the identification of the most reasonable method. The multivariate mathematical procedures used are regionalized classification via k means cluster analysis, canonical-correlation analysis and multidimensional scaling. Canonical-correlation analysis identifies the influencing factors in the different parts of the cove. Several methods for the identification of the optimum number of clusters have been tested. For the seabed 8 and 12 clusters were identified as reasonable numbers for clustering the Weddell Sea. For the sea surface the numbers 8 and 13 and for the top/bottom analysis 8 and 3 were identified, respectively. Additionally, the results of 20 clusters are presented for the three alternatives offering the first small scale environmental regionalization of the Weddell Sea. Especially the results of 12 clusters identify marine-influenced regions which can be clearly separated from those determined by the geological catchment area and the ones dominated by river discharge.

Multivariate statistical analysis on the kaolinite/chlorite ratios from 20 South Atlantic sediment cores

Multivariate statistical analysis on the kaolinite/chlorite ratios from 20 South Atlantic sediment cores allowed for the extraction of two processes controlling the fluctuations of the kaolinite/chlorite ratio during the last 130,000 yrs, (1) the relative strength of North Atlantic Deep Water (NADW) inflow into the South Atlantic Ocean and (2) the influx of aeolian sediments from the south African continent. The NADW fluctuation can be traced in the entire deep South Atlantic while the dust signal is restricted to the vicinity of South Africa. Our data indicate that NADW formation underwent significant changes in response to glacial/interglacial climate changes with enhanced export to the Southern Hemisphere during interglacials. The most pronounced phases with Enhanced South African Dust Export (ESADE) occurred during cold Marine Isotope Stage (MIS) 5d and across the Late Glacial/Holocene transition from 16 ka to 4 ka (MIS 2 to 1). This particular pattern is attributed to the interaction of Antarctic Sea Ice extent, the position of the westerlies and the South African monsoon system.

Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes

The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive asymptotic theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated asymptotic properties.