Generalizations and extensions of the Fokker-Planck-Kolmogorov equations

The problem of determining probability density functions of general transformations of random processes is considered in this thesis. A method of solution is developed in which partial differential equations satisfied by the unknown density function are derived. These partial differential equations are interpreted as generalized forms of the classical Fokker-Planck-Kolmogorov equations and are shown to imply the classical equations for certain classes of Markov processes. Extensions of the generalized equations which overcome degeneracy occurring in the steady-state case are also obtained.

The equations of Darling and Siegert are derived as special cases of the generalized equations thereby providing unity to two previously existing theories. A technique for treating non-Markov processes by studying closely related Markov processes is proposed and is seen to yield the Darling and Siegert equations directly from the classical Fokker-Planck-Kolmogorov equations.

As illustrations of their applicability, the generalized Fokker-Planck-Kolmogorov equations are presented for certain joint probability density functions associated with the linear filter. These equations are solved for the density of the output of an arbitrary linear filter excited by Markov Gaussian noise and for the density of the output of an RC filter excited by the Poisson square wave. This latter density is also found by using the extensions of the generalized equations mentioned above. Finally, some new approaches for finding the output probability density function of an RC filter-limiter-RC filter system driven by white Gaussian noise are included. The results in this case exhibit the data required for complete solution and clearly illustrate some of the mathematical difficulties inherent to the use of the generalized equations.

Locational distribution of gene functional classes in Arabidopsis thaliana

Riley, M. C., Clare, A., King, R. D. (2007). Locational distribution of gene functional classes in Arabidopsis thaliana. BMC Bioinformatics 8, Article No: 112 Sponsorship: EPSRC / RAEng

On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

On Fuzzy Implication Classes - Towards Extensions of Fuzzy Rule-Based Systems

Atualmente, há diferentes definições de implicações fuzzy aceitas na literatura. Do ponto de vista teórico, esta falta de consenso demonstra que há discordâncias sobre o real significado de "implicação lógica" nos contextos Booleano e fuzzy. Do ponto de vista prático, isso gera dúvidas a respeito de quais "operadores de implicação" os engenheiros de software devem considerar para implementar um Sistema Baseado em Regras Fuzzy (SBRF). Uma escolha ruim destes operadores pode implicar em SBRF's com menor acurácia e menos apropriados aos seus domínios de aplicação. Uma forma de contornar esta situação e conhecer melhor os conectivos lógicos fuzzy. Para isso se faz necessário saber quais propriedades tais conectivos podem satisfazer. Portanto, a m de corroborar com o significado de implicação fuzzy e corroborar com a implementação de SBRF's mais apropriados, várias leis Booleanas têm sido generalizadas e estudadas como equações ou inequações nas lógicas fuzzy. Tais generalizações são chamadas de leis Boolean-like e elas não são comumente válidas em qualquer semântica fuzzy. Neste cenário, esta dissertação apresenta uma investigação sobre as condições suficientes e necessárias nas quais três leis Booleanlike like — y ≤ I(x, y), I(x, I(y, x)) = 1 e I(x, I(y, z)) = I(I(x, y), I(x, z)) — se mantém válidas no contexto fuzzy, considerando seis classes de implicações fuzzy e implicações geradas por automorfismos. Além disso, ainda no intuito de implementar SBRF's mais apropriados, propomos uma extensão para os mesmos

PARTITIONING THE BLOCKS OF A STEINER TRIPLE SYSTEM INTO PARTIAL PARALLEL CLASSES

Does there exist a Steiner Triple System on v points, whose blocks can be partitioned into partial parallel classes of size m, where m ≤ [v⁄3], m | b and b is the number of blocks of the STS(v)? We give the answer for 9 ≤ v ≤ 43. We also show that whenever 2|b, v ≡ 3 (mod 6) we can find an STS(v) whose blocks can be partitioned into partial parallel classes of size 2, and whenever 4|b , v ≡ 3 (mod 6), there exists an STS(v) whose blocks can be partitioned into partial parallel classes of size 4.

Mistreatment and self-neglect in community dwelling older adults: Studies of construct validity, measurement invariance and latent classes

Mistreatment and self-neglect significantly increase the risk of dying in older adults. It is estimated that 1 to 2 million older adults experience elder mistreatment and self-neglect every year in the United States. Currently, there are no elder mistreatment and self-neglect assessment tools with construct validity and measurement invariance testing and no studies have sought to identify underlying latent classes of elder self-neglect that may have differential mortality rates. Using data from 11,280 adults with Texas APS substantiated elder mistreatment and self-neglect 3 studies were conducted to: (1) test the construct validity and (2) the measurement invariance across gender and ethnicity of the Texas Adult Protective Services (APS) Client Assessment and Risk Evaluation (CARE) tool and (3) identify latent classes associated with elder self-neglect. Study 1 confirmed the construct validity of the CARE tool following adjustments to the initial hypothesized CARE tool. This resulted in the deletion of 14 assessment items and a final assessment with 5 original factors and 43 items. Cross-validation for this model was achieved. Study 2 provided empirical evidence for factor loading and item-threshold invariance of the CARE tool across gender and between African-Americans and Caucasians. The financial status domain of the CARE tool did not function properly for Hispanics and thus, had to be deleted. Subsequent analyses showed factor loading and item-threshold invariance across all 3 ethnic groups with the exception of some residual errors. Study 3 identified 4-latent classes associated with elder self-neglect behaviors which included individuals with evidence of problems in the areas of (1) their environment, (2) physical and medical status, (3) multiple domains and (4) finances. Overall, these studies provide evidence supporting the use of APS CARE tool for providing unbiased and valid investigations of mistreatment and neglect in older adults with different demographic characteristics. Furthermore, the findings support the underlying notion that elder self-neglect may not only occur along a continuum, but that differential types may exist. All of which, have very important potential implications for social and health services distributed to vulnerable mistreated and neglected older adults.^

Enzyme-mediated spatial segregation on individual polymeric support beads: application to generation and screening of encoded combinatorial libraries.

Proteolysis of short N alpha-protected peptide substrates bound to polyoxyethylene-polystyrene beads releases selectively free amino sites in the enzyme-accessible "surface" area. The substantial majority of functional sites in the "interior" of the polymeric support are not reached by the enzyme and remain uncleaved (protected). Subsequent synthesis with two classes of orthogonal protecting groups-N alpha-tert-butyloxycarbonyl (Boc) and N alpha-9-fluorenylmethyloxy-carbonyl (Fmoc)-allows generation of two structures on the same bead. The surface structure is available for receptor interactions, whereas the corresponding interior structure is used for coding. Coding structures are usually readily sequenceable peptides. This "shaving" methodology was illustrated by the preparation of a peptide-encoded model peptide combinatorial library containing 1.0 x 10(5) members at approximately 6-fold degeneracy. From this single library, good ligands were selected for three different receptors: anti-beta-endorphin anti-body, streptavidin, and thrombin, and the binding structures were deduced correctly by sequencing the coding peptides present on the same beads.

Raman spectroscopic study of vivianites of different origins

Raman spectroscopy has been used to study a selection of vivianites from different origins. A band is identified at around 3480 cm-1 whose intensity is sample dependent. The band is attributed to the stretching vibration of Fe3+ OH units which are formed through the autooxidation of the vivianite minerals either by self-oxidation or by photocatalytic oxidation according to the reaction: (Fe2+)3(PO4)2·8H2O + 1/2O2 (Fe2+)3– x(Fe3+)x(PO4)2(OH)x·(8–x)H2O in which some of the water of crystallization is converted to hydroxyl anions. Complexity of the OH stretching region through the overlap of broad bands is reflected in the water HOH deformation modes at 1660 cm–1. Using the infrared bands at 3281, 3105 and 3025 cm–1, hydrogen bond distances of 2.734(5), 2.675(2) and 2.655(2) Å are calculated. Vivianites are characterised by an intense band at 950 cm–1 assigned to the PO4 symmetric stretching vibration. Low Raman intensity bands are observed at ~1077, ~1050, 1015 and ~ 985 cm–1 assigned to the phosphate PO4 antisymmetric stretching vibrations. Multiple antisymmetric stretching vibrations are due to the reduced tetrahedral symmetry. This loss of degeneracy is also reflected in the bending modes. Two bands are observed at ~ 423 and ~ 456 cm–1 assigned to the2bending modes. For the vivianites four bands are observed at ~ 584, ~ 571, ~ 545 and ~ 525 cm–1 assigned to the 4modes of vivianite.

Cardiac state diagnosis using higher order spectra of heart rate variability

Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart, by the sympathetic and parasympathetic branches of the autonomic nervous system. Heart rate variability analysis is an important tool to observe the heart's ability to respond to normal regulatory impulses that affect its rhythm. A computer-based intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are nonlinear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of nonlinear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and seven classes of arrhythmia. We present some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. We also extracted features from the HOS and performed an analysis of variance (ANOVA) test. The results are very promising for cardiac arrhythmia classification with a number of features yielding a p-value < 0.02 in the ANOVA test.

On the Classification of Recursive Languages

A one-sided classifier for a given class of languages converges to 1 on every language from the class and outputs 0 infinitely often on languages outside the class. A two-sided classifier, on the other hand, converges to 1 on languages from the class and converges to 0 on languages outside the class. The present paper investigates one-sided and two-sided classification for classes of recursive languages. Theorems are presented that help assess the classifiability of natural classes. The relationships of classification to inductive learning theory and to structural complexity theory in terms of Turing degrees are studied. Furthermore, the special case of classification from only positive data is also investigated.

Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

Mind change complexity of learning logic programs

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m: • is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m. The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

A parallel computation of power system equations

Streaming SIMD Extensions (SSE) is a unique feature embedded in the Pentium III and P4 classes of microprocessors. By fully exploiting SSE, parallel algorithms can be implemented on a standard personal computer and a theoretical speedup of four can be achieved. In this paper, we demonstrate the implementation of a parallel LU matrix decomposition algorithm for solving power systems network equations with SSE and discuss advantages and disadvantages of this approach.

Molecular analysis of the myosin gene family in Arabidopsis thaliana

Myosin is believed to act as the molecular motor for many actin-based motility processes in eukaryotes. It is becoming apparent that a single species may possess multiple myosin isoforms, and at least seven distinct classes of myosin have been identified from studies of animals, fungi, and protozoans. The complexity of the myosin heavy-chain gene family in higher plants was investigated by isolating and characterizing myosin genomic and cDNA clones from Arabidopsis thaliana. Six myosin-like genes were identified from three polymerase chain reaction (PCR) products (PCR1, PCR11, PCR43) and three cDNA clones (ATM2, MYA2, MYA3). Sequence comparisons of the deduced head domains suggest that these myosins are members of two major classes. Analysis of the overall structure of the ATM2 and MYA2 myosins shows that they are similar to the previously-identified ATM1 and MYA1 myosins, respectively. The MYA3 appears to possess a novel tail domain, with five IQ repeats, a six-member imperfect repeat, and a segment of unique sequence. Northern blot analyses indicate that some of the Arabidopsis myosin genes are preferentially expressed in different plant organs. Combined with previous studies, these results show that the Arabidopsis genome contains at least eight myosin-like genes representing two distinct classes.

Analysis of cardiac and epileptic signals using higher order spectra

The theory of nonlinear dyamic systems provides some new methods to handle complex systems. Chaos theory offers new concepts, algorithms and methods for processing, enhancing and analyzing the measured signals. In recent years, researchers are applying the concepts from this theory to bio-signal analysis. In this work, the complex dynamics of the bio-signals such as electrocardiogram (ECG) and electroencephalogram (EEG) are analyzed using the tools of nonlinear systems theory. In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The Electrocardiogram (ECG) is an important biosignal representing the sum total of millions of cardiac cell depolarization potentials. It contains important insight into the state of health and nature of the disease afflicting the heart. Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart by the sympathetic and parasympathetic branches of the autonomic nervous system. Heart rate variability analysis is an important tool to observe the heart's ability to respond to normal regulatory impulses that affect its rhythm. A computerbased intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are non-linear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of non-linear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and four classes of arrhythmia. This thesis presents some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. Several features were extracted from the HOS and subjected an Analysis of Variance (ANOVA) test. The results are very promising for cardiac arrhythmia classification with a number of features yielding a p-value < 0.02 in the ANOVA test. An automated intelligent system for the identification of cardiac health is very useful in healthcare technology. In this work, seven features were extracted from the heart rate signals using HOS and fed to a support vector machine (SVM) for classification. The performance evaluation protocol in this thesis uses 330 subjects consisting of five different kinds of cardiac disease conditions. The classifier achieved a sensitivity of 90% and a specificity of 89%. This system is ready to run on larger data sets. In EEG analysis, the search for hidden information for identification of seizures has a long history. Epilepsy is a pathological condition characterized by spontaneous and unforeseeable occurrence of seizures, during which the perception or behavior of patients is disturbed. An automatic early detection of the seizure onsets would help the patients and observers to take appropriate precautions. Various methods have been proposed to predict the onset of seizures based on EEG recordings. The use of nonlinear features motivated by the higher order spectra (HOS) has been reported to be a promising approach to differentiate between normal, background (pre-ictal) and epileptic EEG signals. In this work, these features are used to train both a Gaussian mixture model (GMM) classifier and a Support Vector Machine (SVM) classifier. Results show that the classifiers were able to achieve 93.11% and 92.67% classification accuracy, respectively, with selected HOS based features. About 2 hours of EEG recordings from 10 patients were used in this study. This thesis introduces unique bispectrum and bicoherence plots for various cardiac conditions and for normal, background and epileptic EEG signals. These plots reveal distinct patterns. The patterns are useful for visual interpretation by those without a deep understanding of spectral analysis such as medical practitioners. It includes original contributions in extracting features from HRV and EEG signals using HOS and entropy, in analyzing the statistical properties of such features on real data and in automated classification using these features with GMM and SVM classifiers.