Generalized Fractional Evolution Equation

2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20

On Li’s Coefficients for Some Classes of L-Functions

AMS Subj. Classification: 11M41, 11M26, 11S40

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.

Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99

l-stable Functions and Constrained Optimization

Иван Гинчев - Класът на ℓ-устойчивите в точка функции, дефиниран в [2] и разширяващ класа на C1,1 функциите, се обобщава от скаларни за векторни функции. Доказани са някои свойства на ℓ-устойчивите векторни функции. Показано е, че векторни оптимизационни задачи с ограничения допускат условия от втори ред изразени чрез посочни производни, което обобщава резултати от [2] и [5].

Verification of Procedural Programs via Building their Generalized Nets Models

Магдалина Василева Тодорова - В статията е описан подход за верификация на процедурни програми чрез изграждане на техни модели, дефинирани чрез обобщени мрежи. Подходът интегрира концепцията “design by contract” с подходи за верификация от тип доказателство на теореми и проверка на съгласуваност на модели. За целта разделно се верифицират функциите, които изграждат програмата относно спецификации според предназначението им. Изгражда се обобщен мрежов модел, специфициащ връзките между функциите във вид на коректни редици от извиквания. За главната функция на програмата се построява обобщен мрежов модел и се проверява дали той съответства на мрежовия модел на връзките между функциите на програмата. Всяка от функциите на програмата, която използва други функции се верифицира и относно спецификацията, зададена чрез мрежовия модел на връзките между функциите на програмата.

Application of the D-Fullness Technique for Breakdown Point Study of the Trimmed Likelihood Estimator to a Generalized Logistic Model

2000 Mathematics Subject Classification: 62J12, 62F35

Invariant Functions on Neil Parabola in Cn

2000 Mathematics Subject Classification: Primary 32F45.

On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

MSC 2010: 46F30, 46F10

Inverse Problems Involving Generalized Axial-Symmetric Helmholtz Equation

MSC 2010: 35J05, 33C10, 45D05

Bayesian and Frequentist Two-Sample Predictions of the Inverse Weibull Model Based on Generalized Order Statistics

2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.

Seizure detection in subdural recordings using nonlinear decision functions

This dissertation proposed a new approach to seizure detection in intracranial EEG recordings using nonlinear decision functions. It implemented well-established features that were designed to deal with complex signals such as brain recordings, and proposed a 2-D domain of analysis. Since the features considered assume both the time and frequency domains, the analysis was carried out both temporally and as a function of different frequency ranges in order to ascertain those measures that were most suitable for seizure detection. In retrospect, this study established a generalized approach to seizure detection that works across several features and across patients. ^ Clinical experiments involved 8 patients with intractable seizures that were evaluated for potential surgical interventions. A total of 35 iEEG data files collected were used in a training phase to ascertain the reliability of the formulated features. The remaining 69 iEEG data files were then used in the testing phase. ^ The testing phase revealed that the correlation sum is the feature that performed best across all patients with a sensitivity of 92% and an accuracy of 99%. The second best feature was the gamma power with a sensitivity of 92% and an accuracy of 96%. In the frequency domain, all of the 5 other spectral bands considered, revealed mixed results in terms of low sensitivity in some frequency bands and low accuracy in other frequency bands, which is expected given that the dominant frequencies in iEEG are those of the gamma band. In the time domain, other features which included mobility, complexity, and activity, all performed very well with an average a sensitivity of 80.3% and an accuracy of 95%. ^ The computational requirement needed for these nonlinear decision functions to be generated in the training phase was extremely long. It was determined that when the duration dimension was rescaled, the results improved and the convergence rates of the nonlinear decision functions were reduced dramatically by more than a 100 fold. Through this rescaling, the sensitivity of the correlation sum improved to 100% and the sensitivity of the gamma power to 97%, which meant that there were even less false negatives and false positives detected. ^

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Mixtures of g-priors in Generalized Linear Models

Mixtures of Zellner's g-priors have been studied extensively in linear models and have been shown to have numerous desirable properties for Bayesian variable selection and model averaging. Several extensions of g-priors to Generalized Linear Models (GLMs) have been proposed in the literature; however, the choice of prior distribution of g and resulting properties for inference have received considerably less attention. In this paper, we extend mixtures of g-priors to GLMs by assigning the truncated Compound Confluent Hypergeometric (tCCH) distribution to 1/(1+g) and illustrate how this prior distribution encompasses several special cases of mixtures of g-priors in the literature, such as the Hyper-g, truncated Gamma, Beta-prime, and the Robust prior. Under an integrated Laplace approximation to the likelihood, the posterior distribution of 1/(1+g) is in turn a tCCH distribution, and approximate marginal likelihoods are thus available analytically. We discuss the local geometric properties of the g-prior in GLMs and show that specific choices of the hyper-parameters satisfy the various desiderata for model selection proposed by Bayarri et al, such as asymptotic model selection consistency, information consistency, intrinsic consistency, and measurement invariance. We also illustrate inference using these priors and contrast them to others in the literature via simulation and real examples.