Sensory thresholds obtained from MEG data:cortical psychometric functions

Sensory sensitivity is typically measured using behavioural techniques (psychophysics), which rely on observers responding to very large numbers of stimulus presentations. Psychophysics can be problematic when working with special populations, such as children or clinical patients, because they may lack the compliance or cognitive skills to perform the behavioural tasks. We used an auditory gap-detection paradigm to develop an accurate measure of sensory threshold derived from passively-recorded MEG data. Auditory evoked responses were elicited by silent gaps of varying durations in an on-going noise stimulus. Source modelling was used to spatially filter the MEG data and sigmoidal ‘cortical psychometric functions’ relating response amplitude to gap duration were obtained for each individual participant. Fitting the functions with a curve and estimating the gap duration at which the evoked response exceeded one standard deviation of the prestimulus brain activity provided an excellent prediction of psychophysical threshold. Thus we have demonstrated that accurate sensory thresholds can be reliably extracted from MEG data recorded while participants listen passively to a stimulus. Because we required no behavioural task, the method is suitable for studies of populations where variations in cognitive skills or vigilance make traditional psychophysics unsuitable.

Solving Differential Equations by Parallel Laplace Method with Assured Accuracy

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Essential Arity Gap of Boolean Functions

In this paper we investigate the Boolean functions with maximum essential arity gap. Additionally we propose a simpler proof of an important theorem proved by M. Couceiro and E. Lehtonen in [3]. They use Zhegalkin’s polynomials as normal forms for Boolean functions and describe the functions with essential arity gap equals 2. We use to instead Full Conjunctive Normal Forms of these polynomials which allows us to simplify the proofs and to obtain several combinatorial results concerning the Boolean functions with a given arity gap. The Full Conjunctive Normal Forms are also sum of conjunctions, in which all variables occur.

The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points

The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0 (M + ). In addition to direct sums of regularly solvable operators defined on the separate subintervals, there are other regularly solvable restrications of the maximal operator which involve linking the various intervals together in interface like style.

Oscillation Theorems for Perturbed Second Order Nonlinear Differential Equations with Damping

Some oscillation criteria for solutions of a general perturbed second order ordinary differential equation with damping (r(t)x′ (t))′ + h(t)f (x)x′ (t) + ψ(t, x) = H(t, x(t), x′ (t)) with alternating coefficients are given. The results obtained improve and extend some existing results in the literature.

Involutivity and Symple Waves in R^2

A strictly hyperbolic quasi-linear 2×2 system in two independent variables with C2 coefficients is considered. The existence of a simple wave solution in the sense that the solution is a 2-dimensional vector-valued function of the so called Riemann invariant is discussed. It is shown, through a purely geometrical approach, that there always exists simple wave solution for the general system when the coefficients are arbitrary C^2 functions depending on both, dependent and independent variables.

Certain Properties of Fractional Calculus Operators Associated with Generalized Mittag-Leffler Function

Mathematics Subject Classification: 26A33, 33E12, 33C20.

Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15

Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20

Разпределение на простите числа и някои приложения

Petar Popivanov - This talk deals with several classical and more modern results from the theory of primes and is devoted to a larger audience. A short survey is given and almost primes of order two are discussed too. Polynomials with integer coefficients are considered from the point of view of their composite and prime functional values. Exponential type functions mapping N into the set of primes are also constructed.

On Nilpotent Subsemigroups in some Matrix Semigroups

2000 Mathematics Subject Classification: 20M20, 20M10.

Approximation of Univariate Set-Valued Functions - an Overview

2000 Mathematics Subject Classification: 26E25, 41A35, 41A36, 47H04, 54C65.

First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

MSC2010: 30C45, 33C45

Method development for the analysis of smokeless powders and organic gunshot residue by ultra performance liquid chromatography with tandem mass spectrometry

The goal of this project was to develop a rapid separation and detection method for analyzing organic compounds in smokeless powders and then test its applicability on gunshot residue (GSR) samples. In this project, a total of 20 common smokeless powder additives and their decomposition products were separated by ultra performance liquid chromatography (UPLC) and confirmed by tandem mass spectrometry (MS/MS) using multiple reaction monitoring mode (MRM). Some of the targeted compounds included diphenylamines, centralites, nitrotoluenes, nitroglycerin, and various phthalates. The compounds were ionized in the MS source using simultaneous positive and negative electrospray ionization (ESI) with negative atmospheric pressure chemical ionization (APCI) in order to detect all compounds in a single analysis. The developed UPLC/MS/MS method was applied to commercially available smokeless powders and gunshot residue samples recovered from the hands of shooters, spent cartridges, and smokeless powder retrieved from unfired cartridges. Distinct compositions were identified for smokeless powders from different manufacturers and from separate manufacturing lots. The procedure also produced specific chemical profiles when tested on gunshot residues from different manufacturers. Overall, this thesis represents the development of a rapid and reproducible procedure capable of simultaneously detecting the widest possible range of components present in organic gunshot residue.^