We obtain a general form of the multivariate Rayleigh and exponential probability density functions (p.d.f.s) when these are generated by corre lated Gaussian random variables. A general expression for the exponential characteristic function (c.f.) is also derived.

|We extend the characteristic function method (CFM) to more general groups, operators, and signal spaces. We show that the extended CFM can be applied to projected unitary operators as well as discrete-time/periodic signals.

We describe an algorithm for counting points on an arbitrary hyperelliptic curve over a finite field Fpn of odd characteristic, using Monsky-Washnitzer cohomology to compute a p-adic approximation to the characteristic polynomial of Frobenius. For fixed p, the asymptotic running time for a curve of genus g over Fpn with a rational Weierstrass point is O(g4+ǫn3+ǫ).

A framework of a general type of Petrovsky equation is formulated. The characteristic equation for eigenvalues of the system is derived and the associated eigenfunctions are found. For N connected beams with linear feedbacks at joint points, the asymptotic expansions of eigenvalues and eigenfunctions are further developed, and the Riesz basis property and the exponential stability are then conc...

In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and efficiency indicates that some of the methods are preferable to others but that none are completely satisfactory. Mo...

The proliferation of electronic health records (EHRs) frames opportunities for using machine learning to build models that help healthcare providers improve patient outcomes. However, building useful risk stratification models presents many technical challenges including the large number of factors (both intrinsic and extrinsic) influencing a patient’s risk of an adverse outcome and the inheren...

V. V. Uchaikin suggested a mathematical model of an anomalous diffusion in a space. These model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and a turbulence in a plasma. Here a coordinate of diffusing particle has stable distribution and so its density satisfies diffusion equation with partial derivatives. ...

This paper examines a particular class of continuous-time stochastic processes commonly known as af¿ne diffusions (AD) and af¿ne jump-diffusions (AJD) in which the drift, the diffusion and the jump coef¿cients are all af¿ne functions of the state variables. By deriving the joint characteristic function associated with a vector of observed state variables for such models, we are able to examine ...

This paper applies receiver operating characteristics (ROC) analysis to M3 Competition, micro monthly time series for one-month-ahead forecasts. Using the partial area under the curve (PAUC) criterion as a forecast accuracy measure and paired-comparison testing via bootstrapping, we find that complex methods (AutomatANN, Flores-Pearce2, Forecast ProSmart FCS, and Theta) perform best for forecas...