In many situations, in all branches of physics, one encounters the power-like behavior of some variables, which is best described by a Tsallis distribution characterized by a nonextensivity parameter q and scale parameter T . However, there exist experimental results that can be described only by a Tsallis distributions, which are additionally decorated by some log-periodic oscillating factor. ...

Locally optimum detectors for weak random signals are derived for a generalized observation model incorporating signal-dependent and multiplicative noise. It is shown that the locally optimum random-signal detectors in the generalized observation model are interesting generalizations of those that would be obtained in the purely additive noisy signal model. Examples of explicit results for the ...

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Itô stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are shown to be mean-square A-stable for the usual complex scalar linear test problem with multiplicative noise and improve significantly the stabil...

Accurate prediction of future onset of disease from Electronic Health Records (EHRs) has important clinical and economic implications. In this domain the arrival of data comes at semi-irregular intervals and makes the prediction task challenging. We propose a method called multiplicative-forest point processes (MFPPs) that learns the rate of future events based on an event history. MFPPs join p...

We call φ the root function of Φ. The continuity of Φ implies that (1.2) φ(γ) → |γ| as |γ| → ∞. Moreover the converse is true, if φ is continuous and satisfies this asymptotic formula, then the function Φ formed as in (1.1) is a multiplicative distance function. Theorem 1.1. A continuous function φ : C → [0,∞) is the root function of a multiplicative distance function iff it satisfies (1.2). Ar...

We initiate a geometric stability study of groups of the form G/G, where G is a 1-dimensional definably compact, definably connected, definable group in a real closed field M . We consider an enriched structure M ′ with a predicate for G and prove 1-basedness for additive truncations of M , multiplicative truncations, SO2(M) and its truncations; such groups are now interpretable in M ′. We prov...

Synthetic aperture radar (SAR) images are subject to prominent speckle noise, which is generally considered a purely multiplicative noise process. In theory, this multiplicative noise is that the ratio of the standard deviation to the signal value, the “coefficient of variation,” is theoretically constant at every point in a SAR image. Most of the filters for speckle reduction are based on this...

Ludics is a logical theory that J.-Y. Girard developed around 2000. At first glance, it may be considered as a Brouwer-Heyting-Kolmogorov interpretation of Logic as a formula is denoted by the set of its proofs. More primitively, Ludics is a theory of interaction that models (a variant of) second-order multiplicative-additive Linear Logic. A formula is denoted by a set of objects called a behav...

This paper considers techniques for creating enhanced resolution images from irregular samples, with specific application to imaging from scatterometers. Using previously established irregular sampling theory, and developing the idea of sub-band limited Banach space, we show that frequency content in attenuated sidelobes can be recovered using resolution enhancement techniques, thus taking adva...

We introduce the logic of bunched implications, BI, in which multiplicative (or linear) and additive (or intuitionistic) implications live side-by-side. We provide a truth conditional semantics, a proof theory and a categorical semantics of proofs. We explain how BI arises as a logic of resources and sketch a development of this computational interpretation, which is quite diierent from that of...