We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse zonotopes can represent nonconvex sets and are generalizations polytopes, Taylor models. Operations like Minkowski sum, quadratic mapping, reduction the size be computed with complexity w.r.t. dimension system. In particular, reachability analysis nonlinear systems, wrapping effe...

We study the limits of accuracy for weak lensing maps of dark matter using diffuse 21-cm radiation from the pre-reionization epoch using simulations. We improve on previous “optimal” quadratic lensing estimators by using shear and convergence instead of deflection angles. We find that non-Gaussianity provides a limit to the accuracy of weak lensing reconstruction, even if instrumental noise is ...

Detecting a small number of outliers from a set of data observations is always challenging. In this paper, we present an approach that exploits space transformation and uses spectral analysis in the newly transformed space for outlier detection. Unlike most existing techniques in the literature which rely on notions of distances or densities, this approach introduces a novel concept based on lo...

Using a new domain-theoretic characterisation we show that Berry’s constructive semantics is a conservative approximation of the recently proposed sequentially constructive (SC) model of computation. We prove that every Berry-constructive program is deterministic and deadlock-free under sequentially admissible scheduling. This gives, for the first time, a natural interpretation of Berry-constru...

We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic cluster operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is satisfied. This condition is treated on average in a composite particle mean-field approach, which consists of an ansatz that decouples the composite fermio...

Several interior point algorithms have been proposed for solving nonlinear monotone complementarity problems. Some of them have polynomial worst-case complexity but have to connne to short steps, whereas some of the others can take long steps but no polynomial complexity is proven. This paper presents an algorithm which is both long-step and polynomial. In addition, the sequence generated by th...

In [6], Kontsevich and Zorich conjecture that the fundamental groups of strata of the moduli space of abelian differentials are commensurable with various mapping class groups. In this paper we consider a similar question for strata of quadratic differentials, and in particular we construct a quotient group of the fundamental group for a certain family of strata. We do so by mapping a stratum i...

in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...

in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.

In linkage analysis, it is often necessary to include covariates such as age or weight to increase power or avoid spurious false positive findings. However, if a covariate term in the model is specified incorrectly (e.g., a quadratic term misspecified as a linear term), then the inclusion of the covariate may adversely affect power and accuracy of the identification of quantitative trait loci (...