Related papers: MultivariateResidues - a Mathematica package for c…

We develop a new approach to the study of the multipoint loci of holomorphic maps between complex manifolds. We relate the $k$-fold locus to the curvilinear component of the Hilbert scheme of $k$ points on the source space of the map, and…

We argue that one does not need to know the explicit solutions of the scattering equations in order to evaluate a given amplitude. We consider the most general quantity consistent with SL(2,C) invariance that can appear in an amplitude that…

A new method to derive Multivariate Quadratic equation systems (MQ) for the input and output bit variables of a cryptographic S-box from its algebraic expressions with the aid of the computer mathematics software system SageMath is…

Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…

A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…

The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…

We present a restricted version of some affine Jacobi's residue formula (on an affine algebraic variety) with applications to higher dimensional (and affine) analogues of Wood's (or Reiss's) relations about the interpolation of pieces of…

This paper gives the recursion formula for mixed multiplicities of maximal degrees with respect to joint reductions of ideals, which is one of important results in the mixed multiplicity theory. Using this result, we give consequences on…

We propose a technique of compensating the spurious reflections implied by the multiple-scattering (MS) method, commonly used for analyzing finite photonic crystal (PC) systems, to obtain exact values of characteristic parameters, such as…

Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…

The aim of our paper is to formulate and solve problems concerning multitime multiple recurrence equations. We discuss in detail the generic properties and the existence and uniqueness of solutions. Among the general things, we discuss in…

In this paper, we derive an explicit combinatorial formula for the number of $k$-subset sums of quadratic residues over finite fields.

We present the first public version of Caravel, a C++17 framework for the computation of multi-loop scattering amplitudes in quantum field theory, based on the numerical unitarity method. Caravel is composed of modules for the…

We consider the topic of multivariate regression on manifold-valued output, that is, for a multivariate observation, its output response lies on a manifold. Moreover, we propose a new regression model to deal with the presence of grossly…

Quantum reservoir computing is a promising paradigm for processing temporal data. So far, the primary focus has been on univariate time series. However, the most relevant and complex real-world data is multidimensional. In this paper, we…

Modeling data using manifold values is a powerful concept with numerous advantages, particularly in addressing nonlinear phenomena. This approach captures the intrinsic geometric structure of the data, leading to more accurate descriptors…

The classical methods of multivariate analysis are based on the eigenvalues of one or two sample covariance matrices. In many applications of these methods, for example to high dimensional data, it is natural to consider alternative…

Regression models, where the response variable is circular, are common in areas such as biology, geology and meteorology. A typical model assumes that the conditional distribution of the response follows a von-Mises distribution. However,…

Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…

Historically, analysis for multiscale PDEs is largely unified while numerical schemes tend to be equation-specific. In this paper, we propose a unified framework for computing multiscale problems through random sampling. This is achieved by…