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Two-sample tests have been extensively employed in various scientific fields and machine learning such as evaluation on the effectiveness of drugs and A/B testing on different marketing strategies to discriminate whether two sets of samples…
We propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the $q_T$ spectra of gauge bosons ($\gamma^*$, Higgs) in $pp$ collisions in the regime of low (but perturbative)…
The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…
Elaborating on our joint work with Abramsky in quant-ph/0402130 we further unravel the linear structure of Hilbert spaces into several constituents. Some prove to be very crucial for particular features of quantum theory while others…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…
This paper provides a complete proof of Simon-Lukic conjecture for orthogonal polynomials on the unit circle. For a probability measure $d\mu = w(\theta) \frac{d\theta}{2\pi} + d\mu_s$ with Verblunsky coefficients…
Hensel's lemma, combined with repeated applications of Weierstrass preparation theorem, allows for the factorization of polynomials with multivariate power series coefficients. We present a complexity analysis for this method and leverage…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly perturbed half-spaces in two and three dimensions. The kernel…
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…
We introduce a randomized iterative fragmentation procedure for finite metric spaces, which is guaranteed to result in a polynomially large subset that is $D$-equivalent to an ultrametric, where $D\in (2,\infty)$ is a prescribed target…
We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a…
Superspace of rank $n$ is a $\mathbb{Q}$-algebra with $n$ commuting generators $x_1, \dots, x_n$ and $n$ anticommuting generators $\theta_1, \dots, \theta_n$. We present an extension of the Vandermonde determinant to superspace which…
We consider $N\times N$ Hermitian random matrices $H$ consisting of blocks of size $M\geq N^{6/7}$. The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from…
The method of realizing certain self-reciprocal transforms as (absolute) scattering, previously presented in summarized form in the case of the Fourier cosine and sine transforms, is here applied to the self-reciprocal transform f(y)->…
Motivated by topological Tverberg-type problems and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R^d without triple, quadruple, or, more…
The widespread adoption of the \emph{maximum mean discrepancy} (MMD) in goodness-of-fit testing has spurred extensive research on its statistical performance. However, recent studies indicate that the inherent structure of MMD may constrain…
High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…
Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly,…
In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding…