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We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…

Statistics Theory · Mathematics 2021-08-05 Shuzhen Yang , Jianfeng Yao

A general conversion strategy by involving a shifted parameter $\theta$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such…

Numerical Analysis · Mathematics 2022-04-13 Baoli Yin , Guoyu Zhang , Yang Liu , Hong Li

Let Gamma\D be an arithmetic quotient of a symmetric space of non-compact type. A spine D_0 is a Gamma-equivariant deformation retraction of D with dimension equal to the virtual cohomological dimension of Gamma. We explicitly construct a…

Number Theory · Mathematics 2007-05-23 Dan Yasaki

We study (pre-)sheaves in bicategories on geometric categories: smooth manifolds, manifolds with a Lie group action and Lie groupoids. We present three main results: we describe equivariant descent, we generalize the plus construction to…

Algebraic Topology · Mathematics 2011-05-30 Thomas Nikolaus , Christoph Schweigert

We study weakest precondition reasoning about the (co)variance of outcomes and the variance of run-times of probabilistic programs with conditioning. For outcomes, we show that approximating (co)variances is computationally more difficult…

Logic in Computer Science · Computer Science 2016-06-28 Benjamin Lucien Kaminski , Joost-Pieter Katoen , Christoph Matheja

A semi-process is an analog of the semi-flow for non-autonomous differential equations or inclusions. We prove an abstract result on the existence of measurable semi-processes in the situations where there is no uniqueness. Also, we allow…

Dynamical Systems · Mathematics 2017-07-21 Jorge E. Cardona , Lev Kapitanski

A. Gray presented an interesting $O\left( n\right) $ invariant decomposition of the covariant derivative of the Ricci tensor. Manifolds whose Ricci tensor satisfies the defining property of each orthogonal class are called Einstein-like…

Differential Geometry · Mathematics 2021-04-27 Hoda K. El-Sayed , Carlo Alberto Mantica , Sameh Shenawy , Noha Syied

We introduce an entropic quantity for two-dimensional (2D) quantum spin systems to characterize gapped quantum phases modeled by local commuting projector code Hamiltonians. The definition is based on a recently introduced specific operator…

Quantum Physics · Physics 2020-01-31 Kohtaro Kato , Pieter Naaijkens

High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…

Methodology · Statistics 2016-06-28 Sang-Yun Oh , Bala Rajaratnam , Joong-Ho Won

Let $\overline{M}$ be a compact smoothly stratified pseudo-manifold endowed with a wedge metric $g$. Let $\overline{M}_\Gamma$ be a Galois $\Gamma$-covering. Under additional assumptions on $\overline{M}$, satisfied for example by Witt…

Differential Geometry · Mathematics 2024-09-12 Francesco Bei , Paolo Piazza , Boris Vertman

We analize the algebraic structure of consistent and covariant anomalies in gauge and gravitational theories: using a complex extension of the Lie algebra it is possible to describe them in a unified way. Then we study their representations…

High Energy Physics - Theory · Physics 2010-11-01 Luca Griguolo

We show how conformal invariance predicts the functional form of two-point correlators in one-dimensional periodic quantum systems. Numerical evidence for this functional form in a wide class of models --- including long-ranged ones --- is…

Condensed Matter · Physics 2007-05-23 Rudolf A. R"omer , Bill Sutherland

This paper studies a regression model where both predictor and response variables are random functions. We consider a functional linear model where the conditional mean of the response variable at each time point is given by a linear…

Statistics Theory · Mathematics 2017-03-23 Masaaki Imaizumi , Kengo Kato

The multi-reference alignment (MRA) problem involves reconstructing a signal from multiple noisy observations, each transformed by a random group element. In this paper, we focus on the group \(\mathrm{SO}(2)\) of in-plane rotations and…

Numerical Analysis · Mathematics 2025-05-07 Gil Drozatz , Tamir Bendory , Nir Sharon

We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…

Cellular Automata and Lattice Gases · Physics 2015-06-26 Navot Israeli , Nigel Goldenfeld

Consider the mutually catalytic branching process with finite branching rate $\gamma$. We show that as $\gamma\to\infty$, this process converges in finite-dimensional distributions (in time) to a certain discontinuous process. We give…

Probability · Mathematics 2010-10-20 Achim Klenke , Leonid Mytnik

We derive product and series representations of the gamma function using Newton interpolation series. Using these identities, a new formula for the coefficients in the Taylor series of the reciprocal gamma function is found. We also find…

Number Theory · Mathematics 2025-03-14 David Peter Hadrian Ulgenes

We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…

High Energy Physics - Theory · Physics 2009-10-22 Gerald B. Cleaver , David C. Lewellen

We exhibit a class of "relatively curved" $\vec{\gamma}(t) := (\gamma_1(t),\dots,\gamma_n(t))$, so that the pertaining multi-linear maximal function satisfies the sharp range of H\"{o}lder exponents, \[ \left\| \sup_{r > 0} \ \frac{1}{r}…

Classical Analysis and ODEs · Mathematics 2020-07-28 Ben Krause

We compute the torsion-free linear maps from the Lie algebra su(2) into itself, deduce a new determination of the integrable complex structures and their equivalence classes under the action of the automorphism group for u(2) and…

Rings and Algebras · Mathematics 2008-12-15 Louis Magnin