相关论文: Measure and integral with purely ordinal scales

We provide a sharp monotonicity theorem about the distribution of subharmonic functions on manifolds, which can be regarded as a new, measure theoretic form of the uncertainty principle. As an illustration of the scope of this result, we…

The density of zeros of the partition function of the Ising model on a class of treelike lattices is studied. An exact closed-form expression for the pertinent critical exponents is derived by using a couple of recursion relations which…

General Relativity (GR) exists in different formulations, which are equivalent in pure gravity. Once matter is included, however, observable predictions generically depend on the version of GR. In order to quantify the resulting ambiguity,…

Three techniques for performing gauge-invariant, noncompact lattice simulations of nonabelian gauge theories are discussed. In the first method, the action is not itself gauge invariant, but a kind of lattice gauge invariance is restored by…

We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to…

Many outcomes of interest in the social and health sciences, as well as in modern applications in computational social science and experimentation on social media platforms, are ordinal and do not have a meaningful scale. Causal analyses…

We present an elementary method of explicit calculation of Young measures for certain class of functions. This class contains in particular functions of a highly oscillatory nature which appear in optimization problems and homogenization…

The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising…

This study introduces a novel spatial autoregressive model in which the dependent variable is a function that may exhibit functional autocorrelation with the outcome functions of nearby units. This model can be characterized as a…

We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…

Functional data analysis has been extensively conducted. In this study, we consider a partially functional model, under which some covariates are scalars and have linear effects, while some other variables are functional and have…

This article analyzes directed lattice paths, when a boundary reflecting or absorbing condition is added to the classical models. The lattice paths are characterized by two time-independent sets of rules (also called steps) which have a…

Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…

We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure…

A novel basis of discrete analytic polynomials on a rhombic lattice is introduced and the associated convolution product is studied. A class of discrete analytic functions that are rational with respect to this product is also described.

We perform perturbative computations in a lattice gauge theory with a conformal measure that is quadratic in a non-compact abelian gauge field and is nonlocal, as inspired by the induced gauge action in massless QED$_3$. In a previous work,…

We obtain nonperturbative results on the sine-Gordon model using the lattice field technique. In particular, we employ the Fourier accelerated hybrid Monte Carlo algorithm for our studies. We find the critical temperature of the theory…

If $\mu$ is a finite complex measure in the complex plane $\C$ we denote by $C^\mu$ its Cauchy integral defined in the sense of principal value. The measure $\mu$ is called reflectionless if it is continuous (has no atoms) and $C^\mu=0$ at…

Lattice simulations on SU(2) and SU(3) gauge theories with matter fields in the fundamental, adjoint and two index symmetric representations are needed to determine if these theories are near or within the conformal window as required for…

We demonstrate a method to experimentally calibrate the refractive index modulation in photorefractive lattices, a task rarely addressed that is crucial for quantitative comparisons of theories with experiments. We consider the linear…