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This paper proposes an extension of standard mixture stochastic models, by replacing the constant mixture weights with functional weights defined using a classifier. Classifier Weighted Mixtures enable straightforward density evaluation,…
We show that there exist uncountably many (tall and nontall) pairwise nonisomorphic density-like ideals on $\omega$ which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by…
We define a notion of modular forms of half-integral weight on the quaternionic exceptional groups. We prove that they have a well-behaved notion of Fourier coefficients, which are complex numbers defined up to multiplication by $\pm 1$. We…
We study certain filtrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warfield. To indicate the consequences of our…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
For a wide range of functions $W\colon\mathbb{N}\to\mathbb{N}$, we establish a general result for estimating weighted averages of the form \[ \mathbb{E}^{W}_{n \le N} f(\vartheta(n))= \frac{1}{W(N)}\sum_{n=1}^N (W(n)-W(n-1))f(\vartheta(n)),…
A generic feature of inflationary models in supergravity/string constructions is vacuum misalignment for the moduli fields. The associated production of moduli particles leads to an epoch in the post-inflationary history in which the energy…
We propose a novel quantum integrable model for every non-simply laced simple Lie algebra ${\mathfrak g}$, which we call the folded integrable model. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the…
We discuss the most common types of weight functions in harmonic analysis and how they occur in \tfa . As a general rule, submultiplicative weights characterize algebra properties, moderate weights characterize module properties,…
We define a general class of superconformal inflationary attractor models studied in our previous papers [1,2], which include, among others, inflationary models of 'induced gravity' which were argued to retain perturbative unitarity up to…
We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring $R$), which is assumed to carry an involution of the form $X^*=Y$, $R^*\subseteq R$. We prove…
Some properties of $m$-density points and density-degree functions are studied. Moreover the following main results are provided: \vskip2mm \begin{itemize} \item {\it Let $\lambda$ be a continuous differential form of degree $h$ in…
The problem of error density estimation for a functional single index model with dependent errors is studied. A Bayesian method is utilized to simultaneously estimate the bandwidths in the kernel-form error density and regression function,…
The heavyweight stellar initial mass function (IMF) observed in the cores of massive early-type galaxies (ETGs) has been linked to formation of their cores in an initial swiftly-quenched rapid starburst. However, the outskirts of ETGs are…
In 1958, Helson and Lowdenslager extended the theory of analytic functions to a general class of groups with ordered duals. In this context, analytic functions on such a group $G$ are defined as the integrable functions whose Fourier…
Classifier-Free Guidance (CFG) enhances the quality and condition adherence of text-to-image diffusion models. It operates by combining the conditional and unconditional predictions using a fixed weight. However, recent works vary the…
Let $I\subset (0,\infty )$ be an interval that is closed with respect to the multiplication. The operations $C_{f,g}\colon I^{2}\rightarrow I$ of the form \begin{equation*} C_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left(…
A goodness-of-fit index measures the consistency of consumption data with a given model of utility-maximization. We show that for the class of well-behaved (i.e., continuous and increasing) utility functions there is no goodness-of-fit…
The general construction of lattice (co)homology assigns to a lattice $\mathbb{Z}^r$ and a weight function $w:\mathbb{Z}^r \to \mathbb{Z}$ a bigraded $\mathbb{Z}[U]$-module $\mathbb{H}_*$. The weight function $w$ is often obtained from some…
The energy density spectrum is an observable of gravitational waves. Divergence has appeared in the energy density spectra of the scalar induced gravitational waves for different gauge fixings. To resolve the discrepancy, we investigate the…