Related papers: Online premeans and their computation complexity
We prove that whenever $M_1,\dots,M_n\colon I^k \to I$, ($n,k \in \mathbb{N}$) are symmetric, continuous means on the interval $I$ and $S_1,\dots,S_m\colon I^k \to I$ ($m <n$) satisfies a sort of embeddability assumptions then for every…
In this paper, the generating functions of Garvans so-called $k$-ranks are used, to define a family of mock Eisenstein series. The $k$-rank moments are then expressed as partition traces of these functions. We explore the modular properties…
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these…
This paper realizes of two families of combinatorial symmetric functions via the complex character theory of the finite general linear group $\mathrm{GL}_{n}(\mathbb{F}_{q})$: chromatic quasisymmetric functions and vertical strip LLT…
Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their…
We calculate the murmuration density for the family of Hecke $L$-functions of imaginary quadratic fields associated to non-trivial characters. This density exhibits a universality property like Zubrilina's density for the murmurations of…
We establish a one-to-one correspondence between numerical semigroups of genus $g$ and almost symmetric numerical semigroups with Frobenius number $F$ and type $F-2g$, provided that $F$ is greater than $4g-1$.
This paper introduces a novel extension of Fr\'{e}chet means, called \textit{generalized Fr\'{e}chet means} as a comprehensive framework for characterizing features in probability distributions in general topological spaces. The generalized…
We introduce an asymmetric distance in the space of learning tasks, and a framework to compute their complexity. These concepts are foundational for the practice of transfer learning, whereby a parametric model is pre-trained for a task,…
Let $\mathrm{R}$ be a real closed field, $S \subset \mathrm{R}^n$ a closed and bounded semi-algebraic set, and $\mathbf{f}=(f_1,\ldots,f_p):S \rightarrow \mathrm{R}^p$ a continuous semi-algebraic map inducing a $p$-parameter semi-algebraic…
We present a general, efficient technique for providing contextual predictions that are "multivalid" in various senses, against an online sequence of adversarially chosen examples $(x,y)$. This means that the resulting estimates correctly…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
A collection of families $(\mathcal{F}_{1}, \mathcal{F}_{2} , \cdots , \mathcal{F}_{k}) \in \mathcal{P}([n])^k$ is cross-Sperner if there is no pair $i \not= j$ for which some $F_i \in \mathcal{F}_i$ is comparable to some $F_j \in…
We present some Markovian approaches to prove universality results for some functions on the symmetric group. Some of those statistics are already studied in [Kammoun, 2018, 2020] but not the general case. We prove, in particular, that the…
This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model complex data of various modalities like images and text,…
The theory of quasi-arithmetic means is a powerful tool in the study of covariance functions across space-time. In the present study we use quasi-arithmetic functionals to make inferences about the permissibility of averages of functions…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Permutation resemblance measures the distance of a function from being a permutation. Here we show how to determine the permutation resemblance through linear integer programming techniques. We also present an algorithm for constructing…
In this paper, a new mixture family of multivariate normal distributions, formed by mixing multivariate normal distribution and skewed distribution, is constructed. Some properties of this family, such as characteristic function, moment…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…