Related papers: Proxy principles in combinatorial set theory
The super-parametric density estimators and its related algorism were suggested by Y. -S. Tsai et al [7]. The number of parameters is unlimited in the super- parametric estimators and it is a general theory in sense of unifying or…
Bona [2007+] studied the distribution of ascents, plateaux and descents in the class of Stirling permutations, introduced by Gessel and Stanley [1978]. Recently, Janson [2008+] showed the connection between Stirling permutations and plane…
Balancing predictive power and interpretability has long been a challenging research area, particularly in powerful yet complex models like neural networks, where nonlinearity obstructs direct interpretation. This paper introduces a novel…
This note discusses the paper "Penalising model component complexity" by Simpson et al. (2017). While we acknowledge the highly novel approach to prior construction and commend the authors for setting new-encompassing principles that will…
Many algorithms are specified with respect to a fixed but unspecified parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key. Our aim is…
We propose a novel architecture for Graph Neural Networks that is inspired by the idea behind Tree Kernels of measuring similarity between trees by taking into account their common substructures, named fragments. By imposing a series of…
This paper finally fully elaborates the tree pulldown method used by one of us (Harrington) to settle McLaughlin's conjecture. This method enables the construction of a computable tree $T_0$ whose paths are incomparable over $0^{(\alpha)}$…
Building on early work by Stevo Todorcevic, we describe a theory of stationary subtrees of trees of successor-cardinal height. We define the diagonal union of subsets of a tree, as well as normal ideals on a tree, and we characterize…
Algorithmic meta-theorems, stating that graph properties expressible in some particular logic can be decided efficiently in graph classes having some specific structural properties, are now standard in sequential graph algorithms. One of…
We introduce a nonasymptotic framework for sub-Poisson distributions with moment generating function dominated by that of a Poisson distribution. At its core is a new notion of optimal sub-Poisson variance proxy, analogous to the variance…
We present efficient combinatorial parameterized algorithms for several classical graph-based counting problems in computational chemistry, including (i) Kekule structures, (ii) the Hosoya index, (iii) the Merrifield-Simmons index, and (iv)…
Crystal property prediction, governed by quantum mechanical principles, is computationally prohibitive to solve exactly for large many-body systems using traditional density functional theory. While machine learning models have emerged as…
We present new, exceptionally efficient proofs of Poisson--Dirichlet limit theorems for the scaled sizes of irreducible components of random elements in the classic combinatorial contexts of arbitrary assemblies, multisets, and selections,…
In this paper, we introduce the $k\times n$ (with $k\leq n$) truncated, supplemented Pascal matrix which has the property that any $k$ columns form a linearly independent set. This property is also present in Reed-Solomon codes; however,…
Reversible evolution of macroscopic and mesoscopic systems can be conveniently constructed from two ingredients: an energy functional and a Poisson bracket. The goal of this paper is to elucidate how the Poisson brackets can be constructed…
We present two sets of theoretical results on the grouped lasso with overlap of Jacob, Obozinski and Vert (2009) in the linear regression setting. This method allows for joint selection of predictors in sparse regression, allowing for…
In a recent paper published in Nature, Y.I. Sobolev et al. introduced the concept of trajectoids: convex, rigid objects, which roll without slip or spin on a flat plane along a prescribed periodic, unbounded planar path. A geometric…
Conjugate pairs of distributions over infinite dimensional spaces are prominent in statistical learning theory, particularly due to the widespread adoption of Bayesian nonparametric methodologies for a host of models and applications. Much…
We demonstrate propagation rules of subsystem code constructions by extending, shortening and combining given subsystem codes. Given an $[[n,k,r,d]]_q$ subsystem code, we drive new subsystem codes with parameters $[[n+1,k,r,\geq d]]_q$,…
Motivated by the goal of constructing a model in which there are no $\kappa$-Aronszajn trees for any regular $\kappa>\aleph_1$, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square…