Related papers: Permutation Models Arising From Topological Ideals
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple…
We study some representations of symmetric groups arising from a certain ideal in the coordinate ring of affine n-space. Our results give graded and representation-theoretic enhancements of sequence 337 of the Online Encyclopaedia of…
Deterministic many-body systems governed by simple interactions can self-organize into macroscopic patterns, and the determinants of long-time behavior are assumed to be encoded in the initial configuration. Here we show that predictability…
In this paper, we tackle the problem of innovation spreading from a modeling point of view. We consider a networked system of individuals, with a competition between two groups. We show its relation to the innovation spreading issues. We…
Recently, evolving networks are becoming a suitable form to model many real-world complex systems, due to their peculiarities to represent the systems and their constituting entities, the interactions between the entities and the…
Let $\mathcal{I}$ be an analytic P-ideal [respectively, a summable ideal] on the positive integers and let $(x_n)$ be a sequence taking values in a metric space $X$. First, it is shown that the set of ideal limit points of $(x_n)$ is an…
The problem of model collapse has presented new challenges in iterative training of generative models, where such training with synthetic data leads to an overall degradation of performance. This paper looks at the problem from a…
We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…
The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
The associated prime ideals of powers of polymatroidal ideals are studied, including the stable set of associated prime ideals of this class of ideals. It is shown that polymatroidal ideals have the persistence property and for transversal…
A symmetric chain of ideals is a rule that assigns to each finite set $S$ an ideal $I_S$ in the polynomial ring $\mathbb{C}[x_i]_{i \in S}$ such that if $\phi \colon S \to T$ is an embedding of finite sets then the induced homomorphism…
We investigate the asymptotic properties of permutations drawn from the Luce model, a natural probabilistic framework in which permutations are generated sequentially by sampling without replacement, with selection probabilities…
By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
Tabular foundation models with different architectures converge in accuracy across a range of classification and regression tasks. This raises questions a leaderboard cannot answer: (i) whether the models execute the same in-context…