相关论文: Iterating the RSK Bijection

We present a version of the RSK correspondence based on the Pitman transform and geometric considerations. This version unifies ordinary RSK, dual RSK and continuous RSK. We show that this version is both a bijection and an isometry, two…

Like the LR-tableau, a socle tableau is given as a skew diagram with certain entries. Unlike in the LR-tableau, the entries in the socle tableau are weakly increasing in each row, strictly increasing in each column and satisfy a modified…

Any permutation in the finite symmetric group can be written as a product of simple transpositions $s_i = (i~i+1)$. For a fixed permutation $\sigma \in \mathfrak{S}_n$ the products of minimal length are called reduced decompositions or…

In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is…

Referring Expression Comprehension (REC) is one of the most important tasks in visual reasoning that requires a model to detect the target object referred by a natural language expression. Among the proposed pipelines, the one-stage…

We study a renormalization group (RG) map for tensor networks that include two-dimensional lattice spin systems such as the Ising model. Numerical studies of such RG maps have been quite successful at reproducing the known critical…

Combining the representations of the words that make up a sentence into a cohesive whole is difficult, since it needs to account for the order of words, and to establish how the words present relate to each other. The solution we propose…

The row projection (resp., column projection) of a two-dimensional language $L$ is the one-dimensional language consisting of all first rows (resp., first columns) of each two-dimensional word in $L$. The operation of row projection has…

The replication dynamics (differential equation system) is the foundation of evolutionary game theory. When n=2, there are four possible types of replication dynamics. When n=3, there are 49 possible types of replication dynamics. However,…

Starting with a combinatorial partition theorem for words over an infinite alphabet dominated by a fixed sequence, established recently by the authors, we prove recurrence results for topological dynamical systems indexed by such words. In…

Given a finite poset $P$, we study the _whirling_ action on vertex-labelings of $P$ with the elements $\{0,1,2,\dotsc ,k\}$. When such labelings are (weakly) order-reversing, we call them $k$-bounded $P$-partitions. We give a general…

Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of…

In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under- or over-budgeted for…

In the dynamics of a rotation of the unit circle by an irrational angle $\alpha\in(0,1)$, we study the evolution of partitions whose atoms are finite unions of left-closed right-open intervals with endpoints lying on the past trajectory of…

We find a countable partition $P$ on\textbf{} a Lebesgue space, labeled $\{1,2,3...$\}, for any non-periodic measure preserving transformation $T$ such that $P$ generates $T$ and for the $T,P$ process, if you see an $n$ on time -1 then you…

In transcendental dynamics significant progress has been made by studying points whose iterates escape to infinity at least as fast as iterates of the maximum modulus. Here we take the novel approach of studying points whose iterates escape…

When proving the correctness of a method for slicing probabilistic programs, it was previously discovered by the authors that for a fixed point iteration to work one needs a non-standard starting point for the iteration. This paper presents…

Recently, Blecher and Knopfmacher applied the notion of fixed points to integer partitions. This has already been generalized and refined in various ways such as $h$-fixed points for an integer parameter $h$ by Hopkins and Sellers. Here, we…

We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…

We propose a generalization of modern representation learning objectives by reframing them as recursive divergence alignment processes over localized conditional distributions While recent frameworks like Information Contrastive Learning…