相关论文: Iterating the RSK Bijection

We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…

We define a class L_{n, k} of permutations that generalizes alternating (up-down) permutations and give bijective proofs of certain pattern-avoidance results for this class. As a special case of our results, we give two bijections between…

We present some accelerated variants of fixed point iterations for computing the minimal non-negative solution of the unilateral matrix equation associated with an M/G/1-type Markov chain. These variants derive from certain staircase…

Consider a continuous word embedding model. Usually, the cosines between word vectors are used as a measure of similarity of words. These cosines do not change under orthogonal transformations of the embedding space. We demonstrate that,…

The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a…

The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…

Reading comprehension (RC) is a challenging task that requires synthesis of information across sentences and multiple turns of reasoning. Using a state-of-the-art RC model, we empirically investigate the performance of single-turn and…

In learning-to-rank for information retrieval, a ranking model is automatically learned from the data and then utilized to rank the sets of retrieved documents. Therefore, an ideal ranking model would be a mapping from a document set to a…

We prove limit theorems for the number of fixed points, descents, and inversions of iterated random-to-top shuffles in two asymptotic regimes. Our proofs are analytic, and they utilize new combinatorial decompositions that represent each…

Recently, deep architectures, such as recurrent and recursive neural networks have been successfully applied to various natural language processing tasks. Inspired by bidirectional recurrent neural networks which use representations that…

Reciprocal recommender system (RRS), considering a two-way matching between two parties, has been widely applied in online platforms like online dating and recruitment. Existing RRS models mainly capture static user preferences, which have…

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…

We present a probabilistic language model for time-stamped text data which tracks the semantic evolution of individual words over time. The model represents words and contexts by latent trajectories in an embedding space. At each moment in…

We consider two orthogonal points of view on finite permutations, seen as pairs of linear orders (corresponding to the usual one line representation of permutations as words) or seen as bijections (corresponding to the algebraic point of…

Along with some known and less known results, we discuss new insights relating combinatorics of words and the ordering of the rationals from a dynamical systems point of view, somehow continuing along the path started in [BI]. We obtain in…

We study a class of stochastic resetting (SR) processes in which a diffusing particle alternates between free motion and confinement by an externally controlled potential. When the particle is recaptured, it undergoes a return trajectory…

A di-sk tree is a rooted binary tree whose nodes are labeled by $\oplus$ or $\ominus$, and no node has the same label as its right child. The di-sk trees are in natural bijection with separable permutations. We construct a combinatorial…

There is growing interest in termination reasoning for non-linear programs and, meanwhile, recent dynamic strategies have shown they are able to infer invariants for such challenging programs. These advances led us to hypothesize that…

Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…

A two-dimensional arrangement of toothpicks is constructed by the following iterative procedure. At stage 1, place a single toothpick of length 1 on a square grid, aligned with the y-axis. At each subsequent stage, for every exposed…