Related papers: On Descents in Standard Young Tableaux
We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. Andre on the number of up-down permutations. The…
Unnormalised latent variable models are a broad and flexible class of statistical models. However, learning their parameters from data is intractable, and few estimation techniques are currently available for such models. To increase the…
Many problems involve the use of models which learn probability distributions or incorporate randomness in some way. In such problems, because computing the true expected gradient may be intractable, a gradient estimator is used to update…
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…
Web graphs form a family of planar directed graphs with boundary that can be used to model quantum $\mathfrak{sl}_n$-invariant vectors. Standard Young tableaux on an $n \times k$ rectangle naturally index a basis for $\mathfrak{sl}_n$ web…
We give an explicit formula for the exponents (i.e. the spectra up to the shift by one) of an irreducible plane curve singularity in terms of Puiseux pairs. As an application we prove in this case Hertling's conjecture that the variance…
In this paper, by using the representation theorem for sublinear expectations, we give a simple proof to obtain two inequalities about the sample mean for independent random vectors under sublinear expectations.
Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that…
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…
A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…
Latent traversal is a popular approach to visualize the disentangled latent representations. Given a bunch of variations in a single unit of the latent representation, it is expected that there is a change in a single factor of variation of…
Since its original formulation, Jensen's inequality has played a fundamental role across mathematics, statistics, and machine learning, with its probabilistic version highlighting the nonnegativity of the so-called Jensen's gap, i.e., the…
A survey paper, to appear as a chapter in a forthcoming Handbook on Enumeration.
This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation…
The series of papers is devoted to the study of convergence for pairs of surfaces and smooth functions thereon. We model such pairs with varifolds and multiple-valued functions to capture their limits. In the present paper, we study Young…
In this article, we consider a generalization of Young tableaux in which we allow some consecutive pairs of cells with decreasing labels. We show that this leads to a rich variety of combinatorial formulas, which suggest that these new…
We show that the variance of centred linear statistics of eigenvalues of GUE matrices remains bounded for large $n$ for some classes of test functions less regular than Lipschitz functions. This observation is suggested by the limiting form…
In queueing theory, Lorden's inequality can be used for bounds estimation of the moments of backward and forward renewal times. Two random variables called backwards renewal time and forward renewal time for this process are defined.…
We present a new method for minimizing the sum of a differentiable convex function and an $\ell_1$-norm regularizer. The main features of the new method include: $(i)$ an evolving set of indices corresponding to variables that are predicted…
We prove that the number of oscillating tableaux of length $n$ with at most $k$ columns, starting at $\emptyset$ and ending at the one-column shape $(1^m)$, is equal to the number of standard Young tableaux of size~$n$ with $m$ columns of…