Multi-modal models that learn semantic representations from both linguistic and perceptual input outperform language-only models on a range of evaluations, and better reflect human concept acquisition. Most perceptual input to such models corresponds to concrete noun concepts and the superiority of the multimodal approach has only been established when evaluating on such concepts. We therefore ...

Taking a photo outside, can we predict the immediate future, like how the cloud would move in the sky? We answer this question by presenting a generative adversarial network (GAN) based two-stage approach to generating realistic time-lapse videos of high resolution. Given the first frame, our model learns to generate long-term future frames. The first stage aims to generate videos of similar co...

This paper develops an abstract framework for constructing “seminormal forms” for cellular algebras. That is, given a cellular R–algebra A which is equipped with a family of JM–elements we give a general technique for constructing orthogonal bases for A, and for all of its irreducible representations, when the JM–elements separate A. The seminormal forms for A are defined over the field of frac...

This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpasshighpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This m...

In this paper we formulate and prove a statistical version of the Candès-Tao restricted isometry property (SRIP for short) which holds in general for any incoherent dictionary which is a disjoint union of orthonormal bases. In addition, we prove that, under appropriate normalization, the eigenvalues of the associated Gram matrix fluctuate around λ = 1 according to the Wigner semicircle distribu...

Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, and sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with indep...

We study a problem related to Kontsevich’s homological mirror symmetry conjecture for the case of a generic curve Y with bi-degree (2,2) in a product of projective lines P×P. We calculate two differenent monodromy representations of period integrals for the affine variety X obtained by the dual polyhedron mirror variety construction from Y. The first method that gives a full representation of t...

We use the notation defined in this paper. Let X be a supersingular K3 surface in characteristic p = p with Artin invariant σ = sigma. • GramSX[p, sigma] is a Gram matrix of the lattice Λp,σ, which is isomorphic to SX . • h0[p, sigma] is a vector h0 of Λp,σ with ⟨h0, h0⟩Λ > 0. • Rh0[p, sigma] is the set R(h0). • amplelist[p, sigma] is an ample list of vectors a = [h0, ρ1, . . . , ρK ]. We ident...

In this paper we study the inequalities of the determinants of the positive definite matrices and the invertible matrices by applying the integral method and matrix theory such that extensions of Fan Ky’s inequality are established. And then an improvement of Fan Ky’s inequality is given by using the positive definiteness of Gram matrix. Mathematics Subject Classification (2010): 15A15, 26D15.

A class of associative algebras called cyclotomic Temperley-Lieb algebras is introduced in terms of generators and relations. They are closely related to the group algebras of complex reflection groups on one hand and generalizations of the usual Temperley-Lieb algebras on the other hand. It is shown that the cyclotomic Temperley-Lieb algebras can be defined by means of labelled Temperley-Lieb ...