Visual recognition faces the difficult problem of recognizing objects despite the multitude of their appearances. Ample neuroscientific evidence shows that the cortex uses a topographic code to represent visual stimuli. We therefore develop a bilinear probabilistic model that learns transformations to build an invariant topographic code in an unsupervised way. Simulations for the simple over-co...

Given three complex Banach spaces X,Y, Z and u : X × Y → Z a bounded bilinear map. For f(z) = ∑m n=0 xnz n where xn ∈ X and g(z) = ∑k n=0 ynz n where yn ∈ X, we define the u-convolution of f an g as the polynomial given by f ∗u g(z) = ∑min{m,k} n=0 u(xn, yn)z n. It is shown that whenever X and Y veryfies the vector-valued analogue of certain inequalities due to Littlewood and Paley for Hardy sp...

Let V be a vector space of dimension n+1 over a field k, and consider the scheme X = PV ∼= Pk ∼= Proj(k[x0, . . . , xn]). Consider F a quasi-coherent sheaf over X. We can examine its Cech cohomology which coincides with its sheaf (nonetale) cohomology because X is Noetherian and separated (cf. Hartshorne, ch. III theorem 4.5.). Particularly, H(X,F) ∼= Γ(F , X). However Γ(F , X) ∼= HomX(OX ,F). ...

This paper is a sequel to [6], in which we introduced quadratic forms on a module over a supertropical semiring R and analyzed the set of bilinear companions of a single quadratic form V → R in case the module V is free. Any (semi)module over a semiring gives rise to what we call its minimal ordering, which is a partial order iff the semiring is “upper bound.” Any polynomial map q (or quadratic...

In this work we present our entry for the Voice Conversion Challenge 2016, denoting new features to previous work on GMM-based voice conversion. We incorporate frequency warping and pitch transposition strategies to perform a normalisation of the spectral conditions, with benefits confirmed by objective and perceptual means. Moreover, the results of the challenge showed our entry among the high...

It is shown that the bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. Z R f(x− αt)g(x− βt) dt t map L1(R)×L2(R)→ L(R) uniformly in the real parameters α, β when 2 < p1, p2 <∞ and 1 < p = p1p2 p1+p2 < 2. Combining this result with the main result in [9], it follows that the operators H1,α map L (R) × L∞(R) → L(R) uniformly in the real parameter α ∈ [0, 1], as conjectured by A. Calderón.

Both vector 1-forms (tensor elds of type (1,1)) and Lie brackets map (tangent) vectors to the same. The former do so in a manner that is linear over the ring of functions; the latter are bilinear, but only over the constants. By composing one Lie bracket and m vector 1-forms (we consider 2 m 4) in all possible ways many maps of vector elds are obtained, bilinear over the constants. We study lin...

The notion of the square submodule of a module M over an arbitrary commutative ring R, which is denoted by RM, was introduced by Aghdam and Najafizadeh in [3]. In fact, RM is the R−submodule of M generated by the images of all bilinear maps on M. Furthermore, given a submodule N of an R−module M, we say that M is nil modulo N if μ(M×M) ≤ N for all bilinear maps μ on M. The main question about t...

We construct an interactive identification scheme based on the bilinear Diffie-Hellman problem and analyze its security. This scheme is practical in terms of key size, communication complexity, and availability of identity-variance provided that an algorithm of computing the Weil-pairing is feasible. We prove that this scheme is secure against active attacks as well as passive attacks if the bi...

We construct two efficient Identity Based Encryption (IBE) systems that are selective identity secure without the random oracle model in groups equipped with a bilinear map. Selective identity secure IBE is a slightly weaker security model than the standard security model for IBE. In this model the adversary must commit ahead of time to the identity that it intends to attack, whereas in the sta...