The border rank of the matrix multiplication operator for n× n matrices is a standard measure of its complexity. Using techniques from algebraic geometry and representation theory, we show the border rank is at least 2n2−n. Our bounds are better than the previous lower bound (due to Lickteig in 1985) of 2 n 2 + 2 −1 for all n≥ 3. The bounds are obtained by finding new equations that bilinear ma...

Dynamic Frequency Warping (DFW) offers an appealing alternative to GMM-based voice conversion, which suffers from ”over-smoothing” that hinders speech quality. However, to adjust spectral power after DFW, previous work returns to GMMtransformation. This paper proposes a more effective DFWwith amplitude scaling (DFWA) that functions on the acoustic class level and is independent of GMM-transform...

We study identifiability for bilinear inverse problems under sparsity and subspace constraints. We show that, up to a global scaling ambiguity, almost all such maps are injective on the set of pairs of sparse vectors if the number of measurements m exceeds 2(s1+ s2)− 2, where s1 and s2 denote the sparsity of the two input vectors, and injective on the set of pairs of vectors lying in known subs...

Problem Let LK be a separable algebraic extension of fields. Solutions of the problem We give three solutions to the above problem. First solution First solution of the problem: We first prove the following lemma: Lemma 1. Under the conditions of the problem, let x ∈ L, a ∈ V and b ∈ W be arbitrary. Let α = h (a, b) and β = h (a, xb) − xh (a, b). Then, every positive n ∈ N satisfies h (a, x n b...

We propose a new secret key traitor tracing scheme using bilinear maps, in which the size of the enabling-block in a broadcast message is independent of the number of subscribers. The proposed traitor tracing scheme can identify malicious subscribers (also called traitors) from a pirate decoder, which is collusively made by k or fewer traitors. Further, any malicious subscriber cannot falsify a...

Let A be a Banach algebra, and let E be a Banach A-bimodule. A linear map S :AMNE is intertwining if the bilinear map (a, b)PN (δ"S ) (a, b)B a[Sb®S(ab)­Sa[b, A¬AMNE, is continuous, and a linear map D :AMNE is a deriŠation if δ"D ̄ 0, so that a derivation is an intertwining map. Derivations from A to E are not necessarily continuous. The purpose of the present paper is to prove that the continui...

Recent GPU advances have popularized pixel-shader based techniques for per-pixel displacement mapping. An important step in the process is to compute intersection of ray with a bilinear patch approximating the displacement map. Accurate ray-patch intersection can significantly enhance the quality of rendered images. However, the increase in quality comes at a significant computation cost result...

We propose a fully functional identity-based encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming a variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic curves is an example of such a map. We give precise definitions for secure identity based encryption schemes and ...

We propose stacked two-dimensional lattice designs of frustrated and SO(3) symmetric spin models consisting antiferromagnetic (AFM) triangular ferromagnetic (FM) sixfold sublattices that realize emergent Z3 Potts nematic order. Considering bilinear-biquadratic interactions, our describe an SO(3)-symmetric AFM subject to a fluctuating magnetization arising from the FM coupled sublattice. focus o...

Grishin algebras are a generalisation of Boolean algebras that provide algebraic models for classical bilinear logic with two mutually cancelling negation connectives. We show how to build complete Grishin algebras as algebras of certain subsets (“propositions”) of cover systems that use an orthogonality relation to interpret the negations. The variety of Grishin algebras is shown to be closed ...