Quantitative structure-property relationship (QSPR) models for the flash points of 758 organic compounds are developed using geometrical, topological, quantum mechanical and electronic descriptors calculated by CODESSA PRO software. Multilinear regression models link the structures to their reported flash point values. We also report a nonlinear model based on an artificial neural network. The ...

The complexity of Iterated Matrix Multiplication is a central theme in Computational Complexity theory, as the problem is closely related to the problem of separating various complexity classes within P. In this paper, we study the algebraic formula complexity of multiplying d many 2×2 matrices, denoted IMMd, and show that the well-known divide-andconquer algorithm cannot be significantly impro...

It is shown that multilinear Calderón-Zygmund operators are bounded on products of Hardy spaces.

Across a range of applications, low multilinear rank approximation (LMLRA) is used to compress large tensors into more compact form, while preserving most their information. A specific instance LMLRA the singular value decomposition (MLSVD), which can be for principal component analysis (MLPCA). MLSVDs are obtained by computing SVDs all tensor unfoldings, but, in practical it often not necessar...

We introduce a solid harmonic wavelet scattering representation, invariant to rigid motion and stable to deformations, for regression and classification of 2D and 3D signals. Solid harmonic wavelets are computed by multiplying solid harmonic functions with Gaussian windows dilated at different scales. Invariant scattering coefficients are obtained by cascading such wavelet transforms with the c...

Topological indices have been applied to build QSAR models for a set of 20 antimalarial cyclic peroxy cetals. In order to evaluate the reliability of the proposed linear models leave-n-out and Internal Test Sets (ITS) approaches have been considered. The proposed procedure resulted in a robust and consensued prediction equation and here it is shown why it is superior to the employed standard cr...

Expressions are multilinear when variable occurrences are linear and products have factors using different variables. We demonstrate that multilinear expressions are either constant or have never a local minimum or a local maximum. Therefore the interval of multilinear expressions may be computed precisely studying their values at the bounds of the variables therein. We then propose a technique...

Abstract. As the classical (p, q)-Poincaré inequality is known to fail for 0 < p < 1, we introduce the notion of weighted multilinear Poincaré inequality as a natural alternative when m-fold products and 1/m < p are considered. We prove such weighted multilinear Poincaré inequalities in the subelliptic context associated to vector fields of Hörmader type. We do so by establishing multilinear re...

We propose an efficient Key-policy Attribute-based Encryption (KP-ABE) scheme for general (monotone) Boolean circuits based on secret sharing and on a very particular and simple form of leveled multilinear maps, called chained multilinear maps. The number of decryption key components is substantially reduced in comparison with the scheme in [6], and the size of the multilinear map (in terms of ...

We propose a new way to obfuscate programs, using composite-order multilinear maps. Our construction operates directly on straight-line programs (arithmetic circuits), rather than converting them to matrix branching programs as in other known approaches. This yields considerable efficiency improvements. For an NC circuit of size s and depth d, with n inputs, we require only O(ds + n) multilinea...