Multilinear Techniques Research Articles

Modeling liquid-liquid equilibrium of quaternary systems with Integrated Quadratic Solvation Relationship (IQSR) in conjunction with the boundary constraints identified by ternary subsystems

The Integrated Quadratic Solvation Relationship (IQSR) method is studied with respect to its applicability to three main classes of quaternary liquid-liquid equilibrium systems in combination with their ternary subsystems. We utilize multilinear methodology with a wide range of numerical simulation scenarios to generate an appropriate quadratic functionality of six physical indices combined with the boundary constraints of relevant systems. The IQSR method is applied to the estimation of four newly-proposed extraction factors to demonstrate its attractive application. By building-up three general hybrid forms including twelve adjustable coefficients we are able to validate the examined multilinear technique against the equilibrium data that span total 52 literature liquid-liquid systems being subjected to statistical analysis. It is concluded that the IQSR method offers mathematical reliability due to its robustness, initialization/parameterization-free nature and ease of hybridization with standard Gibbs energy model so long as solvent effects are concerned.

Identification of Natural Compounds against Neurodegenerative Diseases Using In Silico Techniques.

The aim of this study was to identify new potentially active compounds for three protein targets, tropomyosin receptor kinase A (TrkA), N-methyl-d-aspartate (NMDA) receptor, and leucine-rich repeat kinase 2 (LRRK2), that are related to various neurodegenerative diseases such as Alzheimer’s, Parkinson’s, and neuropathic pain. We used a combination of machine learning methods including artificial neural networks and advanced multilinear techniques to develop quantitative structure–activity relationship (QSAR) models for all target proteins. The models were applied to screen more than 13,000 natural compounds from a public database to identify active molecules. The best candidate compounds were further confirmed by docking analysis and molecular dynamics simulations using the crystal structures of the proteins. Several compounds with novel scaffolds were predicted that could be used as the basis for development of novel drug inhibitors related to each target.

Multispectral Periocular Classification With Multimodal Compact Multi-Linear Pooling

Feature-level fusion approaches for multispectral biometrics are mainly grouped into two categories: 1) concatenation and 2) elementwise multiplication. While concatenation of feature vectors has benefits in allowing all elements to interact, it is difficult to learn output classification. Differently, elementwise multiplication has the benefits in enabling multiplicative interaction, but it is difficult to learn input embedding. In this paper, we propose a novel approach to combine the benefits of both categories based on a compact representation of two feature vectors’ outer product, which is called the multimodal compact multi-linear pooling technique. We first propose to expand the bilinear pooling technique for two inputs to a multi-linear technique to accommodate for multiple inputs (multiple inputs from multiple spectra are frequent in the multispectral biometric context). This fusion approach not only allows all elements to interact and enables multiplicative interaction, but also uses a small number of parameters and low computation complexity. Based on this fusion proposal, we subsequently propose a complete multispectral periocular recognition system. Employing higher order spectra features with an elliptical sampling approach proposed by Algashaam et al. , our proposed system achieves the state-of-the-art performance in both our own and the IIIT multispectral periocular data sets. The proposed approach can also be extended to other biometric modalities.

Multilinear Maximum Distance Embedding Via L1-Norm Optimization

Dimensionality reduction plays an important role in many machine learning and pattern recognition tasks. In this paper, we present a novel dimensionality reduction algorithm called multilinear maximum distance embedding (M2DE), which includes three key components. To preserve the local geometry and discriminant information in the embedded space, M2DE utilizes a new objective function, which aims to maximize the distances between some particular pairs of data points, such as the distances between nearby points and the distances between data points from different classes. To make the mapping of new data points straightforward, and more importantly, to keep the natural tensor structure of high-order data, M2DE integrates multilinear techniques to learn the transformation matrices sequentially. To provide reasonable and stable embedding results, M2DE employs the L1-norm, which is more robust to outliers, to measure the dissimilarity between data points. Experiments on various datasets demonstrate that M2DE achieves good embedding results of high-order data for classification tasks.

Quantitative association of vocal-tract and facial behavior

This paper examines the degrees of correlation among vocal-tract and facial movement data and the speech acoustics. Multilinear techniques are applied to support the claims that facial motion during speech is largely a by-product of producing the speech acoustics and further that the spectral envelope of the speech acoustics can be better estimated by the 3D motion of the face than by the midsagittal motion of the anterior vocal-tract (lips, tongue and jaw). Experimental data include measurements of the motion of markers placed on the face and in the vocal-tract, as well as the speech acoustics, for two subjects. The numerical results obtained show that, for both subjects, 91% of the total variance observed in the facial motion data could be determined from vocal-tract motion by means of simple linear estimators. For the inverse path, i.e. recovery of vocal-tract motion from facial motion, the results indicate that about 80% of the variance observed in the vocal-tract can be estimated from the face. Regarding the speech acoustics, it is observed that, in spite of the nonlinear relation between vocal-tract geometry and acoustics, linear estimators are sufficient to determine between 72 and 85% (depending on subject and utterance) of the variance observed in the RMS amplitude and LSP parametric representation of the spectral envelope. A dimensionality analysis is also carried out, and shows that between four and eight components are sufficient to represent the mappings examined. Finally, it is shown that even the tongue, which is an articulator not necessarily coupled with the face, can be recovered reasonably well from facial motion since it frequently displays the same kind of temporal pattern as the jaw during speech.

Multi-algebra duplication.

This paper was inspired by [5]. First, we define a new kind of duplication which differs from the usual one in that we have different multiplication tables for male and female gametes. [5] deals with the special case where the tables correspond to different recombination rates for males and females for two linked loci. Furthermore, we use the factoring and "multilinear technique" discussed in [2] and [3] to simplify the proofs in [5].

Covering graphs by the minimum number of equivalence relations

An equivalence graph is a vertex disjoint union of complete graphs. For a graphG, let eq(G) be the minimum number of equivalence subgraphs ofG needed to cover all edges ofG. Similarly, let cc(G) be the minimum number of complete subgraphs ofG needed to cover all its edges. LetH be a graph onn vertices with maximal degree ≦d (and minimal degree ≧1), and letG= $$\bar H$$ be its complement. We show that $$\log _2 n - \log _2 d \leqq eq(G) \leqq cc(G) \leqq 2e^2 (d + 1)^2 \log _e n.$$ The lower bound is proved by multilinear techniques (exterior algebra), and its assertion for the complement of ann-cycle settles a problem of Frankl. The upper bound is proved by probabilistic arguments, and it generalizes results of de Caen, Gregory and Pullman.

An extremal problem for sets with applications to graph theory

Let X 1, …, X n be n disjoint sets. For 1 ⩽ i ⩽ n and 1 ⩽ j ⩽ h let A ij and B ij be subsets of X i that satisfy | A ij | ⩽ r i and | B ij | ⩽ s i for 1 ⩽ i ⩽ n, 1 ⩽ j ⩽ h, (∪ i A ij) ∩ (∪ i B ij) = ⊘ for 1 ⩽ j ⩽ h, (∪ i A ij) ∩ (∪ i B il) ≠ ⊘ for 1 ⩽ j < l ⩽ h. We prove that h⩽ Π i=1 n r i+s i r i . This result is best possible and has some interesting consequences. Its proof uses multilinear techniques (exterior algebra).

Intersection patterns of convex sets

LetK1,…Kn be convex sets inRd. For 0≦i =0, then {fx161-1} This inequality was conjectured by Katchalski and Perles. Equality holds, e.g., ifK1=…=Kr=Rd andKr+1,…,Kn aren−r hyperplanes in general position inRd. The proof uses multilinear techniques (exterior algebra). Applications to convexity and to extremal set theory are given.

Linear operators preserving the decomposable numerical range

Multilinear techniques are used to characterize unitary matrices in terms of a generalized numerical range. This characterization is then applied to analyze the structure of all linear operators on matrices which preserve this numerical range. The results generalize V. J. Pellegrini's determination of all linear operators preserving the classical numerical range.

Redfield's Theorems and Multilinear Algebra

1. Introduction. The remarkable 1927 paper by J. H. Redfield [13] which anticipated many recent combinatorial results in Polya counting theory and, in fact, predated Polya's theorem by ten years has been discussed at length by Harary and Palmer [8], Foulkes [5; 6], Sheehan [15; 16] and Read [12], not to mention de Bruijn [3] and others. We shall, in this paper, demonstrate how multilinear techniques may be used in this context. The Redfield superposition theorem and decomposition theorem turn out to be statements about a group acting on finite function spaces, and may thus be dealt with in multilinear terms. We shall prove Redfield's results and an extension due to Foulkes [5].