Linguistic Matrix Theory

32 pages, 3 figures32 pages, 3 figures32 pages, 3 figuresRecent research in computational linguistics has developed algorithms which associate matrices with adjectives and verbs, based on the distribution of words in a corpus of text. These matrices are linear operators on a vector space of context words. They are used to construct the meaning of composite expressions from that of the elementary constituents, forming part of a compositional distributional approach to semantics. We propose a Matrix Theory approach to this data, based on permutation symmetry along with Gaussian weights and their perturbations. A simple Gaussian model is tested against word matrices created from a large corpus of text. We characterize the cubic and quartic departures from the model, which we propose, alongside the Gaussian parameters, as signatures for comparison of linguistic corpora. We propose that perturbed Gaussian models with permutation symmetry provide a promising framework for characterizing the nature of universality in the statistical properties of word matrices. The matrix theory framework developed here exploits the view of statistics as zero dimensional perturbative quantum field theory. It perceives language as a physical system realizing a universality class of matrix statistics characterized by permutation symmetry

Heritability of Polycystic Ovary Syndrome in a Dutch Twin-family study

Background: Polycystic ovary syndrome (PCOS) is one of the most common endocrine disorders among women of reproductive age. There is evidence for a genetic component in PCOS based on familial clustering of cases. Objective: In the present study, the heritability of PCOS was estimated. Design/Participants: Data from 1332 monozygotic twins (genetically identical) and 1873 dizygotic twins/singleton sisters of twins (who share on average 50% of their segregating genes) registered with The Netherlands Twin Register were used. PCOS was defined as less than nine menstrual cycles and acne or hirsutism in agreement with the 2003 Rotterdam consensus. Results: Results point to a strong contribution of familial factors to PCOS. The resemblance in monozygotic twin sisters (tetrachoric correlation 0.71) for PCOS was about twice as large as in dizygotic twin and other sisters (tetrachoric correlation 0.38). Univariate analyses point to strong contributions of genetic factors to the variance in PCOS. Next, a trivariate genetic analysis of oligomenorrhea, acne, and hirsutism was carried out. This analysis confirmed that the familial component in PCOS is due to genetic factors. Conclusions: This study demonstrated a large influence of genetic factors to the pathogenesis of PCOS, justifying the search for susceptibility genes. Copyright © 2006 by The Endocrine Society

On the Quantum-like Contextuality of Ambiguous Phrases

Language is contextual as meanings of words are dependent on their contexts. Contextuality is, concomitantly, a well-defined concept in quantum mechanics where it is considered a major resource for quantum computations. We investigate whether natural language exhibits any of the quantum mechanics' contextual features. We show that meaning combinations in ambiguous phrases can be modelled in the sheaf-theoretic framework for quantum contextuality, where they can become possibilistically contextual. Using the framework of Contextuality-by-Default (CbD), we explore the probabilistic variants of these and show that CbD-contextuality is also possible

Audiovisual, Genre, Neural and Topical Textual Embeddings for TV Programme Content Representation

TV programmes have their contents described by multiple means: textual subtitles, audiovisual files, and metadata such as genres. In order to represent these contents, we develop vectorial representations for their low-level multimodal features, group them with simple clustering techniques, and combine them using middle and late fusion. For textual features, we use LSI and Doc2Vec neural embeddings; for audio, MFCC's and Bags of Audio Words; for visual, SIFT, and Bags of Visual Words. We apply our model to a dataset of BBC TV programmes and use a standard recommender and pairwise similarity matrices of content vectors to estimate viewers' behaviours. The late fusion of genre, audio and video vectors with both of the textual embeddings significantly increase the precision and diversity of the results

Analysing Ambiguous Nouns and Verbs with Quantum Contextuality Tools

Psycholinguistic research uses eye-tracking to show that polysemous words are disambiguated differently from homonymous words, and that ambiguous verbs are disambiguated differently than ambiguous nouns. Research in Compositional Distributional Semantics uses cosine distances to show that verbs are disambiguated more efficiently in the context of their subjects and objects than when on their own. These two frameworks both focus on one ambiguous word at a time and neither considers ambiguous phrases with two (or more) ambiguous words. We borrow methods and measures from Quantum Information Theory, the framework of Contextuality-by-Default and degrees of contextual influences, and work with ambiguous subject-verb and verb-object phrases of English, where both the subject/object and the verb are ambiguous. We show that differences in the processing of ambiguous verbs versus ambiguous nouns, as well as between different levels of ambiguity in homonymous versus polysemous nouns and verbs can be modelled using the averages of the degrees of their contextual influences

Sentence entailment in compositional distributional semantics

Distributional semantic models provide vector representations for words by gathering co-occurrence frequencies from corpora of text. Compositional distributional models extend these from words to phrases and sentences. In categorical compositional distributional semantics, phrase and sentence representations are functions of their grammatical structure and representations of the words therein. In this setting, grammatical structures are formalised by morphisms of a compact closed category and meanings of words are formalised by objects of the same category. These can be instantiated in the form of vectors or density matrices. This paper concerns the applications of this model to phrase and sentence level entailment. We argue that entropy-based distances of vectors and density matrices provide a good candidate to measure word-level entailment, show the advantage of density matrices over vectors for word level entailments, and prove that these distances extend compositionally from words to phrases and sentences. We exemplify our theoretical constructions on real data and a toy entailment dataset and provide preliminary experimental evidence.Comment: 8 pages, 1 figure, 2 tables, short version presented in the International Symposium on Artificial Intelligence and Mathematics (ISAIM), 201

Toward Sustainable Tackling of Biofouling Implications and Improved Performance of TFC FO Membranes Modified by Ag-MOF Nanorods

In this work, nanorods with high antibacterial properties were synthesized with silver acetate as the metal source and 2-aminoterephthalic acid as the organic linker and were then embedded into thin-film composite (TFC) membranes to amend their performance as well as to alleviate biofouling. Silver metal-organic framework (Ag-MOF) nanorods with a length smaller than 40 nm were incorporated within the polyamide thin selective layer of the membranes during interfacial polymerization. The interaction of the synthesized nanorods with the polyamide was favored because of the presence of amine-containing functional groups on the nanorod's surface. The results of X-ray photoelectron spectroscopy, scanning electron microscopy, energy-dispersive X-ray spectroscopy, and atomic force microscopy characterizations proved the presence of Ag-MOF nanorods in the selective layer of thin-film nanocomposite (TFN) membranes. TFN membranes demonstrated improved water permeance, salt selectivity, and superior antibacterial properties. Specifically, the increased hydrophilicity and antibacterial potential of the TFN membranes led to a synergetic effect toward biofouling mitigation. The number of live bacteria attached to the surface of the neat TFC membrane decreased by more than 92% when a low amount of Ag-MOF nanorods (0.2 wt %) was applied. Following contact of the TFN membrane surface with Escherichia coli and Staphylococcus aureus, full inactivation, and degradation of bacteria cells were observed with microscopy, colony-forming unit tests, and disc inhibition zone analyses. This result translated to a negligible amount of the biofilm formed on the active layer. Indeed, the incorporation of Ag-MOF nanorods decreased the metal-ion release rate and therefore provided prolonged antibacterial performance

Timelike Hopf Duality and Type IIA^* String Solutions

The usual T-duality that relates the type IIA and IIB theories compactified on circles of inversely-related radii does not operate if the dimensional reduction is performed on the time direction rather than a spatial one. This observation led to the recent proposal that there might exist two further ten-dimensional theories, namely type IIA^* and type IIB^*, related to type IIB and type IIA respectively by a timelike dimensional reduction. In this paper we explore such dimensional reductions in cases where time is the coordinate of a non-trivial U(1) fibre bundle. We focus in particular on situations where there is an odd-dimensional anti-de Sitter spacetime AdS_{2n+1}, which can be described as a U(1) bundle over \widetilde{CP}^n, a non-compact version of CP^n corresponding to the coset manifold SU(n,1)/U(n). In particular, we study the AdS_5\times S^5 and AdS_7\times S^4 solutions of type IIB supergravity and eleven-dimensional supergravity. Applying a timelike Hopf T-duality transformation to the former provides a new solution of the type IIA^* theory, of the form \widetilde{CP}^2\times S^1\times S^5. We show how the Hopf-reduced solutions provide further examples of ``supersymmetry without supersymmetry.'' We also present a detailed discussion of the geometrical structure of the Hopf-fibred metric on AdS_{2n+1}, and its relation to the horospherical metric that arises in the AdS/CFT correspondence.Comment: Latex, 26 page

How accessibility influences citation counts: The case of citations to the full text articles available from ResearchGate

It is generally believed that the number of citations to an article can positively be correlated to its free online availability. In the present study, we investigated the possible impact of academic social networks on the number of citations. We chose the social web service “ResearchGate” as a case. This website acts both as a social network to connect researchers, and at the same time, as an open access repository to publish post-print version of the accepted manuscripts and final versions of open access articles. We collected the data of 1823 articles published by the authors from four different universities. By analyzing these data, we showed that although different levels of full text availability are observed for the four universities, there is always a significant positive correlation between full text availability and the citation count. Moreover, we showed that both post-print version and publisher’s version (i.e., final published version) of the archived manuscripts receive more citations than non-OA articles, and the difference in the citation counts of post-print manuscripts and publisher’s version articles is nonsignificant