Fundamental limitations in the purifications of tensor networks

We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix product density operator valid for all system sizes, but for which there does not exist a TI purification valid for all system sizes. The proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states. The result also holds for classical states.

Fiber Pathways for Language in the Developing Brain: A Diffusion Tensor Imaging (DTI) Study

The present study characterized two fiber pathways important for language, the superior longitudinal fasciculus/arcuate fasciculus (SLF/AF) and the frontal aslant tract (FAT), and related these tracts to speech, language, and literacy skill in children five to eight years old. We used Diffusion Tensor Imaging (DTI) to characterize the fiber pathways and administered several language assessments. The FAT was identified for the first time in children. Results showed no age-related change in integrity of the FAT, but did show age-related change in the left (but not right) SLF/AF. Moreover, only the integrity of the right FAT was related to phonology but not audiovisual speech perception, articulation, language, or literacy. Both the left and right SLF/AF related to language measures, specifically receptive and expressive language, and language content. These findings are important for understanding the neurobiology of language in the developing brain, and can be incorporated within contemporary dorsal-ventral-motor models for language.

Generalised finite volume strategies for simulating transport in strongly orthotropic porous media

In this work two different finite volume computational strategies for solving a representative two-dimensional diffusion equation in an orthotropic medium are considered. When the diffusivity tensor is treated as linear, this problem admits an analytic solution used for analysing the accuracy of the proposed numerical methods. In the first method, the gradient approximation techniques discussed by Jayantha and Turner [Numerical Heat Transfer, Part B: Fundamentals, 40, pp.367–390, 2001] are applied directly to the

Effective hybrid recommendation combining users-searches correlations using tensors

Most recommendation methods employ item-item similarity measures or use ratings data to generate recommendations. These methods use traditional two dimensional models to find inter relationships between alike users and products. This paper proposes a novel recommendation method using the multi-dimensional model, tensor, to group similar users based on common search behaviour, and then finding associations within such groups for making effective inter group recommendations. Web log data is multi-dimensional data. Unlike vector based methods, tensors have the ability to highly correlate and find latent relationships between such similar instances, consisting of users and searches. Non redundant rules from such associations of user-searches are then used for making recommendations to the users.

Individual user behaviour modelling for effective web recommendation

With the growth of the Web, E-commerce activities are also becoming popular. Product recommendation is an effective way of marketing a product to potential customers. Based on a user’s previous searches, most recommendation methods employ two dimensional models to find relevant items. Such items are then recommended to a user. Further too many irrelevant recommendations worsen the information overload problem for a user. This happens because such models based on vectors and matrices are unable to find the latent relationships that exist between users and searches. Identifying user behaviour is a complex process, and usually involves comparing searches made by him. In most of the cases traditional vector and matrix based methods are used to find prominent features as searched by a user. In this research we employ tensors to find relevant features as searched by users. Such relevant features are then used for making recommendations. Evaluation on real datasets show the effectiveness of such recommendations over vector and matrix based methods.

Identifying interests of web users for effective recommendations

Search log data is multi dimensional data consisting of number of searches of multiple users with many searched parameters. This data can be used to identify a user’s interest in an item or object being searched. Identifying highest interests of a Web user from his search log data is a complex process. Based on a user’s previous searches, most recommendation methods employ two-dimensional models to find relevant items. Such items are then recommended to a user. Two-dimensional data models, when used to mine knowledge from such multi dimensional data may not be able to give good mappings of user and his searches. The major problem with such models is that they are unable to find the latent relationships that exist between different searched dimensions. In this research work, we utilize tensors to model the various searches made by a user. Such high dimensional data model is then used to extract the relationship between various dimensions, and find the prominent searched components. To achieve this, we have used popular tensor decomposition methods like PARAFAC, Tucker and HOSVD. All experiments and evaluation is done on real datasets, which clearly show the effectiveness of tensor models in finding prominent searched components in comparison to other widely used two-dimensional data models. Such top rated searched components are then given as recommendation to users.

User behaviour modelling in a multi-dimensional environment for personalization and recommendation

Handling information overload online, from the user's point of view is a big challenge, especially when the number of websites is growing rapidly due to growth in e-commerce and other related activities. Personalization based on user needs is the key to solving the problem of information overload. Personalization methods help in identifying relevant information, which may be liked by a user. User profile and object profile are the important elements of a personalization system. When creating user and object profiles, most of the existing methods adopt two-dimensional similarity methods based on vector or matrix models in order to find inter-user and inter-object similarity. Moreover, for recommending similar objects to users, personalization systems use the users-users, items-items and users-items similarity measures. In most cases similarity measures such as Euclidian, Manhattan, cosine and many others based on vector or matrix methods are used to find the similarities. Web logs are high-dimensional datasets, consisting of multiple users, multiple searches with many attributes to each. Two-dimensional data analysis methods may often overlook latent relationships that may exist between users and items. In contrast to other studies, this thesis utilises tensors, the high-dimensional data models, to build user and object profiles and to find the inter-relationships between users-users and users-items. To create an improved personalized Web system, this thesis proposes to build three types of profiles: individual user, group users and object profiles utilising decomposition factors of tensor data models. A hybrid recommendation approach utilising group profiles (forming the basis of a collaborative filtering method) and object profiles (forming the basis of a content-based method) in conjunction with individual user profiles (forming the basis of a model based approach) is proposed for making effective recommendations. A tensor-based clustering method is proposed that utilises the outcomes of popular tensor decomposition techniques such as PARAFAC, Tucker and HOSVD to group similar instances. An individual user profile, showing the user's highest interest, is represented by the top dimension values, extracted from the component matrix obtained after tensor decomposition. A group profile, showing similar users and their highest interest, is built by clustering similar users based on tensor decomposed values. A group profile is represented by the top association rules (containing various unique object combinations) that are derived from the searches made by the users of the cluster. An object profile is created to represent similar objects clustered on the basis of their similarity of features. Depending on the category of a user (known, anonymous or frequent visitor to the website), any of the profiles or their combinations is used for making personalized recommendations. A ranking algorithm is also proposed that utilizes the personalized information to order and rank the recommendations. The proposed methodology is evaluated on data collected from a real life car website. Empirical analysis confirms the effectiveness of recommendations made by the proposed approach over other collaborative filtering and content-based recommendation approaches based on two-dimensional data analysis methods.

Enriching XML documents clustering by using concise structure and content

With the growing number of XML documents on theWeb it becomes essential to effectively organise these XML documents in order to retrieve useful information from them. A possible solution is to apply clustering on the XML documents to discover knowledge that promotes effective data management, information retrieval and query processing. However, many issues arise in discovering knowledge from these types of semi-structured documents due to their heterogeneity and structural irregularity. Most of the existing research on clustering techniques focuses only on one feature of the XML documents, this being either their structure or their content due to scalability and complexity problems. The knowledge gained in the form of clusters based on the structure or the content is not suitable for reallife datasets. It therefore becomes essential to include both the structure and content of XML documents in order to improve the accuracy and meaning of the clustering solution. However, the inclusion of both these kinds of information in the clustering process results in a huge overhead for the underlying clustering algorithm because of the high dimensionality of the data. The overall objective of this thesis is to address these issues by: (1) proposing methods to utilise frequent pattern mining techniques to reduce the dimension; (2) developing models to effectively combine the structure and content of XML documents; and (3) utilising the proposed models in clustering. This research first determines the structural similarity in the form of frequent subtrees and then uses these frequent subtrees to represent the constrained content of the XML documents in order to determine the content similarity. A clustering framework with two types of models, implicit and explicit, is developed. The implicit model uses a Vector Space Model (VSM) to combine the structure and the content information. The explicit model uses a higher order model, namely a 3- order Tensor Space Model (TSM), to explicitly combine the structure and the content information. This thesis also proposes a novel incremental technique to decompose largesized tensor models to utilise the decomposed solution for clustering the XML documents. The proposed framework and its components were extensively evaluated on several real-life datasets exhibiting extreme characteristics to understand the usefulness of the proposed framework in real-life situations. Additionally, this research evaluates the outcome of the clustering process on the collection selection problem in the information retrieval on the Wikipedia dataset. The experimental results demonstrate that the proposed frequent pattern mining and clustering methods outperform the related state-of-the-art approaches. In particular, the proposed framework of utilising frequent structures for constraining the content shows an improvement in accuracy over content-only and structure-only clustering results. The scalability evaluation experiments conducted on large scaled datasets clearly show the strengths of the proposed methods over state-of-the-art methods. In particular, this thesis work contributes to effectively combining the structure and the content of XML documents for clustering, in order to improve the accuracy of the clustering solution. In addition, it also contributes by addressing the research gaps in frequent pattern mining to generate efficient and concise frequent subtrees with various node relationships that could be used in clustering.

Quantum-like non-separability of concept combinations, emergent associates and abduction

Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled (non-separable) particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint (true theoretic) probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified.

Microstructural magnetic resonance imaging of articular cartilage

The focus of this Editorial is recent developments in magnetic resonance imaging (MRI) modalities for evaluation of the microstructure and macromolecular organisation of articular cartilage. We place a specific emphasis on three types of measurements: (1) MRI transverse spin-relaxation mapping (T2 mapping); (2) diffusion-tensor imaging; and (3) compression micro-MRI (uMRI) measurements of articular cartilage in vitro. Such studies have a significant role to play in improving the understanding of the fundamental biomechanics of articular cartilage and in the development of in vitro models of early osteoarthritis. We discuss how the supramolecular organisation of the cartilage extracellular matrix and its behaviour under mechanical compression can be inferred from diffusion-tensor and T2 maps with in-plane resolution ~100 um. The emphasis is on in vitro studies performed under controlled physiological conditions but in vivo applications of T2 mapping and DTI are also briefly discussed.

Contribution to single-point closure Reynolds-stress modelling of inhomogeneous flow

This paper is concerned with recent advances in the development of near wall-normal-free Reynolds-stress models, whose single point closure formulation, based on the inhomogeneity direction concept, is completely independent of the distance from the wall, and of the normal to the wall direction. In the present approach the direction of the inhomogeneity unit vector is decoupled from the coefficient functions of the inhomogeneous terms. A study of the relative influence of the particular closures used for the rapid redistribution terms and for the turbulent diffusion is undertaken, through comparison with measurements, and with a baseline Reynolds-stress model (RSM) using geometric wall normals. It is shown that wall-normal-free rsms can be reformulated as a projection on a tensorial basis that includes the inhomogeneity direction unit vector, suggesting that the theory of the redistribution tensor closure should be revised by taking into account inhomogeneity effects in the tensorial integrity basis used for its representation.

QUT_Para at TREC 2012 Web Track : word associations for retrieving web documents

Many existing information retrieval models do not explicitly take into account in- formation about word associations. Our approach makes use of rst and second order relationships found in natural language, known as syntagmatic and paradigmatic associ- ations, respectively. This is achieved by using a formal model of word meaning within the query expansion process. On ad hoc retrieval, our approach achieves statistically sig- ni cant improvements in MAP (0.158) and P@20 (0.396) over our baseline model. The ERR@20 and nDCG@20 of our system was 0.249 and 0.192 respectively. Our results and discussion suggest that information about both syntagamtic and paradigmatic associa- tions can assist with improving retrieval eectiveness on ad hoc retrieval.

Kernel analysis on Grassmann manifolds for action recognition

Modelling video sequences by subspaces has recently shown promise for recognising human actions. Subspaces are able to accommodate the effects of various image variations and can capture the dynamic properties of actions. Subspaces form a non-Euclidean and curved Riemannian manifold known as a Grassmann manifold. Inference on manifold spaces usually is achieved by embedding the manifolds in higher dimensional Euclidean spaces. In this paper, we instead propose to embed the Grassmann manifolds into reproducing kernel Hilbert spaces and then tackle the problem of discriminant analysis on such manifolds. To achieve efficient machinery, we propose graph-based local discriminant analysis that utilises within-class and between-class similarity graphs to characterise intra-class compactness and inter-class separability, respectively. Experiments on KTH, UCF Sports, and Ballet datasets show that the proposed approach obtains marked improvements in discrimination accuracy in comparison to several state-of-the-art methods, such as the kernel version of affine hull image-set distance, tensor canonical correlation analysis, spatial-temporal words and hierarchy of discriminative space-time neighbourhood features.