The determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. II. mixed invariants of Eeven degree in the Ricci Spinor

We continue our analysis of the polynomial invariants of the Riemann tensor in a four-dimensional Lorentzian space. We concentrate on the mixed invariants of even degree in the Ricci spinor Φ_ABȦḂ and show how, using constructive graph-theoretic methods, arbitrary scalar contractions between copies of the Weyl spinor ψ_ABCD, its conjugate ψ_ȦḂĊḊ and an even number of Ricci spinors can be expressed in terms of paired contractions between these spinors. This leads to an algorithm for the explicit expression of dependent invariants as polynomials of members of the complete set. Finally, we rigorously prove that the complete set as given by Sneddon [J. Math. Phys. 39, 1659-1679 (1998)] for this case is both complete and minimal.

Facets of the polytope of the asymmetric travelling salesman problem with replenishment arcs

The Asymmetric Travelling Salesman Problem with Replenishment Arcs (RATSP) is a new class of problems arising from work related to aircraft routing. Given a digraph with cost on the arcs, a solution of the RATSP, like that of the Asymmetric Travelling Salesman Problem, induces a directed tour in the graph which minimises total cost. However the tour must satisfy additional constraints: the arc set is partitioned into replenishment arcs and ordinary arcs, each node has a non-negative weight associated with it, and the tour cannot accumulate more than some weight limit before a replenishment arc must be used. To enforce this requirement, constraints are needed. We refer to these as replenishment constraints.

In this paper, we review previous polyhedral results for the RATSP and related problems, then prove that two classes of constraints developed in V. Mak and N. Boland [Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs, Technical Report TR M05/03, School of Information Technology, Deakin University, 2005] are, under appropriate conditions, facet-defining for the RATS polytope.

Polyhedral studies for minimum-span graph labelling with integer distance constraints

This paper studies the polytope of the minimum-span graph labelling problems with integer distance constraints (DC-MSGL). We first introduce a few classes of new valid inequalities for the DC-MSGL defined on general graphs and briefly discuss the separation problems of some of these inequalities. These are the initial steps of a branch-and-cut algorithm for solving the DC-MSGL. Following that, we present our polyhedral results on the dimension of the DC-MSGL polytope, and that some of the inequalities are facet defining, under reasonable conditions, for the polytope of the DC-MSGL on triangular graphs.

On the discrete time dynamics of a self-stabilizing MCA learning algorithm

The stability of minor component analysis (MCA) learning algorithms is an important problem in many signal processing applications. In this paper, we propose an effective MCA learning algorithm that can offer better stability. The dynamics of the proposed algorithm are analyzed via a corresponding deterministic discrete time (DDT) system. It is proven that if the learning rate satisfies some mild conditions, almost all trajectories of the DDT system starting from points in an invariant set are bounded, and will converge to the minor component of the autocorrelation matrix of the input data. Simulation results will be furnished to illustrate the theoretical results achieved.

Interacting amino acid preferences of 3D pattern pairs at the binding sites of transient and obligate protein complexes

To assess the physico-chemical characteristics of protein-protein interactions, protein sequences and overall structural folds have been analyzed previously. To highlight this, discovery and examination of amino acid patterns at the binding sites defined by structural proximity in 3-dimensional (3D) space are essential. In this paper, we investigate the interacting preferences of 3D pattern pairs discovered separately in transient and obligate protein complexes. These 3D pattern pairs are not necessarily sequence-consecutive, but each residue in two groups of amino acids from two proteins in a complex is within certain °A threshold to most residues in the other group. We develop an algorithm called AA-pairs by which every pair of interacting proteins is represented as a bipartite graph, and it discovers all maximal quasi-bicliques from every bipartite graph to form our 3D pattern pairs. From 112 and 2533 highly conserved 3D pattern pairs discovered in the transient and obligate complexes respectively, we observe that Ala and Leu is the highest occuring amino acid in interacting 3D patterns of transient (20.91%) and obligate (33.82%) complexes respectively. From the study on the dipeptide composition on each side of interacting 3D pattern pairs, dipeptides Ala-Ala and Ala-Leu are popular in 3D patterns of both transient and obligate complexes. The interactions between amino acids with large hydrophobicity difference are present more in the transient than in the obligate complexes. On contrary, in obligate complexes, interactions between hydrophobic residues account for the top 5 most occuring amino acid pairings.

Empirical evaluation of segmentation algorithms for lung modelling

Lung modelling has emerged as a useful method for diagnosing lung diseases. Image segmentation is an important part of lung modelling systems. The ill-defined nature of image segmentation makes automated lung modelling difficult. Also, low resolution of lung images further increases the difficulty of the lung image segmentation. It is therefore important to identify a suitable segmentation algorithm that can enhance lung modelling accuracies. This paper investigates six image segmentation algorithms, used in medical imaging, and also their application to lung modelling. The algorithms are: normalised cuts, graph, region growing, watershed, Markov random field, and mean shift. The performance of the six segmentation algorithms is determined through a set of experiments on realistic 2D CT lung images. An experimental procedure is devised to measure the performance of the tested algorithms. The measured segmentation accuracies as well as execution times of the six algorithms are then compared and discussed.

Stability and convergence analysis of transform-domain LMS adaptive filters with second-order autoregressive process

In this paper, the stability and convergence properties of the class of transform-domain least mean square (LMS) adaptive filters with second-order autoregressive (AR) process are investigated. It is well known that this class of adaptive filters improve convergence property of the standard LMS adaptive filters by applying the fixed data-independent orthogonal transforms and power normalization. However, the convergence performance of this class of adaptive filters can be quite different for various input processes, and it has not been fully explored. In this paper, we first discuss the mean-square stability and steady-state performance of this class of adaptive filters. We then analyze the effects of the transforms and power normalization performed in the various adaptive filters for both first-order and second-order AR processes. We derive the input asymptotic eigenvalue distributions and make comparisons on their convergence performance. Finally, computer simulations on AR process as well as moving-average (MA) process and autoregressive-moving-average (ARMA) process are demonstrated for the support of the analytical results.

Finite-time consensus algorithm of multi-agent networks

This paper is concerned with leader-follower finite-time consensus control of multi-agent networks with input disturbances. Terminal sliding mode control scheme is used to design the distributed control law. A new terminal sliding mode surface is proposed to guarantee finite-time consensus under fixed topology, with the common assumption that the position and the velocity of the active leader is known to its neighbors only. By using the finite-time Lyapunov stability theorem, it is shown that if the directed graph of the network has a directed spanning tree, then the terminal sliding mode control law can guarantee finite-time consensus even under the assumption that the time-varying control input of the active leader is unknown to any follower.

On performance of transform domain adaptive filters with Markov-2 inputs

In this paper, the analysis for the performance of the discrete Fourier transform LMS adaptive filter (DFT-LMS) and the discrete cosine transform LMS adaptive filter (DCT-LMS) for the Markov-2 inputs is presented. To improve the convergence property of the least mean squares (LMS) adaptive filter, the DFT-LMS and DCT-LMS preprocess the inputs with the fixed orthogonal transforms and power normalization. We derive the asymptotic results for the eigenvalues and eigenvalue distributions of the preprocessed input autocorrelation matrices with DFT-LMS and DCT-LMS for Markov-2 inputs. These results explicitly show the superior decorrelation property of DCT-LMS over that of DFT-LMS, and also provide the upper bounds for the eigenvalue spreads of the finite-length DFT-LMS and DCT-LMS adaptive filters. Simulation results are demonstrated to support the analytic results.

Strategic knowledge for the identification and construction of goal states

There is widespread recognition that goal recognition strategies, in the context of structural analysis and cognitive (user) models, represent a major field of contemporary research into discourse understanding. This thesis reports a goal interpretation paradigm that embraces both a novel goal structure formalism and strategic knowledge. The goal interpretation processes involve the identification of goal primitives and the construction of goal states. The mechanisms developed for goal interpretation rely on explicit goal recognition (selection) and confirmation of feasibility. A goal state contains all the information required by the planner. By constructing a goal state, the chance of failure in planning is greatly reduced and the efficiency of the planning system is vastly improved. These mechanisms are not limited to inference. Other mechanisms are reported include goal structure processing, goal primitives identification and searching strategies, extended heuristic classification method and a new conceptual graph operation (i.e. SPLIT).

Syzygies of the polynomial invariants of the Riemann tensor

This thesis introduces a novel way of writing polynomial invariants as network graphs, and applies this diagrammatic notation scheme, in conjunction with graph theory, to derive algorithms for constructing relationships (syzygies) between different invariants. These algorithms give rise to a constructive solution of a longstanding classical problem in invariant theory.

Underdetermined blind source separation based on relaxed sparsity condition of sources

Recently, Aissa-El-Bey et al. have proposed two subspacebased methods for underdetermined blind source separation (UBSS) in time-frequency (TF) domain. These methods allow multiple active sources at TF points so long as the number of active sources at any TF point is strictly less than the number of sensors, and the column vectors of the mixing matrix are pairwise linearly independent. In this correspondence, we first show that the subspace-based methods must also satisfy the condition that any M × M submatrix of the mixing matrix is of full rank. Then we present a new UBSS approach which only requires that the number of active sources at any TF point does not exceed that of sensors. An algorithm is proposed to perform the UBSS.

High functional coherence in k-partite protein cliques of protein interaction networks

We introduce a new topological concept called k-partite protein cliques to study protein interaction (PPI) networks. In particular, we examine functional coherence of proteins in k-partite protein cliques. A k-partite protein clique is a k-partite maximal clique comprising two or more nonoverlapping protein subsets between any two of which full interactions are exhibited. In the detection of PPI’s k-partite maximal cliques, we propose to transform PPI networks into induced K-partite graphs with proteins as vertices where edges only exist among the graph’s partites. Then, we present a k-partite maximal clique mining (MaCMik) algorithm to enumerate k-partite maximal cliques from K-partite graphs. Our MaCMik algorithm is applied to a yeast PPI network. We observe that there does exist interesting and unusually high functional coherence in k-partite protein cliques—most proteins in k-partite protein cliques, especially those in the same partites, share the same functions. Therefore, the idea of k-partite protein cliques suggests a novel approach to characterizing PPI networks, and may help function prediction for unknown proteins.

Picture this : a simple graph that reveals much ado about research

Funnel graphs provide a simple, yet highly effective, means to identify key features of an empirical literature. This paper illustrates the use of funnel graphs to detect publication selection bias, identify the existence of genuine empirical effects and discover potential moderator variables that can help to explain the wide variation routinely found among reported research findings. Applications include union–productivity effects, water price elasticities, common currency-trade effects, minimum-wage employment effects, efficiency wages and the price elasticity of prescription drugs.