SWGMM: a semi-wrapped Gaussian mixture model for clustering of circular–linear data

Finite mixture models are widely used to perform model-based clustering of multivariate data sets. Most of the existing mixture models work with linear data; whereas, real-life applications may involve multivariate data having both circular and linear characteristics. No existing mixture models can accommodate such correlated circular–linear data. In this paper, we consider designing a mixture model for multivariate data having one circular variable. In order to construct a circular–linear joint distribution with proper inclusion of correlation terms, we use the semi-wrapped Gaussian distribution. Further, we construct a mixture model (termed SWGMM) of such joint distributions. This mixture model is capable of approximating the distribution of multi-modal circular–linear data. An unsupervised learning of the mixture parameters is proposed based on expectation maximization method. Clustering is performed using maximum a posteriori criterion. To evaluate the performance of SWGMM, we choose the task of color image segmentation in LCH space. We present comprehensive results and compare SWGMM with existing methods. Our study reveals that the proposed mixture model outperforms the other methods in most cases.     

A Two-Stage Approach for Network Monitoring

A goal of network tomography is to infer the status (e.g. delay) of congested links internal to a network, through end-to-end measurements at boundary nodes (end-hosts) via insertion of probe signals. Because (a) probing constitutes traffic overhead, and (b) in any typical scenario, the number of congested links is a small fraction of the total number in the network, a desirable design objective is to identify those (few) congested links using a minimum number of probes. In this paper, we make a contribution to solving this problem, by proposing a new two-stage approach for this problem. First, we develop a binary observation model linking end-to-end observations with individual link statuses and derive necessary and sufficient conditions for whether at least one link in the network is congested. Stage I of the proposed method shows that achieving 1-identifiability with a minimum number of probes is equivalent to the familiar minimum set covering problem that can be efficiently solved via a greedy heuristic. A sequential algorithm is described, leading to a significantly lowered computational complexity vis-a-vis a batch algorithm. Next, a binary splitting algorithm originally developed in group testing is used to identify the location of the congested links. The proposed scheme is evaluated by simulations in OPNET and experiments on the PlanetLab testbed to validate the advantages of our 2-stage approach vis-a-vis a conventional (batch) algorithm.     

On preconditioning for a parallel solution of the Richards equation

In this paper, we present a class of preconditioning methods for a parallel solution of the three-dimensional Richards equation. The preconditioning methods Jacobi scaling, block-Jacobi, incomplete lower–upper, incomplete Cholesky and algebraic multigrid were applied in combination with a parallel conjugate gradient solver and tested for robustness and convergence using two model scenarios. The first scenario was an infiltration into initially dry, sandy soil discretised in 500,000 nodes. The second scenario comprised spatially distributed soil properties using 275,706 numerical nodes and atmospheric boundary conditions. Computational results showed a high efficiency of the nonlinear parallel solution procedure for both scenarios using up to 64 processors. Using 32 processors for the first scenario reduced the wall clock time to slightly more than 1% of the single processor run. For scenario 2 the use of 64 processors reduces the wall clock time to slightly more than 20% of the 8 processors wall clock time. The difference in the efficiency of the various preconditioning methods is moderate but not negligible. The use of the multigrid preconditioning algorithm is recommended, since on average it performed best for both scenarios.     

Automatic Construction and Verification of Isotopy Invariants

We extend our previous study of the automatic construction of isomorphic classification theorems for algebraic domains by considering the isotopy equivalence relation. Isotopism is an important generalisation of isomorphism, and is studied by mathematicians in domains such as loop theory. This extension was not straightforward, and we had to solve two major technical problems, namely, generating and verifying isotopy invariants. Concentrating on the domain of loop theory, we have developed three novel techniques for generating isotopic invariants, by using the notion of universal identities and by using constructions based on subblocks. In addition, given the complexity of the theorems that verify that a conjunction of the invariants form an isotopy class, we have developed ways of simplifying the problem of proving these theorems. Our techniques employ an interplay of computer algebra, model generation, theorem proving, and satisfiability-solving methods. To demonstrate the power of the approach, we generate isotopic classification theorems for loops of size 6 and 7, which extend the previously known enumeration results. This work was previously beyond the capabilities of automated reasoning techniques. The author’s work was supported by EPSRC MathFIT grant GR/S31099.     

Transport of the dicyanogold(i) anion

We have shown that dicyanogold(I), [Au(CN)(2)](-) is a common metabolite found in blood and urine samples of patients treated with different gold based drugs. Some patients have high levels of gold within their red blood cells (RBCs). Size exclusion and C18 reversed phase chromatography show that the majority of the gold in RBC lysates is bound to protein, but small molecules such as dicyanogold(I) and gold-glutathione complexes are also present. Dicyanogold incubation with red blood cells in vitro leads to a rapid and complete uptake of gold. This uptake is unaffected by DIDS, an inhibitor of the anion channel, but is blocked by the addition of external cyanide. Dicyanogold is also readily taken up by H9 cells, a continuous CD(4+) cell line. This uptake is significantly inhibited by N-ethylmaleimide, suggesting a requirement for sulfhydryl groups. Dicyanogold inhibits the replication of the AIDS virus, HIV, in a cell culture model.     

Dispersed spatial input demand functions

Most recent attempts to improve the empirical performance of classical trade models by formulation of probabilistic models of the DSPE (Dispersed Spatial Price Equilibrium) type have concentrated on determination of flows of a single commodity. However, a further challenge is to develop consistent probabilistic multi-sector spatial input demand functions and the corresponding spatial supply functions as part of an eventual probabilistic spatial CGE (Computable General Equilibrium) framework. In this paper, we derive short-run aggregate spatial input demand functions as the generators of the spatial supply functions, introducing via entropy some distributional assumptions about the average behaviour of the representative firm. In order to remain compatible with entropy principles, all demand functions are derived in a form guaranteeing compliance with a probabilistic accounting framework, calibrated on observed quantities, costs and prices. Firstly, the paper develops dispersed spatial input demand functions using various classical production functions, such as Linear and CES, accounting for the transport costs and tariffs incurred by the supply of intermediate inputs. It then formulates dispersed interregional input demand functions based on multiregional input-output production functions, transcending the normal relations connecting input and output via constant coefficients, with solution via a price-sensitive iterative adjustment technique. Finally, guidelines for an extension to a long-run analysis are sketched.     

Outage Performance of Uplink (UL) NOMA Network

Wireless Personal Communications - This paper proposes and analyses the power allocation coefficient normalization for successive interference cancellation in power-domain non-orthogonal multiple...