Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.

Modelling personal thermal sensations using C-Support Vector Classification (C-SVC) algorithm

The personalised conditioning system (PCS) is widely studied. Potentially, it is able to reduce energy consumption while securing occupants’ thermal comfort requirements. It has been suggested that automatic optimised operation schemes for PCS should be introduced to avoid energy wastage and discomfort caused by inappropriate operation. In certain automatic operation schemes, personalised thermal sensation models are applied as key components to help in setting targets for PCS operation. In this research, a novel personal thermal sensation modelling method based on the C-Support Vector Classification (C-SVC) algorithm has been developed for PCS control. The personal thermal sensation modelling has been regarded as a classification problem. During the modelling process, the method ‘learns’ an occupant’s thermal preferences from his/her feedback, environmental parameters and personal physiological and behavioural factors. The modelling method has been verified by comparing the actual thermal sensation vote (TSV) with the modelled one based on 20 individual cases. Furthermore, the accuracy of each individual thermal sensation model has been compared with the outcomes of the PMV model. The results indicate that the modelling method presented in this paper is an effective tool to model personal thermal sensations and could be integrated within the PCS for optimised system operation and control.

On mathematical and physical principles of transformations of the coherent radar backscatter matrix

The congruential rule advanced by Graves for polarization basis transformation of the radar backscatter matrix is now often misinterpreted as an example of consimilarity transformation. However, consimilarity transformations imply a physically unrealistic antilinear time-reversal operation. This is just one of the approaches found in literature to the description of transformations where the role of conjugation has been misunderstood. In this paper, the different approaches are examined in particular in respect to the role of conjugation. In order to justify and correctly derive the congruential rule for polarization basis transformation and properly place the role of conjugation, the origin of the problem is traced back to the derivation of the antenna height from the transmitted field. In fact, careful consideration of the role played by the Green’s dyadic operator relating the antenna height to the transmitted field shows that, under general unitary basis transformation, it is not justified to assume a scalar relationship between them. Invariance of the voltage equation shows that antenna states and wave states must in fact lie in dual spaces, a distinction not captured in conventional Jones vector formalism. Introducing spinor formalism, and with the use of an alternate spin frame for the transmitted field a mathematically consistent implementation of the directional wave formalism is obtained. Examples are given comparing the wider generality of the congruential rule in both active and passive transformations with the consimilarity rule.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.

Tensor LRR and sparse coding-based subspace clustering

Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data, and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established state-of-the-art methods.

Spatial expansion and population structure of the neotropical malaria vector, Anopheles darlingi (Diptera: Culicidae)

Extensive population structuring is known to occur in Anopheles darlingi, the primary malaria vector of the Neotropics. We analysed the phylogeographic structure of the species using the mitochondrial cytochrome oxidase I marker. Diversity is divided into six main population groups in South America: Colombia, central Amazonia, southern Brazil, south-eastern Brazil, and two groups in north-east Brazil. The ancestral distribution of the taxon is hypothesized to be central Amazonia, and there is evidence of expansion from this region during the late Pleistocene. The expansion was not a homogeneous front, however, with at least four subgroups being formed due to geographic barriers. As the species spread, populations became isolated from each other by the Amazon River and the coastal mountain ranges of south-eastern Brazil and the Andes. Analyses incorporating distances around these barriers suggest that the entire South American range of An. darlingi is at mutation-dispersal-drift equilibrium. Because the species is distributed throughout such a broad area, the limited dispersal across some landscape types promotes differentiation between otherwise proximate populations. Moreover, samples from the An. darlingi holotype location in Rio de Janeiro State are substantially derived from all other populations, implying that there may be additional genetic differences of epidemiological relevance. The results obtained contribute to our understanding of gene flow in this species and allow the formulation of human mosquito health protocols in light of the potential population differences in vector capacity or tolerance to control strategies. (C) 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 97, 854-866.

Alboserpin, a Factor Xa Inhibitor from the Mosquito Vector of Yellow Fever, Binds Heparin and Membrane Phospholipids and Exhibits Antithrombotic Activity

The molecular mechanism of factor Xa (FXa) inhibition by Alboserpin, the major salivary gland anticoagulant from the mosquito and yellow fever vector Aedes albopictus, has been characterized. cDNA of Alboserpin predicts a 45-kDa protein that belongs to the serpin family of protease inhibitors. Recombinant Alboserpin displays stoichiometric, competitive, reversible and tight binding to FXa (picomolar range). Binding is highly specific and is not detectable for FX, catalytic site-blocked FXa, thrombin, and 12 other enzymes. Alboserpin displays high affinity binding to heparin (K(D) similar to 20 nM), but no change in FXa inhibition was observed in the presence of the cofactor, implying that bridging mechanisms did not take place. Notably, Alboserpin was also found to interact with phosphatidylcholine and phosphatidylethanolamine but not with phosphatidylserine. Further, annexin V (in the absence of Ca(2+)) or heparin outcompetes Alboserpin for binding to phospholipid vesicles, suggesting a common binding site. Consistent with its activity, Alboserpin blocks prothrombinase activity and increases both prothrombin time and activated partial thromboplastin time in vitro or ex vivo. Furthermore, Alboserpin prevents thrombus formation provoked by ferric chloride injury of the carotid artery and increases bleeding in a dose-dependent manner. Alboserpin emerges as an atypical serpin that targets FXa and displays unique phospholipid specificity. It conceivably uses heparin and phosphatidylcholine/phosphatidylethanolamine as anchors to increase protein localization and effective concentration at sites of injury, cell activation, or inflammation.

Development of an adenoviral vector with robust expression driven by p53

Here we introduce a new adenoviral vector where transgene expression is driven by p53. We first developed a synthetic promoter, referred to as PGTx beta containing a p53-responsive element, a minimal promoter and the first intron of the rabbit P-globin gene. Initial assays using plasmid-based vectors indicated that expression was tightly controlled by p53 and was 5-fold stronger than the constitutive CMV immediate early promoter/enhancer. The adenoviral vector, AdPG, was also shown to offer p53-responsive expression in prostate carcinoma cells LNCaP (wt p53), DU-145 (temperature sensitive mutant of p53) and PC3 (p53-null, but engineered to express temperature-sensitive p53 mutants). AdPG served as a sensor of p53 activity in LNCaP cells treated with chemotherapeutic agents. Since p53 can be induced by radiotherapy and chemotherapy, this new vector could be further developed for use in combination with conventional therapies to bring about cooperation between the genetic and pharmacologic treatment modalities. (c) 2007 Elsevier Inc. All rights reserved.

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

THE POINCARE-BENDIXSON THEOREM ON THE KLEIN BOTTLE FOR CONTINUOUS VECTOR FIELDS

We present a version of the Poincare-Bendixson Theorem on the Klein bottle K(2) for continuous vector fields. As a consequence, we obtain the fact that K(2) does not admit continuous vector fields having a omega-recurrent injective trajectory.