An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Development of moving magnet type linear motor for dual piston compressor for pulse tube cryocooler

This paper describes the design, fabrication and testing of a moving magnet type linear motor of dual piston configuration for a pulse tube cryocooler for ground applications. Eight radially magnetized segmented magnets were used to form one set of a magnet ring. Four magnet rings of such type were constructed, in which one pair of rings has north-pole on its outer diameter and south-pole on inner diameter, while the other pair is it's complementary. The magnets were mounted with opposite poles together on the magnet holder with an axial moving shaft having a piston mounted on both ends of the shaft. The shaft movement was restricted to the axial direction by using C-clamp type flexures, mounted on both sides of the shaft. The force requirement for driving the compressor was calculated based on which the electrical circuit of motor is designed by proper selection of wire gauge and Ampere-turns. The flexure spring force estimation was done through simulation using ANSYS 11.0 and was verified experimentally; while the magnet spring force was determined experimentally. The motor with mounted piston was tested using a variable voltage and variable frequency power supply capable of driving 140 watts of load.

A noisy linear map underlies oscillations in cell size and gene expression in bacteria.

During bacterial growth, a cell approximately doubles in size before division, after which it splits into two daughter cells. This process is subjected to the inherent perturbations of cellular noise and thus requires regulation for cell-size homeostasis. The mechanisms underlying the control and dynamics of cell size remain poorly understood owing to the difficulty in sizing individual bacteria over long periods of time in a high-throughput manner. Here we measure and analyse long-term, single-cell growth and division across different Escherichia coli strains and growth conditions. We show that a subset of cells in a population exhibit transient oscillations in cell size with periods that stretch across several (more than ten) generations. Our analysis reveals that a simple law governing cell-size control-a noisy linear map-explains the origins of these cell-size oscillations across all strains. This noisy linear map implements a negative feedback on cell-size control: a cell with a larger initial size tends to divide earlier, whereas one with a smaller initial size tends to divide later. Combining simulations of cell growth and division with experimental data, we demonstrate that this noisy linear map generates transient oscillations, not just in cell size, but also in constitutive gene expression. Our work provides new insights into the dynamics of bacterial cell-size regulation with implications for the physiological processes involved.

Plant Functional Type (PFT) map over Siberia derived from GlobCover 2005 dataset, link to dataset in NetCDF format

High-latitude ecosystems play an important role in the global carbon cycle and in regulating the climate system and are presently undergoing rapid environmental change. Accurate land cover data sets are required to both document these changes as well as to provide land-surface information for benchmarking and initializing Earth system models. Earth system models also require specific land cover classification systems based on plant functional types (PFTs), rather than species or ecosystems, and so post-processing of existing land cover data is often required. This study compares over Siberia, multiple land cover data sets against one another and with auxiliary data to identify key uncertainties that contribute to variability in PFT classifications that would introduce errors in Earth system modeling. Land cover classification systems from GLC 2000, GlobCover 2005 and 2009, and MODIS collections 5 and 5.1 are first aggregated to a common legend, and then compared to high-resolution land cover classification systems, vegetation continuous fields (MODIS VCFs) and satellite-derived tree heights (to discriminate against sparse, shrub, and forest vegetation). The GlobCover data set, with a lower threshold for tree cover and taller tree heights and a better spatial resolution, tends to have better distributions of tree cover compared to high-resolution data. It has therefore been chosen to build new PFT maps for the ORCHIDEE land surface model at 1 km scale. Compared to the original PFT data set, the new PFT maps based on GlobCover 2005 and an updated cross-walking approach mainly differ in the characterization of forests and degree of tree cover. The partition of grasslands and bare soils now appears more realistic compared with ground truth data. This new vegetation map provides a framework for further development of new PFTs in the ORCHIDEE model like shrubs, lichens and mosses, to represent the water and carbon cycles in northern latitudes better. Updated land cover data sets are critical for improving and maintaining the relevance of Earth system models for assessing climate and human impacts on biogeochemistry and biophysics.

Existence Theorems for Generalized Hammerstein Equations

In this paper we obtain existence theorems for generalized Hammerstein-type equations K(u)Nu + u = 0, where for each u in the dual X* of a real reflexive Banach space X, K(u): X -- X* is a bounded linear map and N: X* - X is any map (possibly nonlinear). The method we adopt is totally different from the methods adopted so far in solving these equations. Our results in the reflexive spacegeneralize corresponding results of Petry and Schillings.

Distributed Function Computation over Fields and Rings via Linear Compression of Sources

The setting considered in this paper is one of distributed function computation. More specifically, there is a collection of N sources possessing correlated information and a destination that would like to acquire a specific linear combination of the N sources. We address both the case when the common alphabet of the sources is a finite field and the case when it is a finite, commutative principal ideal ring with identity. The goal is to minimize the total amount of information needed to be transmitted by the N sources while enabling reliable recovery at the destination of the linear combination sought. One means of achieving this goal is for each of the sources to compress all the information it possesses and transmit this to the receiver. The Slepian-Wolf theorem of information theory governs the minimum rate at which each source must transmit while enabling all data to be reliably recovered at the receiver. However, recovering all the data at the destination is often wasteful of resources since the destination is only interested in computing a specific linear combination. An alternative explored here is one in which each source is compressed using a common linear mapping and then transmitted to the destination which then proceeds to use linearity to directly recover the needed linear combination. The article is part review and presents in part, new results. The portion of the paper that deals with finite fields is previously known material, while that dealing with rings is mostly new.Attempting to find the best linear map that will enable function computation forces us to consider the linear compression of source. While in the finite field case, it is known that a source can be linearly compressed down to its entropy, it turns out that the same does not hold in the case of rings. An explanation for this curious interplay between algebra and information theory is also provided in this paper.

Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form

In this paper, we study the asymptotic distribution of a simple two-stage (Hannan-Rissanen-type) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed.

Beyond the topological map : developing alternate mappings in self organisation

The self organising map is a well established unsupervised
learning technique which is able to form sophisticated representations of an input data set. However, conventional Self Organising Map (SOM) algorithms are limited to the production of topological maps — that is, maps where distance between points on the map have a direct relationship to the Euclidean distance between the training vectors corresponding to those points.

It would be desirable to be able to create maps which form clusters on primitive attributes other than Euclidean distance; for example, clusters based upon orientation or shape. Such maps could provide a novel approach to pattern recognition tasks by providing a new method to associate groups of data.

In this paper, it is shown that the type of map produced by SOM algorithms is a direct consequence of the lateral connection strategy employed. Given this knowledge, a technique is required to establish the feasability of using an alternative lateral connection strategy. Such a technique is presented. Using this technique, it is possible to rule out lateral connection strategies that will not produce output states useful to the organisation process. This technique is demonstrated using conventional Laplacian interconnection as well as a number of novel interconnection strategies.

Elements of Non-Linear Hamiltonian Dynamics

In this paper we present a set of generic results on Hamiltonian non-linear dynamics. We show the necessary conditions for a Hamiltonian system to present a non-twist scenario and from that we introduce the isochronous resonances. The generality of these resonances is shown from the Hamiltonian given by the Birkhof-Gustavson normal form, which can be considered a toy model, and from an optic system governed by the non-linear map of the annular billiard. We also define a special kind of transport barrier called robust torus. The meanders and shearless curves are also presented and we show the most robust shearless barrier associated with the rotation numbers.

Visualization of oligonucleotide probes and point mutations in interphase nuclei and DNA fibers using rolling circle DNA amplification

Rolling circle amplification (RCA) is a surface-anchored DNA replication reaction that can be exploited to visualize single molecular recognition events. Here we report the use of RCA to visualize target DNA sequences as small as 50 nts in peripheral blood lymphocytes or in stretched DNA fibers. Three unique target sequences within the cystic fibrosis transmembrane conductance regulator gene could be detected simultaneously in interphase nuclei, and could be ordered in a linear map in stretched DNA. Allele-discriminating oligonucleotide probes in conjunction with RCA also were used to discriminate wild-type and mutant alleles in the cystic fibrosis transmembrane conductance regulator, p53, BRCA-1, and Gorlin syndrome genes in the nuclei of cultured cells or in DNA fibers. These observations demonstrate that signal amplification by RCA can be coupled to nucleic acid hybridization and multicolor fluorescence imaging to detect single nucleotide changes in DNA within a cytological context or in single DNA molecules. This provides a means for direct physical haplotyping and the analysis of somatic mutations on a cell-by-cell basis.

State estimation schemes for independent component coupled hidden Markov models

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13, 17]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6]. In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood EM algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large. The contribution in this article is to develop new recursive formulae for a filter-based EM algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results. © Taylor & Francis Group, LLC.

The impact of powder flowing properties on dosator filling system operation

Purpose: To study the impact of powder flow properties on dosator filling systems, with particular focus on improvements in dose weight accuracy and repeatability. Method: This study evaluates a range of critical powder flow properties such as: flow function, cohesion, wall friction, adhesion to wall surfaces, density/compressibility data, stress ratio “K” and gas permeability. The characterisations of the powders considered in this study were undertaken using an annular shear cell using a sample size of 0.5 litres. This tester also incorporated the facility to measure bed expansion during shear in addition to contraction under consolidation forces. A modified Jenike type linear wall friction tester was used to develop the failure loci for the powder sample in conjunction with multiple wall samples (representing a variety of material types and surface finishes). Measurements of the ratio of applied normal stress versus lateral stress were determined using a piece of test equipment specifically designed for the purpose. Results: The correct characterisation of powders and the incorporation of this data into the design of process equipment are recognised as critical for reliable and accurate operation. An example of one aspect of this work is the stress ratio “K”. This characteristic is not well understood or correctly interpreted in many cases – despite its importance. Fig 1 [Omitted] (illustrates a sample of test data. The slope of the line gives the stress ratio in a uniaxial compaction system – indicating the behaviour of the material under compaction during dosing processes. Conclusions: A correct assessment of the bulk powder properties for a given formulation can allow prediction of: cavity filling behaviour (and hence dosage), efficiency of release from dosator, and strength and stability of extruded dose en route to capsule filling Influences over the effectiveness of dosator systems have been shown to be impacted upon by: bed pre-compaction history, gas permeability in the bed (with respect to local density effects), and friction effects for materials of construction for dosators

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Simulation des fonctions de texture bidirectionnelles

Le réalisme des objets en infographie exige de simuler adéquatement leur apparence sous divers éclairages et à différentes échelles. Une solution communément adoptée par les chercheurs consiste à mesurer avec l’aide d’appareils calibrés la réflectance d’un échantillon de surface réelle, pour ensuite l’encoder sous forme d’un modèle de réflectance (BRDF) ou d’une texture de réflectances (BTF). Malgré des avancées importantes, les données ainsi mises à la portée des artistes restent encore très peu utilisées. Cette réticence pourrait s’expliquer par deux raisons principales : (1) la quantité et la qualité de mesures disponibles et (2) la taille des données. Ce travail propose de s’attaquer à ces deux problèmes sous l’angle de la simulation. Nous conjecturons que le niveau de réalisme du rendu en infographie produit déjà des résultats satisfaisants avec les techniques actuelles. Ainsi, nous proposons de précalculer et encoder dans une BTF augmentée les effets d’éclairage sur une géométrie, qui sera par la suite appliquée sur les surfaces. Ce précalcul de rendu et textures étant déjà bien adopté par les artistes, il pourra mieux s’insérer dans leurs réalisations. Pour nous assurer que ce modèle répond aussi aux exigences des représentations multi-échelles, nous proposons aussi une adaptation des BTFs à un encodage de type MIP map.