Minimal crystallizations of 3-manifolds

We have introduced the weight of a group which has a presentation with number of relations is at most the number of generators. We have shown that the number of facets of any contracted pseudotriangulation of a connected closed 3-manifold M is at least the weight of the fundamental group of M. This lower bound is sharp for the 3-manifolds RP3, L(3, 1), L(5, 2), S-1 x S-1 x S-1, S-2 x S-1, S-2 (x) under bar S-1 and S-3/Q(8), where Q(8) is the quaternion group. Moreover, there is a unique such facet minimal pseudotriangulation in each of these seven cases. We have also constructed contracted pseudotriangulations of L(kq - 1, q) with 4(q + k - 1) facets for q >= 3, k >= 2 and L(kq + 1, q) with 4(q + k) facets for q >= 4, k >= 1. By a recent result of Swartz, our pseudotriangulations of L(kg + 1, q) are facet minimal when kg + 1 are even. In 1979, Gagliardi found presentations of the fundamental group of a manifold M in terms of a contracted pseudotriangulation of M. Our construction is the converse of this, namely, given a presentation of the fundamental group of a 3-manifold M, we construct a contracted pseudotriangulation of M. So, our construction of a contracted pseudotriangulation of a 3-manifold M is based on a presentation of the fundamental group of M and it is computer-free.

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

Study of liquid fuel transport in a small carburetted engine in the context of cold-start HC emission control

In the present study, a detailed visualization of the transport of fuel film has been performed in a small carburetted engine with a transparent manifold at the exit of the carburettor. The presence of fuel film is observed significantly on the lower half of the manifold at idling, while at load conditions, the film is found to be distributed all throughout the manifold walls. Quantitative measurement of the fuel film in a specially-designed manifold of square cross section has also been performed using the planar laser-induced fluorescence (PLIF) technique. The measured fuel film thickness is observed to be of the order of 1 nun at idling, and in the range of 0.1 to 0.4 mm over the range of load and speed studied. These engine studies are complemented by experiments conducted in a carburettor rig to study the state of the fuel exiting the carburettor. Laser-based Particle/Droplet Image Analysis (PDIA) technique is used to identify fuel droplets and ligaments and estimate droplet diameters. At a throttle position corresponding to idling, the fuel exiting the carburettor is found to consist of very fine droplets of size less than 15 mu m and large fuel ligaments associated with length scales of the order of 500 mu m and higher. For a constant pressure difference across the carburettor, the fuel consists of droplets with an SMD of the order of 30 mu m. Also, the effect of liquid fuel film on the cold start HC emissions is studied. Based on the understanding obtained from these studies, strategies such as manifold heating and varying carburettor main jet nozzle diameter are implemented. These are observed to reduce emissions under both idling and varying load conditions.

Non-existence of tight neighborly triangulated manifolds with beta(1)=2

All triangulated d-manifolds satisfy the inequality ((f0-d-1)(2)) >= ((d+2)(2))beta(1) for d >= 3. A triangulated d-manifold is called tight neighborly if it attains equality in this bound. For each d >= 3, a (2d + 3)-vertex tight neighborly triangulation of the Sd-1-bundle over S-1 with beta(1) = 1 was constructed by Kuhnel in 1986. In this paper, it is shown that there does not exist a tight neighborly triangulated manifold with beta(1) = 2. In other words, there is no tight neighborly triangulation of (Sd-1 x S-1)(#2) or (Sd-1 (sic) S-1)(#2) for d >= 3. A short proof of the uniqueness of K hnel's complexes for d >= 4 under the assumption beta(1) not equal 0 is also presented.

On the stability of the L-p-norm of the Riemannian curvature tensor

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M where R(g) and dv (g) denote the corresponding Riemannian curvature tensor and volume form and p a (0, a). First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for for certain values of p. Then we conclude that they are strict local minimizers for for those values of p. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for for certain values of p.

SOME UNSTABLE CRITICAL METRICS FOR THE L-n/2-NORM OF THE CURVATURE TENSOR

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M given by R-n/2(g) := integral(M) vertical bar R(g)vertical bar(n//2) dv(g) where R(g), dv(g) denote the Riemannian curvature and volume form corresponding to g. We show that there are locally symmetric spaces which are unstable critical points for this functional.

Streptococcus pneumoniae Genome Database (SPGDB): A database for strain specific comparative analysis of Streptococcus pneumoniae genes and proteins

Streptococcus pneumoniae causes pneumonia, septicemia and meningitis. S. pneumoniae is responsible for significant mortality both in children and in the elderly. In recent years, the whole genome sequencing of various S. pneumoniae strains have increased manifold and there is an urgent need to provide organism specific annotations to the scientific community. This prompted us to develop the Streptococcus pneumoniae Genome Database (SPGDB) to integrate and analyze the completely sequenced and available S. pneumoniae genome sequences. Further, links to several tools are provided to compare the pool of gene and protein sequences, and proteins structure across different strains of S. pneumoniae. SPGDB aids in the analysis of phenotypic variations as well as to perform extensive genomics and evolutionary studies with reference to S. pneumoniae. (C) 2014 Elsevier Inc. All rights reserved.

Performance Assessment of a Small Biogas-fuelled Power Generator Prototype

This study reports the development and performance evaluation of prototypes of biogas-fuelled stationary power generators in the range of 1 kW. Strategies to achieve high engine efficiency namely pulsed manifold injection, electronic throttle control and dual spark plugs, have been incorporated in the prototype. A complete closed-loop control of the engine operation to maintain a steady engine speed of 3000 rpm (+/- 5%) across the entire load range while maintaining an optimum fuel-air equivalence ratio is made possible by an electronic control unit (ECU) controlling the injection duration, ignition timing and throttle position. This study specifically focuses on the response of the generator to transient loads, and the overall efficiency obtained. The results obtained from testing the prototype have been found to be satisfactory and show that biogas power generators for low power applications can be made efficient (overall efficiency of 19% at electrical load of 640 W) using the strategies of biogas fuel injection.

Strongly minimal triangulations of (S (3) x S (1))(#3) and (S (3) x S (1))(#3)

A triangulated d-manifold K, satisfies the inequality for da parts per thousand yen3. The triangulated d-manifolds that meet the bound with equality are called tight neighbourly. In this paper, we present tight neighbourly triangulations of 4-manifolds on 15 vertices with as an automorphism group. One such example was constructed by Bagchi and Datta (Discrete Math. 311 (citeyearbd102011) 986-995). We show that there are exactly 12 such triangulations up to isomorphism, 10 of which are orientable.

GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

A gap theorem for Ricci-flat 4-manifolds

Let (M, g) be a compact Ricci-fiat 4-manifold. For p is an element of M let K-max(P) (respectively K-min(p)) denote the maximum (respectively the minimum) of sectional curvatures at p. We prove that if K-max(p) <= -cK(min)(P) for all p is an element of M, for some constant c with 0 <= c < 2+root 6/4 then (M, g) is fiat. We prove a similar result for compact Ricci-flat Kahler surfaces. Let (M, g) be such a surface and for p is an element of M let H-max(p) (respectively H-min(P)) denote the maximum (respectively the minimum) of holomorphic sectional curvatures at p. If H-max(P) <= -cH(min)(P) for all p is an element of M, for some constant c with 0 <= c < 1+root 3/2, then (M, g) is flat. (C) 2015 Elsevier B.V. All rights reserved.

Fermionic edge states and new physics

We investigate the properties of the Dirac operator on manifolds with boundaries in the presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given. We show that the problem with the above boundary condition can be mapped to one where the manifold is extended beyond the boundary and the boundary condition is replaced by a delta function potential of suitable strength. We also briefly highlight how the problem of the self-adjointness of the operators in the presence of moving boundaries can be simplified by suitable transformations which render the boundary fixed and modify the Hamiltonian and the boundary condition to reflect the effect of moving boundary.

Enhanced Metastatic Potential in a 3D Tissue Scaffold toward a Comprehensive in Vitro Model for Breast Cancer Metastasis

Metastasis is clinically the most challenging and lethal aspect of breast cancer. While animal-based xenograft models are expensive and time-consuming, conventional two-dimensional (2D) cell culture systems fail to mimic in vivo signaling. In this study we have developed a three-dimensional (3D) scaffold system that better mimics the topography and mechanical properties of the breast tumor, thus recreating the tumor microenvironment in vitro to study breast cancer metastasis. Porous poly(e-caprolactone) (PCL) scaffolds of modulus 7.0 +/- 0.5 kPa, comparable to that of breast tumor tissue were fabricated, on which MDA-MB-231 cells proliferated forming tumoroids. A comparative gene expression analysis revealed that cells growing in the scaffolds expressed increased levels of genes implicated in the three major events of metastasis, viz., initiation, progression, and the site-specific colonization compared to cells grown in conventional 2D tissue culture polystyrene (TCPS) dishes. The cells cultured in scaffolds showed increased invasiveness and sphere efficiency in vitro and increased lung metastasis in vivo. A global gene expression analysis revealed a significant increase in the expression of genes involved in cell cell and cell matrix interactions and tissue remodeling, cancer inflammation, and the PI3K/Akt, Wnt, NF-kappaB, and HIFI signaling pathways all of which are implicated in metastasis. Thus, culturing breast cancer cells in 3D scaffolds that mimic the in vivo tumor-like microenvironment enhances their metastatic potential. This system could serve as a comprehensive in vitro model to investigate the manifold mechanisms of breast cancer metastasis.

Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 approximate to 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with N-A not equal N-B. The ground state (GS) and spin densities rho(r) = < S-r(z)> at site r are quite different for junctions with S = 1/2, 1, 3/2, and 2. The GS has finite total spin S-G = 2S(S) for even (odd) N and for M-G = S-G in the S-G spin manifold, rho(r) > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized S-z = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.

Tight triangulations of closed 3-manifolds

A triangulation of a closed 2-manifold is tight with respect to a field of characteristic two if and only if it is neighbourly; and it is tight with respect to a field of odd characteristic if and only if it is neighbourly and orientable. No such characterization of tightness was previously known for higher dimensional manifolds. In this paper, we prove that a triangulation of a closed 3-manifold is tight with respect to a field of odd characteristic if and only if it is neighbourly, orientable and stacked. In consequence, the Kuhnel-Lutz conjecture is valid in dimension three for fields of odd characteristic. Next let F be a field of characteristic two. It is known that, in this case, any neighbourly and stacked triangulation of a closed 3-manifold is F-tight. For closed, triangulated 3-manifolds with at most 71 vertices or with first Betti number at most 188, we show that the converse is true. But the possibility of the existence of an F-tight, non-stacked triangulation on a larger number of vertices remains open. We prove the following upper bound theorem on such triangulations. If an F-tight triangulation of a closed 3-manifold has n vertices and first Betti number beta(1), then (n - 4) (617n - 3861) <= 15444 beta(1). Equality holds here if and only if all the vertex links of the triangulation are connected sums of boundary complexes of icosahedra. (C) 2015 Elsevier Ltd. All rights reserved.