Minimal set of generators for the derivation module of certain monomial curves

Let K be a field of characteristic zero and let m(0),..., m(e-1) be a sequence of positive integers. Let C be an algebroid monomial curve in the affine e-space A(K)(e) defined parametrically by X-0 = T-m0,..., Xe-1 = Tme-1 and let A be the coordinate ring of C. In this paper, we assume that some e - 1 terms of m(0),..., m(e-1) form an arithmetic sequence and construct a minimal set of generators for the derivation module Der(K)(A) of A and write an explicit formula for mu (Der(K)(A)).

Minimal Triangulations of Manifolds

Finding vertex-minimal triangulations of closed manifolds is a very difficult problem. Except for spheres and two series of manifolds, vertex-minimal triangulations are known for only few manifolds of dimension more than 2 (see the table given at the end of Section 5). In this article, we present a brief survey on the works done in last 30 years on the following:(i) Finding the minimal number of vertices required to triangulate a given pl manifold. (ii) Given positive integers n and d, construction of n-vertex triangulations of different d-dimensional pl manifolds. (iii) Classifications of all the triangulations of a given pl manifold with same number of vertices.In Section 1, we have given all the definitions which are required for the remaining part of this article. A reader can start from Section 2 and come back to Section 1 as and when required. In Section 2, we have presented a very brief history of triangulations of manifolds. In Section 3,we have presented examples of several vertex-minimal triangulations. In Section 4, we have presented some interesting results on triangulations of manifolds. In particular, we have stated the Lower Bound Theorem and the Upper Bound Theorem. In Section 5, we have stated several results on minimal triangulations without proofs. Proofs are available in the references mentioned there. We have also presented some open problems/conjectures in Sections 3 and 5.

Minimal unsatisfiable sets: Classification and bounds

Proving the unsatisfiability of propositional Boolean formulas has applications in a wide range of fields. Minimal Unsatisfiable Sets (MUS) are signatures of the property of unsatisfiability in formulas and our understanding of these signatures can be very helpful in answering various algorithmic and structural questions relating to unsatisfiability. In this paper, we explore some combinatorial properties of MUS and use them to devise a classification scheme for MUS. We also derive bounds on the sizes of MUS in Horn, 2-SAT and 3-SAT formulas.

Minimal triangulation, complementarity and projective planes

Brehm and Kuhnel proved that if M-d is a combinatorial d-manifold with 3d/2 + 3 vertices and \ M-d \ is not homeomorphic to Sd then the combinatorial Morse number of M-d is three and hence d is an element of {0, 2, 4, 8, 16} and \ M-d \ is a manifold like a projective plane in the sense of Eells and Kuiper. We discuss the existence and uniqueness of such combinatorial manifolds. We also present the following result: ''Let M-n(d) be a combinatorial d-manifold with n vertices. M-n(d) satisfies complementarity if and only if d is an element of {0, 2, 4, 8, 16} with n = 3d/2 + 3 and \ M-n(d) \ is a manifold like a projective plane''.

Real-time monitoring of critical nodes with minimal number of Phasor Measurement Units

This paper presents a method for placement of Phasor Measurement Units, ensuring the monitoring of vulnerable buses which are obtained based on transient stability analysis of the overall system. Real-time monitoring of phase angles across different nodes, which indicates the proximity to instability, the very purpose will be well defined if the PMUs are placed at buses which are more vulnerable. The issue is to identify the key buses where the PMUs should be placed when the transient stability prediction is taken into account considering various disturbances. Integer Linear Programming technique with equality and inequality constraints is used to find out the optimal placement set with key buses identified from transient stability analysis. Results on IEEE-14 bus system are presented to illustrate the proposed approach.

Minimal residual method provides optimal regularization parameter for diffuse optical tomography

The inverse problem in the diffuse optical tomography is known to be nonlinear, ill-posed, and sometimes under-determined, requiring regularization to obtain meaningful results, with Tikhonov-type regularization being the most popular one. The choice of this regularization parameter dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. An automated method for optimal selection of regularization parameter that is based on regularized minimal residual method (MRM) is proposed and is compared with the traditional generalized cross-validation method. The results obtained using numerical and gelatin phantom data indicate that the MRM-based method is capable of providing the optimal regularization parameter. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). DOI: 10.1117/1.JBO.17.10.106015]

Leptonic minimal flavour violation in warped extra dimensions

Lepton mass hierarchies and lepton flavour violation are revisited in the framework of Randall-Sundrum models. Models with Dirac-type as well as Majorana-type neutrinos are considered. The five-dimensional c-parameters are fit to the charged lepton and neutrino masses and mixings using chi(2) minimization. Leptonic flavour violation is shown to be large in these cases. Schemes of minimal flavour violation are considered for the cases of an effective LLHH operator and Dirac neutrinos and are shown to significantly reduce the limits from lepton flavour violation.

OTCYMIST: Otsu-Canny minimal spanning tree for born-digital images

Text segmentation and localization algorithms are proposed for the born-digital image dataset. Binarization and edge detection are separately carried out on the three colour planes of the image. Connected components (CC's) obtained from the binarized image are thresholded based on their area and aspect ratio. CC's which contain sufficient edge pixels are retained. A novel approach is presented, where the text components are represented as nodes of a graph. Nodes correspond to the centroids of the individual CC's. Long edges are broken from the minimum spanning tree of the graph. Pair wise height ratio is also used to remove likely non-text components. A new minimum spanning tree is created from the remaining nodes. Horizontal grouping is performed on the CC's to generate bounding boxes of text strings. Overlapping bounding boxes are removed using an overlap area threshold. Non-overlapping and minimally overlapping bounding boxes are used for text segmentation. Vertical splitting is applied to generate bounding boxes at the word level. The proposed method is applied on all the images of the test dataset and values of precision, recall and H-mean are obtained using different approaches.

Grassmannian fusion frames and its use in block sparse recovery

Tight fusion frames which form optimal packings in Grassmannian manifolds are of interest in signal processing and communication applications. In this paper, we study optimal packings and fusion frames having a specific structure for use in block sparse recovery problems. The paper starts with a sufficient condition for a set of subspaces to be an optimal packing. Further, a method of using optimal Grassmannian frames to construct tight fusion frames which form optimal packings is given. Then, we derive a lower bound on the block coherence of dictionaries used in block sparse recovery. From this result, we conclude that the Grassmannian fusion frames considered in this paper are optimal from the block coherence point of view. (C) 2013 Elsevier B.V. All rights reserved.

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.

Error analysis of discontinuous Galerkin methods for the Stokes problem under minimal regularity

In this article, we analyse several discontinuous Galerkin (DG) methods for the Stokes problem under minimal regularity on the solution. We assume that the velocity u belongs to H-0(1)(Omega)](d) and the pressure p is an element of L-0(2)(Omega). First, we analyse standard DG methods assuming that the right-hand side f belongs to H-1(Omega) boolean AND L-1(Omega)](d). A DG method that is well defined for f belonging to H-1(Omega)](d) is then investigated. The methods under study include stabilized DG methods using equal-order spaces and inf-sup stable ones where the pressure space is one polynomial degree less than the velocity space.

Memory-induced anomalous dynamics in a minimal random walk model

A discrete-time dynamics of a non-Markovian random walker is analyzed using a minimal model where memory of the past drives the present dynamics. In recent work N. Kumar et al., Phys. Rev. E 82, 021101 (2010)] we proposed a model that exhibits asymptotic superdiffusion, normal diffusion, and subdiffusion with the sweep of a single parameter. Here we propose an even simpler model, with minimal options for the walker: either move forward or stay at rest. We show that this model can also give rise to diffusive, subdiffusive, and superdiffusive dynamics at long times as a single parameter is varied. We show that in order to have subdiffusive dynamics, the memory of the rest states must be perfectly correlated with the present dynamics. We show explicitly that if this condition is not satisfied in a unidirectional walk, the dynamics is only either diffusive or superdiffusive (but not subdiffusive) at long times.

Spinning strings and minimal surfaces in AdS(3) with mixed 3-form fluxes

Motivated by the recent proposal for the S-matrix in AdS(3) x S-3 with mixed three form fluxes, we study classical folded string spinning in AdS(3) with both Ramond and Neveu-Schwarz three form fluxes. We solve the equations of motion of these strings and obtain their dispersion relation to the leading order in the Neveu-Schwarz flux b. We show that dispersion relation for the spinning strings with large spin S acquires a term given by -root lambda/2 pi b(2) log(2) S in addition to the usual root lambda/pi log S term where root lambda is proportional to the square of the radius of AdS(3). Using SO(2, 2) transformations and re-parmetrizations we show that these spinning strings can be related to light like Wilson loops in AdS(3) with Neveu-Schwarz flux b. We observe that the logarithmic divergence in the area of the light like Wilson loop is also deformed by precisely the same coefficient of the b(2) log(2) S term in the dispersion relation of the spinning string. This result indicates that the coefficient of b(2) log(2) S has a property similar to the coefficient of the log S term, known as cusp-anomalous dimension, and can possibly be determined to all orders in the coupling lambda using the recent proposal for the S-matrix.

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.

Invisible decays of the heavier Higgs boson in the minimal supersymmetric standard model

We consider the possibility that the heavier CP-even Higgs boson (H-0) in the minimal supersymmetric standard model (MSSM) decays invisibly into neutralinos in the light of the recent discovery of the 126 GeV resonance at the CERN Large Hadron Collider (LHC). For this purpose we consider the minimal supersymmetric standard model with universal, nonuniversal and arbitrary boundary conditions on the supersymmetry breaking gaugino mass parameters at the grand unified scale. Typically, scenarios with universal and nonuniversal gaugino masses do not allow invisible decays of the lightest Higgs boson (h(0)), which is identified with the 126 GeV resonance, into the lightest neutralinos in the MSSM. With arbitrary gaugino masses at the grand unified scale, such an invisible decay is possible. The second lightest Higgs boson can decay into various invisible final states for a considerable region of the MSSM parameter space with arbitrary gaugino masses as well as with the gaugino masses restricted by universal and nonuniversal boundary conditions at the grand unified scale. The possibility of the second lightest Higgs boson of the MSSM decaying into invisible channels is more likely for arbitrary gaugino masses at the grand unified scale. The heavier Higgs boson decay into lighter particles leads to the intriguing possibility that the entire Higgs boson spectrum of the MSSM may be visible at the LHC even if it decays invisibly, during the searches for an extended Higgs boson sector at the LHC. In such a scenario the nonobservation of the extended Higgs sector of the MSSM may carefully be used to rule out regions of the MSSM parameter space at the LHC.