ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 23 Jan 2022 07:02:28 GMT2022-01-23T07:02:28Z504791- Divide-and-conquer approach for the exemplar breakpoint distancehttps://scholarbank.nus.edu.sg/handle/10635/103155Title: Divide-and-conquer approach for the exemplar breakpoint distance
Authors: Nguyen, C.T.; Tay, Y.C.; Zhang, L.
Abstract: Motivation: A one-to-one correspondence between the sets of genes in the two genomes being compared is necessary for the notions of breakpoint and reversal distances. To compare genomes where there are paralogous genes, Sankoff formulated the exemplar distance problem as a general version of the genome rearrangement problem. Unfortunately, the problem is NP-hard even for the breakpoint distance. Results: This paper proposes a divide-and-conquer approach for calculating the exemplar breakpoint distance between two genomes with multiple gene families. The combination of our approach and Sankoff's branch-and-bound technique leads to a practical program to answer this question. Tests with both simulated and real datasets show that our program is much more efficient than the existing program that is based only on the branch-and-bound technique. © The Author 2005. Published by Oxford University Press. All rights reserved.
Sun, 15 May 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1031552005-05-15T00:00:00Z
- Convergence Analysis of an Infeasible Interior Point Algorithm Based on a Regularized Central Path for Linear Complementarity Problemshttps://scholarbank.nus.edu.sg/handle/10635/103065Title: Convergence Analysis of an Infeasible Interior Point Algorithm Based on a Regularized Central Path for Linear Complementarity Problems
Authors: Zhou, G.; Toh, K.-C.; Zhao, G.
Abstract: Most existing interior-point methods for a linear complementarity problem (LCP) require the existence of a strictly feasible point to guarantee that the iterates are bounded. Based on a regularized central path, we present an infeasible interior-point algorithm for LCPs without requiring the strict feasibility condition. The iterates generated by the algorithm are bounded when the problem is a P* LCP and has a solution. Moreover, when the problem is a monotone LCP and has a solution, we prove that the convergence rate is globally linear and it achieves ε-feasibility and ε-complementarity in at most O(n 2 ln(1/ε)) iterations with a properly chosen starting point.
Mon, 01 Mar 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030652004-03-01T00:00:00Z
- On the implementation of a log-barrier progressive hedging method for multistage stochastic programshttps://scholarbank.nus.edu.sg/handle/10635/103807Title: On the implementation of a log-barrier progressive hedging method for multistage stochastic programs
Authors: Liu, X.; Toh, K.-C.; Zhao, G.
Abstract: A progressive hedging method incorporated with self-concordant barrier for solving multistage stochastic programs is proposed recently by Zhao [G. Zhao, A Lagrangian dual method with self-concordant barrier for multistage stochastic convex nonlinear programming, Math. Program. 102 (2005) 1-24]. The method relaxes the nonanticipativity constraints by the Lagrangian dual approach and smoothes the Lagrangian dual function by self-concordant barrier functions. The convergence and polynomial-time complexity of the method have been established. Although the analysis is done on stochastic convex programming, the method can be applied to the nonconvex situation. We discuss some details on the implementation of this method in this paper, including when to terminate the solution of unconstrained subproblems with special structure and how to perform a line search procedure for a new dual estimate effectively. In particular, the method is used to solve some multistage stochastic nonlinear test problems. The collection of test problems also contains two practical examples from the literature. We report the results of our preliminary numerical experiments. As a comparison, we also solve all test problems by the well-known progressive hedging method. © 2010 Elsevier B.V. All rights reserved.
Sat, 15 May 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1038072010-05-15T00:00:00Z
- Proper partial geometries with Singer groups and pseudogeometric partial difference setshttps://scholarbank.nus.edu.sg/handle/10635/103978Title: Proper partial geometries with Singer groups and pseudogeometric partial difference sets
Authors: Leung, K.H.; Ma, S.L.; Schmidt, B.
Abstract: A partial geometry admitting a Singer group G is equivalent to a partial difference set in G admitting a certain decomposition into cosets of line stabilizers. We develop methods for the classification of these objects, in particular, for the case of abelian Singer groups. As an application, we show that a proper partial geometry Π = pg (s + 1, t + 1, 2) with an abelian Singer group G can only exist if t = 2 (s + 2) and G is an elementary abelian 3-group of order (s + 1)3 or Π is the Van Lint-Schrijver partial geometry. As part of the proof, we show that the Diophantine equation (3m - 1) / 2 = (2r w - 1) / (2r - 1) has no solutions in integers m, r ≥ 1, w ≥ 2, settling a case of Goormaghtigh's equation. © 2007 Elsevier Inc. All rights reserved.
Tue, 01 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1039782008-01-01T00:00:00Z
- New Hadamard matrices of order 4 p2 obtained from Jacobi sums of order 16https://scholarbank.nus.edu.sg/handle/10635/103601Title: New Hadamard matrices of order 4 p2 obtained from Jacobi sums of order 16
Authors: Leung, K.H.; Ma, S.L.; Schmidt, B.
Abstract: Let p ≡ 7 mod 16 be a prime. Then there are integers a, b, c, d with a ≡ 15 mod 16, b ≡ 0 mod 4, p2 = a2 + 2 ( b2 + c2 + d2 ), and 2 ab = c2 - 2 cd - d2. We show that there is a regular Hadamard matrix of order 4 p2 provided that p = a ± 2 b or p = a + δ1 2 b + 4 δ2 c + 4 δ1 δ2 d with δi = ± 1. © 2006 Elsevier Inc. All rights reserved.
Sat, 01 Jul 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1036012006-07-01T00:00:00Z
- Corrigendum to "Generalized Markoff maps and McShane's identity" [Adv. Math. 217 (2008) 761-813] (DOI:10.1016/j.aim.2007.09.004)https://scholarbank.nus.edu.sg/handle/10635/104677Title: Corrigendum to "Generalized Markoff maps and McShane's identity" [Adv. Math. 217 (2008) 761-813] (DOI:10.1016/j.aim.2007.09.004)
Authors: Tan, S.P.; Wong, Y.L.; Zhang, Y.
Sun, 20 Dec 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1046772009-12-20T00:00:00Z
- Circulant weighing matrices of weight 22thttps://scholarbank.nus.edu.sg/handle/10635/102987Title: Circulant weighing matrices of weight 22t
Authors: Arasu, K.T.; Leung, K.H.; Ma, S.L.; Nabavi, A.; Ray-Chaudhuri, D.K.
Abstract: A weighing matrix of weight k is a square matrix M with entries 0,± 1 such that MM T =kI n . We study the case that M is a circulant and k = 22t for some positive integer t. New structural results are obtained. Based on these results, we make a complete computer search for all circulant weighing matrices of order 16. © Springer Science+Business Media, LLC 2006.
Sun, 01 Oct 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1029872006-10-01T00:00:00Z
- McShane's identity for classical Schottky groupshttps://scholarbank.nus.edu.sg/handle/10635/103539Title: McShane's identity for classical Schottky groups
Authors: Tan, S.P.; Wong, Y.L.; Zhang, Y.
Abstract: In 1998, Greg McShane demonstrated a remarkable identity for the lengths of simple closed geodesics on cusped hyperbolic surfaces. In 2006, we generalized this to hyperbolic cone-surfaces, possibly with cusps and/or geodesic boundary. In this paper, we generalize the identity further to the case of classical Schottky groups. As a consequence, we obtain some surprising new identities in the case of Fuchsian Schottky groups. For classical Schottky groups of rank 2, we also give generalizations of the Weierstrass identities, given by McShane in 2004.
Mon, 01 Sep 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1035392008-09-01T00:00:00Z
- Computable categoricity and the Ershov hierarchyhttps://scholarbank.nus.edu.sg/handle/10635/103019Title: Computable categoricity and the Ershov hierarchy
Authors: Khoussainov, B.; Stephan, F.; Yang, Y.
Abstract: In this paper, the notions of Fα-categorical and Gα-categorical structures are introduced by choosing the isomorphism such that the function itself or its graph sits on the α-th level of the Ershov hierarchy, respectively. Separations obtained by natural graphs which are the disjoint unions of countably many finite graphs. Furthermore, for size-bounded graphs, an easy criterion is given to say when it is computable-categorical and when it is only G2-categorical; in the latter case it is not Fα-categorical for any recursive ordinal α. © 2008 Elsevier B.V. All rights reserved.
Sat, 01 Nov 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030192008-11-01T00:00:00Z
- Nonexistence of abelian difference sets: Lander's conjecture for prime power ordershttps://scholarbank.nus.edu.sg/handle/10635/103613Title: Nonexistence of abelian difference sets: Lander's conjecture for prime power orders
Authors: Leung, K.H.; Ma, S.L.; Schmidt, B.
Abstract: In 1963 Ryser conjectured that there are no circulant Hadamard matrices of order > 4 and no cyclic difference sets whose order is not coprime to the group order. These conjectures are special cases of Lander's conjecture which asserts that there is no abelian group with a cyclic Sylow p-subgroup containing a difference set of order divisible by p. We verify Lander's conjecture for all difference sets whose order is a power of a prime greater than 3.
Mon, 01 Nov 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1036132004-11-01T00:00:00Z
- On the groups of units of finite commutative chain ringshttps://scholarbank.nus.edu.sg/handle/10635/104698Title: On the groups of units of finite commutative chain rings
Authors: Hou, X.-D.; Leung, K.H.; Ma, S.L.
Abstract: A finite commutative chain ring is a finite commutative ring whose ideals form a chain. Let R be a finite commutative ring with maximal ideal M and characteristic pn such that R/M ≅ GF(pr) and pR = Me, ≤s, where s is the nilpotency of M. When (P - 1) ł e, the structure of the group of units R× of R has been determined; it only depends on the parameters p, n, r, e, s. In this paper, we give an algorithmic method which allows us to compute the structure of R× when (p - 1) e; such a structure not only depends on the parameters p, n, r, e, s, but also on the Eisenstein polynomial which defines R as an extension over the Galois ring GR(pn, r). In the case (p - 1) ł e, we strengthen the known result by listing a set of linearly independent generators for R×. In the case (p - 1) e but p ł e, we determine the structure of R× explicitly. © 2002 Elsevier Science (USA). All rights reserved.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1046982003-01-01T00:00:00Z
- The SL(2, ℂ) character variety of a one-holed torushttps://scholarbank.nus.edu.sg/handle/10635/104355Title: The SL(2, ℂ) character variety of a one-holed torus
Authors: Tan, S.P.; Wong, Y.L.; Zhang, Y.
Abstract: In this note we announce several results concerning the SL(2, ℂ) character variety χ of a one-holed torus. We give a description of the largest open subset χBQ of χ on which the mapping class group Γ acts properly discontinuously, in terms of two very simple conditions, and show that a series identity generalizing McShane's identity for the punctured torus holds for all characters in this subset. We also give variations of the McShane-Bowditch identities for characters fixed by an Anosov element of Γ with applications to closed hyperbolic three-manifolds. Finally we give a definition of end invariants for SL(2, ℂ) characters and give a partial classification of the set of end invariants of a character in χ. © 2005 American Mathematical Society.
Sat, 01 Jan 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1043552005-01-01T00:00:00Z
- Constructions of relative difference sets with classical parameters and circulant weighing matriceshttps://scholarbank.nus.edu.sg/handle/10635/103057Title: Constructions of relative difference sets with classical parameters and circulant weighing matrices
Authors: Leung, K.H.; Ma, S.L.; Schmidt, B.
Abstract: In this paper, a new family of relative difference sets with parameters (m, n, k, λ) = ((q7 - 1)/(q - 1), 4(q - 1), q6, q5/4) is constructed where q is a 2-power. The construction is based on the technique used in [2]. By a similar method, we also construct some new circulant weighing matrices of order qd-1 where q is a 2-power, d is odd and d≥5. © 2002 Elsevier Science (USA).
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030572002-01-01T00:00:00Z
- A multiple-cut analytic center cutting plane method for semidefinite feasibility problemshttps://scholarbank.nus.edu.sg/handle/10635/44200Title: A multiple-cut analytic center cutting plane method for semidefinite feasibility problems
Authors: Toh, K.-C.; Zhao, G.; Sun, J.
Abstract: We consider the problem of finding a point in a nonempty bounded convex body F in the cone of symmetric positive semidefinite matrices S+ m. Assume that Γ is defined by a separating oracle, which, for any given m × m symmetric matrix Ŷ, either confirms that Ŷ ∈ Γ or returns several selected cuts, i.e., a number of symmetric matrices Ai, i = 1,...,p, p ≤ pmax, such that Γ is in the polyhedron {Y ∈ S+ m | Ai • Y ≤ Ai • Ŷ, i = 1, ⋯,p}. We present a multiple-cut analytic center cutting plane algorithm. Starting from a trivial initial point, the algorithm generates a sequence of positive definite matrices which are approximate analytic centers of a shrinking polytope in S+ m. The algorithm terminates with a point in F within O(m3pmax/ε2) Newton steps (to leading order), where e is the maximum radius of a ball contained in Γ.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/442002002-01-01T00:00:00Z
- On Lander's conjecture for difference sets whose order is a power of 2 or 3https://scholarbank.nus.edu.sg/handle/10635/103719Title: On Lander's conjecture for difference sets whose order is a power of 2 or 3
Authors: Leung, K.H.; Ma, S.L.; Schmidt, B.
Abstract: Let p be a prime and let b be a positive integer. If a (v, k, λ, n) difference set D of order n = p b exists in an abelian group with cyclic Sylow p-subgroup S, then p ε {2,3} and |S| = p. Furthermore, either p = 2 and v ≡ λ ≡ 2 (mod 4) or the parameters of D belong to one of four families explicitly determined in our main theorem. © 2009 Springer Science+Business Media, LLC.
Thu, 01 Jul 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1037192010-07-01T00:00:00Z
- End invariants for SL(2,ℂ) characters of the one-holed torushttps://scholarbank.nus.edu.sg/handle/10635/103199Title: End invariants for SL(2,ℂ) characters of the one-holed torus
Authors: Tan, S.P.; Wong, Y.L.; Zhang, Y.
Abstract: We define and study the set ε(p) of end invariants of an SL(2, ℂ) character p of the one-holed torus T. We show that the set ε(p) is the entire projective lamination space ℘ℒ of T if and only if p corresponds to the dihedral representation or p is real and corresponds to an SU(2) representation; and that otherwise, ε(p) is closed and has empty interior in ℘ℒ. For real characters p, we give a complete classification of ε(p), and show that ε(p) has either 0, 1 or infinitely many elements, and in the last case, ε(p) is either a Cantor subset of ℘ℒ or is ℘ℒ itself. We also give a similar classification for "imaginary" characters where the trace of the commutator is less than 2. Finally, we show that for characters with discrete simple length spectrum (not corresponding to dihedral or SU(2) representations), ε(p) is a Cantor subset of ℘ℒ if it contains at least three elements. © 2008 by The Johns Hopkins University Press.
Tue, 01 Apr 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1031992008-04-01T00:00:00Z
- A multiplier theoremhttps://scholarbank.nus.edu.sg/handle/10635/102685Title: A multiplier theorem
Authors: Leung, K.H.; Ma, S.L.; Schmidt, B.
Abstract: We show that the assumption n1 > λ in the Second Multiplier Theorem can be replaced by a divisibility condition weaker than the condition in McFarland's multiplier theorem, thus obtaining significant progress towards the multiplier conjecture. © 2014 Elsevier Inc.
Thu, 01 May 2014 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1026852014-05-01T00:00:00Z
- Generalized Markoff maps and McShane's identityhttps://scholarbank.nus.edu.sg/handle/10635/103330Title: Generalized Markoff maps and McShane's identity
Authors: Tan, S.P.; Wong, Y.L.; Zhang, Y.
Abstract: We study the (relative) SL (2, C) character varieties of the one-holed torus and the action of the mapping class group on the (relative) character variety. We show that the subset of characters satisfying two simple conditions called the Bowditch Q-conditions is open in the relative character variety and that the mapping class group acts properly discontinuously on this subset. Furthermore, this is the largest open subset for which this holds. We also show that a generalization of McShane's identity holds for all characters satisfying the Bowditch Q-conditions. Finally, we show that further variations of the McShane-Bowditch identity hold for characters which are fixed by an Anosov element of the mapping class group and which satisfy a relative version of the Bowditch Q-conditions, with applications to identities for incomplete hyperbolic structures on punctured torus bundles over the circle, and also for closed hyperbolic 3-manifolds which are obtained by hyperbolic Dehn surgery on such manifolds. © 2007 Elsevier Inc. All rights reserved.
Wed, 30 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033302008-01-30T00:00:00Z
- Delambre-Gauss formulas for augmented, right-angled hexagons in hyperbolic 4-spacehttps://scholarbank.nus.edu.sg/handle/10635/103119Title: Delambre-Gauss formulas for augmented, right-angled hexagons in hyperbolic 4-space
Authors: Tan, S.P.; Wong, Y.L.; Zhang, Y.
Abstract: We study the geometry of right-angled hexagons in the hyperbolic 4-space H 4 via Clifford numbers or quaternions. We show how to augment alternate sides of such a hexagon and arbitrarily orient each line and plane involved, so that for the non-augmented sides, we can define quaternion half side-lengths whose angular parts are obtained from half the Euler angles associated to a certain orientation-preserving isometry of the Euclidean 3-space. We also define appropriate complex half side-lengths for the augmented sides of the augmented hexagon. We further explain how to geometrically read off the quaternion half side-lengths for a given oriented, augmented, right-angled hexagon in H 4. Our main result is a set of generalized Delambre-Gauss formulas for oriented, augmented, right-angled hexagons in H 4, involving the quaternion half side-lengths and the complex half side-lengths. We also show in the appendix how the same method gives Delambre-Gauss formulas for oriented right-angled hexagons in H 3, from which the well-known laws of sines and of cosines can be deduced. These formulas generalize the classical Delambre-Gauss formulas for spherical/hyperbolic triangles. © 2012 Elsevier Ltd.
Wed, 20 Jun 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1031192012-06-20T00:00:00Z
- Weighted fair caching: Occupancy-centric allocation for space-shared resourceshttps://scholarbank.nus.edu.sg/handle/10635/156948Title: Weighted fair caching: Occupancy-centric allocation for space-shared resources
Authors: Shi, Lianjie; WANG XIN; Ma Tianbai; TAY YONG CHIANG
Abstract: © 2018 Elsevier B.V. Traditional cache replacement policies such as LRU and LFU were often designed with the focus on efficiency and aimed at maximizing the hit rates. However, the resource owners of modern computing systems such as cloud infrastructures and content delivery networks often have new objectives such as fairness and revenue to be optimized rather than the overall hit rate. A general resource management framework that allows resource owners to determine various resource allocations is desirable. Although such a mechanism like Weighted Fair Queueing (WFQ) exists for indivisible time-shared resources such as CPU and network bandwidth, no such counterpart exists for space-shared resources such as cache and main memory. 1 In this paper, we propose Weighted Fair Caching (WFC), a capacity-driven cache policy that provides explicitly tunable resource allocations for cache owners in terms of the occupancy rates of contents. Through analysis of the continuous-time Markov Chain model of cache dynamics, we derive the closed-form occupancy rates as a function of the weights of contents, and various properties such as monotonicity and scaling of WFC. We show that WFC can be used to provide fair sharing of cache space among contents, as well as class-based service differentiations. We evaluate the performance of WFC using real data traces from two major video providers. We find that, compared to traditional cache policies, WFC provides better fairness while sacrificing an acceptable amount of hit rates.
Fri, 25 Jan 2019 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1569482019-01-25T00:00:00Z
- Existence of weak solutions to degenerate p-Laplacian equations and integral formulashttps://scholarbank.nus.edu.sg/handle/10635/171596Title: Existence of weak solutions to degenerate p-Laplacian equations and integral formulas
Authors: Chua, Seng Kee; Wheeden, Richard L.
Abstract: We study the problem of solving some general integral formulas and
then apply the conclusions to obtain results about the existence of
weak solutions of various degenerate p-Laplacian equations. Our methods
are a combination of classical Variational Calculus, the Mountain Pass
Lemma without the Palais-Smale condition, and an abstract version of
Lions' concentration compactness principle II
Fri, 18 Aug 2017 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1715962017-08-18T00:00:00Z
- Determination of all possible orders of weight 16 circulant weighing matriceshttps://scholarbank.nus.edu.sg/handle/10635/103124Title: Determination of all possible orders of weight 16 circulant weighing matrices
Authors: Arasu, K.T.; Hin Leung, K.H.; Lun Ma, S.L.; Nabavi, A.; Ray-Chaudhuri, D.K.
Abstract: We show that a circulant weighing matrix of order n and weight 16 exists if and only if n ≥ 21 and n is a multiple of 14, 21 or 31. © 2005 Elsevier Inc. All rights reserved.
Wed, 01 Nov 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1031242006-11-01T00:00:00Z
- Injectivity radius and gonality of a compact Riemann surfacehttps://scholarbank.nus.edu.sg/handle/10635/103430Title: Injectivity radius and gonality of a compact Riemann surface
Authors: Hwang, J.-M.; To, W.-K.
Abstract: We obtain a sharp lower bound for the volumes of purely 1-dimensional complex analytic subvarieties in a geodesic tubular neighborhood of the diagonal of the Cartesian product of a compact Riemann surface with itself. This leads to a lower bound of the Seshadri number of the canonical line bundle of the Cartesian product with respect to the diagonal. As a consequence, we obtain an upper bound for the hyperbolic injectivity radii of compact Riemann surfaces of a fixed gonality. In particular, we obtain the limiting behavior of the gonalities of a tower of compact Riemann surfaces. We also give an application of our results to an invariant related to the ample cone of the symmetric product of a Riemann surface. © 2012 by The Johns Hopkins University Press.
Wed, 01 Feb 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034302012-02-01T00:00:00Z
- Normal algebraic surfaces with trivial bicanonical divisorhttps://scholarbank.nus.edu.sg/handle/10635/103635Title: Normal algebraic surfaces with trivial bicanonical divisor
Authors: Gurjar, R.V.; Zhang, D.-Q.
Abstract: Let S be a rational projective algebraic surface, with at worst quotient singular points but with no rational double singular points, such that IKS ∼ 0 for some minimal positive integer I. If I = 2, we prove that the fundamental group π1(S -Sing S) is soluble of order ≤ 256 (Theorem 1). If I ≥ 3 or S has at worst rational double singular points, then, in general, π1(S - Sing S) is not finite (remark to Theorem 1). © 1996 Academic Press, Inc.
Sun, 15 Dec 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1036351996-12-15T00:00:00Z
- Representations of metaplectic groups I: Epsilon dichotomy and local Langlands correspondencehttps://scholarbank.nus.edu.sg/handle/10635/126641Title: Representations of metaplectic groups I: Epsilon dichotomy and local Langlands correspondence
Authors: Gan, W.T.; Savin, G.
Abstract: Using theta correspondence, we classify the irreducible representations of Mp 2n in terms of the irreducible representations of SO 2n+1 and determine many properties of this classification. This is a local Shimura correspondence which extends the well-known results of Waldspurger for n=1. © 2012 Foundation Compositio Mathematica.
Thu, 01 Nov 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1266412012-11-01T00:00:00Z
- Conversion events in gene clustershttps://scholarbank.nus.edu.sg/handle/10635/103075Title: Conversion events in gene clusters
Authors: Song, G.; Hsu, C.-H.; Riemer, C.; Zhang, Y.; Kim, H.; Hoffmann, F.; Zhang, L.; Hardison, R.C.; Green, E.D.; Miller, W.
Abstract: Background: Gene clusters containing multiple similar genomic regions in close proximity are of great interest for biomedical studies because of their associations with inherited diseases. However, such regions are difficult to analyze due to their structural complexity and their complicated evolutionary histories, reflecting a variety of large-scale mutational events. In particular, conversion events can mislead inferences about the relationships among these regions, as traced by traditional methods such as construction of phylogenetic trees or multi-species alignments. Results: To correct the distorted information generated by such methods, we have developed an automated pipeline called CHAP (Cluster History Analysis Package) for detecting conversion events. We used this pipeline to analyze the conversion events that affected two well-studied gene clusters (-globin and -globin) and three gene clusters for which comparative sequence data were generated from seven primate species: CCL (chemokine ligand), IFN (interferon), and CYP2abf (part of cytochrome P450 family 2). CHAP is freely available at http://www.bx.psu.edu/miller-lab. Conclusions: These studies reveal the value of characterizing conversion events in the context of studying gene clusters in complex genomes. © 2011 Song et al; licensee BioMed Central Ltd.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030752011-01-01T00:00:00Z
- Properly Σ 2 minimal degrees and 0″ complementationhttps://scholarbank.nus.edu.sg/handle/10635/103979Title: Properly Σ 2 minimal degrees and 0″ complementation
Authors: Cooper, S.B.; Lewis, A.E.M.; Yang, Y.
Abstract: We show that there exists a properly Σ 2 minimal (Turing) degree b, and moreover that b can be chosen to join with 0′ to 0″ - so that b is a 0″ complement for every degree a such that 0′ ≤ a < 0″. © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Sat, 01 Jan 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1039792005-01-01T00:00:00Z
- Theta lifting of unitary lowest weight modules and their associated cycleshttps://scholarbank.nus.edu.sg/handle/10635/104376Title: Theta lifting of unitary lowest weight modules and their associated cycles
Authors: Nishiyama, K.; Zhu, C.-B.
Abstract: We consider a reductive dual pair (G, G′) in the stable range with G′ the smaller member and of Hermitian symmetric type. We study the theta lifting of(holomorphic) nilpotent K′ ℂ-orbits in relation to the theta lifting of unitary lowest weight representations of G′. We determine the associated cycles of all such representations. In particular, we prove that the multiplicity in the associated cycle is preserved under the theta lifting. We also develop a theory for the lifting of covariants arising from double fibrations by affine quotient maps.
Wed, 01 Dec 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1043762004-12-01T00:00:00Z
- The Critical Curves of the Random Pinning and Copolymer Models at Weak Couplinghttps://scholarbank.nus.edu.sg/handle/10635/104274Title: The Critical Curves of the Random Pinning and Copolymer Models at Weak Coupling
Authors: Berger, Q.; Caravenna, F.; Poisat, J.; Sun, R.; Zygouras, N.
Abstract: We study random pinning and copolymer models, when the return distribution of the underlying renewal process has a polynomial tail with finite mean. We compute the asymptotic behavior of the critical curves of the models in the weak coupling regime, showing that it is universal. This proves a conjecture of Bolthausen, den Hollander and Opoku for copolymer models (Bolthausen et al., in Ann Probab, 2012), which we also extend to pinning models. © 2013 Springer-Verlag Berlin Heidelberg.
Sat, 01 Mar 2014 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1042742014-03-01T00:00:00Z
- A nonzero-sum game approach to convertible bonds: Tax benefit, bankruptcy cost, and early/late callshttps://scholarbank.nus.edu.sg/handle/10635/102702Title: A nonzero-sum game approach to convertible bonds: Tax benefit, bankruptcy cost, and early/late calls
Authors: Chen, N.; Dai, M.; Wan, X.
Abstract: Convertible bonds are hybrid securities that embody the characteristics of both straight bonds and equities. The conflicts of interest between bondholders and shareholders affect the security prices significantly. In this paper, we investigate how to use a nonzero-sum game framework to model the interaction between bondholders and shareholders and to evaluate the bond accordingly. Mathematically, this problem can be reduced to a system of variational inequalities and we explicitly derive the Nash equilibrium to the game. Our model shows that credit risk and tax benefit have considerable impacts on the optimal strategies of both parties. The shareholder may issue a call when the debt is in-the-money or out-of-the-money. This is consistent with the empirical findings of "late and early calls." In addition, the optimal call policy under our model offers an explanation for certain stylized patterns related to the returns of company assets and stocks on call. © 2012 Wiley Periodicals, Inc.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1027022013-01-01T00:00:00Z
- Kolmogorov-Loveland randomness and stochasticityhttps://scholarbank.nus.edu.sg/handle/10635/103465Title: Kolmogorov-Loveland randomness and stochasticity
Authors: Merkle, W.; Miller, J.S.; Nies, A.; Reimann, J.; Stephan, F.
Abstract: An infinite binary sequence X is Kolmogorov-Loveland (or KL-) random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence. One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL-randomness. Our first main result states that KL-random sequences are close to Martin-Löf random sequence at least one of the halves is Martin-Löf random. However, this splitting property does not characterize KL-randomness; we construct a sequence that is not even computably random such that every effective split yields two subsequences that are 2-random. Furthermore, we show for any KL-random sequence A that is computable in the halting problem that, first, for any effective split of A both halves are Martin-Löf random and, second, for any computable, nondecreasing, and unbounded function g and almost all n, the prefix of A of length n has prefix-free Kolmogorov complexity at least n - g(n). Again, the latter property does not characterize KL-randomness, even when restricted to left-r.e. sequences; we construct a left-r.e. sequence that has this property but is not KL-stochastic and, in fact, is not even Mises-Wald-Church stochastic. Turning our attention to KL-stochasticity, we construct a non-empty ∏1 0 class of KL-stochastic sequences that are not weakly 1-random; by the usual basis theorems we obtain such sequences that in addition are left-r.e., are low, or are of hyperimmune-free degree. Our second main result asserts that every KL-stochastic sequence has effective dimension 1, or equivalently, a sequence cannot be KL-stochastic if it has infinitely many prefixes that can be compressed by a factor of α < 1. This improves on a result by Muchnik, who has shown that were they to exist, such compressible prefixes could not be found effectively. © 2005 Elsevier B.V. All rights reserved.
Wed, 01 Mar 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034652006-03-01T00:00:00Z
- Computing the nearest doubly stochastic matrix with a prescribed entryhttps://scholarbank.nus.edu.sg/handle/10635/103033Title: Computing the nearest doubly stochastic matrix with a prescribed entry
Authors: Bai, Z.-J.; Chu, D.; Tan, R.C.E.
Abstract: In this paper a nearest doubly stochastic matrix problem is studied. This problem is to find the closest doubly stochastic matrix with the prescribed (1,1) entry to a given matrix. According to the well-established dual theory in optimization, the dual of the underlying problem is an unconstrained differentiable, but not twice differentiable, convex optimization problem. A Newton-type method is used for solving the associated dual problem, and then the desired nearest doubly stochastic matrix is obtained. Under some mild assumptions, the quadratic convergence of the proposed Newton method is proved. The numerical performance of the method is also demonstrated by numerical examples. © 2007 Society for Industrial and Applied Mathematics.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030332007-01-01T00:00:00Z
- Axisymmetric lower-bound limit analysis using finite elements and second-order cone programminghttps://scholarbank.nus.edu.sg/handle/10635/90913Title: Axisymmetric lower-bound limit analysis using finite elements and second-order cone programming
Authors: Tang, C.; Toh, K.-C.; Phoon, K.-K.
Abstract: In this paper, the formulation of a lower-bound limit analysis for axisymmetric problems by means of finite elements leads to an optimization problem with a large number of variables and constraints. For the Mohr-Coulomb criterion, it is shown that these axisymmetric problems can be solved by second-order cone programming (SOCP). First, a brief introduction to SOCP is given and how axisymmetric lowerbound limit analysis can be formulated in this way is described. Through the use of an efficient toolbox (MOSEK or SDPT3), large-scale SOCP problems can be solved in minutes on a desktop computer. The method is then applied to estimate the collapse load of circular footings and uplift capacity of single or multiplate circular anchors. By comparing the present analysis with the results reported in the literature, it is shown that the results obtained from the proposed method are accurate and computationally more efficient than the numerical lower-bound limit analysis incorporated with linear programming. © 2014 American Society of Civil Engineers.
Wed, 01 Jan 2014 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/909132014-01-01T00:00:00Z
- Initial conditions for bubble universeshttps://scholarbank.nus.edu.sg/handle/10635/103427Title: Initial conditions for bubble universes
Authors: McInnes, B.
Abstract: The "bubble universes" of Coleman and De Luccia play a crucial role in string cosmology. Since our own Universe is supposed to be of this kind, bubble cosmology should supply definite answers to the long-standing questions regarding cosmological initial conditions. In particular, it must explain how an initial singularity is avoided, and also how the initial conditions for inflation were established. I argue that the simplest nonanthropic approach to these problems involves a requirement that the spatial sections defined by distinguished bubble observers should not be allowed to have arbitrarily small volumes. Casimir energy is a popular candidate for a quantum effect which can ensure this, but (because it violates energy conditions) there is a danger that it could lead to nonperturbative instabilities in string theory. I make a simple proposal for the initial conditions of a bubble universe, and show that my proposal ensures that the system is nonperturbatively stable. Thus, low-entropy conditions can be established at the beginning of a bubble universe without violating the second law of thermodynamics and without leading to instability in string theory. These conditions are inherited from the ambient spacetime. © 2008 The American Physical Society.
Mon, 23 Jun 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034272008-06-23T00:00:00Z
- Erratum: On the numerical computation in systems and control (IEEE Transactions on Automatic Control (Nov. 2002) 47 (1786-1799))https://scholarbank.nus.edu.sg/handle/10635/104683Title: Erratum: On the numerical computation in systems and control (IEEE Transactions on Automatic Control (Nov. 2002) 47 (1786-1799))
Authors: Chu, D.; Liu, X.; Tan, R.C.E.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1046832003-01-01T00:00:00Z
- Learnability of automatic classeshttps://scholarbank.nus.edu.sg/handle/10635/43288Title: Learnability of automatic classes
Authors: Jain, S.; Luo, Q.; Stephan, F.
Abstract: The present work initiates the study of the learnability of automatic indexable classes which are classes of regular languages of a certain form. Angluin's tell-tale condition characterises when these classes are explanatorily learnable. Therefore, the more interesting question is when learnability holds for learners with complexity bounds, formulated in the automata-theoretic setting. The learners in question work iteratively, in some cases with an additional long-term memory, where the update function of the learner mapping old hypothesis, old memory and current datum to new hypothesis and new memory is automatic. Furthermore, the dependence of the learnability on the indexing is also investigated. This work brings together the fields of inductive inference and automatic structures. © 2012 2012 Elsevier Inc. All rights reserved.
Sun, 01 Jan 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/432882012-01-01T00:00:00Z
- Arrow of time in string theoryhttps://scholarbank.nus.edu.sg/handle/10635/102883Title: Arrow of time in string theory
Authors: McInnes, B.
Abstract: Inflation allows the problem of the arrow of time to be understood as a question about the structure of spacetime: why was the intrinsic curvature of the earliest spatial sections so much better behaved than it might have been? This is really just the complement of a more familiar problem: what mechanism prevents the extrinsic curvature of the earliest spatial sections from diverging, as classical general relativity suggests? We argue that the stringy version of "creation from nothing", sketched by Ooguri, Vafa, and Verlinde, solves both of these problems at once. The argument, while very simple, hinges on some of the deepest theorems in global differential geometry. These results imply that when a spatially toral spacetime is created from nothing, the earliest spatial sections are forced to be [quasi-classically] exactly locally isotropic. This local isotropy, in turn, forces the inflaton into its minimal-entropy state. The theory explains why the arrow does not reverse in black holes or in a cosmic contraction, if any. © 2007 Elsevier B.V. All rights reserved.
Mon, 15 Oct 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1028832007-10-15T00:00:00Z
- Hadamard difference sets related to Lander's conjecturehttps://scholarbank.nus.edu.sg/handle/10635/103362Title: Hadamard difference sets related to Lander's conjecture
Authors: Feng, T.; Leung, K.H.; Schmidt, B.; Smith, K.W.
Abstract: If a Hadamard difference set exists in H × K, where H is an abelian 2-group and K is a cyclic 3-group, then |. H| > 4|. K|. Furthermore, Lander's conjecture holds for all Hadamard difference sets of order at most 529. © 2014 Elsevier Inc.
Sat, 01 Feb 2014 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033622014-02-01T00:00:00Z
- Invariant hypersurfaces of endomorphisms of projective varietieshttps://scholarbank.nus.edu.sg/handle/10635/103444Title: Invariant hypersurfaces of endomorphisms of projective varieties
Authors: Zhang, D.-Q.
Abstract: We consider surjective endomorphisms f of degree >1 on projective manifolds X of Picard number one and their f -1-stable hypersurfaces V, and show that V is rationally chain connected. Also given is an optimal upper bound for the number of f -1-stable prime divisors on (not necessarily smooth) projective varieties. © 2013 Elsevier Inc.
Sat, 15 Feb 2014 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034442014-02-15T00:00:00Z
- Representations of the two-fold central Extension of SL2 (Q2)https://scholarbank.nus.edu.sg/handle/10635/104051Title: Representations of the two-fold central Extension of SL2 (Q2)
Authors: Loke, H.Y.; Savin, G.
Abstract: We define a notion of pseudospherical type for smooth representations of the nontrivial two fold central extension of SL2(Q2). We describe completely the irreducible representations that contain the pseudospherical type. We relate our results to Kohnen's plus and minus spaces of classical modular forms of half integral weight. © 2010 by Pacific Journal of Mathematics.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1040512010-01-01T00:00:00Z
- Uncountable automatic classes and learninghttps://scholarbank.nus.edu.sg/handle/10635/43055Title: Uncountable automatic classes and learning
Authors: Jain, S.; Luo, Q.; Semukhin, P.; Stephan, F.
Abstract: In this paper we consider uncountable classes recognizable by ω-automata and investigate suitable learning paradigms for them. In particular, the counterparts of explanatory, vacillatory and behaviourally correct learning are introduced for this setting. Here the learner reads in parallel the data of a text for a language L from the class plus an ω-index α and outputs a sequence of ω-automata such that all but finitely many of these ω-automata accept the index α if and only if α is an index for L. It is shown that any class is behaviourally correct learnable if and only if it satisfies Angluin's tell-tale condition. For explanatory learning, such a result needs that a suitable indexing of the class is chosen. On the one hand, every class satisfying Angluin's tell-tale condition is vacillatorily learnable in every indexing; on the other hand, there is a fixed class such that the level of the class in the hierarchy of vacillatory learning depends on the indexing of the class chosen. We also consider a notion of blind learning. On the one hand, a class is blind explanatorily (vacillatorily) learnable if and only if it satisfies Angluin's tell-tale condition and is countable; on the other hand, for behaviourally correct learning, there is no difference between the blind and non-blind version. This work establishes a bridge between the theory of ω-automata and inductive inference (learning theory). © 2010 Elsevier B.V. All rights reserved.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/430552011-01-01T00:00:00Z
- Schnorr trivial sets and truth-table reducibilityhttps://scholarbank.nus.edu.sg/handle/10635/104078Title: Schnorr trivial sets and truth-table reducibility
Authors: Franklin, J.N.Y.; Stephan, F.
Abstract: We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr triviality based on truth-table reducibility. These characterizations allow us to see not only that some natural classes of sets, including maximal sets, are composed entirely of Schnorr triviais, but also that the Schnorr trivial sets form an ideal in the truth-table degrees but not the weak truth-table degrees. This answers a question of Downey, Griffiths and LaForte. © 2010. Association for Symbolic Logic.
Tue, 01 Jun 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1040782010-06-01T00:00:00Z
- A new and fast orthogonal linear discriminant analysis on undersampled problemshttps://scholarbank.nus.edu.sg/handle/10635/52755Title: A new and fast orthogonal linear discriminant analysis on undersampled problems
Authors: Chu, D.; Goh, S.T.
Abstract: Dimensionality reduction has become a ubiquit ous preprocessing step in many applications. Linear discriminant analysis (LDA) has been known to be one of the most optimal dimensionality reduction methods for classification. However, a main disadvantage of LDA is that the so-called total scatter matrix must be nonsingular. But, in many applications, the scatter matrices can be singular since the data points are from a very high-dimensional space, and thus usually the number of the data samples is smaller than the data dimension. This is known as the undersampled problem. Many generalized LDA methods have been proposed in the past to overcome this singularity problem. There is a commonality for these generalized LDA methods; that is, they compute the optimal linear transformations by computing some eigen-decompositions and involving some matrix inversions. However, the eigen-decomposition is computationally expensive, and the involvement of matrix inverses may lead to the methods not numerically stable if the associated matrices are ill-conditioned. Hence, many existing LDA methods have high computational cost and have potential numerical instability problems. In this paper we present a new orthogonal LDA method for the undersampled problem. The main features of our proposed LDA method include the following: (i) the optimal transformation matrix is obtained easily by only orthogonal transformations without computing any eigen-decomposition and matrix inverse, and, consequently, our LDA method is inverse-free and numerically stable; (ii) our LDA method is implemented by using several QR factorizations and is a fast one. The effectiveness of our new method is illustrated by some real-world data sets. © 2010 Society for Industrial and Applied Mathematics.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/527552010-01-01T00:00:00Z
- Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programminghttps://scholarbank.nus.edu.sg/handle/10635/103964Title: Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming
Authors: Chai, J.-S.; Toh, K.-C.
Abstract: We propose to compute the search direction at each interior-point iteration for a linear program via a reduced augmented system that typically has a much smaller dimension than the original augmented system. This reduced system is potentially less susceptible to the ill-conditioning effect of the elements in the (1,1) block of the augmented matrix. Apreconditioner is then designed by approximating the block structure of the inverse of the transformed matrix to further improve the spectral properties of the transformed system. The resulting preconditioned system is likely to become better conditioned toward the end of the interior-point algorithm. Capitalizing on the special spectral properties of the transformed matrix, we further proposed a two-phase iterative algorithm that starts by solving the normal equations with PCG in each IPM iteration, and then switches to solve the preconditioned reduced augmented system with symmetric quasi-minimal residual (SQMR) method when it is advantageous to do so. The experimental results have demonstrated that our proposed method is competitive with direct methods in solving large-scale LP problems and a set of highly degenerate LP problems. © Springer Science+Business Media, LLC 2007.
Sun, 01 Apr 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1039642007-04-01T00:00:00Z
- Fast Algorithms for Large-Scale Generalized Distance Weighted Discriminationhttps://scholarbank.nus.edu.sg/handle/10635/144831Title: Fast Algorithms for Large-Scale Generalized Distance Weighted Discrimination
Authors: Xin Yee Lam; J. S. Marron; Defeng Sun; Kim-Chuan Toh
Thu, 17 May 2018 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1448312018-05-17T00:00:00Z
- Shearing black holes and scans of the quark matter phase diagramhttps://scholarbank.nus.edu.sg/handle/10635/104109Title: Shearing black holes and scans of the quark matter phase diagram
Authors: McInnes, B.
Abstract: Future facilities such as FAIR and NICA are expected to produce collisions of heavy ions generating quark-gluon plasmas (QGPs) with large values of the quark chemical potential; peripheral collisions in such experiments will also lead to large values of the angular momentum density, associated with the internal shearing motion of the plasma. It is well known that shearing motions in fluids can lead to instabilities which cause a transition from laminar to turbulent flow, and such instabilities in the QGP have recently attracted some attention. We set up a holographic model of this situation by constructing a gravitational dual system exhibiting an instability which is indeed triggered by shearing angular momentum in the bulk. We show that holography indicates that the transition to an unstable fluid happens more quickly as one scans across the quark matter phase diagram towards large values of the chemical potential. This may have negative consequences for the observability of quark polarization effects. © 2014 IOP Publishing Ltd.
Tue, 21 Jan 2014 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1041092014-01-21T00:00:00Z
- Strong Approximation Property for Baer Orderings on *-Fieldshttps://scholarbank.nus.edu.sg/handle/10635/104205Title: Strong Approximation Property for Baer Orderings on *-Fields
Authors: Leung, K.H.
Abstract: Let (D, *) be a *-field with [D: Z(D)] being finite. Our main objective is to show that the space of all Baer orderings (resp. weak *-orderings) of (D, *) satisfies the strong approximation property iff every Baer ordering of (D, *) is in fact a weak *-ordering. This shows that the notions of Baer orderings and weak *-orderings are respectively the "correct" analogues for semiorderings and orderings. We also intro-duce the concept of Baer formally real *-fields and Baer preorderings. We prove that a *-field admits a Baer ordering iff it is Baer formally real. In addition, some new results on weak *-orderings are also discussed. © 1994 Academic Press. All rights reserved.
Fri, 01 Apr 1994 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1042051994-04-01T00:00:00Z
- Automorphisms of finite order on gorenstein del pezzo surfaceshttps://scholarbank.nus.edu.sg/handle/10635/102913Title: Automorphisms of finite order on gorenstein del pezzo surfaces
Authors: Zhang, D.-Q.
Abstract: In this paper we shall determine all actions of groups of prime order p with p ≥ 5 on Gorenstein del Pezzo (singular) surfaces Y of Picard number 1. We show that every order-p element in Aut(Y) (= Aut(Ỹ), Ỹ being the minimal resolution of Y) is lifted from a projective transformation of P2. We also determine when Aut(Y) is finite in terms of KY 2, Sing Y and the number of singular members in |-KY|. In particular, we show that either |Aut(Y)| = 2a3b for some 1 ≤ a + b ≤ 7, or for every prime p ≥ 5, there is at least one element gp of order p in Aut(Y) (hence |Aut(Y)| is infinite).
Sun, 01 Dec 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1029132002-12-01T00:00:00Z
- A numerical method for a generalized algebraic Riccati equationhttps://scholarbank.nus.edu.sg/handle/10635/102721Title: A numerical method for a generalized algebraic Riccati equation
Authors: Chu, D.; Lin, W.-W.; Tan, R.C.E.
Abstract: In this paper we develop a numerical method for computing the semistabilizing solution of a generalized algebraic Riccati equation (GARE). The semistabilizing solution of such a GARE has been used to characterize the solvability of the (J, J′)-spectral factorization problem for general rational matrices which have poles and zeros on the extended imaginary axis. The main difficulty for solving such a GARE is that its associated skew-Hamiltonian/Hamiltonian pencil has eigenvalues on the extended imaginary axis; consequently, it is not clear which eigenspace of the associated skew-Hamiltonian/Hamiltonian pencil can characterize the desired semistabilizing solution; i.e., it is not clear which eigenvectors and principal vectors corresponding to the eigenvalues on the extended imaginary axis should be contained in the eigenspace that we wish to compute, and hence the well-known generalized eigenvalue approach for the classical algebraic Riccati equations cannot be directly employed for it. Our proposed method consists of computations of the eigendecomposition of the system pencil corresponding to the eigenvalues on the extended imaginary axis and the stable eigenspace of an augmented matrix pencil; hence, it is a generalization of the generalized eigenvalue approach for the classical algebraic Riccati equations. © 2006 Society for Industrial and Applied Mathematics.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1027212006-01-01T00:00:00Z
- SWARM: The power of structure in community wireless Mesh networkshttps://scholarbank.nus.edu.sg/handle/10635/104508Title: SWARM: The power of structure in community wireless Mesh networks
Authors: Das, S.; Papagiannaki, K.; Banerjee, S.; Tay, Y.C.
Abstract: Community wireless networks (CWNs) have been proposed to spread broadband network access to underprivileged, underprovisioned, and remote areas. Research has focused on optimizing network performance through intelligent routing and scheduling, borrowing solutions from mesh networks. Surprisingly, however, there has been no work on how to make efficient use of multiple channels in CWNs in the presence of multiple gateways and a single radio per device. In fact, today's deployments in underprivileged areas are primarily single-radio and do operate on a single channel. Frequency selection in such CWNs is very complex because it does not only determine the nodes' channel of operation, but also the gateway and the routing tree to the gatewaya rather computationally intensive task. In this paper, we propose, design, implement, and evaluate SWARM, a practical system that allows a CWN to make effective use of the available wireless channels in order to offer globally optimal performance. SWARM improves performance versus current single-channel protocols by up to 7.7× in our experiments. Moreover, while we should be expecting performance gains due to channel diversity, we clearly demonstrate that up to 3.7× improvement is attributed to the network organization into efficient traffic distribution structures. © 2010 IEEE.
Wed, 01 Jun 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1045082011-06-01T00:00:00Z