Showing papers on "Constant (mathematics) published in 2008"
TL;DR: The functionality of the Flexmix package was enhanced and concomitant variable models as well as varying and constant parameters for the component specific generalized linear regression models can be fitted.
Abstract: flexmix provides infrastructure for flexible fitting of finite mixture models in R using the expectation-maximization (EM) algorithm or one of its variants. The functionality of the package was enhanced. Now concomitant variable models as well as varying and constant parameters for the component specific generalized linear regression models can be fitted. The application of the package is demonstrated on several examples, the implementation described and examples given to illustrate how new drivers for the component specific models and the concomitant variable models can be defined.
385 citations
TL;DR: In this paper, the existence and nonexistence of ground state solutions for nonlinear Schrodinger-Maxwell equations were proved for 2 p 5 and 3 p 5, respectively, under the assumption that V is a positive constant.
366 citations
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01 May 2008
TL;DR: It is shown that there exists a constant c > 0 such that every finite group G has a product-free subset of size at least c|G|: that is, a subset X that does not contain three elements x, y and z with xy = z.
Abstract: Babai and Sos have asked whether there exists a constant c > 0 such that every finite group G has a product-free subset of size at least c|G|: that is, a subset X that does not contain three elements x, y and z with xy = z. In this paper we show that the answer is no. Moreover, we give a simple sufficient condition for a group not to have any large product-free subset.
275 citations
01 Apr 2008
TL;DR: It is concluded that the stability result for linear switched systems still holds for such systems with time-varying delay under a certain delay bound, and the delay bound of guaranteeing system stability can be easily obtained based on linear matrix inequalities (LMIs).
Abstract: This correspondence considers the stability problem for a class of linear switched systems with time-varying delay in the sense of Hurwitz convex combination. The bound of derivative of the time-varying delay can be an unknown constant. It is concluded that the stability result for linear switched systems still holds for such systems with time-varying delay under a certain delay bound. Moreover, the delay bound of guaranteeing system stability can be easily obtained based on linear matrix inequalities (LMIs). As a special case, when the time-varying delay becomes constant, the criterion obtained in this correspondence is less conservative than existing ones. The reason for less conservativeness is also explicitly explained in this correspondence. Simulation examples illustrate the effectiveness of the proposed method.
263 citations
TL;DR: Given a compact four dimensional manifold, it is proved existence of conformal metrics with constant Q-curvature under generic assumptions, jointly with the compactness result of [35].
Abstract: Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and min-max schemes, jointly with the compactness result of [35].
253 citations
TL;DR: It is demonstrated that winner selection in two prominent proportional representation voting systems is a computationally intractable problem—implying that these systems are impractical when the assembly is large, and in settings where the size of the Assembly is constant, the problem can be solved in polynomial time.
Abstract: We demonstrate that winner selection in two prominent proportional representation voting systems is a computationally intractable problem—implying that these systems are impractical when the assembly is large. On a different note, in settings where the size of the assembly is constant, we show that the problem can be solved in polynomial time.
220 citations
TL;DR: The energy density of the vacuum, Lambda, is at least 60 orders of magnitude smaller than several known contributions to it as discussed by the authors, and the possibility remains that Lambda is fundamentally variable, though constant over large spacetime regions.
Abstract: The energy density of the vacuum, Lambda, is at least 60 orders of magnitude smaller than several known contributions to it. Approaches to this problem are tightly constrained by data ranging from elementary observations to precision experiments. Absent overwhelming evidence to the contrary, dark energy can only be interpreted as vacuum energy, so the venerable assumption that Lambda=0 conflicts with observation. The possibility remains that Lambda is fundamentally variable, though constant over large spacetime regions. This can explain the observed value, but only in a theory satisfying a number of restrictive kinematic and dynamical conditions. String theory offers a concrete realization through its landscape of metastable vacua.
210 citations
TL;DR: In this article, it was shown that the NP-complete language 3Sat has a verifier that makes two queries to a proof of almost-linear size and achieves subconstant probability of error e = o(1).
Abstract: We show that the NP-Complete language 3Sat has a PCP verifier that makes two queries to a proof of almost-linear size and achieves subconstant probability of error e=o(1). The verifier performs only projection tests, meaning that the answer to the first query determines at most one accepting answer to the second query. The number of bits representing a symbol in the proof depends only on the error e. Previously, by the parallel repetition theorem, there were PCP Theorems with two-query projection tests, but only (arbitrarily small) constant error and polynomial size. There were also PCP Theorems with subconstant error and almost-linear size, but a constant number of queries that is larger than 2.As a corollary, we obtain a host of new results. In particular, our theorem improves many of the hardness of approximation results that are proved using the parallel repetition theorem. A partial list includes the following:(1) 3Sat cannot be efficiently approximated to within a factor of 7/8po(1), unless P=NP. This holds even under almost-linear reductions. Previously, the best known NP-hardness factor was 7/8pe for any constant e>0, under polynomial reductions (Hastad).(2) 3Lin cannot be efficiently approximated to within a factor of 1/2po(1), unless P=NP. This holds even under almost-linear reductions. Previously, the best known NP-hardness factor was 1/2pe for any constant e>0, under polynomial reductions (Hastad).(3) A PCP Theorem with amortized query complexity 1 p o(1) and amortized free bit complexity o(1). Previously, the best-known amortized query complexity and free bit complexity were 1pe and e, respectively, for any constant e>0 (Samorodnitsky and Trevisan).One of the new ideas that we use is a new technique for doing the composition step in the (classical) proof of the PCP Theorem, without increasing the number of queries to the proof. We formalize this as a composition of new objects that we call Locally Decode/Reject Codes (LDRC). The notion of LDRC was implicit in several previous works, and we make it explicit in this work. We believe that the formulation of LDRCs and their construction are of independent interest.
193 citations
12 Jul 2008
TL;DR: Simulation examples as well as comparisons of DE with two other state-of-the-art optimization techniques over the same problems demonstrate the superiority of the proposed approach especially for actuating fractional order plants.
Abstract: Differential Evolution (DE) has recently emerged as a simple yet very powerful technique for real parameter optimization. This article describes an application of DE for the design of Fractional-Order Proportional-Integral-Derivative (FOPID) Controllers involving fractional order integrator and fractional order differentiator. FOPID controllers' parameters are composed of the proportionality constant, integral constant, derivative constant, derivative order and integral order, and its design is more complex than that of conventional integer order PID controller. Here the controller synthesis is based on user-specified peak overshoot and rise time and has been formulated as a single objective optimization problem. In order to digitally realize the fractional order closed loop transfer function of the designed plant, Tustin operator-based CFE (continued fraction expansion) scheme was used in this work. Simulation examples as well as comparisons of DE with two other state-of-the-art optimization techniques (Particle Swarm Optimization and Bacterial Foraging Optimization Algorithm) over the same problems demonstrate the superiority of the proposed approach especially for actuating fractional order plants.
156 citations
TL;DR: A method of Braun, Kerber and Laue which they used for the construction of designs over finite fields to construct constant dimension codes is modified and many new constant Dimension codes with a larger number of codewords than previously known codes are found.
Abstract: In this paper we construct constant dimension space codes with prescribed minimum distance. There is an increased interest in space codes since a paper by Koetter and Kschischang were they gave an application in network coding. There is also a connection to the theory of designs over finite fields. We will modify a method of Braun, Kerber and Laue which they used for the construction of designs over finite fields to do the construction of space codes. Using this approach we found many new constant dimension spaces codes with a larger number of codewords than previously known codes. We will finally give a table of the best found constant dimension space codes.
150 citations
TL;DR: In this paper, static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f ( R ) theories of gravity are studied. But the authors focus on the special case of the exterior spacetime of a cosmic string.
10 Dec 2008
TL;DR: In this article, Braun, Kerber and Laue constructed constant dimension codes with prescribed minimum distance for finite fields, using a modification of the method of Braun and Kerber to construct codes over finite fields.
Abstract: In this paper we construct constant dimension codes with prescribed minimum distance. There is an increased interest in subspace codes in general since a paper [13] by Kotter and Kschischang where they gave an application in network coding. There is also a connection to the theory of designs over finite fields. We will modify a method of Braun, Kerber and Laue [7] which they used for the construction of designs over finite fields to construct constant dimension codes. Using this approach we found many new constant dimension codes with a larger number of codewords than previously known codes. We finally give a table of the best constant dimension codes we found.
Posted Content•
TL;DR: In this paper, it was shown that a polarised manifold with a constant scalar curvature and discrete automorphisms is K-stable, which refines the K-semistability proved by S. K. Donaldson.
Abstract: We show that a polarised manifold with a constant scalar curvature Kahler metric and discrete automorphisms is K-stable. This refines the K-semistability proved by S. K. Donaldson.
06 Jul 2008
TL;DR: The capacity of Gaussian relay networks is uniformly characterized within a constant number of bits, for all channel parameters, within the information-theoretic cut-set upper bound on the capacity of these networks.
Abstract: We present an achievable rate for general Gaussian relay networks. We show that the achievable rate is within a constant number of bits from the information-theoretic cut-set upper bound on the capacity of these networks. This constant depends on the topology of the network, but not the values of the channel gains. Therefore, we uniformly characterize the capacity of Gaussian relay networks within a constant number of bits, for all channel parameters.
TL;DR: In this article, the authors used Riemann-Hilbert methods to compute the constant that arises in the asymptotic behavior of the Airy-kernel determinant of random matrix theory.
Abstract: The authors use Riemann-Hilbert methods to compute the constant that arises in the asymptotic behavior of the Airy-kernel determinant of random matrix theory.
Posted Content•
TL;DR: In this paper, the authors complete a program to determine which toric surfaces admit Kahler metrics of constant scalar curvature, and they show that all of them admit them.
Abstract: This paper completes a programme to determine which toric surfaces admit Kahler metrics of constant scalar curvature/
TL;DR: In this article, the flat potential still exists when V(phi)/K^2(phi) is asymptotically constant and the ratio of the dimensionless self-coupling constant of the inflaton field and the non-minimal coupling constant is small.
Abstract: Inflationary scenarios based on simple non-minimal coupling and its generalizations are studied. Generalizing the form of non-minimal coupling to "K(phi)R" with an arbitrary function K(phi), we show that the flat potential still is obtainable when V(phi)/K^2(phi) is asymptotically constant. Very interestingly, if the ratio of the dimensionless self-coupling constant of the inflaton field and the non-minimal coupling constant is small the cosmological observables for general monomial cases are in good agreement with recent observational data.
TL;DR: A general model is proposed, obtained by looking for an approximate solution with constant velocity profile to the incompressible Euler equations, that has an energy dissipation equation that is consistent with the depth integrated energy equation of the Euler system.
Abstract: In this work, we study the modeling of one-dimensional avalanche flows made of a moving layer over a static base, where the interface between the two can be time dependent. We propose a general model, obtained by looking for an approximate solution with constant velocity profile to the incompressible Euler equations. This model has an energy dissipation equation that is consistent with the depth integrated energy equation of the Euler system. It has physically relevant steady state solutions, and, for constant slope, it gives a particular exact solution to the incompressible hydrostatic Euler equations. Then, we propose a simplified model, for which the energy conservation holds only up to third-order terms. Its associated eigenvalues depend on the mass exchange velocity between the static and moving layers. We show that a simplification used in some previously proposed models gives a non-consistent energy equation. Our models do not use, nor provide, any equation for the moving interface, thus other arguments have to be used in order to close the system. With special assumptions, and in particular small velocity, we can nevertheless obtain an equation for the evolution of the interface. Furthermore, the unknown parameters of the model proposed by Bouchaud et al. (J Phys Paris I 4,1383–1410, 1994) can be derived. For the quasi-stationary case we compare and discuss the equation for the moving interface with Khakhar’s model (J Fluid Mech 441,225–264, 2001).
TL;DR: In this article, the authors considered the Timoshenko system with an indefinite damping mechanism and proved that the system is still exponentially stable under the same conditions as in the positive constant damping case, provided a ¯ = ∫ 0 L a (x ) d x > 0 and provided a − a ¯ ‖ L 2 ϵ, for ϵ small enough.
TL;DR: A new implementation of restarted Krylov subspace methods for evaluating f (A)b for a function f ,a matrix A and a vector b is proposed and the convergence behavior of this scheme is discussed and a new stopping criterion based on an error indicator is given.
Patent•
21 Feb 2008
TL;DR: In this article, a method for rendering software resistant to reverse engineering was proposed, which replaces at least one first constant (mathematical expression, etc.) in a computational expression with a second mixed mathematical and bitwise-Boolean expression, the first constant being simpler than the second expression and the second one being based on the value or the variables found in the first expression.
Abstract: A method for rendering software resistant to reverse engineering. Replace at least one first constant (mathematical expression, etc.) in a computational expression with a second mixed mathematical and bitwise-Boolean expression, the first constant being simpler than the second expression and the second expression being based on the value or the variables found in the first constant (or expression). Evaluation of the second mixed mathematical and bitwise-Boolean expression produces a value preserving the value of the first constant, either: with the original value of the first constant or the original value of the result of the first expression, in which case the second mixed mathematical and bitwise-Boolean expression is obtained from the first constant by converting the first constant by mathematical identities; or, in an encoded form, as a new value, which can be converted back to the original value of the first constant by applying an information-preserving decoding function, in which case the second mixed mathematical and bitwise-Boolean expression is obtained from the first constant by modifying the first constant by a combination of conversion according to mathematical identities and transformation according to an information preserving encoding function.
TL;DR: The asymptotical current–voltage characteristic curve of the device is shown to be a very good approximation of the numerical I–V curve and an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system.
Abstract: Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst-Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current-voltage (I-V ) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I-V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages).
TL;DR: In this paper, a unified model of dark energy and matter was presented using the modified variable Chaplygin gas for interacting dark energy in a non-flat universe, where the two entities interact with each other non-gravitationally which involves a coupling constant.
Abstract: A unified model of dark energy and matter is presented using the modified variable Chaplygin gas for interacting dark energy in a non-flat universe. The two entities interact with each other non-gravitationally which involves a coupling constant. Due to dynamic interaction, the variation in this constant arises that henceforth changes the equations of state of these quantities. We have derived the effective equations of state corresponding to matter and dark energy in this interacting model. Moreover, the case of phantom energy is deduced by putting constraints on the parameters involved.
TL;DR: In this paper, Akhmet et al. considered the problem of differential equations with piecewise constant argument of generalized type (EPCAG) and provided necessary and sufficient conditions for stability of the zero solution.
Abstract: In this paper we continue to consider differential equations with piecewise constant argument of generalized type (EPCAG) [M.U. Akhmet, Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. TMA 66 (2007) 367–383]. A deviating function of a new form is introduced. The linear and quasilinear systems are under discussion. The structure of the sets of solutions is specified. Necessary and sufficient conditions for stability of the zero solution are obtained. Our approach can be fruitfully applied to the investigation of stability, oscillations, controllability and many other problems of EPCAG. Some of the results were announced at The International Conference on Hybrid Systems and Applications, University of Louisiana, Lafayette, 2006.
TL;DR: Both trivial and endemic equilibrium are found, and their stability is investigated, and sufficient conditions for global stability of endemic equilibrium is obtained using Lyapunov functional approach.
01 Dec 2008
TL;DR: In this article, a fractional-order proportional-integral-derivative (PIlambdaDdelta) controller was designed to minimize the integral time absolute error (ITAE) criterion.
Abstract: Particle swarm optimization (PSO) is extensively used for real parameter optimization in diverse fields of study. This paper describes an application of PSO to the problem of designing a fractional-order proportional-integral-derivative (PIlambdaDdelta) controller whose parameters comprise proportionality constant, integral constant, derivative constant, integral order (lambda) and derivative order (delta). The presence of five optimizable parameters makes the task of designing a PIiquestDiquest controller more challenging than conventional PID controller design. Our design method focuses on minimizing the integral time absolute error (ITAE) criterion. The digital realization of the deigned system utilizes the Tustin operator-based continued fraction expansion scheme. We carry out a simulation that illustrates the effectiveness of the proposed approach especially for realizing fractional-order plants. This paper also attempts to study the behavior of fractional PID controller vis-a-vis that of its integer-order counterpart and demonstrates the superiority of the former to the latter.
TL;DR: Analysis and numerical simulations indicate that there exists a threshold value such that if the total weight is below this threshold value, then the optimal favorable region is a circular-type domain at one of the four corners, and a strip at the one end with shorter edge otherwise.
Abstract: This paper is concerned with an indefinite weight linear eigenvalue
problem in cylindrical domains. We investigate the minimization of the positive
principal eigenvalue under the constraint that the weight is bounded by
a positive and a negative constant and the total weight is a fixed negative
constant. Biologically, this minimization problem is motivated by the question
of determining the optimal spatial arrangement of favorable and unfavorable
regions for a species to survive. Both our analysis and numerical simulations
for rectangular domains indicate that there exists a threshold value such that
if the total weight is below this threshold value, then the optimal favorable
region is a circular-type domain at one of the four corners, and a strip at the
one end with shorter edge otherwise.
Journal Article•
TL;DR: An exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent is proved.
Abstract: We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multilinear, if the polynomial computed by each of its gates is multilinear). We also prove a super-polynomial separation between the size of product-depth d and product-depth d + 1 multilinear circuits (where d is constant). That is, there exists a polynomial f such that
TL;DR: In this correspondence, a generic construction of optimal constant composition codes using zero-difference balanced functions is introduced, which generalizes the earlier construction of optimality codes employing perfect nonlinear functions.
Abstract: Constant composition codes are a special class of constant weight codes, and include permutation codes as a subclass. They have applications in communications engineering. In this correspondence, a generic construction of optimal constant composition codes using zero-difference balanced functions is introduced. It generalizes the earlier construction of optimal constant composition codes employing perfect nonlinear functions. In addition, two classes of optimal constant composition codes with new parameters are reported.
TL;DR: In this paper, the authors considered deterministic models for the transmission of a rumor in an age-independent case and introduced four models, which are classified according to whether the population is closed or not and whether the rumor is constant or variable.
Abstract: In this paper, we consider deterministic models for the transmission of a rumor. First, we investigate the age-independent case and introduce four models, which are classified according to whether the population is closed or not and whether the rumor is constant or variable. After formulating the models as finite-dimensional ODE systems, we show that the solutions converge to an equilibrium as t → ∞ . Next, we investigate a model for the transmission of a constant rumor in an age-structured population with age-dependent transmission coefficients. We formulate the model as an abstract Cauchy problem on an infinite-dimensional Banach space and show the existence and uniqueness of solutions. Then, under some appropriate assumptions, we examine the existence of its nontrivial equilibria and the stability of its trivial equilibrium. We show that the spectral radius R 0 ≔ r ( T ˜ ) for some positive operator T ˜ is the threshold. We also show sufficient conditions for the local stability of the nontrivial equilibria. Finally, we show that the model is uniformly strongly persistent if R 0 > 1 .