Showing papers on "Constant (mathematics) published in 2010"
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TL;DR: The betareg package is described which provides the class of beta regressions in the R system for statistical computing and incorporates features such as heteroskedasticity or skewness which are commonly observed in data taking values in the standard unit interval, such as rates or proportions.
Abstract: The class of beta regression models is commonly used by practitioners to model variables that assume values in the standard unit interval (0, 1). It is based on the assumption that the dependent variable is beta-distributed and that its mean is related to a set of regressors through a linear predictor with unknown coefficients and a link function. The model also includes a precision parameter which may be constant or depend on a (potentially different) set of regressors through a link function as well. This approach naturally incorporates features such as heteroskedasticity or skewness which are commonly observed in data taking values in the standard unit interval, such as rates or proportions. This paper describes the betareg package which provides the class of beta regressions in the R system for statistical computing. The underlying theory is briefly outlined, the implementation discussed and illustrated in various replication exercises.
1,706 citations
TL;DR: The aim of this paper is to present OpenMEEG, both from the theoretical and the practical point of view, and to compare its performances with other competing software packages, to show that it represents the state of the art for forward computations.
Abstract: Interpreting and controlling bioelectromagnetic phenomena require realistic physiological models and accurate numerical solvers. A semi-realistic model often used in practise is the piecewise constant conductivity model, for which only the interfaces have to be meshed. This simplified model makes it possible to use Boundary Element Methods. Unfortunately, most Boundary Element solutions are confronted with accuracy issues when the conductivity ratio between neighboring tissues is high, as for instance the scalp/skull conductivity ratio in electro-encephalography. To overcome this difficulty, we proposed a new method called the symmetric BEM, which is implemented in the OpenMEEG software. The aim of this paper is to present OpenMEEG, both from the theoretical and the practical point of view, and to compare its performances with other competing software packages. We have run a benchmark study in the field of electro- and magneto-encephalography, in order to compare the accuracy of OpenMEEG with other freely distributed forward solvers. We considered spherical models, for which analytical solutions exist, and we designed randomized meshes to assess the variability of the accuracy. Two measures were used to characterize the accuracy. the Relative Difference Measure and the Magnitude ratio. The comparisons were run, either with a constant number of mesh nodes, or a constant number of unknowns across methods. Computing times were also compared. We observed more pronounced differences in accuracy in electroencephalography than in magnetoencephalography. The methods could be classified in three categories: the linear collocation methods, that run very fast but with low accuracy, the linear collocation methods with isolated skull approach for which the accuracy is improved, and OpenMEEG that clearly outperforms the others. As far as speed is concerned, OpenMEEG is on par with the other methods for a constant number of unknowns, and is hence faster for a prescribed accuracy level. This study clearly shows that OpenMEEG represents the state of the art for forward computations. Moreover, our software development strategies have made it handy to use and to integrate with other packages. The bioelectromagnetic research community should therefore be able to benefit from OpenMEEG with a limited development effort.
914 citations
TL;DR: In this article, the thermodynamics of black holes in various dimensions are described in the presence of a negative cosmological constant which is treated as a thermodynamic variable, interpreted as a pressure in the equation of state.
Abstract: The thermodynamics of black holes in various dimensions are described in the presence of a negative cosmological constant which is treated as a thermodynamic variable, interpreted as a pressure in the equation of state. The black hole mass is then identified with the enthalpy, rather than the internal energy, and heat capacities are calculated at constant pressure not at constant volume. The Euclidean action is associated with a bridge equation for the Gibbs free energy and not the Helmholtz free energy. Quantum corrections to the enthalpy and the equation of state of the BTZ black hole are studied.
463 citations
05 Dec 2010
TL;DR: The polynomial commitment schemes are useful tools to reduce the communication cost in cryptographic protocols and are applied to four problems in cryptography: verifiable secret sharing, zero-knowledge sets, credentials and content extraction signatures.
Abstract: We introduce and formally define polynomial commitment schemes, and provide two efficient constructions. A polynomial commitment scheme allows a committer to commit to a polynomial with a short string that can be used by a verifier to confirm claimed evaluations of the committed polynomial. Although the homomorphic commitment schemes in the literature can be used to achieve this goal, the sizes of their commitments are linear in the degree of the committed polynomial. On the other hand, polynomial commitments in our schemes are of constant size (single elements). The overhead of opening a commitment is also constant; even opening multiple evaluations requires only a constant amount of communication overhead. Therefore, our schemes are useful tools to reduce the communication cost in cryptographic protocols. On that front, we apply our polynomial commitment schemes to four problems in cryptography: verifiable secret sharing, zero-knowledge sets, credentials and content extraction signatures.
381 citations
TL;DR: In this article, the authors show that at least 12 degrees-of-freedom is achievable for all values of complex Gaussian channel coefficients except for a subset of measure zero for the class of linear beamforming and interference alignment schemes considered in this paper.
Abstract: It has been conjectured by Ho-Madsen and Nosratinia that complex Gaussian interference channels with constant channel coefficients have only one degree-of-freedom regardless of the number of users While several examples are known of constant channels that achieve more than 1 degree-of-freedom, these special cases only span a subset of measure zero In other words, for almost all channel coefficient values, it is not known if more than 1 degree-of-freedom is achievable In this paper, we settle the Host-Madsen-Nosratinia conjecture in the negative We show that at least 12 degrees-of-freedom are achievable for all values of complex channel coefficients except for a subset of measure zero For the class of linear beamforming and interference alignment schemes considered in this paper, it is also shown that 12 is the maximum number of degrees-of-freedom achievable on the complex Gaussian 3 user interference channel with constant channel coefficients, for almost all values of channel coefficients To establish the achievability of 12 degrees-of-freedom we use the novel idea of asymmetric complex signaling - ie, the inputs are chosen to be complex but not circularly symmetric It is shown that unlike Gaussian point-to-point, multiple-access and broadcast channels where circularly symmetric complex Gaussian inputs are optimal, for interference channels optimal inputs are in general asymmetric With asymmetric complex signaling, we also show that the 2 user complex Gaussian X channel with constant channel coefficients achieves the outer bound of 4/3 degrees-of-freedom, ie, the assumption of time-variations/frequency-selectivity used in prior work to establish the same result, is not needed
260 citations
TL;DR: In this paper, the authors proposed a model for constant on-time current-mode control, where the inductor, switches, and modulator are treated as a single entity and modeled based on the describing function method.
Abstract: Constant on-time current-mode control has been widely used to improve light-load efficiency, because it can reduce the switching frequency to save switching-related loss. Therefore, an accurate model for constant on-time control is indispensable to system design. However, available models for constant on-time control are unable to provide accurate physical insight or predict system response very well. This paper introduces a new modeling approach for constant on-time control. The inductor, the switches, and the pulsewidth-modulated modulator are treated as a single entity and modeled based on the describing function method. The fundamental difference between constant on-time control and constant-frequency peak-current-mode control is analyzed through the proposed model. This proposed modeling method can be easily extended to other current-mode controls, including V2 controls. A simple equivalent circuit representation is proposed for the sake of easy understanding and simulation of current-mode controls. Simulation and experimental results are used to verify the proposed model.
171 citations
01 Jan 2010
TL;DR: In this paper, a molecular dynamics simulation method which can generate congenergurations belonging to the canonical...T, V, N† ensemble or the constant temperature constant pressure...T, P, N† ensembles is proposed.
Abstract: A molecular dynamics simulation method which can generate con®gurations belonging to the canonical ...T , V , N† ensemble or the constant temperature constant pressure ...T , P, N† ensemble, is proposed. The physical system of interest consists of N particles (f degrees of freedom), to which an external, macroscopic variable and its conjugate momentum are added. This device allows the total energy of the physical system to uctuate. The equilibrium distribution of the energy coincides with the canonical distribution both in momentum and in coordinate space. The method is tested for an atomic uid (Ar) and works well.
169 citations
TL;DR: This method improves the accuracy of split-step finite difference method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost.
167 citations
01 Sep 2010
TL;DR: The power stage, the switches and the PWM modulator are treated as a single entity and modeled based the describing function method and can accurately predict sub-harmonic oscillation.
Abstract: Recently, V2 constant on-time control has been widely used to improve light-load efficiency. In the V2 implementation, the nonlinear PWM modulator is much more complicated than usual, since not only is the inductor current information fed back to the modulator but also the capacitor voltage ripple information. Generally speaking, there is no subharmonic oscillation in constant on-time control. However, the delay due to the capacitor ripple results in subharmonic oscillation in V2 constant on-time control. So far, there has been no accurate model to predict the instability issue due to the capacitor ripple. This paper presents a new modeling approach for the V2 constant on-time control. The power stage, the switches, and the PWM modulator are treated as a single entity and modeled based on the describing function method. The model for the V2 constant on-time control achieved by the new approach can accurately predict subharmonic oscillations. Two solutions are discussed to solve the instability issue. The extension of the model to other types of V2 current-mode control and multiphase application is also shown in this paper. Simulation and experimental results verify the proposed model.
147 citations
TL;DR: The chiral-limit vacuum quark condensate is qualitatively equivalent to the pseudoscalar meson leptonic decay constant in the sense that they are both obtained as the chiral limit value of well-defined gauge-invariant hadron-to-vacuum transition amplitudes that possess a spectral representation in terms of current quark mass as mentioned in this paper.
Abstract: We show that the chiral-limit vacuum quark condensate is qualitatively equivalent to the pseudoscalar meson leptonic decay constant in the sense that they are both obtained as the chiral-limit value of well-defined gauge-invariant hadron-to-vacuum transition amplitudes that possess a spectral representation in terms of the current-quark mass. Thus, whereas it might sometimes be convenient to imagine otherwise, neither is essentially a constant mass-scale that fills all spacetime. This means, in particular, that the quark condensate can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wave functions.
146 citations
TL;DR: In this paper, a complete numerical study of cosmological models with a time dependent coupling between the dark energy component driving the present accelerated expansion of the Universe and the Cold Dark Matter (CDM) fluid is presented.
Abstract: We present a complete numerical study of cosmological models with a time dependent coupling between the dark energy component driving the present accelerated expansion of the Universe and the Cold Dark Matter (CDM) fluid. Depending on the functional form of the coupling strength, these models show a range of possible intermediate behaviors between the standard LCDM background evolution and the widely studied case of interacting dark energy models with a constant coupling. These different background evolutions play a crucial role in the growth of cosmic structures, and determine strikingly different effects of the coupling on the internal dynamics of nonlinear objects. By means of a suitable modification of the cosmological N-body code GADGET-2 we have performed a series of high-resolution N-body simulations of structure formation in the context of interacting dark energy models with variable couplings. Depending on the type of background evolution, the halo density profiles are found to be either less or more concentrated with respect to LCDM, contrarily to what happens for constant coupling models where concentrations can only decrease. However, for some specific choice of the interaction function the reduction of halo concentrations can be larger than in constant coupling scenarios. In general, we find that time dependent interactions between dark energy and CDM can in some cases determine stronger effects on structure formation as compared to the constant coupling case, with a significantly weaker impact on the background evolution of the Universe, and might therefore provide a more viable possibility to alleviate the tensions between observations and the LCDM model on small scales than the constant coupling scenario. [Abridged]
TL;DR: In this paper, a large database from direct numerical simulations of isotropic turbulence, including recent simulations for box sizes up to 4096 3 and the Taylor-Reynolds number R λ ≈ 1000, is used to investigate the bottleneck effect in the three-dimensional energy spectrum and second-order structure functions, and to determine the Kolmogorov constant, C K.
Abstract: A large database from direct numerical simulations of isotropic turbulence, including recent simulations for box sizes up to 4096 3 and the Taylor-Reynolds number R λ ≈ 1000, is used to investigate the bottleneck effect in the three-dimensional energy spectrum and second-order structure functions, and to determine the Kolmogorov constant, C K . The difficulties in estimating C K at any finite Reynolds number, introduced by intermittency and the bottleneck, are assessed. The data conclusively show that the bottleneck effects decreases with the Reynolds number. On this basis, an alternative to the usual procedure for determining C K is suggested; this proposal does not depend on the particular choices of fitting ranges or power-law behaviour in the inertial range. Within the resolution of the numerical data, C K thus determined is a Reynolds-number-independent constant of ≈1.58 in the three-dimensional spectrum. A simple model including non-local transfer is proposed to reproduce the observed scaling features of the bottleneck.
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TL;DR: The empirical basis for and mathematical formulations of this pattern are reviewed, and the relationship of constant final yield to density-dependent mortality (self-thinning) is clarified.
Abstract: Constant final yield is an empirical generalization concerning the total biomass production of plant stands growing at different densities after a period of growth. Total standing biomass initially increases in proportion to density, levels off, and then remains constant as density increases further. We review the empirical basis for and mathematical formulations of this pattern, and we clarify the relationship of constant final yield to density-dependent mortality (self-thinning). There are several mechanisms that can explain the pattern, and it has a clear evolutionary basis. Constant final yield is a key to understanding population- and community-level phenomena. Establishing whether or not a plant community is at or close to constant final yield is important for understanding and predicting its behavior. It represents the maximum biomass for a genotype in an environment after a period of growth and, as such, can serve as a baseline for the measurement of disturbance in plant communities.
TL;DR: In this paper, the authors present a formulation using simplices with constant sectional curvature adjusted to the presence of a cosmological constant, which allows to replace the length variables by three- or four-dimensional dihedral angles as basic variables.
Abstract: In Regge calculus, space-time is usually approximated by a tri- angulation with flat simplices. We present a formulation using simplices with constant sectional curvature adjusted to the presence of a cosmological constant. As we will show, such a formulation allows us to replace the length variables by three- or four-dimensional dihedral angles as basic variables. Moreover, we will introduce a first-order formulation, which, in contrast to using flat simplices, does not require any constraints. These considerations could be useful for the construction of quantum gravity models with a cosmological constant.
TL;DR: In this paper, the effects of relatively large temperature changes in the heat-transfer process and on the fluid properties were investigated for velocity measurements taken using hot-wire anemometry.
Abstract: Changes in the ambient fluid temperature change the calibration curve for velocity measurements taken using hot-wire anemometry. New correction methods are proposed to account for the effects of relatively large temperature changes in the heat-transfer process and on the fluid properties. The corrections do not assume any particular heat-transfer correlation, and they do not require multiple calibrations over a range of temperatures. The corrections are derived for the constant temperature and constant current modes of operation.
TL;DR: In this article, the dark energy models in anisotropic Bianchi type-I (B-I) space-time with variable EoS parameter and constant deceleration parameter have been investigated.
Abstract: New dark energy models in anisotropic Bianchi type-I (B-I) space-time with variable EoS parameter and constant deceleration parameter have been investigated in the present paper. The Einstein's field equations have been solved by applying a variation law for generalized Hubble's parameter in B-I space-time. The variation law for Hubble's parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein's field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The equation of state (EoS) parameter $\omega$ is found to be time dependent and its existing range for this model is in good agreement with the recent observations of SNe Ia data, SNe Ia data (with CMBR anisotropy) and galaxy clustering statistics. The cosmological constant $\Lambda$ is found to be a decreasing function of time and it approaches a small positive value at late time (i.e. the present epoch) which is corroborated by results from recent supernovae Ia observations.
TL;DR: In this article, a sharp Hardy inequality for fractional integrals for functions that are supported in a general domain is proved, and the constant is the same as the one for the half-space and hence their result settles a recent conjecture of Bogdan and Dyda.
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TL;DR: In this article, it was shown that the number of birational automorphisms of a variety of general type X is bounded by c \cdot \vol(X,K_X), where c is a constant which only depends on the dimension of X.
Abstract: We show that the number of birational automorphisms of a variety of general type X is bounded by c \cdot \vol(X,K_X), where c is a constant which only depends on the dimension of X.
TL;DR: In this article, the authors examined the drawbacks of the heat balance integral methods and developed a logarithmic approximating function, which allows the model to capture moving peaks in the temperature profile.
TL;DR: This paper applies the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type to a model of recurrent neural networks (RNNs) and obtains sufficient conditions for global exponential stability of the equilibrium point.
30 May 2010
TL;DR: This is the first construction of a constant-round non-malleable protocol based on only one-wayness, or to admit a black-box proof of security under any standard-type assumption.
Abstract: We present a constant-round non-malleable commitment scheme based on the existence of sub-exponential one-way functions and using a black-box proof of security As far as we know, this is the first construction of a constant-round non-malleable protocol based on only one-wayness, or to admit a black-box proof of security under any standard-type assumption
TL;DR: In this paper, the authors obtained the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables with constant interest force and constant premium rate.
Abstract: In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables With constant interest force and constant premium rate, we establish a uniform simple asymptotic formula for ruin probability of the renewal model in the case where the initial surplus is large
01 Jan 2010
TL;DR: Asymptotic results for the game of Cops and Robbers played on a random graph G(n, p) focusing on the case when the cop number does not grow with the size of a graph are presented.
Abstract: In this paper, we study the vertex pursuit game of Cops and Robbers where cops try to capture a robber loose on the vertices of a graph. The minimum number of cops required to win on a given graph G is the cop number of G. We present asymptotic results for the game of Cops and Robbers played on a random graph G(n, p) focusing on the case when the cop number does not grow with the size of a graph. A few open problems are discussed.
TL;DR: In this article, it was shown that there are no Ricci flat warped products with fibers that have non-positive Einstein constant and for Ricci solitons, the quantity RCjr fj 2 is a positive constant.
Abstract: m d f d fD 0 by studying the associated PDE 1 f fC m exp.2 f=m/D 0 for 0. By developing a gradient estimate for f , we show there are no nonconstant solutions. We then apply this to show that there are no nontrivial Ricci flat warped products with fibers that have nonpositive Einstein constant. We also show that for nontrivial steady gradient Ricci solitons, the quantity RCjr fj 2 is a positive constant.
TL;DR: A model of cellular neural networks (CNNs) is developed using the concept of differential equations with piecewise constant arguments of generalized type and the Lyapunov-Razumikhin technique is applied to find sufficient conditions for the uniform asymptotic stability of equilibria.
TL;DR: In this article, an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type is introduced, and sufficient conditions for the existence of the unique equilibrium are obtained.
Abstract: In this paper we introduce an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type Sufficient conditions for the existence of the unique equilibrium are obtained Existence and uniqueness of solutions of such systems are established Stability criterion based on linear approximation is proposed Some sufficient conditions for the existence and stability of periodic solutions are derived An example with numerical simulations is given to illustrate our results
TL;DR: In this paper, the decomposition rate of a single organic compartment is modeled as a function f (t), i.e. the remaining organic matter at time t is: X t = X 0 ⋅ e − ∫ 0 t f ( t ) d t and thus the problem of integrating the function that describes the change in the rate of decomposition is addressed.
01 Sep 2010
TL;DR: It is known that hypersurfaces with constant mean curvature in a Riemannian manifold of constant sectional curvature c are solutions to the variational problem of extremizing the area function for volumepreserving variations.
Abstract: It is well known that hypersurfaces \(M^n\)with constant mean curvature in a Riemannian manifold \(\overline{M}{n+1}(c)\)of constant sectional curvature c are solutions to the variational problem of extremizing the area function for volumepreserving variations.
TL;DR: In this article, the Om statistic and the GA were used to derive a null test on the spatially flat cosmological constant modelCDM. This is done in two steps: first, they apply the GA to the Constitution SNIa data in order to acquire a model independent reconstruction of the expansion history of the Universe H(z) and second, they use the reconstructed H(x) in conjunction with the Om statistics, which is constant only for the CDM model, to derive their constraints.
Abstract: We use the Om statistic and the Genetic Algorithms (GA) in order to derive a null test on the spatially flat cosmological constant modelCDM. This is done in two steps: first, we apply the GA to the Constitution SNIa data in order to acquire a model independent reconstruction of the expansion history of the Universe H(z) and second, we use the reconstructed H(z) in conjunction with the Om statistic, which is constant only for theCDM model, to derive our constraints. We find that while �CDM is consistent with the data at the 2σ level, some deviations fromCDM model at low redshifts can be accommodated.
TL;DR: In this paper, the existence and uniqueness of T -periodic solutions for a second order differential equation with a piecewise constant singularity which changes sign was studied and other questions like stability and robustness of the periodic solution were considered.
Abstract: Motivated by some relevant physical applications, we study the existence and uniqueness of T -periodic solutions for a second order differential equation with a piecewise constant singularity which changes sign. Other questions like the stability and robustness of the periodic solution are considered. 1991 Mathematics Subject Classification. 34C25.