Revisiting the old problem of general-relativistic adiabatic collapse of a uniform-density self-gravitating sphere

The problem of general-relativistic adiabatic collapse of a uniform-density perfect sphere has been studied since Wyman (Phys. Rev. 70, 396, (1946)) [1]. Apparently, there could be bouncing and oscillating solutions in such a case, as claimed by numerous authors since then. Consequently, various authors invoked such models for explaining pulsations of compact objects. However, here, for this age-old problem, we prove that for an assumed nonstatic adiabatically evolving sphere, density homogeneity implies (isotropic) pressure homogeneity too. This proof is based on the simple fact that in general relativity (GR), given one time coordinate t, one can employ another time coordinate t → t* = f(t) without any loss of generality. Since this proof does not use any exterior boundary condition, it is valid in a cosmological scenario too. However, here we focus on the evolution of an isolated sphere having a boundary. And the proof obtained here shows that a uniform-density perfect fluid collapse can occur only if the (isotropic) pressure is p = 0, i.e., only when the problem is reduced to the one treated by Oppenheimer and Snyder. For such an isolated sphere, we offer a supporting proof. This result is important and nontrivial because in the past 65 years innumerable authors working on this problem failed to see that the collapse of a supposed homogeneous sphere is (actually) synonymous to the old Oppenheimer-Snyder problem.     

Deterministic asynchronous automata for infinite traces

This paper shows the equivalence between the family of recognizable languages over infinite traces and the family of languages which are recognized by deterministic asynchronous cellular Muller automata. We thus give a proper generalization of McNaughton's Theorem from infinite words to infinite traces. Thereby we solve one of the main open problems in this field. As a special case we obtain that every closed (w.r.t. the independence relation) word language is accepted by someI-diamond deterministic Muller automaton.This research has been supported by the ESPRIT Basic Research Action No. 6317 ASMICS 2.     

Stochastic suppression and stabilization of delay differential systems

In this paper, we investigate stochastic suppression and stabilization for nonlinear delay differential system ${\dot{x}}(t)=f(x(t),x(t-\delta(t)),t)In this paper, we investigate stochastic suppression and stabilization for nonlinear delay differential system ${\dot{x}}(t)=f(x(t),x(t-\delta(t)),t)$, where δ(t) is the variable delay and f satisfies the one‐sided polynomial growth condition. Since f may defy the linear growth condition or the one‐sided linear growth condition, this system may explode in a finite time. To stabilize this system by Brownian noises, we stochastically perturb this system into the nonlinear stochastic differential system dx(t)=f(x(t), x(t?δ(t)), t)dt+qx(t)dw₁(t)+σ|x(t)|^βx(t)dw₂(t) by introducing two independent Brownian motions w₁(t) and w₂(t). This paper shows that the Brownian motion w₂(t) may suppress the potential explosion of the solution of this stochastic system for appropriate choice of β under the condition σ≠0. Moreover, for sufficiently large q, the Brownian motion w₁(t) may exponentially stabilize this system. Copyright © 2010 John Wiley & Sons, Ltd.     

Random solution of a stochastic integral equation :almost sure and mean square convergence of successive approximations

A non-linear random integral equation of the Volterra type of the form was considered by Tsokos (1960), where ω?Ω, the underlying set of the probability measure space (Ω A, P). He was concerned with the existence of a unique random solution to this equation, where a random solution is defined to be a second-order stochastic process, x(t; ω), which satisfies the equation almost surely. The present paper shows that a sequence of successive approximations, x_n)tω) converges to the unique random solution at each t≥0 with probability one and in mean square under the conditions of Tsokos' theorem. The rate of convergence of the successive approximations and a bound on the mean square error of approximation are also given.     

Space-efficient recognition of sparse self-reducible languages

Mahaney and others have shown that sparse self-reducible sets have time-efficient algorithms, and have concluded that it is unlikely that NP has sparse complete sets. Mahaney's work, intuition, and a 1978 conjecture of Hartmanis notwithstanding, nothing has been known about the density of complete sets for feasible classes until now. This paper shows that sparse self-reducible sets have space-efficient algorithms, and in many cases, even have time-space-efficient algorithms. We conclude that NL, NC ^k , AC ^k , LOG(DCFL), LOG(CFL), and P lack complete (or even Turing-hard) sets of low density unless implausible complexity class inclusions hold. In particular, if NL (respectively P, _k , or NP) has a polylog-sparse logspace-hard set, then NLSC (respectively PSC, _k , or PHSC), and if P has subpolynomially sparse logspace-hard sets, then PPSPACE.     

The effect of temporal psychological distance on reliance on word-of-mouth for information about destination image attributes

This study examines the effect of temporal psychological distance on travellers’ reliance on three types of word-of-mouth (WOM): traditional WOM (tWOM), social media WOM (SNS-WOM), and online review WOM (OR-WOM) in the search for information related to the relaxation, excitement, cost level, and safety destination image attributes. High and low temporal distance was manipulated using distances of 12 months and 2 months, respectively. A series of t-tests of 283 valid responses (155 and 128 for the 12-month and 2-month scenarios, respectively) shows a significant difference in reliance on tWOM when respondents sought safety attribute information, for SNS-WOM when respondents sought relaxation and safety attribute information, and for OR-WOM when respondents sought relaxation attribute information. Thus, this study shows that in terms of temporal distance, WOM is not a homogeneous block. They have sufficiently different characteristics (e.g. level of tie strength and synchronous/asynchronous modes), which, when they interact with the nature of the destination attributes, results in differing reliance on the three types of WOM under various temporal distances. This study thus contributes to construal level theory research and provides a better understanding of the different characteristics of the three types of WOM.     

A Unifying Approach to Edge-valued and Arithmetic Transform Decision Diagrams

This paper shows that binary decision diagrams (BDDs) and their generalizations are not only representations of switching and integer-valued functions, but also Fourier-like series expansions of them. Furthermore, it shows that edge-valued binary decision diagrams (EVBDDs) are related to arithmetic transform decision diagrams (ACDDs), which are the integer counterparts of the functional decision diagrams (FDDs). Finally, it shows that the complexity of multi-terminal binary decision diagrams (MTBDDs), EVBDDs and ACDDs of a function f depends on the structure of the truth-vector of f, partial arithmetic transform spectra of f and the arithmetic transform spectrum of f, respectively.     

Proof Synthesis and Reflection for Linear Arithmetic

This article presents detailed implementations of quantifier elimination for both integer and real linear arithmetic for theorem provers. The underlying algorithms are those by Cooper (for Z) and by Ferrante and Rackoff (for ℝ). Both algorithms are realized in two entirely different ways: once in tactic style, i.e. by a proof-producing functional program, and once by reflection, i.e. by computations inside the logic rather than in the meta-language. Both formalizations are generic because they make only minimal assumptions w.r.t. the underlying logical system and theorem prover. An implementation in Isabelle/HOL shows that the reflective approach is between one and two orders of magnitude faster.     

Optimization of sonic crystal attenuation properties by <Emphasis Type="Italic">ev-MOGA</Emphasis> multiobjective evolutionary algorithm

This paper shows a promising method for acoustic barrier design using a new acoustic material called Sonic Crystals (SCs). The configuration of these SCs is set as a multiobjective optimization problem which is very difficult to solve with conventional optimization techniques. The paper presents a new parallel implementation of a Multiobjective Evolutionary Algorithm called ev-MOGA (also known as ) and its application in a complex design problem. ev-MOGA algorithm has been designed to converge towards a reduced, but well distributed, representation of the Pareto Front (solution of the multiobjective optimization problem). The algorithm is presented in detail and its most important properties are discussed. To reduce the ev-MOGA computational cost when objective functions are substantial, a basic parallelization has been implemented on a distributed platform. Partially supported by MEC (Spanish Government) and FEDER funds: projects DPI2005-07835, MAT2006-03097 and Generalitat Valenciana (Spain) projects GV06/026, GV/2007/191.     

Comments on ‘A Lur'e-type Lyapunov function for multimachine power systems with transfer conductances’

This note shows that the Lyapunov function constructed for the example multimachine power system by Saeki et al. (1985) is in error. The derivative of the Lyapunov function along the trajectories is not negative-semidefinite. This problem raises questions as to whether the hypotheses of Saeki et al. (1985 Theorem 1) can be satisfied in a multimachine power system with transfer conductances.     

Feedback stabilization of a linear control system in Hilbert space with ana priori bounded control

This paper derives a feedback controlf(t), ‖f(t)‖_E≦r,r>0, which forces the infinite-dimensional control systemdu/dt=Au+Bf, u(0)=u _o ≠H to have the asymptotic behavioru(t)→0 ast→∞ inH. HereA is the infinitesimal generator of aC _o semigroup of contractionse ^At on a real Hilbert spaceH andB is a bounded linear operator mapping a Hilbert space of controlsE intoH. An application to the boundary feedback control of a vibrating beam is provided in detail and an application to the stabilization of the NASA Spacecraft Control Laboratory is sketched. This research was sponsored in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF Contract/Grants AFOSR 81-0172 and AFOSR 87-0315.     

A new modified CPW‐fed wideband circularly polarized half‐split cylindrical dielectric resonator antenna with different permittivity of two layers in radial direction

In this article, a wideband circularly polarized half‐split cylindrical dielectric resonator antenna (HS‐CDRA) having two layers with different permittivity in radial direction is investigated. Designed antenna is excited by a new modified CPW fed which consists of signal line, helps to realization of circular polarization, half‐split cylindrical dielectric resonator (HS‐CDR), to confirm that circular polarization in proposed antenna. HS‐CDR is made of two different materials which can supports to enhance the input impedance bandwidth and 3‐dB axial ratio bandwidth. From the distributions of E‐fields in HS‐CDRA, it is observed that TM_11δ mode has been excited. To confirmed the circular polarization in proposed antenna, E‐field distribution on different phases (φ = 0º, 90º, 180º, and 270º) have been plotted. This antenna provides measured ?10 dB input impedance bandwidth of 25.94% (centered on 4.70 GHz) and 3‐dB axial ratio bandwidth in broadside direction of 17.34% (centered on 4.90 GHz). The average gain and radiation efficiency in working band are 1.56 dBi and 93.43% in broadside direction, respectively. CP radiation pattern shows that the proposed antenna has left hand circular polarization and this developed antenna could be useful for wireless applications like WLAN/Wi‐MAX bands.     

Analysis of the energy‐based swing‐up control of the Acrobot

This paper addresses the energy‐based swing‐up control problem for the Acrobot, a two‐link underactuated robot with a single actuator at the joint of the two links. In line with the energy‐based control approach, this paper presents a necessary and sufficient condition for non‐existence of any singular point in the derived control law, and provides a complete analysis of the convergence of the energy and the motion of the Acrobot. Specifically, for any initial state of the Acrobot, this paper shows clearly how to choose control parameters such that the Acrobot will eventually either be swung up to any arbitrarily small neighbourhood of the upright equilibrium point, or remain in a set containing a finite number of equilibrium points. Moreover, this paper shows that these equilibrium points are unstable. Furthermore, imposing a stronger condition on a control parameter yields that the equilibrium set contains only the downward equilibrium point, which is shown to be hyperbolic and unstable. This proves that the Acrobot will eventually enter the basin of attraction of any stabilizing controller for all initial conditions with the exception of a set of Lebesgue measure zero. Copyright © 2007 John Wiley & Sons, Ltd.     

Social psychophysiological compliance in a four-person research team

A continuous, non-invasive and objective measure of teamwork effectiveness could be very useful to the human factors design community. Social psychophysiological compliance (SPC), estimated by scoring the extent that heart rate variation was synchronous across team members, was explored as a predictor of teamwork effectiveness during 20 real planning meetings over a 6-month period. Speech activity and heart rate variability of all four (2 male, 2 female) team members were continuously monitored. Exploratory analyses tested if team member ratings of various aspects of teamwork effectiveness were predicted by SPC scored (1) over whole meetings, (2) during one team member's speech, (3) during periods in which two team members spoke in sequence or (4) over 30-s periods and averaging highest values. SPC during periods of sequential speech negatively predicted team members' ratings of Team productivity, Quality of communication, and Ability to work together. SPC shows potential as an objective, non-invasive means to monitor teamwork effectiveness but this relationship warrants further investigation and replication before use in ergonomics applications.     

On alternation

Summary Every alternating t(n)-time bounded multitape Turing machine can be simulated by an alternating t(n)-time bounded 1-tape Turing machine. Every nondeterministic t(n)-time bounded 1-tape Turing machine can be simulated by an alternating (n + (t(n)) ^1/2)-timebounded 1-tape Turing machine. For wellbehaved functions t(n) every nondeterministic t(n)-time bounded 1-tape Turing machine can be simulated by a deterministic ((nlogn)^1/2 + (t(n))^1/2)-tape bounded off-line Turing machine. These results improve or extend results by Chandra-Stockmeyer, Lipton-Tarjan and Paterson. A preliminary version of this paper was presented at the 19th IEEE-FOCS     

Packing Random Intervals On-Line

Starting at time 0, unit-length intervals arrive and are placed on the positive real line by a unit-intensity Poisson process in two dimensions; the probability of an interval arriving in the time interval [t,t+ t] with its left endpoint in [y,y+ y] is t y + o( t y ). Fix x 0. An arriving interval is accepted if and only if it is contained in [0,x] and overlaps no interval already accepted. We study the number N _x (t) of intervals accepted during [0,t] . By Laplace-transform methods, we derive large-x estimates of EN _x (t) and VarN _x (t) with error terms exponentially small in x uniformly in t (0,T) , where T is any fixed positive constant. We prove that, as , EN _x (t) , VarN _x (t) , uniformly in t (0,T) , where and are given by explicit, albeit complicated formulas. Using these asymptotic estimates we show that N _x (t) satisfies a central limit theorem, i.e., for any fixed t where (0,1) is a standard normal random variable, and denotes convergence in distribution. This stochastic, on-line interval packing problem generalizes the classical parking problem, the latter corresponding only to the absorbing states of the interval packing process, where successive packed intervals are separated by gaps less than 1 in length. We verify that, as , (t) and (t) converge to _* = 0.748 . . . and _* = 0.03815 . . ., the constants of Rényi and Mackenzie for the parking problem. Thus, by comparison with the parking analysis in a single space variable, ours is a transient analysis involving both a time and a space variable. Our interval packing problem has applications similar to those of the parking problem in the physical sciences, but the primary source of our interest is the modeling of reservation systems, especially those designed for multimedia communication systems to handle high-bandwidth, real-time demands. Received December 4, 1997; revised February 15, 1998.     

Sporadic model building for efficiency enhancement of the hierarchical BOA

Efficiency enhancement techniques—such as parallelization and hybridization—are among the most important ingredients of practical applications of genetic and evolutionary algorithms and that is why this research area represents an important niche of evolutionary computation. This paper describes and analyzes sporadic model building, which can be used to enhance the efficiency of the hierarchical Bayesian optimization algorithm (hBOA) and other estimation of distribution algorithms (EDAs) that use complex multivariate probabilistic models. With sporadic model building, the structure of the probabilistic model is updated once in every few iterations (generations), whereas in the remaining iterations, only model parameters (conditional and marginal probabilities) are updated. Since the time complexity of updating model parameters is much lower than the time complexity of learning the model structure, sporadic model building decreases the overall time complexity of model building. The paper shows that for boundedly difficult nearly decomposable and hierarchical optimization problems, sporadic model building leads to a significant model-building speedup, which decreases the asymptotic time complexity of model building in hBOA by a factor of to where n is the problem size. On the other hand, sporadic model building also increases the number of evaluations until convergence; nonetheless, if model building is the bottleneck, the evaluation slowdown is insignificant compared to the gains in the asymptotic complexity of model building. The paper also presents a dimensional model to provide a heuristic for scaling the structure-building period, which is the only parameter of the proposed sporadic model-building approach. The paper then tests the proposed method and the rule for setting the structure-building period on the problem of finding ground states of 2D and 3D Ising spin glasses.     

Aboveground forest biomass based on OLSR and an ANN model integrating LiDAR and optical data in a mountainous region of China

Aboveground forest biomass (B_agf) and height of forest canopy (H_fc) are of great significance for the determination of carbon sources and sinks, carbon cycling and global change research. In this paper, B_agf of coniferous and broadleaf forest in the Chinese Three Gorges region is estimated by integrating light detection and ranging (LiDAR) and Landsat derived data. For a better B_agf estimation, a synergetic extrapolation method for regional H_fc is explored based on a specific relationship between LiDAR footprint H_fc and optical data such as vegetation index (VI), leaf area index (LAI) and forest vegetation cover (FVC). Then, an ordinary least squares regression (OLSR) and a back propagation neural network (BP-NN) model for regional B_agf estimation from synergetic LiDAR and optical data are developed and compared. Validation results show that the OLSR can achieve higher accuracy of H_fc estimation for all forest types (R² = 0.751, Root mean square error (RMSE) = 5.74 m). The OLSR estimated B_agf shows a good agreement with field measurements. The accuracy of regional B_agf estimated by the BP-NN model (RMSE = 12.23 t ha^–1) is superior to that estimated by the OLSR method (RMSE = 17.77 t ha^–1) especially in areas with complex topography.     

The numerical solution of the time-dependent matrix equation A(t)V(t) + WA(t) = G(t)

A rapidly convergent iterative method for the solution of matrix equations of the form

A(t)V(t) + WA (t) = G(t)

is outlined. Such matrix equations arise in the study of parabolic systems and in the application of Lyapunov methods in the stability analysis of linear time-invariant systems. The desired solution at each time step is obtained by solving a comparatively small ordered matrix equation of the form

AV + WA=G rather than resorting to the conventional systems of linear algebraic equations with a composite coefficient matrix of order mn × mn.     

Fast fault-tolerant parallel communication and on-line maintenance for hypercubes using information dispersal

A space-efficient Information Dispersal Algorithm (IDA) is applied to fault-tolerant parallel communication in the hypercube. LetN denote the size of the network. Our routing scheme runs in 2·logN+1 time using constant size buffers (if the routing information is not counted). Its probability of successful routing is at least 1–N ^{–2.419·logN+1.5}, proving Rabin's conjecture. The scheme runswithin the said time bound without queueing delay, and it toleratesO(N) random link failures with high probability.Optimal on-line and efficient wire maintenance on the hypercube can be realized if our fault-tolerant routing scheme is used. Let denote the total number of links in the hypercube. It is shown that a constant fraction (/352) of the wires can be disabled simultaneously without disrupting the ongoing computation or degrading the routing performance much. This property suggests various on-line maintenance procedures.This research was supported by NSF Grant MCS-8121431 at Harvard University. This paper is based on Chapters 4, 5, and 8 of the author's Ph.D. dissertation.