performance analysis of optimum combining with multiple interferers in flat rayleigh fading this paper is a performance analysis of optimum combining in the presence of multiple equal power interferers and noise when the number of interferers is less than the number of antenna elements desired signal and interferers are subject to flat rayleigh fading and the propagation channels are independent an approximate expression of the probability density function of the output signal to interference plus noise ratio sinr is derived analytically it is then applied to obtain the cumulative distribution function of the sinr and the bit error rate ber of some binary modulations including coherent binary phase shift keying in the case of a single interferer an exact analysis is performed to prove the validity of the approximation in the case of multiple interferers the accuracy of the approximation is assessed through simulations although limited to equipower interferers this analysis is a convenient way of assessing the performance of optimum combining in some typical situations and comparing it with that of maximal ratio combining the final results are remarkably simple and provide a useful complement to previous analyzes especially in the region of reasonably high bers which are of practical interest

density matrix renormalization group study of current and activity fluctuations near nonequilibrium phase transitions cumulants of a fluctuating current can be obtained from a free energy like generating function which for markov processes equals the largest eigenvalue of a generalized generator we determine this eigenvalue with the density matrix renormalization group for stochastic systems we calculate the variance of the current in the different phases and at the phase transitions of the totally asymmetric exclusion process our results can be described in the terms of a scaling ansatz that involves the dynamical exponent z we also calculate the generating function of the dynamical activity total number of configuration changes near the absorbing state transition of the contact process its scaling properties can be expressed in terms of known critical exponents

exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

vibration analysis of annular like plates abstract the existence of eccentricity of the central hole for an annular plate results in a significant change in the natural frequencies and mode shapes of the structure in this paper the vibration analysis of annular like plates is presented based on numerical and experimental approaches using the finite element analysis code nastran the effects of the eccentricity hole size and boundary condition on vibration modes are investigated systematically through both global and local analyses the results show that analyses for perfect symmetric conditions can still roughly predict the mode shapes of recessive modes of the plate with a slightly eccentric hole they will however lead to erroneous results for dominant modes in addition the residual displacement mode shape is verified as an effective parameter for identifying damage occurring in plate like structures experimental modal analysis on a clamped free annular like plate is performed and the results obtained reveal good agreement with those obtained by numerical analysis this study provides guidance on modal analysis vibration measurement and damage detection of plate like structures

random matrix eigenvalue problems in structural dynamics natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of linear structural systems considering that the system parameters are known only probabilistically we obtain the moments and the probability density functions of the eigenvalues of discrete linear stochastic dynamic systems current methods to deal with such problems are dominated by mean centred perturbation based methods here two new approaches are proposed the first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is best in some sense the second approach is based on an asymptotic approximation of multidimensional integrals a closed form expression is derived for a general rth order moment of the eigenvalues two approaches are presented to obtain the probability density functions of the eigenvalues the first is based on the maximum entropy method and the second is based on a chi square distribution both approaches result in simple closed form expressions which can be easily calculated the proposed methods are applied to two problems and the analytical results are compared with monte carlo simulations it is expected that the small randomness assumption usually employed in mean centred perturbation based methods can be relaxed considerably using these methods

estimates of error probability for complex gaussian channels with generalized likelihood ratio detection we derive approximate expressions for the probability of error in a two class hypothesis testing problem in which the two hypotheses are characterized by zero mean complex gaussian distributions these error expressions are given in terms of the moments of the test statistic employed and we derive these moments for both the likelihood ratio test appropriate when class densities are known and the generalized likelihood ratio test appropriate when class densities must be estimated from training data these moments are functions of class distribution parameters which are generally unknown so we develop unbiased moment estimators in terms of the training data with these accurate estimates of probability of error can be calculated quickly for both the optimal and plug in rules from available training data we present a detailed example of the behavior of these estimators and demonstrate their application to common pattern recognition problems which include quantifying the incremental value of larger training data collections evaluating relative geometry in data fusion from multiple sensors and selecting a good subset of available features

idempotency of linear combinations of an idempotent matrix and a tripotent matrix abstract the problem of characterizing situations in which a linear combination c c 1 a c 2 b of an idempotent matrix a and a tripotent matrix b is an idempotent matrix is thoroughly studied in two particular cases of this problem when either b or b is an idempotent matrix a complete solution follows from the main result in linear algebra appl 321 2000 3 in the present paper a complete solution is established in all the remaining cases when b is an essentially tripotent matrix in the sense that both idempotent matrices b 1 and b 2 constituting its unique decomposition b b 1 b 2 are nonzero the problem is considered also under the additional assumption that the differences a b 1 and a b 2 are hermitian matrices this obviously covers the case when a b 1 and b 2 are hermitian themselves when the problem can be interpreted from a statistical point of view

on multivariate rayleigh and exponential distributions in this paper expressions for multivariate rayleigh and exponential probability density functions pdfs generated from correlated gaussian random variables are presented we first obtain a general integral form of the pdfs and then study the case when the complex gaussian generating vector is circular we consider two specific circular cases the exchangeable case when the variates are evenly correlated and the exponentially correlated case expressions for the multivariate pdf in these cases are obtained in integral form as well as in the form of a series of products of univariate pdfs we also derive a general expression for the multivariate exponential characteristic function cf in terms of determinants in the exchangeable and exponentially correlated cases cf expressions are obtained in the form of a series of products of univariate gamma cfs the cf of the sum of exponential variates in these cases is obtained in closed form finally the bivariate case is presented mentioning its main features while the integral forms of the multivariate pdfs provide a general analytical framework the series and determinant expressions for the exponential cfs and the series expressions for the pdfs can serve as a useful tool in the performance analysis of digital modulation over correlated rayleigh fading channels using diversity combining

direct evaluation of large deviation functions we introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities such as current or density that are local in time the large deviation functions are given in terms of the typical properties of a modified dynamics and since they no longer involve rare events can be evaluated efficiently and over a wider ranges of values we illustrate the method with the current fluctuations of the totally asymmetric exclusion process and with the work distribution of a driven lorentz gas

finite size scaling of current fluctuations in the totally asymmetric exclusion process we study the fluctuations of the current j t of the totally asymmetric exclusion process with open boundaries using a density matrix renormalization group approach we calculate the cumulant generating function of the current this function can be interpreted as a free energy for an ensemble in which histories are weighted by exp sj t we show that in this ensemble the model has a first order spacetime phase transition at s 0 we numerically determine the finite size scaling of the cumulant generating function near this phase transition both in the non equilibrium steady state and for large times

a simulation based approach to two stage stochastic programming with recourse in this paper we consider stochastic programming problems where the objective function is given as an expected value function we discuss monte carlo simulation based approaches to a numerical solution of such problems in particular we discuss in detail and present numerical results for two stage stochastic programming with recourse where the random data have a continuous multivariate normal distribution we think that the novelty of the numerical approach developed in this paper is twofold first various variance reduction techniques are applied in order to enhance the rate of convergence successful application of those techniques is what makes the whole approach numerically feasible second a statistical inference is developed and applied to estimation of the error validation of optimality of a calculated solution and statistically based stopping criteria for an iterative alogrithm 1998 the mathematical programming society inc published by elsevier science b v

aspects on single symbol signaling on the frequency flat rayleigh fading channel the optimal single symbol detector on the rayleigh fading channel computes a functional quadratic form in the time continuous received signal a drawback is that closed form solutions of integral equations based on the channel statistics are required this makes simplified discrete receivers attractive a class of suboptimal receivers that transforms the received random process to a set of discrete observables is derived the set of observables constitutes a random vector in a finite dimensional receiver signal space given this vector the maximum likelihood detector computes a quadratic form in the received vector the discretization implies a loss of information therefore such a detector is not in general optimal given the received time continuous signal the purpose is however to achieve close to optimal performance when the number of observables becomes large this class of detectors is analyzed using exact error probability calculations which reveal several interesting properties the length of the observation interval and the number of discrete observables have significant influences on the error probability when the time variations of the fading process are rapid compared with the symbol duration by increasing the number of observables the error floor is lowered and the implicit diversity order is increased this implicit diversity arises as soon as more than one observable per symbol interval is used and is a consequence of the information bearing signal being a random process matched filter receivers use few discrete observables per symbol interval and thus suffer from high error floors and low implicit diversity orders on fast fading channels the error probability is highly dependent on the shapes and durations of the modulator waveforms for instance pulses of long duration give lower error probabilities than shorter pulses and for a certain type of orthogonal waveforms there is no error floor

asymptotically optimal discrete time nonlinear filters from stochastically convergent state process approximations we consider the problem of approximating optimal in the mmse sense nonlinear filters in a discrete time setting exploiting properties of stochastically convergent state process approximations more specifically we consider a class of nonlinear partially observable stochastic systems comprised by a possibly nonstationary hidden stochastic process the state observed through another conditionally gaussian stochastic process the observations under general assumptions we show that given an approximating process which for each time step is stochastically convergent to the state process in some appropriate sense an approximate filtering operator can be defined which converges to the true optimal nonlinear filter of the state in a strong and well defined sense i e compactly in time and uniformly in a completely characterized measurable set of probability measure almost unity also providing a purely quantitative justification of egoro s theorem for the problem at hand the results presented in this paper can form a common basis for the analysis and characterization of a number of heuristic approaches for approximating a large class of optimal nonlinear filters such as approximate grid based techniques known to perform well in a variety of applications

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

performance of direct sequence spread spectrum rake receivers with random spreading sequences in this paper we derive error probability expressions for binary phase shift keying bpsk and quaternary phase shift keying qpsk spread direct sequence spread spectrum dsss systems employing random spreading sequences with rake receivers the derived expressions accurately take into account the effect of interpath interference which usually has been neglected in previous analyses selection equal gain and maximal ratio techniques are considered for diversity combining two possible finger assignment strategies one based on the instantaneous amplitudes and another based on the average powers of the multipath components are considered for the assignment of multipath components to the available demodulating fingers in the rake receiver also various simple and in many cases closed form approximations for the error probabilities are derived and their accuracies are assessed

estimating the variance in nonparametric regression what is a reasonable choice the exact mean squared error mse of estimators of the variance in nonparametric regression based on quadratic forms is investigated in particular two classes of estimators are compared hall kay and titterington s optimal difference based estimators and a class of ordinary difference based estimators which generalize methods proposed by rice and gasser sroka and jennen steinmetz for small sample sizes the mse of the first estimator is essentially increased by the magnitude of the integrated first two squared derivatives of the regression function it is shown that in many situations ordinary difference based estimators are more appropriate for estimating the variance because they control the bias much better and hence have a much better overall performance it is also demonstrated that rice s estimator does not always behave well data driven guidelines are given to select the estimator with the smallest mse

precise error rate analysis of bandwidth efficient bpsk in nakagami fading and cochannel interference the bit error rate ber of bandlimited binary phase shift keying in a fading and cochannel interference cci environment is derived for the case of perfect coherent detection the fading and interference model assumed is general and of interest for microcellular system studies the model allows both desired signal and interfering signals to experience arbitrary amounts of fading severity a precise ber expression is derived using a characteristic function method using this accurate analytical result the impact of the interfering users fading severity on the desired user error rate is examined the bers obtained under perfect coherent detection are also valid as lower performance bounds for practical realizable receivers where ideal coherent detection is difficult to implement the error rate performance of a novel bandwidth efficient pulse shape is determined for the general fading and cci environment analysis and numerical results show that the new pulse can provide better ber performance than the widely used raised cosine pulse

mean and variance of the lqg cost function linear quadratic gaussian lqg systems are well understood and methods to minimize the expected cost are readily available less is known about the statistical properties of the resulting cost function the contribution of this paper is a set of analytic expressions for the mean and variance of the lqg cost function these expressions are derived using two different methods one using solutions to lyapunov equations and the other using only matrix exponentials both the discounted and the non discounted cost function are considered as well as the finite time and the infinite time cost function the derived expressions are successfully applied to an example system to reduce the probability of the cost exceeding a given threshold

the natural vibration of a conical shell with an annular end plate in this paper natural frequencies and mode shapes for a conical shell with an annular end plate or a round end plate are investigated in detail by combining the vibration theory with the transfer matrix method the governing equations of vibration for this structure are expressed in terms of a matrix differential equation and a novel recurrence formula method that can close in on analytical solution of transfer matrix is presented once the transfer matrix of single component has been determined and the product of each component matrix and the joining matrix can obtain entire structure matrix the frequency equations and mode shape functions are represented in terms of the elements of the structural transfer matrices the 3d finite element numerical simulations have verified the present formulas of natural frequencies and mode shapes the conclusions show that the transfer matrix method can accurately obtain natural vibration characteristics of the conical shell with an annular end plate

bit error probabilities mdpsk over the nonselective rayleigh fading channel with diversity reception data transmission using m ary differential phase shift keying mdpsk over the nonselective rayleigh fading channel with diversity reception is considered while previous studies on error probability mostly assume no fading fluctuation the author considers exclusively the case in which the fading process fluctuates from one symbol interval to the next exact bit error probability results for 2 4 and 8 dpsk as well as tight upper bounds are derived some applications of the results are discussed

an exact formula for the statistics of the current in the tasep with open boundaries we study the totally asymmetric exclusion process on a finite one dimensional lattice with open boundaries i e in contact with two reservoirs at different potentials the total time integrated current through the system is a random variable that scales linearly with time in the long time limit we conjecture a parametric representation for the generating function of the cumulants of the current which is related to the large deviation function by laplace transform this formula is valid for all system sizes and for all values of the boundary coupling parameters

the performance of the maximum ratio combining method in correlated rician fading channels for antenna diversity signal combining the performance of the maximum ratio combining method for the combining of antenna diversity signals in correlated rician fading channels is rigorously studied the distribution function of the normalized signal to noise ratio snr is expanded in terms of a power series and calculated numerically this power series can easily take into account the signal correlations and antenna gains and can be applied to any number of receiving antennas an application of the method to dual antenna diversity systems produces useful distribution curves for the normalized snr which can be used to find the diversity gain it is revealed that signal correlation in rician fading channels helps to increase the diversity gain rather than to decrease it as in the rayleigh fading channels it is also shown that with a relative strong direct signal component the diversity gain can be much higher than that without a direct signal component

error probability for coherent and differential psk over arbitrary rician fading channels with multiple cochannel interferers this paper discusses the performance of communication systems using binary coherent and differential phase shift keyed psk modulation in correlated rician fading channels with diversity reception the presence of multiple rician faded cochannel users which may have arbitrary and nonidentical parameters is modeled exactly exact bit error probability bep expressions are derived via the moment generating functions mgfs of the relevant decision statistics which are obtained through coherent detection with maximum ratio combining for coherent psk modulation and differential detection with equal gain combining egc for differential modulation evaluating the exact expressions requires a complexity that is exponential in the number of interferers to avoid this potentially time consuming operation we derive two low complexity approximate methods each for coherent and differential modulation formats which are more accurate than the traditional gaussian approximation approach two new and interesting results of this analysis are 1 unlike in the case of rayleigh fading channels increasing correlation between diversity branches may lead to better performance in rician fading channels and 2 the phase distribution of the line of sight or static fading components of the desired user has a significant influence on the bep performance in correlated diversity channels

a note on the rank subtractivity ordering abstract some well known matrix partial orderings can be created by supplementing the so called rank subtractivity partial ordering by an appropriate preordering in this note a new partial ordering with the same property is introduced this new ordering is seen to be weaker than the other orderings but still preserving some inheritance properties

influence of the poisson ratio on the natural frequencies of stepped thickness circular plate the natural frequencies of simply supported and clamped stepped thickness plates are determined using classical plate solutions with exact continuity conditions at the step the effect of incorporating the poisson ratio in the continuity conditions on the natural frequencies for nodal diameters 0 1 and nodal interior circle numbers 0 1 2 is thoroughly investigated for engineering applications a design criterion is proposed for simply supported and clamped plates based on an approximate linear model for the natural frequencies the literature lacks experimental results on this type of plates hence in this paper experimental results are presented for four models with two poisson s ratios and prove their consistency with the proposed criterion

an exact performance analysis of mrc ostbc over generalized fading channels a unified analytical framework for evaluating the performance of maximal ratio combining mrc and orthogonal space time block coding ostbc over generalized fading channels is presented the basic motivation for developing such a framework pertains to analyzing the distribution of a sum of squared random variables rvs belonging to different families of fading distributions following a novel analytical approach stemming from the definition of a common moment generating function mgf model for these families of distributions the probability density function pdf and the cumulative distribution function cdf of a general sum of squared rvs are expressed by simple infinite gamma series expansions based on these expressions the capacity and error probability of mrc ostbc over generalized fading channels is thoroughly studied the developed theory is used to evaluate the performance of ostbc for a mixed nakagami m rice fading model and novel analytical results are presented the accuracy of the derived expressions is validated by extensive monte carlo simulations

universal cumulants of the current in diffusive systems on a ring we calculate exactly the first cumulants of the integrated current and of the activity which is the total number of changes of configurations of the symmetric simple exclusion process on a ring with periodic boundary conditions our results indicate that for large system sizes the large deviation functions of the current and of the activity take a universal scaling form with the same scaling function for both quantities this scaling function can be understood either by an analysis of bethe ansatz equations or in terms of a theory based on fluctuating hydrodynamics or on the macroscopic fluctuation theory of bertini de sole gabrielli jona lasinio and landim

ziv zakai bounds on time delay estimation in unknown convolutive random channels using the ziv zakai bound zzb methodology we develop a bayesian mean square error bound on time delay estimation tde in convolutive random channels and compare it with time delay estimator performance and a crame r rao bound the channel is modeled as a tapped delay line whose taps are gaussian random variables that may be nonzero mean and correlated a model widely adopted in many applications such as wideband fading in a multipath channel the time delay has a uniform prior distribution a zzb is developed that incorporates the prior on the random time delay as well as the convolutive random gaussian channel and does not assume the receiver has knowledge of the channel realization the zzb provides good performance prediction for maximum a posteriori map time delay estimation tracking the low medium and high signal to noise ratio snr regimes the convolutive channel model includes important special cases such as narrowband gaussian channels corresponding to rayleigh rician fading wideband multipath channels with a power decay profile such as exponential decay and known channels we show that the associated crame r rao bound is tight only at high snr whereas the zzb predicts threshold behavior and tde breakdown as the snr decreases when compared to a zzb that assumes knowledge of the channel realization the zzb developed here provides a more realistic and tighter bound revealing the performance loss due to lack of channel knowledge the map estimator incorporates knowledge of the channel statistics and so performs much better than a maximum likelihood estimator that minimizes mean square error but does not use knowledge of the random channel statistics several examples illustrate the estimator and bound behaviors

universal large deviation function of the kardar parisi zhang equation in one dimension using the bethe ansatz we calculate the whole large deviation function of the displacement of particles in the asymmetric simple exclusion process asep on a ring when the size of the ring is large the central part of this large deviation function takes a scaling form independent of the density of particles we suggest that this scaling function found for the asep is universal and should be characteristic of all the systems described by the kardar parisi zhang equation in 1 1 dimension simulations done on two simple growth models are in reasonable agreement with this conjecture

completion of an orthogonal projector and a related inverse mapping problem we study the completion problem for an orthogonal projector a of r n from knowledge of one or several of its columns as well as the related matrix inverse problem of finding an orthogonal projector a with ax y for two given n by k matrices x and y using geometric properties of orthogonal projections and of the singular value decomposition we derive theoretical and numerical solutions for these problems we give algorithms and test their matlab implementations

convergence of large deviation estimators we study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium nonequilibrium and manmade stochastic systems we give conditions for the convergence of these estimators with sample size based on the boundedness or unboundedness of the quantity sampled and discuss how statistical errors should be defined in different parts of the convergence region our results shed light on previous reports of phase transitions in the statistics of free energy estimators and establish a general framework for reliably estimating large deviation functions from simulation and experimental data and identifying parameter regions where this estimation converges

asymptotic distribution method for structural reliability analysis in high dimensions in the reliability analysis of safety critical complex engineering structures a very large number of the system parameters can be considered as random variables the difficulty in computing the failure probability using the classical first and second order reliability methods form and sorm increases rapidly with the number of variables or dimension there are mainly two reasons behind this the first is the increase in computational time with the increase in the number of random variables in principle this problem can be handled with superior computational tools the second reason which is perhaps more fundamental is that there are some conceptual difficulties typically associated with high dimensions this means that even when one manages to carry out the necessary computations the application of existing form and sorm may still lead to incorrect results in high dimensions this paper is aimed at addressing this issue based on the asymptotic distribution of quadratic form in gaussian random variables two formulations for the case when the number of random variables n n is provided the first is called strict asymptotic formulation and the second is called weak asymptotic formulation both approximations result in simple closed form expressions for the probability of failure of an engineering structure the proposed asymptotic approximations are compared with existing approximations and monte carlo simulations using numerical examples

computation of current cumulants for small nonequilibrium systems we analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems recently discussed in the framework of full counting statistics for mesoscopic systems this method is based on identifying the current cumulants from a rayleigh schrodinger perturbation expansion for the generating function here it is derived from a simple path distribution identity and extended to the joint statistics of multiple currents for a possible thermodynamical interpretation we compare this approach to a generalized onsager machlup formalism we present calculations for a boundary driven kawasaki dynamics on a one dimensional chain both for attractive and repulsive particle interactions

noncoherent amplify and forward cooperative networks robust detection and performance analysis we develop closed form generalized likelihood ratio test glrt sequence detectors for multi relay amplify and forward af cooperative networks employing m ary differential phase shift keying m dpsk and noncoherent m ary frequency shift keying m fsk the proposed detectors achieve robust performance in a wide range of fading environments where prior knowledge of channels signal powers noise variances and relay functionalities is unavailable to the destination a comprehensive error probability performance analysis is carried out in rayleigh fading specifically we derive unified pairwise error probability pep expressions for both detectors in a dual hop network which are valid for arbitrary modulation order m and arbitrary sequence length ns we also derive unified bit error probability bep expressions for both detectors employing binary signalings in various networks for ns 1 it is further shown that both detectors achieve near full diversity orders finally the superiorities of the proposed detectors over the state of the art noncoherent detectors are justified through extensive comparisons in practical scenarios for example in a multi relay network where the relays are uniformly distributed between the source and destination the proposed detector for noncoherent fsk with ns 1 outperforms the well known maximum energy selector by almost 15 db in high signal to noise ratios

explicit analytical expressions for outage and error rate of diversity cellular systems in the presence of multiple interferers and correlated rayleigh fading the outage probability of maximal ratio combining diversity with an arbitrary number of antennas in the presence of an arbitrary number of cochannel interferers and thermal noise is derived when the branch gains of the desired user signal and interfering signals experience rayleigh fading and have the same correlation matrix two special cases when the correlation matrix is equicorrelated and when the correlation matrix has different eigenvalues are considered for both the equal power cochannel interference case and the unequal power cochannel interference case further the average bit error rate of a coherent binary phase shift keying bpsk modulated cellular system using maximal ratio combining diversity in cochannel interference and correlated rayleigh fading is derived the effects of the average signal to noise ratio snr and the average signal power to interference power ratio on the system performance are examined

on the cumulative distribution function of quadratic form receivers over generalized fading channels with tone interference in this paper we develop a general and unified framework for estimating the cumulative distribution function cdf of quadratic form receivers the expression of the cdf that we finally achieve takes on the form of a single integral with finite limits and integrand composed of elementary functions which can be readily integrated using standard techniques in particular the specific contribution of this manuscript is twofold i we present a comprehensive framework for the analysis of multi channel reception systems using either non coherent or differentially coherent detectors diversity systems with practical i e noisy channel estimators and transmitted reference tr receiver architectures working in frequency selective fading channels and ii we show that the framework can be efficiently used for performance assessment of wireless systems over generalized fading channels and under mild assumptions over generalized fading channels further impaired by in band multi tone interference

accurate evaluation for mdpsk with noncoherent diversity the error probability analysis of m ary differential phase shift keying signals with noncoherent diversity combining over general fading channels is not available in the literature except for some simple cases the difficulty lies in the philosophy which attempts to explicitly determine the phase distribution expressions of the received signal and this often leads to a mathematically intractable issue in this paper we take a novel approach by formulating the phase distribution in terms of joint moment generating functions of the real and imaginary parts of the decision variable at the receiver output we further derive fast convergent techniques for two dimensional 2 d inverse laplace transform enabling us to accurately evaluate the phase distribution the error probability formulas thus obtained involve a twofold integral which can be efficiently evaluated by using our algorithms developed on the basis of the 2 d trapezoidal summation and gauss chebyshev quadrature the new technique is very general taking into account the effects of arbitrary diversity order symbol alphabet size m and arbitrary diversity branches correlation numerical results are also presented for illustration

new simple closed form ber expressions for mrc diversity bpsk in correlated rayleigh fading and cci exact closed form expressions are derived for the bit error rate of binary phase shift keying in rayleigh fading channels with maximal ratio combining diversity in the presence of cochannel interference and additive white gaussian noise the desired signal and the interferer signals are subject to correlated rayleigh fading and binary phase shift keying modulation is used by all users

diffusions conditioned on occupation measures a markov process fluctuating away from its typical behavior can be represented in the long time limit by another markov process called the effective or driven process having the same stationary states as the original process conditioned on the fluctuation observed we construct here this driven process for diffusions spending an atypical fraction of their evolution in some region of state space corresponding mathematically to stochastic differential equations conditioned on occupation measures as an illustration we consider the langevin equation conditioned on staying for a fraction of time in different intervals of the real line including the positive half line which leads to a generalization of the brownian meander problem other applications related to quasi stationary distributions metastable states noisy chemical reactions queues and random walks are discussed

classical jacobi polynomials closed form solutions for transverse vibrations this paper deals with transverse vibrations of nonuniform homogeneous beams and plates classes of beams and axisymmetrical circular plates whose boundary value problems of free transverse vibrations and free transverse axisymmetrical vibrations respectively can be reduced to an eigenvalue singular problem singularities occur at both ends of orthogonal polynomials are reported exact natural frequencies and jacobi polynomials as exact mode shapes which result directly from eigenvalues and eigenfunctions of eigenvalue singular problems of classical orthogonal polynomials are reported for these classes the above classes of beams and plates hereafter called jacobi classes are given by geometry and boundary conditions the geometry consists of parabolic thickness variation with respect to the axial coordinate for beams and with respect to the radius for plates beams belonging to this class have either one or two sharp ends singularities along with certain boundary conditions plates have zero thickness at zero and outer radii the boundary value problems associated with plates and beams of two sharp ends are free boundary problems two other boundary value problems hinged free and sliding free are reported for beams with one sharp end also exact natural frequencies and mode shapes for uniformly rotating beams with hinged free boundary are reported

relaxation times in the asep model using a dmrg method we compute the largest relaxation times for the totally asymmetric exclusion process tasep with open boundary conditions with a dmrg method this allows us to reach much larger system sizes than in previous numerical studies we are then able to show that the phenomenological theory of the domain wall indeed predicts correctly the largest relaxation time for large systems besides we can obtain results even when the domain wall approach breaks down and show that the kpz dynamical exponent z 3 2 is recovered in the whole maximal current phase

how should we assess the fit of rasch type models approximating the power of goodness of fit statistics in categorical data analysis we investigate the performance of three statistics r 1 r 2 glas in psychometrika 53 525 546 1988 and m 2 maydeu olivares joe in j am stat assoc 100 1009 1020 2005 psychometrika 71 713 732 2006 to assess the overall fit of a one parameter logistic model 1pl estimated by marginal maximum likelihood ml r 1 and r 2 were specifically designed to target specific assumptions of rasch models whereas m 2 is a general purpose test statistic we report asymptotic power rates under some interesting violations of model assumptions different item discrimination presence of guessing and multidimensionality as well as empirical rejection rates for correctly specified models and some misspecified models all three statistics were found to be more powerful than pearson s x 2 against two and three parameter logistic alternatives 2pl and 3pl and against multidimensional 1pl models the results suggest that there is no clear advantage in using goodness of fit statistics specifically designed for rasch type models to test these models when marginal ml estimation is used

box type approximations in nonparametric factorial designs abstract linear rank statistics in nonparametric factorial designs are asymptotically normal and in general heteroscedastic in a comprehensive simulation study the asymptotic chi squared law of the corresponding quadratic forms is shown to be a rather poor approximation of the finite sample distribution motivated by this problem we propose simple finite sample size approximations for the distribution of quadratic forms in factorial designs under a normal heteroscedastic error structure these approximations are based on an f distribution with estimated degrees of freedom that generalizes ideas of patnaik and box simulation studies show that the nominal level is maintained with high accuracy and in most cases the power is comparable to the asymptotic maximin wald test data driven guidelines are given to select the most appropriate test procedure these ideas are finally transferred to nonparametric factorial designs where the same quadratic forms as in the parametric case are applied to the vector

a unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels we present a unified approach to determine the exact bit error rate ber of noncoherent and differentially coherent modulations with single and multichannel reception over additive white gaussian noise and generalized fading channels the multichannel reception results assume independent fading in the channels and are applicable to systems that employ post detection equal gain combining our approach relies on an alternate form of the marcum q function and leads to expressions of the ber involving a single finite range integral which can be readily evaluated numerically aside from unifying the past results the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution the best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions

large deviation function for entropy production in driven one dimensional systems the large deviation function for entropy production is calculated by solving a time independent eigenvalue problem for a particle driven along a periodic potential in an intermediate force regime the large deviation function shows pronounced deviations from a gaussian behavior with a characteristic kink at zero entropy production such a feature can also be extracted from the analytical solution of the asymmetric random walk to which the driven particle can be mapped in a certain parameter range

fixed domain asymptotics for a subclass of matern type gaussian random fields stein statist sci 4 1989 432 433 proposed the matern type gaussian random fields as a very flexible class of models for computer experiments this article considers a subclass of these models that are exactly once mean square differentiable in particular the likelihood function is determined in closed form and under mild conditions the sieve maximum likelihood estimators for the parameters of the covariance function are shown to be weakly consistent with respect to fixed domain asymptotics

ber analysis of bpsk signals in ricean faded cochannel interference the bit error rate of a binary phase shift keying bpsk signal in ricean faded cochannel interference is studied a precise bit error rate expression is derived for a bandlimited bpsk signal corrupted by an arbitrary number of asynchronous ricean faded interfering signals an error rate estimation based on a saddlepoint approximation is also provided it is shown that this approximation is highly accurate for the special case when there is one synchronous ricean faded interfering signal in an interference limited environment an asymptotic error rate analysis based on the saddle point approximation reveals that fading in the cochannel interfering signal can have different impacts on the desired user s error rate performance our study shows that when the signal to interference ratio sir is sufficiently large the error floor of the desired user signal decreases with an increase of the rice factor in the interfering user s fading channel however the opposite phenomenon can happen when the sir is small

some new twists to problems involving the gaussian probability integral using an alternate form of the gaussian probability integral discovered a number of years ago it is shown that the solution to a number of previously considered communication problems can be simplified and in some cases made more accurate i e exact rather than bounded these problems include the evaluation of 1 the bit error probability of uncoded phase shift keying psk with costas loop tracking 2 word error probability of antipodal modulation in the presence of fading 3 bit error probability of coded m ary psk mpsk over the memoryless fading channel with given channel state information 4 conditional symbol error probability of mpsk in the presence of carrier synchronization error and 5 the average error probability for the binary additive white gaussian noise awgn intersymbol interference channel also obtained is a generalization of this new alternate form to the case of a two dimensional gaussian probability integral with arbitrary correlation which can be used to evaluate the symbol error probability of mpsk with i q unbalance

calculating error probabilities for intersymbol and cochannel interference the probability of error in a binary symmetric channel with intersymbol interference and additive noise is efficiently calculated by numerical quadrature of a laplace inversion integral along a contour in the complex plane passing through a saddlepoint of the integrand for gaussian noise a bound is set on the truncation error incurred by necessarily restricting the integration to a finite interval the probability of error resulting from cochannel interference is calculated by a similar technique

natural frequencies of transverse vibrations of non uniform circular and annular plates abstract this paper presents a method for the free transverse vibration analysis of thin elastic isotropic uniform and non uniform circular and annular plates the circumferential mode numbers n 0 and n 1 are dealt with in this paper the method is a hybrid of plate theory and finite element analysis the plate is subdivided into one circular and many annular finite elements two new finite elements were developed the first type being a circular plate and the second an annular plate the displacement functions of the finite element model are the classical solution shape functions of plate theory mass and stiffness matrices are determined by precise analytical integration the free vibrations of uniform circular and annular plates are studied by this method as well as non uniform plates the results obtained reveal that the frequencies calculated by this method are in good agreement with those obtained by other authors this method combines the advantages of the standard finite element analysis and the high accuracy formulation provided by the use of displacement functions derived from plate theory instead of the usual low order polynomials the present method is remarkable for the fact that it enables us to determine with equal precision both low and high natural frequencies

residuals for the linear model with general covariance structure a general theory is presented for residuals from the general linear model with correlated errors it is demonstrated that there are two fundamental types of residual associated with this model referred to here as the marginal and the conditional residual these measure respectively the distance to the global aspects of the model as represented by the expected value and the local aspects as represented by the conditional expected value these residuals may be multivariate some important dualities are developed which have simple implications for diagnostics the results are illustrated by reference to model diagnostics in time series and in classical multivariate analysis with independent cases

error rates of dpsk systems with mimo egc diversity reception over rayleigh fading channels this paper analyzes the average bit error probability bep of the differential binary and quaternary phase shift keying dbpsk and dqpsk respectively with multiple input multiple output mimo systems employing postdetection equal gain combining mimo egc diversity reception over rayleigh fading channels finite closed form expressions for the average bep of dbpsk and dqpsk are presented two approaches are introduced to analyze the error rate of dqpsk the proposed structure for the differential phase shift keying dpsk with mimo egc provides a reduced complexity and low cost receiver for mimo systems compared to the coherent phase shift keying system psk with mimo employing maximal ratio combining mimo mrc diversity reception finally a useful procedure for computing the associated legendre functions of the second kind with half odd integer order and arbitrarily degree is presented

quadratic forms in random variables theory and applications textbook for a one semester graduate course for students specializing in mathematical statistics or in multivariate analysis or reference for theoretical as well as applied statisticians confines its discussion to quadratic forms and second degree polynomials in real normal random vectors and matr

tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute this paper concerns with the tripotency of a linear combination of three matrices which has a background in statistical theory we demonstrate all the possible cases that lead to the tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute by utilizing block technique and returning the partitioned matrices to their original forms we derive the sufficient and necessary conditions such that a linear combination of three mutually commuting involutory matrices is tripotent

a closed form ber expression for bpsk using mrc in correlated cci and rayleigh fading an exact closed form expression for the average bit error rate ber of coherent bpsk using maximal ratio combining mrc with correlated branches in the presence of cochannel interference cci and noise is derived this expression is valid for an arbitrary correlation structure under the assumption that the branch gains of the desired user signal and interfering signals experience correlated rayleigh fading with the same correlation eigenvector matrix

idempotency of linear combinations of two idempotent matrices abstract a complete solution is established to the problem of characterizing all situations where a linear combination of two different idempotent matrices p 1 and p 2 is also an idempotent matrix including naturally three such situations known in the literature viz if the combination is either the sum p 1 p 2 or one of the differences p 1 p 2 p 2 p 1 and appropriate additional conditions are fulfilled the solution asserts that in the particular case where p 1 and p 2 are complex matrices such that p 1 p 2 is hermitian these three situations exhaust the list of all possibilities and that this list extends when the above assumption on p 1 and p 2 is violated a statistical interpretation of the idempotency problem considered in this note is also pointed out

current fluctuations in the one dimensional symmetric exclusion process with open boundaries we calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of n sites with open boundary conditions for large system size n the generating function of the integrated current depends on the densities a and b of the two reservoirs and on the fugacity z the parameter conjugated to the integrated current through a single parameter based on our expressions for these first four cumulants we make a conjecture which leads to a prediction for all the higher cumulants in the case a 1 and b 0 our conjecture gives the same universal distribution as the one obtained by lee levitov and yakovets for one dimensional quantum conductors in the metallic regime

a measure of data collapse for scaling data collapse is a way of establishing scaling and extracting associated exponents in problems showing self similar or self affine characteristics as for example in equilibrium or non equilibrium phase transitions in critical phases in dynamics of complex systems and many others we propose a measure to quantify the nature of data collapse via a minimization of this measure the exponents and their error bars can be obtained the procedure is illustrated by considering finite size scaling near phase transitions and quite strikingly recovering the exact exponents

sharp spectral bounds of several graph parameters using eigenvector norms abstract we investigate the role of the 1 and norms of eigenvectors in spectral graph theory in particular we produce several randomized algorithms which show that various graph theoretic parameters can be tightly bounded by the eigenvalues as well as norms of the corresponding eigenvectors further in some cases these inequalities can determine the parameters exactly our results include a spectral bound for the densest subgraph problem an adapted converse to the expander mixing lemma and an adapted spectral approach to the maximum cut problem

adjusting power for a baseline covariate in linear models the analysis of covariance provides a common approach to adjusting for a baseline covariate in medical research with gaussian errors adding random covariates does not change either the theory or the computations of general linear model data analysis however adding random covariates does change the theory and computation of power analysis many data analysts fail to fully account for this complication in planning a study we present our results in five parts i a review of published results helps document the importance of the problem and the limitations of available methods ii a taxonomy for general linear multivariate models and hypotheses allows identifying a particular problem iii we describe how random covariates introduce the need to consider quantiles and conditional values of power iv we provide new exact and approximate methods for power analysis of a range of multivariate models with a gaussian baseline covariate for both small and large samples the new results apply to the hotelling lawley test and the four tests in the univariate approach to repeated measures unadjusted huynh feldt geisser greenhouse box the techniques allow rapid calculation and an interactive graphical approach to sample size choice v calculating power for a clinical trial of a treatment for increasing bone density illustrates the new methods we particularly recommend using quantile power with a new satterthwaite style approximation

on the use of the variogram in checking for independence in spatial data the variogram is a standard tool in the analysis of spatial data and its shape provides useful information on the form of spatial correlation that may be present however it is also useful to be able to assess the evidence for the presence of any spatial correlation a method of doing this based on an assessment of whether the true function underlying the variogram is constant is proposed nonparametric smoothing of the squared differences of the observed variables on a suitably transformed scale is used to estimate variogram shape a statistic based on a ratio of quadratic forms is proposed and the test is constructed by investigating the distributional properties of this statistic under the assumption of an independent gaussian process the power of the test is investigated reference bands are proposed as a graphical follow up an example is discussed