finite size scaling properties of the damage distance and dynamical critical exponent for the ising model abstract with the damage spreading method scaling properties of the damage distance on the ising model with heat bath dynamics are studied numerically with the parallel flipping scheme the scaling curves fall on two curves which depend on the odd or even lattice sizes the both scaling curves give the consistent dynamical exponent as z 2 16 0 04 for d 2 and z 2 09 0 05 for d 3 respectively by shifting one of them two curves overlap each other perfectly meanwhile all the scaling curves obtained by single spin flipping processes with different odd or even lattice sizes fall on a single curve from which the consistent dynamical critical exponent with the parallel scheme is obtained z 2 18 0 02 for d 2 and z 2 08 0 04 for d 3

parametric glrt for multichannel adaptive signal detection this paper considers the problem of detecting a multichannel signal in the presence of spatially and temporally colored disturbance a parametric generalized likelihood ratio test glrt is developed by modeling the disturbance as a multichannel autoregressive ar process maximum likelihood ml parameter estimation underlying the parametric glrt is examined it is shown that the ml estimator for the alternative hypothesis is nonlinear and there exists no closed form expression to address this issue an asymptotic ml aml estimator is presented which yields asymptotically optimum parameter estimates at reduced complexity the performance of the parametric glrt is studied by considering challenging cases with limited or no training signals for parameter estimation such cases especially when training is unavailable are of great interest in detecting signals in heterogeneous fast changing or dense target environments but generally cannot be handled by most existing multichannel detectors which rely more heavily on training at an adequate level compared with the recently introduced parametric adaptive matched filter pamf and parametric rao detectors the parametric glrt achieves higher data efficiency offering improved detection performance in general

direction of arrival estimation using parametric signal models we consider the problem of estimating the directions of arrival doas of narrowband sources with known center frequency the paper evaluates the potential improvement in estimation accuracy by using spatial temporal processing for signals obeying a deterministic parametric model one would expect that prior information about the temporal structure of the signals will yield some gain in performance by deriving the cramer rao bound crb on the doa estimates we quantify this gain and identify the cases for which the gain is significant we show that for the single source case spatial temporal processing does not yield any gain in performance relative to conventional spatial processing for multiple noncoherent signals incorporating temporal processing can achieve the single source performance yielding a significant gain for the case of multiple sources with small spatial separation relative to the beamwidth of the array however spatial temporal processing cannot yield any gain in performance for multiple coherent signals

a new parametric glrt for multichannel adaptive signal detection a parametric generalized likelihood ratio test glrt for multichannel signal detection in spatially and temporally colored disturbance was recently introduced by modeling the disturbance as a multichannel autoregressive ar process the detector however involves a highly nonlinear maximum likelihood estimation procedure which was solved via a two dimensional iterative search method initialized by a suboptimal estimator in this paper we present a simplified glrt along with a new estimator for the problem both the estimator and the glrt are derived in closed form at considerably lower complexity with adequate training data the new glrt achieves a similar detection performance as the original one however for the more interesting case of limited training the original glrt may become inferior due to poor initialization because of its simpler form the new glrt also offers additional insight into the parametric multichannel signal detection problem the performance of the proposed detector is assessed using both a simulated dataset which was generated using multichannel ar models and the kassper dataset a widely used dataset with challenging heterogeneous effects found in real world environments

subspace based estimation of time delays and doppler shifts this paper considers the problem of estimating the time delays and doppler shifts of a known waveform received via several distinct paths by an array of antennas the general maximum likelihood estimator is presented and is shown to require a 2d dimensional nonlinear minimization where d is the number of received signal reflections two alternative solutions based on signal and noise subspace fitting are proposed requiring only a d dimensional minimization in particular we show how to decouple the required search into a two step procedure where the delays are estimated and the dopplers solved for explicitly initial conditions for the time delay search can be obtained by applying generalizations of the music and esprit algorithms which are also outlined in the paper simulation examples are included to illustrate the algorithms performance relative to the cramer rao bound

computationally efficient angle estimation for signals with known waveforms this paper presents a large sample decoupled maximum likelihood deml angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise the deml estimator decouples the multidimensional problem of the exact ml estimator to a set of 1 d problems and hence is computationally efficient we shall derive the asymptotic statistical performance of the deml estimator and compare the performance with its cramer rao bound crb i e the best possible performance for the class of asymptotically unbiased estimators we will show that the deml estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms we will also show that for moderately correlated signals with known waveforms the deml estimator is no longer a large sample maximum likelihood ml estimator but the deml estimator may still be used for angle estimation and the performance degradation relative to the crb is small we shall show that the deml estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix finally several numerical examples showing the performance of the deml estimator are presented in this paper

the dynamical critical exponent of the two three and five dimensional kinetic ising model abstract we present monte carlo simulation results for the dynamical critical exponent z of the two three and five dimensional kinetic ising model we used glauber as well as metropolis dynamics both type of dynamics lead to the same z values in two and three dimensions the z values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at tc for very large systems up to 169984 2 3072 3 and 48 5 for the two dimensional case we obtain z 2 21 0 03 and for the three dimensional case z 2 08 0 03 for the five dimensional glauber case the requirement z 2 gives a critical point j kbtc 0 11391 from monte carlo simulations whereas new series expansions with four more terms give 0 113935 0 000015 for this ratio

red bond exponents of the critical and the tricritical ising model in three dimensions using the wolff and geometric cluster algorithms and finite size scaling analysis we investigate the critical ising and the tricritical blume capel models with nearest neighbor interactions on the simple cubic lattice the sampling procedure involves the decomposition of the ising configuration into geometric clusters each of which consists of a set of nearest neighboring spins of the same sign connected with bond probability p these clusters include the well known kasteleyn fortuin clusters as a special case for p 1 exp 2k where k is the ising spin spin coupling along the critical line k kc the size distribution of geometric clusters is investigated as a function of p we observe that unlike in the case of two dimensional tricriticality the percolation threshold in both models lies at pc 1 exp 2kc further we determine the corresponding red bond exponents as yr 0 757 2 and 0 501 5 for the critical ising and the tricritical blume capel models respectively on this basis we conjecture yr 1 2 for the latter model

statistical and systematic errors in monte carlo sampling we have studied the statistical and systematic errors which arise in monte carlo simulations and how the magnitude of these errors depends on the size of the system being examined when a fixed amount of computer time is used we find that depending on the degree of self averaging exhibited by the quantities measured the statistical errors can increase decrease or stay the same as the system size is increased the systematic underestimation of response functions due to the finite number of measurements made is also studied we develop a scaling formalism to describe the size dependence of these errors as well as their dependence on the bin length size of the statistical sample both at and away from a phase transition the formalism is tested using simulations of thed 3 ising model at the infinite lattice transition temperature we show that for a 96 96 96 system noticeable systematic errors systematic underestimation of response functions are still present for total run lengths of 106 monte carlo steps site mcs with measurements taken at regular intervals of 10 mcs

efficient maximum likelihood doa estimation for signals with known waveforms in the presence of multipath we present a large sample maximum likelihood ml algorithm for estimating the directions of arrival doa s and signal amplitudes of known possibly coherent signals impinging on an array of sensors the algorithm is an extension of the deml method of li et al that handles coherent multipath that may be present in the signals the algorithm is computationally efficient because the nonlinear minimization step decouples into a set of minimizations of smaller dimension

transfer matrix test of the two cell mean field renormalization group abstract a transfer matrix approach has been worked out to test the predictions of the two cell mean field renormalization group mfrg for the square ising cells with linear size up to l 11 the convergence of the finite size critical couplings towards the exact value both for mfrg and for the cluster mfa is shown and the limit of the ratio yh yt consistent with the corresponding universal value is found applications within mfa are also briefly discussed

uniqueness of equilibrium strategies in dynamic mean variance problems with random coefficients abstract this paper is concerned with the uniqueness issue of open loop equilibrium investment strategies of dynamic mean variance portfolio selection problems with random coefficients a unified method is developed to treat both the problems with deterministic risk free return rate state dependent risk aversion and those with full random coefficients constant risk aversion to do so some new necessity conditions for the existence of equilibrium investment strategies are established which considerably extends the analogue in 9 with distinctive ideas some new interesting facts are revealed for example if risk free return rate is random it is shown that there exists a unique open loop equilibrium investment strategy relying on initial wealth even when risk aversion is merely a constant but not state dependent

complex amplitude estimation in the known steering matrix and generalized waveform case we consider a special growth curve sgc model with a known steering matrix and generalized waveform in the presence of unknown interference and noise several estimators of the complex amplitude based on this model are derived including the methods of approximate maximum likelihood aml minimum variance distortionless response mvdr and amplitude and phase estimation apes we analyze the statistical properties of these estimators and show that in the presence of temporally white but spatially correlated noise and interference aml is asymptotically statistically efficient for a large snapshot number while mvdr and apes are asymptotically equivalent but not statistically efficient via several numerical examples we also show that when the noise and interference are both spatially and temporally correlated the apes estimator can achieve better estimation accuracy and exhibit greater robustness than the other methods

bayesian complex amplitude estimation and adaptive matched filter detection in low rank interference we propose a bayesian method for complex amplitude estimation in low rank interference we assume that the received signal follows the generalized multivariate analysis of variance gmanova patterned mean structure and is corrupted by low rank spatially correlated interference and white noise an iterated conditional modes icm algorithm is developed for estimating the unknown complex signal amplitudes and interference and noise parameters we also discuss initialization of the icm algorithm and propose a non bayesian adaptive matched filter amf signal detector that utilizes the icm estimation results numerical simulations demonstrate the performance of the proposed methods

on maximum entropy principle superstatistics power law distribution and renyi parameter abstract the equilibrium distributions of probabilities are derived on the basis of the maximum entropy principle mep for the renyi and tsallis entropies new s forms for the renyi and tsallis distribution functions are found which are normalised with corresponding entropies in contrast to the usual z forms normalised with partition functions z the superstatistics based on the gibbs distribution of energy fluctuations gives rise to a distribution function of the same structure that the renyi and tsallis distributions have the long range tail of the renyi distribution is the power law distribution with the exponent s expressed in terms of the free renyi parameter q as s 1 1 q the condition s 0 gives rise to the requirement q q can be uniquely determined with the use of a further extension of mep as the condition for maximum of the difference between the renyi and boltzmann entropies for the same power law distribution dependent on q it is found that the maximum is realized for q within the range from 0 25 to 0 5 and the exponent s varies from 1 3 to 2 in dependence on parameters of stochastic systems

simultaneous analysis of several models in the three dimensional ising universality class we investigate several three dimensional lattice models believed to be in the ising universality class by means of monte carlo methods and finite size scaling these models include spin 1 models with nearestneighbor interactions on the simple cubic and on the diamond lattice for the simple cubic lattice we also include models with third neighbor interactions of varying strength and some equivalent neighbor models also included are a spin 1 model and a hard core lattice gas separate analyses of the numerical data confirm the ising like critical behavior of these systems on this basis we analyze all these data simultaneously such that the universal parameters occur only once this leads to an improved accuracy the thermal magnetic and irrelevant exponents are determined as y t51 5868 3 y h52 4816 1 and y i520 821 5 respectively the binder ratio is estimated as q5 m 2 2 m 4 50 62 341 4

on the combinatorial solution of the ising model an attempt to generalise the combinatorial solution of the two dimensional 2d nearest neighbour nn ising model to three dimensions is reported a generating function which fully exposes the symmetry of the lattice is derived for the 2d square ising model a natural extension to the 3d simple cubic sc lattice is shown to be false a certain circumstance for the 2d case leads to the conjecture that tanh j ktc square root 5 2 cos pi 8 for the scnn ising model

array signal processing in the known waveform and steering vector case the amplitude estimation of a signal that is known only up to an unknown scaling factor with interference and noise present is of interest in several applications including using the emerging quadrupole resonance qr technology for explosive detection in such applications a sensor array is often deployed for interference suppression this paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori two approaches viz the capon and the maximum likelihood ml methods are considered for the signal amplitude estimation in the presence of temporally white but spatially colored interference and noise we derive closed form expressions for the expected values and mean squared errors mses of the two estimators a comparative study shows that the ml estimate is unbiased whereas the capon estimate is biased downwards for finite data sample lengths we show that both methods are asymptotically statistically efficient when the number of data samples is large but not when the signal to noise ratio snr is high furthermore we consider a more general scenario where the interference and noise are both spatially and temporally correlated we model the interference and noise vector as a multichannel autoregressive ar random process an alternating least squares als method for parameter estimation is presented we show that in most cases the als method is superior to the model mismatched ml m sup 3 l method which ignores the temporal correlation of the interference and noise

a diagonal growth curve model and some signal processing applications we consider a variation of the growth curve gc model referred to as the diagonal growth curve dgc model where the steering vectors and waveforms are both known and the complex amplitude matrix is constrained to be diagonal a closed form approximate maximum likelihood aml estimator for this model is derived based on the maximum likelihood principle we analyze the statistical properties of this method theoretically and show that the aml estimate is unbiased and asymptotically statistically efficient for a large snapshot number via several numerical examples in array signal processing and spectral analysis we also show that the proposed aml estimator can achieve better estimation accuracy and exhibit greater robustness than the best existing methods

a general stochastic maximum principle for optimal control problems the maximum principle for nonlinear stochastic optimal control problems in the general case is proved the control domain need not be convex and the diffusion coefficient can contain a control variable

time evolution of damage in the ising model the time evolution of the damage in the ising model with the heat bath and glauber dynamics has been investigated with the damage spreading method the damage density d t and the average distance r t of damaged sites from the origin have been measured numerically from the simulational data the scaling forms have been established as d t tx r t t1z and d t r t df and the corresponding exponents x z and df have been estimated

potts model on directed small world voronoi delaunay lattices abstract the critical properties of the potts model with q 3 and 4 states in two dimensions on directed small world voronoi delaunay random lattices with quenched connectivity disorder are investigated this disordered system is simulated by applying the monte carlo update heat bath algorithm the potts model on these directed small world random lattices presents in fact a second order phase transition with new critical exponents for q 3 and value of the rewiring probability p 0 01 but for q 4 the system exhibits only a first order phase transition independent of p 0 p 1

amplitude estimation of a signal with known waveform in the presence of steering vector uncertainties in this correspondence we address the problem of estimating the amplitude of a signal with known waveform received on an array of sensors and we consider the case where there exist uncertainties about the spatial signature of the signal of interest closed form expressions for the crame spl acute r rao bound are derived and the respective influence of the uncertainties and the number of snapshots is studied the maximum likelihood estimator mle of the signal of interest amplitude along with the covariance matrix of the interferences and noise is also derived and an iterative algorithm is presented to obtain the ml estimates

asymptotically optimal linear shrinkage of sample lmmse and mvdr filters conventional implementations of the linear minimum mean square lmmse and minimum variance distortionless response mvdr estimators rely on the sample matrix inversion smi technique i e on the sample covariance matrix scm this approach is optimal in the large sample size regime nonetheless in small sample size situations those sample estimators suffer a large performance degradation thus the aim of this paper is to propose corrections of these sample methods that counteract their performance degradation in the small sample size regime and keep their optimality in large sample size situations to this aim a twofold approach is proposed first shrinkage estimators are considered as they are known to be robust to the small sample size regime namely the proposed methods are based on shrinking the sample lmmse or sample mvdr filters towards a variously called matched filter or conventional bartlett beamformer in array processing second random matrix theory is used to obtain the optimal shrinkage factors for large filters the simulation results highlight that the proposed methods outperform the sample lmmse and mvdr also provided that the sample size is higher than the observation dimension they improve classical diagonal loading dl and ledoit wolf lw techniques which counteract the small sample size degradation by regularizing the scm finally compared to state of the art dl the proposed methods reduce the computational cost and the proposed shrinkage of the lmmse obtains performance gains

time inconsistent stochastic linear quadratic control in this paper we formulate a general time inconsistent stochastic linear quadratic lq control problem the time inconsistency arises from the presence of a quadratic term of the expected state as well as a state dependent term in the objective functional we define an equilibrium instead of optimal solution within the class of open loop controls and derive a sufficient condition for equilibrium controls via a flow of forward backward stochastic differential equations when the state is one dimensional and the coefficients in the problem are all deterministic we find an explicit equilibrium control as an application we then consider a mean variance portfolio selection model in a complete financial market where the risk free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes applying the general sufficient condition we obtain explicit equilibrium strategies when the risk premium is both deterministic and stochastic

computer simulation studies of critical phenomena abstract the recent strides which have been made in the use of computer simulations to study phase transitions and critical phenomena are reviewed we describe how the use of a combination of recently developed histogram techniques and sophisticated monte carlo simulation algorithms have allowed the determination of the static critical behavior of the d 3 ising and heisenberg models with unprecedented precision we also discuss the study of dynamic critical behavior in simple spin models by both monte carlo and spin dynamics methods recent estimates for dynamic critical exponents are reviewed including the first high precision estimate for true dynamics

maximum likelihood angle estimation for signals with known waveforms maximum likelihood estimation mle of the arrival angles of narrowband plane waves when one or all signals have known waveforms is considered computationally efficient and rapidly converging algorithms that iteratively maximize the likelihood functions are presented cramer rao bounds for these estimators are obtained the conditions under which incorporating knowledge of one or all of the signal waveforms in the estimators improves the accuracy of the angle estimates are described

open loop equilibrium strategy for mean variance asset liability management portfolio selection problem with debt ratio abstract in this study we consider a time consistent mean variance asset liability management portfolio selection problem in which the liability is controllable the objective is to find an equilibrium investment strategy and an equilibrium debt ratio in the financial market consisting of one risk free asset and one risky asset by using forward backward stochastic differential equations fbsdes we derive a sufficient condition and a necessary condition for the open loop equilibrium strategies the uniqueness of the strategies is also provided furthermore to illustrate our results we provide numerical examples to show how the parameters impact on the equilibrium strategies and the corresponding efficient frontier

performance analysis of multivariate complex amplitude estimators we consider multivariate complex amplitude estimation in the presence of unknown interference and noise two multivariate approaches maximum likelihood ml and capon are provided we derive the closed form expression of the crame spl acute r rao bound crb for the unknown complex amplitudes we also analyze the bias properties and mean squared errors mse of the two estimators a comparative study shows that the multivariate ml estimator is unbiased whereas the multivariate capon estimator is biased downward for finite snapshots both estimators are asymptotically statistically efficient when the number of snapshots is large

on the mean square error performance of adaptive minimum variance beamformers based on the sample covariance matrix the authors examine the mean square error mse performance of two common implementations of adaptive linearly constrained minimum variance lcmv beamformers that employ the sample covariance matrix the type i beamformer is representative of block processing methods where the same input data is used both to compute the adaptive weights and to form the beamformer output the type ii beamformer as in many recursive schemes applies adaptive weights computed from previous data to the current input due to correlation between the adaptive weights and the input data the type i lcmv beamformer exhibits signal cancellation which is shown here to cause signal estimate bias to explicitly account for signal cancellation the mean square error mse and output signal to noise ratio snr measures of the bias corrected type i beamformer are analyzed thus extending previous results further new analytical results for these performance measures are given for the type ii lcmv beamformer comparison of bias corrected type i and type ii implementations indicate that both methods yield exactly the same mse and output snr performance

time inconsistent stochastic linear quadratic control characterization and uniqueness of equilibrium in this paper we continue our study on a general time inconsistent stochastic linear quadratic control problem originally formulated in y hu h jin and x y zhou siam j control optim 50 2012 pp 1548 1572 we derive a necessary and sufficient condition for equilibrium controls via a flow of forward backward stochastic differential equations when the state is one dimensional and the coefficients in the problem are all deterministic we prove that the explicit equilibrium control constructed in y hu h jin and x y zhou siam j control optim 50 2012 pp 1548 1572 is indeed unique our proof is based on the derived equivalent condition for equilibria as well as a stochastic version of the lebesgue differentiation theorem finally we show that the equilibrium strategy is unique for a mean variance portfolio selection model in a complete financial market where the risk free rate is a deterministic function of time but all the other market parameters are possibly stochastic pro

time delay and spatial signature estimation using known asynchronous signals this paper considers the problem of estimating the parameters of known signals received asynchronously by an array of antennas the parameters of primary interest are the time delays of the signals and their spatial signatures at the array estimates of the signal directions of arrival are also considered but are of secondary importance in this work maximum likelihood algorithms and more computationally efficient approximations are developed for both the case where all received signals are identical the channel estimation overlapping echo problem and where they are all distinct conditions are also derived under which the standard matched filter approach yields consistent and statistically efficient parameter estimates the issue of solution uniqueness is addressed and in particular an upper bound on the number of signals whose parameters may be uniquely identified is derived for a number of different cases typically the bound is far greater than the number of sensors and is limited only by the number of data samples collected some representative simulation examples are also included to illustrate the algorithms performance relative to the cramer rao bound

characterizations of closed loop equilibrium solutions for dynamic mean variance optimization problems abstract herein we study the dynamic mean variance portfolio optimization problems with deterministic coefficients an intrinsic characterization of closed loop equilibrium solutions is obtained for the first time our approach proposed here not only essentially differs from that in existing literature but also avoids conventional complicated convergence arguments applying the characterization obtained we prove that this optimization problem actually admits unique closed loop equilibrium solution

large system analysis of a glrt for detection with large sensor arrays in temporally white noise this paper addresses the behaviour of a classical multi antenna glrt test that allows to detect the presence of a known signal corrupted by a multi path propagation channel and by an additive temporally white gaussian noise with unknown spatial covariance matrix the paper is focused on the case where the number of sensors m is large and of the same order of magnitude as the sample size n a context which is modeled by the large system asymptotic regime m n in such a way that m n c for c 0 the purpose of this paper is to study the behaviour of a glrt statistics in this regime and to show that the corresponding theoretical analysis allows to accurately predict the performance of the test when m and n are of the same order of magnitude

extended high temperature series for the classical heisenberg model in three dimensions extended series expansions are derived for the high temperature susceptibility of the classical heisenberg model on three dimensional lattices series coefficients are presented to twelfth order for the simple cubic sc and face centred cubic fcc lattices and to eleventh order for the body centred cubic bcc lattice the results are in agreement with earlier calculations apart from a small discrepancy at the tenth order on the fcc lattice extrapolation studies on the extended series are used to obtain revised estimates for the critical points kc and the susceptibility exponent gamma on the fcc lattice the authors also investigate the possibility of a confluent non analytic correction to the dominant singularity while the coefficients are consistent with the presence of such a correction term with an exponent delta 1 of 0 55 as predicted by renormalisation group rg calculations the amplitude of the correction term appears to be very small compared with that of the first analytic correction term

critical temperatures of the d 3 s 1 2 ising model the effect of confluent corrections to scaling much attention has been paid to the d 3 s 1 2 ising model on the bcc lattice in recent years because the best high temperature series expansions were available for this lattice however in order to compare series estimates of critical exponents and temperatures with independent evaluations via the monte carlo method lattices of lower coordination number must be considered since monte carlo studies are usually made on these a study of extant susceptibility series on the fcc sc diamond and tetrahedron lattices is reported on and some comments are made on aspects of recent monte carlo analyses of the d 3 s 1 2 ising model on the sc and diamond lattices

ising universality in three dimensions a monte carlo study we investigate three ising models on the simple cubic lattice by means of monte carlo methods and finite size scaling these models are the spin 1 2 ising model with nearest neighbour interactions a spin 1 2 model with nearest neighbour and third neighbour interactions and a spin 1 model with nearest neighbour interactions the results are in accurate agreement with the hypothesis of universality analysis of the finite size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field we find that the correction to scaling amplitudes are strongly dependent on the introduction of further neighbour interactions or a third spin state in a spin 1 ising model these corrections appear to be very small this is very helpful for the determination of the universal constants of the ising model the renormalization exponents of the ising model are determined as yt 1 587 2 yh 2 4815 15 and yi 0 82 6 the universal ratio q m2 2 m4 is equal to 0 6233 4 for periodic systems with cubic symmetry the critical point of the nearest neighbour spin 1 2 model is kc 0 2216546 10

open loop equilibrium strategy for mean variance portfolio problem under stochastic volatility abstract we formulate the open loop control framework for time consistent mean variance tcmv portfolio problems in incomplete markets with stochastic volatility sv we offer the existence and uniqueness results of the tcmv equilibrium controls for general sv models and derive explicit closed form equilibrium controls for several popular models including the heston hull white and 3 2 sv models the uniqueness of the equilibrium controls are related to the mean reverting speed of the volatility and the investment horizon

on the corrections to scaling in three dimensional ising models the leading correction to scaling amplitudes for the spin 1 2 nearest neighbor sc bcc and fee ising models are considered with the particular aim of determining their signs on the basis of previous two variable series analyses by chen fisher and nickel and renormalization group 4 d expansions it is concluded that the correction amplitudes for the susceptibility correlation length specific heat and spontaneous magnetization arenegative for all three lattices thus for example the effective exponent eff t asymptotically approaches the true susceptibility exponent fromabove other earlier and more recent high temperature series and field theoretic analyses are seen to be consistent with this result however the usual nonasymptotic perturbative field theoretic approaches are essentially committed to positive correction amplitudes the question of the signs therefore relates directly to the applicability of these non asymptotic field theoretic calculations to three dimensional ising models as well as to different experimental systems

joint estimation of time delays and directions of arrival of multiple reflections of a known signal we present an efficient algorithm for estimating the time delays and the directions of arrival doas of multiple reflections of a known signal the algorithm is based on an iterative scheme that transforms the multidimensional maximum likelihood criterion into two sets of simple one dimensional 1 d maximization problems simulation results illustrating the performance of the algorithm in comparison with the cramer rao bound are included

adaptive convergence of linearly constrained beamformers based on the sample covariance matrix a statistical analysis of the adaptive convergence behavior of linearly constrained beamformers is given assuming the sample covariance estimator is used to estimate the covariance matrix the sensor data are assumed to be gaussian distributed and independent from data vector to data vector the output power and mean squared error in the absence of the desired signal are shown to be multiples of chi squared random variables the presence of the desired signal results in an excess mean squared error that is beta distributed and depends only on the signal power number of data vectors and number of adaptive degrees of freedom the expected value of the excess mean squared error resulting from the signal presence is directly proportional to the signal power and number of adaptive degrees of freedom but is inversely proportional to the number of data vectors