asymptotics of work distributions in nonequilibrium systems the asymptotic behavior of the work distribution in driven nonequilibrium systems is determined using the method of optimal fluctuations for systems described by langevin dynamics the corresponding euler lagrange equation together with the appropriate boundary conditions and an equation for the leading pre exponential factor are derived the method is applied to three representative examples and the results are used to improve the accuracy of free energy estimates based on the application of the jarzynski equation

spatial spectral filtering with linearly constrained minimum variance beamformers in this paper orthogonal low dimension models for broad band sources as observed by an array delay line structure are developed the models are termed broad band source representation spaces and are subspaces of the observation space they are generated from eigenstructures of source sample covariance matrices and represent sources efficiently in the 2nd order statistical sense for a single broad band source propagating in a pure delay environment and observed with an isotropic array an accurate indication of the model dimension is derived which is independent on the array configuration being a function of the observed source time bandwidth product only using these representations procedures are described for controlling the spatial and spectral response of linearly constrained minimum variance broad band array beamformers the procedures employ linear constraints to control complex gain characteristics over selected bands of frequency for multiple points of 3 d regions of source locations and do not require the use of steering delays the constraints are derived from source representation spaces and are termed eigenvector constraints simulations are presented which illustrate the effectiveness of the new linear constraints

a class of blocks behaving like blocks of p solvable groups abstract we define a class of blocks having similar properties to blocks of p solvable groups and show that a version of the fong swan theorem holds for irreducible brauer characters in such blocks we also show that the height of an irreducible character in such block is bounded by the exponent of the central quotient of a defect group which in particular implies that if further the defect groups are abelian then every irreducible character in the block has height zero

sub gaussian and subexponential fluctuation response inequalities sub gaussian and subexponential distributions are introduced and applied to study the fluctuation response relation out of equilibrium a bound on the difference in expected values of an arbitrary sub gaussian or subexponential physical quantity is established in terms of its sub gaussian or subexponential norm based on that we find that the entropy difference between two states is bounded by the energy fluctuation in these states moreover we obtain generalized versions of the thermodynamic uncertainty relation in different regimes operational issues concerning the application of our results in an experimental setting are also addressed and nonasymptotic bounds on the errors incurred by using the sample mean instead of the expected value in our fluctuation response inequalities are derived

blocks with trivial intersection defect groups we show that each block whose defect groups intersect pairwise trivially either has cyclic or generalised quaternion defect groups or is morita equivalent to one of a given list of blocks of central extensions of automorphism groups of non abelian simple groups in particular we classify all blocks of automorphism groups of non abelian simple groups whose defect groups are non cyclic and intersect pairwise trivially a consequence is that donovans conjecture holds for blocks whose defect groups intersect pairwise trivially

pattern optimization of a reflector antenna with planar array feeds and cluster feeds we study pattern optimization of a parabolic reflector with planar array feeds and cluster feeds the optimization is carried out within the conjugate gradient method cgm in which the optimum weight vector of a linearly constrained minimum variance lcmv beam former is used as the initial condition optimization with the cgm to determine element weights is found to yield better sidelobe suppression and true settlement of desired scan direction compared to the lcmv beam former and conjugate field matching cfm techniques for the continuous beam scanning case the proposed method is also applied to multibeam reflector antenna design

on sampling continuous aperture distributions for discrete planar arrays the theory of sampling continuous distributions for the purpose of determining planar array excitation coefficients is examined the cause of pattern degradation associated with conventional sampling is identified and a new method called integrated sampling is introduced which provides superior results implementation details are given for the specific case of a rectangular grid planar array with a roughly circular boundary numerical examples are provided for both uniform and taylor distributions in order to perform comparative studies and to demonstrate the advantages of the new technique

synthesis of modular contiguously clustered linear arrays through a sparseness regularized solver an innovative methodology for the design of modular and contiguously clustered linear arrays is proposed the approach formulates the subarraying problem as a pattern matching one in which elementary modules taken from a user defined dictionary are combined to synthesize the final antenna layout by recasting such a synthesis problem within the compressive sensing framework an efficient solver is used to determine the array architecture starting from the a priori specification of the features e g the length of the admissible subarrays a set of representative numerical experiments is discussed to assess the advantages and drawbacks of the proposed algorithm also in comparison with some state of the art methods

a simple algorithm to achieve desired patterns for arbitrary arrays a simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented the method can be applied to nonuniform array geometries in which the individual elements have arbitrary and differing radiation patterns the method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification computation of each successive pattern is based on the solution of a linearly constrained least squares problem the constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values phase values for the sidelobes do not change during this process and problems associated with choosing a specific phase value are therefore avoided experimental evidence suggests that the procedure terminates in remarkably few iterations even for arrays with significant numbers of elements

optimum weighted smoothing in finite data the authors consider a generalized smoothing problem and develop a procedure to obtain a set of optimum weights which gives minimum mean squared error in the estimates of directions of arrival doas of signals in finite data when the signals are arbitrarily correlated using the optimum weights they study the optimum tradeoff between the number of subarrays and the subarray size for a fixed total size of the array the computation of optimum weights however requires full knowledge of the scenario since exact doas powers and correlations of signals are unknown a priori a method for estimating these weights from the observed finite data is given it is shown through empirical studies that the optimum weights can be approximated by taylor weights which serve as near optimum weights simulation results are included to support the theoretical assertions

perfect generalized characters inducing the alperin mckay conjecture it is well known that the perfect isometries predicted in broue s conjecture do not always exist when the defect groups are non abelian even when the blocks have equivalent brauer categories we consider perfect generalized characters which induce bijections between the sets of irreducible characters of height zero of a block and of its brauer correspondent in the normalizer of a defect group in this way the perfect isometries predicted in broue s conjecture for blocks with abelian defect groups are generalized whilst such generalized characters do not exist in general we show that they do exist when the defect groups are non abelian trivial intersection subgroups of order p 3 as well as for 2b 2 q for q a power of two and psu 3 q for all q further we show that these blocks satisfy a generalized version of an isotypy

work fluctuations in a time dependent harmonic potential rigorous results beyond the overdamped limit we investigate the stochastic motion of a brownian particle in the harmonic potential with a time dependent force constant it may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a time dependent field we use the path integral formalism to solve the langevin equation and the associated fokker planck kramers equation rigorous relations are derived to generate the probability density function for the time dependent nonequilibrium work production beyond the overdamped limit we find that the work distribution exhibits an exponential tail with a power law prefactor accompanied by an interesting oscillatory feature multiple pseudo locking unlocking transitions due to the inertial effect some exactly solvable cases are discussed in the overdamped limit

approximate synthesis of nonseparable design responses for rectangular arrays a method is presented for the approximation of any real symmetrical nonseparable array design response polynomial of order m 1 by n 1 for rectangular arrays with m by n uniformly spaced elements m geq n previously a sampling method has been used to exactly synthesize response functions of a single variable by n element line arrays 1 and nonseparable functions of two variables by n times n square arrays the sampling method is extended herein to apply to rectangular arrays by deriving the element weights for an m by n rectangular array that exactly yield the values of any desired real symmetrical array response function on an m by n grid of the interelement phase shifts this would yield the designed array response exactly everywhere if the design equation were of order m 1 with respect to one dimension and of order n 1 with respect to the other dimension to approximate this condition the original design function of order n 1 in both dimensions is modified to make it of order m 1 in one dimension and of order n 1 along a single grid line in the other dimension a second function is derived with these roles reversed the resulting function has the form of the original design function exactly equaling it along the n grid lines of m points each and along the single perpendicular chosen grid line of n points and closely approximating it throughout the entire range of the variables this technique is illustrated for chebyshev response functions for which the two approximating functions are derived and evaluated for several combinations of m and n the responses are shown to have generally uniform sidelobe regions with all but a small percentage of the sidelobes within 1 db of the designed sidelobe value

fluctuation properties of an effective nonlinear system subject to poisson noise we study the work fluctuations of a particle confined to a moving harmonic potential under the influence of friction and external asymmetric poissonian shot noise this type of noise generalizes the usual gaussian noise and induces an effective interaction between the noise and the potential leading to an effectively nonlinear system with singular features on the basis of an analytic solution we investigate the roles of time scales symmetries and singularities in the context of nonequilibrium fluctuations our results highlight the nonuniversality of the steady state fluctuation theorem in stochastic systems

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

minimum variance beamforming with phase independent derivative constraints a set of first and second order derivative constraints that can be used in minimum variance beamformers to achieve flat main beam response is presented efficient algorithms are derived for the implementation of these constraints in contrast to conventional derivative constraint methods which constrain both the magnitude power and phase responses of the beamformer the method only constrains the magnitude response the unnecessary constraint on the phase is a major drawback to the conventional methods since it causes the beamformer performance to vary with the particular spatial reference point used to define the array element positions this phenomenon is clearly undesirable because the choice of a reference point is generally made for notational convenience as a direct sequence of the phase constraint an inappropriately chosen reference point can easily result in a beamformer response which has undesirably high sidelobes the problem is avoided through the use of phase independent derivative constraints

pattern synthesis with multipoint accurate array response control in this paper the problem of pattern synthesis with antenna arrays is addressed and new approaches based on the recently developed accurate array response control textrm a 2 textrm rc algorithm are presented it is shown that the array weight vector obtained by the textrm a 2 textrm rc algorithm to control the normalized response at a single direction in each step belongs to a specific set thus an appropriate weight vector chosen from the intersection of weight vector sets corresponding to the desired responses at multiple directions is capable of simultaneously controlling those responses this results in the so called multipoint accurate array response control textrm ma 2 textrm rc algorithm moreover in order to avoid possible beam axis shift in pattern synthesis a modified textrm ma 2 textrm rc textrm m 2 textrm a 2 textrm rc algorithm is proposed by imposing a derivative constraint on the direction of beam axis representative numerical examples are provided to demonstrate the effectiveness of the proposed textrm ma 2 textrm rc and textrm m 2 textrm a 2 textrm rc algorithms for multipoint responses control and pattern synthesis

a flexible array synthesis method using quadratic programming a highly flexible synthesis method for an arbitrary array is proposed to best approximate a desired array pattern in a minimum mean square error sense the basic idea of the technique is to form a quadratic program with its cost function given by the mean square error between the array response and a properly selected pattern described by a known mathematical function this quadratic program can be a constrained or unconstrained optimization problem depending on the requirements of the desired array pattern in formulating the quadratic program no assumption has been made on the gain phase response or characteristics of the individual array elements therefore one can synthesize an array of arbitrary shape to any appropriate pattern with the characteristic of the array elements taken into consideration as long as one is able to model the array accurately the proposed method is used to synthesize arrays of different shapes linear as well as planar arrays including rectangular and circular planar arrays using a chebyshev polynomial or zero function as a design template to illustrate the feasibility of the proposed method

a hybrid approach to the synthesis of subarrayed monopulse linear arrays in this paper a hybrid approach for the synthesis of the ldquooptimalrdquo compromise between sum and difference patterns for subarrayed monopulse antennas is presented first the subarray configuration is determined by exploiting the knowledge of the optimum difference mode coefficients to reduce the dimension of the searching space in the second step the subarray weights are computed by means of a convex programming procedure which takes advantages from the convexity for a fixed clustering of the problem at hand a set of representative results is reported to assess the effectiveness of the proposed approach comparisons with state of the art techniques are also presented

a multi objective approach to subarrayed linear antenna arrays design based on memetic differential evolution in this paper we present a multi objective optimization approach to subarrayed linear antenna arrays design we define this problem as a bi objective one we consider two objective functions for directivity maximization and sidelobe level minimization memetic algorithms mas are hybrid algorithms that combine the benefits of a global search evolutionary algorithm ea with a local search method in this paper we introduce a new memetic multi objective evolutionary algorithm namely the memetic generalized differential evolution mgde3 this algorithm is a memetic extension of the popular generalized differential evolution gde3 algorithm another popular moea is the nondominated sorting genetic algorithm ii nsga ii mgde3 gde3 and nsga ii are applied to the synthesis of uniform and nonuniform subarrayed linear arrays providing an extensive set of solutions for each design case depending on the desired array characteristics the designer can select the most suitable solution the results of the proposed method are compared with those reported in the literature indicating the advantages and applicability of the multi objective approach

equilibrium free energies from nonequilibrium measurements using maximum likelihood methods we present a maximum likelihood argument for the bennett acceptance ratio method and derive a simple formula for the variance of free energy estimates generated using this method this derivation of the acceptance ratio method using a form of logistic regression a common statistical technique allows us to shed additional light on the underlying physical and statistical properties of the method for example we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements

pattern characteristics of linear arrays using the constrained least squares distribution the constrained least squares cls distribution is a method for obtaining distribution functions that yield low sidelobe patterns with specified constraints on the aperture efficiency and are especially useful for the transmit patterns of active array antennas the widely used taylor distribution optimizes only pattern performance while the cls distribution optimizes pattern performance while taking into account the constraints on both the peak element amplitude and the total effective radiated voltage erv of the aperture distribution the paper compares the pattern characteristics of linear arrays with cls and taylor distributions the results help to establish guidelines on when a cls distribution would be preferable over a taylor distribution when a specified aperture efficiency is important

a numerical pattern synthesis algorithm for arrays a numerical technique for pattern synthesis in arrays is presented for a given set of elements the technique allows one to find a set of array coefficients that steer the main beam in a given direction and yield sidelobes meeting a specified criterion if such a set of array coefficients exists if the pattern specifications cannot be met with the given elements the algorithm finds the best attainable pattern the advantage of this technique is that it can be used with an arbitrary set of array elements different elements in the array can have different element patterns and the array can have arbitrary nonuniform spacing between elements the synthesis technique is based on adaptive array theory the given array elements are assumed to be used as the elements of an adaptive array the main beam is pointed in the proper direction by choosing the steering vector for that direction and the sidelobes are controlled by introducing a large number of interfering signals at many angles throughout the sidelobe region the algorithm iterates on the interference powers until a suitable pattern is obtained

numerical synthesis of arbitrary discrete arrays a numerical algorithm for the synthesis of arbitrary discrete arrays is given the technique is based on the algorithm of c a olen and r t compton 1990 but employs a different iterative recursive algorithm yielding an optimum convergence rate it is shown that the new algorithm converges to the optimum solution in a significantly reduced number of iterations compared with the technique of olen and compton use of the technique is illustrated by applying the synthesis procedure to a ten element linear array and to a conformal array consisting of ten dipoles located on a parabolic curve

taylor patterns for discrete arrays the equivalent of a taylor pattern for continuous apertures is developed for discrete arrays this array factor can be realized exactly since it belongs to the appropriate class of patterns a method for determining the element excitations is also presented as an example the pattern and excitations are calculated for a 41 element array with bar n 6 and a 25 db design sidelobe level comparison is made with the patterns obtained by applying root matching and sampling of a continuous taylor aperture

optimized weighting of uniform subarrays of unequal sizes amplitude weighting at the subarray outputs alone causes grating lobes in array factors an approach that disrupts the periodic quantization by dividing the array into subarrays of unequal sizes and amplitude weighting at the subarray ports is presented a hybrid genetic algorithm optimizes the subarray size and subarray weights to minimize the maximum sidelobe level

an adaptive generalized sidelobe canceller with derivative constraints an adaptive broad band beamforming structure is presented which employs a gradient based weight adjustment algorithm to minimize output variance subject to a set of j linear constraints on broadband directional derivatives in the desired look direction a generalized sidelobe cancelling structure is employed in which a nonadaptive conventional beamformer operates in parallel with an adaptive beamformer the conventional portion has a broad band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped delay line filters blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped delay lines as a result an unconstrained least mean square lms power minimization algorithm is employed to adapt the delay line weights it is shown that with the addition of the directional derivative constraints the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints a design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented

state dependent diffusion thermodynamic consistency and its path integral formulation the friction coefficient of a particle can depend on its position as it does when the particle is near a wall we formulate the dynamics of particles with such state dependent friction coefficients in terms of a general langevin equation with multiplicative noise whose evaluation requires the introduction of specific rules two common conventions the ito and the stratonovich provide alternative rules for evaluation of the noise but other conventions are possible we show that the requirement that a particle s distribution function approach the boltzmann distribution at long times dictates that a drift term must be added to the langevin equation this drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise we explore the consequences of this result in a number of examples with spatially varying diffusion coefficients we also derive a path integral representation for arbitrary interpretation of the noise and use it in a perturbative study of correlations in a simple system

path integral analysis of jarzynski s equality analytical results we apply path integrals to study nonequilibrium work theorems in the context of brownian dynamics deriving in particular the equations of motion governing the most typical and most dominant trajectories for the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time dependent natural frequency we find such trajectories evaluate the work weighted propagators and validate jarzynski s equality

on the generalization of taylor and bayliss n bar array distributions taylor s asymptotic analysis theory is used to design the generalized taylor and bayliss patterns such a design technique allows generating array factors with arbitrary sidelobe level and envelope taper for both the taylor and bayliss patterns array excitation is obtained by the elliott s pattern zero matching technique a few examples are provided to validate the presented theory also variation of different array characteristics with respect to the sidelobe tapering is explained through graphical data

a new low side lobe pattern synthesis technique for conformal arrays the application of the new nonlinear optimization algorithms to array design is demonstrated by the low side lobe pattern synthesis of conformal arrays by adopting the information of array element realized gain patterns the authors formulate synthesis problems as nonlinearly constrained optimization problems and propose a direct method to solve them the technique allows them to find a set of array coefficients that yield a pattern meeting a specified side lobe level and achieving the maximum directivity if such a set of array coefficients exists if the side lobe specifications cannot be met with the given array the technique will result in a set of coefficients that yield a pattern meeting the best attainable side lobe level and having directivity as high as possible simplified synthesis problems for an axial dipole array in an infinite perfectly conducting cylinder are discussed and numerical results are given the synthesis technique works for general array patterns

the mckay conjecture and brauer s induction theorem let g be an arbitrary finite group the mckay conjecture asserts that g and the normaliser ng p of a sylow p subgroup p in g have the same number of characters of degree not divisible by p that is of p degree we propose a new refinement of the mckay conjecture which suggests that one may choose a correspondence between the characters of p degree of g and ng p to be compatible with induction and restriction in a certain sense this refinement implies in particular a conjecture of isaacs and navarro we also state a corresponding refinement of the broue abelian defect group conjecture we verify the proposed conjectures in several special cases

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

an effective approach for the optimal focusing of array fields subject to arbitrary upper bounds a new approach to the optimal focusing of array fields subject to arbitrary upper bounds is presented the approach formulates the problem as the minimization of a linear function in a convex set unlike other approaches this one guarantees the achievement of the global optimum by using local optimization techniques and can moreover deal with any convex constraint on the unknowns such as near field constraints optimization is performed by two ad hoc developed solution algorithms which exploit the geometrical characteristics of the problem at hand thus leading to extremely effective and computationally efficient numerical codes an extensive numerical analysis has been performed in all cases of linear planar and circular arc arrays the enhanced performance of the proposed technique with respect to the solution algorithms available in the literature fully confirms the effectiveness of the approach

sparsening conformal arrays through a versatile bcs based method sparsening conformal arrangements is carried out through a versatile multi task bayesian compressive sensing mt bcs strategy the problem formulated in a probabilistic fashion as a pattern matching synthesis is that of determining the sparsest excitation set locations and weights fitting a reference pattern subject to user defined geometrical constraints results from a set of representative numerical experiments are presented to illustrate the key features of the proposed approach as well as to assess also through comparisons its potentials in terms of matching accuracy element saving and computational costs

inverse scattering using a joint l1 l2 norm based regularization inverse scattering problems suffer from ill posedness and ill conditioning necessitating the use of regularization methods to get meaningful solutions commonly used regularizations are l2 norm based but these generate over smooth solutions we propose a regularization method using both the l1 and l2 norms to obtain sharp object boundaries while also achieving good interior reconstruction of the object permittivity knowledge about the permittivity can also be used as a priori information the applicability of the method is demonstrated on synthetically generated data for two dimensional 2 d microwave imaging using the born iterative method bim the optimization routine systematically estimates all parameters while minimizing the cost function different objects chosen to represent realistic features have been considered to evaluate the performance the reconstructed images indicate that the method can produce accurate object localization shape identification and good permittivity estimation

on finite groups of p local rank one and conjectures of dade and robinson abstract we use the classification of finite simple groups to demonstrate that conjecture 4 1 of g r robinson 1996 proc london math soc 3 72 312 330 and dade s projective conjecture hold for finite groups of p local rank one

stationary and transient work fluctuation theorems for a dragged brownian particle recently wang et al carried out a laboratory experiment where a brownian particle was dragged through a fluid by a harmonic force with constant velocity of its center this experiment confirmed a theoretically predicted work related integrated transient fluctuation theorem itft which gives an expression for the ratio for the probability to find positive or negative values for the fluctuations of the total work done on the system in a given time in a transient state the corresponding integrated stationary state fluctuation theorem issft was not observed using an overdamped langevin equation and an arbitrary motion for the center of the harmonic force all quantities of interest for these theorems and the corresponding nonintegrated ones tft and ssft respectively are theoretically explicitly obtained in this paper while the tft and the itft are satisfied for all times the ssft and the issft only hold asymptotically in time suggestions for further experiments with arbitrary velocity of the harmonic force and in which also the issft could be observed are given in addition a nontrivial long time relation between the itft and the issft was discovered which could be observed experimentally especially in the case of a resonant circular motion of the center of the harmonic force

near field radar imaging via compressive sensing a novel two dimensional 2 d compressive sensing cs based method is presented for near field radar imaging first an accurate near field approximation is proposed based on which the circular wavefront curvature of spherical waves can be compensated by mapping the images to a rectified new grid more importantly the near field approximation makes the two dimensions of the scattered data separable for the range and cross range directions which makes it possible to solve the 2 d reflectivity matrix for the image reconstruction directly then a 2 d proximal subgradient algorithm for near field radar imaging based on a fast iterative shrinkage thresholding algorithm fista is introduced to resolve the memory usage and computation time issues simulation and experimental results are provided to demonstrate the performance of the proposed method with comparisons to the traditional fourier based method and to the conjugate gradient cg based method which proves that the proposed method is an effective way to solve the near field radar imaging problem

on ti and ti defect blocks abstract we show that every trivial intersection block of a finite group as introduced by j l alperin and m broue 1979 ann of math 110 143 157 has trivial intersection ti defect groups but that the converse is not true in general we then present some conditions equivalent to b being a ti block generalizing the idea of a k generated p core to b subgroups in particular we give further weight to olsson s assertion that ti blocks are a better generalization of groups with ti sylow p subgroups than are ti defect blocks finally we describe the role of the generalized k generated p core in the control of fusion of subpairs

new refinements of the mckay conjecture for arbitrary finite groups let g be an arbitrary finite group and fix a prime number p the mckay conjecture asserts that g and the normalizer in g of a sylow p subgroup have equal numbers of irreducible characters with degrees not divisible by p the alperin mckay conjecture is version of this as applied to individual brauer p blocks of g we offer evidence that perhaps much stronger forms of both of these conjectures are true

instantons and intermittency we describe the method for finding the non gaussian tails of the probability distribution function pdf for solutions of a stochastic differential equation such as the convection equation for a passive scalar the random driven navier stokes equation etc the existence of such tails is generally regarded as a manifestation of the intermittency phenomenon our formalism is based on the wkb approximation in the functional integral for the conditional probability of large fluctuation we argue that the main contribution to the functional integral is given by a coupled field force configuration char22 the instanton as an example we examine the correlation functions of the passive scalar u advected by a large scale velocity field ensuremath delta correlated in time we find the instanton determining the tails of the generating functional and show that it is different from the instanton that determines the probability distribution function of high powers of u we discuss the simplest instantons for the navier stokes equation textcopyright 1996 the american physical society

large deviations conditioned on large deviations i markov chain and langevin equation we present a systematic analysis of stochastic processes conditioned on an empirical observable q t defined in a time interval 0 t for large t we build our analysis starting with a discrete time markov chain results for a continuous time markov process and langevin dynamics are derived as limiting cases in the large t limit we show how conditioning on a value of q t modifies the dynamics for a langevin dynamics with weak noise and conditioned on q t we introduce large deviation functions and calculate them using either a wkb method or a variational formulation this allows us in particular to calculate the typical trajectory and the fluctuations around this trajectory when conditioned on a certain value of q t for large t

design of subarrayed linear and planar array antennas with sll control based on an excitation matching approach in this paper the synthesis of subarrayed antennas with subarrays having different weights and dimensions is considered the problem is formulated as the definition of the element clustering into spatially contiguous subarrays and the corresponding weights to obtain a pattern with the lowest i e minimum achievable sidelobe level sll the problem is addressed with an unconstrained approach based on an excitation matching method where the synthesis of subarray weights and sizes is simultaneously carried out successively a hybrid version of such an approach is proposed to directly enforce into the optimization procedure the sll constraints a set of representative results concerned with both sum and difference patterns are shown furthermore some comparisons with state of the art hybrid evolutionary based techniques are reported as well

rare events and the convergence of exponentially averaged work values equilibrium free energy differences are given by exponential averages of nonequilibrium work values such averages however often converge poorly as they are dominated by rare realizations i show that there is a simple and intuitively appealing description of these rare but dominant realizations this description is expressed as a duality between forward and reverse processes and provides both heuristic insights and quantitative estimates regarding the number of realizations needed for convergence of the exponential average analogous results apply to the equilibrium perturbation method of estimating free energy differences the pedagogical example of a piston and gas r c lua and a y grosberg j phys chem b 109 6805 2005 is used to illustrate the general discussion

error correction on a tree an instanton approach we introduce a method that allows analytical or semianalytical estimating of the post error correction bit error rate ber when a forward error correction is utilized for transmitting information through a noisy channel the generic method that applies to a variety of error correction schemes in the regimes where the ber is low is illustrated using the example of a finite size code approximated by a treelike structure exploring the statistical physics formulation of the problem we find that the ber decreases with the signal to noise ratio nonuniformly i e crossing over through a sequence of phases the higher the signal to noise ratio the lower the symmetry of the phase dominating ber the last 50 years have witnessed a tremendous increase in the amount of data transmitted through various communication systems this also leads to tightening of the conditions for error free data transfer in the presence of noise and other transmission related impairments the problem of dealing with errors in information flow has a fundamental importance and has been studied extensively in information and coding theory in 1948 shannon 1 proved that applying an error corrected code can result in an error free communication in the thermodynamic limit of an infinitely long message as long as the rate of transmitted information is kept below a certain value known as the channel capacity constructing well performing capacity approaching yet practical codes has been a challenge until the discovery that some classes of codes based on random construction 2 can achieve near optimum performance when used for transmission over white additive gaussian noise channels 3 in the past few years several codes have been designed with performances very close to this limit 4 generally these codes are referred to as codes on graphs and their prime examples are low density parity check ldpc codes and turbo codes a linear block code for which ldpc codes are an example can be represented as the set

an innovative approach based on a tree searching algorithm for the optimal matching of independently optimum sum and difference excitations an innovative approach for the optimal matching of independently optimum sum and difference patterns through sub arrayed monopulse linear arrays is presented by exploiting the relationship between the independently optimal sum and difference excitations the set of possible solutions is considerably reduced and the synthesis problem is recast as the search of the best solution in a noncomplete binary tree towards this end a fast resolution algorithm that exploits the presence of elements more suitable to change subarray membership is presented the results of a set of numerical experiments are reported in order to validate the proposed approach pointing out its effectiveness also in comparison with state of the art optimal matching techniques

extended heat fluctuation theorems for a system with deterministic and stochastic forces heat fluctuations over a time tau in a nonequilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components a brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity using a langevin equation we find the exact fourier transform of the distribution of these fluctuations for all tau by a saddle point method we obtain analytical results for the inverse fourier transform which for not too small tau agree very well with numerical results from a sampling method as well as from the fast fourier transform algorithm due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid the conventional heat fluctuation theorem is for infinite and for finite tau replaced by an extended fluctuation theorem that differs noticeably and measurably from it in particular for large fluctuations the ratio of the probability for absorption of heat by the particle from the fluid to the probability to supply heat by the particle to the fluid is much larger here than in the conventional fluctuation theorem

complex weight sparse linear array synthesis by bayesian compressive sampling an innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed in the framework of sparseness constrained optimization the approach exploits the multi task mt bayesian compressive sensing bcs theory to enable the design of complex non hermitian layouts with arbitrary radiation and geometrical constraints by casting the pattern matching problem into a probabilistic formulation a relevance vector machine rvm technique is used as solution tool the numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability flexibility and numerical efficiency of the mt bcs approach also in comparison with state of the art sparse arrays synthesis methods