prime power graphs for groups of lie type abstract we associate a weighted graph g to each finite simple group g of lie type we show that with an explicit list of exceptions g determines g up to isomorphism and for these exceptions g nevertheless determines the characteristic of g this result was motivated by algorithmic considerations we prove that for any finite simple group g of lie type input as a black box group with an oracle to compute the orders of group elements g and the characteristic of g can be computed by a monte carlo algorithm in time polynomial in the input length the characteristic is needed as part of the input in a previous constructive recognition algorithm for g

on the subgroup structure of classical groups in this paper we establish a result on the subgroup structure of classical groups over algebraically closed elds and use this to give a new proof of a fundamental theorem of m aschbacher on subgroups of nite classical groups let v be a nite dimensional vector space over an algebraically closed eld k and let g be one of the classical algebraic groups sl v sp v or so v our result is a reduction theorem concerning the subgroups of g we de ne a certain collection c of natural proper subgroups of g and prove that any closed nite or in nite subgroup of g either lies in a member of c or is roughly speaking a simple group acting irreducibly on v aschbacher s result is an analogous reduction theorem for subgroups of nite classical groups we obtain this as a relatively easy consequence of our main result by taking xed points under the action of a frobenius morphism using a standard process involving lang s theorem the proof of the main result uses elementary linear algebra together with a few basic facts from the theory of algebraic groups various complications which arise in the nite group setting in as become much more straightforward in the algebraic group setting in particular questions involving extension elds do not occur and issues of conjugacy are easily settled when we descend to nite invent math 134 427 453 1998

large element orders and the characteristic of lie type simple groups we show that the three largest element orders determine the characteristic of lie type simple groups of odd characteristic this result was motivated by algorithmic needs in computations with matrix groups

an experimental comparison between maximum entropy and minimum relative entropy spectral analysis it is known that the minimum relative entropy spectral analysis mresa of j e shore and r w johnson 1980 and j e shore 1981 provides an even better power spectrum estimation than the maximum entropy spectral analysis mesa by its explicit inclusion of a prior estimate that catches certain important shape features of the unknown true power spectrum since the kinds of prior estimates that catch certain important shape features of the unknown true power spectrum are generally hard to determine a comparison between mesa and mresa is undertaken in order to justify mresa the results indicate that unless the shape information of the true spectrum is correctly caught by the prior spectrum it is safer to use mesa

tensor products are projective geometries abstract given a finite dimensional vector space v we construct a family of projective geometries whose flats are certain subspaces of v and show that there is a one to one correspondence between this family of projective geometries and the set of equivalence classes of tensor decompositions of v this provides a practical method for finding a tensor decomposition of a finite dimensional kg module or proving that no nontrivial tensor decomposition exists

simple irreducible subgroups of exceptional algebraic groups a closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup in this paper we classify all irreducible subgroups of exceptional algebraic groups g which are connected closed and simple of rank at least 2 consequences are given concerning the representations of such subgroups on various g modules for example with one exception the conjugacy classes of irreducible simple connected subgroups of rank at least 2 are determined by their composition factors on the adjoint module of g

iterative image reconstruction algorithms based on cross entropy minimization the related problems of minimizing the functionals f x alpha kl y px 1 alpha kl p x and g x alpha kl px y 1 alpha kl x p respectively over the set of vectors x or 0 are considered kl a b is the cross entropy or kullback leibler distance between two nonnegative vectors a and b iterative algorithms for minimizing both functionals using the method of alternating projections are derived a simultaneous version of the multiplicative algebraic reconstruction technique mart algorithm called smart is introduced and its convergence is proved

nonextensive triangle equality and other properties of tsallis relative entropy minimization kullback leibler relative entropy has unique properties in cases involving distributions resulting from relative entropy minimization tsallis relative entropy is a one parameter generalization of kullback leibier relative entropy in the nonextensive thermostatistics in this paper we present the properties of tsallis relative entropy minimization and present some differences with the classical case in the representation of such a minimum relative entropy distribution we highlight the use of the q product an operator that has been recently introduced to derive the mathematical structure behind the tsallis statistics one of our main results is the generalization of triangle equality of relative entropy minimization to the nonextensive case

minimum relative entropy forward probabilistic modeling the pioneering work of jaynes in bayesian maximum entropy methods has been successfully explored in many disciplines the principle of maximum entropy pme is a powerful and versatile tool of inferring a probability distribution from constraints that do not completely characterize that distribution minimum relative entropy mre is a method which has all the important attributes of the maximum entropy approach with the advantage that prior information may be easily included in this paper we use mre to determine the prior probability density function pdf of a set of model parameters based on limited information the resulting pdf is used in monte carlo simulations to provide expected values in field variables such as concentration and confidence limits we compare the probabilistic results from a traditional advection dispersion ade model based on volumetric averaging concepts with that of a model based on the assumption that the hydraulic conductivity is a stationary stochastic process the results suggest that although naff s 1990 model satisfies the observed data to a better degree than ade model the upper and lower confidence bands about the mean value are larger than the ade results this result we attribute to the fact that naff s 1990 model simply contains more parameters each of which is unknown and has to be estimated there is no statistical difference between the expected values of second spatial moments for the two models the examples presented in this paper illustrate problems associated with assigning gaussian pdfs as priors in a probabilistic model first such an assumption for the input parameters actually injects more information into the problem than may actually exist whether consciously or unconsciously this fact is borne out by comparison with minimum relative entropy theory second the output parameters as suggested from the monte carlo analysis cannot be assumed to be gaussian distributed even when the prior pdf is gaussian in form in a practical setting the significance of this result and the approximation of gaussian form would depend on the toxicity and environmental standards that apply to the problem

adaptive coded modulation for fading channels we apply coset codes to adaptive modulation in fading channels adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable therefore trellis and lattice codes designed for additive white gaussian noise awgn channels can be superimposed on adaptive modulation for fading channels with the same approximate coding gains we first describe the methodology for combining coset codes with a general class of adaptive modulation techniques we then apply this methodology to a spectrally efficient adaptive m ary quadrature amplitude modulation mqam to obtain trellis coded adaptive mqam we present analytical and simulation results for this design which show an effective coding gain of 3 db relative to uncoded adaptive mqam for a simple four state trellis code and an effective 3 6 db coding gain for an eight state trellis code more complex trellis codes are shown to achieve higher gains we also compare the performance of trellis coded adaptive mqam to that of coded modulation with built in time diversity and fixed rate modulation the adaptive method exhibits a power savings of up to 20 db

maximum entropy and spectral estimation a review the method of maximum entropy is reviewed with emphasis on its relationship to entropy rate wiener filters autoregressive processes extrapolation the levinson algorithm lattice all pole and all pass filters and stability

on the capacity of time varying channels with periodic feedback the capacity of time varying channels with periodic feedback at the transmitter is evaluated it is assumed that the channel state information csi is perfectly known at the receiver and is fed back to the transmitter at the regular time intervals the system capacity is investigated in two cases 1 finite state markov channel and 2 additive white gaussian noise channel with time correlated fading in the first case it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel in the second case the channel capacity and the optimal adaptive coding is obtained it is shown that the optimal adaptation can be achieved by a single gaussian codebook while adaptively allocating the total power based on the side information at the transmitter

a general method of minimum cross entropy spectral estimation a new general approach to estimating power spectra is presented based on minimizing a cross entropy functional involving spectral densities examples are worked out using this approach as well as shore s 5 minimum cross entropy spectral analysis mcesa and burg s 7 maximum entropy spectral analysis mesa the results show that aside from its wider applicability ease of implementation and pedagogical advantage the method performs better than mesa and equally well or better than mcesa

effective black box constructive recognition of classical groups abstract we describe a black box las vegas algorithm to construct standard generators for classical groups defined over finite fields we assume that the field has size at least 4 and that oracles to solve certain problems are available subject to these assumptions the algorithm runs in polynomial time a practical implementation of our algorithm is distributed with the computer algebra system magma

on a generalization of m group abstract in this paper we show that if for every nonlinear complex irreducible character of a finite group g some multiple of is induced from an irreducible character of some proper subgroup of g then g is solvable this is a generalization of taketa s theorem on the solvability of m group

minimal and random generation of permutation and matrix groups we prove explicit bounds on the numbers of elements needed to generate various types of finite permutation groups and finite completely reducible matrix groups and present examples to show that they are sharp in all cases the bounds are linear in the degree of the permutation or matrix group in general and logarithmic when the group is primitive they can be combined with results of lubotzky to produce explicit bounds on the number of random elements required to generate these groups with a specified probability these results have important applications to computational group theory our proofs are inductive and largely theoretical but we use computer calculations to establish the bounds in a number of specific small cases

on finite groups satisfying the permutizer condition abstract a group g satisfies the permutizer condition p if each proper subgroup h of g permutes with some cyclic subgroup not contained in h the structure of finite groups with p is studied the main result being that such groups are soluble with chief factors of order 4 or a prime the classification of finite simple groups is used as is detailed information about maximal factorizations of almost simple groups

strong involutions in finite special linear groups of odd characteristic abstract let t be an involution in gl n q whose fixed point space e has dimension k between n 3 and 2 n 3 for each g gl n q such that t t g has even order t t g contains a unique involution z g which commutes with t we prove that with probability at least c log n for some c 0 the restriction z g e is an involution on e with fixed point space of dimension between k 3 and 2 k 3 this result has implications in the analysis of the complexity of recognition algorithms for finite classical groups in odd characteristic we discuss how similar results for involutions in other finite classical groups would solve a major open problem in our understanding of the complexity of constructing involution centralisers in those groups

low dimensional projective indecomposable modules for chevalley groups in defining characteristic abstract the paper studies lower bounds for the dimensions of projective indecomposable modules for chevalley groups g in defining characteristic p the main result extending earlier one by malle and weigel 2008 determines the modules in question of dimension equal to the order of a sylow p subgroup of g we also substantially generalize a result by ballard 1978 on lower bounds for the dimensions of projective indecomposable modules and find lower bounds in some cases where ballard s bounds are vacuous

fixed point spaces in primitive actions of simple algebraic groups let g be a simple algebraic group of adjoint type acting primitively on an algebraic variety we study the dimensions of the subvarieties of fixed points of involutions in g in particular we obtain a close to best possible function f h where h is the coxeter number of g with the property that with the exception of a small finite number of cases there exists an involution t in g such that the dimension of the fixed point space of t is at least f h dim

minimum cross entropy spectral analysis the principle of minimum cross entropy minimum directed divergence minimum discrimination information minimum relative entropy is summarized discussed and applied to the classical problem of estimating power spectra given values of the autocorrelation function this new method differs from previous methods in its explicit inclusion of a prior estimate of the power spectrum and it reduces to maximum entropy spectral analysis as a special case the prior estimate can be viewed as a means of shaping the spectral estimator cross entropy minimization yields a family of shaped spectral estimators consistent with known autocorrelations results are derived in two equivalent ways once by minimizing the cross entropy of underlying probability densities and once by arguments concerning the cross entropy between the input and output of linear filters several example minimum cross entropy spectra are included

a moment based variational approach to tomographic reconstruction we describe a variational framework for the tomographic reconstruction of an image from the maximum likelihood ml estimates of its orthogonal moments we show how these estimated moments and their correlated error statistics can be computed directly and in a linear fashion from given noisy and possibly sparse projection data moreover thanks to the consistency properties of the radon transform this two step approach moment estimation followed by image reconstruction can be viewed as a statistically optimal procedure furthermore by focusing on the important role played by the moments of projection data we immediately see the close connection between tomographic reconstruction of nonnegative valued images and the problem of nonparametric estimation of probability densities given estimates of their moments taking advantage of this connection our proposed variational algorithm is based on the minimization of a cost functional composed of a term measuring the divergence between a given prior estimate of the image and the current estimate of the image and a second quadratic term based on the error incurred in the estimation of the moments of the underlying image from the noisy projection data we show that an iterative refinement of this algorithm leads to a practical algorithm for the solution of the highly complex equality constrained divergence minimization problem we show that this iterative refinement results in superior reconstructions of images from very noisy data as compared with the classical filtered back projection fbp algorithm

on conjugacy classes of maximal subgroups of finite simple groups and a related zeta function we prove that the number of conjugacy classes of maximal subgroups of bounded order in a finite group of lie type of bounded rank is bounded for exceptional groups this solves a longstanding open problem the proof uses among other tools some methods from geometric invariant theory using this result we provide a sharp bound for the total number of conjugacy classes of maximal subgroups of lie type groups of fixed rank drawing conclusions regarding the behaviour of the corresponding zeta function g s m maxg g m s which appears in many probabilistic applications more specifically we are able to show that for simple groups g and for any fixed real number s 1 g s 0 as g this confirms a conjecture made in 27 we also apply these results to prove the conjecture made in 29 that the symmetric group sn has n o 1 conjugacy classes of primitive maximal subgroups 2000 mathematics classification numbers 20e28 20g15 20d06

cross entropy approximation of structured gaussian covariance matrices we apply two variations of the principle of minimum cross entropy the kullback information measure to fit parameterized probability density models to observed data densities for an array beamforming problem with p incident narrowband point sources sensors and colored noise both approaches yield eigenvector fitting methods similar to that of the music algorithm and of the oblique transformation in factor analysis furthermore the corresponding cross entropies ce are related to the mdl model order selection criterion

a new look at entropy for solving linear inverse problems entropy based methods are widely used for solving inverse problems particularly when the solution is known to be positive here we address linear ill posed and noisy inverse problems of the form z ax n with a general convex constraint x spl isin x where x is a convex set although projective methods are well adapted to this context we study alternative methods which rely highly on some information based criteria our goal is to clarify the role played by entropy in this field and to present a new point of view on entropy using general tools and results coming from convex analysis we present then a new and broad scheme for entropic based inversion of linear noisy inverse problems this scheme was introduced by navaza in 1985 in connection with a physical modeling for crystallographic applications and further studied by dacunha castelle and gamboa 1990 important features of this paper are i a unified presentation of many well known reconstruction criteria ii proposal of new criteria for reconstruction under various prior knowledge and with various noise statistics iii a description of practical inversion of data using the aforementioned criteria and iv a presentation of some reconstruction results

resolution of singularities and modular galois theory i shall sketch a brief history of the desingularization problem from riemann thru zariski to hironaka including the part i played in it and the work on galois theory which this led me to and how that caused me to search out many group theory gurus i shall also formulate several conjectures and suggest numerous thesis problems

constructive recognition of classical groups in even characteristic abstract let g x gl d f be a classical group in its natural representation defined over a finite field f of even characteristic we present las vegas algorithms to construct standard generators for g which permit us to write an element of g as a straight line program in x and to construct an involution as a straight line program in x if f 4 then the algorithms run in time polynomial in the size of the input subject to the existence of a discrete logarithm oracle for f

representations commutative algebra and hurwitz groups abstract characteristic zero representations of the 2 3 7 triangle group in degrees up to seven are constructed by using janet s algorithm for solving polynomial equations these are used to find families of hurwitz groups i e finite epimorphic images for some varieties of representations it is investigated whether additional relations can be uniformly imposed and still result in subvarieties of representations the methods are of more general interest some remarks about the interaction of positive characteristics and characteristic zero are made

a systolic architecture for new split algorithms for arbitrary toeplitz plus hankel matrices recently new fast algorithms have been developed for computing the optimal linear least squares prediction filters for arbitrary toeplitz plus hankel covariances the authors propose a systolic architecture that can fully express the inherent concurrency of this highly parallelizable algorithm the simplification of this array structure for centrosymmetric covariances is also addressed

representations of the symmetric group which are irreducible over subgroups let f be an algebraically closed field of characteristic p and n be the symmetric group on n letters in this paper we classify all pairs g d where d is an irreducible f n module of dimension greater than 1 and g is a proper subgroup of n such that the restriction d g is irreducible provided p 3

cross entropy minimization given fully decomposable subset and aggregate constraints corresp the principle of maximum entropy and the principle of minimum cross entropy minimum directed divergence minimum discrimination information have been applied recently to problems in queuing theory and computer system performance modeling these information theoretic principles estimate probability distributions based on information in the form of known expected values in the case of queuing theory and computer system modeling the known expected values arise from rate balance equations this correspondence concerns situations in which the system state probabilities decompose into disjoint subsets and in which the known expected values are either expectations conditional on a specific subset or expectations involving aggregate subset probabilities new properties of minimum cross entropy distributions are derived and an efficient method of computing these distributions is derived computational examples are included in the case of queuing theory and computer system modeling the disjoint subsets correspond to internal device states and the aggregate probabilities correspond to overall device states the results here apply when one has both rate balance equations for device equilibrium involving internal device state probabilities as well as rate balance equations for system equilibrium involving aggregate device state probabilities

a computationally compact divergence measure for speech processing the directed divergence which is a measure based on the discrimination information between two signal classes is investigated a simplified expression for computing the directed divergence is derived for comparing two gaussian autoregressive processes such as those found in speech this expression alleviates both the computational cost reduced by two thirds and the numerical problems encountered in computing the directed divergence in addition the simplified expression is compared with the itakura saito distance which asymptotically approaches the directed divergence although the expressions for these two distances closely resemble each other only moderate correlations between the two were found on a set of actual speech data

the length and depth of algebraic groups let g be a connected algebraic group an unrefinable chain of g is a chain of subgroups g g 0 g 1 cdots g t 1 where each g i is a maximal connected subgroup of g i 1 we introduce the notion of the length respectively depth of g defined as the maximal respectively minimal length of such a chain working over an algebraically closed field we calculate the length of a connected group g in terms of the dimension of its unipotent radical r u g and the dimension of a borel subgroup b of the reductive quotient g r u g in particular a simple algebraic group of rank r has length dim b r which gives a natural extension of a theorem of solomon and turull on finite quasisimple groups of lie type we then deduce that the length of any connected algebraic group g exceeds frac 1 2 dim g we also study the depth of simple algebraic groups in characteristic zero we show that the depth of such a group is at most 6 this bound is sharp in the positive characteristic setting we calculate the exact depth of each exceptional algebraic group and we prove that the depth of a classical group over a fixed algebraically closed field of positive characteristic tends to infinity with the rank of the group finally we study the chain difference of an algebraic group which is the difference between its length and its depth in particular we prove that for any connected algebraic group g with soluble radical r g the dimension of g r g is bounded above in terms of the chain difference of g

subgroups of type a1 containing a fixed unipotent element in an algebraic group keywords simple algebraic groups unipotent elements subgroups of type a 1 frobenius morphisms graph morphisms finite groups of lie type reference ctg article 2000 003doi 10 1006 jabr 2000 8353 record created on 2008 12 16 modified on 2017 05 12

minimum cross entropy pattern classification and cluster analysis this paper considers the problem of classifying an input vector of measurements by a nearest neighbor rule applied to a fixed set of vectors the fixed vectors are sometimes called characteristic feature vectors codewords cluster centers models reproductions etc the nearest neighbor rule considered uses a non euclidean information theoretic distortion measure that is not a metric but that nevertheless leads to a classification method that is optimal in a well defined sense and is also computationally attractive furthermore the distortion measure results in a simple method of computing cluster centroids our approach is based on the minimization of cross entropy also called discrimination information directed divergence k l number and can be viewed as a refinement of a general classification method due to kullback the refinement exploits special properties of cross entropy that hold when the probability densities involved happen to be minimum cross entropy densities the approach is a generalization of a recently developed speech coding technique called speech coding by vector quantization

spectral expressions of information measures of gaussian time series and their relation to aic and cat interrelations among the spectral expressions of the information measures of kullback leibler 1959 and renyi 1961 for discrimination between two stationary gaussian time series are discussed the spectral expression of fisher s information rate matrix is also treated as well as two intuitively acceptable discrimination functions it is shown that all of them are equivalent except for scalar multiplication and are expressed by fisher s information rate matrix in the sense of their second order taylor series approximation finally a relation between two criteria for order determination of models for time series data namely h akaike s 1974 information criterion aic and the criterion of autoregressive transfer functions cat is discussed in connection with these spectral expressions

invariant forms on irreducible modules of simple algebraic groups let g be a simple linear algebraic group over an algebraically closed field k of characteristic p 0p 0 and let v be an irreducible rational g module with highest weight when v is self dual a basic question to ask is whether v has a non degenerate g invariant alternating bilinear form or a non degenerate g invariant quadratic form if p 2p 2 the answer is well known and easily described in terms of in the case where p 2p 2 we know that if v is self dual it always has a non degenerate g invariant alternating bilinear form however determining when v has a non degenerate g invariant quadratic form is a classical problem that still remains open we solve the problem in the case where g is of classical type and is a fundamental highest weight i i and in the case where g is of type alal and r s r s for 1 r s l1 r s l we also give a solution in some specific cases when g is of exceptional type as an application of our results we refine seitz s 1987 description of maximal subgroups of simple algebraic groups of classical type one consequence of this is the following result if x y sl v x y sl v are simple algebraic groups and v xv x is irreducible then one of the following holds 1 v yv y is not self dual 2 both or neither of the modules v yv y and v xv x have a non degenerate invariant quadratic form 3 p 2p 2 x so v x so v and y sp v y sp v

algorithms determining finite simple images of finitely presented groups we address the question for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection we prove both positive and negative results for a collection of finite simple groups that contains infinitely many alternating groups or contains classical groups of unbounded dimensions we prove that there is no such algorithm on the other hand for families of simple groups of lie type of bounded rank we obtain positive results for example for any fixed untwisted lie type x there is an algorithm that determines whether or not any given finitely presented group has simple images of the form x q for infinitely many q and if there are finitely many the algorithm determines them

large subgroups of simple groups abstract let g be a finite group a proper subgroup h of g is said to be large if the order of h satisfies the bound h 3 g in this note we determine all the large maximal subgroups of finite simple groups and we establish an analogous result for simple algebraic groups in this context largeness is defined in terms of dimension an application to triple factorisations of simple groups both finite and algebraic is discussed

the algorithmic theory of polycyclic by finite groups a group is said to be polycyclic by finite or a pf group for short if it has a polycyclic normal subgroup of finite index equivalently pf groups are exactly the groups which have a series of finite length whose infinite factors are cyclic by a well known theorem of p hall every pf group is finitely presented and in fact pf groups form the largest known sectionclosed class of finitely presented groups it is this fact that makes pf groups natural objects of study from the algorithmic standpoint the general aim of the algorithmic theory of pf groups can be described as the collection of information about a pf group which can in principle

iterative convex i projection algorithms for maximum entropy and minimum cross entropy computations general multiple constraint minimum cross entropy and maximum entropy problems can be solved by the iterative solution of single constraint subproblems existing theoretical results justify iterative i projection algorithms that may be computationally expedient in some cases an iterative algorithm for j e shore s ibid vol it 28 no 6 p 956 61 nov 1982 minimum cross entropy spectral analysis is developed as an example

abundant p singular elements in finite classical groups abstract in 1995 isaacs kantor and spaltenstein proved that for a finite simple classical group g defined over a field with q elements and for a prime divisor p of g distinct from the characteristic the proportion of p singular elements in g elements with order divisible by p is at least a constant multiple of 1 1 p e where e is the order of q modulo p motivated by algorithmic applications we define a subfamily of p singular elements called p abundant elements which leave invariant certain large subspaces of the natural g module we find explicit upper and lower bounds for the proportion of p abundant elements in g and prove that it approaches a positive limiting value as the dimension of g tends to infinity it turns out that the limiting proportion of p abundant elements is at least a constant multiple of the isaacs kantor spaltenstein lower bound for the proportion of all p singular elements

estimating the entropy of a signal with applications we present a new estimator of the entropy of continuous signals we model the unknown probability density of data in the form of an ar spectrum density and use regularized long ar models to identify the ar parameters we then derive both an analytical expression and a practical procedure for estimating the entropy from sample data we indicate how to incorporate recursive and adaptive features in the procedure we evaluate and compare the new estimator with other estimators based on histograms kernel density models and order statistics finally we give several examples of applications an adaptive version of our entropy estimator is applied to detection of law changes blind deconvolution and source separation

volume image registration by cross entropy optimization cross entropy ce an information theoretic measure quantifies the difference between two probability density functions this measure is applied to volume image registration when a good prior estimation of the joint distribution of the voxel values of two images in registration is available the ce can be minimized to find an optimal registration if such a prior estimation is not available one seeks the registration which gives a joint distribution different from unlikely ones as much as possible i e the ce is maximized to find an optimal registration when the unlikely distribution is a uniform one ce maximization reduces to joint entropy minimization when the unlikely distribution is proportional to one of the marginal distributions it reduces to conditional entropy minimization when the unlikely distribution is the product of two marginal distributions it degenerates to mutual information maximization these different ces are added together and are used as criteria for image registration the accuracy and robustness of this new approach are tested and compared using a likely joint distribution and various unlikely joint distributions and their combinations

channel capacity and error exponents of variable rate adaptive channel coding for rayleigh fading channels we have evaluated the information theoretical performance of variable rate adaptive channel coding for rayleigh fading channels the channel states are detected at the receiver and fed back to the transmitter by means of a noiseless feedback link based on the channel state informations the transmitter can adjust the channel coding scheme accordingly coherent channel and arbitrary channel symbols with a fixed average transmitted power constraint are assumed the channel capacity and the error exponent are evaluated and the optimal rate control rules are found for rayleigh fading channels with feedback of channel states it is shown that the variable rate scheme can only increase the channel error exponent the effects of additional practical constraints and finite feedback delays are also considered finally we compare the performance of the variable rate adaptive channel coding in high bandwidth expansion systems cdma and high bandwidth efficiency systems tdma

minimum cross entropy analysis with entropy type constraints abstract in this paper we study the cross entropy optimization problem with entropy type constraints a simple geometric inequality is used to derive its dual problem and to show the strong duality theorem we found this geometric dual is a computationally attractive canonical program that is always consistent a dual to primal conversion formula and a dual perturbation algorithm are also derived for computations

primitive permutation groups of bounded orbital diameter we give a description of infinite families of finite primitive permutation groups for which there is a uniform finite upper bound on the diameter of all orbital graphs this is equivalent to describing families of finite permutation groups such that every ultraproduct of the family is primitive a key result is that in the almost simple case with socle of fixed lie rank apart from very specific cases there is such a diameter bound this is proved using recent results on the model theory of pseudofinite fields and difference fields

topological generation of exceptional algebraic groups abstract let g be a simple algebraic group over an algebraically closed field k and let c 1 c t be non central conjugacy classes in g in this paper we consider the problem of determining whether there exist g i c i such that g 1 g t is zariski dense in g first we establish a general result which shows that if is an irreducible subvariety of g t then the set of tuples in generating a dense subgroup of g is either empty or dense in in the special case c 1 c t by considering the dimensions of fixed point spaces we prove that this set is dense when g is an exceptional algebraic group and t 5 assuming k is not algebraic over a finite field in fact for g g 2 we only need t 4 and both of these bounds are best possible as an application we show that many faithful representations of exceptional algebraic groups are generically free we also establish new results on the topological generation of exceptional groups in the special case t 2 which have applications to random generation of finite exceptional groups of lie type in particular we prove a conjecture of liebeck and shalev on the random r s generation of exceptional groups

transitive subgroups of primitive permutation groups abstract we investigate the finite primitive permutation groups g which have a transitive subgroup containing no nontrivial subnormal subgroup of g the conclusion is that such primitive groups are rather rare and that their existence is intimately connected with factorisations of almost simple groups a corollary is obtained on primitive groups which contain a regular subgroup heavily involved in our proofs are some new results on subgroups of simple groups which have orders divisible by various primes for example another corollary implies that for every simple group t apart from l 3 3 u 3 3 and l 2 p with p a mersenne prime there is a collection consisting of two or three odd prime divisors of t such that if m is a subgroup of t of order divisible by every prime in then m is divisible by all the prime divisors of t and we obtain a classification of such subgroups m

variations on a theme of steinberg abstract the steinberg tensor product theorem is a fundamental tool for studying irreducible representations of simple algebraic groups over fields of positive characteristic this paper is concerned with extending the result replacing the target group sl v by an arbitrary simple algebraic group

on restrictions of modular spin representations of symmetric and alternating groups let f be an algebraically closed field of characteristic p and h be an almost simple group or a central extension of an almost simple group an important problem in representation theory is to classify the subgroups g of h and fh modules v such that the restriction v g is irreducible for example this problem is a natural part of the program of describing maximal subgroups in finite classical groups in this paper we investigate the case of the problem where h is the schur s double cover n or s n

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

a neural net algorithm for multidimensional minimum relative entropy spectral analysis a neural net algorithm is presented to solve the general 1 d or multidimensional minimum relative entropy spectral analysis the problem is formulated as a primal constrained optimization and is reduced to solving an initial value problem of differential equation of lyapunov type the initial value problem of lyapunov system comprises the basis of the neural net algorithm experiments with simulated data convincingly showed that the algorithm did provide the multidimensional minimum relative entropy spectral estimator with the autocorrelation matching property with computational efficiency

properties of cross entropy minimization the principle of minimum cross entropy minimum directed divergence minimum discrimination information is a general method of inference about an unknown probability density when there exists a prior estimate of the density and new information in the form of constraints on expected values various fundamental properties of cross entropy minimization are proven and collected in one place cross entropy s well known properties as an information measure are extended and strengthened when one of the densities involved is the result of cross entropy minimization the interplay between properties of cross entropy minimization as an inference procedure and properties of cross entropy as an information measure is pointed out examples are included and general analytic and computational methods of finding minimum cross entropy probability densities are discussed

rate distortion speech coding with a minimum discrimination information distortion measure an information theory approach to the theory and practice of linear predictive coded lpc speech compression systems is developed it is shown that a traditional lpc system can be viewed as a minimum distortion or nearest neighbor system where the distortion measure is a minimum discrimination information between a speech process model and an observed frame of actual speech this distortion measure is used in an algorithm for computer aided design of block source codes subject to a fidelity criterion to obtain a 750 bits s speech compression system that resembles an lpc system but has a much lower rate a larger memory requirement and requires no on line lpc analysis quantitative and informal subjective comparisons are made among our system and lpc systems

jaynes principle and maximum entropy spectral estimation this paper makes use of jaynes principle to include prior information into a maximum entropy spectral estimate such information is often available but is not included in the usual maximum entropy method the paper develops an algorithm which is particularly simple to implement for equispaced correlation lags a numerical example demonstrates the effectiveness of the technique and its superiority to the usual maximum entropy method

the permutizer condition in infinite soluble groups abstract a group satisfies the permutizer condition p if each proper subgroup permutes with some cyclic subgroup not contained in it here we characterize the classes of soluble minimax groups and finitely generated soluble groups with p

estimating proportions of elements in finite groups of lie type abstract we show that certain closure properties on subsets q of a finite group g of lie type enable the ratio q g to be determined by finding the proportions of elements of q in the maximal tori of g and the proportions of certain related subsets of the weyl group we prove fundamental results about these subsets q including those necessary for moving between these groups and their automorphism groups normal subgroups and central quotients as a sample application of these new techniques we derive upper and lower bounds for the proportion of elements with order divisible by certain natural sets of primes for the finite classical groups thereby improving existing results

irreducible disconnected subgroups of exceptional algebraic groups this dissertation is concerned with the study of irreducible embeddings of simple algebraic groups of exceptional type it is motivated by the role of such embeddings in the study of positive dimensional closed subgroups of classical algebraic groups the classification of the maximal closed connected subgroups of simple algebraic groups was carried out by e b dynkin g m seitz and d m testerman their analysis for the classical groups was based primarily on a striking result if g is a simple algebraic group and o g sl v is a tensor indecomposable irreducible rational representation then with specified exceptions the image of g is maximal among closed connected subgroups of one of the classical groups sl v sp v or so v in the case of closed not necessarily connected subgroups of the classical groups one is interested in considering irreducible embeddings of simple algebraic groups and their automorphism groups given a simple algebraic group y defined over an algebraically closed field k one is led to study the embeddings g 0 g is a closed non connected positive dimensional subgroup of y and v is a nontrivial irreducible rational ky module such that v g is irreducible we obtain a precise description of such triples g y v

minimum cross entropy spectral analysis of multiple signals this paper presents a new information theoretic method for simultaneously estimating a number of power spectra when a prior estimate of each is available and new information is obtained in the form of values of the autocorrelation function of their sum one application of this method is the separate estimation of the spectra of a signal and additive noise based on autocorrelations of the signal plus noise a derivation of the method from the principle of minimum cross entropy is given and the method is compared to minimum cross entropy spectral analysis of which it is a generalization some basic mathematical properties are discussed three numerical examples are included two based oil synthetic spectra and one based on actual speech data

on irreducible subgroups of simple algebraic groups let g be a simple algebraic group over an algebraically closed field k of characteristic p geqslant 0 let h be a proper closed subgroup of g and let v be a nontrivial irreducible kg module which is p restricted tensor indecomposable and rational assume that the restriction of v to h is irreducible in this paper we study the triples g h v of this form when g is a classical group and h is positive dimensional combined with earlier work of dynkin seitz testerman and others our main theorem reduces the problem of classifying the triples g h v to the case where g is an orthogonal group v is a spin module and h normalizes an orthogonal decomposition of the natural kg module

a computer assisted analysis of some matrix groups abstract we use algorithms developed recently for the study of linear groups to investigate a sequence of matrix groups defined over gf 2 these are images of representations of certain finitely presented groups considered by soicher in a study of simplicial complexes related to the suzuki sequence graphs

invariable generation and the chebotarev invariant of a finite group a subset s of a finite group g invariably generates g if g sg s s s for each choice of g s g s s we give a tight upper bound on the minimal size of an invariable generating set for an arbitrary finite group g in response to a question in kowalski and zywina 2010 kz we also bound the size of a randomly chosen set of elements of g that is likely to generate g invariably along the way we prove that every finite simple group is invariably generated by two elements

the number of homomorphisms from finite groups to classical groups we provide upper and lower bounds for the number of completely reducible homomorphisms from a finite group to general linear and unitary groups over arbitrary finite fields and to orthogonal and symplectic groups over finite fields of odd characteristic