a general theory of canonical induction formulae abstract so far there exist three independent constructions of two different canonical versions of brauer s induction theorem for complex characters due to v snaith p symonds and the author canonical in this context means functorial with respect to restrictions along group homomorphisms in this article we axiomatize the situation in which the above canonical induction formulae are constructed mackey functors and related structures arise in this way naturally as a convenient language this approach allows us to construct canonical induction formulae for arbitrary mackey functors in particular we obtain canonical induction formulae for the brauer character ring the group of projective characters the ring of trivial source modules and the ring of linear source modules in most cases it is not difficult to construct such formulae over the rational numbers a much more subtle question is whether the constructed formula comes from a canonical induction formula defined over the integers we give a sufficient condition in the general framework of mackey functors for a canonical induction formula to be integral as an application we show how canonical induction formulae allow the construction of functorial maps on representation rings in terms of functorial maps on subrings as for example the span of linear characters in the case of the canonical brauer induction formula this will be used in a subsequent article in the case of adams operations and chern classes

isomorphic rings of monomial representations abstract let d g and d g be the rings of monomial representations of finite groups g and g of odd order we prove that the isomorphy d g d g implies the isomorphy b g b g of the respective burnside rings moreover we prove that the isomorphy d g d g with finite z groups g and g i e groups which have only cyclic sylow subgroups implies the isomorphy g g in particular a group g of squarefree order is uniquely determined up to isomorphy by the ring d g

monomial resolutions of trivial source modules abstract for trivial source modules admitting a filtration related to their generalized brauer constructions a resolution in terms of monomial modules is given which provides a categorical interpretation for the canonical induction formula applied to these modules

the ring of equivariant vector bundles on finite sets abstract for a finite group we define a ring of equivariant vector bundles on finite sets which is an expanded version of the green ring of representations of the group we give a new proof of a decomposition of this ring into a direct sum of ideals we use this decomposition to present boltje s derivation of an explicit formula for conlon induction we show that some properties of characters of the green ring have analogs for this ring of vector bundles

fibred permutation sets and the idempotents and units of monomial burnside rings we study the units of monomial burnside rings and the idempotents of monomial burnside algebras introducing a tenduction map we realise the unit group and the torsion unit group as a mackey functor

a transform tree code for stationary gaussian sources a new tree code is introduced for discrete time stationary gaussian sources with hounded integrable power spectra and the squared error distortion measure the codewords in the tree are reconstructions of karhunen loeve transforms of the source words the branching factor and the number of code letters per branch may vary with level in the tree a theorem that guarantees the existence of an optimal code for any code rate using such a tree is proved the proof uses the random coding argument in conjunction with a theorem on survival of a branching process with random environment a suboptimal but computationally affordable realization of the theorem s coding technique was used for encoding simulations for six autoregressive sources at rates of 1 0 0 50 0 25 and 0 10 bits per source symbol the average distortion results were generally within 1 db of the distortion rate bound but varied widely depending on the source and rate the results were compared with those for transform quantization simulations for the same sources and rates the tree code always performed better but only by an average of 0 44 db all sources and rates longer source blocks and more intensive search would certainly improve the performance of the tree codes but at the expense of extra computation and storage

vector scalar classification for transform image coding this paper introduces vector scalar classification vsc for discrete cosine transform dct coding of images two main characteristics of vsc differentiate it from previously proposed classification methods first pattern classification is effectively performed in the energy domain of the dct subvectors using vector quantization second the subvectors instead of the dct vectors are mapped into a prescribed number of classes according to a pattern to class link established by scalar quantization simulation results demonstrate that the dct coding systems based on vsc are superior to the other proposed dct coding systems and are competitive compared to the best subband and wavelet coding systems reported in the literature

multifractal characterization of protein contact networks abstract the multifractal detrended fluctuation analysis of time series is able to reveal the presence of long range correlations and at the same time to characterize the self similarity of the series the rich information derivable from the characteristic exponents and the multifractal spectrum can be further analyzed to discover important insights into the underlying dynamical process in this paper we employ multifractal analysis techniques in the study of protein contact networks to this end initially a network is mapped to three different time series each of which is generated by a stationary unbiased random walk to capture the peculiarities of the networks at different levels we accordingly consider three observables at each vertex the degree the clustering coefficient and the closeness centrality to compare the results with suitable references we consider also instances of three well known network models and two typical time series with pure monofractal and multifractal properties the first result of notable interest is that time series associated to protein contact networks exhibit long range correlations strong persistence which are consistent with signals in between the typical monofractal and multifractal behavior successively a suitable embedding of the multifractal spectra allows to focus on ensemble properties which in turn gives us the possibility to make further observations regarding the considered networks in particular we highlight the different role that small and large fluctuations of the considered observables play in the characterization of the network topology

infection promotes species coexistence rock paper scissors game with epidemic on graphs abstract we combine the rock paper scissors rps game with sis epidemic model we study the effect of infection on population dynamics of rps games with epidemic by using the metapopulation dynamic model on graphs via infection an individual r changes to i with infection rate an infected individual i returns to r with recovery rate all agents move by random walk between patches subpopulations and the rps game with epidemic is performed in each patch the dynamics are represented by the reaction diffusion equations in diffusively coupled reactors we obtain the solutions of the reaction diffusion equations for the mean field dynamics in a single patch analytically the numerical solutions are obtained for metapopulation dynamics on graphs with three nodes the analytical solutions are also obtained for metapopulation dynamics on complete graph when the recovery rate is lower than the critical value infected individuals survive the dynamics exhibit stable focuses and all species coexist infection promotes the coexistence of species

a generalized brauer construction and linear source modules for a complete discrete valuation ring 0 with residue field f a subgroup h of a finite group g and a homomorphism p h ox we define a functor v 4 v h p from the category of og modules to the category of fng h p modules and investigate its behaviour with respect to linear source modules

ring of subquotients of a finite group ii pure bisets abstract this sequel to o coskun 2009 6 focuses on the structure of the ring g of subquotients of the finite group g we show that this ring is isomorphic with the grothendieck ring of the category of pure g g bisets which are bisets containing no isogations we also determine over a field of characteristic zero the mackey functor structure and the primitive idempotents of g main tool of this determination is the marks of subquotients on each other

alcahestic subalgebras of the alchemic algebra and a correspondence of simple modules the unified treatment of the five module theoretic notions transfer inflation transport of structure by an isomorphism deflation and restriction is given by the theory of biset functors introduced by bouc in this paper we construct the algebra realizing biset functors as representations the algebra has a presentation similar to the well known mackey algebra we adopt some natural constructions from the theory of mackey functors and give two new constructions of simple biset functors we also obtain a criterion for semisimplicity in terms of the biset functor version of the mark homomorphism the criterion has an elementary generalization to arbitrary finite dimensional algebras over a field

on hurst exponent estimation under heavy tailed distributions abstract in this paper we show how the sampling properties of the hurst exponent methods of estimation change with the presence of heavy tails we run extensive monte carlo simulations to find out how rescaled range analysis r s multifractal detrended fluctuation analysis m f d f a detrending moving average d m a and generalized hurst exponent approach g h e estimate hurst exponent on independent series with different heavy tails for this purpose we generate independent random series from stable distribution with stability exponent changing from 1 1 heaviest tails to 2 gaussian normal distribution and we estimate the hurst exponent using the different methods r s and g h e prove to be robust to heavy tails in the underlying process g h e provides the lowest variance and bias in comparison to the other methods regardless the presence of heavy tails in data and sample size utilizing this result we apply a novel approach of the intraday time dependent hurst exponent and we estimate the hurst exponent on high frequency data for each trading day separately we obtain hurst exponents for s p500 index for the period beginning with year 1983 and ending by november 2009 and we discuss the surprising result which uncovers how the market s behavior changed over this long period

brauer relations for finite groups in the ring of semisimplified modular representations abstract let g be a finite group and p be a prime we study the kernel of the map between the burnside ring of g and the grothendieck ring of f p g modules taking a g set to its associated permutation module we are able for all finite groups to classify the primitive quotient of the kernel that is for each g the kernel modulo elements coming from the kernel for proper subquotients of g we are able to identify exactly which groups have non trivial primitive quotient and we give generators for the primitive quotient in the soluble case

distributions of the two dimensional dct coefficients for images for a two dimensional discrete cosine transform dct image coding system there have been different assumptions concerning the distributions of the transform coefficients this paper presents results of distribution tests that indicate that for many images the statistics of the coefficients are best approximated by a gaussian distribution for the dc coefficient and a laplacian distribution for the other coefficients furthermore from a simulation of the dct coding system it is shown that the assumption that the coefficients are laplacian yields a higher actual output signal to noise ratio and a much better agreement between theory and simulation than the gaussian assumption

foncteurs d ensembles munis d une double action resume sommaire 1 introduction 2 notations generalites 3 ensembles munis d une double action 3 1 notations 3 2 formule de mackey 3 3 decomposition d un morphisme 3 4 sous categories 3 4 1 ensembles p q libres 3 4 2 groupes reductifs 4 foncteurs simples 5 une theorie de vortex et de source 6 une seconde theorie de vortex et source 7 le foncteur de burnside 7 1 un homomorphisme deb g dans end g 7 2 les sous foncteurs du foncteur de burnside en caracteristique 0 7 2 1 premier exemple 7 2 2 les constantesmg n 7 2 3 lesb groupes 7 2 4 les sous foncteurs deb 7 2 5 exemples deb groupes 8 exemples de foncteurs simples 8 1 le cas des foncteurs de mackey globaux 8 2 les foncteurssh k 8 3 certains foncteurs simples en caracteristique 0 9 l algebreegg end g egg 9 1 une base naturelle 9 2 multiplication 9 3 semi simplicite 10 le foncteur des representations complexes 10 1 caracteres 10 2 sous foncteurs et decomposition 10 3 semi simplicite

some remarks on g functors and the brauer morphism keywords finite group g functor restriction maps transfer maps mackey s formula frobenius reciprocity brauer morphism defect base nilpotent ideal burnside ring idempotent formula induction formula symmetric g functor character ring green ring reference ctg article 1988 003 record created on 2008 12 16 modified on 2017 05 12

toward a multilevel representation of protein molecules computational intelligence methods are typically designed according to the assumption that the input space is essentially a vector space when departing from vector based pattern representations many theoretical and practical problems arise which are mostly due to the absence of an intuitive geometric interpretation of the data however since such representations could offer additional insights when used in real world applications of data driven inference systems their exploitation is also a practical and convenient choice here we apply several state of the art classification methods for non geometric data with the aim to compare different representations of the proteins gathered from niwa et al 2009 35 such representations include sequences of objects and labeled contact graphs enriched with chemico physical attributes the experiment performed by niwa et al provides the unique possibility to analyze the relative aggregation folding propensity of the elements of the entire escherichia coli e coli proteome in a cell free standardized microenvironment by this comparison we are able to identify also some interesting general properties of proteins notably i we suggest a threshold around 250 residues discriminating easily foldable from hardly foldable molecules consistent with other independent experiments and ii we highlight the relevance of contact graph spectra for folding behavior discrimination and characterization of the e coli solubility data the soundness of the experimental results presented in this paper is proved by the statistically relevant relationships discovered among the chemico physical description of proteins and the developed cost matrix of substitution that we used in the various discrimination systems

prioritized dct for compression and progressive transmission of images an approach is based on the block discrete cosine transform dct the novelty of this approach is that the transform coefficients of all image blocks are coded and transmitted in absolute magnitude order the resulting ordered by magnitude transmission is accomplished without sacrificing coding efficiency by using partition priority coding coding and transmission are adaptive to the characteristics of each individual image and therefore very efficient another advantage of this approach is its high progression effectiveness since the largest transform coefficients that capture the most important characteristics of images are coded and transmitted first this method is well suited for progressive image transmission further compression of the image data is achieved by multiple distribution entropy coding a technique based on arithmetic coding experiments show that the approach compares favorably with previously reported dct and subband image codecs

the units of a partial burnside ring relative to the young subgroups of a symmetric group the unit group of a partial burnside ring relative to the young subgroups of the symmetric group sn on n letters is included in the image by the tom dieck homomorphism as a consequence of this fact the alternating character n of sn is expressed explicitly as a z linear combinations of permutation characters associated with finite left sn sets sn y for the young subgroups y

characteristic times of biased random walks on complex networks we consider degree biased random walkers whose probability to move from a node to one of its neighbors of degree k is proportional to k ensuremath alpha where ensuremath alpha is a tuning parameter we study both numerically and analytically three types of characteristic times namely i the time the walker needs to come back to the starting node ii the time it takes to visit a given node for the first time and iii the time it takes to visit all the nodes of the network we consider a large data set of real world networks and we show that the value of ensuremath alpha which minimizes the three characteristic times differs from the value ensuremath alpha mathrm min ensuremath 1 analytically found for uncorrelated networks in the mean field approximation in addition to this we found that assortative networks have preferentially a value of ensuremath alpha mathrm min in the range ensuremath 1 ensuremath 0 5 while disassortative networks have ensuremath alpha mathrm min in the range ensuremath 0 5 0 we derive an analytical relation between the degree correlation exponent ensuremath nu and the optimal bias value ensuremath alpha mathrm min which works well for real world assortative networks when only local information is available degree biased random walks can guarantee smaller characteristic times than the classical unbiased random walks by means of an appropriate tuning of the motion bias

transform trellis coding of images at low bit rates a transform trellis coding scheme is used to encode images at rates below 1 b pel resulting in high snr values and very good subjective performance a discrete cosine transform dct is used to decorrelate the data samples and a trellis encoder is used to encode the transformed coefficients to overcome image nonstationarity a clustering algorithm is used to segment the transformed image into distinct regions and a separate trellis diagram is then constructed for each cluster to further improve the image quality particularly to reduce the blocking effect a scalar quantizer is used to quantize large magnitude coefficients of the error image in the transform domain the performance of the proposed scheme is found to be better than that of other recently reported schemes

multifractality of complex networks we demonstrate analytically and numerically the possibility that the fractal property of a scale free network cannot be characterized by a unique fractal dimension and the network takes a multifractal structure it is found that the mass exponents q for several deterministic stochastic and real world fractal scale free networks are nonlinear functions of q which implies that structural measures of these networks obey the multifractal scaling in addition we give a general expression of q for some class of fractal scale free networks by a mean field approximation the multifractal property of network structures is a consequence of large fluctuations of local node density in scale free networks

the and constructions for biset functors abstract in this article we define the construction and the construction that was crucial in the theory of canonical induction formulas see 3 in the setting of biset functors thus providing the necessary framework to define and construct canonical induction formulas for representation rings that are most naturally viewed as biset functors additionally this provides a unified approach to the study of a class of functors including the burnside ring the monomial burnside ring and global representation ring

induction formulae for mackey functors with applications to representations of the twisted quantum double of a finite group abstract in the theory of canonical induction formulae for mackey functors boltje 4 demonstrated that the plus constructions together with the mark morphism are useful for the study of canonical versions of induction theorems analogous to those in representation theory of finite groups in this paper we present a short exact sequence for the plus constructions derived from cauchy frobenius lemma and apply it to the proof of boltje s integrality result for canonical induction formulae the methods appearing in boltje s theory combined with the dress construction for mackey functors are applicable to induction theorems on representations of the twisted quantum double of a finite group as a sequel to such a research we describe canonical versions of two induction theorems whose origins are artin s induction theorem and brauer s induction theorem on c characters of a finite group

a mackey functor theoretic interpretation of biset functors abstract in this article we consider a formulation of biset functors using the 2 category of finite sets with variable finite group actions we introduce a 2 category s on which a biset functor can be regarded as a special kind of mackey functors this gives an analog of dress definition of a mackey functor in the context of biset functors

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

generalized burnside rings and group cohomology we define the cohomological burnside ring b n g m of a finite group g with coefficients in a zgmodule m as the grothendieck ring of the isomorphism classes of pairs x u where x is a g set and u is a cohomology class in a cohomology group h n x g m the cohomology groups h x g m are defined in such a way that h x g m i h hi m when x is the disjoint union of transitive g sets g hi i fa is an abelian group with trivial action then b 1 g a is the same as the monomial burnside ring over a and when m is taken as a g monoid then b 0 g m is equal to the crossed burnside ring b c g m we discuss the generalizations of the ghost ring and the mark homomorphism and prove the fundamental theorem for cohomological burnside rings we also give an interpretation of b 2 g m in terms of twisted

multiple burnside rings and brauer induction formulae abstract let g be a finite group and suppose that g is an operator group of a finite group a define s g a h h s g and z 1 h a where s g is the set of subgroups of g and z 1 h a is the set of crossed homomorphisms from h to a we view g as an operator group of the opposite group a of a and make s g a into a left a g set the ring g a is defined to be a commutative ring consisting of all formal z linear combinations of a g orbits in s g a idempotent formulae for q z g a not only imply a generalization of dress induction theorem but bring in the case where z 1 g a is the set of linear c characters of g boltje s explicit formula for brauer s induction theorem and its hyperelementary version

adaptivity versus tree searching in dpcm the interaction is studied between the effects of tree searching and predictor and quantizer adaptation in a differential pulse code modulation dpcm speech digitzer a 2 s male sentance is digitized at 1 and 2 bits sample the maximum entropy method computes a new source model every 8 ms and a variety of strategiesare used to adapt the quantizer results are displayed m plots of local snr versus time it is found that the predictor the quantizer and the tree search each contribute roughly independently to the total snr adaptivity contributes in total 6 7 db and tree searching 2 3 db local gains of both types can be higher

composition factors from the table of marks let b g be the burnside ring for a finite group g and let t g be the table of marks of g it is known that in general neither b g nor t g determines the finite group g that is one can easily construct pairs of non isomorphic finite groups such that their table of marks is the same hence their burnside rings are isomorphic in this note we show that the composition factors of g are determined by the table of marks t g

dynamic bit allocation subband excited transform coding method and apparatus in an adaptive subband excited transform speech encoding system a range of quantizers are available and are dynamically selected for each window of speech the quantizers designated for individual subbands are determined to minimize mean squared error distortion in the recreated signal while using no more than a predetermined number of quantization bits per window of speech

on the isomorphism problem for the ring of monomial representations of a finite group in this paper we are concerned with the problem of finding properties of a finite group g in the ring d g of monomial representations of g we determine the conductors of the primitive idempotents of q zd g where c is a primitive g th root of unity and prove a structure theorem for the torsion units of d g using these results we show that an abelian group g is uniquely determined by the ring d g we state an explicit formula for the primitive idempotents of z p zd g where z p is a localization of z we get further results for nilpotent and p nilpotent groups and we obtain properties of sylow subgroups of g from d g

a note on green functors with inflation abstract this note is motivated by the problem to understand given a commutative ring f which g sets x y give rise to isomorphic f g representations f x f y a typical step in such investigations is an argument that uses induction theorems to give very general sufficient conditions for all such relations to come from proper subquotients of g in the present paper we axiomatise the situation and prove such a result in the generality of mackey functors and green functors with inflation our result includes as special cases a result of deligne on monomial relations a result of the first author and tim dokchitser on brauer relations in characteristic 0 and a new result on brauer relations in characteristic p 0 we will need the new result in a forthcoming paper on brauer relations in positive characteristic

multiplicative induction and units for the ring of monomial representations abstract let g be a finite group and let a be a finite abelian g group for each subgroup h of g h a denotes the ring of monomial representations of h with coefficients in a which is a generalization of the burnside ring h of h we research the multiplicative induction map h a g a derived from the tensor induction map h g and also research the unit group of g a the results are explained in terms of the first cohomology groups h 1 k a for k g we see that tensor induction for 1 cocycles plays a crucial role in a description of multiplicative induction the unit group of g a is identified as a finitely generated abelian group we especially study the group of torsion units of g a and study the unit group of g as well

epidemic spreading driven by biased random walks abstract random walk is one of the basic mechanisms of many network related applications in this paper we study the dynamics of epidemic spreading driven by biased random walks in complex networks in our epidemic model infected nodes send out infection packets by biased random walks to their neighbor nodes and this causes the infection of susceptible nodes that receive the packets infected nodes recover from the infection at a constant rate and will not be infected again after recovery we obtain the largest instantaneous number of infected nodes and the largest number of ever infected nodes respectively by tuning the parameter of the biased random walks simulation results on model and real world networks show that spread of the epidemic becomes intense and widespread with increase of either delivery capacity of infected nodes average node degree or homogeneity of node degree distribution

a tree coding theorem for stationary gaussian sources and the squared error distortion measure for a class of stationary gaussian sources and the squared error distortion measure an asymptotically optimal tree coding scheme is derived using tree codes with finite branch length the distribution of the reproduction process is derived in an explicit form and using the random coding argument and results from the theory of branching processes with stationary ergodic environmental processes the source coding theorem is proved the theorem is applicable to all gaussian sources with a power spectrum that satisfies the lip 1 condition with no restriction on the coding rate

tree encoding of stationary ergodic sources with a fidelity criterion tree source coding theorems with a single letter fidelity criterion are proved for stationary ergodic sources using tree codes with a fixed branch length the higher than exponential convergence of distortions is shown for binary symmetric sources and hamming distortion measure when an excess in rate is allowed

hubs repelling laplacian and related diffusion on graphs networks abstract we define and study here a graph unsymmetric laplacian matrix that operates a diffusive process biased towards low degree nodes we prove that this matrix is positive semidefine with all eigenvalues real we also prove that the rate of convergence of a diffusive process controlled by the hubs repelling laplacian depends on the first nontrivial eigenvalue of this laplacian such rate of convergence depends on the existence of low degree nodes connected to high degree ones we find several bounds for the algebraic connectivity based on this laplacian we then study two real world scenarios with the hubs repelling diffusion the propagation of flight delays in the air transportation network of usa and the cost efficient information diffusion across the human brain functional coactivation network finally we find some conditions for the nodes of a network to be good spreaders under the hubs repelling dynamics

mackey functors induction from restriction functors and coinduction from transfer functors abstract boltje s plus constructions extend two well known constructions on mackey functors the fixed point functor and the fixed quotient functor in this paper we show that the plus constructions are induction and coinduction functors of general module theory as an application we construct simple mackey functors from simple restriction functors and simple transfer functors we also give new proofs for the classification theorem for simple mackey functors and semisimplicity theorem of mackey functors

an optimal transform trellis code with applications to speech this paper presents a rate distortion derived transform trellis coding ttc scheme with applications to gaussian ar sources and speech data the optimal encoder consists of a karhunen loeve transform klt on the source output followed by a search on a trellis structured random code where the decoder is a time variant nonlinear filter the scheme is implementable and applicable to stationary gaussian sources with a bounded and continuous power spectrum and the squared error distortion measure the code construction is based on the power or eigenvalue spectrum of the source with no restriction on the coding rate the ttc scheme is first applied to encode a gaussian ar source often used to model speech simulations were conducted at several rates using an optimal klt and the suboptimal discrete cosine transform dct results demonstrate that the dct performs as well as the klt and both yield average distortions very close to the distortion rate function for speech data an adaptive version of the dct ttc scheme is applied to encode two speech sentences at several coding rates the adaptation is controlled by an estimate of the short term eigenvalue spectrum which is transmitted as side information to the receiver the proposed scheme is a very efficient speech waveform coder that provides reconstructed speech with very high signal to noise ratio values and very good perceptual quality at low bit rates

predictive vector quantization of images the purpose of this paper is to present new image coding schemes based on a predictive vector quantization pvq approach the predictive part of the encoder is used to partially remove redundancy and the vq part further removes the residual redundancy and selects good quantization levels for the global waveform two implementations of this coding approach have been devised namely sliding block pvq and block tree pvq simulations on real images show significant improvement over the conventional dpcm and tree codes using these new techniques the strong robustness property of these coding schemes is also experimentally demonstrated

wavelet versus detrended fluctuation analysis of multifractal structures we perform a comparative study of applicability of the multifractal detrended fluctuation analysis mfdfa and the wavelet transform modulus maxima wtmm method in proper detecting of monofractal and multifractal character of data we quantify the performance of both methods by using different sorts of artificial signals generated according to a few well known exactly soluble mathematical models monofractal fractional brownian motion bifractal levy flights and different sorts of multifractal binomial cascades our results show that in the majority of situations in which one does not know a priori the fractal properties of a process choosing mfdfa should be recommended in particular wtmm gives biased outcomes for the fractional brownian motion with different values of hurst exponent indicating spurious multifractality in some cases wtmm can also give different results if one applies different wavelets we do not exclude using wtmm in real data analysis but it occurs that while one may apply mfdfa in a more automatic fashion wtmm must be applied with care in the second part of our work we perform an analogous analysis on empirical data coming from the american and from the german stock market for this data both methods detect rich multifractality in terms of broad f alpha but mfdfa suggests that this multifractality is poorer than in the case of wtmm

fibered biset functors abstract the theory of biset functors introduced by serge bouc gives a unified treatment of operations in representation theory that are induced by permutation bimodules in this paper by considering fibered bisets we introduce and describe the basic theory of fibered biset functors which is a natural framework for operations induced by monomial bimodules the main result of this paper is the classification of simple fibered biset functors

tree coding of image subbands the authors consider the encoding of image subbands with a tree code that is asymptotically optimal for gaussian sources and the mean squared error mse distortion measure they first prove that optimal encoding of ideally filtered subbands of a gaussian image source achieves the rate distortion bound for the mse distortion measure the optimal rate and distortion allocation among the subbands is a by product of this proof a bound is derived which shows that subband coding is closer than full band coding to the rate distortion bound for a finite length sequence the tree codes are then applied to encode the image subbands both nonadaptively and adaptively since the tree codes are stochastic and the search of the code tree is selective a relatively few reproduction symbols may have an associated squared error a hundred times larger than the target for the subband correcting these symbols through a postcoding procedure improves the signal to noise ratio and visual quality significantly with a marginal increase in total rate

the table of marks the kostka matrix and the character table of the symmetric group abstract in this article we introduce a short proof of t k c where t is the table of marks with respect to the young subgroups k is the kostka matrix and c is the character table of the symmetric group s n as a corollary of the result we could determine the explicit elements of the unit group of the generalized burnside ring with respect to the young subgroups of s n

fractional rate multitree speech coding the authors present both forward and backward adaptive speech coders that operate at 9 6 12 and 16 kb s using integer and fractional rate trees weighted squared error distortion measures the m l tree search algorithm and incremental path map symbol release they introduce the concept of multitree source codes and illustrate how the multitree structure allows scalar quantizer based codes and scalar adaptation rules to be used for fractional rate tree coding with a frequency weighted distortion measure the forward and backward adaptive multitree coders produce near toll quality speech at 16 kb s while the backward adaptive 9 6 kb s multitree coder substantially outperforms adaptive predictive coding and has an encoding delay of less than 2 ms performance results are present in terms of unweighted and weighted signal to noise ratio and segmental signal to noise ratio sound spectrograms and subjective listening tests

categorifying induction formulae via divergent series abstract we show how to get explicit induction formulae for finite group representations and more generally for rational green functors by summing a divergent series over dwyer s subgroup and centralizer decomposition spaces this results in formulae with rational coefficients the former space yields a well known induction formula the latter yields a new one as essentially immediate corollaries of the existing literature we get similar formulae in group cohomology and stable splittings of classifying spaces

global representation rings abstract in this paper we combine the concepts of burnside ring and character ring in what we call the global representation ring of a finite group we compute all ring homomorphisms from this ring to the complex numbers we compute its spectrum its connected components and determine the primitive idempotents

an induction theorem for the unit groups of burnside rings of 2 groups abstract let g be a 2 group and b g denote the group of units of the burnside ring of g for each subquotient h k of g there is a generalized induction map from b h k to b g defined as the composition of inflation and multiplicative induction maps we prove that the product of generalized induction maps b h k b g is surjective when the product is taken over the set of all subquotients that are isomorphic to the trivial group or a dihedral 2 group of order 2 n with n 4 as an application we give an algebraic proof for a theorem by tornehave the unit group for the burnside ring of a 2 group aarhus universitet preprint series 1983 84 41 may 1984 which states that tom dieck s exponential map from the real representation ring of g to b g is surjective we also give a sufficient condition for the surjectivity of the exponential map from the burnside ring of g to b g

a trellis code construction and coding theorem for stationary gaussian sources corresp for stationary discrete time gaussian sources and the squared error distortion measure a trellis source code is constructed the encoder consists of a karhunen loeve transform on the source output followed by a search on a trellis structured code where the decoder is a time variant nonlinear filter the corresponding code theorem is proved using the random coding argument the proof technique follows that of viterbi and omura who proved the trellis coding theorem for memoryless sources the resultant coding scheme is implementable and applicable at any nonzero rate to a stationary gaussian source with a bounded and continuous power spectrum therefore for stationary sources it is more general than berger s tree coding scheme which is restricted to autoregressive gaussian sources in a region of high rate low distortion

the species and idempotents of the green algebra of a finite group with a cyclic sylow subgroup we study the green algebra a kg generated by the isomorphism classes of indecomposable kg modules where k is a field with chark p 0 and g a finite group with a cyclic sylow p subgroup more precisely we discuss the homomorphisms a kg c called species and state a formula for the idempotents of a kg

ring of subquotients of a finite group i linearization abstract we introduce the ring g of subquotients of a finite group g as an abelian group it is free on the set of conjugacy classes of subquotients of the group g the ring g integrally extends the burnside ring and there is a linearization map with range the grothendieck ring of the mackey algebra