abstract phase space networks describing reactive dynamics abstract an abstract network approach is proposed for the description of the dynamics in reactive processes the phase space of the variables concentrations in reactive systems is partitioned into a finite number of segments which constitute the nodes of the abstract network transitions between the nodes are dictated by the dynamics of the reactive process and provide the links between the nodes these are weighted networks since each link weight reflects the transition rate between the corresponding states nodes with this construction the network properties mirror the dynamics of the underlying process and one can investigate the system properties by studying the corresponding abstract network as a working example the lattice limit cycle llc model is used its corresponding abstract network is constructed and the transition matrix elements are computed via kinetic dynamic monte carlo simulations for this model it is shown that the degree distribution follows a power law with exponent 1 while the average clustering coefficient c n scales with the network size number of nodes n as c n n 1 46 the computed exponents classify the llc abstract reactive network into the scale free networks this conclusion corroborates earlier investigations demonstrating the formation of fractal spatial patterns in llc reactive dynamics due to stochasticity and to clustering of homologous species the present construction of abstract networks based on the partition of the phase space is generic and can be implemented with appropriate adjustments in many dynamical systems and in time series analysis

character sheaves v this paper is part of a series s 131 devoted to the study of a class g of irreducible perverse sheaves called character sheaves on a connected reductive algebraic group g the numbering of chapters sections and references will continue that of s 131 this paper is a step towards the classification of character sheaves on g one of the main results is the following one under certain assumptions there is a natural surjective map with finite fibers from g to the set of all pairs 9 c up to conjugacy by the weyl group where 9 is a tame local system on the maximal torus and c is a two sided cell in the stabilizer w of 9 in the weyl group the assumptions made on g are

direct multichannel predictive deconvolution the levinson principle generally can be used to compute recursively the solution of linear equations it can also be used to update the error terms directly this is used to do single channel deconvolution directly on seismic data without computing or applying a digital filter multichannel predictive deconvolution is used for seismic multiple attenuation in a standard procedure the prediction error filter matrices are computed with a levinson recursive algorithm using a covariance matrix of the input data the filtered output is the prediction errors or the nonpredictable part of the data starting with the classical levinson recursion wehave derived new algorithms for direct recursive calculationof the prediction errors without computing the data covariance matrix or computing the prediction error filters one algorithm generates recursively the one step forward and backward predic tion errors and the l step forward prediction error computing only the filter matrices with the highest index a numeri

seismic sparse layer reflectivity inversion using basis pursuit decomposition a basis pursuit inversion of seismic reflection data for reflection coefficients is introduced as an alternative method of incorporating a priori information in the seismic inversion process the inversion is accomplished by building a dictionary of functions representing reflectivity patterns and constituting the seismic trace as a superposition of these patterns basis pursuit decomposition finds a sparse number of reflection responses that sum to form the seismic trace when the dictionary of functions is chosen to be a wedge model of reflection coefficient pairs convolved with the seismic wavelet the resulting reflectivity inversion is a sparse layer inversion rather than a sparse spike inversion synthetic tests suggest that a sparse layer inversion using basis pursuit can better resolve thin beds than a comparable sparse spike inversion application to field data indicates that sparse layer inversion results in the potentially improved detectability and resolution of some thin layers and reveals a

higher order corrections in the approximation of low dimensional manifolds and the construction of simplified problems with the csp method in systems of stiff ordinary differential equations odes both fast and slow time scales are encountered the fast time scales are responsible for the development of low dimensional manifolds on which the solution moves according to the slow time scales in this paper methodologies for constructing highly accurate i expressions describing the manifold and ii simplified non stiff equations governing the slow evolution of the solution on the manifold are developed according to an iterative procedure proposed in the computational singular perturbation csp method it is shown that the increasing accuracy achieved with each iteration is directly related to the time rates of change of the csp vectors spanning the manifold along the solution trajectory here an algorithm is presented which implements these calculations and is validated on the basis of two simple examples

depth zero supercuspidal l packets and their stability in this paper we verify the local langlands correspondence for pure inner forms of unramied p adic groups and tame langlands parameters in general position for each such parameter we explicitly construct in a natural way a nite set l packet of depth zero supercuspidal representations of the appropriate p adic group and we verify some expected properties of this l packet in particular we prove with some conditions on the base eld that the appropriate sum of characters of the representations in our l packet is stable no proper subset of our l packets can form a stable combination our l packets are also consistent with the conjectures of b gross and d prasad on restriction from so2n 1 to so2n 24 these l packets are in general quite large for example sp2n has an l packet containing 2 n representations of which exactly two are generic in fact on a quasi split form eachl packet contains exactly one generic representation for every rational orbit of hyperspecial vertices in the reduced bruhattits building when the group has connected center every depth zero generic supercuspidal representation appears in one of these l packets we emphasize that there is nothing new about the representations we construct they are induced from deligne lusztig representations on subgroups of nite

explicit time scale splitting algorithm for stiff problems auto ignition of gaseous mixtures behind a steady shock a new explicit algorithm based on the computational singular perturbation csp method is presented this algorithm is specifically designed to solve stiff problems and its performance increases with stiffness the key concept in its structure is the splitting of the fast from the slow time scales in the problem realized by embedding csp concepts into an explicit scheme in simple terms the algorithm marches in time with only the terms producing the slow time scales while the contribution of the terms producing the fast time scales is taken into account at the end of each integration step as a correction the new algorithm is designed for the integration of stiff systems of pdes by means of explicit schemes for simplicity in the presentation and discussion of the different features of the new algorithm a simple test case is considered involving the auto ignition of a methane air mixture behind a normal shock wave which is described by a system of odes the performance of the new algorithm accuracy and computational efficiency is then compared with the well known lsode package its merits when used for the solution of systems of pdes are discussed although when dealing with a stiff system of odes the new algorithm is shown to provide equal accuracy with that delivered by lsode at the cost of higher execution time the results indicate that its performance could be superior when facing a stiff system of pdes

hochschild homology of affine hecke algebras abstract let h h r q be an affine hecke algebra with complex possibly unequal parameters q which are not roots of unity we compute the hochschild and the cyclic homology of h it turns out that these are independent of q and that they admit an easy description in terms of the extended quotient of a torus by a weyl group both of which are canonically associated to the root datum r for positive q we also prove that the representations of the family of algebras h r q c come in families which depend analytically on analogous results are obtained for graded hecke algebras and for schwartz completions of affine hecke algebras

physical understanding of complex multiscale biochemical models via algorithmic simplification glycolysis in saccharomyces cerevisiae abstract large scale models of cellular reaction networks are usually highly complex and characterized by a wide spectrum of time scales making a direct interpretation and understanding of the relevant mechanisms almost impossible we address this issue by demonstrating the benefits provided by model reduction techniques we employ the computational singular perturbation csp algorithm to analyze the glycolytic pathway of intact yeast cells in the oscillatory regime as a primary object of research for many decades glycolytic oscillations represent a paradigmatic candidate for studying biochemical function and mechanisms using a previously published full scale model of glycolysis we show that due to fast dissipative time scales the solution is asymptotically attracted on a low dimensional manifold without any further input from the investigator csp clarifies several long standing questions in the analysis of glycolytic oscillations such as the origin of the oscillations in the upper part of glycolysis the importance of energy and redox status as well as the fact that neither the oscillations nor cell cell synchronization can be understood in terms of glycolysis as a simple linear chain of sequentially coupled reactions

lagrangian construction for representations of hecke algebras 1 let k be a non archimedean local field with the residue field consisting of q elements according to langlands philosophy irreducible complex representations of a reductive k group g should roughly speaking correspond to homomorphisms of the weil deligne group into the socalled l group let zc g be the iwahori subgroup the category of admissible gkmodules generated by z fixed vectors is known to be equivalent to the category of finite dimensional representations of the hecke algebra h z g z langlands philosophy suggests via that equivalence the following classification of irreducible hecke algebra modules stated in purely complex terms and not involving any local held

affine cellular algebras abstract graham and lehrer have defined cellular algebras and developed a theory that allows in particular to classify simple representations of finite dimensional cellular algebras many classes of finite dimensional algebras including various hecke algebras and diagram algebras have been shown to be cellular and the theory due to graham and lehrer successfully has been applied to these algebras we will extend the framework of cellular algebras to algebras that need not be finite dimensional over a field affine hecke algebras of type a and infinite dimensional diagram algebras like the affine temperley lieb algebras are shown to be examples of our definition the isomorphism classes of simple representations of affine cellular algebras are shown to be parameterised by the complement of finitely many subvarieties in a finite disjoint union of affine varieties in this way representation theory of non commutative algebras is linked with commutative algebra moreover conditions on the cell chain are identified that force the algebra to have finite global cohomological dimension and its derived category to admit a stratification these conditions are shown to be satisfied for the affine hecke algebra of type a if the quantum parameter is not a root of the poincare polynomial

on a uniqueness property of supercuspidal unipotent representations abstract the formal degree of a unipotent discrete series character of a simple linear algebraic group over a non archimedean local field in the sense of lusztig 17 is a rational function of q evaluated at q q the cardinality of the residue field the irreducible factors of this rational function are q and cyclotomic polynomials we prove that the formal degree of a supercuspidal unipotent representation determines its lusztig langlands parameter up to twisting by weakly unramified characters for split exceptional groups this result follows from the work of m reeder 28 and for the remaining exceptional cases this is verified in 7 in the present paper we treat the classical families the main result of this article characterizes unramified lusztig langlands parameters which support a cuspidal local system in terms of formal degrees the result implies the uniqueness of so called cuspidal spectral transfer morphisms as introduced in 22 between unipotent affine hecke algebras up to twisting by unramified characters in 23 the essential uniqueness of arbitrary unipotent spectral transfer morphisms was reduced to the cuspidal case

on classical saito kurokawa liftings there exist two different generalizations of the classical saito kurokawa lifting to modular forms with square free level one lifting produces modular forms with respect to 0 m the other one with respect to the paramodular group m we shall give an alternative and unified construction of both liftings using group theoretic methods the construction shows that a single elliptic modular form may in fact have many saito kurokawa liftings we also obtain precise information about the spin l function of the resulting siegel modular forms

unipotent representations of complex semisimple groups algebraic group over r or c in this paper we restrict attention to c we generalize arthur s definition slightly or perhaps simply make it more precise all of the resulting representations except for a finite set are then unitarily induced from representations of the same kind on proper parabolic subgroups we call the finite set remaining special unipotent representations a precise definition will be given later definition 1 17 our main result theorem iii of this introduction is a character formula for any special unipotent representation of course such a formula can be deduced from the kazhdan lusztig conjecture cf v3 the advantages of theorem iii are that it is in closed form and that it lends itself to verification of some conjectures of arthur in a so let g be a connected complex semisimple lie group and q its lie algebra choose

sparse multichannel blind deconvolution abstractwe developed a sparse multichannel blind deconvolution smbd method the method is a modification of the multichannel blind deconvolution technique often called euclid deconvolution in which the multichannel impulse response of the earth is estimated by solving an homogeneous system of equations classical euclid deconvolution is unstable in the presence of noise and requires the correct estimation of the length of the seismic wavelet the proposed method on the other hand can tolerate moderate levels of noise and does not require a priori knowledge of the length of the wavelet smbd solves the homogeneous system of equations arising in euclid deconvolution by imposing sparsity on the unknown multichannel impulse response trivial solutions to the aforementioned homogeneous system of equations are avoided by seeking sparse solutions on the unit sphere we tested smbd with synthetic and real data examples synthetic examples were used to judge the viability of the method in terms of noise we f

stochastic sparse spike deconvolution sparse spike deconvolution can be viewed as an inverse problem where the locations and amplitudes of a number of spikes reflectivity are estimated from noisy data seismic traces the main objective is to find the least number of spikes that when convolved with the available band limited seismicwaveletestimate fitthedatawithinagiventolerance errormisfit thedetectionofthespikes timelagsisahighly nonlinearoptimizationproblemthatcanbesolvedusingvery fastsimulatedannealingsa amplitudesareeasilyestimated using linear least squares at each sa iteration at this stage quadratic regularization is used to stabilize the solution to reduce its nonuniqueness and to provide meaningful reflectivitysequences thusavoidingtheneedtoconstrainthe spikes time lags and or amplitudes to force valid solutions impedanceconstraintsalsocanbeincludedatthisstage providing the low frequencies required to recover the acoustic impedance oneadvantageoftheproposedmethodoverother sparse spike deconvolution techniques is that the uncertaintyoftheobtainedsolutionscanbeestimatedstochastically further errorsinthephaseofthewaveletestimatearetolerated foranoptimumconstant phaseshiftisobtainedtocalibratetheeffectivewaveletthatispresentinthedata results using synthetic data including simulated data for the marmousi2 modelandfield 3d data show that physically meaningful high resolution sparse spike sections can be derived fromband limitednoisydata evenwhentheavailablewaveletestimateisinaccurate

the role of slow system dynamics in predicting the degeneracy of slow invariant manifolds the case of vdp relaxation oscillations abstract the development of dissipative time scales which are much faster than the rest force the solution of a system of 1st order odes to land and then evolve on a slow invariant manifold the slow evolution on this manifold can be approximated by a reduced system which is constructed with asymptotic analysis and is free of the fast scales in this work the dynamics of the reduced system are compared to the fast and slow dynamics of the original system the comparison is based on the van der pol system which is typical of those exhibiting relaxation oscillation behavior and is characterized by successive dissipative and explosive phases special attention is given to the dissipative phase during which the solution evolves on a slow invariant manifold and the fast slow time scale gap tends to contract it is shown that one cannot predict from the dynamics of the van der pol system the approaching explosive phase and the associated degeneracy of the manifold such a prediction is possible only through the dynamics of the reduced system which involves an explosive component that is absent in the original system this explosive component accelerates as higher order effects are incorporated in the reduced system resulting in a smaller gap between the fast time scale of the original system and the fast time scale of the reduced one this feature sets a limit on the accuracy singular perturbation techniques can deliver even in the presence of a reasonably large fast slow time scale gap in the dynamics of the original system given a fast slow system predicting forthcoming changes in the dimensions of the manifold is very important when it is desired to identify the underlying major physical mechanisms or to control the process

an efficient iterative algorithm for the approximation of the fast and slow dynamics of stiff systems the relation between the iterative algorithms based on the computational singular perturbation csp and the invariance equation ie methods is examined the success of the two methods is based on the appearance of fast and slow time scales in the dynamics of stiff systems both methods can identify the low dimensional surface in the phase space slow invariant manifold sim where the state vector is attracted under the action of fast dynamics it is shown that this equivalence of the two methods can be expressed by simple algebraic relations csp can also construct the simplified non stiff system that models the slow dynamics of the state vector on the sim an extended version of ie is presented which can also perform this task this new ie version is shown to be exactly similar to a modified version of csp which results in a very efficient algorithm especially in cases where the sim dimension is small so that significant model simplifications are possible

wavelet estimation revisited this article deals with the ubiquitous problem of wavelet estimation in essence the problem consists of estimating at best two unknowns from one equation in the seismic case as it is well known the model of the recorded seismic trace xt is generally formulated as a convolution xt wt rt where wt is the seismic source signature or wavelet and rt is the reflectivity series which is comprised of all primary and multiple reflections since in general we can assume that rt is white or nearly so the amplitude signature of wt may be estimated with some degree of confidence it is of course the phase of wt that presents the difficulty it turns out perhaps somewhat counterintuitively that except for rather special circumstances the phase of a signal uniquely determines the signal to within a scale factor the amplitude spectrum plays no part whatsoever we explore this further below no wonder then that the phase is the all important factor

asymptotic analysis of two reduction methods for systems of chemical reactions abstract this paper concerns two methods for reducing large systems of chemical kinetics equations namely the method of intrinsic low dimensional manifolds ildms due to maas and pope combust flame 88 1992 239 and an iterative method due to fraser j chem phys 88 1988 4732 and further developed by roussel and fraser j chem phys 93 1990 1072 both methods exploit the separation of fast and slow reaction time scales to find low dimensional manifolds in the space of species concentrations where the long term dynamics are played out the asymptotic expansions of these manifolds e 0 where e measures the ratio of the reaction time scales are compared with the asymptotic expansion of m e the slow manifold given by geometric singular perturbation theory it is shown that the expansions of the ildm and m e agree up to and including terms of o e the former has an error at o e 2 that is proportional to the local curvature of m 0 the error vanishes if and only if the curvature is zero everywhere the iterative method generates term by term the asymptotic expansion of m e starting from m 0 the ith application of the algorithm yields the correct expansion coefficient at o e i while leaving the lower order coefficients invariant thus after l applications the expansion is accurate up to and including the terms of o e l the analytical results are illustrated on a planar system from enzyme kinetics michaelis menten henri and a model planar system due to davis and skodje

mixed phase deconvolution we describe a new algorithm for mixed phase deconvolution it is valid only for pulses whose z transform has no zeros on the unit circle that is the amplitude spectrum cannot be zero for any frequency using the z transform of a discrete time signal and assuming that the signal has zeros inside the unit circle the inverse of its minimum delay component may be estimated by solving the extended yule walker eyw system of equations with the lag of the autocorrelation function acf on diagonal of the coefficient matrix this property of the solution of eyw equations is exploited to derive mixed phase inverse filters and their corresponding mixed phase pulses for different values of a suite of inverse filters is generated using the same acf to choose the best decomposition and its corresponding mixed phase inverse filter we have used the value of which gives the maximum value of the lp norm of the filtered signal the optimal value of does not seem to be very sensitive to the choice of norm

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

algorithmic asymptotic analysis of the nf κb signaling system the results of a detailed step by step asymptotic analysis of the nf b signaling system are reported in the case where the system exhibits limit cycle behavior the analysis is based on the dimensional form of the model and exploits the various fast slow time scale gaps that develop as the solution evolves along the limit cycle it is shown that under the action of fast time scales of dissipative character the limit cycle is confined on a low dimensional surface in the phase space the cycle can be divided in three parts each one related to a different characteristic time scale the first part refers to the slow rate of nf b release in the cytoplasm the second part refers to the even slower rate by which the free nf b enters into the nucleus the last part refers to the fast rate by which the nuclear nf b is first produced and then depleted it is demonstrated that these and many other findings regarding the fast variables the equilibrated fast processes the rate limiting and or driving steps etc can be acquired by simple algorithmic tools