stochastic flow cascades we introduce and explore a stochastic flow cascade sfc model a general statistical model for the unidirectional flow through a tandem array of heterogeneous filters examples include the flow of i liquid through heterogeneous porous layers ii shocks through tandem shot noise systems iii signals through tandem communication filters the sfc model combines together the langevin equation convolution filters and moving averages and poissonian randomizations a comprehensive analysis of the sfc model is carried out yielding closed form results levy laws are shown to universally emerge from the sfc model and characterize both heavy tailed retention times noah effect and long ranged correlations joseph effect

a measure valued differentiation approach to sensitivities of quantiles quantiles play an important role in modelling quality of service in the service industry and in modelling risk in the financial industry the recent discovery that efficient simulation based estimators can be obtained for quantile sensitivities has led to an intensive search for sample path differentiation based estimators for quantile sensitivities in this paper we present a novel approach to quantile sensitivity estimation our approach elaborates on the concept of measure valued differentiation thereby we overcome the main obstacle of the sample path approach which is the requirement that the sample cost have to be lipschitz continuous with respect to the parameter of interest specifically we perform a sensitivity analysis of the value at risk in financial models in addition we discuss an application of our sensitivity estimator to queueing networks

single run gradient estimation via measure valued differentiation we show how single run based measure valued differentiation gradient estimators can be obtained the key idea is to apply a change of measure a posterior to the mathematical analysis of the derivative from the point of view of the likelihood ratio method we show that likelihood ratio type gradient estimators can be applied in situations where the mathematical conditions needed for applying a likelihood ratio analysis are not met

power law shot noise the behavior of power law shot noise for which the associated impulse response functions assume a decaying power law form is explored expressions are obtained for the moments moment generating functions amplitude probability density functions autocorrelation functions and power spectral densities for a variety of parameters of the process for certain parameters the power spectral density exhibits 1 f type behavior over a substantial range of frequencies so that the process serves as a source of 1 f sup alpha shot noise for alpha in the range 0

shot noise systems with random relaxations we explore a model of a random relaxation shot noise system in which i the shot inflow is a general poisson point process with possibly infinite poissonian rates and ii the exponential relaxations governing the shot decay are randomized this system model is applicable to physical environments polluted by radioactive contamination of heterogeneous types the statistics of random relaxation shot noise systems are analyzed quantitatively and comprehensively stationary structure correlation structure process distribution fractality and asymptotic fractality and the display both separately and simultaneously of the noah and joseph effects results are obtained explicitly and in closed form and facilitate the design of tractable shot noise systems with unique features

application of computational mechanics to the analysis of natural data an example in geomagnetism we discuss how the ideal formalism of computational mechanics can be adapted to apply to a noninfinite series of corrupted and correlated data that is typical of most observed natural time series specifically a simple filter that removes the corruption that creates rare unphysical causal states is demonstrated and the concept of effective soficity is introduced we believe that computational mechanics cannot be applied to a noisy and finite data series without invoking an argument based upon effective soficity a related distinction between noise and unresolved structure is also defined noise can only be eliminated by increasing the length of the time series whereas the resolution of previously unresolved structure only requires the finite memory of the analysis to be increased the benefits of these concepts are demonstrated in a simulated times series by a the effective elimination of white noise corruption from a periodic signal using the expletive filter and b the appearance of an effectively sofic region in the statistical complexity of a biased poisson switch time series that is insensitive to changes in the word length memory used in the analysis the new algorithm is then applied to an analysis of a real geomagnetic time series measured at halley antarctica two principal components in the structure are detected that are interpreted as the diurnal variation due to the rotation of the earth based station under an electrical current pattern that is fixed with respect to the sun earth axis and the random occurrence of a signature likely to be that of the magnetic substorm in conclusion some useful terminology for the discussion of model construction in general is introduced

network amplification of local fluctuations causes high spike rate variability fractal firing patterns and oscillatory local field potentials we investigate a model for neural activity in a two dimensional sheet of leaky integrate and fire neurons with feedback connectivity consisting of local excitation and surround inhibition each neuron receives stochastic input from an external source independent in space and time as recently suggested by softky and koch 1992 1993 independent stochastic input alone cannot explain the high interspike interval variability exhibited by cortical neurons in behaving monkeys we show that high variability can be obtained due to the amplification of correlated fluctuations in a recurrent network furthermore the cross correlation functions have a dual structure with a sharp peak on top of a much broader hill this is due to the inhibitory and excitatory feedback connections which cause hotspots of neural activity to form within the network these localized patterns of excitation appear as clusters or stripes that coalesce disintegrate or fluctuate in size while simultaneously moving in a random walk constrained by the interaction with other clusters the synaptic current impinging upon a single neuron shows large fluctuations at many time scales leading to a large coefficient of variation cv for the interspike interval statistics the power spectrum associated with single units shows a 1 f decay for small frequencies and is flat at higher frequencies while the power spectrum of the spiking activity averaged over many cells equivalent to the local field potential shows no 1 f decay but a prominent peak around 40 hz in agreement with data recorded from cat and monkey cortex gray et al 1990 eckhorn et al 1993 firing rates exhibit self similarity between 20 and 800 msec resulting in 1 f like noise consistent with the fractal nature of neural spike trains teich 1992

extreme value theory for constrained physical systems we investigate extreme value theory for physical systems with a global conservation law which describes renewal processes mass transport models and long range interacting spin models as shown previously a special feature is that the distribution of the extreme value exhibits a nonanalytical point in the middle of the support we expose exact relationships between constrained extreme value theory and well known quantities of the underlying stochastic dynamics all valid beyond the midpoint in general i e even far from the thermodynamic limit for example for renewal processes the distribution of the maximum time between two renewal events is exactly related to the mean number of these events in the thermodynamic limit we show how our theory is suitable to describe typical and rare events which deviate from classical extreme value theory for example for the renewal process we unravel dual scaling of the extreme value distribution pointing out two types of limiting laws a normalizable scaling function for the typical statistics and a non normalized state describing the rare events

zeta functions of regular arithmetic schemes at s 0 lichtenbaum conjectured in 22 the existence of a weil etale cohomology in order to describe the vanishing order and the special value of the zeta function of an arithmetic scheme x at s 0 in terms of euler poincare characteristics assuming the conjectured finite generation of some motivic cohomology groups we construct such a cohomology theory for regular schemes proper over spec z in particular we compute uncon ditionally the right weil etale cohomology of number rings and projective spaces over number rings we state a precise version of lichtenbaum s con jecture which expresses the vanishing order resp the special value of the zeta function x s at s 0 as the rank resp the determinant of a single perfect complex of abelian groups r w c x z then we relate this conjecture to soule s conjecture and to the tamagawa number conjecture lichtenbaum s conjecture for projective spaces over the ring of integers of an abelian number field follows

class field theory for arithmetic schemes let x be a regular arithmetic scheme i e a regular integral separated scheme flat and of finite type over spec mathbb z generalising classical class field theory for number fields we define a class group cx and show there is a natural surjective map c x rightarrow pi 1 ab x whose kernel is the connected component of 0

on the weil etale cohomology of number fields we give a direct description of the category of sheaves on lichtenbaum s weil etale site of a number ring then we apply this result to define a spectral sequence relating weil etale cohomology to artin verdier etale cohomology finally we construct complexes of etale sheaves computing the expected weil etale cohomology

the k theory of fields in characteristic p we show that for a field k of characteristic p h i k n is uniquely p divisible for i n we use higher chow groups as our definition of motivic cohomology this implies that the natural map k n m k k n k from milnor k theory to quillen k theory is an isomorphism up to uniquely p divisible groups and that k n m k and k n k are p torsion free as a consequence one can calculate the k theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de rham witt sheaves for example k n x p r 0 for n dimx another consequence is gersten s conjecture with finite coefficients for smooth varieties over discrete valuation rings with residue characteristic p as the last consequence bloch s cycle complexes localized at p satisfy all beilinson lichtenbaum milne axioms for motivic complexes except possibly the vanishing conjecture

sensitivity estimation for gaussian systems in this paper we address the construction of efficient algorithms for the estimation of gradients of general performance measures of gaussian systems exploiting a clever coupling between the normal and the maxwell distribution we present a new gradient estimator and we show that it outperforms both the single run based infinitesimal perturbation analysis ipa estimator and the score function sf estimator in the one dimensional case for a dense class of test functions next we present an example of the multi dimensional case with a system from the area of stochastic activity networks our numerical experiments show that this new estimator also has significantly smaller sample variance than ipa and sf to increase efficiency in addition to variance reduction we present an optimized method for generating the maxwell distribution which minimizes the cpu time

gaussian approximation for the wireless multi access interference distribution the problem of gaussian approximation for the wireless multi access interference distribution in large spatial wireless networks is addressed first a principled methodology is presented to establish rates of convergence of the multi access interference distribution to a gaussian distribution for general bounded and power law decaying path loss functions the model is general enough to also include various random wireless channel dynamics such as fading and shadowing arising from multi path propagation and obstacles existing in the communication environment it is shown that the wireless multi access interference distribution converges to the gaussian distribution with the same mean and variance at a rate 1 where 0 is a parameter controlling the intensity of the planar possibly non stationary poisson point process generating node locations an explicit expression for the scaling coefficient is obtained as a function of fading statistics and the path loss function second an extensive numerical and simulation study is performed to illustrate the accuracy of the derived gaussian approximation bounds a good statistical fit between the interference distribution and its gaussian approximation is observed for moderate to high values of

polylogarithms regulators and arakelov motivic complexes we construct an explicit regulator map from bloch s higher chow group complex to the deligne complex of a complex algebraic variety x we define the arakelov motivic complex as the cone of this map shifted by one its last cohomology group is a version of the arakelov chow group defined by h gillet and c soule we relate the grassmannian n logarithms defined as in g5 to the geometry of symmetric space sln c su n for n 2 we recover lobachevsky s formula expressing the volume of an ideal geodesic simplex in the hyperbolic space via the dilogarithm using the relationship with symmetric spaces we construct the borel regulator on k2n 1 c via the grassmannian n logarithms we study the chow dilogarithm and prove a reciprocity law which strengthens suslin s reciprocity law for milnor s group k 3 on curves our note g5 can serve as an introduction to this paper

power spectrum of mass and activity fluctuations in a sandpile we consider a directed abelian sandpile on a strip of size 2 ifmmode times else texttimes fi n driven by adding a grain randomly at the left boundary after every t timesteps we establish the exact equivalence of the problem of mass fluctuations in the steady state and the number of zeros in the ternary base representation of the position of a random walker on a ring of size 3 n we find that while the fluctuations of mass have a power spectrum that varies as 1 f for frequencies in the range 3 ensuremath 2n ensuremath ll f ensuremath ll 1 t the activity fluctuations in the same frequency range have a power spectrum that is linear in f

motivic cohomology over dedekind rings we study properties of bloch s higher chow groups on smooth varieties over dedekind rings we prove the vanishing of open image in new window for i n and the existence of a gersten resolution for open image in new window if the residue characteristic is p we also show that the bloch kato conjecture implies the beilinson lichtenbaum conjecture open image in new window an identification open image in new window for m invertible and a gersten resolution with arbitrary finite coefficients over a complete discrete valuation ring of mixed characteristic 0 p we construct a map from motivic cohomology to syntomic cohomology which is a quasi isomorphism provided the bloch kato conjecture holds

including long range dependence in integrate and fire models of the high interspike interval variability of cortical neurons many different types of integrate and fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains within this context the variability of spike trains has been almost exclusively measured using the coefficient of variation of interspike intervals however another important statistical property that has been found in cortical spike trains and is closely associated with their high firing variability is long range dependence we investigate the conditions if any under which such models produce output spike trains with both interspike interval variability and long range dependence similar to those that have previously been measured from actual cortical neurons we first show analytically that a large class of high variability integrate and fire models is incapable of producing such outputs based on the fact that their output spike trains are always mathematically equivalent to renewal processes this class of models subsumes a majority of previously published models including those that use excitation inhibition balance correlated inputs partial reset or nonlinear leakage to produce outputs with high variability next we study integrate and fire models that have nonpoissonian renewal point process inputs instead of the poisson point process inputs used in the preceding class of models the confluence of our analytical and simulation results implies that the renewal input model is capable of producing high variability and long range dependence comparable to that seen in spike trains recorded from cortical neurons but only if the interspike intervals of the inputs have infinite variance a physiologically unrealistic condition finally we suggest a new integrate and fire model that does not suffer any of the previously mentioned shortcomings by analyzing simulation results for this model we show that it is capable of producing output spike trains with interspike interval variability and long range dependence that match empirical data from cortical spike trains this model is similar to the other models in this study except that its inputs are fractional gaussian noise driven poisson processes rather than renewal point processes in addition to this model s success in producing realistic output spike trains its inputs have long range dependence similar to that found in most subcortical neurons in sensory pathways including the inputs to cortex analysis of output spike trains from simulations of this model also shows that a tight balance between the amounts of excitation and inhibition at the inputs to cortical neurons is not necessary for high interspike interval variability at their outputs furthermore in our analysis of this model we show that the superposition of many fractional gaussian noise driven poisson processes does not approximate a poisson process which challenges the common assumption that the total effect of a large number of inputs on a neuron is well represented by a poisson process

fractal renewal processes two relatively simple renewal processes whose power spectral densities vary as 1 f sup d are constructed 1 a standard renewal point process with 0

on galois structure invariants associated to tate motives we establish the equivalence of two definitions of invariants measuring the galois module structure of k groups of rings of integers in number fields due to chinburg et al on the one hand and the authors on the other we also make some remarks concerning the possibility of yet another such definition via lichtenbaum complexes

spectral representation of fractional brownian motion in n dimensions and its properties fractional brownian motion fbm provides a useful model for processes with strong long term dependence such as 1 f sup spl beta spectral behavior however fbm s are nonstationary processes so that the interpretation of such a spectrum is still a matter of speculation to facilitate the study of this problem another model is provided for the construction of fbm from a white noise like process by means of a stochastic or ito integral in frequency of a stationary uncorrelated random process also a generalized power spectrum of the nonstationary fbm process is defined this new approach to fbm can be used to compute all of the correlations power spectra and other properties of fbm in this paper a number of these fbm properties are developed from this model such as the t sup h law of scaling the power law of fractional order the correlation of two arbitrary fbm s and the evaluation of the fractal dimension under various transformations this new treatment of fbm using a spectral representation is extended also for the first time to two or more topological dimensions in order to analyze the features of isotropic n dimensional fbm

on motivic cohomology with z l coefficients in this paper we prove the conjecture of bloch and kato which relates milnor s k theory of a field with its galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the nisnevich and etale topologies

the weil etale topology for number rings there should be a grothendieck topology for an arithmetic scheme x such that the euler characteristic of the cohomology groups of the constant sheaf z with compact support at infinity gives up to sign the leading term of the zeta function of x at s 0 we construct a topology the weil etale topology for the ring of integers in a number field whose cohomology groups hl z determine such an euler characterstic if we restrict to 3

scaling of swimming sequences in copepod behavior data analysis and simulation abstract we consider symbolic sequences of copepod behavior classified as break and slow swimming states successive residence times for each state have been recorded for 327 symbolic times series obtained from 52 different trajectories we performed a symbolic dynamics analysis of the succession of states and showed that the probability densities of the duration of each state obey power laws for large times we analyzed the transition between states and showed as expected the non markovian properties of this dynamics we further simulate a copepod trajectory using an alternate renewal process for the generation of the sequence time series and using a brownian motion for the copepod motion during swimming periods

modeling heterogeneous network interference using poisson point processes cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells relays and distributed antennas unfortunately the resulting interference environment is also becoming more complicated making evaluation of different communication strategies challenging in both analysis and simulation leveraging recent applications of stochastic geometry to analyze cellular systems this paper proposes to analyze downlink performance in a fixed size cell which is inscribed within a weighted voronoi cell in a poisson field of interferers a nearest out of cell interferer out of cell interferers outside a guard region and cross tier interferers are included in the interference calculations bounding the interference power as a function of distance from the cell center the total interference is characterized through its laplace transform an equivalent marked process is proposed for the out of cell interference under additional assumptions to facilitate simplified calculations the interference distribution is approximated using the gamma distribution with second order moment matching the gamma approximation simplifies calculation of the success probability and average rate incorporates small scale and large scale fading and works with co tier and cross tier interference simulations show that the proposed model provides a flexible way to characterize outage probability and rate as a function of the distance to the cell edge

fractal renewal processes generate 1 f noise 1 mathit f mathit d noise occurs in an impressive variety of physical systems and numerous complex theories have been proposed to explain it we construct two relatively simple renewal processes whose power spectral densities vary as 1 mathit f mathit d i a standard renewal point process with 0d1 and ii a finite valued alternating renewal process with 0d2 the resulting event number statistics coincidence rates minimal coverings and autocorrelation functions are shown also to follow power law forms these fractal characteristics derive from interevent time probability density functions which themselves decay in a power law fashion a number of applications are considered trapping in amorphous semiconductors electronic burst noise movement in systems with fractal boundaries the digital generation of 1 mathit f mathit d noise and ionic currents in cell membranes

statistical properties of one dimensional binary sequences with power law power spectrum abstract by the fourier filtering method we generate one dimensional binary sequences from coarse grained continuous sequences with preset exponents 0 using the spectrum analysis we find that the corresponding binary sequences have pure 1 f power spectrum and spectrum exponents 0 0 2 0 where f is the frequency we evaluate numerically the relation between and 0 using the autocorrelation function analysis the detrended fluctuation analysis the duration time analysis and the entropy analysis we investigate extensively the statistical properties of such binary sequences we find that the statistical properties are basically different for 1 and 1 and binary sequences become more and more ordered as increases

weak differentiability of product measures in this paper we study cost functions over a finite collection of random variables for these types of models a calculus of differentiation is developed that allows us to obtain a closed form expression for derivatives where differentiation has to be understood in the weak sense the technique for proving the results is new and establishes an interesting link between functional analysis and gradient estimation the key contribution of this paper is a product rule of weak differentiation in addition a product rule of weak analyticity is presented that allows for taylor series approximations of finite products measures in particular from characteristics of the individual probability measures a lower bound i e domain of convergence can be established for the set of parameter values for which the taylor series converges to the true value applications of our theory to the ruin problem from insurance mathematics and to stochastic activity networks arising in project evaluation review techniques are provided

duality via cycle complexes we show that bloch s complex of relative zero cycles can be used as a dualizing complex over perfect fields and number rings this leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields finite fields local fields of mixed characteristic and rings of integers in number rings generalizing results which so far have only been known for smooth schemes or in low dimensions and unifying the p adic and l adic theory as an application we generalize rojtman s theorem to normal projective schemes

the bloch kato conjecture and a theorem of suslin voevodsky we give a new proof of the theorem of suslin voevodsky which shows that the bloch kato conjecture implies a portion of the beilinsonlichtenbaum conjectures our proof does not rely on resolution of singularities and thereby extends the suslin voevodsky theorem to positive characteristic

universal generation of 1 f noises this paper establishes a universal mechanism for the generation of 1 f noises the mechanism is based on a signal superposition model which superimposes signals transmitted from independent sources all sources transmit a statistically common yet arbitrary stochastic signal pattern each source has its own random transmission parameters amplitude frequency and initiation epoch we explore randomizations of the transmission parameters which render the power spectrum of the super imposed signal invariant with respect of the stochastic signal pattern transmitted analysis shows that the aforementioned randomizations yield superimposed signals which are 1 f noises the result obtained is in effect a randomized central limit theorem for 1 f noises

average sensitive and blackwell optimal policies in denumerable markov decisionchains with unbounded rewards in this paper we consider a discrete time markov decision chain with a denumerable state space and compact action sets and we assume that for all states the rewards and transition probabilities depend continuously on the actions the first objective of this paper is to develop an analysis for average optimality without assuming a special markov chain structure in doing so we present a set of conditions guaranteeing average optimality which are automatically fulfilled in the finite state and action model the second objective is to study simultaneously average and discount optimality as veinott veinott a f jr 1969 on discrete dynamic programming with sensitive discount optimality criteria ann math statist 40 1635 1660 did for the finite state and action model we investigate the concepts of n discount and blackwell optimality in the denumerable state space using a laurent series expansion for the discounted rewards under the same condition as for average optimality we establish solutions to the n discount optimality equations for every n

dry friction avalanches experiment and theory experimental evidence and theoretical models are presented supporting the conjecture that dry friction stick slip is described by self organized criticality we use the data obtained with a pin on disk tribometer set to measure lateral force to examine the variation of the friction force as a function of time we study nominally flat surfaces of matching aluminum and steel the probability distribution of force drops follows a negative power law with exponents ensuremath mu in the range 3 2 3 5 the frequency power spectrum follows a 1 f ensuremath alpha pattern with ensuremath alpha in the range 1 1 8 we first compare these experimental results with the well known robin hood model of self organized criticality we find good agreement between theory and experiment for the force drop distribution but not for the power spectrum we explain this on a physical basis and propose a model which takes explicitly into account the stiffness and inertia of the tribometer specifically we numerically solve the equation of motion of a block on a friction surface pulled by a spring and show that for certain spring constants the motion is characterized by the same power law spectrum as in experiments we propose a physical picture relating the fluctuations of the force drops to the microscopic geometry of the surface

analytically solvable autocorrelation function for weakly correlated interevent times long term temporal correlations observed in event sequences of natural and social phenomena have been characterized by algebraically decaying autocorrelation functions such temporal correlations can be understood not only by heterogeneous interevent times iets but also by correlations between iets in contrast to the role of heterogeneous iets on the autocorrelation function little is known about the effects due to the correlations between iets to rigorously study these effects we derive an analytical form of the autocorrelation function for the arbitrary iet distribution in the case with weakly correlated iets where the farlie gumbel morgenstern copula is adopted for modeling the joint probability distribution function of two consecutive iets our analytical results are confirmed by numerical simulations for exponential and power law iet distributions for the power law case we find a tendency of the steeper decay of the autocorrelation function for the stronger correlation between iets our analytical approach enables us to better understand long term temporal correlations induced by the correlations between iets

power law shot noise and its relationship to long memory spl alpha stable processes we consider the shot noise process whose associated impulse response is a decaying power law kernel of the form t sup spl beta 2 1 we show that this power law poisson model gives rise to a process that at each time instant is an spl alpha stable random variable if spl beta 1 the power law poisson process has a power law spectrum we show that although in the case spl beta 1 the power spectrum does not exist the process still exhibits long memory in a generalized sense the power law shot noise process appears in many applications in engineering and physics the proposed results can be used to study such processes as well as to synthesize a random process with long range dependence

stochastic approximation methods for systems over an infinitehorizon the paper develops efficient and general stochastic approximation sa methods for improving the operation of parametrized systems of either the continuous or discrete event dynamical systems types and which are of interest over a long time period for example one might wish to optimize or improve the stationary or average cost per unit time performance by adjusting the systems parameters the number of applications and the associated literature are increasing at a rapid rate this is partly due to the increasing activity in computing pathwise derivatives and adapting them to the average cost problem although the original motivation and the examples come from an interest in the infinite horizon problem the techniques and results are of general applicability in sa we present an updating and review of powerful ordinary differential equation type methods in a fairly general context and based on weak convergence ideas the results and proof techniques are applicable to a wide variety of applications exploiting the full potential of these ideas can greatly simplify and extend much current work their breadth as well as the relative ease of using the basic ideas are illustrated in detail via typical examples drawn from discrete event dynamical systems piecewise deterministic dynamical systems and a stochastic differential equations model in these particular illustrations we use either infinitesimal perturbation analysis type estimators mean square derivative type estimators or finite difference type estimators markov and non markov models are discussed the algorithms for distributed asynchronous updating as well as the fully synchronous schemes are developed

informational and causal architecture of continuous time renewal processes we introduce the minimal maximally predictive models epsilon text machines of processes generated by certain hidden semi markov models their causal states are either discrete mixed or continuous random variables and causal state transitions are described by partial differential equations as an application we present a complete analysis of the epsilon text machines of continuous time renewal processes this leads to closed form expressions for their entropy rate statistical complexity excess entropy and differential information anatomy rates

weil etale cohomology over finite fields we calculate the derived functors r for the base change from the weil etale site to the etale site for a variety over a finite field for smooth and proper varieties we apply this to express tate s conjecture and lichtenbaum s conjecture on special values of functions in terms of weil etale cohomology of the motivic complex n

intrinsic fractality of classic shot noise we revisit the classic shot noise of campbell and schottky char22 a stochastic process governed by ornstein uhlenbeck dynamics driven by a poissonian noise exploring the order statistics of the shot magnitudes composing its stationary noise level we show that classic shot noise is intrinsically fractal this fractality is manifested by mathbf i intrinsic paretian and scale invariant structures mathbf ii an intrinsic power law scaling mathbf iii an intrinsic statistical resilience to random power law perturbations

measure valued differentiation for stationary markov chains we study general state space markov chains that depend on a parameter say sufficient conditions are established for the stationary performance of such a markov chain to be differentiable with respect to specifically we study the case of unbounded performance functions and thereby extend the result on weak differentiability of stationary distributions of markov chains to unbounded mappings first a closed form formula for the derivative of the stationary performance of a general state space markov chain is given using an operator theoretic approach in a second step we translate the derivative formula into unbiased gradient estimators specifically we establish phantom type estimators and score function estimators we illustrate our results with examples from queueing theory

an etale cohomology duality theorem for number fields with a real embedding abstract the restriction on 2 primary components in the artin verdier duality theorem 2 has been eliminated by zink 9 who has shown that the sheaf of units for the etale topology over the ring of integers of any number field acts as a dualizing sheaf for a modified cohomology of sheaves the present paper provides an alternate means of removing the 2 primary restriction like zink s it involves a topology which includes infinite primes but it avoids modified cohomology and will be more directly applicable in the proof of a theorem of lichtenbaum regarding zetaand l functions 4 5 related results including the cohomology of units sheaves the norm theorem and punctual duality theorem of mazur 6 are also affected by the use of a topology including the infinite primes the corresponding results in the new setting are included here

non linear shot noise levy noah joseph abstract we introduce and study a generic non linear shot noise system model shots of random magnitudes arrive to the system stochastically following an arbitrary time homogeneous poisson point process after hitting the system the magnitude of an arriving shot decays to zero the decay is governed by an arbitrary differential equation dynamics shots are independent and their overall effect on the system is additive the system s noise level at time t equals the sum of the magnitudes at time t of all the shots arriving to the system prior to time t the resulting shot noise is i a levy process when the decay dynamics are degenerate ii a levy driven ornstein uhlenbeck process when the decay dynamics are linear and iii a stationary non markov process when the decay dynamics are non linear the resulting shot noise admits an underlying levy structure which we explicitly compute and can yield both the noah effect and the joseph effect closed form analytic formulae for various statistics are derived including the log laplace transform and cumulants of the stationary noise level the process auto covariance function and the process range of dependence

evolutionary dynamics on measurable strategy spaces asymmetric games abstract the theory of evolutionary dynamics in asymmetric games has been mainly studied for games with a finite strategy space in this paper we introduce an evolutionary dynamics model for asymmetric games where the strategy sets are measurable spaces separable metric spaces under this hypothesis the replicator dynamics is in a banach space we specify conditions under which the replicator dynamics has a solution furthermore under suitable assumptions a critical point of the system is stable finally an example illustrates our results

studying the sinr process of the typical user in poisson networks using its factorial moment measures based on a stationary poisson point process a wireless network model with random propagation effects shadowing and or fading is considered in order to examine the process formed by the signal to interference plus noise ratio sinr values experienced by a typical user with respect to all the base stations in the down link channel this sinr process is completely characterized by deriving its factorial moment measures which involve numerically tractable explicit integral expressions this novel framework naturally leads to expressions for the k coverage probability including the case of random sinr threshold values considered in multi tier network models while the k coverage probabilities correspond to the marginal distributions of the order statistics of the sinr process a more general relation is presented connecting the factorial moment measures of the sinr process to the joint densities of these order statistics this gives a way for calculating the exact values of the coverage probabilities arising in a general scenario of signal combination and interference cancellation between base stations the presented framework consisting of the mathematical representations of sinr characteristics with respect to the factorial moment measures holds for the whole domain of sinr and is amenable to considerable model extension

universal poisson process limits for general random walks abstract this paper considers ensembles of general independent and identically distributed random walks taking the ensemble size to grow infinitely large and also taking the running time of the random walks to grow infinitely large universal poisson process limits are obtained specifically it is established that the positions of general linear random walks converge universally to poisson processes over the real line with uniform and exponential intensities and it is established that the positions of general geometric random walks converge universally to poisson processes over the positive half line with harmonic and power intensities corollaries to these universal convergence results yield the extreme value statistics of gumbel weibull and frechet

spectral 1 f noise derived from extremized physical information we consider the evolution of a temporal signal x t that is an intrinsic random field of order zero in the sense of a certain measurement estimation experiment the state of disorder of x t should increase toward an equilibrium state the disorder of x t is measured by its physical information scri and the equilibrium state is determined by the condition that scri be an extremum the equilibrium state is shown to have a power spectrum s ensuremath omega of the form mathrm ensuremath omega mathrm ensuremath mathrm ensuremath alpha 1 ensuremath le ensuremath alpha ensuremath le 2 that of 1 f noise

theory of non markovian stochastic resonance we consider a two state model of non markovian stochastic resonance sr within the framework of the theory of renewal processes residence time intervals are assumed to be mutually independent and characterized by some arbitrary nonexponential residence time distributions which are modulated in time by an externally applied signal making use of a stochastic path integral approach we obtain general integral equations governing the evolution of conditional probabilities in the presence of an input signal these equations generalize earlier integral renewal equations by cox and others to the case of driving induced nonstationarity on the basis of these equations a response theory of two state renewal processes is formulated beyond the linear response approximation moreover a general expression for the linear response function is derived the connection of the developed approach with the phenomenological theory of linear response for manifest non markovian sr put forward i goychuk and p hanggi phys rev lett 91 070601 2003 is clarified and its range of validity is scrutinized the theory is then applied to sr in symmetric non markovian systems and to the class of single ion channels possessing a fractal kinetics

symbolic strings and spatial 1 f spectra abstract some string dynamics which are expected to show non trivial correlations are proposed and studied it is because we were motivated by the observation that some dna sequences show spatial 1 f correlation our model is based on a rule by which one string is split into two parts in the middle and another string is inserted between them when the strings are made longer the basic model shows long range correlations with a structure characteristic of cyclic patterns on the log log plot of the spectrum the effects of string cross over and point mutation are also studied the cross over destroys the structures appearing in the basic model and makes 1 f like correlation clear the point mutation makes the power spectrum flat as is expected from the white noise nature the analogy of the cross over model with real dna evolution dynamics is suggested

estimating the intermittency of point processes with applications to human activity and viral dna abstract the intermittency of a point process is the extent to which the number of events in a time window has pronounced departures from typical values combining point process and multifractal formalisms indicates that the correlation codimension can be used to quantify intermittency the correlation codimension is easily estimated and is simply related to other second order scaling exponents such as those of the fano factor and spectral density the correlation codimensions are derived for various uncorrelated fractal and fractal rate point processes in addition the estimation of intermittency as the correlation codimension of experimental events is illustrated with applications to experimental data human activity during bed rest is highly intermittent while other human activity and viral dna composition are non intermittent

langevin unification of fractional motions we present a physical langevin based theory explaining the emergence and pervasiveness of the following fractional motions brownian motion l vy motion fractional brownian motion and fractional l vy motion a general form of micro level langevin dynamics with infinitely many degrees of freedom is considered transcending from the micro level to the macro level the infinitely many degrees of freedom collapse to two characteristic exponents and the aforementioned fractional motions emerge universally the exponents categorize the fractional motions and determine their statistical and topological properties the theory establishes a unified langevin bedrock to fractional motions which are widely applied prototypical models of random transport in the sciences

on motivic decompositions arising from the method of bialynicki birula recently v chernousov s gille and a merkurjev have obtained a decomposition of the motive of an isotropic smooth projective homogeneous variety analogous to the bruhat decomposition using the method of a bialynicki birula and a corollary which is essentially due to s del bano i generalize this decomposition to the case of a possibly anisotropic smooth projective variety homogeneous under the action of an isotropic reductive group this answers a question of n karpenko