rbf methods in a stochastic volatility framework for greeks computation abstract in this paper we aim to apply a new proposed meshless approach for heston pde resolution in mathematical finance most classical models may be reformulated as partial differential equations pde which are commonly solved by finite difference and monte carlo methods alternatively bio inspired methods may be considered to select parameters and to solve said pdes in particular we focus on heston model pde and we solve it via radial basis functions rbf methods moreover some considerations on the computation of model parameters through learning approaches have been discussed we aim to price a vanilla call option focusing on the derivation of the formulae for its greeks profiles eventually we conclude rbfs are an accurate alternative method to price derivatives in a stochastic volatility framework especially since they allow for a fast and precise computation of greeks

adams filtration and generalized hurewicz maps for infinite loopspaces we study the hurewicz map begin aligned h pi x rightarrow r omega infty x end aligned where omega infty x is the 0th space of a spectrum x and r is the generalized homology theory associated to a connective commutative s algebra r we prove that the decreasing filtration of the domain associated to an r based adams resolution is compatible with a filtration of the range associated to the augmentation ideal filtration of the augmented commutative s algebra sigma infty omega infty x the proof of our main theorem makes much use of composition properties of this filtration and its interaction with topological andre quillen homology an application is a connectivity theorem localize away from p 1 and suppose x is c 1 connected with c 0 if alpha in pi x has adams filtration s and alpha cp s then h alpha 0 in r omega infty x when specialized to mod p homology this implies a finiteness theorem if h x mathbb z p is finitely presented as a module over the steenrod algebra then the image of the hurewicz map in h omega infty x mathbb z p is finite we illustrate these theorems with calculations of the mod 2 hurewicz image of bo its connected covers and omega infty tmf and the mod p hurewicz image of all the spaces in the bp and bp langle n rangle spectra en route we get new proofs of theorems of milnor and wilson in the special case when x is the suspension spectrum of a space z and r h mathbb z 2 we recover results announced by lannes and zarati in the 1980s relating the adams filtration of pi s z to dyer lashof length in h qz mathbb z 2 and generalize them to all primes p for any x we also get parallel results for the hurewicz map for morava e theory where pi x is now given the adams novikov filtration

a first passage time distribution for a discrete version of the ornstein uhlenbeck process the probability of the first entrance to the negative semi axis for a one dimensional discrete ornstein uhlenbeck o u process is studied in this work the discrete o u process is a simple generalization of the random walk and many of its statistics may be calculated using essentially the same formalism in particular the case in which sparre andersen s theorem applies for normal random walks is considered and it is shown that the universal features of the first passage probability do not extend to the discrete o u process finally an explicit expression for the generating function of the probability of first entrance to the negative real axis at step n is calculated and analysed for a particular choice of the step distribution

numerical determination of hitting time distributions from their laplace transforms simple cases abstract an important problem in probabilistic modeling consists of the determination of the distribution function of a positive random variable in particular a hitting time from its laplace transform in this note we use two versions of the method of maximum entropy to invert the laplace transform using a few of its values on the real line or equivalently a few fractional moments of the exponential of the variable to compare the performance of the methods we consider some simple one dimensional examples in which the laplace transform can be computed by solving a differential equation exactly and comparisons can be made

determination of the distribution of total loss from the fractional moments of its exponential in the insurance and banking industries as in many branches of engineering in many instances a model can be proposed to describe either the accumulated losses or the accumulated damage or stress such models are of the compound type namely random sums of independent positive random variables and a reliable statistical model is available for both but computing the distribution of such random sums is a hard problem that has received much attention here we propose a technique based on the maximum entropy method which makes use of the fractional moments of the exponential of the accumulated loss which is available since for many models the laplace transform can be exactly determined here we provide an answer to the question of how to determine distribution of a total severity when the only information that we have consists of the laplace transform of the compound distribution our technique yields fairly good reconstructions from a low number of fractional moments

a fast algorithm for scalar nevanlinna pick interpolation in this paper we derive a fast algorithm for the scalar nevanlinna pick interpolation givenn distinct pointsz i in the unit disk z 1 andn complex numbersw i satisfying the pick condition for 1 i n the new nevanlinna pick interpolation algorithm requires onlyo n arithmetic operations to evaluate the interpolatory rational function at a particular value ofz in contrast to the classical algorithm which requireso n 2 arithmetic operations to compute the so called fenyves array which is inherent in the classical algorithm the new algorithm bypasses the generation of the fenyves array to speed up the computation and also yields a parallel scheme requiring onlyo logn arithmetic operations on a concurrent read exclusive write parallel random access machine withn processors we must remark that the rational functionf z computed by the new algorithm is one degree higher than the function computed by the classical algorithm

a uniqueness theorem for stable homotopy theory roughly speaking the stable homotopy category of algebraic topology is obtained from the homotopy category of topological spaces by inverting the suspension functor yielding a linear approximation to the homotopy category of spaces the isomorphism classes of objects in the stable homotopy category represent the generalized cohomology theories defined by the eilenberg steenrod axioms es45 without the dimension axiom which distinguishes ordinary from generalized cohomology theories the first construction of the full stable homotopy category was given by boardman b69 nowadays manymodels for the stable homotopy category are known most of which have the additional structure of a closed model category in the sense of quillen q67 in m83 h r margolis introduced a short list of axioms and conjectured that they characterize the stable homotopy category up to an equivalence of categories in theorem 3 2 we prove that these axioms do uniquely specify the stable homotopy category whenever there is some underlying quillen model category we also prove amore structured version theuniqueness theorembelow which states that the model category of spectra itself is uniquely determined by certain equivalent conditions up to so called quillen equivalence of

the goodwillie tower of the identity functor and the unstable periodic homotopy of spheres we investigate goodwillie s taylor tower of the identity functor from spaces to spaces more specifically we reformulate johnson s description of the goodwillie derivatives of the identity and prove that in the case of an odd dimensional sphere the only layers in the tower that are not contractible are those indexed by powers of a prime moreover in the case of a sphere the tower is finite in v k periodic homotopy

auditory discrimination of force of impact the auditory discrimination of force of impact was measured for three groups of listeners using sounds synthesized according to first order equations of motion for the homogenous isotropic bar morse and ingard 1968 theoretical acoustics pp 175 191 the three groups were professional percussionists nonmusicians and individuals recruited from the general population without regard to musical background in the two interval forced choice procedure listeners chose the sound corresponding to the greater force of impact as the length of the bar varied from one presentation to the next from the equations of motion a maximum likelihood test for the task was determined to be of the form log a log f 0 where a and f are the amplitude and frequency of any one partial and 0 5 relative decision weights on log f were obtained from the trial by trial responses of listeners and compared to percussionists generally outperformed the other groups however the obtained decision weights of all listeners deviated significantly from and showed variability within groups far in excess of the variability associated with replication providing correct feedback after each trial had little effect on the decision weights the variability in these measures was comparable to that seen in studies involving the auditory discrimination of other source attributes

tate cohomology and periodic localization of polynomial functors in this paper we show that goodwillie calculus as applied to functors from stable homotopy to itself interacts in striking ways with chromatic aspects of the stable category localized at a fixed prime p let t n be the telescope of a v n self map of a finite s module of type n the periodicity theorem of hopkins and smith implies that the bousfield localization functor associated to t n is independent of choices goodwillie s general theory says that to any homotopy functor f from s modules to s modules there is an associated tower under f p d f such that f p d f is the universal arrow to a d excisive functor our first main theorem says that p d f pd 1f always admits a homotopy section after localization with respect to t n and so also after localization with respect to morava k theory k n thus after periodic localization polynomial functors split as the product of their homogeneous factors this theorem follows from our second main theorem which is equivalent to the following for any finite group g the tate spectrum mathcal t g t n is weakly contractible this strengthens and extends previous theorems of greenlees sadofsky hovey sadofsky and mahowald shick the periodicity theorem is used in an essential way in our proof the connection between the two theorems is via a reformulation of a result of mccarthy on dual calculus

lifting homotopy t algebra maps to strict maps abstract the settings for homotopical algebra categories such as simplicial groups simplicial rings a spaces e ring spectra etc are often equivalent to categories of algebras over some monad or triple t in such cases t is acting on a nice simplicial model category in such a way that t descends to a monad on the homotopy category and defines a category of homotopy t algebras in this setting there is a forgetful functor from the homotopy category of t algebras to the category of homotopy t algebras under suitable hypotheses we provide an obstruction theory in the form of a bousfield kan spectral sequence for lifting a homotopy t algebra map to a strict map of t algebras once we have a map of t algebras to serve as a basepoint the spectral sequence computes the homotopy groups of the space of t algebra maps and the edge homomorphism on 0 is the aforementioned forgetful functor we discuss a variety of settings in which the required hypotheses are satisfied including monads arising from algebraic theories and operads we also give sufficient conditions for the e 2 term to be calculable in terms of quillen cohomology groups we provide worked examples in g spaces g spectra rational e algebras and a algebras explicit calculations connected to rational unstable homotopy theory show that the forgetful functor from the homotopy category of e ring spectra to the category of h ring spectra is generally neither full nor faithful we also apply a result of the second named author and nick kuhn to compute the homotopy type of the space e coker j l k 2 r

poincare koszul duality we prove a duality for factorization homology which generalizes both usual poincare duality for manifolds and koszul duality for mathcal e n algebras the duality has application to the hochschild homology of associative algebras and enveloping algebras of lie algebras we interpret our result at the level of topological quantum field theory

material identification of real impact sounds effects of size variation in steel glass wood and plexiglass plates identification of the material of struck objects of variable size was investigated previous studies on this issue assumed recognition to be based on acoustical measures of damping this assumption was tested comparing the power of a damping measure in explaining identification data with that of several other acoustical descriptors listeners performance was perfect with respect to gross material categories steel glass and wood plexiglass comprising materials of vastly different mechanical properties impaired performance was observed for materials within the same gross category identification being based on the size of the objects alone the damping descriptor accounted for the identification of the gross categories however other descriptors such as signal duration explained the results equally well materials within the same gross category were identified mainly on the basis of signal frequency overall poor support for the relevance of damping to material perception was found an analysis of the acoustical support for perfect material identification was carried out sufficient acoustical information for perfect performance was found thus procedural biases for the origin of the effects of size could be discarded pointing toward their cognitive rather than methodological nature identification performance was explained in terms of the regularities of the everyday acoustical environment

stochastic order parameter equation of isometric force production revealed by drift diffusion estimates we address two questions that are central to understanding human motor control variability what kind of dynamical components contribute to motor control variability i e deterministic and or random ones and how are those components structured to this end we derive a stochastic order parameter equation for isometric force production from experimental data using drift diffusion estimates we show that the force variability increases with the required force output because of a decrease of deterministic stability and an accompanying increase of noise intensity a structural analysis reveals that the deterministic component consists of a linear control loop while the random component involves a noise source that scales with force output in addition we present evidence for the existence of a subject independent overall noise level of human isometric force production

homotopical localizations of spaces for a map f of spaces dror farjoun and the author have constructed an f localization functor where a space y is called f local when map f y is an equivalence this very general construction gives all known idempotent homotopy functors of spaces the main theorem of this paper shows that f localization functors always preserve fiber sequences of connected h spaces up to small error terms for instance the localization with respect to the n th morava k theory preserves such fiber sequences up to error terms with at most three nontrivial homotopy groups this implies for example that a k 1 homology equivalence of h spaces must induce an isomorphism of v 1 periodic homotopy groups results are also obtained on the a nullification or a periodization functors which are just the f localization functors for the maps f from spaces a to points two spaces are said to have the same nullity when they give the same nullification functors and it is shown that arbitrary sets of nullity classes have both least upper bounds and greatest lower bounds the a nullifications of nilpotent postnikov spaces are completely determined

a proof of convergence for ant algorithms a proof of convergence for ant algorithms is developed ant algorithms were modeled as branching random processes the branching random walk and branching wiener process to derive rates of birth and death of ant paths substitution is then carried out in birth death processes which proves that a stable distribution is surely reached this indicates that ant algorithms converge with probability one this analogy models ant algorithms complexity parameters such as the number of cycles the degrees of freedom of problem and the number of ants

edge detection in noisy data using finite mixture distribution analysis abstract an algorithm which identifies discontinuities in noisy data is presented the signal is modelled as step edges with additive normally distributed noise present using finite mixture analysis and information criteria a variable number of mixtures are identified together with the location of the respective edges separating them the problem is solved using a dynamic programming approach which ensures globally optimal edge positions according to the signal model of a finite mixture of normal distributions the computational complexity is of order mn 2 where m is the number of discontinuities in the mixture and n is the number of data points in the signal the algorithm is tested on a range of real and synthetic signals and yields as accurate edge positions as a corresponding minimum square error method among applications for this algorithm is edge detection in medical images and examples from ultrasound imaging are included

james maps and en ring spaces we parametrize by operad actions the multiplicative analysis of the total james map given by caruso and ourselves the target of the total james map q c r n x it qdq r n x q o is an en ring space and is a en map where en is the little n cubes operad this implies that has an n fold delooping with domain n x it also implies an algorithm for the calculation of and thus of each q on mod p homology when n 00 and p 2 this algorithm is the essential starting point for kuhn s proof of the whitehead conjecture in 2 4 we analyzed the behavior with respect to pairings of the lames maps iq ex qdq e x used in 4 to obtain the stable splittings of spaces ex in particular we proved that if the given coefficient system e has a sum then the product of the targets is a ring space and the product of the iq s is an exponential h map in fact this is only a fragment of the full structure present in the most interesting examples in the first two sections we give a parametrized elaboration of this analysis we assume the given coefficient system e is a module over an operad and we deduce essentially that

an introduction to stochastic modeling stochastic modeling probability review the major discrete distributions rtant continuous distributions some elementary exercises useful functions integrals and sums conditional probability and conditional expectation the discrete case the dice game craps random sums conditioning on a continuous random variable markov chains introduction definitions transition probability matrices of a markov chain some markov chain models first step analysis some special markov chains functionals of random walks and success runs another look at first step analysis the long run behavior of markov chains regular transition probability matrices examples the classification of states the basic limit theorem of markov chains reducible markov chains sequential decisions and markov chains poisson processes the poisson distribution and the poisson processes the law of rare events distributions associated with the poisson process the uniform distribution and poisson processes spatial poisson processes compound and marked poisson processes continuous time markov chains pure birth processes ptire death processes birth and death processes the limiting behavior of birth and death processes birth and death processes with absorbing states finite state continuous time markov chains set valued processes renewal phenomena definition of a renewal process and related concepts some examples of renewal processes the poisson process viewed as a renewal process the asymptotic 3ehavior as renewal process

numerical determination of hitting time distributions from their laplace transforms one dimensional diffusions abstract in a previous paper we studied a method to determine the probability density of barrier crossing times by a brownian motion from the knowledge of its laplace transform this knowledge combined with the method of maximum entropy yields quite good reconstructions the aim of this work is to extend the previous analysis in two directions on one hand we consider diffusions with non constant coefficients this forces us to determine the laplace transform numerically or by means of simulations on the other hand and this is the gist of this note as numerical problems involve errors we consider as well two possible extensions of the maximum entropy procedure which allow us to incorporate those errors into the probability reconstruction process

generalized group characters and complex oriented cohomology theories let bg be the classifying space of a finite group g given a multiplicative cohomology theory e the assignment g 7i e bg is a functor from groups to rings endowed with induction transfer maps in this paper we investigate these functors for complex oriented cohomology theories e using the theory of complex representations of finite groups as a model for what one would like to know an analogue of artin s theorem is proved for all complex oriented e the abelian subgroups of g serve as a detecting family for e bg modulo torsion dividing the order of g when e is a complete local ring with residue field of characteristic p and associated formal group of height n we construct a character ring of class functions that computes 1 e bg the domain of the characters is gn p the set of n tuples of elements in g each of which has order a power of p a formula for induction is also found the ideas we use are related to the lubin tate theory of formal groups the construction applies to many cohomology theories of current interest completed versions of elliptic cohomology e n theory etc the nth morava k theory euler characteristic for bg is computed to be the number of g orbits in gn p for various groups g including all symmetric groups we prove that k n bg concentrated in even degrees our results about e bg extend to theorems about e eg gx where x is a finite g cw complex

on the telescopic homotopy theory of spaces in telescopic homotopy theory a space or spectrum x is approximated by a tower of localizations lnx n 0 taking account of vn periodic homotopy groups for progressively higher n for each n 1 we construct a telescopic kuhn functor n carrying a space to a spectrum with the same vn periodic homotopy groups and we construct a new functor n left adjoint to n using these functors we show that the nth stable monocular homotopy category comprising the nth fibers of stable telescopic towers embeds as a retract of the nth unstable monocular homotopy category in two ways one giving infinite loop spaces and the other giving infinite ln suspension spaces we deduce that ravenel s stable telescope conjectures are equivalent to unstable telescope conjectures in particular we show that the failure of ravenel s nth stable telescope conjecture implies the existence of highly connected infinite loop spaces with trivial johnson wilson e n homology but nontrivial vn periodic homotopy groups showing a fundamental difference between the unstable chromatic and telescopic theories as a stable chromatic application we show that each spectrum is k n equivalent to a suspension spectrum as an unstable chromatic application we determine the e n localizations and k n localizations of infinite loop spaces in terms of e n localizations of spectra under suitable conditions we also determine the e n localizations and k n localizations of arbitrary postnikov h spaces

analysis of inverse stochastic resonance and the long term firing of hodgkin huxley neurons with gaussian white noise abstract in order to explain the occurrence of a minimum in firing rate which occurs for certain mean input levels as noise level increases inverse stochastic resonance isr in hodgkin huxley hh systems we analyze the underlying transitions from a stable equilibrium point to limit cycle and vice versa for a value of at which isr is pronounced properties of the corresponding stable equilibrium point are found a linearized approximation around this point has oscillatory solutions from whose maxima spikes tend to occur a one dimensional diffusion is also constructed for small noise properties of the basin of attraction of the limit cycle spike are investigated heuristically long term trials of duration 500000 ms are carried out for values of from 0 to 2 0 the graph of mean spike count versus is divided into 4 regions r 1 r 4 where r 3 contains the minimum associated with isr in r 1 transitions to the basin of attraction of the rest point are not observed until a small critical value of c 1 is reached at the beginning of r 2 the sudden decline in firing rate when is just greater than c 1 implies that there is only a small range of noise levels 0 c 1 where repetitive spiking is safe from annihilation by noise the firing rate remains small throughout r 3 at a larger critical value c 2 which signals the beginning of r 4 the probability of transitions from the basin of attraction of the equilibrium point to that of the limit cycle apparently becomes greater than zero and the spike rate thereafter increases with increasing the quantitative scheme underlying the isr curve is outlined in terms of the properties of exit time random variables in the final subsection several statistical properties of the main random variables associated with long term spiking activity are given including distributions of exit times from the two relevant basins of attraction and the interspike interval

maximum entropy formalism and analytic extrapolation the maximum entropy principle is used to obtain a new analytic extrapolation method just complementary to the pade type method which leads to rigorous upper and lower bounds on the extrapolated function on the cut complex plane among the large class of functions that could equally well represent an analytical function in the experimental region a choice is made of the unique function that maximizes the entropy functional associated to this set of functions the result is the least biased function compatible with the actual experimental data this extrapolation method is applied to kaon nucleon experimental data in order to obtain the most reasonable values for the kny coupling constants compatible with the available experimental data and analytical constraints

a maximum entropy method for inverting laplace transforms of probability density functions summary this papers presents a maximum entropy method for inverting laplace transforms of density functions of positive random variables the maximum entropy density is very flexible and can assume a variety of different shapes accurate approximations to the true density can be obtained even when only a few transform values are available numerical evidence is provided for gamma lognormal inverse gaussian and pareto distributions

auditory detection of hollowness the airborne sounds produced by freely vibrating hollow and solid bars were synthesized according to the equations of bar motion from theoretical acoustics and were presented to listeners over headphones in a two interval forced choice task listeners were asked to distinguish between the hollow and solid bar sounds as bar length was varied at random from one presentation to the next all other physical properties of the bar were held constant across trials listener decision strategies for detecting hollowness in iron aluminum and wood bars were determined from regression weights describing the relation between the listener s response and the frequency intensity and decay modulus of the individual partials comprising these sounds the obtained weights were compared to those of a hypothetical listener that bases judgments on the acoustic relations intrinsic to hollowness as determined from the equations for motion results indicate that listeners adopt roughly one of two decision strategies either basing judgments on the appropriate acoustic relations or basing judgments predominantly on frequency alone the decision strategy of some listeners also changed from one type to the other with a change in bar material or upon replication of the same condition the results are interpreted in terms of the vulnerability of the intrinsic acoustic relations to small perturbations in acoustic parameters as would be associated with listener internal noise they demonstrate that basic limits of human sensitivity can have a profound effect on the identification of rudimentary source attributes from sound even in conditions where acoustic variation is largely dictated by physical variation in the source

complex variable and regularization methods of inversion of the laplace transform in this paper three methods are derived for approximating f given its laplace transform g on 0 oo i e fo f t exp st dt g s assuming that g e l 0 oo the first method is based on a sinc like rational approximation of 9 the second on a sinc solution of the integral equation fo0 f t exp st dt g s via standard regularization and the third method is based on first converting fo0 f t exp st dt g s to a convolution integral over r and then finding a sinc approximation to f via the application of a special regularization procedure to solve the fourier transform problem we also obtain bounds on the error of approximation which depend on both the method of approximation and the regularization parameter

input recovery from noisy output data using regularized inversion of the laplace transform in a dynamical system the input is to be recovered from finitely many measurements blurred by random error of the output of the system as usual the differential equation describing the system is reduced to multiplication with a polynomial after applying the laplace transform it appears that there exists a natural unbiased estimator for the laplace transform of the output from which an estimator of the input can be obtained by multiplication with the polynomial and subsequent application of a regularized inverse of the laplace transform it is possible moreover to balance the effect of this inverse so that ill posedness remains restricted to its actual source differentiation the rate of convergence of the integrated mean square error is a positive power of the number of data the order of the differential equation has an adverse effect on the rate which on the other hand increases with the smoothness of the input as usual

orientability of moduli spaces of spin 7 instantons and coherent sheaves on calabi yau 4 folds abstract suppose x g is a compact spin 7 manifold e g a riemannian 8 manifold with holonomy spin 7 or a calabi yau 4 fold let g be u m or su m and p x be a principal g bundle we show that the infinite dimensional moduli space b p of all connections on p modulo gauge is orientable in a certain sense we deduce that the moduli space m p spin 7 b p of irreducible spin 7 instanton connections on p modulo gauge as a manifold or derived manifold is orientable this improves theorems of cao and leung 9 and munoz and shahbazi 42 if x is a calabi yau 4 fold the derived moduli stack m of complexes of coherent sheaves on x is a 2 shifted symplectic derived stack m by pantev toen vaquie vezzosi 46 and so has a notion of orientation by borisov joyce 7 we prove that m is orientable by relating algebro geometric orientations on m to differential geometric orientations on b p for u m bundles p x and using orientability of b p this has applications to defining donaldson thomas type invariants counting semistable coherent sheaves on a calabi yau 4 fold as in donaldson and thomas 15 cao and leung 8 and borisov and joyce 7

regime switching volatility calibration by the baum welch method regime switching volatility models provide a tractable method of modelling stochastic volatility currently the most popular method of regime switching calibration is the hamilton filter we propose using the baum welch algorithm an established technique from engineering to calibrate regime switching models instead we demonstrate the baum welch algorithm and discuss the significant advantages that it provides compared to the hamilton filter we provide computational results of calibrating and comparing the performance of the baum welch and the hamilton filter to s p 500 and nikkei 225 data examining their performance in and out of sample

tensor product markov chains abstract we analyze families of markov chains that arise from decomposing tensor products of irreducible representations this illuminates the burnside brauer theorem for building irreducible representations the mckay correspondence and pitman s 2 m x theorem the chains are explicitly diagonalizable and we use the eigenvalues eigenvectors to give sharp rates of convergence for the associated random walks for modular representations the chains are not reversible and the analytical details are surprisingly intricate in the quantum group case the chains fail to be diagonalizable but a novel analysis using generalized eigenvectors proves successful

correlation coefficients and correlation ratios as estimates of observer weights in multiple observation tasks advantages of correlational methods are described for estimating the relative reliance or weight observers give to different elements of a complex display when performing auditory or visual discriminations correlational methods differ from other such methods by providing a least squares estimate of weights rather than a maximum likelihood estimate based on a presumed model the main benefit is that these methods can be generally applied in cases where the statistical properties of elements are unknown where correlations exist between elements or where it is necessary to evaluate decision models that are inherently nonlinear

the bousfield kuhn functor and topological andre quillen cohomology we construct a natural transformation from the bousfield kuhn functor evaluated on a space to the topological andre quillen cohomology of the k n local spanier whitehead dual of the space and show that the map is an equivalence in the case where the space is a sphere this results in a method for computing unstable v n periodic homotopy groups of spheres from their morava e cohomology as modules over the dyer lashof algebra of morava e theory we relate the resulting algebraic computations to the algebraic geometry of isogenies between lubin tate formal groups

auditory correlates of perceived mallet hardness for a set of recorded percussive sound events a psychophysical investigation of timbre was undertaken with the intent of deriving quantitative results that could be useful in musical applications recordings of metal objects being struck with percussion mallets were rated by subjects on a unidimensional perceptual scale of perceived mallet hardness four acoustical parameters of the attack portion first 325 ms were defined and evaluated as predictors of perceived mallet hardness rating to measure these parameters a critical band filter bank was employed two curves were extracted from the filter bank output 1 spectral level log of area under spectrum over time and 2 spectral centroid over time for each curve two parameters were measured the mean and the slope of the spectral level curve and the mean and the time weighted average of the spectral centroid curve multiple regression analysis was used to relate the perceptual ratings to these four acoustical parameters and a good fit was achieved multiple r squared 0 725 f 1135 8 p 0

generalized ornstein uhlenbeck process by doob s theorem and the time evolution of financial prices abstract we generalize the ornstein uhlenbeck ou process using doob s theorem we relax the gaussian and stationary conditions assuming a linear and time homogeneous process the proposed generalization retains much of the simplicity of the original stochastic process while exhibiting a somewhat richer behavior analytical results are obtained using transition probability and the characteristic function formalism and compared with empirical stock market data which are notorious for the non gaussian behavior the analysis focus on the decay patterns and the convergence study of the first four cumulants considering the logarithmic returns of stock prices it is shown that the proposed model offers a good improvement over the classical ou model

statistical properties of a discrete version of the ornstein uhlenbeck process a discrete version of the ornstein uhlenbeck process is discussed which arises from a simple generalization of the master equation of the random walk the calculation of the statistical properties of the free propagator for this process can be obtained using essentially the same formalism as for simple random walks these calculations are carried out in some detail for the one dimensional case the usual equation for the evolution of the probability distribution of the ornstein uhlenbeck process is recovered in the continuum limit if the jump distribution has a finite variance however the discrete process is also well defined for long tailed jump distributions and thus can be used to describe a levy walk under the effect of a harmonic potential finally a brief discussion of the generalization of this process to describe random walks in general potentials is presented and briefly compared with results arising from the fractional diffusion approach

molecular analysis of the effect of relative tone level on multitone pattern discrimination molecular psychophysics attempts to model the observer s response to stimuli as they vary from trial to trial the approach has gained popularity in multitone pattern discrimination studies as a means of estimating the relative reliance or decision weight listeners give to different tones in the pattern various factors affecting decision weights have been examined but one largely ignored is the relative level of tones in the pattern in the present study listeners detected a level increment in a sequence of 5 100 ms 2 0 khz tone bursts alternating in level between 40 and 80db spl the level increment was made largest on the 40 db tones yet despite this all four highly practiced listeners gave near exclusive weight to the 80 db tones the effect was the same when the tones were replaced by bursts of broadband gaussian noise alternating in level it was reduced only when the level differences were made 10db and it was entirely reversed only when the low level tones alternated with louder bursts of ga

probability of stochastic processes and spacetime geometry abstract we made a first attempt to associate a probabilistic description of stochastic processes like birth death processes with spacetime geometry in the schwarzschild metrics on distance scales from the macro to the micro domains we idealize an ergodic system in which system states communicate through a curved path composed of transition arrows where each arrow corresponds to a positive analogous birth or death rate

discrimination of the spectral density of multitone complexes spectral density d defined as the number of partials comprising a sound divided by its bandwidth has been suggested as cue for the identification of the size and shape of sound sources few data are available however on the ability of listeners to discriminate differences in spectral density in a cue comparison forced choice procedure with feedback three highly practiced listeners discriminated differences in the spectral density of multitone complexes varying in bandwidth w 500 1500 hz center frequency fc 500 2000 hz and number of tones n 6 31 to reduce extraneous cues for discrimination the overall level of the complexes was roved and the frequencies were drawn at random uniformly over a fixed bandwidth and center frequency for each presentation psychometric functions were obtained relating percent correct discrimination to d in each condition for d 0 02 hz 1 they increased with d

filling of a poisson trap by a population of random intermittent searchers we extend the continuum theory of random intermittent search processes to the case of n independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi infinite track each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state we assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process the hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target the particle is removed from the system after delivering its cargo as a further generalization of previous models we assume that up to n successive particles can find the target and deliver its cargo assuming that the rate of target detection scales as 1 n we show that there exists a well defined mean field limit n rightarrow infty in which the stochastic model reduces to a deterministic system of linear reaction hyperbolic equations for the concentrations of particles in each of the internal states these equations decouple from the stochastic process associated with filling the target with cargo the latter can be modeled as a poisson process in which the time dependent rate of filling lambda t depends on the concentration of stationary particles within the target domain hence we refer to the target as a poisson trap we analyze the efficiency of filling the poisson trap with n particles in terms of the waiting time density f n t the latter is determined by the integrated poisson rate mu t int 0 t lambda s ds which in turn depends on the solution to the reaction hyperbolic equations we obtain an approximate solution for the particle concentrations by reducing the system of reaction hyperbolic equations to a scalar advection diffusion equation using a quasi steady state analysis we compare our analytical results for the mean field model with monte carlo simulations for finite n we thus determine how the mean first passage time mfpt for filling the target depends on n and n

spectral and temporal cues for perception of material and action categories in impacted sound sources in two experiments similarity ratings and categorization performance with recorded impact sounds representing three material categories wood metal glass being manipulated by three different categories of action drop strike rattle were examined previous research focusing on single impact sounds suggests that temporal cues related to damping are essential for material discrimination but spectral cues are potentially more efficient for discriminating materials manipulated by different actions that include multiple impacts e g dropping rattling perceived similarity between material categories across different actions was correlated with the distribution of long term spectral energy spectral centroid similarity between action categories was described by the temporal distribution of envelope energy temporal centroid or by the density of impacts moreover perceptual similarity correlated with the pattern of confusion in categorization judgments listeners tended to confuse materials with similar spectral centroids and actions with similar temporal centroids and onset densities to confirm the influence of these different features spectral cues were removed by applying the envelopes of the original sounds to a broadband noise carrier without spectral cues listeners retained sensitivity to action categories but not to material categories conversely listeners recognized material but not action categories after envelope scrambling that preserved long term spectral content

auditory discrimination of material changes in a struck clamped bar the principles of theoretical acoustics were applied to approximately reconstruct the sound pressure waveform at the ear as would be generated by an idealized struck clamped bar the result is an inharmonic sum of damped sinusoids whose individual acoustic parameters frequency intensity and decay modulus are for a fixed geometry and fixed driving force uniquely determined by the material composition of the bar in the standard 2ifc procedure listeners were asked to discriminate changes in material composition based on their perception of the acoustic waveform listener strategies for discriminating such changes were estimated by perturbing slightly the individual acoustic parameters from trial to trial and computing correlations with the listener s response cf r a lutfi and e oh j acoust soc am 95 2963 a 1994 in general the correlations reveal that listeners fail to make optimal use of the information in the acoustic waveform by tending to give undue weight for a given material change to changes in component frequency in some case the accompanying reduction in performance efficiency amounted to 80

localization of andre quillen goodwillie towers and the periodic homology of infinite loopspaces abstract let k n be the n th morava k theory at a prime p and let t n be the telescope of a v n self map of a finite complex of type n in this paper we study the k n homology of x the 0th space of a spectrum x and many related matters we give a sampling of our results let p x be the free commutative s algebra generated by x it is weakly equivalent to the wedge of all the extended powers of x we construct a natural map s n x l t n p x l t n x of commutative algebras over the localized sphere spectrum l t n s the induced map of commutative cocommutative k n hopf algebras s n x k n p x k n x satisfies the following properties it is always monic it is an isomorphism if x is n connected n 1 x is torsion and t i x 0 for 1 i n 1 it is an isomorphism only if k i x 0 for 1 i n 1 it is universal the domain of s n x preserves k n isomorphisms and if f is any functor preserving k n isomorphisms then any natural transformation f x k n x factors uniquely through s n x the construction of our natural transformation uses the telescopic functors constructed and studied previously by bousfield and the author and thus depends heavily on the nilpotence theorem of devanitz hopkins and smith our proof that s n x is always monic uses topological andre quillen homology and goodwillie calculus in nonconnective settings

convergence of percolation probability functions to cumulative distribution functions on square lattices with 1 0 neighborhood abstract we consider a percolation model on square lattices with sites weighted by beta distributed random variables s beta a b with a positive real parameters a 0 and b 0 using the monte carlo method we estimate the percolation probability p as a relative frequency p averaged over the target subset of sites on a square lattice as a result of the comparative analysis we formulate two empirical hypotheses the first on the correspondence of percolation thresholds p c to p 0 quantiles where level p 0 0 592746 coincides with the percolation threshold for the site percolation model on a square lattice of random variables s i weighing sites of the square lattice and the second on the convergence of statistical estimates of percolation probability functions p p to cumulative distribution functions f s i p of these variables s i for the supercritical values of the occupation probability p p c

derived koszul duality and tq homology completion of structured ring spectra abstract working in the context of symmetric spectra we consider algebraic structures that can be described as algebras over an operad o topological quillen homology or tq homology is the spectral algebra analog of quillen homology and stabilization working in a framework for homotopical descent the associated tq homology completion map appears as the unit map of an adjunction comparing the homotopy categories of o algebra spectra with coalgebra spectra over the associated comonad via tq homology we prove that this adjunction between homotopy categories can be turned into an equivalence by replacing o algebras with the full subcategory of 0 connected o algebras we also construct the spectral algebra analog of the unstable adams spectral sequence that starts from the tq homology groups tq x of an o algebra x and prove that it converges strongly to x when x is 0 connected

estimation of current reliability in a duane based reliability growth model in this article i investigate the statistical inference concerning the current field stage reliability of a reliability growth model the model assuming a step intensity structure evolves from the physical consideration of the duane learning curve property and incorporates the effect of a testanalyze and fix program that is typically undertaken in a developmental testing program both exact and large sample distributional results are derived for the maximum likelihood and the least squares estimators of the current intensity under the assumption that the step intensity model represents the reality i provide an assessment of the extent of misspecification when the widely used power law process model is fit to the failure data of a system experiencing recurrent failures extensive simulation results are carried out to supplement the theoretical findings an illustration with a dataset is provided as a demonstration of the application of the inference results

sensory constraints on auditory identification of the material and geometric properties of struck bars a computational formula is derived for estimating the constraints limited auditory sensitivity imposes on auditory identification of the material and geometric properties of struck bars the formula combines a model of the transverse motion of the bar with empirical psychometric functions to map out null regions in the bar s physical parameter space where changes in the frequency amplitude and decay of partials are likely below threshold for detection parameters of the physical space include bar density young s modulus fluid and viscoelastic damping factors bar length and bar cross sectional area as related to bar shape and hollowness the formula is used to estimate the possible effect of limited sensitivity in past studies on the auditory identification of bar attributes the results suggest that sensitivity may indeed have played a role in some studies and that apparent discrepancies in results may be understood based on whether the predominant source of damping was internal or external to the bar the formula identifies conditions representing an expected bound on identification performance and thereby may be used to aid in the design of future studies for which the struck bar is the sound source of choice