hamiltonian perspective on compartmental reaction diffusion networks inspired by the recent developments in modeling and analysis of reaction networks we provide a geometric formulation of the reversible reaction networks under the influence of diffusion using the graph knowledge of the underlying reaction network the obtained reaction diffusion system is a distributed parameter port hamiltonian system on a compact spatial domain motivated by the need for computer based design we offer a spatially consistent discretization of the pde system and in a systematic manner recover a compartmental ode model on a simplicial triangulation of the spatial domain exploring the properties of a balanced weighted laplacian matrix of the reaction network and the laplacian of the simplicial complex we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points the paper rules out the possibility of the persistence of spatial patterns for the compartmental balanced reaction diffusion networks

brown comenetz duality and the adams spectral sequence we show that the class of p complete connective spectra with nitely presented cohomology over the steenrod algebra admits a duality the ory related to brown comenetz duality this construction also produces a full plane version of the classical adams spectral sequence for such spectra which converges to the homotopy groups of a nite localization

joint data and channel estimation using blind trellis search techniques a novel method of maximum likelihood sequence estimation is proposed for data that are transmitted over unknown linear channels this procedure does not require a startup sequence for estimating the channel impulse response rather the data and the channel are simultaneously estimated it is implemented without any loss of optimality by a trellis search algorithm which searches for the best data sequence from among a number of hypothesized trellises which are constructed from the observed sequence the number of states in each trellis and the number of trellises grow exponentially with the channel memory a suboptimal trellis search algorithm is proposed whose complexity at best is slightly higher than that of the adaptive viterbi algorithm operating with a known channel response a simplified channel estimation algorithm when the number of data alphabets is greater than 2 is also proposed fast convergence of the algorithm in estimating the channel is demonstrated for binary pulse amplitude modulation over a variety of channels convergence over a wide range of snr occurs within 100 symbols the channel estimation algorithm for multi level signals converges within 500 1000 symbols we finally present an application of this algorithm to the problem of sequence estimation in the presence of rapidly time varying intersymbol interference the algorithm provides reliable zero delay decisions which results in a better channel tracking algorithm when compared to previously proposed schemes

a theoretical investigation into the performance of the hopfield model an analysis is made of the behavior of the hopfield model as a content addressable memory cam and as a method of solving the traveling salesman problem tsp the analysis is based on the geometry of the subspace set up by the degenerate eigenvalues of the connection matrix the dynamic equation is shown to be equivalent to a projection of the input vector onto this subspace in the case of content addressable memory it is shown that spurious fixed points can occur at any corner of the hypercube that is on or near the subspace spanned by the memory vectors analysed is why the network can frequently converge to an invalid solution when applied to the traveling salesman problem energy function with these expressions the network can be made robust and can reliably solve the traveling salesman problem with tour sizes of 50 cities or more

variable elimination in chemical reaction networks with mass action kinetics we consider chemical reaction networks taken with mass action kinetics the steady states of such a system are solutions to a system of polynomial equations even for small systems the task of finding the solutions is daunting we develop an algebraic framework and procedure for linear elimination of variables the procedure reduces the variables in the system to a set of core variables by eliminating variables corresponding to a set of noninteracting species the steady states are parameterized algebraically by the core variables and a graphical condition is given that ensures that a steady state with positive core variables necessarily takes positive values for all variables further we characterize graphically the sets of eliminated variables that are constrained by a conservation law and show that this conservation law takes a specific form

systematic measures of biological networks i invariant measures and entropy this paper is part i of a two part series devoted to the study of systematic measures in a complex biological network modeled by a system of ordinary differential equations as the mathematical complement to our previous work with collaborators the series aims at establishing a mathematical foundation for characterizing three important systematic measures degeneracy complexity and robustness in such a biological network and studying connections among them to do so we consider in part i stationary measures of a fokker planck equation generated from small white noise perturbations of a dissipative system of ordinary differential equations some estimations of concentration of stationary measures of the fokker planck equation in the vicinity of the global attractor are presented the relationship between the differential entropy of stationary measures and the dimension of the global attractor is also given 2016 wiley periodicals inc

computing zero deficiency realizations of kinetic systems in the literature there exist strong results on the qualitative dynamical properties of chemical reaction networks also called kinetic systems governed by the mass action law and having zero deficiency however it is known that different network structures with different deficiencies may correspond to the same kinetic differential equations in this paper an optimization based approach is presented for the computation of deficiency zero reaction network structures that are linearly conjugate to a given kinetic dynamics through establishing an equivalent condition for zero deficiency the problem is traced back to the solution of an appropriately constructed mixed integer linear programming problem furthermore it is shown that weakly reversible deficiency zero realizations can be determined in polynomial time using standard linear programming two examples are given for the illustration of the proposed methods 2015 elsevier b v all rights reserved

blind equalization of digital communication channels using high order moments the authors describe algorithms for blind equalization of digital communication channels of the quadrature amplitude modulation qam type these algorithms are based on the fourth order statistical moments of the received data sequence the first of the two is a linear least squares type algorithm the second algorithm is of the nonlinear least squares type the algorithms use the fourth order statistical moments of the symbol sequence to explicitly estimate the channel impulse response the estimated impulse response is used in turn to construct a linear mean square error equalizer the performance of this equalizer is not optimal in any sense but it is adequate for channels with mild intersymbol interference or when the number of data points available for estimating the channel response is very large

multiple equilibria in complex chemical reaction networks semiopen mass action systems in two earlier articles we provided sufficient conditions on mass action reaction network structure for the preclusion of multiple positive steady states in the context of what chemical engineers call the continuous flow stirred tank reactor in such reactors all species are deemed to be present in the effluent stream a fact which played a strong role in the proofs when certain species are deemed to be entrapped within the reactor the questions that must be asked are more subtle and the mathematics becomes substantially more difficult here we extend results of the earlier papers to semiopen reactors and show that very similar results obtain provided that the network of chemical reactions satisfies certain weak structural conditions weak reversibility is sufficient but not necessary

quasi steady state reduction for compartmental systems abstract we present a method to determine an asymptotic reduction in the sense of tikhonov and fenichel for singularly perturbed compartmental systems in the presence of slow transport it turns out that the reduction can be derived from the individual interaction terms alone we apply the result to spatially discretized reaction diffusion systems and obtain based on the reduced discretized systems a heuristic to reduce reaction diffusion systems in presence of slow diffusion

brief stabilization of positive systems with first integrals positive systems possessing first integrals are considered these systems frequently occur in applications this paper is devoted to two stabilization problems the first is concerned with the design of feedbacks to stabilize a given level set secondly it is shown that the same feedback allows to globally stabilize an equilibrium point if it is asymptotically stable with respect to initial conditions in its level set two examples are provided and the results are compared with those in the literature

k means clustering based data detection and symbol timing recovery for burst mode optical receiver burst mode receivers are key components of optical transmission systems including passive optical networks and have received much attention in recent years we present new efficient methods for burst optical signal detection in burst mode data transmission using a modified k means clustering technique we also develop a data aided feedforward symbol timing recovery method based on a polynomial interpolation and maximum likelihood estimation theory a performance criterion considering the error caused by the interpolation approximation is derived for this method the proposed detection and timing recovery approaches can be implemented effectively and rapidly therefore they are very suitable for burst mode receivers we also provide some numerical examples to demonstrate the performance of the proposed methods

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

brief paper optimal distributed linear averaging a new optimal distributed linear averaging odla problem is presented in this paper this problem is motivated by the distributed averaging problem which arises in the context of distributed algorithms in computer science and coordination of groups of autonomous agents in engineering the aim of the odla problem is to compute the average of the initial values at nodes of a graph through an optimal distributed algorithm in which the nodes in the graph can only communicate with their neighbors optimality is given by a minimization problem of a quadratic cost functional under infinite horizon we show that this problem has a very close relationship with the notion of semistability by developing new necessary and sufficient conditions for semistability of linear discrete time systems we convert the proposed odla problem into an equivalent constrained optimization problem and then derive a solvable fixed structure convex optimization problem

new approach to the stability of chemical reaction networks piecewise linear in rates lyapunov functions piecewise linear in rates pwlr lyapunov functions are introduced for a class of chemical reaction networks crns in addition to their simple structure these functions are robust with respect to arbitrary monotone reaction rates of which mass action is a special case the existence of such functions ensures the convergence of trajectories towards equilibria and can be used to establish their asymptotic stability with respect to the corresponding stoichiometric compatibility class we give the definition of these lyapunov functions prove their basic properties and provide algorithms for constructing them examples are provided relationship with consensus dynamics are discussed and future directions are elaborated

polyhedral lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the jacobian is non singular for a vast class of dynamical networks including chemical reaction networks crns with monotonic reaction rates the existence of a polyhedral lyapunov function plf implies structural i e parameter free local stability global structural stability is ensured under the additional assumption that each of the variables chemical species concentrations in crns is subject to a spontaneous infinitesimal dissipation this paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation showing that the existence of a plf structurally ensures global convergence if and only if the system jacobian passes a structural non singularity test it is also shown that if the jacobian is structurally non singular under positivity assumptions for the system partial derivatives the existence of an equilibrium is guaranteed for systems subject to positivity constraints it is shown that if the system admits a plf under structural non singularity assumptions global convergence within the positive orthant is structurally ensured while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise linear in rate lyapunov function

persistence in chemical reaction networks with arbitrary time delays we give a sufficient condition for a chemical reaction network with time delays to be persistent that is any positive solution to the delay differential equation describing the time evolution of

morava modules and brown comenetz duality fix a prime number p and let x be a finite spectrum whose n 1 st morava k theory is trivial but whose n th morava k theory is nontrivial n 0 we prove following a method outlined to us by m j hopkins that if 2 p n 2 n 2 the morava module of the brown comenetz dual of the e n localization of x is isomorphic to a suspension of the pontryagin dual of the morava module of x to complete this proof we found it necessary to develop a more canonical construction of certain modified adams spectral sequences this construction should be of independent interest

localization and periodicity in unstable homotopy theory in this paper we develop a hierarchy of natural localizations of spaces called the vn periodizations for n 0 which may be used to expose and study periodic phenomena in unstable homotopy theory these vn periodizations act less radically than the corresponding homological localizations 2 and respect fibrations to a very considerable extent a major part of this paper is devoted to developing the general theory of periodizations of spaces thereby providing a foundation for the study of the vn periodization and many others some of this general theory has been developed independently by dror farjoun 13 14 and we refer the reader to his work for an alternative approach with other interesting general results during the past decade remarkable progress was made by ravenel hopkins devinatz and smith 12 16 17 33 toward a global understanding of stable periodic phenomena and we hope that the present paper will help to prepare the way for a similar understanding of unstable periodic phenomena an excellent exposition of localization and periodicity in stable homotopy theory is now available in ravenel s book 35 major features of stable homotopy are understood chromatically as manifestations of more basic periodic phenomena these phenomena belong to a hierarchy starting with those detected rationally followed by those detected in classical k theory and in the successive morava k theories most fundamentally each finite cw spectrum has an intrinsic periodicity given by a vn self map which becomes a selfequivalence after suitable localization for simplicity we describe our results in the pointed homotopy category hoo of connected cw complexes for spaces w y e hoo we call y w periodic or w local when the pointed mapping space map w y is contractible or equivalently when xt w y for t 0 as shown more generally in 3 corollary 7 2 10 or 13 there is a natural initial example x pwx of a map from x to a w periodic space pwx in hoo and we call this the w periodization or w localization of x our notation is derived from the classical example where w sn l and pwx is the n th postnikov section

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

cluster based blind nonlinear channel estimation a cluster based maximum likelihood sequence estimator mlse for nonlinear channels was described which consists of a clustering network and an mlse implemented by the viterbi algorithm the cluster based mlse can be used for digital communication through nonlinear finite length channels because channel mapping estimation is used instead of channel estimation in the conventional mlse the clustering network of the cluster based mlse which estimates the channel mapping between the signal input vectors and the noiseless channel outputs is a supervised network and requires a training sequence we propose a blind channel mapping estimator to estimate the channel mapping without using the training sequence the blind channel mapping estimator has a clustering block and a mapping block the clustering block estimates the channel outputs which represent the channel mapping subject to an unknown permutation operation because no training sequence is utilized that permutation operation is resolved by the mapping block and therefore the channel mapping is obtained introducing the blind channel mapping estimator into the cluster based mlse a blind cluster based mlse for nonlinear channels can be done computer simulations of the blind channel mapping estimator and the blind mlse for nonlinear channels are presented

global asymptotic stability for a class of nonlinear chemical equations we consider a class of nonlinear differential equations that arises in the study of chemical reaction systems known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable more specifically we will consider chemical reaction systems that are weakly reversible have a deficiency of zero and are equipped with mass action kinetics we show that if for each c in mathbb r 0 m the intersection of the stoichiometric compatibility class c s with the subsets on the boundary that could potentially contain equilibria l w are at most discrete then global asymptotic stability follows previous global stability results for the systems considered in this paper required c s cap l w emptyset for each c in mathbb r m 0

systematic measures of biological networks ii degeneracy complexity and robustness this paper is part ii of a two part series devoted to the study of systematic measures in a complex bionetwork modeled by a system of ordinary differential equations in this part we quantify several systematic measures of a biological network including degeneracy complexity and robustness we will apply the theory of stochastic differential equations to define degeneracy and complexity for a bionetwork robustness of the network will be defined according to the strength of attractions to the global attractor based on the study of stationary probability measures and entropy made in part i of this series we will investigate some fundamental properties of these systematic measures in particular the connections between degeneracy complexity and robustness 2016 wiley periodicals inc

the deficiency zero theorem and global asymptotic stability for a class of chemical reaction networks with arbitrary time delays abstract the deficiency zero theorem dzt is extended to be applied to chemical reaction networks crns with time delays the time evolution of concentrations of species in which networks is described by delay differential equations ddes the extended dzt provides a sufficient condition for a positive equilibrium point of ddes to exist and be locally asymptotically stable furthermore it is proven that the absence of boundary equilibria is a sufficient condition for the positive equilibrium point to be globally asymptotically stable these results are natural analogues of theorems proven for crns without time delays

a reaction network approach to the theory of acoustic wave turbulence abstract we propose a new approach to study the long time dynamics of the wave kinetic equation in the statistical description of acoustic turbulence the approach is based on rewriting the discrete version of the wave kinetic equation in the form of a chemical reaction network then employing techniques used to study the global attractor conjecture to investigate the long time dynamics of the newly obtained chemical system we show that the solution of the chemical system converges to an equilibrium exponentially in time in addition a resonance broadening modification of the acoustic wave kinetic equation is also studied with the same technique for the near resonance equation if the resonance broadening frequency is larger than a threshold the solution of the system goes to infinity as time evolves

observer design for a class of nonlinear systems a viable design methodology to construct observers for a class of nonlinear systems is developed the proposed technique is based on the off line solution of a riccati equation and can be solved using commercially available software packages for globally valid results the class of systems considered is characterized by globally lipschitz nonlinearities local results relax this assumption to only a local requirement for a more general description of nonlinear systems the methodology yields approximate observers locally the proposed theory is used to design an observer for a single link flexible joint robot this observer estimates the robot link variables based on the joint measurements

spectral conditions for stability and stabilization of positive equilibria for a class of nonlinear cooperative systems nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication biological economical and neural network applications for this class of positive systems we provide conditions that guarantee existence uniqueness and stability of strictly positive equilibria these conditions can be formulated directly in terms of the spectral radius of the jacobian of the system if control inputs are available then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant

local equivalence of reversible and general markov kinetics a b s t r a c t we consider continuous time markov kinetics with a finite number of states and a positive equilibrium p this class of systems is significantly wider than the systems with detailed

stability of nonnegative lur e systems a stability instability trichotomy for a class of nonnegative continuous time lur e systems is derived asymptotic exponential and input to state stability concepts are considered the presented trichotomy rests on perron frobenius theory absolute stability theory and recent input to state stability results for lur e systems applications of the results derived arise in various fields including density dependent population dynamics and two examples are discussed in detail

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

sensitivity and network topology in chemical reaction systems in living cells biochemical reactions are catalyzed by specific enzymes and connect to one another by sharing substrates and products forming complex networks in our previous studies we established a framework determining the responses to enzyme perturbations only from network topology and then proved a theorem called the law of localization explaining response patterns in terms of network topology in this paper we generalize these results to reaction networks with conserved concentrations which allows us to study any reaction system we also propose network characteristics quantifying robustness we compare e coli metabolic network with randomly rewired networks and find that the robustness of the e coli network is significantly higher than that of the random networks

local dissipative hamiltonian description of reversible reaction networks in this letter we show that closed reversible chemical reaction networks with independent elementary reactions admit a global pseudo hamiltonian structure which is at least locally dissipative around any equilibrium point the structure matrix of the hamiltonian description reflects the graph topology of the reaction network and it is a smooth function of the concentrations of the chemical species in the positive orthant the physical interpretation of the description is briefly explained and two illustrative examples are presented for global and local dissipative hamiltonian description respectively

input to state stability of rate controlled biochemical networks in this paper the study of the class of biochemical systems known as zero deficiency networks is extended to the case of time varying kinetic parameters we show that the resulting class of nonlinear systems with inputs satisfies a notion of input to state stability uniformly over a set of parameters in particular the input to state stability estimates allow us to characterize the robustness of zero deficiency networks with respect to perturbations in the parameters as well as study their stability when the reaction rates are controlled by an independent process

piecewise linear lyapunov functions for structural stability of biochemical networks we consider the problem of assessing structural stability of biochemical reaction networks with monotone reaction rates namely of establishing if all the networks with a certain structure are stable regardless of specific parameter values we investigate stability by absorbing the network equations in a linear differential inclusion and seeking for a polyhedral lyapunov function proper to the considered network structure a numerical recursive procedure is devised to test stability for a wide class of mono and bimolecular reaction networks which we name unitary the procedure is shown to be very efficient since due to the particular structure of the problem it requires iterations in the space of integer valued matrices we also consider a similar less conservative procedure that allows us to test even when the lyapunov function cannot be found whether the system evolution is structurally bounded in this case we absorb the equations in a positive linear differential inclusion to show the effectiveness of the proposed procedure we report the outcomes of both a stability and a boundedness test for many non trivial biochemical reaction networks and we analyze well established models in the literature

channel dependent constrained combinatorial clustering constrained combinatorial clustering ccc is a new approach for grouping multiple features where the clustering metric depends on an unknown communication channel assignment features assigned to the same channel cannot be from the same source and conversely channels assigned to the same source must be distinct while the number of sources and their states are unknown the channels are assumed to be known except for additive noise potential clustering assignments are checked for compatibility with the constraints in a structured way that results in significant computational savings with respect to exhaustive enumeration especially when combined with a k best channel assignment algorithm that has polynomial complexity by combining two channel assignment methods exhaustive and k best with two clustering techniques ccc and greedy four new algorithms are presented to solve this novel problem along with detailed computational complexity analyses the main algorithm ccc is a top down clustering strategy based on assignment aggregation in a channel constrained environment the approaches are compared on a one dimensional simulation significant performance differences in source estimation accuracy and estimated number of sources are observed at low signal to noise ratios snrs and for low values of k some novel permutation symmetry properties arising from the study which lead to a new type of self affine set or discrete fractal are also presented

preclusion of switch behavior in networks with mass action kinetics we study networks taken with mass action kinetics and provide a jacobian criterion that applies to an arbitrary network to preclude the existence of multiple positive steady states within any stoichiometric class for any choice of rate constants we are concerned with the characterization of injective networks that is networks for which the species formation rate function is injective in the interior of the positive orthant within each stoichiometric class we show that a network is injective if and only if the determinant of the jacobian of a certain function does not vanish the function consists of components of the species formation rate function and a maximal set of independent conservation laws the determinant of the function is a polynomial in the species concentrations and the rate constants linear in the latter and its coefficients are fully determined the criterion also precludes the existence of degenerate steady states further we relate injectivity of a network to that of the network obtained by adding outflow or degradation reactions for all species

uniform and strict persistence in monotone skew product semiflows with applications to non autonomous nicholson systems abstract we determine sufficient conditions for uniform and strict persistence in the case of skew product semiflows generated by solutions of non autonomous families of cooperative systems of odes or delay fdes in terms of the principal spectrums of some associated linear skew product semiflows which admit a continuous separation our conditions are also necessary in the linear case we apply our results to a noncooperative almost periodic nicholson system with a patch structure whose persistence turns out to be equivalent to the persistence of the linearized system along the null solution

a network dynamics approach to chemical reaction networks abstracta treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics in particular of consensus dynamics by starting from the complex balanced assumption the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory and which directly relates to the thermodynamics and port hamiltonian formulation of the system central in this formulation is the definition of a balanced laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality this immediately leads to the characterisation of the set of equilibria and their stability furthermore the assumption of complex balancedness is revisited from the point of view of kirchhoff s matrix tree theorem both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics and provide additional perspectives to the latte

the glansdorff prigogine stability criterion for biochemical reaction networks local stability analysis of steady states in mathematical models of biochemical reaction networks is an important tool for systems biology the second variation of the gibbs energy around a steady state is a positive definite function and a candidate for a lyapunov function a sufficient condition for the local stability is the local negative definiteness of the time derivative of this function this is expressed by the glansdorff prigogine stability criterion previously the criterion was criticized to be overly conservative and difficult to check here we derive an easily testable form of the criterion for models of biochemical networks the criterion can be evaluated with incomplete knowledge of the parameters for ideal mass action kinetics it depends only on the steady state fluxes for reaction systems in ideal solutions the glansdorff prigogine criterion is overly conservative and we give a tighter criterion that depends on the same subset of the parameters as the glansdorff prigogine criterion whenever these criteria are indefinite there exist parameter values such that the steady state is unstable by means of simple example systems we explore these aspects and discuss the possible uses of the criteria for systems biology

odd primary periodic phenomena in the classical adams spectral sequence we study certain periodic phenomena in the cohomology of the mod p steenrod algebra which are related to the polynomial generators v e ir bp a chromatic resolution of the e2 term of the classical adams spectral sequence is constructed one of the major goals of homotopy theory is the understanding of 1r s the stable homotopy groups of spheres a technique for studying these groups is by the construction of certain systematic families of classes first due to m g barratt 3 one way to express this idea is as follows let x be a finite complex all spaces and complexes are objects in the stable category localized at a prime p a self map of degree i v ixx is nonnilpotent if the k fold composition vk vovo ov 3kix x is essential for all k 0 definition 1 for a given nonnilpotent map v a class a e 7rj so is vperiodic if a can be decomposed as st x x t 1 ayst i where x k denotes the k skeleton of x and the composite kix v kx p a st i is essential for all k 0 4 a v periodic class a e xr so determines an infinite systematic family in the following manner for each k 0 there exists an integer e with 0 0 determines a class or classes in lr ki e t i so here are several well known examples of this sort of phenomenon example 2 let mp denote the mod p moore space p 3 then adams 1 has constructed a nonnilpotent map a eymp mp where q 2 p1 this map determines a family of nontrivial classes at t 1 with at e lrqt so given by the following diagram eqtm at mp 1 1 sqt at s1 received by the editors august 28 1986 1980 mathematics subject classification 1985 revision primary 55t15 55s10 supported in part by the n s f 1988 american mathematical society 0002 9947 88 1 00 25 per page

nonlinear dynamics of networks the groupoid formalism a formal theory of symmetries of networks of coupled dynamical systems stated in terms of the group of permutations of the nodes that preserve the network topology has existed for some time global network symmetries impose strong constraints on the corresponding dynamical systems which affect equilibria periodic states heteroclinic cycles and even chaotic states in particular the symmetries of the network can lead to synchrony phase relations resonances and synchronous or cycling chaos symmetry is a rather restrictive assumption and a general theory of networks should be more flexible a recent generalization of the group theoretic notion of symmetry replaces global symmetries by bijections between certain subsets of the directed edges of the network the input sets now the symmetry group becomes a groupoid which is an algebraic structure that resembles a group except that the product of two elements may not be defined the groupoid formalism makes it possible to extend group theoretic methods to more general networks and in particular it leads to a complete classification of robust patterns of synchrony in terms of the combinatorial structure of the network many phenomena that would be nongeneric in an arbitrary dynamical system can become generic when constrained by a particular network topology a network of dynamical systems is not just a dynamical system with a high dimensional phase space it is also equipped with a canonical set of observables the states of the individual nodes of the network moreover the form of the underlying ode is constrained by the network topology which variables occur in which component equations and how those equations relate to each other the result is a rich and new range of phenomena only a few of which are yet properly understood

multiple equilibria in complex chemical reaction networks ii the species reaction graph for mass action kinetics the capacity for multiple equilibria in an isothermal homogeneous continuous flow stirred tank reactor is determined by the structure of the underlying network of chemical reactions we suggest a new graph theoretical method for discriminating between complex reaction networks that can admit multiple equilibria and those that cannot in particular we associate with each network a species reaction graph which is similar to reaction network representations drawn by biochemists and we show that if the graph satisfies certain weak conditions the differential equations corresponding to the network cannot admit multiple equilibria em no matter what values the rate constants take because these conditions are very mild they amount to powerful and quite delicate necessary conditions that a network must satisfy if it is to have the capacity to engender multiple equilibria broad qualitative results of this kind are especially apt for individual reaction rate constants are rare

the image of j in the ehp sequence the ehp sequence is based on a result of james j who showed that there is h a map h such that s q sn s2n 1 is a fibration when localized at 2 the map sn sn is usually labeled e the boundary homomorphism in the homotopy sequence is usually labeled p for our purposes it will be most convenient to combine all the ehp sequences into one system this gives the following filtration of o201 s q s

new processing techniques based on the constant modulus adaptive algorithm this paper presents three extensions of the constant modulus algorithm cma introduced in an earlier paper as a means of correcting degradations in constant enyelope waveforms as originally formulated the cma employs an fir filter with complex coefficients and accepts complex quadrature input data in this paper first a real input real coefficient version of the algorithm is shown to perform arbitrarily close to the fully complex version secondly the algorithm is extended for the enhancement of signals having a nonconstant but known envelope as might arise in data signals with pulse shaping lastly a multichannel version of cma wherein several observations are linearly combined is presented for joint adaptation of multiple filters this approach can be used for example as a means of spatial or polarization beamsteering to reject additive interferers and compensate for channel induced polarization rotation

weak dynamical nonemptiability and persistence of chemical kinetics systems a frequently desirable characteristic of chemical kinetics systems is that of persistence the property that if all the species are initially present then none of them may tend toward extinction it is known that solutions of deterministically modeled mass action systems may approach only portions of the boundary of the positive orthant which correspond to semilocking sets alternatively called siphons consequently most recent work on persistence of these systems has been focused on these sets in this paper we focus on a result which states that for a conservative mass action system persistence holds if every critical semilocking set is dynamically nonemptiable and the system contains no nested locking sets we will generalize this result by introducing the notion of a weakly dynamically nonemptiable semilocking set and making novel use of the well known farkas lemma we will also connect this result to known results regarding complex balanced systems and systems with facets

periodic phenomena in the classical adams spectral sequence we investigate certain periodic phenomena in the classical adams sepctral sequence which are related to the polynomial generators v 7 in bp we define the notion of a class a in exta z 2 z 2 being v periodic or v torsion and prove that classes that are v1 torsion are also vk torsion for all k such that 0 k 6 n this allows us to define a chromatic filtration of exta z 2 z 2 paralleling the chromatic filtration of the novikov spectral sequence e2 term given in 13

nontangency based lyapunov tests for convergence and stability in systems having a continuum of equilibria this paper focuses on the stability analysis of systems having a continuum of equilibria two notions that are of particular relevance to such systems are convergence and semistability convergence is the property whereby every solution converges to a limit point that may depend on the initial condition semistability is the additional requirement that all solutions converge to limit points that are lyapunov stable we give new lyapunov function based results for convergence and semistability of nonlinear systems these results do not make assumptions of sign definiteness on the lyapunov function instead our results use a novel condition based on nontangency between the vector field and invariant or negatively invariant subsets of the level or sublevel sets of the lyapunov function or its derivative and represent extensions of previously known stability results involving semidefinite lyapunov functions to illustrate our results we deduce convergence and semistability of the kinetics of the michaelis menten chemical reaction and the closed loop dynamics of a scalar system under a universal adaptive stabilizing feedback controller

local duality in algebra and topology abstract the first goal of this paper is to provide an abstract framework in which to formulate and study local duality in various algebraic and topological contexts for any stable category c together with a collection of compact objects k c we construct local cohomology and local homology functors satisfying an abstract version of local duality when specialized to the derived category of a commutative ring a and a suitable ideal in a we recover the classical local duality due to grothendieck as well as generalizations by greenlees and may more generally applying our result to the derived category of quasi coherent sheaves on a quasi compact and separated scheme x implies the local duality theorem of alonso tarrio jeremias lopez and lipman as a second objective we establish local duality for quasi coherent sheaves over many algebraic stacks in particular those arising naturally in stable homotopy theory after constructing an appropriate model of the derived category in terms of comodules over a hopf algebroid we show that in familiar cases the resulting local cohomology and local homology theories coincide with functors previously studied by hovey and strickland furthermore our framework applies to global and local stable homotopy theory in a way which is compatible with the algebraic avatars of these theories in order to aid computability we provide spectral sequences relating the algebraic and topological local duality contexts

semistability of complex balanced kinetic systems with arbitrary time delays abstract in this letter we introduce a class of delayed kinetic systems derived from mass action type reaction network models we define the time delayed positive stoichiometric compatibility classes and the notion of complex balanced time delayed kinetic systems we prove the uniqueness of equilibrium solutions within the time delayed positive stoichiometric compatibility classes for such models in our main result we prove the semistability of the equilibrium solutions for complex balanced systems with arbitrary time delays using an appropriate lyapunov krasovskii functional and lasalle s invariance principle as a consequence we obtain that every positive complex balanced equilibrium solution is locally asymptotically stable relative to its positive stoichiometric compatibility class

correction to structure and stability of certain chemical networks and applications to the kinetic proofreading model of t cell receptor signal transduction deals with the theory of structure stability robustness and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks the results given here extend but are also heavily based upon certain previous work by feinberg 1977 1979 1987 1995 and horn and jackson 1972 of which a self contained and streamlined exposition is included the theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by mckeithan 1995 for t cell receptor signal transduction

neural gas network for vector quantization and its application to time series prediction a neural network algorithm based on a soft max adaptation rule is presented this algorithm exhibits good performance in reaching the optimum minimization of a cost function for vector quantization data compression the soft max rule employed is an extension of the standard k means clustering procedure and takes into account a neighborhood ranking of the reference weight vectors it is shown that the dynamics of the reference weight vectors during the input driven adaptation procedure are determined by the gradient of an energy function whose shape can be modulated through a neighborhood determining parameter and resemble the dynamics of brownian particles moving in a potential determined by the data point density the network is used to represent the attractor of the mackey glass equation and to predict the mackey glass time series with additional local linear mappings for generating output values the results obtained for the time series prediction compare favorably with the results achieved by backpropagation and radial basis function networks

analysis of structures causing instabilities we present a simple new method to systematically identify all topological structures e g positive feedback loops potentially leading to locally unstable steady states icsa the instability causing structure analysis systems without any instability causing structure i e not fulfilling the necessary topological condition for instabilities cannot have unstable steady states it follows that common bistability or multistability and hopf bifurcations are excluded and sustained oscillations and deterministic chaos are most unlikely the icsa leads to new insights into the topological organization of chemical and biochemical systems such as metabolic gene regulatory and signal transduction networks

exponential time decay of solutions to reaction cross diffusion systems of maxwell stefan type the large time asymptotics of weak solutions to maxwell stefan diffusion systems for chemically reacting fluids with different molar masses and reversible reactions are investigated the diffusion matrix of the system is generally neither symmetric nor positive definite but the equations admit a formal gradient flow structure which provides entropy free energy estimates the main result is the exponential decay to the unique equilibrium with a rate that is constructive up to a finite dimensional inequality the key elements of the proof are the existence of a unique detailed balance equilibrium and the derivation of an inequality relating the entropy and the entropy production the main difficulty comes from the fact that the reactions are represented by molar fractions while the conservation laws hold for the concentrations the idea is to enlarge the space of n partial concentrations by adding the total concentration viewed as an independent variable thus working with n 1 variables further results concern the existence of global bounded weak solutions to the parabolic system and an extension of the results to complex balance systems

the dynamics of weakly reversible population processes near facets this paper concerns the dynamical behavior of weakly reversible deterministically modeled population processes near the facets codimension one faces of their invariant manifolds and proves that the facets of such systems are repelling it has been conjectured that any population process whose network graph is weakly reversible has strongly connected components is persistent we prove this conjecture to be true for the subclass of weakly reversible systems for which only facets of the invariant manifold are associated with semilocking sets or siphons an important application of this work pertains to chemical reaction systems that are complex balancing for these systems it is known that within the interior of each invariant manifold there is a unique equilibrium the global attractor conjecture states that each of these equilibria is globally asymptotically stable relative to the interior of the invariant manifold in which it lies our results pertaining to weakly reversible systems imply that thi

qualitative theory of compartmental systems dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations many nonlinear that are called compartmental systems in this paper the authors define compartmental systems specify their relations to other nonnegative systems and discuss examples of applications the authors review the qualitative results on linear and nonlinear compartmental systems including their relation to cooperative systems they review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems providing a framework for unifying them under a few general theorems in the course of that they complete the solution of a problem posed by bellman and show that closed nonlinear autonomous n compartment systems can show the full gamut of possible behaviors of systems of odes finally to provide additional structure to this study the authors show how to partiti

instantaneous limits of reversible chemical reactions in presence of macroscopic convection abstract chemically reacting systems frequently involve fast reversible reactions additional slow reactions as well as mass transport due to macroscopic convection in this situation the passage to infinite reaction speed is a means to reduce the complexity of the reaction kinetics and to avoid the need for explicit values of the rate constants thereby the large stiffness of the original system of differential equations is also removed in the present paper this instantaneous reaction limit is studied for systems with independent fast reversible reactions where the rate functions are given by mass action kinetics under realistic assumptions the limiting dynamical system is derived and convergence of the solutions is obtained as the rate constants tend to infinity the proof is based on lyapunov functions techniques and exploits the structure of rate functions that results from mass action kinetics this approach is complementary to the quasi steady state approximation which is often applied in chemical engineering the differences are illustrated by means of a classical enzyme substrate reaction scheme

persistence in dynamical systems soit un espace metrique localement compact de metrique d et soit e un sous ensemble clos de a frontiere e et interieur e on suppose que l on a un flot continu 7b f defini sur e tel que e est invariant par 7b f on considere la notion de persistance et on donne un critere de persistance

analysis of autocatalytic networks in biology autocatalytic networks in particular the glycolytic pathway constitute an important part of the cell metabolism changes in the concentration of metabolites and catalyzing enzymes during the lifetime of the cell can lead to perturbations from its nominal operating condition we investigate the effects of such perturbations on stability properties e g the extent of regions of attraction of a particular family of autocatalytic network models numerical experiments demonstrate that systems that are robust with respect to perturbations in the parameter space have an easily verifiable in terms of proof complexity region of attraction properties motivated by the computational complexity of optimization based formulations we take a compositional approach and exploit a natural decomposition of the system induced by the underlying biological structure into a feedback interconnection of two input output subsystems a small subsystem with complicating nonlinearities and a large subsystem with simple dynamics this decomposition simplifies the analysis of large pathways by assembling region of attraction certificates based on the input output properties of the subsystems it enables numerical as well as analytical construction of block diagonal lyapunov functions for a large family of autocatalytic pathways

nilpotence for modules over the mod 2 steenrod algebra ii we imitate much of the work of hopkins and smith in 7 in the context of modules over the mod 2 steenrod algebra a our main result is an analog of the periodicity theorem of 7 implying for example the existence of infinitely many non nilpotent elements in ext a f2 f2