designing the optimal bit balancing energetic cost speed and reliability we consider the challenge of operating a reliable bit that can be rapidly erased we find that both erasing and reliability times are non monotonic in the underlying friction leading to a trade of

entropy production and kullback leibler divergence between stationary trajectories of discrete systems the irreversibility of a stationary time series can be quantified using the kullback leibler divergence kld between the probability of observing the series and the probability of observing the time reversed series moreover this kld is a tool to estimate entropy production from stationary trajectories since it gives a lower bound to the entropy production of the physical process generating the series in this paper we introduce analytical and numerical techniques to estimate the kld between time series generated by several stochastic dynamics with a finite number of states we examine the accuracy of our estimators for a specific example a discrete flashing ratchet and investigate how close the kld is to the entropy production depending on the number of degrees of freedom of the system that are sampled in the trajectories

relaxation dynamics of maximally clustered networks we study the relaxation dynamics of fully clustered networks maximal number of triangles to an unclustered state under two different edge dynamics the double edge swap corresponding to degree preserving randomization of the configuration model and single edge replacement corresponding to full randomization of the erd ifmmode mbox h o else h o fi s r enyi random graph we derive expressions for the time evolution of the degree distribution edge multiplicity distribution and clustering coefficient we show that under both dynamics networks undergo a continuous phase transition in which a giant connected component is formed we calculate the position of the phase transition analytically using the erd ifmmode mbox h o else h o fi s r enyi phenomenology

clausius inequality and h theorems for some models of random wealth exchange a b s t r a c t we discuss a possibility of deriving an h theorem for nonlinear discrete time evolution equation that describes random wealth exchanges in such kinetic models economical agents exchange wealth in pairwise collisions just as particles in a gas exchange their energy it appears useful to reformulate the problem and represent the dynamics as a combination of two processes the first is a linear transformation of a two particle distribution function during the act of exchange while the second one corresponds to new random pairing of agents and plays a role of some kind of feedback control this representation leads to a clausius type inequality which suggests a new interpretation of the exchange process as an irreversible relaxation due to a contact with a reservoir of a special type only in some special cases when equilibrium distribution is exactly a gamma distribution this inequality results in the h theorem with monotonically growing entropy functional which differs from the boltzmann entropy by an additional term but for arbitrary exchange rule the evolution has some features of relaxation to a non equilibrium steady state and it is still unclear if any general h theorem could exist

oscillation analysis of numerical solutions for delay differential equations with real coefficients abstract the paper is mainly concerned with the oscillations of numerical solutions by the linear methods for a kind of linear delay differential equations with positive and negative coefficients some conditions under which the numerical solutions are oscillatory are obtained and it is proved that oscillations of the analytical solutions are preserved by the numerical solutions under mild conditions numerical experiments are given to demonstrate our results

vector valued stochastic delay equations a weak solution and its markovian representation abstract a class of stochastic delay equations in a type 2 umd banach space e driven by the cylindrical wiener process is studied we investigate two concepts of solutions weak and generalised strong and give conditions under which they are equivalent we present an evolution equation approach in a banach space e p e l p 1 0 e proving that the solutions can be reformulated as e p valued markov processes based on the markovian representation we prove the existence and continuity of the solutions the results are applied to stochastic reaction diffusion equations with delays

exact epidemic analysis for the star topology a methodology is formulated for studying the effects of network structure on the dynamics and spread of an epidemic we study the well known sis susceptible infected susceptible epidemic model and introduce exact moment equations relevant for any network connections the equations take into account all possible 2n states of the network and the specific topology of the network at hand for the star topology we are able to calculate the threshold value analytically and also the proportion of infected individuals at steady state for any parameters our analytical results are verified with computer simulations this study of epidemic dynamics on the star network evaluates both the threshold as well as the stability properties of the model s steady state

isometric immersions into ⁿ ℝ and ℍⁿ ℝ and applications to minimal surfaces we give a necessary and sufficient condition for an n dimensional riemannian manifold to be isometrically immersed in s n x or n in terms of its first and second fundamental forms and of the projection of the vertical vector field on its tangent plane we deduce the existence of a one parameter family of isometric minimal deformations of a given minimal surface in s 2 or 2 x r obtained by rotating the shape operator

new approximations and policy implications from a delayed dynamic model of a fast pandemic abstract we study an seiqr susceptible exposed infectious quarantined recovered model due to young et al 2019 for an infectious disease with time delays for latency and an asymptomatic phase for fast pandemics where nobody has prior immunity and everyone has immunity after recovery the seiqr model decouples into two nonlinear delay differential equations ddes with five parameters one parameter is set to unity by scaling time the simple subcase of perfect quarantining and zero self recovery before quarantine with two free parameters is examined first the method of multiple scales yields a hyperbolic tangent solution and a long wave short delay approximation yields a first order ordinary differential equation ode with imperfect quarantining and nonzero self recovery the long wave approximation is a second order ode these three approximations each capture the full outbreak from infinitesimal initiation to final saturation low dimensional dynamics in the ddes is demonstrated using a six state non delayed reduced order model obtained by galerkin projection numerical solutions from the reduced order model match the dde over a range of parameter choices and initial conditions finally stability analysis and numerics show how a well executed temporary phase of social distancing can reduce the total number of people affected the reduction can be by as much as half for a weak pandemic and is smaller but still substantial for stronger pandemics an explicit formula for the greatest possible reduction is given

emergence and size of the giant component in clustered random graphs with a given degree distribution standard techniques for analyzing network models usually break down in the presence of clustering here we introduce a new analytic tool the free excess degree distribution which extends the generating function framework making it applicable for clustered networks c 0 the methodology is general and provides a new expression for the threshold point at which the giant component emerges and shows that it scales as 1 c 1 in addition the size of the giant component may be predicted even for more complicated scenarios such as the removal of a fixed fraction of nodes at random

harmonic maps and constant mean curvature surfaces in h 2 x r we introduce a it hyperbolic gauss map into the poincar e disk for any surface in bbb h 2 times bbb r with regular vertical projection and prove that if the surface has constant mean curvature h 1 2 this hyperbolic gauss map is harmonic conversely we show that every nowhere conformal harmonic map from an open simply connected riemann surface sigma into the poincar e disk is the hyperbolic gauss map of a two parameter family of such surfaces as an application we obtain that any holomorphic quadratic differential on sigma can be realized as the abresch rosenberg holomorphic differential of some and generically infinitely many complete surfaces with h 1 2 in bbb h 2 times bbb r a similar result applies to minimal surfaces in the heisenberg group rm nil 3 finally we classify all complete minimal vertical graphs in bbb h 2 times bbb r

complete minimal varieties in hyperbolic space it is a basic problem in the subject of minimal varieties to determine the class of complete minimal and area minimizing varieties m k in a given riemannian manifold n besides being of their own intrinsic interest the cases r of euclidean space and mn sn of the sphere are fundamental in understanding the local structure of minimal varieties due to the existence of tangent cones to general minimal varieties there has been much study of the complete areaminimizing varieties in these cases in particular relating to the bernstein conjecture and minimizing cones e g l2 f1 nevertheless many deep problems remain unsolved this paper is centered around the question of existence of complete areaminimizing varieties in hyperbolic space h here by way of contrast to the situation in ir n or s we find a comparatively complete solution to the problem of existence in fact the main result of this paper exhibits a wealth of complete area minimizing varieties in h in all dimensions and codimensions more precisely we have

uniqueness of minimal surfaces whose boundary is a horizontal graph and some bernstein problems in mathbb h 2 times mathbb r we deduce that a connected compact immersed minimal surface in mathbb h 2 times mathbb r whose boundary has an injective horizontal projection on an admissible convex curve in partial infty mathbb h 2 times mathbb r and satisfies an admissible bounded slope condition is the morrey s solution of the plateau problem and is a horizontal minimal graph we prove that there is no entire horizontal minimal graph in mathbb h 2 times mathbb r

percolation on random networks with arbitrary k core structure the k core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks we now propose its explicit integration in a theoretical model we introduce a hard core random network hrn model that generates maximally random networks with arbitrary degree distribution and arbitrary k core structure we then solve exactly the bond percolation problem on the hrn model and produce fast and precise analytical estimates for the corresponding real networks extensive comparison with real databases reveals that our approach performs better than existing models while requiring less input information

stability analysis of general linear methods for nonlinear neutral delay differential equations abstract the present paper is concerned with the numerical solution to initial value problems of neutral delay differential equations nddes the sufficient conditions for the stability and asymptotic stability of the general linear methods for a class r of nonlinear systems of nddes are derived numerical test is given that confirm the theoretical results in the end

generating uniformly distributed random networks the analysis of real networks taken from the biological social and physical sciences often requires a carefully posed statistical null hypothesis approach one common method requires comparing real networks to an ensemble of random matrices that satisfy realistic constraints in which each different matrix member is equiprobable we discuss existing methods for generating uniformly distributed constrained random matrices describe their shortcomings and present an efficient technique that should have many practical applications

properly embedded minimal annuli in mathbb h 2 times mathbb r in this paper we study the moduli space of properly alexandrov embedded minimal annuli in mathbb h 2 times mathbb r with horizontal ends we say that the ends are horizontal when they are graphs of mathcal c 2 alpha functions over partial infty mathbb h 2 contrary to expectation we show that one can not fully prescribe the two boundary curves at infinity but rather one can prescribe one of the boundary curves but the other one only up to a translation and a tilt along with the position of the neck and the vertical flux of the annulus we also prove general existence theorems for minimal annuli with discrete groups of symmetries

convergence analysis of fitted numerical method for a singularly perturbed nonlinear volterra integro differential equation with delay abstract in this paper the initial value problem for a quasilinear singularly perturbed delay volterra integro differential equation was considered by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder term in integral form a fitted difference scheme is constructed and analysed it is shown that the method displays first order uniform convergence in perturbation parameter some numerical results are given to confirm the theoretical analysis

nonequilibrium detailed fluctuation theorem for repeated discrete feedback we extend the framework of forward and reverse processes commonly utilized in the derivation and analysis of the nonequilibrium work relations to thermodynamic processes with repeated discrete feedback within this framework we derive a generalization of the detailed fluctuation theorem which is modified by the addition of a term that quantifies the change in uncertainty about the microscopic state of the system upon making measurements of physical observables during feedback as an application we extend two nonequilibrium work relations the nonequilibrium work fluctuation theorem and the relative entropy work relation

thermodynamics of genuine nonequilibrium states under feedback control for genuine nonequilibrium states that even at fixed external control parameter exhibit dissipation we extend the hatano sasa equality to processes with feedback control the resulting bound on the maximal extractable work is substantially sharper than what would follow from applying the sagawa ueda equality to transitions involving such states for repeated measurements at short enough intervals the power thus extracted can even exceed the average cost of driving as demonstrated explicitly with a simple analytically solvable example

lower bounds on dissipation upon coarse graining by different coarse graining procedures we derive lower bounds on the total mean work dissipated in brownian systems driven out of equilibrium with several analytically solvable examples we illustrate how when and where the information on the dissipation is captured

numerical modelling in biosciences using delay differential equations our principal purposes here are i to consider from the perspective of applied mathematics models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics ii to review the application of numerical techniques to investigate these models we show that there are prima facie reasons for using such models i they have a richer mathematical framework compared with ordinary differential equations for the analysis of biosystem dynamics ii they display better consistency with the nature of certain biological processes and predictive results we analyze both the qualitative and quantitative role that delays play in basic time lag models proposed in population dynamics epidemiology physiology immunology neural networks and cell kinetics we then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences comparing them with those implemented by the bio modellers

concentration of total curvature of minimal surfaces in mathbb h 2 times mathbb r we prove a phenomenon of concentration of total curvature for stable minimal surfaces in the product space mathbb h 2 times mathbb r where mathbb h 2 is the hyperbolic plane under some geometric conditions on its asymptotic boundary an oriented stable minimal surface immersed in mathbb h 2 times mathbb r has infinite total curvature we exhibit an example of a minimal graph such that in a domain whose asymptotic boundary is a vertical segment the total curvature is finite but the total curvature of the graph is infinite by the theorem cited before we also present some simple and peculiar examples of infinite total curvature minimal surfaces in mathbb h 2 times mathbb r and their asymptotic boundaries

correlation powered information engines and the thermodynamics of self correction information engines can use structured environments as a resource to generate work by randomizing ordered inputs and leveraging the increased shannon entropy to transfer energy from a thermal reservoir to a work reservoir we give a broadly applicable expression for the work production of an information engine generally modeled as a memoryful channel that communicates inputs to outputs as it interacts with an evolving environment the expression establishes that an information engine must have more than one memory state in order to leverage input environment correlations to emphasize this functioning we designed an information engine powered solely by temporal correlations and not by statistical biases as employed by previous engines key to this is the engine s ability to synchronize the engine automatically returns to a desired dynamical phase when thrown into an unwanted dissipative phase by corruptions in the input that is by unanticipated environmental fluctuations this self correcting mechanism is robust up to a critical level of corruption beyond which the system fails to act as an engine we give explicit analytical expressions for both work and critical corruption level and summarize engine performance via a thermodynamic function phase diagram over engine control parameters the results reveal a thermodynamic mechanism based on nonergodicity that underlies error correction as it operates to support resilient engineered and biological systems

infinite boundary value problems for constant mean curvature graphs in h2 r and s2 r we extend the classical existence and uniqueness theory of jenkins serrin h 0 and spruck h 0 for the constant mean curvature equation over a domain in r 2 to domains in h 2 or s 2 this theory allows prescribed boundary data including plus or minus infinity on entire arcs of the boundary necessarily these arc must have curvature 2h or 2h with respect to the domain we give necessary and sufficient conditions for existence in terms of so called admissible polygons the key idea as in previous proofs is to study the flux of monotone increasing and decreasing sequences of solutions

numerical bifurcation analysis of immunological models with time delays in recent years a large number of mathematical models that are described by delay differential equations ddes have appeared in the life sciences to analyze the models dynamics numerical methods are necessary since analytical studies can only give limited results in turn the availability of efficient numerical methods and software packages encourages the use of time delays in mathematical modelling which may lead to more realistic models we outline recently developed numerical methods for bifurcation analysis of ddes and illustrate the use of these methods in the analysis of a mathematical model of human hepatitis b virus infection

a finite difference method for a singularly perturbed delay integro differential equation we consider the singularly perturbed initial value problem for a linear first order volterra integro differential equation with delay our purpose is to construct and analyse a numerical method with uniform convergence in the perturbation parameter the numerical solution of this problem is discretized using implicit difference rules for differential part and the composite numerical quadrature rules for integral part on a layer adapted mesh error estimations for the approximate solution are established numerical examples supporting the theory are presented

universal interpretation of efficacy parameter in perturbed nonequilibrium systems abstract the fluctuation theorems have remained one of the cornerstones in the study of systems that are driven far out of equilibrium and they provide strong constraints on the fraction of trajectories that behave atypically in light of the second law they have mainly been derived for a predetermined external drive applied to the system however to improve the efficiency of a process one needs to incorporate protocols that are modified by receiving feedbacks about the recent state of the system during its evolution in such a case the forms of the conventional fluctuation theorems get modified the correction term involving terms that depend on the way the reverse conjugate process is defined namely the rules of using feedback in order to generate the exact time reversed conjugate protocols we show in this paper that this can be done in a large number of ways and in each case we would get a different expression for the correction terms this would in turn lead to several lower bounds on the mean work that must be performed on the system or on the entropy changes here we analyze a form of the extended fluctuation theorems that involves the efficacy parameter and find that this form retains a consistent physical meaning regardless of the design of feedback along the conjugate process as opposed to the case of the previously mentioned form of the modified fluctuation theorems

rival approaches to mathematical modelling in immunology in order to formulate quantitatively correct mathematical models of the immune system one requires an understanding of immune processes and familiarity with a range of mathematical techniques selection of an appropriate model requires a number of decisions to be made including a choice of the modelling objectives strategies and techniques and the types of model considered as candidate models the authors adopt a multidisciplinary perspective

jarzynski type equalities in gambling role of information in capital growth we study the capital growth in gambling with and without side information and memory effects we derive several equalities for gambling which are of similar form to the jarzynski equality and its extension to systems with feedback controls those relations provide us with new measures to quantify the effects of information on the statistics of capital growth in gambling we discuss the implications of the equalities and show that they reproduce the known upper bounds of average capital growth rates

fluctuation relations for a driven brownian particle we consider a driven brownian particle subject to both conservative and nonconservative applied forces whose probability evolves according to the kramers equation we derive a general fluctuation relation expressing the ratio of the probability of a given brownian path in phase space with that of the time reversed path in terms of the entropy flux to the heat reservoir this fluctuation relation implies those of seifert jarzynski and gallavotti cohen in different special cases

bayesian second law of thermodynamics we derive a generalization of the second law of thermodynamics that uses bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution by allowing an experimenter s knowledge to be updated by the measurement process this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information theoretic idea that knowledge of a stochastically evolving system degrades over time the bayesian second law can be written as h m 2 f m 0 where h m is the change in the cross entropy between the original phase space probability distribution and the measurement updated distribution m and 2 f m is the expectation value of a generalized heat flow out of the system we also derive refined versions of the second law that bound the entropy increase from below by a non negative number as well as bayesian versions of integral fluctuation theorems we demonstrate the formalism using simple analytical and numerical examples

introduction to the numerical analysis of stochastic delay differential equations abstract we consider the problem of the numerical solution of stochastic delay differential equations of ito form d x t f x t x t d t g x t x t d w t t 0 t and x t t for t 0 with given f g wiener noise w and given 0 with a prescribed initial function we indicate the nature of the equations of interest and give a convergence proof for explicit single step methods some illustrative numerical examples using a strong euler maruyama scheme are provided

reconstruction of time delayed feedback systems from time series for various classes of time delay systems we propose the methods of their model delay differential equation reconstruction from time series the methods are based on the characteristic location of extrema in the time series of time delay systems and the projection of infinite dimensional phase space of these systems to suitably chosen low dimensional subspaces we verify our methods by using them for the recovery of time delay differential equations from their chaotic solutions and for modelling experimental systems with delay induced dynamics from their chaotic time series

a halfspace theorem for mean curvature h 12 surfaces in h2 r abstract we prove a vertical halfspace theorem for surfaces with constant mean curvature h 1 2 properly immersed in the product space h 2 r where h 2 is the hyperbolic plane and r is the set of real numbers the proof is a geometric application of the classical maximum principle for second order elliptic pde using the family of noncompact rotational h 1 2 surfaces in h 2 r

entropy production and fluctuation theorems for langevin processes under continuous non markovian feedback control continuous feedback control of langevin processes may be non markovian due to a time lag between the measurement and the control action we show that this requires one to modify the basic relation between dissipation and time reversal and to include a contribution arising from the noncausal character of the reverse process we then propose a new definition of the quantity measuring the irreversibility of a path in a nonequilibrium stationary state which can also be regarded as the trajectory dependent total entropy production this leads to an extension of the second law which takes a simple form in the long time limit as an illustration we apply the general approach to linear systems that are both analytically tractable and experimentally relevant

thermodynamic uncertainty relations including measurement and feedback thermodynamic uncertainty relations quantify how the signal to noise ratio of a given observable is constrained by dissipation fluctuation relations generalize the second law of thermodynamics to stochastic processes we show that any fluctuation relation directly implies a thermodynamic uncertainty relation considerably increasing their range of applicability in particular we extend thermodynamic uncertainty relations to scenarios which include measurement and feedback since feedback generally breaks time reversal invariance the uncertainty relations involve quantities averaged over the forward and the backward experiment defined by the associated fluctuation relation this implies that the signal to noise ratio of a given experiment can in principle become arbitrarily large as long as the corresponding backward experiment compensates e g by being sufficiently noisy we illustrate our results with the szilard engine as well as work extraction by free energy reduction in a quantum dot

on reducible nonlinear time delayed stochastic systems fluctuation dissipation relations transitions to bistability and secondary transitions to non stationarity we show the conditions under which nonlinear time delayed dynamical systems with multiplicative noise sources can be transformed into linear time delayed systems with additive noise sources we show that for such reducible systems analytical expressions for stationary distributions can be obtained we demonstrate that fluctuation dissipation relations of reducible systems become trivial and we show that reducible systems may exhibit delay and noise induced transitions to bistability and secondary transitions to non stationarity our general findings are exemplified for three models a gompertz model a hongler model and a model involving a 1 x 2 noise amplitude

multivariate markov processes for stochastic systems with delays application to the stochastic gompertz model with delay using the method of steps we describe stochastic processes with delays in terms of markov diffusion processes thus multivariate langevin equations and fokker planck equations are derived for stochastic delay differential equations natural periodic and reflective boundary conditions are discussed both ito and stratonovich calculus are used in particular our fokker planck approach recovers the generalized delay fokker planck equation proposed by guillouzic et al the results obtained are applied to a model for population growth the gompertz model with delay and multiplicative white noise

variational calculation of the limit cycle and its frequency in a two neuron model with delay we consider a model system of two coupled hopfield neurons which is described by delay differential equations taking into account the finite signal propagation and processing times when the delay exceeds a critical value a limit cycle emerges via a supercritical hopf bifurcation first we calculate its frequency and trajectory perturbatively by applying the poincar e lindstedt method then the perturbation series are resummed by means of the shohat expansion in good agreement with numerical values however with increasing delay the accuracy of the results from the shohat expansion worsens we thus apply variational perturbation theory vpt to the perturbation expansions to obtain more accurate results which moreover hold even in the limit of large delays

thermodynamics of information processing based on enzyme kinetics an exactly solvable model of an information pump motivated by the recent proposed models of the information engine proc natl acad sci usa 109 11641 2012 and the information refrigerator phys rev lett 111 030602 2013 we propose a minimal model of the information pump and the information eraser based on enzyme kinetics this device can either pump molecules against the chemical potential gradient by consuming the information to be encoded in the bit stream or partially erase the information initially encoded in the bit stream by consuming the gibbs free energy the dynamics of this model is solved exactly and the phase diagram of the operation regimes is determined the efficiency and the power of the information machine is analyzed the validity of the second law of thermodynamics within our model is clarified our model offers a simple paradigm for the investigating of the thermodynamics of information processing involving the chemical potential in small systems

theoretical analysis of destabilization resonances in time delayed stochastic second order dynamical systems and some implications for human motor control a linear stochastic delay differential equation of second order is studied that can be regarded as a kramers model with time delay an analytical expression for the stationary probability density is derived in terms of a gaussian distribution in particular the variance as a function of the time delay is computed analytically for several parameter regimes strikingly in the parameter regime close to the parameter regime in which the deterministic system exhibits hopf bifurcations we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks these peaks are interpreted as delay induced destabilization resonances arising from oscillatory ghost instabilities on the basis of the obtained theoretical findings reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided 2006 the american physical society

perpetual extraction of work from a nonequilibrium dynamical system under markovian feedback control by treating both control parameters and dynamical variables as probabilistic variables we develop a succinct theory of perpetual extraction of work from a generic classical nonequilibrium system subject to a heat bath via repeated measurements under a markovian feedback control it is demonstrated that a problem for perpetual extraction of work in a nonequilibrium system is reduced to a problem of markov chain in the higher dimensional phase space we derive a version of the detailed fluctuation theorem which was originally derived for classical nonequilibrium systems by horowitz and vaikuntanathan phys rev e 82 061120 2010 in a form suitable for the analyses of perpetual extraction of work since our theory is formulated for generic dynamics of probability distribution function in phase space its application to a physical system is straightforward as simple applications of the theory two exactly solvable models are analyzed the one is a nonequilibrium two state system and the other is a particle confined to a one dimensional harmonic potential in thermal equilibrium for the former example it is demonstrated that the observer on the transitory steps to the stationary state can lose energy and that work larger than that achieved in the stationary state can be extracted for the latter example it is demonstrated that the optimal protocol for the extraction of work via repeated measurements can differ from that via a single measurement the validity of our version of the detailed fluctuation theorem which determines the upper bound of the expected work in the stationary state is also confirmed for both examples these observations provide useful insights into exploration for realistic modeling of a machine that extracts work from its environment

random networks with tunable degree distribution and clustering we present an algorithm for generating random networks with arbitrary degree distribution and clustering frequency of triadic closure we use this algorithm to generate networks with exponential power law and poisson degree distributions with variable levels of clustering such networks may be used as models of social networks and as a testable null hypothesis about network structure finally we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network and on the size of the giant component some analysis of these effects is presented

time reversal and entropy there is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time reversal symmetry and the entropy production in such processes we explain on an elementary mathematical level the relations between entropy production phase space contraction and time reversal starting from a deterministic dynamics both closed and open systems in the transient and in the steady regime are considered the main result identifies under general conditions the statistical mechanical entropy production as the source term of time reversal breaking in the path space measure for the evolution of reduced variables this provides a general algorithm for computing the entropy production and to understand in a unified way a number of useful in equalities we also discuss the markov approximation important are a number of old theoretical ideas for connecting the microscopic dynamics with thermodynamic behavior

nonequilibrium thermodynamics of feedback control we establish a general theory of feedback control on classical stochastic thermodynamic systems and generalize nonequilibrium equalities such as the fluctuation theorem and the jarzynski equality in the presence of feedback control with multiple measurements our results are generalizations of the previous relevant works to the situations with general measurements and multiple heat baths the obtained equalities involve additional terms that characterize the information obtained by measurements or the efficacy of feedback control a generalized szilard engine and a feedback controlled ratchet are shown to satisfy the derived equalities

fluctuation theorems in the presence of information gain and feedback in this study we rederive the fluctuation theorems in the presence of feedback by assuming the known jarzynski equality and detailed fluctuation theorems we find that both the classical and quantum systems can be analyzed using a similar treatment in terms of state space trajectories we first briefly reproduce the already known work theorems for a classical system in order to show its equivalence with the quantum treatment we then extend the treatment to arrive at new results namely the generalizations of seifert s entropy production theorem and the hatano sasa fluctuation theorem in the presence of feedback we have also derived the extended version of the tasaki crooks fluctuation theorem for a quantum particle in the presence of multiple loop feedback for deriving the extended quantum fluctuation theorems we have considered open systems no assumption is made on the nature of environment and the strength of system bath coupling however it is assumed that the measurement process involves classical errors

maximum work extraction and implementation costs for nonequilibrium maxwell s demons we determine the maximum amount of work extractable in finite time by a demon performing continuous measurements on a quadratic hamiltonian system subjected to thermal fluctuations in terms of the information extracted from the system the maximum work demon is found to apply a high gain continuous feedback involving a kalman bucy estimate of the system state and operates in nonequilibrium a simple and concrete electrical implementation of the feedback protocol is proposed which allows for analytic expressions of the flows of energy entropy and information inside the demon this let us show that any implementation of the demon must necessarily include an external power source which we prove both from classical thermodynamics arguments and from a version of landauer s memory erasure argument extended to nonequilibrium linear systems

properties of highly clustered networks we propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient among other things our results indicate that increased clustering leads to a decrease in the size of the giant component of the network we also study susceptible infective recovered type epidemic processes within the model and find that clustering decreases the size of epidemics but also decreases the epidemic threshold making it easier for diseases to spread in addition clustering causes epidemics to saturate sooner meaning that they infect a near maximal fraction of the network for quite low transmission rates

stochastic thermodynamics with arbitrary interventions we extend the theory of stochastic thermodynamics in three directions i instead of a continuously monitored system we consider measurements only at an arbitrary set of discrete times ii we allow for imperfect measurements and incomplete information in the description and iii we treat arbitrary manipulations e g feedback control operations which are allowed to depend on the entire measurement record for this purpose we define for a driven system in contact with a single heat bath the four key thermodynamic quantities internal energy heat work and entropy along a single trajectory for a causal model the first law at the trajectory level and the second law on average is verified we highlight the special case of bayesian or bare measurements incomplete information but no average disturbance which allows us to compare our theory with the literature and to derive a general inequality for the estimated free energy difference in jarzynski type experiments an analysis of a recent maxwell demon experiment using real time feedback control is also given as a mathematical tool we prove a classical version of stinespring s dilation theorem which might be of independent interest

existence of barriers for surfaces with prescribed curvatures in m2 r abstract we present a deformation process of surfaces from a product space m 1 r into another product space m 2 r such that the relation of the principal curvatures of the deformed surfaces can be controlled in terms of the curvatures of m 1 and m 2 thus we obtain subsolutions for the existence or barriers for the non existence of surfaces with prescribed curvatures in a general product space m r

fluctuation theorem for hidden entropy production elimination of seemingly unnecessary variables in markovian models may cause a difference in the value of irreversible entropy production between the original and reduced dynamics we show that such difference which we call the hidden entropy production obeys an integral fluctuation theorem if all variables are time reversal invariant or if the density function is symmetric with respect to the change of sign of the time reversal antisymmetric variables the theorem has wide applicability since the proposed condition is mostly satisfied in the case where the hidden fast variables are equilibrated the main consequence of this theorem is that the entropy production decreases by the coarse graining procedure by contrast in the case where a stochastic process is obtained by coarse graining a deterministic and reversible dynamics the entropy production may increase implying that the integral fluctuation theorem should not hold for such reductions we reveal with an explicit example that the nonequilibrated time reversal antisymmetric variables play a crucial role in distinguishing these two cases thus guaranteeing the consistency of the presented theorem

stability analysis of volterra delay integro differential equations and their backward differentiation time discretization we study the stability of the analytical solutions of initial value problems of a general class of systems of volterra delay integro differential equations numerical methods based on backward differentiation formulae and repeated quadrature formulae are suggested nonlinear and linear stability conditions for the presented methods are derived

fluctuation theorem with information exchange role of correlations in stochastic thermodynamics we establish the fluctuation theorem in the presence of information exchange between a nonequilibrium system and other degrees of freedom such as an observer and a feedback controller where the amount of information exchange is added to the entropy production the resulting generalized second law sets the fundamental limit of energy dissipation and energy cost during the information exchange our results apply not only to feedback controlled processes but also to a much broader class of information exchanges and provide a unified framework of nonequilibrium thermodynamics of measurement and feedback control

uncertainty relations and fluctuation theorems for bayes nets recent research has considered the stochastic thermodynamics of multiple interacting systems representing the overall system as a bayes net i derive fluctuation theorems governing the entropy production ep of arbitrary sets of the systems in such a bayes net i also derive conditional fluctuation theorems governing the distribution of ep in one set of systems conditioned on the ep of a different set of systems i then derive thermodynamic uncertainty relations relating the ep of the overall system to the precisions of probability currents within the individual systems

delay fokker planck equations novikov s theorem and boltzmann distributions as small delay approximations we study time delayed stochastic systems that can be described by means of so called delay fokker planck equations using novikov s theorem we first show that the theory of delay fokker planck equations is on an equal footing with the theory of ordinary fokker planck equations subsequently we derive stationary distributions in the case of small time delays in the case of additive noise systems these distributions can be cast into the form of boltzmann distributions involving effective potential functions

an asymptotic theorem for minimal surfaces and existence results for minimal graphs in mathbb h 2 times mathbb r in this paper we prove a general and sharp asymptotic theorem for minimal surfaces in mathbb h 2 times mathbb r as a consequence we prove that there is no properly immersed minimal surface whose asymptotic boundary is a jordan curve homologous to zero in partial infty mathbb h 2 times mathbb r such that is contained in a slab between two horizontal circles of partial infty mathbb h 2 times mathbb r with width equal to we construct vertical minimal graphs in mathbb h 2 times mathbb r over certain unbounded admissible domains taking certain prescribed finite boundary data and certain prescribed asymptotic boundary data our admissible unbounded domains in mathbb h 2 times 0 are non necessarily convex and non necessarily bounded by convex arcs each component of its boundary is properly embedded with zero one or two points on its asymptotic boundary satisfying a further geometric condition

rate of mutual information between coarse grained non markovian variables the problem of calculating the rate of mutual information between two coarse grained variables that together specify a continuous time markov process is addressed as a main obstacle the coarse grained variables are in general non markovian therefore an expression for their shannon entropy rates in terms of the stationary probability distribution is not known a numerical method to estimate the shannon entropy rate of continuous time hidden markov processes from a single time series is developed with this method the rate of mutual information can be determined numerically moreover an analytical upper bound on the rate of mutual information is calculated for a class of markov processes for which the transition rates have a bipartite character our general results are illustrated with explicit calculations for four state networks

computational approaches to parameter estimation and model selection in immunology one of the significant challenges in biomathematics and other areas of science is to formulate meaningful mathematical models our problem is to decide on a parametrized model which is in some sense most likely to represent the information in a set of observed data in this paper we illustrate the computational implementation of an information theoretic approach associated with a maximum likelihood treatment to modelling in immunology the approach is illustrated by modelling lcmv infection using a family of models based on systems of ordinary differential and delay differential equations the models which use parameters that have a scientific interpretation are chosen to fit data arising from experimental studies of virus cytotoxic t lymphocyte kinetics the parametrized models that result are arranged in a hierarchy by the computation of akaike indices the practical illustration is used to convey more general insight because the mathematical equations that comprise the models are solved numerically the accuracy in the computation has a bearing on the outcome and we address this and other practical details in our discussion

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

generalized jarzynski equality under nonequilibrium feedback control the jarzynski equality is generalized to situations in which nonequilibrium systems are subject to a feedback control the new terms that arise as a consequence of the feedback describe the mutual information content obtained by measurement and the efficacy of the feedback control our results lead to a generalized fluctuation dissipation theorem that reflects the readout information and they can be experimentally tested using small thermodynamic systems we illustrate our general results by introducing an information ratchet which can transport a brownian particle in one direction and extract positive work from the particle

on a stable one leg methods for solving nonlinear volterra functional differential equations abstract this paper is concerned with the stability of the one leg methods for nonlinear volterra functional differential equations vfdes the contractivity and asymptotic stability properties are first analyzed for quasi equivalent and a stable one leg methods by use of two lemmas proven in this paper to extend the analysis to the case of strongly a stable one leg methods nevanlinna and liniger s technique of introducing new norm is used to obtain the conditions for contractivity and asymptotic stability of these methods as a consequence it is shown that one leg methods 1 2 1 with linear interpolation are unconditionally contractive and asymptotically stable and 2 step adams type method and 2 step bdf method are conditionally contractive and asymptotically stable the bounded stability of the midpoint rule is also proved with the help of the concept of semi equivalent one leg methods

general and exact approach to percolation on random graphs we present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs our contribution can be summarized in three main points i we introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite size quenched or random multitype graphs ii we define a very general random graph ensemble that encompasses most of the models published to this day and also makes it possible to model structural properties not yet included in a theoretical framework site and bond percolation on this ensemble is solved exactly in the infinite size limit using probability generating functions i e the percolation threshold the size and the composition of the giant extensive and small components several examples and applications are also provided iii our approach can be adapted to model interdependent graphs whose most striking feature is the emergence of an extensive component via a discontinuous phase transition in an equally general fashion we show how a graph can successively undergo a continuous then a discontinuous phase transition and preliminary results suggest that clustering increases the amplitude of the discontinuity at the transition

preserving stability implicit euler method for nonlinear volterra and neutral functional differential equations in banach space this paper is concerned with the contractivity and asymptotic stability properties of the implicit euler method iem for nonlinear functional differential equations fdes these properties are first analyzed for volterra fdes and then the analysis is extended to the case of neutral fdes nfdes such an extension is particularly important since nfdes are more general and have received little attention in the literature the main result we establish is that the iem with linear interpolation can completely preserve these stability properties of the analytical solution to such fdes

delay fokker planck equations perturbation theory and data analysis for nonlinear stochastic systems with time delays we study nonlinear stochastic systems with time delayed feedback using the concept of delay fokker planck equations introduced by guillouzic l heureux and longtin we derive an analytical expression for stationary distributions using first order perturbation theory we demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data in addition we show that the fokker planck perspective for stochastic systems with time delays is consistent with the so called extended phase space approach to time delayed systems

periodic solutions and chaos in a non linear model for the delayed cellular immune response abstract we model the cellular immune response using a set of non linear delayed differential equations we observe that the stationary solution becomes unstable above a critical immune response time the exponents characterizing the approach to this bifurcation point as well as the critical slow dynamics are obtained in the periodic regime the minimum virus load is substantially reduced with respect to the stationary solution further increasing the delay time the dynamics display a series of bifurcations evolving to a chaotic regime characterized by a set of 2d portraits