theoretical analysis and performance of ofdm signals in nonlinear awgn channels orthogonal frequency division multiplexing ofdm baseband signals may be modeled by complex gaussian processes with rayleigh envelope distribution and uniform phase distribution if the number of carriers is sufficiently large the output correlation function of instantaneous nonlinear amplifiers and the signal to distortion ratio can be derived and expressed in an easy way as a consequence the output spectrum and the bit error rate ber performance of ofdm systems in nonlinear additive white gaussian noise channels are predictable both for uncompensated amplitude modulation amplitude modulation am am and amplitude modulation pulse modulation am pm distortions and for ideal predistortion the aim of this work is to obtain the analytical expressions for the output correlation function of a nonlinear device and for the ber performance the results in closed form solutions are derived for am am and am pm curves approximated by bessel series expansion and for the ideal predistortion case

on the distribution of the peak to average power ratio in ofdm signals the distribution of the peak to average power ratio papr in strictly band limited orthogonal frequency division multiplexing ofdm signals is studied assuming that the base band ofdm signal is characterized as a band limited complex gaussian process we first attempt to derive the exact distribution of the papr in the band limited ofdm signals since this distribution cannot be expressed in a closed form we further develop a simple closed form approximation based on the level crossing rate analysis comparisons of the proposed distributions with those obtained by computer simulations show good agreement and convergence with an increase in the number of subcarriers

testing preorders for probabilistic processes can be characterized by simulations the domestic dog may be exceptionally well suited for behavioral genetic studies owing to its population history and the striking behavior differences among breeds to explore to what extent and ho

an analysis of band limited communication systems from amplifier efficiency and distortion perspective considering growing concerns toward green communications not only their bandwidth efficiency but also their power consumption is expected to gain increasing importance for future communication systems a power amplifier pa is one of the most power consuming analog devices at the transmitter in communication systems and a precise estimation of the power consumption at the transmitter circuit requires the knowledge of its efficiency that depends on the distribution of input signal envelope and the amount of input back off in this paper we develop a simple analytical model that can be used for estimating achievable efficiency of a linear pa as well as the amount of resulting nonlinear distortion for a given modulated signal exclusively from its envelope distribution based on this model the trade off relationships between the efficiency and signal to distortion power ratio for several spectrally efficient linear modulations are examined it is also shown that in some special cases of gaussian input and memoryless nonlinearity pa models the results can be represented in simple closed form expressions

on the large order behavior of φ44 we continue the rigorous study of the large order behavior of the perturbation series for the 4 model in 4 dimensions started in 1 in this paper we prove a result announced in 1 we show that the exact radius of convergence of the borel transform of the renormalized perturbation series for 44 is greater than or equal to the expected value given by the position of the first renormalon 2 this result holds for any vector 2 2 model withn components and makes use of the lipatov bound of 1 this result is based on a partial resummation of counterterms similar to the one of 3 but in a phase space analysis of the renormalized series

ward type identities for the two dimensional anderson model at weak disorder using the particular momentum conservation laws in dimension d 2 we rewrite the anderson model in terms of low momentum long range fields at the price of introducing electron loops the corresponding loops satisfy a ward type identity hence are much smaller than expected this fact should be useful for the study of the weak coupling model in the middle of the spectrum of the free hamiltonian

random walks in asymmetric random environments we consider random walks on zd with transition ratesp x y given by a random matrix ifp is a small random perturbation of the simple random walk we show that the walk remains diffusive for almost all environmentsp ifd 2 the result also holds for a continuous time markov process with a random drift the corresponding path space measures converge weakly in the scaling limit to the wiener process for almost everyp

the variational problems for classical n vector models we prove existence and regularity properties of solutions of the variational problems introduced in the previous paper 1 for classical lattice n vector models these results form a basis of our renormalization group approach to low temperature expansions for the considered models

renormalization and localization expansions ii expectation values of the fluctuation measures this paper is a continuation of 5 the k 1 st renormalization transformation applied to a density k is studied further the new contributions to the effective action obtained in 5 are renormalized and their localization expansions are constructed this completes proofs of theorems 1 and 4 in 5

limit laws for random matrices and free products in earlier articles we studied a kind of probability theory in the framework of operator algebras with the tensor product replaced by the free product we prove here that free random variables naturally arise as limits of random matrices and that wigner s semicircle law is a consequence of the central limit theorem for free random variables in this way we obtain a non commutative limit distribution of a general gaussian random matrix as an operator in a certain operator algebra wigner s law being given by the trace of the spectral measure of the selfadjoint component of this operator

axiomatizations for probabilistic finite state behaviors we study a process calculus which combines both nondeterministic and probabilistic behavior in the style of segala and lynch s probabilistic automata we consider various strong and weak behavioral equivalences and we provide complete axiomatizations for finite state processes restricted to guarded recursion in case of the weak equivalences we conjecture that in the general case of unguarded recursion the natural weak equivalences are undecidable this is the first work to our knowledge that provides a complete axiomatization for weak equivalences in the presence of recursion and both nondeterministic and probabilistic choice

quasi linear flows on tori regularity of their linearization under suitable conditions a flow on a torus c p close with p large enough to a quasi periodic diophantine rotation is shown to be linearizable i e conjugable to the quasi periodic rotation by a map that is analytic in the perturbation size this result is parallel to moser s theorem stating conjugability in class c p for some p p the extra conditions restrict the class of perturbations that are allowed

anomalous scaling in the n point functions of a passive scalar a recent analysis of the four point correlation function of the passive scalar advected by a time decorrelated random flow is extended to the n point case it is shown that all stationary state inertial range correlations are dominated by homogeneous zero modes of singular operators describing their evolution we compute analytically the zero modes governing the n point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the two point function of the advecting velocity field the implications of these calculations for the dissipation correlations are discussed textcopyright 1996 the american physical society

branching bisimulation congruence for probabilistic systems a notion of branching bisimilarity for the alternating model of probabilistic systems compatible with parallel composition is defined for a congruence result an internal transition immediately followed by a non trivial probability distribution is not considered inert a weaker definition of branching bisimilarity for the same model has been given earlier here we show that our branching bisimulation is the coarsest congruence for parallel composition that is included in the weaker version to support the use of the present equivalence as a reduction technique we also show that probabilistic ctl formulae are preserved by our equivalence and we provide a polynomial time algorithm deciding branching bisimilarity

frequency independent and frequency dependent nonlinear models of twt amplifiers simple two parameter formulas are presented for the functions involved in the amplitude phase and the quadrature nonlinear models of a twt amplifier and are shown to fit measured data very well also a closed form expression is derived for the output signal of a twt amplifier excited by two phase modulated carriers and an expression containing a single integral is given when more than two such earriers are involved finally a frequencydependent quadrature model is proposed whose parameters are obtainable from single tone measurements

self avoiding walk in 5 or more dimensions using an expansion based on the renormalization group philosophy we prove that for a t step weakly self avoiding random walk in five or more dimensions the variance of the endpoint is of order t and the scaling limit is gaussian as t

reactive generative and stratified models of probabilistic processes abstract we introduce three models of probabilistic processes namely reactive generative and stratified these models are investigated within the context of pccs an extension of milner s sccs in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1 for each model we present a structural operational semantics of pccs and a notion of bisimulation equivalence which we prove to be a congruence we also show that the models form a hierarchy the reactive model is derivable from the generative model by abstraction from the relative probabilities of different actions and the generative model is derivable from the stratified model by abstraction from the purely probabilistic branching structure moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities

high order moments and gaussianity of single carrier and ofdm signals this paper analyzes the high order moments of linearly modulated single carrier as well as orthogonal frequency division multiplexing ofdm signals assuming that the modulated symbols that form resulting continuous signal waveform are statistically independent for a single carrier case with the ideal low pass filter used for pulse shaping closed form expressions of the moments with up to the eighth order are derived the proposed approach is then extended to gaussianity assessment of ofdm signals we show how the moments of ofdm signals can approach to those of gaussian distribution as the number of subcarriers increases for a given modulation constraint on each subcarrier also reported is the peculiar nonstationary behavior of the fourth order moments in the case of bpsk modulated ofdm signals

equivalence of euclidean and wightman field theories a new inversion formula for the laplace transformation of tempered distributions with supports in the closed positive semiaxis is obtained the inverse laplace transform of a tempered distribution is defined by means of a limit of a special distribution constructed from this distribution the weak spectral condition on the euclidean green s functions implies that some of the limits needed for the inversion formula exist for any euclidean green s function with an even number of variables we then prove that the initial osterwalder schrader axioms 1 and the weak spectral condition are equivalent with the wightman axioms

construction of ym 4 with an infrared cutoff we provide the basis for a rigorous construction of the schwinger functions of the pure su 2 yang mills field theory in four dimensions in the trivial topological sector with a fixed infrared cutoff but no ultraviolet cutoff in a regularized axial gauge the construction exploits the positivity of the axial gauge at large field for small fields a different gauge more suited to perturbative computations is used this gauge and the corresponding propagator depends on large background fields of lower momenta the crucial point is to control in a non perturbative way the combined effect of the functional integrals over small field regions associated to a large background field and of the counterterms which restore the gauge invariance broken by the cutoff we prove that this combined effect is stabilizing if we use cutoffs of a certain type in momentum space we check the validity of the construction by showing that slavnov identities which express infinitesimal gauge invariance do hold non perturbatively

ccs expressions finite state processes and three problems of equivalence abstract we examine the computational complexity of testing finite state processes for equivalence in milner s calculus of communicating systems ccs the equivalence problems in ccs are presented as refinements of the familiar problem of testing whether two nondeterministic finite automata nfa are equivalent i e accept the same language three notions of equivalence proposed for ccs are investigated namely observational equivalence strong observational equivalence and failure equivalence we show that observational equivalence can be tested in polynomial time as defined in ccs observational equivalence is the limit of a sequence of successively finer equivalence relations k where 1 is nondeterministic finite automaton equivalence we prove that for each fixed k deciding k is pspace complete we show that strong observational equivalence can be decided in polynomial time by reducing it to generalized partitioning a new combinatorial problem of independent interest finally we demonstrate that testing for failure equivalence is pspace complete even for a very restricted type of process

optimization of sndr for amplitude limited nonlinearities many components used in communication systems are nonlinear and have a peak power or peak amplitude constraint nonlinearity generates distortions and thus signal to noise and distortion ratio sndr is an appropriate performance measure in this paper we are interested in finding the nonlinear mapping that maximizes the sndr subject to the peak amplitude constraint the answer is a soft limiter with gain calculated based on the noise power and the probability density function of the input amplitude we also investigate a bounding relationship between the sndr and capacity of the nonlinear channel the results of this paper can be applied for efficient transmission of high peak to average power ratio signals or for optimal linearization of nonlinear devices

a tutorial on empa a theory of concurrent processes with nondeterminism priorities probabilities and time we give an overview of empa a process algebra for modeling and analyzing concurrent systems where nondeterminism priorities probabilities and time are present aiming at a reasonable trade off between the expressive power of the calculus and the complexity of its underlying theory

the short distance behavior of φ 4 3 we consider the 3 4 quantum field theory on a torus and study the short distance behavior we reproduce the standard result that the singularities can be removed by a simple mass renormalization for the resulting model we give anl p bound on the short distance regularity of the correlation functions to obtain these results we develop a systematic treatment of the generating functional for correlations using a renormalization group method incorporating background fields

branching bisimulation for probabilistic systems characteristics and decidability we address the concept of abstraction in the setting of probabilistic reactive systems and study its formal underpinnings for the strictly alternating model of hansson in particular we define the notion of branching bisimilarity and study its properties by studying two other equivalence relations viz coloured trace equivalence and branching bisimilarity using maximal probabilities we show that both alternatives coincide with branching bisimilarity the alternative characterisations have their own merits and focus on different aspects of branching bisimilarity coloured trace equivalence can be understood without knowledge of probability theory and is independent of the notion of a scheduler branching bisimilarity rephrased in terms of maximal probabilities gives rise to an algorithm of polynomial complexity for deciding the equivalence together they give a better understanding of branching bisimilarity furthermore we show that the notions of branching bisimilarity in the alternating model of hansson and in the nonalternating model of segala differ branching bisimilarity in the latter setting turns out to discriminate between systems that are intuitively branching bisimilar

a polynomial time algorithm for the equivalence of probabilistic automata two probabilistic automata are equivalent if for any string x the two automata accept x with equal probability this paper presents an o n 1 n 2 4 algorithm for determining whether two probabilistic automata u 1 and u 2 are equivalent where n 1 and n 2 are the number of states in u 1 and u 2 respectively this improves the best previous result which showed that the problem was in conp the existence of this algorithm implies that the covering and equivalence problems for uninitiated probabilistic automata are also polynomial time solvable the algorithm used to determine the equivalence of probabilistic automata can also solve the path equivalence problem for nondeterministic finite automata without lambda transitions and the equivalence problem for unambiguous finite automata in polynomial time this paper studies the approximate equivalence or delta equivalence problem for probabilistic automata an algorithm for the approximate equivalence problem for positive p

performance analysis of deliberately clipped ofdm signals we analyze the performance of the clipped orthogonal frequency division multiplexing ofdm system in terms of peak power reduction capability and degradation of channel capacity the clipping is performed on the baseband ofdm signals with and without oversampling followed by the ideal low pass filter first the effect of the envelope clipping on the peak to average power ratio papr and the instantaneous power of the band limited ofdm signal is studied we then discuss the channel capacity of the oversampled and clipped ofdm signals over the additive white gaussian noise and ideally interleaved rayleigh fading channels the capacity is calculated based on the assumption that the distortion terms caused by the clipping are gaussian it is shown that the snr penalty due to the clipping can be considerably alleviated by using optimal coding and reducing the information data rate the results are justified by the simulation results using near optimal turbo codes

rf power amplifier linearization through amplitude and phase predistortion this paper presents a novel technique for power amplifier linearization in digital microwave radio systems the proposed technique is based on the use of a predistortion circuit whose am am and am pm responses are separately implemented as polynomial approximations of the respective responses of the ideal linearizer the proposed scheme is shown to attain superior performance in comparison with other well known predistortion structures such as those based on the cancellation of third or fifth order distortion with no substantial aggravation in implementation complexity

a low temperature expansion for classical n vector models iii a complete inductive description fluctuation integrals we give a complete inductive description of the effective densities generated by applications of the renormalization transformations to the densities of the classical n vector models described in the paper 1 and we formulate the main theorems of this sequence of papers this description includes now all the large field domains which we ve excluded from the discussions of 1 4 we apply the renormalization transformation to a density satisfying the inductive hypotheses we introduce large field small field partitions and we determine and analyze the fluctuation integrals in the general setting

a general sos theory for the specification of probabilistic transition systems this article focuses on the formalization of the structured operational semantics approach for languages with primitives that introduce probabilistic and non deterministic behavior we define a general theoretic framework and present the rule format that guarantees that bisimulation equivalence in the probabilistic setting is a congruence for any operator defined in this format we show that the bisimulation is fully abstract w r t the format and possibilistic trace equivalence in the sense that bisimulation is the coarsest congruence included in trace equivalence for any operator definable within the format in other words bisimulation is the smallest congruence relation guaranteed by the format we also provide a conservative extension theorem and show that languages that include primitives for exponentially distributed time behavior such as imc and markov automata based language fit naturally within our framework

discrete time generative reactive probabilistic processes with different advancing speeds we present a process algebra expressing probabilistic external internal choices multi way synchronizations and processes with different advancing speeds in the context of discrete time i e where time is not continuous but is represented by a sequence of discrete steps as in discrete time markov chains dtmcs to this end we introduce a variant of csp that employs a probabilistic asynchronous parallel operator whose synchronization mechanism is based on a mixture of the classical generative and reactive models of probability in particular differently from existing discrete time process algebras where parallel processes are executed in synchronous locksteps the parallel operator that we adopt allows processes with different probabilistic advancing speeds mean number of actions executed per time unit to be modeled moreover our generative reactive synchronization mechanism makes it possible to always derive dtmcs in the case of fully specified systems we then present a sound and complete axiomatization of probabilistic bisimulation over finite processes of our calculus that is a smooth extension of the axiom system for a standard process algebra thus solving the open problem of cleanly axiomatizing action restriction in the generative model as a further result we show that when evaluating steady state based performance measures which are expressible by attaching rewards to actions our approach provides an exact solution even if the advancing speeds are considered not to be probabilistic without incurring the state space explosion problem that arises with standard synchronous approaches we finally present a case study on multi path routing showing the expressiveness of our calculus and that it makes it particularly easy to produce scalable specifications

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

higgs 2 3 quantum fields in a finite volume we consider a euclidean model of interacting scalar and vector fields in two and three dimensions and prove a lower bound for vacuum energy in a lattice approximation the bound is independent of a lattice spacing it is proved with the help of renormalization transformations in wilson kadanoff form it extends in principal also to generating functional for schwinger functions

absolute versus relative time in process algebras abstract timed process algebras are useful tools for the specification and verification of real time systems we study the relationships between two of these algebras c i pa closed interval process algebra and tccs temporal ccs which deal with temporal aspects of concurrent systems by following very different interpretations durational actions versus durationless actions absolute time versus relative time timed functional behavior versus time and functional behavior local clocks versus global clocks we show that these different choices are not irreconcilable by presenting simple mappings from c i pa to tccs which preserve the behavioral equivalences over the two timed calculi these results hold whenever basic actions are interpreted as either eager or lazy whenever the starting time of action execution is observed rather than their completion time a study on the size of the labelled transition systems describing the transitional semantics of cipa processes and those describing the transitional semantics of their translated versions is also presented

a general conservative extension theorem in process algebras with inequalities we prove a general conservative extension theorem for transition system based process theories with easy to check and reasonable conditions the core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity that is provable transitions from an original term in the extension are the same as in the original system as a simple corollary of the conservative extension theorem we prove a completeness theorem we also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one we provide many applications to show that our results are useful the applications include but are not limited to various real and discrete time settings in acp atp and ccs and the notions projection renaming stage operator priority recursion the silent step autonomous actions the empty process divergence etc

performance analysis for ofdm signals with peak cancellation peak cancellation pc is known as one of the simplest peak to average power ratio papr reduction techniques that are applicable to various communications standards the salient advantage of pc is its ease of hardware implementation but it induces in band distortion and out of band radiation in order to restrict the amount of distortion within an acceptable level it is critical to carefully design the cancelling pulses as well as the envelope threshold over which pc is applied in most studies however they are determined empirically through computer simulations this paper thus focuses on a rigorous theoretical analysis of pc applied to band limited orthogonal frequency division multiplexing ofdm signals and discusses its validity and limitation for practical applications based on the level crossing rate approximation of the peak distribution we derive a closed form expression for the achievable signal to distortion power ratio sdr we also analyze the adjacent channel leakage ratio aclr as well as error vector magnitude evm with which the symbol error rate ser over an additive white gaussian noise awgn channel is obtained all the theoretical results developed in this work are compared with those based on the corresponding computer simulations to justify our analytical approach it thus serves as a useful and accurate tool for designing cancelling pulses as well as the threshold level for given specific system requirements such as sdr or evm and aclr

grad o perturbations of massless gaussian fields we investigate weak perturbations of the continuum massless gaussian measure by a class of approximately local analytic functionals and use our general results to give a new proof that the pressure of the dilute dipole gas is analytic in the activity

regularity and decay of lattice green s functions in the paper we study a class of lattice covariant laplace operators with external gauge fields we prove that these operators are positive and that their green s functions decay exponentially they also have regularity properties similar to continuous space green s functions all the bounds are uniform in the lattice spacing

random walks polymers percolation and quantum gravity in two dimensions we consider l planar random walks or brownian motions of large length t starting at neighboring points and the probability pl t t l that their paths do not intersect by a 2d quantum gravity method i e a non linear map onto a random riemann surface the former conjecture that l 124 4l2 1 is established this also applies to the half plane where l l3 1 2l as well as to non intersection exponents of unions of paths mandelbrot s conjecture for the hausdorff dimension dh 43 of the frontier of a brownian path follows from dh 2 32 we then consider in two dimensions the most general star shaped copolymer mixing random rw or self avoiding walks saw with specific mutual avoidance interactions thereof its exact conformal scaling dimensions in the plane are derived the harmonic measures or electrostatic potential or diffusion field near a rw or a saw or near a critical percolation cluster are also considered their moments exhibit a multifractal spectrum the generalized dimensions d n as well as the function are derived and are shown to be all identical these are examples of exact conformal multifractality

a local fluctuation theorem abstract a mechanism for the validity of a local version of the fluctuation theorem uniform in the system size is discussed for a reversible chain of weakly coupled anosov systems

observation equivalence as a testing equivalence a notion of testing is developed for transition systems with divergence the forms of testing include traces refusals copying and global testing both denotational and operational formulations of testing are given the equivalence based on this notion of testing is shown to coincide with observation equivalence

the role of am to pm conversion in memoryless nonlinear systems a generalized proof is presented that am to pm conversion can only degrade never improve the intermodulation noise performance of memoryless nonlinear systems with random input signals having even probability density functions and a measure of degradation is defined it is also shown for such signals that am to pm conversion causes a deterministic constant phase shift to be added to the argument of the signal component at the output but has no other effect on its phase this class of inputs includes one or the sum of several psk signals as well as large ensembles that can be modeled as gaussian noise the latter are dealt with by using bussgang s theorem on input output cross correlation in the proof bussgang s theorem is extended to the complex case to include phase as well as amplitude nonlinearities yielding a complex version of the theorem for gaussian inputs it is shown that the undistorted signal and the intermodulation noise at the output of such systems are uncorrelated

renormalization group approach to lattice gauge field theories ii cluster expansions the fluctuation field integral constructed in part i is represented by the exponentiated cluster expansion it is proved that the terms of the expansion satisfy the inductive assumptions this completes the construction of the sequence of effective actions in the small field approximation

validity of the spin wave approximation for the free energy of the heisenberg ferromagnet we consider the quantum ferromagnetic heisenberg model in three dimensions for all spins s 1 2 we rigorously prove the validity of the spin wave approximation for the excitation spectrum at the level of the first non trivial contribution to the free energy at low temperatures our proof comes with explicit constructive upper and lower bounds on the error term it uses in an essential way the bosonic formulation of the model in terms of the holstein primakoff representation in this language the model describes interacting bosons with a hard core on site repulsion and a nearest neighbor attraction this attractive interaction makes the lower bound on the free energy particularly tricky the key idea there is to prove a differential inequality for the two particle density which is thereby shown to be smaller than the probability density of a suitably weighted two particle random process on the lattice

testing preorders for probabilistic processes we present a testing preorder for probabilistic processes based on a quantification of the probability with which processes pass tests the theory enjoys close connections with the classical testing theory of de nicola and hennessy in that whenever a process passes a test with probability 1 respectively some nonzero probability in our setting then the process must respectively may pass the test in the classical theory we also develop an alternative characterization of the probabilistic testing preorders that takes the form of a mapping from probabilistic traces to the interval 0 1 where a probabilistic trace is an alternating sequence of actions and probability distributions over actions finally we give proof techniques derived from the alternative characterizations for establishing preorder relationships between probabilistic processes the utility of these techniques is demonstrated by means of some simple examples

a theoretical characterization of nonlinear distortion effects in ofdm systems this paper presents a theoretical characterization of nonlinear distortion effects in orthogonal frequency division multiplexing ofdm transmission systems in the theoretical framework developed it is shown that the effects on the decision variables of the in band distortion introduced by a bandpass memoryless nonlinearity can be described by means of a complex gain and an additive gaussian term with zero mean and suitable variance analytical expressions for gain and variance are given the conditions which allow this description are emphasized and discussed as a consequence a completely analytical procedure to evaluate error probability is also obtained and illustrated using ofdm discrete multitone modulation dmt systems with rectangular pulse shaping for the soft envelope limiter nonlinearity a closed form is derived a comparison with simulation results is carried out to verify the accuracy of this method

comparative branching time semantics for markov chains this paper presents various semantics in the branching time spectrum of discrete time and continuous time markov chains dtmcs and ctmcs strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterized in terms of the temporal logics probabilistic computation tree logic pctl and continuous stochastic logic csl apart from presenting various existing branching time relations in a uniform manner this paper presents the following new results i strong simulation for ctmcs ii weak simulation for ctmcs and dtmcs iii logical characterizations thereof including weak bisimulation for dtmcs iv a relation between weak bisimulation and weak simulation equivalence and v various connections between equivalences and pre orders in the continuous and discrete time setting the results are summarized in a branching time spectrum for dtmcs and ctmcs elucidating their semantics as well as their relationship

a uniform framework for modeling nondeterministic probabilistic stochastic or mixed processes and their behavioral equivalences labeled transition systems are typically used as behavioral models of concurrent processes their labeled transitions define a one step state to state reachability relation this model can be generalized by modifying the transition relation to associate a state reachability distribution with any pair consisting of a source state and a transition label the state reachability distribution is a function mapping each possible target state to a value that expresses the degree of one step reachability of that state values are taken from a preordered set equipped with a minimum that denotes unreachability by selecting suitable preordered sets the resulting model called ultras from uniform labeled transition system can be specialized to capture well known models of fully nondeterministic processes lts fully probabilistic processes adtmc fully stochastic processes actmc and nondeterministic and probabilistic mdp or nondeterministic and stochastic ctmdp processes this uniform treatment of different behavioral models extends to behavioral equivalences they can be defined on ultras by relying on appropriate measure functions that express the degree of reachability of a set of states when performing multi step computations it is shown that the specializations of bisimulation trace and testing equivalences for the different classes of ultras coincide with the behavioral equivalences defined in the literature over traditional models except when nondeterminism and probability stochasticity coexist then new equivalences pop up

peak power and bandwidth efficient linear modulation in portable wireless communication systems power consumption is of major concern traditional modulation and coding schemes have been designed from the standpoint of minimizing average power however for linear power amplifiers needed for spectrally efficient modulation formats amplifier efficiency and hence power consumption are determined by the peak power of the transmitted signal this paper looks into modulation formats which minimize peak power and retain high spectral efficiency peak power is broken into a sum in terms of decibels of average power and a peak to average power ratio and a variety of modulation formats are evaluated in terms of peak power efficiency in both a gaussian noise and rayleigh fading channel a generalized phase shift keying psk modulation format is developed and shown to offer superior peak power efficiency relative to that of commonly used linear modulation formats two schemes are presented for reducing the peak to average power ratio of various modulation formats first data translation codes are used to avoid data sequences which cause large peaks in the transmitted signal this approach was found to be most productive in quadrature amplitude modulation qam formats finally an adaptive peak suppression algorithm is presented which further reduces the peak to average power ratios of the psk and generalized psk formats the peak suppression algorithm is also applicable to spl pi 4 qpsk and was found to improve peak power efficiency of that format by about 1 25 db over a rayleigh fading channel

near constant envelope trellis shaping for psk signaling in this paper we propose a powerful trellis shaping for peak to average power ratio par reduction of pulse shaped phase shift keying psk systems the proposed approach consists of 1 memory extension of trellis shaping encoder for capturing the full effect of pulse shaping filter impulse response and 2 simple branch metrics that quantify envelope fluctuation of the filter output simulation results demonstrate that achieving near constant envelope is possible even if a pulse shaping filter with a roll off factor as low as 0 1 is employed furthermore due to the circular nature of the resulting signal trajectory the proposed system also exhibits a robustness against sampling timing jitter at the receiver

three partition refinement algorithms we present improved partition refinement algorithms for three problems lexicographic sorting relational coarsest partition and double lexical ordering our double lexical ordering algorithm uses a new efficient method for unmerging two sorted sets

the large field renormalization operation for classical n vector models a renormalization operation of the large field densities for the classical n vector models is constructed in this paper it allows to improve bounds of these densities and thus to prove all inductive hypotheses this completes the construction and analysis of the full renormalization group flow for these models the results will be used in the next paper to analyze the correlation functions

the intersection of brownian paths as a case study of a renormalization group method for quantum field theory a new approach is presented for the study of the probability that the random paths generated by two independent brownian motions in d intersect or more generally are within a short distance a of each other the well known behavior of that function of a above below and at the critical dimension d 4 as well as further corrections are derived here by means of a single renormalization group equation the equation s derivation is expected to shed some light on the function of the o d 4 quantum field theory

constructive field theory and applications perspectives and open problems in this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory they could give work for future mathematical physicists trained with constructive methods well into the 21st century

non expansive e bisimulations for probabilistic processes e bisimulation equivalence has been proposed in the literature as a technique to study the concept of behavioral distance between probabilistic processes in this paper we first consider the generative model of probabilistic processes and introduce two stronger equivalence notions action e bisimulation and global e bisimulation for each of these three equivalence notions we propose an sos transition rule format ensuring the property of non expansiveness non expansiveness means that if the behavioral distance between s i and t i is e i then the behavioral distance between f s 1 s n and f t 1 t n is no more that e 1 e n as expected the stronger the e bisimulation considered the weaker the constraints of the transition rule format then we switch to the reactive model of probabilistic processes and we propose a rule format for e bisimulation and action e bisimulation arguing that global e bisimulation is not needed in such a context

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

kam theorem and quantum field theory we give a new proof of the kam theorem for analytic hamiltonians the proof is inspired by a quantum field theory formulation of the problem and is based on a renormalization group argument treating the small denominators inductively scale by scale the crucial cancellations of resonances are shown to follow from the ward identities expressing the translation invariance of the corresponding field theory

polymers in a weak random potential in dimension four rigorous renormalization group analysis correlation functions of the edwards model of polymers at weak coupling are defined and studied at the critical point in dimension four by a rigorous renormalization group method which validates at any order perturbative renormalization group results on their behaviour at large distances remainders are controlled by a new argument which enlarges the use of methods of constructive field theory to models of statistical physics

the renormalization group according to balaban ii large fields this is an expository account of balaban s approach to the renormalization group the method is illustrated with a treatment of the ultraviolet problem for the scalar 4 model on a toroidal lattice in dimension d 3 in this paper we control the large field contribution to the partition function

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

a complete axiomatisation for observational congruence of finite state behaviours abstract finite state automata with non determinism and silent transitions can be interpreted not as subsets of the free monoid as in classical automata theory but as congruence classes under a congruence relation based upon the notion of weak bisimulation or observational equivalence due to park and milner in this paper a complete axiomatisation for this congruence is presented it extends the previously known complete axiomatisation by hennessy and milner for the case when all computations are finite the extension consists of five simple rules for recursion

weak bisimulation is sound and complete for pctl abstract we investigate weak bisimulation of probabilistic systems in the presence of nondeterminism i e labelled concurrent markov chains lcmc with silent transitions we develop an approach based on allowing convex combinations of computations similar to segala and lynch s use of randomized schedulers the definition of weak bisimulation destroys the additivity property of the probability distributions yielding instead capacities the mathematics behind capacities naturally captures the intuition that when we deal with nondeterminism we must work with bounds on the possible probabilities rather than with their exact values our analysis leads to three new developments we identify a characterization of image finiteness for countable state systems and present a new definition of weak bisimulation for these lcmcs we prove that our definition coincides with that of philippou lee and sokolsky for finite state systems we show that bisimilar states have matching computations the notion of matching involves convex combinations of transitions we study a minor variant of the probabilistic logic pctl the variation arises from an extra path formula to address action labels we show that bisimulation is sound and complete for this variant of pctl this is an extended complete version of a paper that was presented at concur 2002

geometric analysis of φ4 fields and ising models parts i and ii we provide here the details of the proof announced in 1 that ind 4 dimensions the even 4 euclidean field theory with a lattice cut off is inevitably free in the continuum limit in the single phase regime the analysis is nonperturbative and is based on a representation of the field variables or spins in ising systems as source sink creation operators in a system of random currents which may be viewed as the mediators of correlations in this dual representation the onset of long range order is attributed to percolation in an ensemble of sourceless currents and the physical interaction in the 4 field and other aspects of the critical behavior in ising models are directly related to the intersection properties of long current clusters an insight into the criticality of the dimensiond 4 is derived from an analogy foreseen by k symanzik with the intersection properties of paths of brownian motion other results include the proof that in certain respect the critical behavior in ising models is in exact agreement with the mean field approximation in high dimensionsd 4 but not in the low dimensiond 2 for which we establish the universality of hyperscaling

localization expansions i functions of the background configurations expansions of the type described in the inductive hypothesis h 5 in the paper 1 are constructed for local functions of the background configurations i e solutions of the variational problems studied in the previous paper 3 a main part of this construction is a further analysis of a local structure of the solutions

a proof of the gutzwiller semiclassical trace formula using coherent states decomposition the gutzwiller trace formula links the eigenvalues of the schrodinger operator as planck s constant goes to zero the semiclassical regime with the closed orbits of the corresponding classical mechanical system gutzwiller gave a heuristic proof of this trace formula using the feynman integral representation for the propagator of later using the theory of fourier integral operators mathematicians gave rigorous proofs of the formula in various settings here we show how the use of coherent states allows us to give a simple and direct proof

branching time and abstraction in bisimulation semantics in comparative concurrency semantics one usually distinguishes between linear time and branching time semantic equivalences milner s notion of observatin equivalence is often mentioned as the standard example of a branching time equivalence in this paper we investigate whether observation equivalence really does respect the branching structure of processes and find that in the presence of the unobservable action of ccs this is not the case therefore the notion of branching bisimulation equivalence is introduced which strongly preserves the branching structure of processes in the sense that it preserves computations together with the potentials in all intermediate states that are passed through even if silent moves are involved on closed ccs terms branching bisimulation congruence can be completely axiomatized by the single axion scheme a y z y a y z where a ranges over all actions and the usual loaws for strong congruence we also establish that for sequential processes observation equivalence is not preserved under refinement of actions whereas branching bisimulation is for a large class of processes it turns out that branching bisimulation and observation equivalence are the same as far as we know all protocols that have been verified in the setting of observation equivalence happen to fit in this class and hence are also valid in the stronger setting of branching bisimulation equivalence

multiscale formalism for correlation functions of fermions infrared analysis of the tridimensional gross neveu model we present a multiscale formalism for fermionic systems with a smooth uv cutoff establishing a trivial link between the correlation functions and the effective potential flow and study the k point truncated functions of the tridimensional gross neveu model a new efficient method is used to bound these correlation functions and show polynomial tree decay for long distances we are guided by a block lattice mechanism with a property of orthogonality between terms in different scales which leads to simple formulas for the correlations

timed process calculi with deterministic or stochastic delays several deterministically stochastically timed process calculi have been proposed in the literature that apart from their synchronization mechanism mainly differ for the way in which actions and delays are represented in particular a distinction is made between integrated time calculi in which actions are durational and orthogonal time calculi in which actions are instantaneous and delays are expressed separately in a previous work on deterministic time the two approaches have been shown to be reconcilable through an encoding from the integrated time calculus cipa to the orthogonal time calculus tccs which preserves strong timed bisimilarity under certain conditions in this paper the picture is completed by first defining a reverse encoding from tccs to cipa which requires slight modifications to both calculi and is shown to preserve only weak timed bisimilarity under conditions tighter than those for the direct encoding stochastic time is then addressed by exhibiting an encoding from the integrated time calculus mtipp to the orthogonal time calculus iml together with a reverse encoding requiring slight modifications only to the former calculus with both encodings being shown to preserve strong markovian bisimilarity under suitable conditions all the four encodings rely on the assumption that action execution is urgent variants are finally discussed in which action execution is delayable in the sense that an enabled action can let time advance before starting its execution or only the execution of internal actions is urgent which is known as maximal progress

a low temperature expansion for classical n vector models ii renormalization group equations this paper continues the analysis of the low temperature expansions for classicaln vector models started in 1 a main part of it is a derivation of renormalization group equations and a construction of their solutions to do this we have to introduce a fluctuation integral connected with a next renormalization transformation and to make its preliminary analysis the results of the paper are summarized in theorems stating that the renormalization transformation preserves the space of densitites or actions described inductively in 1

relating strong behavioral equivalences for processes with nondeterminism and probabilities we present a comparison of behavioral equivalences for nondeterministic and probabilistic processes whose activities are all observable in particular we consider trace based testing and bisimulation based equivalences for each of them we examine the discriminating power of three variants stemming from three approaches that differ for the way probabilities of events are compared when nondeterministic choices are resolved via schedulers the first approach compares two resolutions with respect to the probability distributions of all considered events the second approach requires that the probabilities of the set of events of a resolution be individually matched by the probabilities of the same events in possibly different resolutions the third approach only compares the extremal probabilities of each event stemming from the different resolutions the three approaches have very reasonable motivations and when applied to fully nondeterministic processes or fully probabilistic processes give rise to the classical well studied relations we shall see that for processes with nondeterminism and probability they instead give rise to a much wider variety of behavioral relations whose discriminating power is thoroughly investigated here in the case of deterministic schedulers

equivalence notions and model minimization in markov decision processes many stochastic planning problems can be represented using markov decision processes mdps a difficulty with using these mdp representations is that the common algorithms for solving them run in time polynomial in the size of the state space where this size is extremely large for most real world planning problems of interest recent ai research has addressed this problem by representing the mdp in a factored form factored mdps however are not amenable to traditional solution methods that call for an explicit enumeration of the state space one familiar way to solve mdp problems with very large state spaces is to form a reduced or aggregated mdp with the same properties as the original mdp by combining equivalent states in this paper we discuss applying this approach to solving factored mdp problems we avoid enumerating the state space by describing large blocks of equivalent states in factored form with the block descriptions being inferred directly from the original factored representation the resulting reduced mdp may have exponentially fewer states than the original factored mdp and can then be solved using traditional methods the reduced mdp found depends on the notion of equivalence between states used in the aggregation the notion of equivalence chosen will be fundamental in designing and analyzing algorithms for reducing mdps optimally these algorithms will be able to find the smallest possible reduced mdp for any given input mdp and notion of equivalence i e find the minimal model for the input mdp unfortunately the classic notion of state equivalence from non deterministic finite state machines generalized to mdps does not prove useful we present here a notion of equivalence that is based upon the notion of bisimulation from the literature on concurrent processes our generalization of bisimulation to stochastic processes yields a non trivial notion of state equivalence that guarantees the optimal policy for the reduced model immediately induces a corresponding optimal policy for the original model with this notion of state equivalence we design and analyze an algorithm that minimizes arbitrary factored mdps and compare this method analytically to previous algorithms for solving factored mdps we show that previous approaches implicitly derive equivalence relations that we define here

self avoiding walk in five or more dimensions i the critical behaviour we use the lace expansion to study the standard self avoiding walk in thed dimensional hypercubic lattice ford 5 we prove that the numbercn ofn step self avoiding walks satisfiescn a n where is the connective constant i e 1 and that the mean square displacement is asymptotically linear in the number of steps i e v 1 2 a bound is obtained forcn x the number ofn step self avoiding walks ending atx the correlation length is shown to diverge asymptotically like z 1 2 the critical two point function is shown to decay at least as fast as x 2 and its fourier transform is shown to be asymptotic to a multiple ofk 2 ask 0 i e 0 we also prove that the scaling limit is gaussian in the sense of convergence in distribution to brownian motion the infinite self avoiding walk is constructed in this paper we prove these results assuming convergence of the lace expansion the convergence of the lace expansion is proved in a companion paper

a renormalizable field theory the massive gross neveu model in two dimensions the euclidean massive gross neveu model in two dimensions is just renormalizable and asymptotically free thanks to the pauli principle bare perturbation theory with an ultra violet cut off and the correct ansatz for the bare mass is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant therefore the theory can be fully constructed in a perturbative way it satisfies the o s axioms and is the borel sum of the renormalized perturbation expansion of the model

performance measure sensitive congruences for markovian process algebras the modeling and analysis experience with process algebras has shown the necessity of extending them with priority probabilistic internal external choice and time while preserving compositionality the purpose of this paper is to make a further step by introducing a way to express performance measures in order to allow the modeler to capture the qos metrics of interest we show that the standard technique of expressing stationary and transient performance measures as weighted sums of state probabilities and transition frequencies can be imported in the process algebra framework technically speaking if we denote by n n the number of performance measures of interest in this paper we define a family of extended markovian process algebras with generative master reactive slaves synchronization mechanism called empagrn including probabilities priorities exponentially distributed durations and sequences of rewards of length n then we show that the markovian bisimulation equivalence mbn is a congruence for empagrn which preserves the specified performance measures and we give a sound and complete axiomatization for finite empagrn terms finally we present a case study conducted with the software tool two towers in which we contrast the average performance of a selection of distributed algorithms for mutual exclusion modeled with empagrn