a data based enumeration technique for fully correlated signals presents a novel method for estimating the number of signals impinging on a uniform linear array using observed sensor data unlike other algorithms that apply rissanen s minimum description length mdl principle to the observed data for source enumeration this method applies it to the prediction errors of a linear model that has been fitted to an appropriate data matrix it is a 1d method that achieves improved performance even for fully correlated signals over contemporary approaches particularly with short data records and closely spaced signals asymptotic consistency is shown and substantiating simulation examples are included

variations on mobile processes the paper investigates a concurrent computation model chi calculus in which communications resemble cut eliminations for classical proofs two bisimilarities local bisimilarity and barbed bisimilarity on chi processes are studied and are shown to be congruence relations the former equivalence turns out to be strictly stronger than the latter it is shown that chi calculus is capable of modeling sequential computation in that it captures the operational semantics of call by name lambda calculus a translation from pi calculus to chi calculus is given demonstrating that practically speaking pi is a sublanguage of chi a higher order version of chi calculus is proposed and examined it combines the communication mechanism of chi calculus and the recursion mechanism of full lambda calculus and therefore extends both

an asymptotic membrane like theory for long wave motion in a pre stressed elastic plate an asymptotically consistent two dimensional theory is developed to help elucidate dynamic response in finitely deformed layers the layers are composed of incompressible elastic material with the theory appropriate for long wave motion associated with the fundamental mode and derived in respect of the most general appropriate strain energy function leading order and refined higher order equations for the mid surface deflection are derived in the case of zero normal initial static stress and in plane tension the leading order equation reduces to the classical membrane equation with its refined counterpart also being obtained the theory is applied to a one dimensional edge loading problem for a semi infinite plate in doing so the leading and higher order governing equations are used as inner and outer asymptotic expansions the latter valid within the vicinity of the associated quasi front a solution is derived by using the method of matched asymptotic expansions

what is a good encoding of guarded choice abstract the calculus with synchronous output and mixed guarded choices is strictly more expressive than the calculus with asynchronous output and no choice this result was recently proved by c palamidessi and as a corollary she showed that there is no fully compositional encoding from the former into the latter that preserves divergence freedom and symmetries this paper argues that there are nevertheless good encodings between these calculi in detail we present a series of encodings for languages with 1 input guarded choice 2 both input and output guarded choice and 3 mixed guarded choice and investigate them with respect to compositionality and divergence freedom the first and second encoding satisfy all of the above criteria but various good candidates for the third encoding inspired by an existing distributed implementation invalidate one or the other criterion while essentially confirming palamidessi s result our study suggests that the combination of strong compositionality and divergence freedom is too strong for more practical purposes

bounded linear logic a modular approach to polynomial time computability typing is a way of describing the interactive behavior of algorithms usual typing systems are mainly concerned with input output specifications e g given terms f a b and a a the computation of f a by normalization yields a result of type b however one can dream of more refined typings that would not only ensure ethereal termination but would for instance yield feasible resource bounds it seems that time complexity does not lend itself naturally to modular manipulation we seek something more primitive

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

on the p calculus and linear logic abstract we detail abramsky s proofs as processes paradigm for interpreting classical linear logic cll girard 1987 into a synchronous version of the calculus recently proposed by milner 1992 1993 the translation is given at the abstract level of proof structures we give a detailed treatment of information flow in proof nets and show how to mirror various evaluation strategies for proof normalization we also give soundness and completeness results for the process calculus translations of various fragments of cll the paper also gives a self contained introduction to some of the deeper proof theory of cll and its process interpretation

on the number of signals resolvable by a uniform linear array an algebraic limitation on the maximum number of directions of arrival of plane waves that can be resolved by a uniform linear sensor array is studied achievable lower and upper bounds are derived on that number as a function of the number of elements in the array number of snapshots and the rank of the source sample correlation matrix the signals are assumed narrow band and of identical and known center frequency the results are also applicable in the coherent signal case and when directions of arrival are estimated from few snapshots while in the multiple snapshot case the lower bounds coincide with known asymptotic results the upper bounds indicate the potential for resolving more signals than by present methods of array processing

fixpoint logics relational machines and computational complexity we establish a general connection between fixpoint logic and complexity on one side we have fixpoint logic parameterized by the choices of 1st order operators inflationary or noninflationary and iteration constructs deterministic nondeterministic or alternating on the other side we have the complexity classes between p and exptime our parameterized fixpoint logics capture the complexity classes p np pspace and exptime but equally is achieved only over ordered structures there is however an inherent mismatch between complexity and logic while computational devices work on encodings of problems logic is applied directly to the underlying mathematical structures to overcome this mismatch we use a theory of relational complexity which bridges the gap between standard complexity and fixpoint logic on one hand we show that questions about containments among standard complexity classes can be translated to questions about containments among relational complexity classes on the other hand the expressive power of fixpoint logic can be precisely characterized in terms of relational complexity classes this tight three way relationship among fixpoint logics relational complexity and standard complexity yields in a uniform way logical analogs to all containments among the complexity classes p np pspace and exptime the logical formulation shows that some of the most tantalizing questions in complexity theory boil down to a single question the relative power of inflationary vs noninflationary 1st order operators

linear logic by levels and bounded time complexity we give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs as programs correspondence girard s seminal results concerning elementary and light linear logic achieve this characterization by enforcing a stratification principle on proofs using the notion of depth in proof nets here we propose a more general form of stratification based on inducing levels in proof nets by means of indices which allows us to extend girard s systems while keeping the same complexity properties in particular it turns out that girard s systems can be recovered by forcing depth and level to coincide a consequence of the higher flexibility of levels with respect to depth is the absence of boxes for handling the paragraph modality we use this fact to propose a variant of our polytime system in which the paragraph modality is only allowed on atoms and which may thus serve as a basis for developing lambda calculus type assignment systems with more efficient typing algorithms than existing ones

a low frequency model for dynamic motion in pre stressed incompressible elastic structures an asymptotic one dimensional theory with minimal essential parameters is constructed to help elucidate two dimensional low frequency dynamic motion in a pre stressed incompressible elastic plate in contrast with the classical theory the long wave limit of the fundamental mode of antisymmetric motion is non zero the occurrence of an associated quasi front therefore offers considerable deviation from the classical case moreover the presence of pre stress makes the plate stiffer and thus may preclude bending in the classical sense discontinuities on the associated leading order wavefronts are smoothed by deriving higher order theories both quasi fronts are shown to be either receding or advancing but of differing type the problems of surface and edge loading are considered and in the latter case a specific problem is formulated and solved to illustrate the theory in the case of antisymmetric motion and an appropriate form of pre stress it is shown that the leading order governing equation for the mid surface deflection is essentially that of waves propagating along an infinite string a higher order equation for which is derived

on timoshenko reissner type theories of plates and shells abstract linear tr theories timoshenko reissner theories of isotropic plates and shells are discussed these theories take into account the transversal shear deformation and rotation inertia the main subject under consideration is the construction of these theories by the asymptotic method and the related error estimates for static and dynamic problems in the dynamic case a method is suggested for the extension of the range of applicability of the tr theory

an abstract approach to stratification in linear logic we study the notion of stratification as used in subsystems of linear logic with low complexity bounds on the cut elimination procedure the so called light subsystems from an abstract point of view introducing a logical system in which stratification is handled by a separate modality this modality which is a generalization of the paragraph modality of girard s light linear logic arises from a general categorical construction applicable to all models of linear logic we thus learn that stratification may be formulated independently of exponential modalities when it is forced to be connected to exponential modalities it yields interesting complexity properties in particular from our analysis stem three alternative reformulations of baillot and mazza s linear logic by levels one geometric one interactive and one semantic

asymptotic long wave models for a pre stressed elastic layer with elastically restrained boundaries abstract long wave dispersion phenomena is investigated in respect of a pre stressed incompressible elastic layer subject to elastically restrained boundary conditions erbc such conditions can be treated as a generalisation of classical free and fixed face boundary conditions allowing investigating of the transition between the neumann and dirichlet statements of the problem symmetric elastically restrained boundary conditions are introduced followed by both a numerical investigation and a multi parameter asymptotic analysis of the dispersion relations all possible asymptotic regimes are grouped into classes based on the magnitude of the associated restraint parameter a long wave low frequency model is developed to describe motion associated with the fundamental modes for small values of the restraint parameters four high frequency models are developed describing asymptotic regimes connected with vibration within the vicinity of the thickness resonances

oblique projection based enumeration of mixed noncoherent and coherent narrowband signals in many application scenarios the signals impinging on the array of sensors comprise the noncoherent uncorrelated and or partially correlated signals and the coherent signals with several groups due to multipath propagation in this paper we consider the problem of estimating the number of noncoherent narrowband signals and that of coherent narrowband signals with multiple groups impinging on a planar sensor array composed of two parallel uniform linear arrays ulas and an oblique projection based enumerator for the mixed signals opems is proposed by utilizing the qr decomposition based ratio criterion qrrc for rank determination of a matrix in the opems the number of noncoherent signals and that of coherent signals in each group are estimated separately where only the elevation angles of noncoherent signals are estimated to isolate the coherent signals from the noncoherent ones and the computationally intensive and time consuming eigendecomposition procedure is avoided the consistency of the proposed opems is analyzed and its effectiveness is verified through numerical examples

on interfacial waves in pre stressed layered incompressible elastic solids interfacial waves along the plane boundary between two pre stressed incompressible elastic solids are considered one of the solids is a half space while the other has arbitrary uniform thickness the principal axes of the underlying pure homogeneous deformation in the two solids are aligned with one axis normal to the interface for propagation along an in plane principal axis the dispersion equation is derived in respect of a general strain energy function conditions on the pre strain pre stress and material parameters that ensure the existence of a unique interfacial wavespeed at low frequencies are obtained and it is shown that in special circumstances non dispersive waves can exist at the low frequency limit asymptotic results at the high frequency limit are also obtained for the case of equibiaxial pre strain more specific conditions are derived for the existence of interfacial waves at the low and high frequency asymptotes and these provide information on the existence of waves for the whole frequency range a particular feature of the structure considered is that it may act as a mechanical filter in different frequency regimes depending on the pre strain pre stress and material parameters when the wavespeed vanishes the dispersion equation reduces to a bifurcation equation solutions of which define states of stress and deformation which form boundaries of the region of stability of the underlying state of stress and deformation in the two materials for given material properties the bifurcation equation is examined separately and an explicit bifurcation criterion is given for equibiaxial deformations the results are illustrated graphically by considering several numerical examples based on a certain class of strain energy functions which includes the neo hookean strain energy function the results highlight low and high frequency features and demonstrate the influence of pre stress and deformation on the multiplicity of propagating modes

an augmented smoothed rank profile algorithm for determination of source coherency structure the problem is discussed of determining the source coherency structure and estimating the directions of arrival in the presence of coherent signals the method is closely related to the smoothed rank profile srp algorithm which shows that for determining the source coherency structure the number of elements required is greater than or equal to the total number of sources plus the highest degree of signal coherency present in the modified approach suggested here it is shown how the srp method can be augmented by the incorporation of forward backward averaged covariance to increase the likelihood of the successful determination of the source coherency structure with a limited number of sensors

a non local asymptotic theory for thin elastic plates the three dimensional dynamic non local elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size the integral constitutive relations incorporating the variation of an exponential non local kernel across the thickness are adopted long wave low frequency approximations are derived for both bending and extensional motions boundary layers specific for non local behaviour are revealed near the plate faces it is established that the effect of the boundary layers leads to the first order corrections to the bending and extensional stiffness in the classical two dimensional plate equations

computational interpretations of linear logic abstract we study girard s linear logic from the point of view of giving a concrete computational interpretation of the logic based on the curry howard isomorphism in the case of intuitionistic linear logic this leads to a refinement of the lambda calculus giving finer control over order of evaluation and storage allocation while maintaining the logical content of programs as proofs and computation as cut elimination in the classical case it leads to a concurrent process paradigm with an operational semantics in the style of berry and boudol s chemical abstract machine this opens up a promising new approach to the parallel implementation of functional programming languages and offers the prospect of typed concurrent programming in which correctness is guaranteed by the typing

an exact correspondence between a typed pi calculus and polarised proof nets this paper presents an exact correspondence in typing and dynamics between polarised linear logic and a typed p calculus based on io typing the respective incremental constraints one on geometric structures of proof nets and one based on types precisely correspond to each other leading to the exact correspondence of the respective formalisms as they appear in olivier laurent 2003 27 for proof nets and kohei honda et al 2004 24 for the p calculus

head linear reduction and pure proof net extraction abstract proof net calculus introduced in girard 1987 has been extended in the paradigm of scott s domains equation d d d which generates a logical point of view for pure calculus in donos 1989 methodologically speaking in this paper the proof theoretic counterpart of bohm s theorem given in bohm 1968 for pure calculus is proposed as extension of the curry howard paradigm technically speaking as the extraction of a subterm using the reduction is possible also subnet extraction can be internalized by cut elimination using proof nets realizes managing and better understanding the procedure of extraction

godel s system t revisited the linear lambda calculus where variables are restricted to occur in terms exactly once has a very weak expressive power in particular all functions terminate in linear time in this paper we consider a simple extension with natural numbers and a restricted iterator only closed linear functions can be iterated we show properties of this linear version of godel s tusing a closed reduction strategy and study the class of functions that can be represented surprisingly this linear calculus offers a huge increase in expressive power over previous linear versions of t which are closed at construction rather than closed at reduction we show that a linear twith closed reduction is as powerful as t

introduction to clarithmetic ii the earlier paper introduction to clarithmetic i constructed an axiomatic system of arithmetic based on computability logic and proved its soundness and extensional completeness with respect to polynomial time computability the present paper elaborates three additional sound and complete systems in the same style and sense one for polynomial space computability one for elementary recursive time and or space computability and one for primitive recursive time and or space computability

linear logic coherence and dinaturality a general coherence theorem for monoidal closed structures is obtained by modifying the logical approach to coherence questions due to lambek 1969 1990 by making use of linear logic linear logic introduced by girard has many advantages which are of use in studying coherence most notably its resource sensitive nature makes it ideal for studying monoidal closed structures the logical approach is also modified by using natural deduction rather than sequent calculus the natural deduction system in question is proof nets also introduced by girard proof nets have several important properties which are exploited to prove the coherence theorem in particular the cut elimination procedure is confluent and strongly normalizing the approach to coherence is to define a general structure the autonomous deductive system for defining many theories of monoidal closed categories an autonomous deductive system is a deductive system with several added features which are suggested by the properties of proof nets it is then possible to give a straightforward criterion for whether a given theory of monoidal closed categories specified by an autonomous deductive system is coherent finally a relationship is established between coherence and the composition problem for dinatural transformations thus the dinatural approach to modelling polymorphic types due to bainbridge et al 1990 can be extended to linear polymorphism

source enumeration in a correlated signal environment the authors present a simple method for determining the number of signals impinging on a uniform linear array that is applicable even in the extreme case of fully correlated signals this technique uses what they term modified rank sequences which is a modification of the construction implicit in the matrix decomposition method of di 1981 they prove that if a particular rank sequence stabilizes the last two terms of the sequence are equal to a value strictly less then the common row size of the defining block matrices then this value equals the number of signals provided that the number of signals has not exceeded a bresler macovski 1986 type bound using the above characterization of stability they formulate an algorithm that either determines the number of signals or indicates that the resolution capability of the algorithm has been exceeded they also provide theorems that show that under certain conditions a rank sequence can stabilize to a value strictly less than the number of signals this result allows them to find simple counterexamples to all of the existing rank sequence methods

relational queries computable in polynomial time we characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe we also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation this proves that the fixed point query hierarchy suggested by chandra and harel collapses at the first fixed point level it is also a general result showing that in finite model theory one application of fixed point suffices

realizability models for a linear dependent pcf abstract recently dal lago and gaboardi have proposed a type system named d l pcf as a framework for implicit computational complexity d l pcf is a non standard type system for pcf programs which is relatively complete with respect to quantitative properties thanks to the use of linear types inspired by bounded linear logic and dependent types a la dependent ml in this work we adapt the framework of quantitative realizability and obtain a model for d l pcf the quantitative realizability model aims at a better understanding of d l pcf type decorations and at giving an abstract semantic proof of intensional soundness

strong normalisation in the π calculus we introduce a typed calculus where strong normalisation is ensured by typability strong normalisation is a useful property in many computational contexts including distributed systems in spite of its simplicity our type discipline captures a wide class of converging name passing interactive behaviour the proof of strong normalisability combines methods from typed calculi and linear logic with process theoretic reasoning it is adaptable to systems involving state non determinism polymorphism control and other extensions strong normalisation is shown to have significant consequences including finite axiomatisation of weak bisimilarity a fully abstract embedding of the simply typed calculus with products and sums and basic liveness in interaction strong normalisability has been extensively studied as a fundamental property in functional calculi term rewriting and logical systems this work is one of the first steps to extend theories and proof methods for strong normalisability to the context of name passing processes

realizability models for bll like languages we give a realizability model of girard scedrov scott s bounded linear logic bll this gives a new proof that all numerical functions representable in that system are polytime our analysis naturally justifies the design of the bll syntax and suggests further extensions

an improved spatial smoothing technique for bearing estimation in a multipath environment it is well known that signal subspace algorithms perform poorly when coherent or highly correlated signals are present recently the so called spatial smoothing technique was devised to preprocess the array covariance matrix so that signal subspace algorithms can be applied irrespective of the signal correlation unfortunately the application of this technique reduces the effective aperture of the array a modified spatial smoothing technique that is capable of increasing the effective aperture of the array over that of conventional spatial smoothing methods is explored it is shown that under certain conditions the modified algorithm may fail to yield the desired increase in array aperture and some simulation results concerning the sensitivity of the modified spatial smoothing algorithm to these conditions are provided

a long wave model for the surface elastic wave in a coated half space the paper deals with the three dimensional problem in linear isotropic elasticity for a coated half space the coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long wave limit an explicit model is derived for the surface wave using the perturbation technique along with the theory of harmonic functions and radon transform the model consists of three dimensional quasi static elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two dimensional hyperbolic equation singularly perturbed by a pseudo differential or integro differential operator the latter equation governs dispersive surface wave propagation whereas the elliptic equations describe spatial decay of displacements and stresses as an illustration the dynamic response is calculated for impulse and moving surface loads the explicit analytical solutions obtained for these cases may be used for the non destructive testing of the thickness of the coating and the elastic moduli of the substrate