positive constrained approximation via rbf based partition of unity method in this paper we discuss the problem of constructing radial basis function rbf based partition of unity pu interpolants that are positive if data values are positive more specifically we compute positive local approximants by adding up several constraints to the interpolation conditions this approach considering a global approximation problem and compactly supported rbfs csrbfs has been previously proposed in wu etal 2010 here the use of the pu technique enables us to intervene only locally and as a consequence to reach a better accuracy this is also due to the fact that we select the optimal number of positive constraints by means of an a priori error estimate and we do not restrict to the use of csrbfs numerical experiments and applications to population dynamics are provided to illustrate the effectiveness of the method in applied sciences

grammian solutions and pfaffianization of a non isospectral and variable coefficient kadomtsev petviashvili equation abstract in this paper we first present the grammian determinant solutions to the non isospectral and variable coefficient kadomtsev petviashvili vckp equation then by using the pfaffianization procedure of hirota and ohta a new non isospectral and variable coefficient integrable coupled system is generated moreover gramm type pfaffian solutions of the pfaffianized system are proposed

results on the propositional μ calculus abstract in this paper we define and study a propositional calculus l which consists essentially of propositional modal logic with a least fixpoint operator l is syntactically simpler yet strictly more expressive than propositional dynamic logic pdl for a restricted version we give an exponential time decision procedure small model property and complete deductive system theory subsuming the corresponding results for pdl

deciding safety properties in infinite state pi calculus via behavioural types in the pi calculus we consider the decidability of model checking properties expressed in shallow logic a simple spatial logic we first introduce a behavioural type system that given a pi process p that might in general be infinite control tries to extract a spatial behavioural type t in the form of a ccs term that is logically equivalent to p employing techniques based on well structured transition systems wsts we prove that model checking t f is decidable for types for a fragment of the logic that can be used to encode interesting safety and reachability properties the wsts technique we rely upon requires first endowing the considered transition system with a well quasi order then defining a finite basis for the denotation of each formula this is achieved by viewing types as forests with a well quasi order that corresponds to a form of forest embedding as a consequence of the logical equivalence between types and processes we obtain the decidability of the considered fragment of the logic for well typed pi processes we discuss un decidability and complexity of model checking also outside the considered decidable fragment of shallow logic

pfaffianization of the two dimensional toda lattice pfaffianization procedure due to hirota and ohta is applied to the two dimensional toda lattice as a result a pfaffianized version of the two dimensional toda lattice is found

on the nonisospectral modified kadomtsev peviashvili equation abstract two types of grammian solutions to the nonisospectral modified kadomtsev peviashvili mkp equation are derived with the help of the pfaffian derivative formulae starting from the grammian solutions obtained we construct the nonisospectral mkp equation with self consistent sources by applying the source generalization procedure whose solutions can be given simultaneously

a rbf partition of unity collocation method based on finite difference for initial boundary value problems abstract meshfree radial basis function rbf methods are popular tools used to numerically solve partial differential equations pdes they take advantage of being flexible with respect to geometry easy to implement in higher dimensions and can also provide high order convergence since one of the main disadvantages of global rbf based methods is generally the computational cost associated with the solution of large linear systems in this paper we focus on a localizing rbf partition of unity method rbf pum based on a finite difference fd scheme specifically we propose a new rbf pum fd collocation method which can successfully be applied to solve time dependent pdes this approach allows to significantly decrease ill conditioning of traditional rbf based methods moreover the rbf pum fd scheme results in a sparse matrix system reducing the computational effort but maintaining at the same time a high level of accuracy numerical experiments show performances of our collocation scheme on two benchmark problems involving unsteady convection diffusion and pseudo parabolic equations

an optimal algorithm for approximate nearest neighbor searching fixed dimensions consider a set of s of n data points in real d dimensional space r d where distances are measured using any minkowski metric in nearest neighbor searching we preprocess s into a data structure so that given any query point q r d is the closest point of s to q can be reported quickly given any positive real e data point p is a 1 e approximate nearest neighbor of q if its distance from q is within a factor of 1 e of the distance to the true nearest neighbor we show that it is possible to preprocess a set of n points in r d in o dn log n time and o dn space so that given a query point q r d and e 0 a 1 e approximate nearest neighbor of q can be computed in o c d e log n time where c d e d 1 6d e d is a factor depending only on dimension and e in general we show that given an integer k 1 1 e approximations to the k nearest neighbors of q can be computed in additional o kd log n time

positivity preserving interpolation of positive data by rational cubics this work is a contribution towards the graphical display of data when it is positive the data are required to be represented in such a way that its visual display looks smooth and pleasant its positive shape is preserved everywhere and the computation cost is economical a c 1 piecewise rational cubic function in its most general form has been utilized for this objective the method is implemented for the 1d data initially and then it is extended to an interpolating rational bicubic form for the data arranged over a rectangular grid simple sufficient conditions are developed on the free parameters in the description of the rational function to visualize the positive data in the form of positive curves and surfaces

a trivariate interpolation algorithm using a cube partition searching procedure in this paper we propose a fast algorithm for trivariate interpolation which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions the partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube partition searching procedure more precisely we construct a cube structure which partitions the domain and strictly depends on the size of its subdomains so that the new searching procedure and accordingly the resulting algorithm enable us to efficiently deal with a large number of nodes complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm

an automata theoretic approach to branching time model checking translating linear temporal logic formulas to automata has proven to be an effective approach for implementing linear time model checking and for obtaining many extensions and improvements to this verification method on the other hand for branching temporal logic automata theoretic techniques have long been thought to introduce an exponential penalty making them essentially useless for model checking recently bernholtz and grumberg 1993 have shown that this exponential penalty can be avoided though they did not match the linear complexity of non automata theoretic algorithms in this paper we show that alternating tree automata are the key to a comprehensive automata theoretic framework for branching temporal logics not only can they be used to obtain optimal decision procedures as was shown by muller et al but as we show here they also make it possible to derive optimal model checking algorithms moreover the simple combinatorial structure that emerges from the automata theoretic approach opens up new possibilities for the implementation of branching time model checking and has enabled us to derive improved space complexity bounds for this long standing problem

efficient computation of partition of unity interpolants through a block based searching technique in this paper we propose a new efficient interpolation tool extremely suitable for large scattered data sets the partition of unity method is used and performed by blending radial basis functions rbfs as local approximants and using locally supported weight functions in particular we present a new space partitioning data structure based on a partition of the underlying generic domain in blocks this approach allows us to examine only a reduced number of blocks in the search process of the nearest neighbour points leading to an optimized searching routine complexity analysis and numerical experiments in two and three dimensional interpolation support our findings some applications to geometric modelling are also considered moreover the associated software package written in matlab is here discussed and made available to the scientific community

expressiveness and complexity of graph logic we investigate the complexity and expressive power of a spatial logic for reasoning about graphs this logic was previously introduced by cardelli gardner and ghelli and provides the simplest setting in which to explore such results for spatial logics we study several forms of the logic the logic with and without recursion and with either an exponential or a linear version of the basic composition operator we study the combined complexity and the expressive power of the four combinations we prove that without recursion the linear and exponential versions of the logic correspond to significant fragments of first order fo and monadic second order mso logics the two versions are actually equivalent to fo and mso on graphs representing strings however when the two versions are enriched with m style recursion their expressive power is sharply increased both are able to express pspace complete problems although their combined complexity and data complexity still belong to pspace

interpolation in the limit of increasingly flat radial basis functions abstract many types of radial basis functions such as multiquadrics contain a free parameter in the limit where the basis functions become increasingly flat the linear system to solve becomes highly ill conditioned and the expansion coefficients diverge nevertheless we find in this study that limiting interpolants often exist and take the form of polynomials in the 1 d case we prove that with simple conditions on the basis function the interpolants converge to the lagrange interpolating polynomial hence differentiation of this limit is equivalent to the standard finite difference method we also summarize some preliminary observations regarding the limit in 2 d

stable computations with gaussian radial basis functions radial basis function rbf approximation is an extremely powerful tool for representing smooth functions in nontrivial geometries since the method is mesh free and can be spectrally accurate a perceived practical obstacle is that the interpolation matrix becomes increasingly ill conditioned as the rbf shape parameter becomes small corresponding to flat rbfs two stable approaches that overcome this problem exist the contour pade method and the rbf qr method however the former is limited to small node sets and the latter has until now been formulated only for the surface of the sphere this paper focuses on an rbf qr formulation for node sets in one two and three dimensions the algorithm is stable for arbitrarily small shape parameters it can be used for thousands of node points in two dimensions and still more in three dimensions a sample matlab code for the two dimensional case is provided

model checking mobile ambients we settle the complexity bounds of the model checking problem for the ambient calculus with public names against the ambient logic we show that if either the calculus contains replication or the logic contains the guarantee operator the problem is undecidable in the case of the replication free calculus and guarantee free logic we prove that the problem is pspace complete for the complexity upper bound we devise a new representation of processes that remains of polynomial size during process execution this allows us to keep the model checking procedure in polynomial space moreover we prove pspace hardness of the problem for several quite simple fragments of the calculus and the logic this suggests that there are no interesting fragments with polynomial time model checking algorithms

pfaffianization of the generalized variable coefficient kadomtsev petviashvili equation abstract in this paper the pfaffianization procedure is applied to the generalized variable coefficient kadomtsev petviashvili vckp equation which can describe the realistic nonlinear phenomena in the fluid dynamics and plasmas using the pfaffianization procedure the coupled system for the generalized vckp equation is derived together with the wronski type pfaffian solution for this generalized coupled vckp system under certain coefficient constraint furthermore the gramm type pfaffian solution for such a coupled system is presented and verified by virtue of the pfaffian identities

on the 2 1 dimensional gardner equation determinant solutions and pfaffianization in this paper we first present the casorati and grammian determinant solutions to the 2 1 dimensional gardner equation then by using the pfaffianization procedure of hirota and ohta a new integrable coupled system is generated from the gardner equation moreover gramm type pfaffian solutions to the pfaffianized system are proposed

fast and stable rational rbf based partition of unity interpolation abstract we perform a local computation via the partition of unity pu method of rational radial basis function rbf interpolants we investigate the well posedness of the problem and we provide error bounds the resulting scheme efficiently implemented by means of the deflation accelerated conjugate gradient dacg enables us to deal with huge data sets and thanks to the use of variably scaled kernels vsks it turns out to be stable for functions with steep gradients or discontinuities which are truly common in applications the results show that the new proposed method outperforms the classical and rescaled pu schemes

c1 positive scattered data interpolation a local c 1 surface construction scheme is presented to preserve the shape of positive scattered data arranged over a triangular grid each boundary curve of the triangle is constructed by a rational cubic function with two free parameters and this rational function is also used for the side vertex interpolation the final surface patch is constructed by taking the convex combination of three side vertex interpolants for each triangular patch there are three boundary curves and three side vertex interpolants simple sufficient data dependent constraints are derived on these free parameters to preserve the shape of the positive scattered data the developed scheme is not only local and computationally economical but visually pleasing as well

abstract interpretation based verification of temporal properties for bioambients this paper concerns the application of formal methods to biological systems modeled specifically in bioambients a variant of the mobile ambients calculus following the semantic based approach of abstract interpretation we define a new static analysis that computes an abstract transition system our analysis has two main advantages with respect to the analyses appearing in the literature i it is able to address temporal properties which are more general than invariant properties ii it supports by means of a particular labeling discipline the validation of systems where several copies of an ambient may appear we also design new weaker and more efficient analyses by means of simple widening operators

lax pair backlund transformation and n soliton like solution for a variable coefficient gardner equation from nonlinear lattice plasma physics and ocean dynamics with symbolic computation abstract in this paper a generalized variable coefficient gardner equation arising in nonlinear lattice plasma physics and ocean dynamics is investigated with symbolic computation the lax pair and backlund transformation are explicitly obtained when the coefficient functions obey the painleve integrable conditions meanwhile under the constraint conditions two transformations from such an equation either to the constant coefficient gardner or modified korteweg de vries mkdv equation are proposed via the two transformations the investigations on the variable coefficient gardner equation can be based on the constant coefficient ones the n soliton like solution is presented and discussed through the figures for some sample solutions it is shown in the discussions that the variable coefficient gardner equation possesses the right and left travelling soliton like waves which involve abundant temporally inhomogeneous features

pfaffianization of the discrete kp equation we use the procedure of ohta and hirota to generate an integrable coupled system of discrete equations from the discrete kp equation

multi soliton and pfaffian solutions of a 2 1 dimensional nonlinear evolution equation via the jaulent miodek hierarchy abstract under investigation in this paper is a 2 1 dimensional nonlinear evolution equation generated by the jaulent miodek hierarchy via the hirota bilinear method multi soliton solutions of such equation are obtained soliton propagation and interactions are analyzed and both the elastic and inelastic interactions are seen with some parameters selected furthermore it is proved that the equation possesses the n soliton solutions expressed in terms of gramm type pfaffian and can be written in the form of a pfaffian identity

reasoning about infinite computations we investigate extensions of temporal logic by connectives defined by finite automata on infinite words we consider three different logics corresponding to three different types of acceptance conditions finite looping and repeating for the automata it turns out however that these logics all have the same expressive power and that their decision problems are all pspace complete we also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem