deco polyominoes permutations and random generation abstract in this paper we introduce a class of polyominoes called deco polyominoes in bijection with the set of permutations of the first k integers we evaluate some typical parameters for this class of polyominoes and define a linear algorithm for randomly generating them moreover we define the polyominoes corresponding to the directed animals on the hexagonal and triangular lattices and examine these polyominoes deco class as far as deco polyominoes corresponding to animals on the hexagonal lattice are concerned we find a bijection with a class of permutations finally we give linear algorithms for randomly generating both hexagonal and triangular deco polyominoes

low density series expansions for directed percolation on square and triangular lattices greatly extended series have been derived for moments of the pair connectedness for bond and site percolation on the directed square and triangular lattices the length of the various series has been at least doubled to more than 110 100 terms for the square lattice bond site problem and more than 55 terms for the bond and site problems on the triangular lattice analysis of the series leads to very accurate estimates for the critical parameters and generally seems to rule out simple rational values for the critical exponents the values of the critical exponents for the average cluster size parallel and perpendicular connectedness lengths are estimated by d 2 277 69 4 k d 1 733 825 25 and d 1 096 844 14 respectively an improved estimate for the percolation probability exponent is obtained from the scaling relation d k c 2 d 0 276 49 4 in all cases the leading correction to scaling term is analytic

new beams of global bifurcation points for a reaction diffusion system with inequalities or inclusions abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability we show that an obstacle e g a unilateral membrane modeled either in terms of inequalities or of inclusions introduces whole beams of new global bifurcation points of spatially non homogeneous stationary solutions which lie in parameter domains which are excluded as bifurcation points for the problem without the obstacle

asymptotic boundary value problems in banach spaces abstract a continuation principle is given for solving boundary value problems on arbitrary possibly infinite intervals to caratheodory differential inclusions in banach spaces for this aim the appropriate fixed point index is defined to condensing decomposable multivalued operators in frechet spaces this index extends and unifies the one for compact maps in andres et al trans amer math soc 351 1999 4861 4903 as well as the one for operators in banach spaces in bader ph d thesis university of munich 1995 as an application we prove the existence of an entirely bounded solution of a semilinear evolution inclusion

functional adaptive model estimation in this article we are interested in modeling the relationship between a scalar y and a functional predictor x t we introduce a highly flexible approach called functional adaptive model estimation fame which extends generalized linear models glms generalized additive models gams and projection pursuit regression ppr to handle functional predictors the fame approach can model any of the standard exponential family of response distributions that are assumed for glm or gam while maintaining the flexibility of ppr for example standard linear or logistic regression with functional predictors as well as far more complicated models can easily be applied using this approach we use a functional principal components decomposition of the predictor functions to aid visualization of the relationship between x t and y we also show how the fame procedure can be extended to deal with multiple functional and standard finite dimensional predictors possibly with missing data we illustrate the fame

a new two variable generating function for convex self avoiding polygons the width of a self avoiding polygon on the square lattice is defined as the minimal horizontal or vertical distance between two of its parallel edges if the polygons are convex this distance is internal the perimeter generating functions for such convex polygons whose widths exceed a threshold can be given explicitly from these expressions a two variable width and perimeter generating function can be constructed the corresponding phase diagram shows two types of critical behaviour which meet at a tricritical point

convex polyominoes and heaps of segments builds a one to one correspondence between some polyominoes called parallelogram polyominoes and some heaps of segments then the author derives explicit expressions for the generating function of convex polyominoes according to their height width and area the author also enumerates two subsets of convex polyominoes namely the directed and convex polyominoes and the parallelogram polyominoes according to these three parameters generating functions of polyominoes having a fixed width are also studied

number of almost convex polygons on the square lattice the generating function for the number nc n of almost convex polygons on the square lattice with concavity index c 1 and perimeter n is derived rigorously the asymptotic behaviour of nc n for large n is determined and this result confirms a conjecture by enting et al 1992

continuity compactness and degree theory for operators in systems involving p laplacians and inclusions the study of weak solutions for systems of nonlinear partial differential equations of elliptic type with inclusions leads to a multivalued operator of superposition type in sobolev spaces we show that under natural assumptions this operator has the properties which allow to apply degree theory fixed point index for multivalued maps more precisely this operator is upper semicontinuous and compact with nonempty convex compact values for the particular case of systems involving p laplacians we show that there is a homeomorphism transforming the whole system to a situation for which a fixed point index is available

the complexity of computing the number of strings of given length in context free languages abstract computing the number of strings of given length contained in a language is related to classical problems of combinatorics formal languages and computational complexity here we study the complexity of this problem in the case of context free languages it is shown that for unambiguous context free languages such a computation is easy and can be carried out by efficient parallel algorithms on the contrary for some context free languages of ambiguity degree two the problem becomes intractable these results are related to other classical subjects concerning counting problems exponential time recognizable languages and sparse sets

second derivative functional regression with applications to near infra red spectroscopy a linear regression method to predict a scalar from a discretized smooth function is presented the method takes into account the functional nature of the predictors and the importance of the second derivative in spectroscopic applications this motivates a functional inner product that can be used as a roughness penalty using this inner product we derive a linear prediction method that is similar to ridge regression but with different shrinkage characteristics we describe its practical implementation and we address the problem of computing the second derivatives nonparametrically we apply the method to a calibration example using near infra red spectra we conclude with a discussion comparing our approach with other regression algorithms

generalized linear regression on sampled signals and curves a p spline approach we consider generalized linear regression with many highly correlated regressors for instance digitized points of a curve on a spatial or temporal domain we refer to this setting as signal regression which requires severe regularization because the number of regressors is large often exceeding the number of observations we solve collinearity by forcing the coefficient vector to be smooth on the same domain dimension reduction is achieved by projecting the signal coefficient vector onto a moderate number of b splines a difference penalty between the b spline coefficients further increases smoothness the p spline framework of eilers and marx the procedure is regulated by a penalty parameter chosen using information criteria or cross validation

existence and multiplicity of solutions for a neumann problem involving the p x laplace operator abstract in this paper we study the following nonlinear neumann boundary value problem div u p x 2 u u p x 2 u f x u x t r u v 0 x t r where r n is a bounded domain with smooth boundary u v is the outer unit normal derivative on 0 is a real number p is a continuous function on with inf x p x 1 f r r is a continuous function using the three critical point theorem due to ricceri under the appropriate assumptions on f we establish the existence of at least three solutions of this problem some known results are generalized

rigorous derivation of the perimeter generating function for the mean squared radius of gyration of convex polygons we have rigorously derived the perimeter generating function for the mean squared radius of gyration of convex polygons this function was first conjectured by jensen his nonrigorous result is based on the analysis of the long series expansions

index models for sparsely sampled functional data the regression problem involving functional predictors has many important applications and a number of functional regression methods have been developed however a common complication in functional data analysis is one of sparsely observed curves that is predictors that are observed with error on a small subset of the possible time points such sparsely observed data induce an errors in variables model where one must account for measurement error in the functional predictors faced with sparsely observed data most current functional regression methods simply estimate the unobserved predictors and treat them as fully observed thus failing to account for the extra uncertainty from the measurement error we propose a new functional errors in variables approach sparse index model functional estimation simfe which uses a functional index model formulation to deal with sparsely observed predictors simfe has several advantages over more traditional methods first the index model implements a nonline

area weighted moments of convex polygons on the square lattice when constructing series expansions for the zero field partition function of the q state potts model on the square lattice using the finite lattice method the series can be extended by one term by adding a correction of q 1 times the number of convex polygons of an appropriate order by virtue of duality such corrections apply for both high and low temperature series for low temperature series corrections to the field dependent partition function are of the same order in the temperature variable as the zero field correction the general corrections are given by area weighted moments of the number of convex polygons the authors obtain conjectured closed form expressions for the two generating functions that give corrections to the first two field derivatives of the low temperature partition function

generalized linear models with functional predictors summary we present a technique for extending generalized linear models to the situation where some of the predictor variables are observations from a curve or function the technique is particularly useful when only fragments of each curve have been observed we demonstrate on both simulated and real data sets how this approach can be used to perform linear logistic and censored regression with functional predictors in addition we show how functional principal components can be used to gain insight into the relationship between the response and functional predictors finally we extend the methodology to apply generalized linear models and principal components to standard missing data problems

on the exhaustive generation of k convex polyominoes the degree of convexity of a convex polyomino p is the smallest integer k such that any two cells of p can be joined by a monotone path inside p with at most k changes of direction in this paper we present a simple algorithm for computing the degree of convexity of a convex polyomino and we show how it can be used to design an algorithm that generates given an integer k all k convex polyominoes of area n in constant amortized time using space o n furthermore by applying few changes we are able to generate all convex polyominoes whose degree of convexity is exactly k

directed compact percolation near a wall iii exact results for the mean length and number of contacts existing exact results for the percolation probability and mean cluster size for compact percolation near a dry wall are extended to the mean cluster length and the mean number of contacts with the wall the results are derived from our previous work on vesicles near an attractive wall and involve elliptic integrals as opposed to the simple rational forms found for the percolation probability and cluster size below the results for the cluster length satisfy previously conjectured differential equations a closed expression is conjectured for the mean size above in terms of a hypergeometric function

exact solution of the convex polygon perimeter and area generating function an explicit expression is derived for the three variable generating function p x y z sigma m or 1 sigma n or 1 sigma r or 1 x2ny2mzrcn m r where cn m r is the number of convex polygons with horizontal width n vertical height m and area r

strip tiling and regular grammars we study the problem of tiling a rectangular p n strip fixed with pieces i e sets of simply connected cells some well known examples are strip tilings with dimers dominoes and or monomers we prove in a constructive way that every tiling problem is equivalent to a regular grammar that is the set of possible tilings constitutes a regular language we propose a straightforward algorithm to transform the tiling problem into its corresponding grammar by means of some standard methods we are then able to obtain some counting generating functions that are rational we go on to give some examples of our method and indicate some of its applications to a number of problems treated in current literature

self avoiding polygons on the square lattice we have developed an improved algorithm that allows us to enumerate the number of self avoiding polygons on the square lattice to perimeter length 90 analysis of the resulting series yields very accurate estimates of the connective constant 2 638 158 529 27 1 biased and the critical exponent 0 500 0005 10 unbiased the critical point is indistinguishable from a root of the polynomial 581x4 7x2 13 0 an asymptotic expansion for the coefficients is given for all n there is strong evidence for the absence of any non analytic correction to scaling exponent

generating functions for classes of self avoiding polygons on the square lattice abstract a transfer matrix technique is presented which allows the explicit calculation of the generating functions for those self avoiding polygons on the square lattice which have a perimeter equal to or two larger than the perimeter of their bounding rectangles

enumeration of polyominoes using macsyma this paper shows the use of a symbolic language macsyma to obtain new exact or asymptotic results in combinatorics the examples are taken among polyominoes sic objects the main purpose of the paper is to show how easy it is to bring some methods into operation in order to obtain new results in enumerative combinatorics from the abstract

unidirectional convex polygons on the honeycomb lattice the authors obtain the exact generating function for a class of self avoiding polygons on the honeycomb lattice which are convex in one of the three lattice directions it is shown that the critical exponent alpha of these unidirectional convex polygons is 3 2

convex polyominoes and algebraic languages uses the so called dsv methodology that links some enumeration problems to the theory of algebraic languages to get a system of q difference equations involving the generating functions of convex polyominoes of convex and directed polyominoes and of parallelogram polyominoes according to their height width and area then the author shows various applications of this system

synergistic development of differential approximants and the finite lattice method in lattice statistics several decades of parallel developments in the calculation and analysis of series expansions for lattice statistics have led to many new insights into critical phenomena these studies have centered on the use of the finite lattice method for series expansions in lattice statistics and the use of differential approximants in analysing such series one of these strands of research ultimately led to the result that a number of unsolved lattice statistics problems cannot be expressed as d finite functions somewhat ironically given power and success of differential approximants in analysing series neither the assumed functional form nor any finite generalisation thereof can fit such cases exactly

enumeration of 4 stack polyominoes in this paper we consider the class of 4 stack polyominoes i e polyominoes which can be decomposed into a central rectangle supporting four stack polyominoes one on each side of the rectangle this class of objects recently introduced by marc noy extends the class of centered convex polyominoes and is included into the class of z convex polyominoes using an inclusion exclusion approach we obtain the enumeration of 4 stack polyominoes according to the number of rows and columns moreover we solve some problems posed by marc noy proving that the generating function of 4 stack polyominoes according to the semi perimeter is algebraic and that their asymptotic behavior is n4 n which is immediately smaller than the asymptotic behavior of z convex polyominoes which is n4 n as a corollary of our result we find the generating function of bi centered polyominoes i e convex polyominoes which are both horizontally and vertically centered

on an involution on dyck paths les derniers resultats concernant l enumeration des polyamines parallelogrammes 4 5 8 9 11 14 selon l aire et le nombre de colonnes font apparaitre des fonctions generatrices s exprimant comme rapport de q analogues de fonctions de bessel dans 13 deux interpretations combinatoires de ces memes fonctions sont donnees d une part en termes de multiparcours d arbres et d autre part en termes de multichaines de chemins de dyck a l aide d une involution sur l ensemble d des chemins de dyck d une bijection entre chemins et multiparcours d arbres et d une bijection entre chemins et multichaines nous donnons dans ce papier une preuve bijective de l equivalence de ces deux interpretations

walks on the slit plane in the first part of this paper we enumerate exactly walks on the square lattice that start from the origin but otherwise avoid the half line we call them walks on the slit plane we count them by their length and by the coordinates of their endpoint the corresponding three variable is algebraic of degree 8 moreover for any point i j the length for walks of this type ending at i j is also algebraic of degree 2 or 4 and involves the famous catalan numbers

a parallel algorithm for the enumeration of self avoiding polygons on the square lattice we have developed a parallel algorithm that allows us to enumerate the number of self avoiding polygons on the square lattice to perimeter length 110 we have also extended the series for the first 10 area weighted moments and the radius of gyration to 100 analysis of the resulting series yields very accurate estimates of the connective constant 2 638 158 530 31 3 biased and the critical exponent 0 500 000 1 2 unbiased in addition we obtain very accurate estimates for the leading amplitudes confirming to a high degree of accuracy various predictions for universal amplitude combinations

on an exactly solvable compact cluster growth model on a square lattice we consider a cluster growth model on a square lattice that is in the compact directed percolation universality class the model is exactly solvable as regards its static cluster properties and expressions are given for various quantities of interest such as the mean perimeter length and the mean cluster size the results also provide new information on area perimeter generating functions for a class of self avoiding polygons on square lattices

perimeter generating functions for the mean squared radius of gyration of convex polygons we have derived long series expansions for the perimeter generating functions of the radius of gyration of various polygons with a convexity constraint using the series we numerically find simple algebraic exact solutions for the generating functions in all cases the size exponent 1

clt in functional linear regression models we propose in this work to derive a clt in the functional linear regression model the main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill posed inverse problem we consider estimators that belong to a large class of regularizing methods and we first show that contrary to the multivariate case it is not possible to state a clt in the topology of the considered functional space however we show that we can get a clt for the weak topology under mild hypotheses and in particular without assuming any strong assumptions on the decay of the eigenvalues of the covariance operator rates of convergence depend on the smoothness of the functional coefficient and on the point in which the prediction is made

functional additive regression we suggest a new method called functional additive regression or far for efficiently performing high dimensional functional regression far extends the usual linear regression model involving a functional predictor x t and a scalar response y in two key respects first far uses a penalized least squares optimization approach to efficiently deal with high dimensional problems involving a large number of functional predictors second far extends beyond the standard linear regression setting to fit general nonlinear additive models we demonstrate that far can be implemented with a wide range of penalty functions using a highly efficient coordinate descent algorithm theoretical results are developed which provide motivation for the far optimization criterion finally we show through simulations and two real data sets that far can significantly outperform competing methods

context free grammars differential operators and formal power series abstract in this paper we introduce the concepts of a formal function over an alphabet and a formal derivative based on a set of substitution rules we call such a set of rules a context free grammar because these rules act like a context free grammar in the sense of a formal language given a context free grammar we can associate each formal function with an exponential formal power series in this way we obtain grammatical interpretations of addition multiplication and functional composition of formal power series a surprising fact about the grammatical calculus is that the composition of two formal power series enjoys a very simple grammatical representation we apply this method to obtain simple demonstrations of faa di bruno s formula and some identities concerning bell polynomials stirling numbers and symmetric functions in particular the lagrange inversion formula has a simple grammatical representation from this point of view one sees that cayley s formula on labeled trees is equivalent to the lagrange inversion formula

two generalizations of column convex polygons column convex polygons were first counted by area several decades ago and the result was found to be a simple rational generating function in this work we generalize that result let a p column polyomino be a polyomino whose columns can have 1 2 p connected components then column convex polygons are equivalent to 1 convex polyominoes the area generating function of even the simplest generalization namely 2 column polyominoes is unlikely to be solvable we therefore define two classes of polyominoes which interpolate between column convex polygons and 2 column polyominoes we derive the area generating functions of those two classes using extensions of existing algorithms the growth constants of both classes are greater than the growth constant of column convex polyominoes rather tight lower bounds on the growth constants complement a comprehensive asymptotic analysis

positive stationary solutions for p laplacian problems with nonpositive perturbation the paper is devoted to the existence of positive solutions of nonlinear elliptic equations with p laplacian we provide a general topological degree that detects solutions of the problem a u f u u m where a x d a x is a maximal monotone operator in a banach space x and f m x is a continuous mapping defined on a closed convex cone m x next we apply this general framework to a class of partial differential equations with p laplacian under dirichlet boundary conditions in the paper we employ general ideas from cwiszewski and kryszewski 2009 5 where a setting suitable for the one dimensional p laplacian was introduced

bayesian generalized monotonic functional mixed models for the effects of radiation dose histograms on normal tissue complications when treating cancer patients with radiation therapy the normal tissue in an organ close to the tumour usually receives some dose of radiation the dose is not of the same intensity throughout the organ this radiation can cause normal tissue complications so for treatment planning purposes it is important to understand the relationship between the distribution of dose intensities in the organ and the occurrence of complications one general summary measure of the dose effect is obtained by integrating a weighting function w d over the dose distribution the weighting function w d should be monotone for biological reasons because the true shape of w d is not known we estimate it non parametrically subject to the monotonicity constraint in our approach w d is written as a weighted sum of monotone basis functions the weights in this sum are formulated as a mixture of point mass at zero and a gamma random variable a key feature of our method is that it allows for flat regions through the use of this mixture prior the model is estimated using a markov chain monte carlo algorithm we illustrate our method with data from a head and neck cancer study in which the irradiation of the parotid gland results in loss of saliva flow

object grammars and bijections a new systematic approach for the specification of bijections between sets of combinatorial objects is presented it is based on the notion of object grammars object grammars give recursive descriptions of objects and generalize context free grammars the study of a particular substitution in these object grammars confirms once more the key role of dyck words in the domain of enumerative and bijective combinatorics

asymptotic matching by the symbolic manipulator macsyma abstract we consider delegating the tedious labor of calculating higher order terms in singular perturbation expansions to a computer by using the algebraic manipulation system macsyma in particular the method of matched asymptotic expansions for two model singular perturbation problems have been studied in detail the first model resembles the boundary layer equation with a small parameter multiplying the highest derivative in this case both the outer and inner expansions are simple power series in e the second model is a turning point problem the asymptotic expansions that resemble the series in low reynolds number flow past a sphere are mixtures of powers and logarithms in e and fraenkel s restricted matching principle is needed we show that macsyma has successfully performed the higher order matching in these two problems

a global bifurcation for nonlinear inclusions abstract for under certain conditions we show a global bifurcation for multi valued boundary value problems involving the laplacian by applying a bifurcation theorem for nonlinear inclusions

covariate adjusted region referenced generalized functional linear model for eeg data electroencephalography eeg studies produce region referenced functional data in the form of eeg signals recorded across electrodes on the scalp it is of clinical interest to relate the highly structured eeg data to scalar outcomes such as diagnostic status in our motivating study resting state eeg is collected on both typically developing td children and children with autism spectrum disorder asd aged 2 to 12 years old the peak alpha frequency paf defined as the location of a prominent peak in the alpha frequency band of the spectral density is an important biomarker linked to neurodevelopment and is known to shift from lower to higher frequencies as children age to retain the most amount of information from the data we consider the oscillations in the spectral density within the alpha band rather than just the peak location as a functional predictor of diagnostic status td vs asd adjusted for chronological age a covariate adjusted region referenced generalized functional linear model is proposed for modeling scalar outcomes from region referenced functional predictors which utilizes a tensor basis formed from one dimensional discrete and continuous bases to estimate functional effects across a discrete regional domain while simultaneously adjusting for additional nonfunctional covariates such as age the proposed methodology provides novel insights into differences in neural development of td and asd children the efficacy of the proposed methodology is investigated through extensive simulation studies

algebraic languages and polyominoes enumeration abstract in this paper the use of algebraic languages theory in solving an open problem in combinatorics is shown by constructing a bijection between convex polyominoes and words of an algebraic language and by solving the corresponding algebraic system we prove that the number of convex polyominoes with perimeter 2n 8 is 2n 11 4 n 4 2n 1 2n n

statistical mechanics of directed models of polymers in the square lattice directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature these are idealized geometric directed lattice models introduced to study phase behaviour in polymers and include dyck paths partially directed paths directed trees and directed vesicles models directed models are closely related to models studied in the combinatorics literature and are often exactly solvable they are also simplified versions of a number of statistical mechanics models including the self avoiding walk lattice animals and lattice vesicles the exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models and this will be explored in this review the combinatorial nature of directed lattice path models makes a study using generating function approaches most natural in contrast the statistical mechanics approach would introduce partition functions and free energies and then investigate these using the general framework of critical phenomena generating function and statistical mechanics approaches are closely related for example questions regarding the limiting free energy may be approached by considering the radius of convergence of a generating function and the scaling properties of thermodynamic quantities are related to the asymptotic properties of the generating function in this review the methods for obtaining generating functions and determining free energies in directed lattice path models of linear polymers is presented these methods include decomposition methods leading to functional recursions as well as the temperley method that is implemented by creating a combinatorial object one slice at a time a constant term formulation of the generating function will also be reviewed the thermodynamic features and critical behaviour in models of directed paths may be informative about the underlying properties that determine phase diagrams for wider classes of models including physical models of polymers of particular interest are adsorption and collapse transitions in models of polymers and copolymers the properties of thermodynamic quantities in those models are described by tricritical scaling this is reviewed for directed path models and the generating function approaches can be used to apply tricritical scaling to models of adsorbing inflating and collapsing directed lattice paths critical exponents for a variety of models can be obtained in this manner and with it a better understanding and a classification of the models

exact solution of the row convex polygon perimeter generating function an explicit expression is obtained for the perimeter generating function g y sigma n or 2 any2n for row convex polygons on the square lattice where an is the number of 2n step row convex polygons an asymptotic expression for an approximately a mu nn 3 2 is obtained where mu 3 22 and a are given the authors also show that the generating function is an algebraic function and that it satisfies an inhomogeneous linear differential equation of degree three

anisotropic step mutual contact and area weighted festoons and parallelogram polyominoes on the triangular lattice we present results for the generating functions of polygons and more general objects that can touch constructed from two fully directed walks on the infinite triangular lattice enumerated according to each type of step and weighted proportional to the area and the number of contacts between the directed sides of the objects in general these directed objects are known as festoons being constructed from the so called friendly directed walks while the subset constructed from vicious walks are staircase polygons also known as parallelogram polyominoes additionally we give explicit formulae for various first area moment generating functions that is when the area is summed over all configurations with a given perimeter these results generalize and summarize nearly all known results on the square lattice since such results can be obtained by setting one of the step weights to zero all our results for the triangular lattice are new and hence provide the opportunity to study subtle changes in scaling between lattices in most cases we give our results both in terms of ratios of infinite q series and as continued fractions

rigorous result for the area weighted moments of convex polygons on the square lattice a generating function for the area weighted moments of the number of convex polygons on the square lattice is derived rigorously a special case of the authors result was obtained first by enting and guttmann 1988 nonrigorously their calculation is based on series expansions

statistics of collapsed lattice animals rigorous results and monte carlo simulations in this paper a two dimensional model of collapsed lattice animals with nearest neighbour contact interactions is introduced and the limiting free energy for the model is proved to exist we also establish that the partition function for collapsed lattice animals is related to the reliability polynomial for the m m grid graph and to the generating function for spanning forests on the m m grid graph from these relationships and using results about directed animals we are able to obtain rigorous upper and lower bounds on the free energy for collapsed lattice animals in addition we present monte carlo evidence that the heat capacity associated with this model remains bounded in the thermodynamic limit in fact we do not find any evidence for a second order phase transition for collapsed lattice animals

attribute grammars are useful for combinatorics abstract the purpose of this paper is to show the use of attribute grammars in solving some combinatorics problems for example we give the generating function for the shape of skew ferrers diagrams according to the number of cells and the number of columns this result is new and proves that skew ferrer diagrams are related to new basic bessel functions

degree and global bifurcation for elliptic equations with multivalued unilateral conditions abstract a bifurcation problem for an elliptic multivalued boundary value problem with a real parameter is considered the existence of global bifurcation between two eigenvalues of a certain type of the laplacian is proved for a class of abstract inclusions with compact multivalued mappings in a hilbert space it is shown how the degree can be determined near the eigenvalues of a particular type of an associated linear single valued problem and the jump of the degree is proved as a consequence global bifurcation for such abstract inclusions is obtained the weak formulation of the boundary value problem mentioned is a particular case

a strip like tiling algorithm we extend our previous results on the connection between strip tiling problems and regular grammars by showing that an analogous algorithm is applicable to other tiling problems not necessarily related to rectangular strips we find generating functions for monomer and dimer tilings of t and l shaped figures holed and slotted strips diagonal strips and combinations of them and show how analogous results can be obtained by using different pieces

informative sensor and feature selection via hierarchical nonnegative garrote placing sensors in every station of a process or every element of a system to monistor its state or performance is usually too expensive or physically impossible therefore a systematic method is needed to select important sensing variables the method should not only be capable of identifying important sensors signals among multistream signals from a distributed sensing system but should also be able to extract a small set of interpretable features from the high dimensional vector of a selected signal for this purpose we develop a new hierarchical regularization approach called hierarchical nonnegative garrote nng at the first level of hierarchy a group nng is used to select important signals and at the second level the individual features within each signal are selected using a modified version of nng that possesses good properties for the estimated coefficients performance of the proposed method is evaluated and compared with other existing methods through monte carlo simulation a case stud

on the area of square lattice polygons we consider the generating function of self avoiding square lattice polygons grouped by both area and perimeter the generating function for polygons of arean is found to diverge atx c 0 251834 with an exponent of zero the mean perimeter of polygons with arean is found to be proportional ton while the mean area of polygons with perimetern is found to be proportional ton 1 5

the perimeter generating functions of three choice imperfect and one punctured staircase polygons we consider the isotropic perimeter generating functions of three choice imperfect and one punctured staircase polygons whose 8th order linear fuchsian odes are previously known we derive simple relationships between the three generating functions and show that all three generating functions are joint solutions of a common 12th order fuchsian linear ode we find that the 8th order differential operators can each be rewritten as a direct sum of a direct product with operators no larger than 3rd order we give closed form expressions for all the solutions of these operators in terms of 2 f 1 hypergeometric functions with rational and algebraic arguments the solutions of these linear differential operators can in fact be expressed in terms of two modular forms since these 2 f 1 hypergeometric functions can be expressed with two rational or algebraic pullbacks