on the multifractal nature of fully developed turbulence and chaotic systems it is generally argued that the energy dissipation of three dimensional turbulent flow is concentrated on a set with non integer hausdorff dimension recently in order to explain experimental data it has been proposed that this set does not possess a global dilatation invariance it can be considered to be a multifractal set the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta model

fractal measures of first passage time of a simple random walk abstract we consider random walks starting at the site i 1 on a one dimensional lattice segment with an absorbing boundary at i 0 and a reflecting boundary at i l we find that the typical value of first passage time fpt is independent of system size l while the mean value diverges linearly with l the qth moment of the fpt diverges with system size as l2q 1 for q 1 2 for a finite but large l the fpt distribution has an 1 t tail cut off by an exponential of the form exp t l2 however if l is set equal to infinity the distribution has an algebraic tail given by t 1 2 we find that the generalised dimensions d q have a nontrivial dependence on q this shows that the fpt distribution is a multifractal we also calculate the singularity spectrum f

the projective geometry of freudenthal s magic square abstract we connect the algebraic geometry and representation theory associated to freudenthal s magic square we give unified geometric descriptions of several classes of orbit closures describing their hyperplane sections and desingularizations and interpreting them in terms of composition algebras in particular we show how a class of invariant quartic polynomials can be viewed as generalizations of the classical discriminant of a cubic polynomial

structure and perimeters of percolation clusters site percolation clusters are simulated at the percolation threshold on the square lattice an algorithm for walks around each cluster is used to obtain information on its fractal geometry the fractal dimensionality of the external perimeter is found to depend on the size of adsorbent particles used to measure it if the vacant perimeter sites have only nearest neighbour connectivity then the perimeter has dimension de 1 37 or 0 03 instead of that of the hull dh 1 75 the authors also measured the mass of internal dangling sites surrounded by the backbone s blobs singly and doubly connected sites the number of blobs and the average linear distance between entry into the exit from a blob

configurations of lines and models of lie algebras abstract the automorphism groups of the 27 lines on the smooth cubic surface or the 28 bitangents to the general quartic plane curve are well known to be closely related to the weyl groups of e 6 and e 7 we show how classical subconfigurations of lines such as double sixes triple systems or steiner sets are easily constructed from certain models of the exceptional lie algebras for e 7 and e 8 we are lead to beautiful models graded over the octonions which display these algebras as plane projective geometries of subalgebras we also interpret the group of the bitangents as a group of transformations of the triangles in the fano plane and show how this allows to realize the isomorphism psl 3 f 2 psl 2 f 7 in terms of harmonic cubes

initiation of damage in the kauffman model an alternate method is presented for initiating damage to the kauffman model a numerical study suggests that this modification increases the efficiency of generating damage clusters without changing their fractal properties

special prehomogeneous vector spaces associated to f4 e6 e7 e8 and simple jordan algebras of rank 3 abstract a simple complex lie algebra has a natural grading g g 2 g 1 g 0 g 1 g 2 associated to the highest root it is related to the quaternionic real form of g the real rank of the associated symmetric space is shown to be at most 4 when the rank is equal to 4 i e g a n c n g 2 the semi simple lie algebra m g 0 g 0 is shown to be the conformal algebra of a rank 3 semi simple jordan algebra v if g is one of the four exceptional lie algebras f4 e6 e7 e8 then v is simple the vector space g 1 is a prehomogeneous vector space under the action of m c where m int m is the adjoint group of m it admits a non zero m invariant polynomial of degree 4 conversely to any simple jordan algebra v of rank 3 is naturally associated a representation of a twofold covering of its conformal group co v on a vector space w such that w is a prehomogeneous vector space under the action of co v c an invariant polynomial of degree 4 is explicitly constructed a geometric description of all the orbits of co v in w is given

fast connected component labeling labeling of connected components in a binary image is one of the most fundamental operations in pattern recognition labeling is required whenever a computer needs to recognize objects connected components in a binary image this paper presents a fast two scan algorithm for labeling of connected components in binary images we propose an efficient procedure for assigning provisional labels to object pixels and checking label equivalence our algorithm is very simple in principle easy to implement and suitable for hardware and parallel implementation we show the correctness of our algorithm analyze its complexity and compare it with other labeling algorithms experimental results demonstrated that our algorithm is superior to conventional labeling algorithms

exact enumeration approach to fractal properties of the percolation backbone and 1 σ expansion an exact numeration approach is developed for the backbone fractal of the incipient infinite cluster at the percolation threshold the authors use this approach to calculate exactly the first low density expansion of lbb p for arbitrary system dimensionality d where lbb p is the mean of backbone bonds and p is the bond occupation probability standard series extrapolation methods provide estimates of the fractal dimension of the backbone for all d these disagree with the sierpinski gasket model of the backbone they also calculate the first low density expansions of lmin p and lred p which are respectively the mean number of bonds in the minimum path between i and j and the mean number of singly connected red bonds

a comparison of algorithms for connected set openings and closings the implementation of morphological connected set operators for image filtering and pattern recognition is discussed two earlier algorithms based on priority queues and hierarchical queues respectively are compared to a more recent union find approach unlike the earlier algorithms which process regional extrema in the image sequentially the union find method allows simultaneous processing of extrema in the context of area openings closings and pattern spectra the union find algorithm outperforms the previous methods on almost all natural and synthetic images tested finally extensions to pattern spectra and the more general class of attribute operators are presented for all three algorithms and memory usages are compared

a regular model for cluster numbers and structure just below percolation threshold a two dimensional deterministic fractal model is proposed to imitate the geometric texture just below percolation threshold the model is constructed for bond percolation via a rule of bond occupation on the square lattice it show the typical percolation behaviour as a function of a parameter p p is the bond concentration the model describes the approach towards the threshold below criticality the critical bond concentration pc and the correlation length exponent nu are found the scaling property of the cluster size distribution is studied below the threshold the critical concentration and critical exponents are shown to agree with those derived from the regular model proposed for the geometric texture above the threshold the scaling relations for the critical exponents are shown to be satisfied

mapping between hopping on hierarchical structures and diffusion on a family of fractals the authors present a simple analytical approach to studying diffusion on hierarchical and fractal structures they show that hopping on one dimensional hierarchical structures can be mapped onto diffusion on a family of loopless fractals

self dual fractal models for the low field hall effect near percolation threshold fractal lattices with the self duality property are proposed to imitate the geometric texture of two dimensional percolating networks at percolation threshold the exponents describing the power law dependence on the scale length of the hall and ohmic conductivities are found the exponent for the hall conductivity agrees with twice that for the ohmic conductivity the model is extended to describe the approach towards the threshold it is found that the model shows the typical percolation behaviour as a function of a parameter p the bond concentration

on fano complete intersections in rational homogeneous varieties complete intersections inside rational homogeneous varieties provide interesting examples of fano manifolds for example if x cap i 1 r d i subset g p is a smooth complete intersection of r ample divisors such that k g p otimes mathcal o g p sum i d i is ample then x is fano we first classify these fano complete intersections which are locally rigid it turns out that most of them are hyperplane sections we then classify general hyperplane sections which are quasi homogeneous

geometry over composition algebras projective geometry abstract the purpose of this article is to introduce projective geometry over composition algebras the analogue of projective spaces and grassmannians over them are defined it will follow from this definition that the projective spaces are in correspondence with jordan algebras and that the points of a projective space correspond to rank one matrices in the jordan algebra a second part thus studies properties of rank one matrices i also give an explicit description of the simply connected chevalley group of type e 6 over the integers

universality and superuniversality of multifractals in nonlinear resistor networks the multifractal functionf is generalized to describe noisy nonlinear random resistor networks an approximant function for the family of noise exponents is introduced that provides a good description of real percolative systems for strong nonlinearities by mapping from this family to the multifractal function one can approximate the latter a scale transformation of in the approximation makes the multifractal function universal for all nonlinearities and by applying an additional transformation this function becomes superuniversal i e independent of the dimension the universality is demonstrated for the mandelbrot given structure and the implications of these results are discussed on real percolative systems

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

approximate similarity reduction for the perturbed mkdv equation via symmetry perturbation and direct method the perturbed mkdv equation with the general form is investigated in terms of the approximate symmetry perturbation method and the approximate direct method the similarity reduction solutions of different orders are obtained for both methods series reduction solutions are consequently derived higher order similarity reduction equations are linear variable coefficient ordinary differential equations by comparison the relation between the results obtained by applying the two methods is revealed

emergent properties in random complex automata abstract studies of large randomly assembled binary boolean node automata have demonstrated that such systems can spontaneously exhibit enormously ordered dynamical behavior an important approach to characterizing these behaviors has consisted of studying ensembles of automata ensemble specifications have been based on 1 choice of boolean function regulating each node in the automaton 2 random or biased mappings of the 2 n automata states into themselves 3 the numbers of inputs k per node this article briefly reviews these approaches reports new results on the expected behavior of threshold automata and automata with a particular class of biased mappings in addition it discusses emergent highly ordered dynamical behavior in random automata rich in a specific class of canalizing boolean functions due to the crystallization of powerful subautomata called forcing structures the ordered behaviors may be of importance in biological evolution in physics and in the design of adaptive automata

multifractality and the kauffman model the author simulates the spread of an initial damage in the kauffman cellular automata at its critical point on the square lattice he calculates various moments of the probability that a site has been damaged n times and checks for multifractality in the critical exponents for different ensembles specifically he finds no evidence for multifractality when the moments of the probabilities are evaluated with lattice size l but multifractal behaviour occurs when the moments are monitored as a function of time t

projective planes over 2 dimensional quadratic algebras abstract the split version of the freudenthal tits magic square stems from lie theory and constructs a lie algebra starting from two split composition algebras 5 20 21 the geometries appearing in the second row are severi varieties 24 we provide an easy uniform axiomatization of these geometries and related ones over an arbitrary field in particular we investigate the entry a 2 a 2 in the magic square characterizing hermitian veronese varieties segre varieties and embeddings of hjelmslev planes of level 2 over the dual numbers in fact this amounts to a common characterization of projective planes over 2 dimensional quadratic algebras in cases of the split and non split galois extensions the inseparable extensions of degree 2 in characteristic 2 and the dual numbers

some special cremona transformations in this paper we continue the study c f c k s t 1 2 of special cremona transformations i e those whose base scheme y is smooth and connected crauder and katz have completely classified these when dim y 2 our main results classify them when they are quadro quadric theorem 2 6 and when codim y 2 theorem 3 2 in the first case they are just the maps given by systems of quadrics through severi varieties by a result of zak there are just four of these the veronese surface v c p5 the segre embedding of p2 x p2 in p8 the grassmannian g 2 6 in p14 and the 16dimensional e6 variety in p26 and in the second either y is a quintic elliptic scroll in p4 or y is defined in pi by the vanishing of the n x n minors of

cumulant renormalisation group and its application to the incipient infinite cluster in percolation the authors introduce the cumulant method into the context of position space renormalisation group the advantage of this method over previous procedures is that one need not systematically evaluate all 2n states of each kadanoff cell where n is the number of elements sites or bonds in the cell they illustrate this method by calculating for bond percolation with an eight bond cell the critical exponents characterizing the following quantities i the mean number of backbone bonds ii the mean number of bonds in the minimum and maximum paths along the backbone iii the mean number of singly connected red bonds and iv the mean number of bonds in all the self avoiding walks connecting the two extreme points they derive previously obtained results of the conductivity and resistivity

multifractal nature of diffusion on hierarchical structures the authors study the moments of the first passage time t of random walks on hierarchical structures using the exact enumeration method they find that the different moments scale with the size of the system with an infinite hierarchy of exponents characterising a multifractal behaviour

wetting velocity near the directed percolation threshold near the directed percolation threshold pd the wetting velocity upsilon scales as 1 upsilon approximately pd p theta the authors extrapolate from calculations on strips of finite width to show that on the two dimensional square lattice theta 1 73 or 0 02 this agrees with a scaling argument by barma and ray phys rev b vol 34 p 3403 1986 which predicts theta nu sub

the sextonions and e712 we fill in the hole in the exceptional series of lie algebras that was observed by cvitanovic deligne cohen and deman more precisely we show that the intermediate lie algebra between e7 and e8 satisfies some of the decomposition and dimension formulas of the exceptional simple lie algebras a key role is played by the sextonions a six dimensional algebra between the quaternions and octonions using the sextonions we show similar results hold for the rows of an expanded freudenthal magic chart we also obtain new interpretations of the adjoint variety of the exceptional group g2

topological properties of percolation clusters percolation properties including the total cluster mass s the shell mass b and the linear geometrical size r are studied as a function of the topological chemical distance parameter l all critical exponents are shown to be related to an apparently new exponent nu defined by r approximately lv critical exponents are calculated exactly for percolation clusters on the cayley tree a model for 6d percolation for which s approximately l2 b approximately l and r2 approximately l for diffusion on such clusters one finds that l3 approximately t numerical estimates of the exponents are obtained for other dimensions a conjecture which relates nu to beta and nu is discussed

ultradiffusion the relaxation of hierarchical systems the authors show that the dynamics of relaxation in hierarchical structures leads to an anomalous decay process which they term ultradiffusion using renormalisation group techniques they explicitly calculate the behaviour of the autocorrelation function in a one dimensional hierarchical system and show its universal power law decay as a function of temperature the authors also demonstrate analytically the emergence of a hierarchy of time scales this phenomenon is relevant to systems ranging from macromolecules to computing structures

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

triality exceptional lie algebras and deligne dimension formulas abstract we give a computer free proof of the deligne cohen and de man formulas for the dimensions of the irreducible g modules appearing in g k k 4 where g ranges over the exceptional complex simple lie algebras we give additional dimension formulas for the exceptional series as well as uniform dimension formulas for other representations distinguished by freudenthal along the rows of his magic chart our proofs use the triality model of the magic square which we review and present a simplified proof of its validity we conclude with some general remarks about obtaining series of lie algebras in the spirit of deligne and vogel

mesoscopic description of random walks on combs combs are a simple caricature of various types of natural branched structures which belong to the category of loopless graphs and consist of a backbone and branches we study continuous time random walks on combs and present a generic method to obtain their transport properties the random walk along the branches may be biased and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone we analyze the overall diffusion properties along the backbone and find normal diffusion anomalous diffusion and stochastic localization diffusion failure respectively depending on the characteristics of the continuous time random walk along the branches and compare our analytical results with stochastic simulations

scaling of the first passage time and the survival probability on exact and quasi exact self similar structures the authors calculate the asymptotic behaviour of the moments of the first passage time and survival probability for random walks on an exactly self similar tree and on a quasi self similar comb by applying an exact decimation approach to the master equations for the hierarchical comb a transition from ordinary to anomalous diffusion occurs at r 2 where r is the ratio of teeth length in successive iterations of the structure in the anomalous regime r 2 the positive integer moments of the first passage time tq scale as ltau q with tau q 1 2q 1 ln r ln 2 where l is the linear distance from input to output the asymptotic behaviour of the survival probability is studied using both scaling theory and by a direct solution of the master equations they find that the characteristic time t in the asymptotic exponential decay of the survival probability exp t t scales as t approximately ltau with tau ln r2 ln 2 i e tau is distinct from tau 1 however substantial corrections to this asymptotic form for tau exist and these are needed to account for the recent simulation data of havlin and matan 1988

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

exact renormalisation group approach to ultradiffusion in a hierarchical structure a model of diffusion in one dimension with a hierarchical pattern of hopping rates is studied by an exact renormalisation method non universal time scaling exponents are obtained for the autocorrelation function range and average diffusion distance

phase transitions on fractals ii sierpinski gaskets for pt i see ibid vol 16 p 1267 1983 the authors construct and investigate a family of fractals which are generalisations of the sierpinski gaskets sgs to all euclidean dimensionalities these fractal lattices have a finite order of ramification and can be considered marginal between one dimensional and higher dimensional geometries physical models defined on them are exactly solvable the authors argue that short range spin models on the sg show no finite temperature phase transitions as examples they solve a few spin models and study the resistor network and percolation problems on these lattices

are there infinitely many independent exponents in the percolation cluster numbers abstract an infinite number of independent exponents is expected not in the average cluster numbers but in the tails of the their probability distribution this effect is somewhat similar to voltage distributions in random resistor networks

low concentration series in general dimension we discuss recent work on the development and analysis of low concentration series for many models the recent breakthrough in the extremely efficient no free end method of series generation facilitates the derivation of 15th order series for multiple moments in general dimension the 15th order series have been obtained for lattice animals percolation and the edwards anderson ising spin glass in the latter cases multiple moments have been found from complete graph tables through to 13th order general dimension 13th order series have been derived for the resistive susceptibility the moments of the logarithms of the distribution of currents in resistor networks and the average transmission coefficient in the quantum percolation problem 11th order series have been found for several other systems including the crossover from animals to percolation the full resistance distribution nonlinear resistive susceptibility and current distribution in dilute resistor networks diffusion on percolation clusters the dilute ising model dilute antiferromagnet in a field and random field ising model and self avoiding walks on percolation clusters series for the dilute spin 1 2 quantum heisenberg ferromagnet are in the process of development analysis of these series gives estimates for critical thresholds amplitude ratios and critical exponents for all dimensions where comparisons are possible our series results are in good agreement with bothe expansion results near the upper critical dimension and with exact results when available in low dimensions and are competitive with other numerical approaches in intermediate realistic dimensions

singularities of duals of grassmannians abstract let x p n be a smooth irreducible nondegenerate projective variety and let x p n denote its dual variety the locus of bitangent hyperplanes i e hyperplanes tangent to at least two points of x is a component of the singular locus of x in this paper we provide a sufficient condition for this component to be of maximal dimension and show how it can be used to determine which dual varieties of grassmannians are normal that last part may be compared to what has been done for hyperdeterminants by j weyman and a zelevinsky 1996 in 23

a family of crossover exponents for the nonlinear resistor network the crossover exponents phi 2 r and phi 3 r for the nonlinear resistor network are calculated to first order in in 6 d using the same formalism used by harris 1987 the result supports the idea of the analytic continuation proposed by harris in calculating the nonlinear crossover exponent phi r for the nonlinear resistor network

thermodynamical formalism for an infinite hierarchy of fractal resistor networks where n is the number of resistors we find a generic phase transition at 3 3c 1 also we develop a transfer matrix technique which determines all even positive moments the thermodynamical formalism is applied to the hilfer blumen hierarchy of generalized sierpinski gasket fractal networks and the crossover from fractal to lattice behavior is studied at this crossover we find a sharp phase transition in the second moment 3 2

length of state cycles of random boolean networks an analytic study in this paper we consider the mean length of transients and the length of state cycles in random boolean networks we present an approximate calculation of these quantities as a function of the size and connectivity of the network where using an annealed approximation we derive a recursive formula for the length of steps of the system using the mean step length and an effective momentary state space we calculate an approximate formula for the probability distribution function pdf of the length of state cycles and transients we compare this pdf with analytical results in special cases and with simulations by the monte carlo procedure

complexity and ultradiffusion the authors present the exact solution to the problem of ultradiffusion in an arbitrary hierarchical space they derive rigorous upper and lower bounds for the dynamic exponent describing the decay of the autocorrelation function they show that the upper bound is saturated by both uniformly and randomly multifurcating hierarchical trees and identify a class of highly unbalanced trees that saturate the lower bound they conclude that the speed of relaxation is a measure of the complexity or lack of self similarity of the underlying tree they point out that complexity may be revealed by the temperature dependence of the dynamic exponent and in particular by the nature of the transition from exponential to power law decay

scaling properties of diffusion on comb like structures the authors study the scaling properties of the probability density of random walks on comb like structures they find that in contrast to the first passage time in which several exponents are needed to characterise their distribution the probability density can be described by a single exponent

nonlinear resistor fractal networks topological distances singly connected bonds and fluctuations the authors consider a fractal network of nonlinear resistors with the voltage v behaving as a power of the current i mod v mod r mod i mod alpha the resistance between two points at a distance l is r l varies as lzeta alpha they prove that zeta 0 describes the scaling of the topological chemical distance while zeta infinity describes that of the number of singly connected red bonds for random resistors they also consider the width of the resistance distribution delta r varies as l zeta 2 alpha values for zeta and zeta 2 are explicitly derived for two model fractals and delta r r is found to grow with l for the sierpinski gasket and alpha 1 612 the relevance of the results to percolation clusters is discussed

jordan algebras exceptional groups and bhargava composition abstract we consider an integral version of the freudenthal construction relating jordan algebras and exceptional algebraic groups we show how this construction is related to higher composition laws of m bhargava in number theory we propose an algorithmic approach to studying orbit spaces of groups underlying bhargava s higher composition laws using this method we discover two new examples of spaces sharing similar properties and indicate several more examples of spaces where such composition laws may be introduced

an embedded system for real time facial expression recognition based on the extension theory this paper presents a novel facial expression recognition scheme based on extension theory the facial region is detected and segmented by using feature invariant approaches accurate positions of the lips are then extracted as the features of a face next based on the extension theory basic facial expressions are classified by evaluating the correlation functions among various lip types and positions of the corners of the mouth additionally the proposed algorithm is implemented using the xscale pxa270 embedded system in order to achieve real time recognition for various facial expressions experimental results demonstrate that the proposed scheme can recognize facial expressions precisely and efficiently

kuchle fivefolds of type c5 we show that kuchle fivefolds of type c5 subvarieties of the grassmannian mathrm mathsf gr 3 7 parameterizing 3 subspaces that are isotropic for a given 2 form and are annihilated by a given 4 form are birational to hyperplane sections of the lagrangian grassmannian mathrm mathsf sgr 3 6 and describe in detail these birational transformations as an application we show that the integral chow motive of a kuchle fivefold of type c5 is of lefschetz type we also discuss kuchle fourfolds of type c5 hyperplane sections of the corresponding kuchle fivefolds an interesting class of fano fourfolds which is expected to be similar to the class of cubic fourfolds in many aspects

probability densities of homogeneous functions explicit approximation and applications to percolating networks the author treats the probability density of homogeneous functions of independent variables assuming these variables are narrowly distributed he finds an explicit approximate form for the laplace transform of the function s density this expression is used to show that if the variables are all gaussian then so is the global function the latter result is also claimed to hold for the total resistance of any random resistor network between two arbitrary terminals he further utilises the result to explicitly find the laplace transform of the conductance density of i a hierarchical structure and ii a random network in 1 in dimensions using the migdal kadanoff procedure in the last case he also finds the scaling of all the cumulants and finds that they exhibit a constant gap

tissus algebriques exceptionnels in pirio and trepreau int math res not imrn doi 10 1093 imrn rnu066 2014 it has been proved that for r 1 n ge 2 and d ge r 1 n 1 2 a d web of t ype r n with maximal rank is algebraizable in the classical sense except maybe when n ge 3 and d r 2 n 1 1 in the present paper one considers this particular case under these hypotheses on n and d one constructs some examples of exceptional algebraic webs these are generalized algebraic webs of maximal rank that are not algebraizable in the classical sense

a novel density based fuzzy clustering algorithm for low dimensional feature space abstract in this paper we propose a novel density based fuzzy clustering algorithm based on active learning method alm which is a methodology of soft computing inspired by some hypotheses claiming that human brain interprets information in pattern like images rather than numerical quantities the proposed clustering algorithm fuzzy unsupervised active learning method fualm is performed in two main phases first each data point spreads in the feature space just like an ink drop that spreads on a sheet of paper as a result of this process densely connected ink patterns are formed that represent clusters in the second phase a fuzzifying process is applied in order to summarize the effects of all members of each cluster finding arbitrary shaped clusters noise robustness and proposing fuzzy clusters are some of the advantages of our proposed clustering algorithm the algorithm is described in full details and its performance is evaluated and compared with well known clustering algorithms on synthetic and real world datasets

on cubic hypersurfaces of dimension seven and eight cubic sevenfolds are examples of fano manifolds of calabi yau type we study them in relation with the cartan cubic the e 6 invariant cubic in pp 26 we show that a generic cubic sevenfold x can be described as a linear section of the cartan cubic in finitely many ways to each such cartan representation we associate a rank nine vector bundle on x with very special cohomological properties in particular it allows to define auto equivalences of the non commutative calabi yau threefold associated to x by kuznetsov finally we show that the generic eight dimensional section of the cartan cubic is rational

an improved joint optimization of multiple level set functions for the segmentation of overlapping cervical cells in this paper we present an improved algorithm for the segmentation of cytoplasm and nuclei from clumps of overlapping cervical cells this problem is notoriously difficult because of the degree of overlap among cells the poor contrast of cell cytoplasm and the presence of mucus blood and inflammatory cells our methodology addresses these issues by utilizing a joint optimization of multiple level set functions where each function represents a cell within a clump that have both unary intracell and pairwise intercell constraints the unary constraints are based on contour length edge strength and cell shape while the pairwise constraint is computed based on the area of the overlapping regions in this way our methodology enables the analysis of nuclei and cytoplasm from both free lying and overlapping cells we provide a systematic evaluation of our methodology using a database of over 900 images generated by synthetically overlapping images of free lying cervical cells where the number of cells within a clump is varied from 2 to 10 and the overlap coefficient between pairs of cells from 0 1 to 0 5 this quantitative assessment demonstrates that our methodology can successfully segment clumps of up to 10 cells provided the overlap between pairs of cells is sim 0 5 we also evaluate our approach quantitatively and qualitatively on a set of 16 extended depth of field images where we are able to segment a total of 645 cells of which only sim 10 are free lying finally we demonstrate that our method of cell nuclei segmentation is competitive when compared with the current state of the art

worst case analysis of set union algorithms this paper analyzes the asymptotic worst case running time of a number of variants of the well known method of path compression for maintaining a collection of disjoint sets under union we show that two one pass methods proposed by van leeuwen and van der weide are asymptotically optimal whereas several other methods including one proposed by rein and advocated by dijkstra are slower than the best methods

cluster structure near the percolation threshold derives exact relations that allow one to describe unambiguously and quantitatively the structure of clusters near the percolation threshold pc in particular the author proves the relations p dpij dp lambda ij where p is the bond density pij is the pair connectedness function and lambda ij is the average number of cutting bonds between i and j from this relation it follows that the average number of cutting bonds between two points separated by a distance of the order of the connectedness length xi diverges as mod p pc mod 1 the remaining multiply connected bonds in the percolating backbone which lump together in blobs diverge with a dimensionality dependent exponent he also shows that in the cell renormalisation group of reynolds et al 1978 1980 the thermal eigenvalue is simply related to the average number of cutting bonds in the spanning cluster he discusses a percolation model in which the blobs can be controlled by varying a parameter and study the influence on the critical exponents

models of the lie algebra f4 abstract we describe the models of the exceptional lie algebra f 4 which are based on its semisimple subalgebras of rank 4 the underlying fact is that any reductive subalgebra of maximal rank of a simple lie algebra induces a grading on this algebra by means of an abelian group in such a way that the nontrivial components of the grading are irreducible modules

on the spreading dimension of percolation and directed percolation clusters the authors study the number an of sites that are accessible after n steps at most on clusters at the percolation threshold on a cayley tree an is of order n2 if the origin belongs to a larger cluster whereas its average over all clusters is of order n this suggests that the intrinsic spreading dimension d defined by an approximately nd is equal to two for fractal percolation clusters in space dimensions d or 6 and depends on d for d 6 for directed percolation clusters they argue that d is related to usual critical exponents by d beta gamma nu sub monte carlo data that support this relation are presented in two dimensions analogous results are derived for lattice animals d 2 on the cayley tree and d 1 nu sub for directed animals in any dimensions

search for multifractality in damage spreading for kauffman cellular automata the authors check how an initial disturbance called the damage spreads through a square lattice of kauffman cellular automata at their critical point they determine the moments of the probability that a site has been damaged n times and check for multifractality in the fractal dimensions or critical exponents of these moments of the damage probability

order propagation near the percolation threshold a new monte carlo method for studying bond percolation clusters is developed and used to identify new critical quantities associated with the percolation threshold the bonds in each cluster are partitioned into three distinct connectivity classes red singly connected backbone bonds blue multiply connected backbone bonds and yellow non backbone bonds often called dangling ends among the new cluster properties studied are the mean number of red bonds a critical quantity diverging at p c with exponent y r approximately 1 and the length of the shortest connected path through the cluster which is critical with exponent y min 1 35 0 02 for all cluster properties studies the authors also compute averages over only the largest clusters the corresponding critical exponents are found to be significantly different from those obtained by averaging over clusters of all sizes

scaling of the first passage time of biased diffusion on hierarchical comb structures biased diffusion on hierarchical comb structures is studied within an exact renormalisation group scheme the scaling exponents of the moments of the first passage time for random walks are obtained it is found that the scaling properties of the diffusion depend only on the direction of bias in a particular case the presence of bias may give rise to a new multifractality

building the component tree in quasi linear time the level sets of a map are the sets of points with level above a given threshold the connected components of the level sets thanks to the inclusion relation can be organized in a tree structure that is called the component tree this tree under several variations has been used in numerous applications various algorithms have been proposed in the literature for computing the component tree the fastest ones considering the worst case complexity have been proven to run in o nln n in this paper we propose a simple to implement quasi linear algorithm for computing the component tree on symmetric graphs based on tarjan s union find procedure we also propose an algorithm that computes the n most significant lobes of a map

damage spreading and multifractality in the travelling salesman problem the authors study numerically the spreading of damage in the euclidean travelling salesman problem there is a critical temperature tc approximately 0 20 0 25 below which damage does not spread they search for multifractal behaviour in the moments of the damage probability distribution multifractality is found in the frozen phase when the moments are monitored as a function of time if they are evaluated with the number of cities multifractal behaviour occurs in the chaotic phase

perceptually motivated image features using contours dong et al examined the ability of 51 computational feature sets to estimate human perceptual texture similarity however none performed well for this task while it is well known that the human visual system is extremely adept at exploiting longer range aperiodic and periodic contour characteristics in images none of the investigated feature sets exploit higher order statistics hos over larger image regions 19 times 19 pixels we therefore hypothesise that long range hos in the form of contour data are useful for perceptual texture similarity estimation we present the results of a psychophysical experiment that shows that contour data are more important than local image patches or global second order data to human observers for this task inspired by this finding we propose a set of perceptually motivated image features pmif that encode the long range hos computed from spatial and angular distributions of contour segments we use two perceptual texture similarity estimation tasks to compare pmif against the 51 feature sets referred to above and four commonly used contour representations this new feature set is also examined in the context of two additional tasks sketch based image retrieval and natural scene recognition the results show that the proposed feature set performs better or at least comparably to all the other feature sets we attribute this promising performance to the fact that the proposed feature set exploits both short range and long range hos

a long time tail for random walk in random scenery consider a simple random walk on d whose sites are colored black or white independently with probabilityq resp 1 q walk and coloring are independent letn k be the number of steps by the walk between itskth and k 1 th visits to a black site i e the length of itskth white run and let k e n k q 1 our main result is a proof that lim k k d 2 k 1 q q d 2 2 d 2 d 2 since it is known thatq 1 k e n 1 n k 1 b e n 1 b e n k 1 b withb the event that the origin is black exhibits a long time tail in the run length autocorrelation function numerical calculations of k 1 k 100 ind 1 2 and 3 show that there is an oscillatory behavior of k for smallk this damps exponentially fast following which the power law sets in fairly rapidly we prove that if the coloring is not independent but is convex in the sense of fkg then the decay of k cannot be faster than

a general approach to connected component labeling for arbitrary image representations an improved and general approach to connected component labeling of images is presented the algorithm presented in this paper processes images in predetermined order which means that the processing order depends only on the image representation scheme and not on specific properties of the image the algorithm handles a wide variety of image representation schemes rasters run lengths quadrees bintrees etc how to adapt the standard union find algorithm to permit reuse of temporary labels is shown this is done using a technique called age balancing in which when two labels are merged the older label becomes the father of the younger label this technique can be made to coexist with the more conventional rule of weight balancing in which the label with more descendants becomes the father of the label with fewer descendants various image scanning orders are examined and classified it is also shown that when the algorithm is specialized to a pixel array scanned in raster order the total processing time is linear in the number of pixels the linear time processing time follows from a special property of the union find algorithm which may be of independent interest this property states that under certain restrictions on the input union find runs in time linear in the number of find and union operations under these restrictions linear time performance can be achieved without resorting to the more complicated gabow tarjan algorithm for disjoint set union

series expansion study of the distribution of currents in the elements of a random diode insulator network the critical exponent zeta k of the kth moment of the current distribution for random diode insulator networks on the square and simple cubic lattices is calculated for a range of k using low density series expansion techniques it is also shown that zeta 1 nu sub where nu sub is the critical exponent of the parallel connectedness length for directed percolation the values of zeta k for the simple cubic lattice are well fitted by a simple exponential formula with zeta k 1 zeta k 1 1 1 2 the skal shklovskii scaling relation for the conductivity is generalised to the kth moment and it follows that the exponent k describing the divergence of flicker noise is given by kappa approximately d 1 nu perpendicular to nu sub zeta 4 2 zeta 2 the authors estimate this for both lattices

multifractal structure of clusters and growing aggregates abstract various phenomena on a given fractal object have different critical behavior this is related to the underlying multifractal structure of the aggregate here we discuss the problem with particular emphasis on a scaling approach which leads to a simple real space renormalization group a mechanism which generates multifractality based on a multiplicative process is also illustrated the multifractal structure of the incipient infinite cluster in percolation and diffusion limited aggregation is discussed in detail