langevin equations and surface growth departamento de fi sica universidad nacional de san luis chacabuco 917 5700 san luis argentina received 9 january 1997 the three approaches usually used to study surface growth are i master equation ii stochastic langevinequation and iii microscopic models all of them give the same scaling exponents recently vvedenskyet al phys rev e 48 852 1993 derived a stochastic langevin equation from a master equation of the birthand death type for the epitaxial growth demonstrating the equivalence of both approaches in this paper astochastic langevin equation is derived from a discrete model the results are the same as those obtained byvvedensky et al demonstrating that the three approaches are equivalent as a nontrivial example our proce dure is used to derive the kardar parisi zhang kpz equation from the ballistic deposition process thismodel with vacancies and overhangs is very dif cult to handle due to the algebraic complications that arisewhen the master equation approach is used s1063 651x 97 11905 5 pacs number s 05 40 1ji introduction

covariant connections on bicovariant differential calculus abstract given a bicovariant differential calculus e d such that the braiding map is diagonalisable in a certain sense the bimodule of two tensors admits a direct sum decomposition into symmetric and anti symmetric tensors this is used to prove the existence of a bicovariant torsionless connection on e following heckenberger and schmudgen we study invariant metrics and the compatibility of covariant connections with such metrics a sufficient condition for the existence and uniqueness of bicovariant levi civita connections is derived this condition is shown to hold for cocycle deformations of classical lie groups

an asymptotic competitive scheme for online bin packing in the online bin packing problem a list of items with integral sizes between 1 to b arrive one by one each item must be irrevocably assigned into a bin of capacity b upon its arrival without any information on the subsequent items and the goal is to minimize the number of used bins in this paper we deal with online bin packing from a new sight we present an asymptotic competitive scheme i e for any 0 the asymptotic competitive ratio is at most where is the smallest possible asymptotic competitive ratio among all online algorithms apart from the technical results the analysis to bridge the online and the off line approaches might be of particular interests

symmetry based determination of space time functions in nonequilibrium growth processes we study the space time correlation and response functions in nonequilibrium growth processes described by linear stochastic langevin equations exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations we derive expressions for the universal scaling functions of two time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion the usefulness of the space time functions is illustrated through the investigation of two atomistic growth models the family model and the restricted family model which are shown to belong to a unique universality class in 1 1 and 2 1 space dimensions this corrects earlier studies which claimed that in 2 1 dimensions the two models belong to different universality classes

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

levi civita connections on the quantum groups slq n oq n and spq n for bicovariant differential calculi on quantum groups various notions on connections and metrics bicovariant connections invariant metrics the compatibility of a connection with a metric levi civita connections are introduced and studied it is proved that for the bicovariant differential calculi on sl q n o q n and sp q n from the classification in 18 there exist unique levi civita connections

noncommutative kahler structures on quantum homogeneous spaces abstract building on the theory of noncommutative complex structures the notion of a noncommutative kahler structure is introduced in the quantum homogeneous space case many of the fundamental results of classical kahler geometry are shown to follow from the existence of such a structure allowing for the definition of noncommutative lefschetz hodge kahler dirac and laplace operators quantum projective space endowed with its heckenberger kolb calculus is taken as the motivating example the general theory is then used to show that the calculus has cohomology groups of at least classical dimension

stochastic equations for simple discrete models of epitaxial growth we derive continuous stochastic equations governing the asymptotic behavior of growth from a master equation for discrete growth models with local relaxation we consider several simple models of epitaxial growth the family the wolf villain and the das sarma tamborenea models and their modifications i n 1 11 dimensions we derive for each model the corresponding langevin equation and identify leading terms that determine the universality class our results for models with local relaxation are in agreement with recent computer simulations the applicability of the method in 211 dimensions is demonstrated in the case of the family model problems of the procedure in particular regularization in the continuous limit are discussed s1063 651x 96 00710 6

new bounds for variable sized online bin packing in the variable sized online bin packing problem one has to assign items to bins one by one the bins are drawn from some fixed set of sizes and the goal is to minimize the sum of the sizes of the bins used we present new algorithms for this problem and show upper bounds for them which improve on the best previous upper bounds we also show the first general lower bounds for this problem the case in which bins of two sizes 1 and alpha in 0 1 are used is studied in detail this investigation leads us to the discovery of several interesting fractal like curves

spin geometry on quantum groups via covariant differential calculi abstract let a be a cosemisimple hopf algebra with antipode s and let be a left covariant first order differential calculus over a such that is self dual see section 2 and invariant under the hopf algebra automorphism s2 a quantum clifford algebra cl g is introduced which acts on woronowicz external algebra a minimal left ideal of cl g which is an a bimodule is called a spinor module metrics on spinor modules are investigated the usual notion of a linear left connection on is extended to quantum clifford algebras and also to spinor modules the corresponding dirac operator and connection laplacian are defined for the quantum group slq 2 and its bicovariant 4d calculi these concepts are studied in detail a generalization of bochner s theorem is given all invariant differential operators over a given spinor module are determined the eigenvalues of the dirac operator are computed

noncommutative riemannian and spin geometry of the standard q sphere we study the quantum sphere open image in new window as a quantum riemannian manifold in the quantum frame bundle approach we exhibit its 2 dimensional cotangent bundle as a direct sum 0 1 1 0 in a double complex we find the natural metric volume form hodge operator laplace and maxwell operators and projective module structure we show that the q monopole as spin connection induces a natural levi civita type connection and find its ricci curvature and q dirac operator open image in new window we find the possibility of an antisymmetric volume form quantum correction to the ricci curvature and lichnerowicz type formulae for open image in new window we also remark on the geometric q borel weil bott construction

a mechanism to synchronize fluctuations in scale free networks using growth models abstract in this paper we study the steady state of the fluctuations of the surface for a model of surface growth with relaxation to any of its lower nearest neighbors sram f family j phys a 19 1986 l441 in scale free networks it is known that for euclidean lattices this model belongs to the same universality class as the model of surface relaxation to the minimum srm for the srm model it was found that for scale free networks with broadness the steady state of the fluctuations scales with the system size n as a constant for 3 and has a logarithmic divergence for 3 a l pastore y piontti p a macri l a braunstein phys rev e 76 2007 046117 it was also shown c e la rocca l a braunstein p a macri phys rev e 77 2008 046120 that this logarithmic divergence is due to non linear terms that arises from the topology of the network in this paper we show that the fluctuations for the sram model scale as in the srm model we also derive analytically the evolution equation for this model for any kind of complex graphs and find that as in the srm model non linear terms appear due to the heterogeneity and the lack of symmetry of the network in spite of that the two models have the same scaling but the srm model is more efficient to synchronize systems

on the online bin packing problem a new framework for analyzing online bin packing algorithms is presented this framework presents a unified way of explaining the performance of algorithms based on the harmonic approach within this framework it is shown that a new algorithm harmonic has asymptotic performance ratio at most 1 58889 it is also shown that the analysis of harmonic 1 presented in richey 1991 is incorrect this is a fundamental logical flaw not an error in calculation or an omitted case the asymptotic performance ratio of harmonic 1 is at least 1 59217 thus harmonic provides the best upper bound for the online bin packing problem to date

bounds for online bin packing with cardinality constraints abstract we study a bin packing problem in which a bin can contain at most k items of total size at most 1 where k 2 is a given parameter items are presented one by one in an online fashion we analyze the best absolute competitive ratio of the problem and prove tight bounds of 2 for any k 4 additionally we present bounds for relatively small values of k with respect to the asymptotic competitive ratio and the absolute competitive ratio in particular we provide tight bounds on the absolute competitive ratio of first fit for k 2 3 4 and improve the known lower bounds on asymptotic competitive ratios for multiple values of k our method for obtaining a lower bound on the asymptotic competitive ratio using a certain type of an input is general and we also use it to obtain an alternative proof of the known lower bound on the asymptotic competitive ratio of standard online bin packing

langevin equations for fluctuating surfaces exact langevin equations are derived for the height fluctuations of surfaces driven by the deposition of material from a molecular beam we consider two types of model deposition models where growth proceeds by the deposition and instantaneous local relaxation of particles with no subsequent movement and models with concurrent random deposition and surface diffusion starting from a chapman kolmogorov equation the deposition relaxation and hopping rules of these models are first expressed as transition rates within a master equation for the joint height probability density function the kramers moyal van kampen expansion of the master equation in terms of an appropriate largeness parameter yields according to a limit theorem due to kurtz stoch proc appl 6 223 1978 a fokker planck equation that embodies the statistical properties of the original lattice model the statistical equivalence of this fokker planck equation solved in terms of its associated langevin equation and solutions of the chapman kolmogorov equation as determined by kinetic monte carlo kmc simulations of the lattice transition rules is demonstrated explicitly by comparing the surface roughness and the lateral height correlations obtained from the two formulations for the edwards wilkinson proc roy soc london ser a 381 17 1982 and wolfvillain europhys lett 13 389 1990 deposition models and for a model with random deposition and surface diffusion in each case as the largeness parameter is increased the langevin equation converges to the surface roughness and lateral height correlations produced by kmc simulations for all times including the crossover between different scaling regimes we conclude by examining some of the wider implications of these results including applications to heteroepitaxial systems and the passage to the continuum limit

twisting of quantum differentials and the planck scale hopf algebra we show that the crossed modules and bicovariant differential calculi on two hopf algebras related by a cocycle twist are in 1 1 correspondence in particular for quantum groups which are cocycle deformation quantisations of classical groups the calculi are obtained as deformation quantisations of the classical ones as an application we classify all bicovariant differential calculi on the planck scale hopf algebra this is a quantum group which has an limit as the functions on a classical but non abelian group and a limit as flat space quantum mechanics we further study the noncommutative differential geometry and fourier theory for this hopf algebra as a toy model for planck scale physics the fourier theory implements a t duality like self duality the noncommutative geometry turns out to be singular when and is therefore not visible in flat space quantum mechanics alone

symmetries and fixed point stability of stochastic differential equations modeling self organized criticality a stochastic nonlinear partial differential equation is constructed for two different models exhibiting self organized criticality the bak tang wiesenfeld btw sandpile model phys rev lett 59 381 1987 phys rev a 38 364 1988 and the zhang model phys rev lett 63 470 1989 the dynamic renormalization group drg enables one to compute the critical exponents however the nontrivial stable fixed point of the drg transformation is unreachable for the original parameters of the models we introduce an alternative regularization of the step function involved in the threshold condition which breaks the symmetry of the btw model although the symmetry properties of the two models are different it is shown that they both belong to the same universality class in this case the drg procedure leads to a symmetric behavior for both models restoring the broken symmetry and makes accessible the nontrivial fixed point this technique could also be applied to other problems with threshold dynamics

fully dynamic bin packing revisited we consider the fully dynamic bin packing problem where items arrive and depart in an online fashion and repacking of previously packed items is allowed the goal is of course to minimize both the number of bins used as well as the amount of repacking a recently introduced way of measuring the repacking costs at each timestep is the migration factor defined as the total size of repacked items divided by the size of an arriving or departing item concerning the trade off between number of bins and migration factor if we wish to achieve an asymptotic competitive ratio of 1 epsilon for the number of bins a relatively simple argument proves a lower bound of omega 1 epsilon for the migration factor we establish a nearly matching upper bound of o 1 epsilon 4 log 1 epsilon using a new dynamic rounding technique and new ideas to handle small items in a dynamic setting such that no amortization is needed the running time of our algorithm is polynomial in the number of items nand in 1 epsilon the previous best trade off was for an asymptotic competitive ratio of 5 4 for the bins rather than 1 epsilon and needed an amortized number of o log n repackings while in our scheme the number of repackings is independent of n and non amortized

derivation of continuum stochastic equations for discrete growth models we present a formalism to derive the stochastic differential equations sdes for several solid on solid growth models our formalism begins with a mapping of the microscopic dynamics of growth models onto the particle systems with reactions and diffusion we then write the master equations for these corresponding particle systems and find the sdes for the particle densities finally by connecting the particle densities with the growth heights we derive the sdes for the height variables applying this formalism to discrete growth models we find the edwards wilkinson equation for the symmetric body centered solid on solid bcsos model the kardar parisi zhang equation for the asymmetric bcsos model and the generalized restricted solid on solid rsos model and the villain lai das sarma equation for the conserved rsos model in addition to the consistent forms of equations for growth models we also obtain the coefficients associated with the sdes

noncommutative principal bundles through twist deformation we construct noncommutative principal bundles deforming principal bundles with a drinfeld twist 2 cocycle if the twist is associated with the structure group then we have a deformation of the fibers if the twist is associated with the automorphism group of the principal bundle then we obtain noncommutative deformations of the base space as well combining the two twist deformations we obtain noncommutative principal bundles with both noncommutative fibers and base space more in general the natural isomorphisms proving the equivalence of a closed monoidal category of modules and its twist related one are used to obtain new hopf galois extensions as twists of hopf galois extensions a sheaf approach is also considered and examples presented

bicovariant differential calculus on quantum groups su q n and so q n following woronowicz s proposal the bicovariant differential calculus on the quantum groupssu q n andso q n is constructed a systematic construction of bicovariant bimodules by using the hat r q matrix is presented the relation between the hopf algebras generated by the linear functionals relating the left and right multiplication of these bicovariant bimodules and theq deformed universal enveloping algebras is given imposing the conditions of bicovariance and consistency with the quantum group structure the differential algebras and exterior derivatives are defined as an application the maurer cartan equations and theq analogue of the structure constants are formulated

new lower bounds for certain classes of bin packing algorithms on line algorithms have been extensively studied for the one dimensional bin packing problem in this paper we investigate two classes of one dimensional bin packing algorithms and we give better lower bounds for their asymptotic worst case behavior for on line algorithms so far the best lower bound was given by van vliet in 1992 12 he proved that there is no on line bin packing algorithm with better asymptotic performance ratio than 1 54014 in this paper we give an improvement on this bound to 248161 1 54037 and we investigate the parametric case as well for those lists where the elements are preprocessed according to their sizes in non increasing order csirik et al 1983 1 proved that no on line algorithm can have an asymptotic performance ratio smaller than 87 we improve this result to 5447

crossover and universality in the wolf villain model the transition rules of the wolf villain model for the deposition and instantaneous relaxation of particles on a lattice are expressed as a langevin equation for the height fluctuations at each site a coarse graining transformation of this equation shows directly that this model belongs to the edwards wilkinson universality class in agreement with kinetic monte carlo simulations the crossover from the mullins herring equation is explained by the transformation under coarse graining of the coefficients in the equation of motion

edwards wilkinson equation from lattice transition rules continuum equations of motion for the height fluctuations of lattice growth models are derived from their transition rules by regularizing and coarse graining the associated discrete langevin equations for models with random deposition followed by instantaneous relaxation to a neighboring site based on identifying the local height minimum our methodology yields the edwards wilkinson equation the application of this procedure to other growth models is discussed

the edwards wilkinson model revisited large scale simulations of dynamic scaling in 2 1 dimensions abstract using extensive simulations of surface growth in the 2 1 dimensional atomistic model of edwards and wilkinson ew we have calculated both interfacial width and the structure factor to extract the dynamic exponent z in contrast to theoretical expectations finite size scaling of the data for both surface properties is achieved using z 1 63 instead of the predicted value of 2 0 a restricted variant of the ew model gives z 2 0 clarifying these non trivial differences in dynamical correlations now represents an intriguing theoretical challenge

discrete growth models on deterministic fractal substrate abstract the growth of the modified family model and the etching model on the sierpinski carpet is studied by means of numerical simulations the evolving interface of the aggregates is described by the well established family vicsek dynamic scaling approach the results of the modified family model prove the universality of the fractional langevin equation introduced by lee and kim s b lee j m kim phys rev e 80 2009 021101 the etching model also shows good scaling behavior we conjecture that the systematic deviations of the data found in the ballistic deposition c m horowitz f roma e v albano phys rev e 78 2008 061118 may be due to the finite size effects of the ballistic deposition model

conservative model for synchronization problems in complex networks in this paper we study the scaling behavior of the interface fluctuations roughness for a discrete model with conservative noise on complex networks conservative noise is a noise which has no external flux of deposition on the surface and the whole process is due to the diffusion it was found that in euclidean lattices the roughness of the steady state w s does not depend on the system size here we find that for scale free networks of n nodes characterized by a degree distribution p k approximately k lambda w s is independent of n for any lambda this behavior is very different than the one found by pastore y piontti phys rev e 76 046117 2007 for a discrete model with nonconservative noise which implies an external flux where w s approximately ln n for lambda 3 and was explained by nonlinear terms in the analytical evolution equation for the interface la rocca phys rev e 77 046120 2008 in this work we show that in these processes with conservative noise the nonlinear terms are not relevant to describe the scaling behavior of w s

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

locality preserving allocations problems and coloured bin packing we study the following problem introduced by chung et al in 2006 we are given online or offline a set of coloured items of different sizes and wish to pack them into bins of equal size so that we use few bins in total at most times optimal and that the items of each colour span few bins at most times optimal we call such allocations approximate as usual in bin packing problems we allow additive constants and consider as the asymptotic performance ratios we prove that for e 0 if we desire small no scheme can beat 1 e 1 e approximate allocations and similarly as we desire small no scheme can beat 1 69103 1 e approximate allocations we give offline schemes that come very close to achieving these lower bounds for the online case we prove that no scheme can even achieve o 1 o 1 approximate allocations however a small restriction on item sizes permits a simple online scheme that computes 2 e 1 7 approximate allocations

the dirac operator on compact quantum groups for the q deformation gq 0 q 1 of any simply connected simple compact lie group g we construct an equivariant spectral triple which is an isospectral deformation of that defined by the dirac operator d on g our quantum dirac operator dq is a unitary twist of d considered as an element of ug cl g the commutator of dq with a regular function on gq consists of two parts one is a twist of a classical commutator and so is automatically bounded the second is expressed in terms of the commutator of the associator with an extension of d we show that in the case of the drinfeld associator the latter commutator is also bounded

fokker planck equation for lattice deposition models an asymptotically exact fokker planck equation for the height fluctuations of lattice deposition models is derived from a van kampen expansion of the master equation using an edwards wilkinson type model as an example the solution of the equivalent langevin equation reproduces the surface roughness and lateral height correlations obtained with kinetic monte carlo kmc simulations our discrete equations of motion thereby provide an exact analytic and computational alternative to kmc simulations of these models