frozen states of a disordered globular heteropolymer the disordered heteropolymer chain with a random sequence of links a simple model of globular protein is investigated using the replica approach in the mean field approximation it is shown that for low dimensions of space d 1 it follows that the set of equilibrium states is ultrametric with an anomalously large number of weakly overlapping states

two dimensional online bin packing with rotation in two dimensional bin packing problems the input items are rectangles which need to be packed in a non overlapping manner the goal is to assign the items into unit squares using an axis parallel packing most previous work on online packing concentrated on items of fixed orientation which must be assigned such that their bottom side is parallel to the bottom of the bin in this paper we study the case of rotatable items which can be rotated by ninety degrees we give almost tight bounds on the asymptotic competitive ratio of bounded space bin packing of rotatable items and introduce a new unbounded space algorithm this improves the results of fujita and hada

the rectangle complexity of functions on two dimensional lattices let x be a non empty set let f z2x all vectors which occur have integer coefficients and for a1 a2 b1 b2 we write or 0 a block is a set of the form b z2 0 such that the complexity of f does not exceed b1b2 in this paper we prove the statement for b n 2 where n is any positive integer

two dimensional on line bin packing problem with rotatable items in this paper we consider a two dimensional version of the on line bin packing problem in which each rectangular item that should be packed into unit square bins is rotatable by 90 two on line algorithms for solving the problem are proposed the second algorithm is an extension of the first algorithms and the worst case ratio of the second one is at least 2 25 and at most 2 565

tight results for next fit and worst fit with resource augmentation it is well known that the two simple algorithms for the classic bin packing problem nf and wf both have an approximation ratio of 2 however wf seems to be a more reasonable algorithm since it never opens a new bin if an existing bin can still be used using resource augmented analysis where the output of an approximation algorithm which can use bins of size b 1 is compared to an optimal packing into bins of size 1 we give a complete analysis of the asymptotic approximation ratio of wf and of nf and use it to show that wf is strictly better than nf for any 1 2 and for b 1

polymer coil globule transition by real space renormalisation a simple real space renormalisation scheme is proposed for the statistics of the polymer coil globule transition in two dimensions this approach describes the coil theta point and globular states of the macromolecule within a single two parameter transformation results from a small cell calculation include the theta point size exponent vtheta 0 494 and crossover exponent phi 0 486

phase diagram of branched polymer collapse the phase diagram of the collapse of a two dimensional infinite branched polymer interacting with the solvent and with itself through contact interactions is studied from the q ensuremath rightarrow 1 limit of an extension of the q state potts model exact solution on the bethe lattice and migdal kadanoff renormalization group calculations shows that there is a line of ensuremath theta transitions from the extended to a single compact phase the ensuremath theta line governed by three different fixed points consists of two lines of extended compact transitions which are in different universality classes and meet in a multicritical point on the other hand directed branched polymers are shown to be completely determined by the strongly embedded case and there is a single ensuremath theta transition which is in the directed percolation universality class textcopyright 1996 the american physical society

zero temperature properties of randomly self interacting polymers we study the zero temperature behavior of several simple models for randomly self interacting polymers in one and 1 1 dimensions results are based on exact enumeration and closed form expressions

an algebraic geometric approach to nivat s conjecture abstract we study multidimensional configurations infinite words and subshifts of low pattern complexity using tools of algebraic geometry we express the configuration as a multivariate formal power series over integers and investigate the setup when there is a non trivial annihilating polynomial a non zero polynomial whose formal product with the power series is zero such annihilator exists for example if the number of distinct patterns of some finite shape d in the configuration is at most the size d of the shape this is our low pattern complexity assumption we prove that the configuration must be a sum of periodic configurations over integers possibly with unbounded values as a specific application of the method we obtain an asymptotic version of the well known nivat s conjecture we prove that any two dimensional non periodic configuration can satisfy the low pattern complexity assumption with respect to only finitely many distinct rectangular shapes d

packing resizable items with application to video delivery over wireless networks motivated by fundamental optimization problems in video delivery over wireless networks we consider the following problem of packing resizable items pri given is a bin of capacity b 0 and a set i of items each item j i has a size s j 0 a packed item must stay in the bin for a fixed common time interval to accommodate additional items in the bin each item j can be compressed to a given size p j 0 s j for at most a fraction q j 0 1 of the packing interval during one continuous sub interval the goal is to pack in the bin for the given time interval a subset of items of maximum cardinality pri is a generalization of the well known knapsack problem and it is strongly np hard already for highly restricted instances our main result is an approximation algorithm that packs for any instance i of pri at least 2 3 opt i 2 items where opt i is the number of items packed in an optimal solution our algorithm yields a better performance ratio for instances in which the maximum compression time of an item is q max 0 1 2 for subclasses of instances arising in realistic scenarios we give an algorithm that packs at least opt i 2 items finally we show that a non trivial subclass of instances admits an asymptotic fully polynomial time approximation scheme afptas

low complexity functions and convex sets in mathbb z k in 1938 morse and hedlund proved that a function f mathbb z rightarrow 0 1 is periodic if the number vert p f n vert of different n blocks f x 1 ldots f x n with x in mathbb z does not exceed n for some n in 1940 they studied such functions f with vert p f n vert n 1 for all positive integers n these are closely related to sturmian sequences which occur in many branches of mathematics computer science and physics

periodicity and local complexity we consider the complexity of bi infinite words in one and two dimensions a result of morse and hedlund in one dimension states that if the complexity p n of a word satisfies p n n for some n then the word is periodic the corresponding question in two dimensions whether p m n mn implies that is periodic is known as the nivat conjecture in this paper we strengthen the one dimensional result of morse and hedlund and prove a weak form of the nivat conjecture namely that if for a bi infinite two dimensional word p m n mn 16 then is periodic

tree shift topological entropy abstract we give a definition of topological entropy for tree shifts prove that the limit in the definition exists and show that it dominates the topological entropy of the associated one dimensional shift of finite type when the labeling of the tree shares the same restrictions

configurational statistics of a disordered polymer chain a problem of the configurational properties of a long flexible polymer chain with a quenched disorder is considered the chain is assumed to be randomly constructed from monomers of two different kinds with different constants for the two body interaction near the theta point i e when the average interaction of monomers is small the spatial correlation of the repulsive and attractive monomers of different kinds leads to an increase of effects of the disorder on large scales there is also the competing effect of the repulsive three body interaction which tends to screen the effects of disorder on large scales for both effects the upper critical dimension is dc 3 a solution of the renormalisation group equation indicates that there always exists a critical scale at which the relative dispersion of sizes of polymers with different random sequences of monomers becomes of the order of unity the magnitude of this critical scale depends strongly on the relation between the constant which characterises the dispersion of the two body interaction b0 and the constant of the repulsive three body interaction v0 if b0 3 32v0 at each physically attainable scale the effects of screening are prevalent and the dispersion of sizes of polymers with different sequences of monomers is small near the theta point if the reverse inequality holds the dispersion of sizes becomes of the order of unity near the theta point

balancedness and coboundaries in symbolic systems abstract this paper studies balancedness for infinite words and subshifts both for letters and factors balancedness is a measure of disorder that amounts to strong convergence properties for frequencies it measures the difference between the numbers of occurrences of a given word in factors of the same length we focus on two families of words namely dendric words and words generated by substitutions the family of dendric words includes sturmian and arnoux rauzy words as well as codings of regular interval exchanges we prove that dendric words are balanced on letters if and only if they are balanced on words in the substitutive case we stress the role played by the existence of coboundaries taking rational values and show simple criteria when frequencies take rational values for exhibiting imbalancedness

nivat s conjecture and pattern complexity in algebraic subshifts abstract we study nivat s conjecture on algebraic subshifts and prove that in some of them every low complexity configuration is periodic this is the case in the ledrappier subshift the 3 dot system and more generally in all two dimensional algebraic subshifts over f p defined by a polynomial without line polynomial factors in more than one direction we also find an algebraic subshift that is defined by a product of two line polynomials that has this property the 4 dot system and another one that does not

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

online algorithms for 1 space bounded 2 dimensional bin packing and square packing in this paper we study 1 space bounded 2 dimensional bin packing and square packing a sequence of rectangular items square items arrive one by one each item must be packed into a square bin of unit size on its arrival without any information about future items when packing items 90 rotation is allowed 1 space bounded means there is only one active bin if the active bin cannot accommodate the coming item it will be closed and a new bin will be opened the objective is to minimize the total number of bins used for packing all items in the sequence our contributions are as follows for 1 space bounded 2 dimensional bin packing we propose an online packing algorithm with a tight competitive ratio of 5 06 a lower bound of 3 17 on the competitive ratio is proven moreover we study 1 space bounded square packing where each item is a square with side length no more than 1 a 4 3 competitive algorithm is achieved and a lower bound of 2 94 on the competitive ratio is given all these bounds surpass the previously best known results

low temperature properties of directed walks with random self interactions we consider a simple model for a chain with random self interactions each monomer on the chain carries a charge which is a random variable and the configurations of the chain are directed walks we show that at zero temperature the end to end distance r and the energy e of chains with total charge q approximately nx scale as r approximately nnu x and e approximately ntheta x the exponents thus depend on the total charge through the parameter x these exponents are measured numerically and compared to the predictions of some simple arguments at a finite temperature r is extensive and appears to be independent of x

the efficiency of the flory approximation the flory approximation 1969 for the self avoiding chain problem is compared with a conventional perturbation theory expansion while in perturbation theory each term is averaged over the unperturbed set of configurations the flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations this imposes restrictions on the integration domain in higher order terms and they can be treated self consistently the accuracy delta nu nu of the flory approximation for self avoiding chain problems is estimated to be 10 1 10 2 for 1 d 4

renormalization group description of polymer excluded volume a description is provided of the chain conformation space renormalization group approach to the treatment of polymer excluded volume this method is transformed into one of identical form to the t hooft veltman renormalization method of field theory thereby enabling comparison with other methods a summary is provided of recent new results obtained by this technique for the full second order dependence of the mean square end to end distance r 2 on chain length and excluded volume as well as a calculation of r 2 for a polyelectrolyte chain with added salt

approximate strip packing in this paper we establish an algorithmic framework between bin packing and strip packing with which strip packing can be very well approximated by applying some bin packing algorithms more precisely we obtain the following results 1 any off line bin packing algorithm can be applied to strip packing maintaining almost the same asymptotic worst case ratio 2 a class of harmonic based algorithms for bin packing such as refined harmonic modified harmonic harmonic can be applied to online strip packing in particular we show that online strip packing admits an upper bound of 1 58889 on the asymptotic competitive ratio for any arbitrarily small 0 this significantly improves the previously best bound of 1 6910 and affirmatively answers an open question posed by csirik and woeginger 1997 moreover the time complexity mainly depends on a sorting procedure and the bin packing algorithms employed

the statistical mechanics of random copolymers random copolymers are polymers with two or more types of monomer where the monomer sequence is determined by some random process once determined the sequence is fixed so random copolymers are an example of a system with quenched randomness we review the statistical mechanics of random copolymers focusing on self avoiding walk models where there are two types of monomers a and b which are randomly distributed along the polymer chain theoretical approximate and numerical results are reviewed for models of the random copolymer adsorption localization and collapse phase transitions we concentrate on what is known about the existence of phase transitions the morita approximation and results about self averaging we also discuss in less detail the replica trick and numerical methods including monte carlo methods exact enumeration and transfer matrix methods important open problems are identified throughout and highlighted in the conclusions

a simple on line bin packing algorithm the one dimensional on line bin packing problem is considered a simple o 1 space and o n time algorithm called harmonic m is presented it is shown that this algorithm can achieve a worst case performance ratio of less than 1 692 which is better than that of the o n space and o n log n time algorithm first fit also shown is that 1 691 is a lower bound for all 0 1 space on line bin packing algorithms finally a revised version of harmonic m an o n space and o n time algorithm is presented and is shown to have a worst case performance ratio of less than 1 636 d

the complexity of functions on lattices abstract let f z 0 1 be a given function in 1938 morse and hedlund observed that if the number of distinct vectors f x 1 f x n x z called complexity is at most n for some positive integer n then f is periodic with period at most n this result is best possible functions with low complexity have been studied to a large extent and relations with or applications to many branches of mathematics computer science and physics are known in the present paper we discuss the above phenomenon in greater generality to begin with we observe that f is periodic if the number of distinct vectors f x a 1 f x a n x z is at most n for some n and given integers a 1 n but that the period cannot be bounded as a function of n only our main topic are multi dimensional functions f z k 0 1 with the property that for some n and distinct vectors a 1 a n z k the number of distinct vectors f x a 1 f x a n x z k is bounded by n we show that such a function with arbitrary k is periodic if n 3 for n 4 there are non periodic examples which we determine completely finally limitations to the general periodicity principle are discussed a conjecture for convex bodies a 1 a n in z 2 is made and we prove it for n 4

a model of continuous polymers with random charges we study a model of polymers with random charges the possible shapes of the polymer are represented by the sample paths of a brownian motion and the cumulative charge distribution along a polymer is modeled by a realization of a brownian bridge charges interact through a general positive definite two body potential we study the infinite volume free energy density for a fixed realization of the brownian motion this is not self averaging but shows on the contrary a sample dependence through the local time of the brownian motion we obtain an explicit series representation for the free energy density this has a finite radius of convergence but the free energy is nevertheless analytic in the inverse temperature in the physical domain

on lazy bin covering and packing problems in this paper we study two interesting variants of the classical bin packing problem called lazy bin covering lbc and cardinality constrained maximum resource bin packing ccmrbp problems for the offline lbc problem we first prove the approximation ratio of the first fit decreasing and first fit increasing algorithms then present an aptas for the online lbc problem we give a competitive analysis for the algorithms of next fit worst fit first fit and a modified harmonic m algorithm the ccmrbp problem is a generalization of the maximum resource bin packing mrbp problem boyar et al 2006 1 for this problem we prove that its offline version is no harder to approximate than the offline mrbp problem

on a conjecture on bidimensional words we prove that given a double sequence w over the alphabet a i e a mapping from z2 to a if there exists a pair n0 m0 z2 such that pw n0 m0 1 100n0m0 then w has a periodicity vector where pw is the complexity function in rectangles of w