relevant parameters in models of cell division control a recent burst of dynamic single cell data makes it possible to characterize the stochastic dynamics of cell division control in bacteria different models were used to propose specific mechanisms but the links between them are poorly explored the lack of comparative studies makes it difficult to appreciate how well any particular mechanism is supported by the data here we describe a simple and generic framework in which two common formalisms can be used interchangeably i a continuous time division process described by a hazard function and ii a discrete time equation describing cell size across generations where the unit of time is a cell cycle in our framework this second process is a discrete time langevin equation with simple physical analogues by perturbative expansion around the mean initial size or interdivision time we show how this framework describes a wide range of division control mechanisms including combinations of time and size control as well as the constant added size mechanism recently found to capture several aspects of the cell division behavior of different bacteria as we show by analytical estimates and numerical simulations the available data are described precisely by the first order approximation of this expansion i e by a linear response regime for the correction of size fluctuations hence a single dimensionless parameter defines the strength and action of the division control against cell to cell variability quantified by a single noise parameter however the same strength of linear response may emerge from several mechanisms which are distinguished only by higher order terms in the perturbative expansion our analytical estimate of the sample size needed to distinguish between second order effects shows that this value is close to but larger than the values of the current datasets these results provide a unified framework for future studies and clarify the relevant parameters at play in the control of cell division

integration of langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions efficient and accurate integration of stochastic partial differential equations with multiplicative noise can be obtained through a split step scheme which separates the integration of the deterministic part from that of the stochastic part the latter being performed by sampling exactly the solution of the associated fokker planck equation we demonstrate the computational power of this method by applying it to the most absorbing phase transitions for which langevin equations have been proposed this provides precise estimates of the associated scaling exponents clarifying the classification of these nonequilibrium problems and confirms or refutes some existing theories

lee distance and topological properties of k ary n cubes in this paper we consider various topological properties of a k ary n cube q sub n sup k using lee distance we feel that lee distance is a natural metric for defining and studying a q sub n sup k after defining a q sub n sup k graph using lee distance we show how to find all disjoint paths between any two nodes given a sequence of radix k numbers a function mapping the sequence to a gray code sequence is presented and this function is used to generate a hamiltonian cycle embedding the graph of a mesh and the graph of a binary hypercube into the graph of a q sub n sup k is considered using a k ary gray code we show the embedding of a k n sub 1 spl times k n sub 2 spl times spl times k n sub m dimensional mesh into a q sub n sup k where n spl sigma sub i l sup m n sub i then using a single digit 4 ary reflective gray code we demonstrate embedding a q sub n into q sub n 2 sup 4 we look at how lee distance may be applied to the problem of resource placement in a q sub n sup k by using a lee distance error correcting code although the results in this paper are only preliminary lee distance error correcting codes have not been applied previously to this problem finally we consider how lee distance can be applied to message routing and single node broadcasting in a q sub n sup k in this section we present two single node broadcasting algorithms that are optimal when single port and multi port i o is used

comparing non nested linear models abstract i consider the usual linear model situation except that there are two possible linear subspaces that may contain the true mean vector and neither of the two subspaces is nested within the other approximate confidence intervals are developed for the difference in mean squared error mse of prediction using the two models not assuming that either model is necessarily correct the confidence intervals are based on parametric bootstrap methods applied to mallows s cp estimate of the difference in mse this approach is shown to relate closely to hotelling s test comparing two simple linear regressions in the simplest case the problem is equivalent to finding a confidence interval for the product of the means of two independent normal observations each with variance one

universality in stochastic exponential growth recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means an analogous result holds for the division time distributions a model is needed to delineate the minimal requirements for these scaling behaviors we formulate a microscopic theory of stochastic exponential growth as a master equation that accounts for these observations in contrast to existing quantitative models of stochastic exponential growth e g the black scholes equation or geometric brownian motion our model the stochastic hinshelwood cycle shc is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next by finding exact analytical solutions to the shc and the corresponding first passage time problem we uncover universal signatures of fluctuations in exponential growth and division the model makes minimal assumptions and we describe how more complex reaction networks can reduce to such a cycle we thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology finance technology and population growth

kinetics of fragmentation a general discussion of the kinetics of continuous irreversible fragmentation processes is presented for a linear process where particle breakup is driven by an external force the authors develop a scaling theory to describe the evolution of the cluster size distribution they treat the general case where the breakup rate of a cluster of mass x varies as xlambda when lambda 0 corresponding to larger clusters more likely to break up the scaled cluster size distribution phi x decays with the scaled mass x as x 2 exp axlambda as x for small mass phi x has the log normal form exp a ln2 x if the breakup kernel has a small size cutoff while phi x has a power law tail in the absence of a cutoff they also show that a conventional scaling picture applies only for the case lambda 0 for lambda 0 they develop an alternative formulation for the cluster size distribution in which the typical mass scale is determined by the initial condition in this regime they also investigate the nature of a shattering transition where mass is lost to a dust phase of zero mass particles they also study the kinetics of a nonlinear collision induced fragmentation process they analyse the asymptotic behaviour of a simple minded class of models in which a two particle collision results in either 1 both particles splitting into two equal pieces 2 only the larger particle splitting in two or 3 only the smaller particle splitting they map out the kinetics of these models by scaling arguments and by analytic and numerical solutions of the rate equations scaling is found to hold for different ranges of homogeneity index for the three models

scaling laws governing stochastic growth and division of single bacterial cells uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge using a unique combination of technologies that yields unprecedented statistical precision we find that the sizes of individual caulobacter crescentus cells increase exponentially in time we also establish that they divide upon reaching a critical multiple 1 8 of their initial sizes rather than an absolute size we show that when the temperature is varied the growth and division timescales scale proportionally with each other over the physiological temperature range strikingly the cell size and division time distributions can both be rescaled by their mean values such that the condition specific distributions collapse to universal curves we account for these observations with a minimal stochastic model that is based on an autocatalytic cycle it predicts the scalings as well as specific functional forms for the universal curves our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes a single temperature dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions

perfect codes for metrics induced by circulant graphs an algebraic methodology for defining new metrics over two dimensional signal spaces is presented in this work we have mainly considered quadrature amplitude modulation qam constellations which have previously been modeled by quotient rings of gaussian integers the metric over these constellations based on the distance concept in circulant graphs is one of the main contributions of this work a detailed analysis of some degree four circulant graphs has allowed us to detail the weight distribution for these signal spaces a new family of perfect codes over gaussian integers will be defined and characterized by providing a solution to the perfect t dominating set problem over the circulant graphs presented finally we will show how this new metric can be extended to other signal sets by considering hexagonal constellations and circulant graphs of degree six

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

classifications and existence of positive solutions of higher order nonlinear neutral differential equations in this paper necessary and sufficient conditions for the existence and classification of positive solutions of the higher order neutral difference email protected email protected kx email protected i 1 mp n ix n t i f n x n s 1 x n s l 0are obtained where r n 0 p n i 0 i 1 2 m and f n s 1 s l is continuous with respect to n and s j j 1 l

optimal distance networks of low degree for parallel computers the authors introduce and study a family of interconnection schemes the midimew networks based on circulant graphs of degree 4 a family of such circulants is determined and shown to be optimal with respect to two distance parameters simultaneously namely maximum distance and average distance among all circulants of degree 4 these graphs are regular point symmetric and maximally connected and one such optimal graph exists for any given number of nodes the proposed interconnection schemes consist of mesh connected networks with wrap around links and are isomorphic to the optimal distance circulants previously considered ways to construct one such network for any number of nodes are shown their good properties to build interconnection schemes for multicomputers are examined and some interesting particular cases are discussed the problem of routing is also addressed and a basic algorithm is provided which is adequate for implementing the routing policy required to convey messages traversing shortest paths between nodes

eventually positive solutions of higher order nonlinear neutral differential equations abstract in this paper some results of ouyang et al ouyang li tang classifications and existence of positive solutions of higher order nonlinear neutral differential equations appl math comput 148 2004 105 120 are improved

sample and population exponents of generalized taylor s law has been verified extensively in ecology where it applies to population abundance physics and other natural sciences its ubiquitous empirical verification suggests a context independent mechanism sample exponents b measured empirically via the scaling of sample mean and variance typically cluster around the value b 2 some theoretical models of population growth however predict a broad range of values for the population exponent b pertaining to the mean and variance of population density depending on details of the growth process is the widely reported sample exponent b 2 the result of ecological processes or could it be a statistical artifact here we apply large deviations theory and finite sample arguments to show exactly that in a broad class of growth models the sample exponent is b 2 regardless of the underlying population exponent we derive a generalized tl in terms of sample and population exponents bjk for the scaling of the kth vs the jth cumulants the sample exponent bjk depends predictably on the number of samples and for finite samples we obtain bjk k j asymptotically in time a prediction that we verify in two empirical examples thus the sample exponent b 2 may indeed be a statistical artifact and not dependent on population dynamics under conditions that we specify exactly given the broad class of models investigated our results apply to many fields where tl is used although inadequately understood

exponential trajectories cell size fluctuations and the adder property in bacteria follow from simple chemical dynamics and division control experiments on steady state bacterial cultures have uncovered several quantitative regularities at the system level these include first the exponential growth of cell size with time and the balanced growth of intracellular chemicals between cell birth and division which are puzzling given the nonlinear and decentralized chemical dynamics in the cell we model a cell as a set of chemical populations undergoing nonlinear mass action kinetics in a container whose volume is a linear function of the chemical populations this turns out to be a special class of dynamical systems that generically has attractors in which all populations grow exponentially with time at the same rate this explains exponential balanced growth of bacterial cells without invoking any regulatory mechanisms and suggests that this could be a robust property of protocells as well second we consider the hypothesis that cells commit themselves to division when a certain internal chemical population reaches a threshold of n molecules we show that this hypothesis leads to a simple explanation of some of the variability observed across cells in a bacterial culture in particular it reproduces the adder property of cell size fluctuations observed recently in e coli the observed correlations among interdivision time birth volume and added volume in a generation and the observed scale of the fluctuations cv 10 30 when n is between 10 and 100 third upon including a suitable regulatory mechanism that optimizes the growth rate of the cell the model reproduces the observed bacterial growth laws including the dependence of the growth rate and ribosomal protein fraction on the medium thus the models provide a framework for unifying diverse aspects of bacterial growth physiology under one roof they also suggest new questions for experimental and theoretical enquiry

codes over tori in this correspondence it is shown how the elements of finite fields when mapped on the surface of a torus can be used for block coding over a three dimensional signal space the block codes are useful for data transmission using the recently defined mannheim distance

quasi perfect codes from cayley graphs over integer rings the problem of searching for perfect codes has attracted great attention since the paper by golomb and welch in which the existence of these codes over lee metric spaces was considered since perfect codes are not very common the problem of searching for quasi perfect codes is also of great interest in this aspect also quasi perfect lee codes have been considered for 2 d and 3 d lee metric spaces in this paper constructive methods for obtaining quasi perfect codes over metric spaces modeled by means of gaussian and eisenstein jacobi integers are given the obtained codes form ideals of the integer ring thus preserving the property of being geometrically uniform codes moreover they are able to correct more error patterns than the perfect codes which may properly be used in asymmetric channels therefore the results in this paper complement the constructions of perfect codes previously done for the same integer rings finally decoding algorithms for the quasi perfect codes obtained in this paper are provided and the relationship of the codes and the lee metric ones is investigated

discriminating between weibull distributions and log normal distributions emerging in branching processes we consider the yule type multiplicative growth and division process and describe the ubiquitous emergence of weibull and log normal distributions in a single framework with the help of the integral transform and series expansion we show that both distributions serve as asymptotic solutions of the time evolution equation for the branching process in particular the maximum likelihood method is employed to discriminate between the emergence of the weibull distribution and that of the log normal distribution further the detailed conditions for the distinguished emergence of the weibull distribution are probed it is observed that the emergence depends on the manner of the division process for the two different types of distribution numerical simulations are also carried out confirming the results obtained analytically

transformation theory how normal is a family of distributions this paper concerns the following question if x is a real valued random variate having a one parameter family of distributions mathscr f to what extent can mathscr f be normalized by a monotone transformation in other words does there exist a single transformation y g x such that y has nearly a normal distribution for every distribution of x in mathscr f the theory developed answers the question without considering the form of g at all in those cases where the answer is positive simple formulas for calculating g are given the paper also considers the relationship between normalization and variance stabilization

stochastic modeling of cell growth with symmetric or asymmetric division we consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources volume or damaged proteins in particular symmetrically or asymmetrically between its progeny assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions we find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies moreover we apply an asymptotic analysis to elucidate the conditions under which the stable distribution when it exists has a power law tail finally we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution we also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control in the appendixes motivated by the asymmetric division of cell volume in saccharomyces cerevisiae we extend our results to the case wherein mother and daughter cells follow different growth policies

origin of lognormal like distributions with a common width in a growth and division process lognormal statistical distributions are observed in a variety of scientific fields the widths of these distributions in the log scale are often similar but the underlying mechanism that maintains these widths within a small range has not been well explained we show that a stochastic process of halving followed by addition can yield a stationary distribution that resembles the universal lognormal distribution with a certain width the mechanism that we propose here would provide insight into the essence of why lognormal like distributions in many systems have a common width

classifications and existence of positive solutions of higher order nonlinear neutral difference equations in this paper necessary and sufficient conditions for the existence and classification of positive solutions of the higher order neutral difference equation dr n d kx n i 1 mp n ix n t i

optimal stochastic restart renders fluctuations in first passage times universal stochastic restart may drastically reduce the expected run time of a computer algorithm expedite the completion of a complex search process or increase the turnover rate of an enzymatic reaction these diverse first passage time fpt processes seem to have very little in common but it is actually quite the other way around here we show that the relative standard deviation associated with the fpt of an optimally restarted process i e one that is restarted at a constant nonzero rate which brings the mean fpt to a minimum is always unity we interpret further generalize and discuss this finding and the implications arising from it

law of corresponding states for open collaborations we study the relation between number of contributors and product size in wikipedia and github in contrast to traditional production this is strongly probabilistic but is characterized by two quantitative nonlinear laws a power law bound to product size for increasing number of contributors and the universal collapse of rescaled distributions a variant of the random energy model shows that both laws are due to the heterogeneity of contributors and displays an intriguing finite size scaling property with no equivalent in standard systems the analysis uncovers the right intensive densities enabling the comparison of projects with different numbers of contributors on equal grounds we use this property to expose the detrimental effects of conflicting interactions in wikipedia

probabilistic structure of the distance between tributaries of given size in river networks we analyze the distribution of the distances between tributaries of a given size or of sizes larger than a given area draining along either an open boundary or the mainstream of a river network by proposing a description of the distance separating prescribed merging contributing areas we also address related variables like mean or bankfull flow rates and channel and riparian area widths which are derived under a set of reasonable hydrologic assumptions the importance of such distributions lies in their ecological hydrologic and geomorphic implications on the spreading of species along the ecological corridor defined by the river network and on the propagation of infections due to water borne diseases particularly in view of exact theoretical predictions explicitly using the alongstream distribution of confluences carrying a given flow use is made here of real river networks suitably extracted from digital elevation models optimal channel networks and exactly solved tree like constructs like the peano and the scheidegger networks the results obtained redefine theoretically in a coherent and general manner and verify observationally the distribution function of the above distances and thus provide the general probabilistic structure of tributaries in river networks specifically we find that the probability of exceedence of the alongstream distance d of tributaries of size larger than a has the explicit form p d exp cd a h 1 h where c is a constant that depends on the choice of boundary conditions and h 1 is the hurst exponent

individuality and universality in the growth division laws of single e coli cells the mean size of exponentially dividing escherichia coli cells in different nutrient conditions is known to depend on the mean growth rate only however the joint fluctuations relating cell size doubling time and individual growth rate are only starting to be characterized recent studies in bacteria reported a universal trend where the spread in both size and doubling times is a linear function of the population means of these variables here we combine experiments and theory and use scaling concepts to elucidate the constraints posed by the second observation on the division control mechanism and on the joint fluctuations of sizes and doubling times we found that scaling relations based on the means collapse both size and doubling time distributions across different conditions and explain how the shape of their joint fluctuations deviates from the means our data on these joint fluctuations highlight the importance of cell individuality single cells do not follow the dependence observed for the means between size and either growth rate or inverse doubling time our calculations show that these results emerge from a broad class of division control mechanisms requiring a certain scaling form of the division hazard rate function which defines the probability rate of dividing as a function of measurable parameters this model free approach gives a rationale for the universal body size distributions observed in microbial ecosystems across many microbial species presumably dividing with multiple mechanisms additionally our experiments show a crossover between fast and slow growth in the relation between individual cell growth rate and division time which can be understood in terms of different regimes of genome replication control

scaling in ecosystems and the linkage of macroecological laws scaling provides an elegant framework for understanding power law behavior and deducing relationships between critical exponents we demonstrate that scaling theory can be generalized to develop a framework for the analysis of diverse empirical macroecological relationships traditionally treated as independent our mathematical arguments predict links between the species area relationship the relative species abundance and community size spectra in excellent accord with empirical data

edge disjoint hamiltonian cycles in gaussian networks gaussian networks are degree four symmetric networks and these are designed based on the concept of gaussian integers the gaussian network can be described in terms of a generator alpha a bi where a and b are integers and i sqrt 1 when gcd a b 1 how to find edge disjoint hamiltonian cycles has been shown before in this paper for any generator alpha a bi even when gcd a b d 1 how to obtain two edge disjoint hamiltonian cycles in these networks is described

on parameter transformations and interval estimation summary parameterizations which reduce the asymptotic bias and skewness of various pivotal quantities arising in large sample theory are discussed for models depending on an unknown scalar parameter transformation formulae by which such parameterizations can be obtained are derived and these formulae extend those for one dimensional curved exponential families given by hougaard 1982 to assess the accuracy of normal approximations to the distributions of the pivots their second order properties are considered and comparisons with the signed square root of the likelihood ratio statistic are drawn

a measure of data collapse for scaling data collapse is a way of establishing scaling and extracting associated exponents in problems showing self similar or self affine characteristics as for example in equilibrium or non equilibrium phase transitions in critical phases in dynamics of complex systems and many others we propose a measure to quantify the nature of data collapse via a minimization of this measure the exponents and their error bars can be obtained the procedure is illustrated by considering finite size scaling near phase transitions and quite strikingly recovering the exact exponents

l networks a topological model for regular 2d interconnection networks a complete family of cayley graphs of degree four denoted as l networks is considered in this paper l networks are 2d mesh based topologies with wrap around connections l networks constitute a graph based model which englobe many previously proposed 2d interconnection networks some of them have been extensively used in the industry as the underlying topology for parallel and distributed computers of different scales tori twisted and doubly twisted tori toroidal diagonal meshes chordal rings and circulant graphs are among others members of the l network family therefore many results obtained in previous studies on these networks can be deduced from the general framework presented in this work in addition the network model presented in this work allows for new results on the domain of low degree interconnection networks particularly closed expressions for the graph distance properties have been derived and an optimal routing algorithm of constant complexity is provided since symmetry has a big impact on network performance we have also identified which l networks are symmetric by studying their group of automorphisms finally a very simple model that predicts the performance of l networks is also presented such model has been contrasted with empirical evaluation

modeling toroidal networks with the gaussian integers in this paper we consider a broad family of toroidal networks denoted as gaussian networks which include many previously proposed and used topologies we will define such networks by means of the gaussian integers the subset of the complex numbers with integer real and imaginary parts nodes in gaussian networks are labeled by gaussian integers which confer these topologies an algebraic structure based on quotient rings of the gaussian integers in this sense gaussian integers reveal themselves as the appropriate tool for analyzing and exploiting any type of toroidal network using this algebraic approach we can characterize the main distance related properties of gaussian networks providing closed expressions for their diameter and average distance in addition we solve some important applications like unicast and broadcast packet routing or the perfect placement of resources over these networks