linear time nearest point algorithms for coxeter lattices the coxeter lattices are a family of lattices containing many of the important lattices in low dimensions this includes an e 7 e 8 and their duals an e 7 and e 8 we consider the problem of finding a nearest point in a coxeter lattice we describe two new algorithms one with worst case arithmetic complexity o nlogn and the other with worst case complexity o n where n is the dimension of the lattice we show that for the particular lattices an and an the algorithms are equivalent to nearest point algorithms that already exist in the literature

critical time scales for advection diffusion reaction processes the concept of local accumulation time lat was introduced by berezhkovskii and co workers to give a finite measure of the time required for the transient solution of a reaction diffusion equation to approach the steady state solution a m berezhkovskii c sample and s y shvartsman biophys j 99 l59 2010 a m berezhkovskii c sample and s y shvartsman phys rev e 83 051906 2011 such a measure is referred to as a critical time here we show that lat is in fact identical to the concept of mean action time mat that was first introduced by mcnabb a mcnabb and g c wake ima j appl math 47 193 1991 although mcnabb s initial argument was motivated by considering the mean particle lifetime mplt for a linear death process he applied the ideas to study diffusion we extend the work of these authors by deriving expressions for the mat for a general one dimensional linear advection diffusion reaction problem using a combination of continuum and discrete approaches we show that mat and mplt are equivalent for certain uniform to uniform transitions these results provide a practical interpretation for mat by directly linking the stochastic microscopic processes to a meaningful macroscopic time scale we find that for more general transitions the equivalence between mat and mplt does not hold unlike other critical time definitions we show that it is possible to evaluate the mat without solving the underlying partial differential equation pde this makes mat a simple and attractive quantity for practical situations finally our work explores the accuracy of certain approximations derived using mat showing that useful approximations for nonlinear kinetic processes can be obtained again without treating the governing pde directly

non semi regular quantum groups coming from number theory in this paper we study c algebraic quantum groups obtained through the bicrossed product construction examples using groups of adeles are given and they provide the first examples of locally compact quantum groups which are not semi regular the crossed product of the quantum group acting on itself by translations does not contain any compact operator we describe all corepresentations of these quantum groups and the associated universal c algebras on the way we provide several remarks on c algebraic properties of quantum groups and their actions

multi stage robust chinese remainder theorem it is well known that the traditional chinese remainder theorem crt is not robust in the sense that a small error in a remainder may cause a large reconstruction error a robust crt was recently proposed for a special case when the greatest common divisor gcd of all the moduli is more than 1 and the remaining integers factorized by the gcd are co prime it basically says that the reconstruction error is upper bounded by the remainder error level tau if tau is smaller than a quarter of the gcd of all the moduli in this paper we consider the robust reconstruction problem for a general set of moduli we first present a necessary and sufficient condition on the remainder errors with a general set of moduli and also a corresponding robust reconstruction method this can be thought of as a single stage robust crt we then propose a two stage robust crt by grouping the moduli into several groups as follows first the single stage robust crt is applied to each group then with these robust reconstructions from all the groups the single stage robust crt is applied again across the groups this is easily generalized to multi stage robust crt with this two stage robust crt the robust reconstruction holds even when the remainder error level tau is above the quarter of the gcd of all the moduli and an algorithm on how to group a set of moduli for a better reconstruction robustness is proposed in some special cases

from a discrete to a continuous model of biological cell movement the process by which one may take a discrete model of a biophysical process and construct a continuous model based upon it is of mathematical interest as well as being of practical use in this work we take the extended potts model applied to biological cell movement to its continuous limit beginning with a single cell moving in one dimension on a lattice and obeying potts model rules of movement we develop an expression for the diffusion coefficient of a collection of noninteracting cells which depends explicitly on the potts model parameters we show how this coefficient varies when the potts parameters for cell membrane elasticity and cell medium adhesion are varied and perform computer simulations which support our theoretical result we explain the relationship between the probability of occupancy of lattice points and the density profile in the continuous limit and extend our analysis by including interactions between the cells in so doing we are able to develop a set of coupled ordinary differential equations showing the evolution of a density profile in the presence of significant cell cell adhesion and show how increases in the strength of this adhesion modulates diffusion in so doing we develop some insights into how continuous models of physical systems can be based upon discrete models which describe the same system

selecting wavelengths for least squares range estimation we consider the problem of estimating the distance or range between two locations by measuring the phase of multiple sinusoidal signals transmitted between the locations traditional estimators developed for optical interferometry include the beat wavelength and excess fractions methods more recently estimators based on the chinese remainder theorem crt and least squares have appeared recent research suggests the least squares estimator to be the most accurate in many cases the accuracy of all of these range estimators depends upon the wavelengths chosen this leads to the problem of selecting wavelengths that maximize accuracy procedures for selecting wavelengths for the beat wavelength and excess fractions methods have previously been described but procedures for the crt and least squares estimators are yet to be developed in this paper we develop an algorithm to automatically select wavelengths for use with the least square range estimator the algorithm minimizes an optimization criterion connected with the mean square error interesting properties of a particular class of lattices simplify the criterion allowing minimization by depth first search monte carlo simulations indicate that wavelengths that minimize the criterion can result in considerably more accurate range estimates than wavelengths selected by ad hoc means

full factors and co amenable inclusions we show that if m is a full factor and n subset m is a co amenable subfactor with expectation then n is also full this answers a question of popa from 1986 we also generalize a theorem of tomatsu by showing that if m is a full factor and sigma g curvearrowright m is an outer action of a compact group g then sigma is automatically minimal and m g is a full factor which has w spectral gap in m finally in the appendix we give a proof of the fact that several natural notions of co amenability for an inclusion n subset m of von neumann algebras are equivalent thus closing the cycle of implications given in anantharaman delaroche s paper in 1995

some prime factorization results for type ii1 factors we prove several unique prime factorization results for tensor products of type ii1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected lie groups of real rank 1 in particular we show that if mathcal r overline otimes mathcal l mathbb f r 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f r m is isomorphic to a subfactor in mathcal r overline otimes mathcal l mathbb f s 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f s n for some 2 ri sj then m n

around property t for quantum groups we study property t for locally compact quantum groups providing several new characterisations especially related to operator algebraic ergodic theory quantum property t is described in terms of the existence of various kazhdan type pairs and some earlier structural results of kyed chen and ng are strengthened and generalised for second countable discrete unimodular quantum groups with low duals property t is shown to be equivalent to property t 1 1 of bekka and valette this is used to extend to this class of quantum groups classical theorems on typical representations due to kerr and pichot and on connections of property t with spectral gaps due to li and ng and with strong ergodicity of weakly mixing actions on a particular von neumann algebra due to connes and weiss finally we discuss in the appendix equivalent characterisations of the notion of a quantum group morphism with dense image

a valued semicircular systems abstract to a von neurnann algebra a and a set of linear maps ij a a i j i such that a ij ij i a a b l2 i is normal and completely positive we associate a von neumann algebra a this von neumann algebra is generated by a and an a valued semicircular system xi i i associated to in many cases there is a faithful conditional expectation e a a if a is tracial then under certain assumptions on a also has a trace one can think of the construction a as an analogue of a crossed product construction we show that most known algebras arising in free probability theory can be obtained from the complex field by iterating the construction of a particular interest are free krieger algebras which by analogy with crossed products and ordinary krieger factors are defined to be algebras of the form l 0 1 the cores of free araki woods factors are free krieger algebras we study the free krieger algebras and as a result obtain several non isomorphism results for free araki woods factors as another source of classification results for free araki woods factors we compute the invariant of connes for free products of von neumann algebras this computation generalizes earlier work on computation of t s and sd invariants for free product algebras

from a discrete to a continuum model of cell dynamics in one dimension multiscale modeling is emerging as one of the key challenges in mathematical biology however the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions for example at the cellular scale how can the appropriate discrete cell level model be identified in a given context additionally how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior in order to begin to address such questions we consider a discrete one dimensional cell based model in which cells are assumed to interact via linear springs from the discrete equations of motion the continuous rouse p e rouse j chem phys 21 1272 1953 model is obtained this formalism readily allows the definition of a cell number density for which a nonlinear fast diffusion equation is derived excellent agreement is demonstrated between the continuum and discrete models subsequently via the incorporation of cell division we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail in the limit of stiff springs where cells can be considered to be incompressible we show that cell velocity can be directly related to cell production this assumption is frequently made in the literature but our derivation places limits on its validity finally the model is compared with a model of a similar form recently derived for a different discrete cell based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models

poisson boundary of the dual of suq n we prove that for any non trivial product type action of su q n 0 q 1 on an itpfi factor n the relative commutant is isomorphic to the algebra l of bounded measurable functions on the quantum flag manifold this is equivalent to the computation of the poisson boundary of the dual discrete quantum group the proof relies on a connection between the poisson integral and the berezin transform our main technical result says that a sequence of berezin transforms defined by a random walk on the dominant weights of su n converges to the identity on the quantum flag manifold

deformation of operator algebras by borel cocycles abstract assume that we are given a coaction of a locally compact group g on a c algebra a and a t valued borel 2 cocycle on g motivated by the approach of kasprzak to rieffel s deformation we define a deformation a of a among other properties of a we show that a k l 2 g is canonically isomorphic to a g g this together with a slight extension of a result of echterhoff et al implies that for groups satisfying the baum connes conjecture the k theory of a remains invariant under homotopies of

tracking and localizing moving targets in the presence of phase measurement ambiguities when tracking a target using phase only signal returns range ambiguities due to the modulo 2 in measured signal phases are a major issue standard approaches to such problems would typically involve the use of diophantine equations in this paper a simpler and robust solution is examined which uses look up tables defined between the phase measurement and target location spaces to determine the phase measurement mapping we show first that when the target motion is significant between data sampling intervals the location ambiguity can be resolved over time via known target in cluster tracking techniques this method determines the optimal allocation of location with respect to phase measurements relative to the quantization of look up table values second when the target is undergoing micromotions jitter which results in the same collection of candidate locations from phase measurements over time the location ambiguity can be resolved using a novel phase distribution discrimination method in this method a probability density function of the ambiguous phase only measurement is derived that takes both sensor noise and target motion distributions into account based on directional statistics optimal locations are inferred from such distributions examples are given to demonstrate the effectiveness of these proposed methods

2 cocycles and twisting of kac algebras we describe the twisting construction with the help of 2 cocycles on hopf von neumann and george kac algebras we show that twisted kac algebras are again kac algebras using this construction we give a wide class of new quantizations of the heisenberg group and describe several series of non trivial finite dimensional hopf algebras kac algebras of dimensions 4n and as twisting of finite groups

classification of minimal actions of a compact kac algebra with amenable dual we show the uniqueness of minimal actions of a compact kac algebra with amenable dual on the afd factor of type ii1 this particularly implies the uniqueness of minimal actions of a compact group our main tools are a rohlin type theorem the 2 cohomology vanishing theorem and the evans kishimoto type intertwining argument

generalized cahn hilliard equation for biological applications recently we considered a stochastic discrete model which describes fronts of cells invading a wound e khain l m sander and c m schneider mizell j stat phys 128 209 2007 in the model cells can move proliferate and experience cell cell adhesion in this work we focus on a continuum description of this phenomenon by means of a generalized cahn hilliard equation gch with a proliferation term as in the discrete model there are two interesting regimes for subcritical adhesion there are propagating pulled fronts similar to those of the fisher kolmogorov equation the problem of front velocity selection is examined and our theoretical predictions are in the good agreement with a numerical solution of the gch equation for supercritical adhesion there is a nontrivial transient behavior where density profile exhibits a secondary peak to analyze this regime we investigated relaxation dynamics for the cahn hilliard equation without proliferation we found that the relaxation process exhibits self similar behavior the results of continuum and discrete models are in good agreement with each other for the different regimes we analyzed

the boundary of universal discrete quantum groups exactness and factoriality we study the c algebras and von neumann algebras associated with the universal discrete quantum groups they give rise to full prime factors and simple exact c algebras the main tool in our work is the study of an amenable boundary action yielding the akemann ostrand property finally this boundary can be identified with the martin or the poisson boundary of a quantum random walk

compressions of free products of von neumann algebras a reduction formula for compressions of von neumann algebra ii 1 factors arising as free products is proved this shows that the fundamental group is bf r for some such algebras additionally by taking a sort of free product with an unbounded semicircular element continuous one parameter groups of trace scaling automorphisms on ii infty factors are constructed this produces type iii 1 factors with core mathcal m otimes b mathcal h where mathcal m can be a full ii 1 factor without the haagerup approximation property

exact and robust reconstructions of integer vectors based on multidimensional chinese remainder theorem md crt the robust chinese remainder theorem crt has been recently proposed for robustly reconstructing a large nonnegative integer from erroneous remainders it has found many applications in signal processing including phase unwrapping and frequency estimation under sub nyquist sampling motivated by the applications in multidimensional md signal processing in this article we propose the md crt and robust md crt for integer vectors specifically by rephrasing the abstract crt for rings in number theoretic terms we first derive the md crt for integer vectors with respect to a general set of integer matrix moduli which provides an algorithm to uniquely reconstruct an integer vector from its remainders if it is in the fundamental parallelepiped of the lattice generated by a least common right multiple of all the moduli for some special forms of moduli we present explicit reconstruction formulae moreover we derive the robust md crt for integer vectors when the remaining integer matrices of all the moduli left divided by their greatest common left divisor gcld are pairwise commutative and coprime two different reconstruction algorithms are proposed and accordingly two different conditions on the remainder error bound for the reconstruction robustness are obtained which are related to a quarter of the minimum distance of the lattice generated by the gcld of all the moduli or the smith normal form of the gcld

optimum statistical estimates in conditions of ambiguity an ambiguity problem arises if a distance is measured by observing phase shift of signals when the range of the measured distance is greater than the wavelength of the signals used this ambiguity generally can be resolved by pumping extra information into the system a classical estimation problem is the obtained at the expense of reduced autonomy of the estimator due to the demand for external information not inherent to the system the interval lambda of the unambiguous estimates can be considerably extended using observations of several different wavelengths lambda sub i this yields lambda as the least common multiple of all lambda sub i a method of developing optimum estimation rules for this case is introduced optimum estimation rules for some typical cases with gaussian observation errors are also developed

a robust generalized chinese remainder theorem for two integers a generalized chinese remainder theorem crt for multiple integers from residue sets has been studied recently where the correspondence between the remainders and the integers in each residue set modulo several moduli is not known a robust crt has also been proposed lately to robustly reconstruct a single integer from its erroneous remainders in this paper we consider the reconstruction problem of two integers from their residue sets where the remainders not only are out of order but also may have errors we prove that two integers can be robustly reconstructed if their remainder errors are less than m 8 where m is the greatest common divisor of all the moduli we also propose an efficient reconstruction algorithm finally we present some simulations to verify the efficiency of the proposed algorithm this paper is motivated from and has applications in the determination of multiple frequencies from multiple undersampled waveforms

a semi finite algebra associated to a subfactor planar algebra we canonically associate to any planar algebra two type ii factors m the subfactors constructed previously by the authors in guionnet et al 2010 6 are isomorphic to compressions of m to finite projections we show that each m is isomorphic to an amalgamated free product of type i von neumann algebras with amalgamation over a fixed discrete type i von neumann subalgebra in the finite depth case existing results in the literature imply that m m is the amplification a free group factor on a finite number of generators as an application we show that the factors mj constructed in guionnet et al in press 6 are isomorphic to interpolated free group factors l f rj rj 1 2 2j 1 i where 2 is the index of the planar algebra and i is its global index other applications include computations of laws of jones wenzl projections

approximation properties and absence of cartan subalgebra for free araki woods factors abstract we show that all the free araki woods factors h r u t have the complete metric approximation property using ozawa popa s techniques we then prove that every nonamenable subfactor n h r u t which is the range of a normal conditional expectation has no cartan subalgebra we finally deduce that the type iii1 factors constructed by connes in the 70s can never be isomorphic to any free araki woods factor which answers a question of shlyakhtenko and vaes

multi species simple exclusion processes abstract a motility mechanism based on a simple exclusion process where the movement of discrete agents on a lattice is either unbiased symmetric or biased asymmetric is considered estimates of diffusivities from tracking data do not describe the population level response of the system this mismatch between the individual level and population level behaviour can be resolved by averaging the individual level mechanism in terms of an expected site occupancy new insight into simple exclusion processes is obtained by representing the system as a series of interacting subpopulations this formalism leads to a system of nonlinear advection diffusion equations which can be interpreted in terms of the agent fluxes these interactions have consequences for both agent based modelling and continuum modelling in cell biology such as tracking subpopulations of cells within a total cell population

canonical extension of actions of locally compact quantum groups abstract in this paper we generalize the notion of the canonical extension of automorphisms of von neumann algebras to the case of actions of locally compact quantum groups in the sense of kustermans and vaes various expected properties will be shown to hold for this new canonical extension as an application we describe the flow of weights of the crossed product of a type iii factor by some special action of a discrete kac algebra

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

when push comes to shove exclusion processes with nonlocal consequences abstract stochastic agent based models are useful for modelling collective movement of biological cells lattice based random walk models of interacting agents where each site can be occupied by at most one agent are called simple exclusion processes an alternative motility mechanism to simple exclusion is formulated in which agents are granted more freedom to move under the compromise that interactions are no longer necessarily local this mechanism is termed shoving a nonlinear diffusion equation is derived for a single population of shoving agents using mean field continuum approximations a continuum model is also derived for a multispecies problem with interacting subpopulations which either obey the shoving rules or the simple exclusion rules numerical solutions of the derived partial differential equations compare well with averaged simulation results for both the single species and multispecies processes in two dimensions while some issues arise in one dimension for the multispecies case

a stochastic model for wound healing we present a discrete stochastic model which represents many of the salient features of the biological process of wound healing the model describes fronts of cells invading a wound we have numerical results in one and two dimensions in one dimension we can give analytic results for the front speed as a power series expansion in a parameter p that gives the relative size of proliferation and diffusion processes for the invading cells in two dimensions the model becomes the eden model for p 1 in both one and two dimensions for small p front propagation for this model should approach that of the fisher kolmogorov equation however as in other cases this discrete model approaches fisher kolmogorov behavior slowly

an algorithm to compute the nearest point in the lattice a_ n the lattice a n is an important lattice because of its covering properties in low dimensions clarkson described an algorithm to compute the nearest lattice point in a n that requires o n log n arithmetic operations in this correspondence we describe a new algorithm while the complexity is still o n log n it is significantly simpler to describe and verify in practice we find that the new algorithm also runs faster

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

quantum groups property t and weak mixing for second countable discrete quantum groups and more generally second countable locally compact quantum groups with trivial scaling group we show that property t is equivalent to every weakly mixing unitary representation not having almost invariant vectors this is a generalization of a theorem of bekka and valette from the group setting and was previously established in the case of low dual by daws skalski and viselter our approach uses spectral techniques and is completely different from those of bekka valette and daws skalski viselter by a separate argument we furthermore extend the result to second countable nonunimodular locally compact quantum groups which are shown in particular not to have property t generalizing a theorem of fima from the discrete setting we also obtain quantum group versions of characterizations of property t of kerr and pichot in terms of the baire category theory of weak mixing representations and of connes and weiss in terms of the prevalence of strongly ergodic actions

the norm of polynomials in large random and deterministic matrices let bf x n x 1 n ldots x p n be a family of n n independent normalized random matrices from the gaussian unitary ensemble we state sufficient conditions on matrices bf y n y 1 n ldots y q n possibly random but independent of xn for which the operator norm of p bf x n bf y n bf y n converges almost surely for all polynomials p limits are described by operator norms of objects from free probability theory taking advantage of the choice of the matrices yn and of the polynomials p we get for a large class of matrices the no eigenvalues outside a neighborhood of the limiting spectrum phenomena we give examples of diagonal matrices yn for which the convergence holds convergence of the operator norm is shown to hold for block matrices even with rectangular gaussian blocks a situation including non white wishart matrices and some matrices encountered in mimo systems

a robust chinese remainder theorem with its applications in frequency estimation from undersampled waveforms the chinese remainder theorem crt allows to reconstruct a large integer from its remainders modulo several moduli in this paper we propose a robust reconstruction algorithm called robust crt when the remainders have errors we show that using the proposed robust crt the reconstruction error is upper bounded by the maximal remainder error range named remainder error bound if the remainder error bound is less than one quarter of the greatest common divisor gcd of all the moduli we then apply the robust crt to estimate frequencies when the signal waveforms are undersampled multiple times it shows that with the robust crt the sampling frequencies can be significantly reduced

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

a closed form robust chinese remainder theorem and its performance analysis chinese remainder theorem crt reconstructs an integer from its multiple remainders that is well known not robust in the sense that a small error in a remainder may cause a large error in the reconstruction a robust crt has been recently proposed when all the moduli have a common factor and the robust crt is a searching based algorithm and no closed from is given in this paper a closed form robust crt is proposed and a necessary and sufficient condition on the remainder errors for the closed form robust crt to hold is obtained furthermore its performance analysis is given it is shown that the reason for the robustness is from the remainder differential process in both searching based and our proposed closed form robust crt algorithms which does no exist in the traditional crt we also propose an improved version of the closed form robust crt finally we compare the performances of the traditional crt the searching based robust crt and our proposed closed form robust crt and its improved version algorithms in terms of both theoretical analysis and numerical simulations the results demonstrate that the proposed closed form robust crt its improved version has the best performance has the same performance but much simpler form than the searching based robust crt

extensions of locally compact quantum groups and the bicrossed product construction abstract in the framework of locally compact quantum groups we study cocycle actions we develop the cocycle bicrossed product construction starting from a matched pair of locally compact quantum groups we define exact sequences and establish a one to one correspondence between cocycle bicrossed products and cleft extensions in this way we obtain new examples of locally compact quantum groups

optimal estimates of two common remainders for a robust generalized chinese remainder theorem estimation of multiple common remainders from a sequence of erroneous residue sets is an important step for the robust generalized chinese remainder theorem crt this paper considers the problem of how to estimate the two common remainders from their residue sets modulo a set of moduli to measure the errors properly under the modular operation we introduce two type circular distances based on these circular distances two estimation methods are proposed by properly grouping the erroneous remainders into two ordered clusters both of the two methods perform better with lower computational complexities than the existing methods in this paper theoretical analysis as well as analytical results for the two proposed methods are obtained for the first method the two optimal estimates are proved to be in a finite set with no more than l candidates where l is the number of the given moduli the second method have closed forms simulation results show that the two proposed methods have nearly the same performance these optimal estimates can improve the performance of the robust generalized crt significantly

models of collective cell spreading with variable cell aspect ratio a motivation for degenerate diffusion models continuum diffusion models are often used to represent the collective motion of cell populations most previous studies have simply used linear diffusion to represent collective cell spreading while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles in the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations furthermore there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate here we provide a link between individual based and continuum models using a multi scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice based exclusion process for round agents that occupy a single lattice site we find that the relevant continuum description of the system is a linear diffusion equation whereas for elongated rod shaped agents that occupy l adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation pme the exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles results suggest that when using continuum models to represent cell population spreading we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models

the unitary implementation of a locally compact quantum group action abstract in this paper we study actions of locally compact quantum groups on von neumann algebras and prove that every action has a canonical unitary implementation paralleling haagerup s classical result on the unitary implementation of a locally compact group action this result is an important tool in the study of quantum groups in action we will use it in this paper to study subfactors and inclusions of von neumann algebras when is an action of the locally compact quantum group m on the von neumann algebra n we can give necessary and sufficient conditions under which the inclusion n n m n is a basic construction here n denotes the fixed point algebra and m n is the crossed product when is an outer and integrable action on a factor n we prove that the inclusion n n is irreducible of depth 2 and regular giving a converse to the results of m enock and r nest 1996 j funct anal 137 466 543 1998 j funct anal 154 67 109 finally we prove the equivalence of minimal and outer actions and we generalize the main theorem of yamanouchi 1999 math scand 84 297 319 every integrable outer action with infinite fixed point algebra is a dual action

distance estimation using wrapped phase measurements in noise measuring a distance using phase measurements is a common practice in many areas of engineering almost inevitably these measurements are accompanied by noise and are always subject to ambiguity resulting from the phase of modulo 2 pi in the presence of phase ambiguity where for instance the unknown distance is far longer than the wavelength of the signal carrying the phase measurement the distance cannot be uniquely determined one way to resolve this phase ambiguity is to measure the signal phase at multiple frequencies converting the phase ambiguity problem into one of solving a family of diophantine equations typically under some reasonable assumptions the diophantine problems can be solved using the chinese reminder theorem as documented in the literature however the existing algorithms can experience significant computational overhead for a given application because an exhaustive search is required in this paper a novel method addressing the phase ambiguity issue using lattice theoretic ideas is proposed and a closed form algorithm is presented for the estimation of the number of wavelengths in the unknown distance using the phase measurements taken at multiple wavelengths the algorithm is extremely efficient as the diophantine equations are solved without searching the unknown distance can then be estimated via a maximum likelihood method using the unwrapped phase measurement a statistical bound of the measurement noise which ensures that the number of whole wavelengths in the unknown distance can be found with a probability close to unity is derived the robustness efficiency and estimation accuracy of the proposed method are demonstrated by the simulated results presented

frequency estimation by phase unwrapping single frequency estimation is a long studied problem with application domains including radar sonar telecommunications astronomy and medicine one method of estimation called phase unwrapping attempts to estimate the frequency by performing linear regression on the phase of the received signal this procedure is complicated by the fact that the received phase is wrapped modulo and therefore must be unwrapped before the regression can be performed in this paper we propose an estimator that performs phase unwrapping in the least squares sense the estimator is shown to be strongly consistent and its asymptotic distribution is derived we then show that the problem of computing the least squares phase unwrapping is related to a problem in algorithmic number theory known as the nearest lattice point problem we derive a polynomial time algorithm that computes the least squares estimator the results of various simulations are described for different values of sample size and snr

the analogues of entropy and of fisher s information measure in free probability theory i analogues of the entropy and fisher information measure for random variables in the context of free probability theory are introduced monotonicity properties and an analogue of the cramer rao inequality are proved

modeling tumor cell migration from microscopic to macroscopic models it has been shown experimentally that contact interactions may influence the migration of cancer cells previous works have modelized this thanks to stochastic discrete models cellular automata at the cell level however for the study of the growth of real size tumors with several million cells it is best to use a macroscopic model having the form of a partial differential equation pde for the density of cells the difficulty is to predict the effect at the macroscopic scale of contact interactions that take place at the microscopic scale to address this we use a multiscale approach starting from a very simple yet experimentally validated microscopic model of migration with contact interactions we derive a macroscopic model we show that a diffusion equation arises as is often postulated in the field of glioma modeling but it is nonlinear because of the interactions we give the explicit dependence of diffusivity on the cell density and on a parameter governing cell cell interactions we discuss in detail the conditions of validity of the approximations used in the derivation and we compare analytic results from our pde to numerical simulations and to some in vitro experiments we notice that the family of microscopic models we started from includes as special cases some kinetically constrained models that were introduced for the study of the physics of glasses supercooled liquids and jamming systems

traveling wave phenomena in some degenerate reaction diffusion equations abstract in this paper we study the existence of travelling wave solutions t w s u x t x ct for the equation formula g u where the reactive part g u is as in the fisher kpp equation and different assumptions are made on the non linear diffusion term d u both functions d and g are defined on the interval 0 1 the existence problem is analysed in the following two cases case 1 d 0 0 d u 0 u 0 1 d and g c 2 0 1 d 0 0 and d 0 0 we prove that if there exists a value of c c for which the equation possesses a travelling wave solution of sharp type it must be unique by using some continuity arguments we show that for 0 c c there are no t w s while for c c the equation has a continuum of t w s of front type the proof of uniqueness uses a monotonicity property of the solutions of a system of ordinary differential equations which is also proved case 2 d 0 d 0 0 d and g c 2 0 1 d 0 0 if in addition we impose d 0 0 with d u 0 u 0 1 we give sufficient conditions on c for the existence of t w s of front type meanwhile if d 0 d u u 0 1 we analyse just one example d u u 2 and g u u 1 u which has oscillatory t w s for 0 c 2 and t w s of front type for c 2 in both the above cases we use higher order terms in the taylor series and the centre manifold theorem in order to get the local behaviour around a non hyperbolic point of codimension one in the phase plane

a new construction of factors of type iii1 abstract we give in this paper a new construction of factors of type iii 1 under certain assumptions we can thanks to a result by popa give a complete classification for this family of factors although these factors are never full we can nevertheless in many cases compute connes invariant we obtain a new example of an uncountable family of pairwise non isomorphic factors of type iii 1 with the same invariant

macroscopic dynamics of biological cells interacting via chemotaxis and direct contact a connection is established between discrete stochastic model describing microscopic motion of fluctuating cells and macroscopic equations describing dynamics of cellular density cells move towards chemical gradient process called chemotaxis with their shapes randomly fluctuating nonlinear diffusion equation is derived from microscopic dynamics in dimensions one and two using excluded volume approach nonlinear diffusion coefficient depends on cellular volume fraction and it is demonstrated to prevent collapse of cellular density a very good agreement is shown between monte carlo simulations of the microscopic cellular potts model and numerical solutions of the macroscopic equations for relatively large cellular volume fractions combination of microscopic and macroscopic models were used to simulate growth of structures similar to early vascular networks

asymptotic structure of free araki woods factors the purpose of this paper is to investigate the structure of shlyakhtenko s free araki woods factors using the framework of ultraproduct von neumann algebras we first prove that all the free araki woods factors gamma h mathbb r u t prime prime are omega solid in the following sense for every von neumann subalgebra q subset gamma h mathbb r u t prime prime that is the range of a faithful normal conditional expectation and such that the relative commutant q cap m omega is diffuse we have that q is amenable next we prove that the continuous cores of the free araki woods factors gamma h mathbb r u t prime prime associated with mixing orthogonal representations u mathbb r rightarrow mathcal o h mathbb r are omega solid type mathrm ii infty factors finally when the orthogonal representation u mathbb r rightarrow mathcal o h mathbb r is weakly mixing we prove a dichotomy result for all the von neumann subalgebras q subset gamma h mathbb r u t prime prime that are globally invariant under the modular automorphism group sigma t varphi u of the free quasi free state varphi u

compact kac algebras and commuting squares abstract we consider commuting squares of finite dimensional von neumann algebras having the algebra of complex numbers in the lower left corner examples include the vertex models the spin models in the sense of subfactor theory and the commuting squares associated to finite dimensional kac algebras to any such commuting square we associate a compact kac algebra and we compute the corresponding subfactor and its standard invariant in terms of it

factoriality type classification and fullness for free product von neumann algebras abstract we give a complete answer to the questions of factoriality type classification and fullness for arbitrary free product von neumann algebras

models of collective cell motion for cell populations with different aspect ratio diffusion proliferation and travelling waves continuum partial differential equation models are often used to describe the collective motion of cell populations with various types of motility represented by the choice of diffusion coefficient and cell proliferation captured by the source terms previously the choice of diffusion coefficient has been largely arbitrary with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual level properties of the cell motility mechanism in this work we provide a new link between individual level models which account for important cell properties such as varying cell shape and volume exclusion and population level partial differential equation models we work in an exclusion process framework considering aligned elongated cells that may occupy more than one lattice site in order to represent populations of agents with different sizes three different idealisations of the individual level mechanism are proposed and these are connected to three different partial differential equations each with a different diffusion coefficient one linear one nonlinear and degenerate and one nonlinear and nondegenerate we test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases we also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion our results show that each model can accurately predict density data for nonproliferative systems but that only one does so for proliferative systems hence great care must be taken to predict density data with varying cell shape

on the classification of full factors of type iii we introduce a new invariant s m for type iii factors m with no almost periodic weights we compute this invariant for certain free araki woods factors we show that connes invariant r cannot distinguish all isomorphism classes of free araki woods factors we show that there exists a continuum of mutually non isomorphic free araki woods factors each without almost periodic weights

amenability of hopf von neumann algebras and kac algebras abstract let m be a hopf von neumann algebra the operator predualm ofmis a completely contractive banach algebra with multiplicationm m m m we call m operator amenableif the completely contractive banach algebram isoperator amenable i e for every operatorm bimodulev every completely bounded derivation fromm into the dualm bimodulev is inner there is a weaker notion of amenability introduced by d voiculescu we say that a hopf von neumann algebra m isvoiculescu amenableif there exists a left invariant mean onm we show that if a hopf von neumann algebra m is operator amenable then it is voiculescu amenable for kac algebras there is astrong voiculescu amenability we show that for discrete kac algebras these amenabilities are all equivalent in fact if we letk m be a discrete kac algebra and letk m be its compact dual kac algebra then the following are equivalent 1 kis operator amenable 2 kis voiculescu amenable 3 the von neumann algebramis hyperfinite 4 kis strong voiculescu amenable 5 kis operator amenable 6 m has a bounded approximate identity

an algebraic framework for group duality abstract a hopf algebra is a pair a whereais an associative algebra with identity and a homomorphism formatoa asatisfying certain conditions if we drop the assumption thatahas an identity and if we allow to have values in the so called multiplier algebram a a we get a natural extension of the notion of a hopf algebra we call this a multiplier hopf algebra the motivating example is the algebra of complex functions with finite support on a group with the comultiplication defined as dual to the product in the group also for these multiplier hopf algebras there is a natural notion of left and right invariance for linear functionals called integrals in hopf algebra theory we show that if such invariant functionals exist they are unique up to a scalar and faithful for a regular multiplier hopf algebra a i e with invertible antipode with invariant functionals we construct in a canonical way the dual it is again a regular multiplier hopf algebra with invariant functionals it is also shown that the dual of is canonically isomorphic with the original multiplier hopf algebra a it is possible to generalize many aspects of abstract harmonic analysis here one can define the fourier transform one can prove plancherel s formula because any finite dimensional hopf algebra is a regular multiplier hopf algebra and has invariant functionals our duality theorem applies to all finite dimensional hopf algebras then it coincides with the usual duality for such hopf algebras but our category of multiplier hopf algebras also includes in a certain way the discrete quantum groups and the compact quantum groups our duality includes the duality between discrete quantum groups and compact quantum groups in particular it includes the duality between compact abelian groups and discrete abelian groups one of the nice features of our theory is that we have an extension of this duality to the non abelian case but within one category this is shown in the last section of our paper where we introduce the algebras of compact type and the algebras of discrete type we prove that also these are dual to each other we treat an example that is sufficiently general to illustrate most of the different features of our theory it is also possible to construct the quantum double of drinfel d within this category this provides a still wider class of examples so we obtain many more than just the compact and discrete quantum within this setting

correcting mean field approximations for birth death movement processes on the microscale migration proliferation and death are crucial in the development homeostasis and repair of an organism on the macroscale such effects are important in the sustainability of a population in its environment dependent on the relative rates of migration proliferation and death spatial heterogeneity may arise within an initially uniform field this leads to the formation of spatial correlations and can have a negative impact upon population growth usually such effects are neglected in modeling studies and simple phenomenological descriptions such as the logistic model are used to model population growth in this work we outline some methods for analyzing exclusion processes which include agent proliferation death and motility in two and three spatial dimensions with spatially homogeneous initial conditions the mean field description for these types of processes is of logistic form we show that under certain parameter conditions such systems may display large deviations from the mean field and suggest computationally tractable methods to correct the logistic type description

aggregation patterns from nonlocal interactions discrete stochastic and continuum modeling conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles we address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities currently no existence theory for such potentials is available we develop and compare two complementary solution methods a continuous pseudoinverse method and a discrete stochastic lattice approach and formally show a connection between the two interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive repulsive potential are determined for a swarming morse potential characteristic slow fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches the discrete approach is found to be remarkably robust to modifications in movement rules related to the potential function the comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two and three dimensional nonlocal interaction conservation equations

convergence to a propagating front in a degenerate fisher kpp equation with advection abstract we consider a fisher kpp equation with density dependent diffusion and advection arising from a chemotaxis growth model we study its behavior as a small parameter related to the thickness of a diffuse interface tends to zero we analyze for small times the emergence of transition layers induced by a balance between reaction and drift effects then we investigate the propagation of the layers convergence to a free boundary limit problem is proved and a sharp estimate of the thickness of the layers is provided

maximum likelihood estimation based robust chinese remainder theorem for real numbers and its fast algorithm robust chinese remainder theorem crt has been recently investigated for both integers and real numbers where the folding integers are accurately recovered from erroneous remainders in this paper we consider the crt problem for real numbers with noisy remainders that follow wrapped gaussian distributions we propose the maximum likelihood estimation mle based crt when the remainder noises may not necessarily have the same variances furthermore we present a fast algorithm for the mle based crt algorithm that only needs to search for the solution among l elements where l is the number of remainders then a necessary and sufficient condition on the remainder errors for the mle crt to be robust is obtained which is weaker than the existing result finally we compare the performances of the newly proposed algorithm and the existing algorithm in terms of both theoretical analysis and numerical simulations the results demonstrate that the proposed algorithm not only has a better performance especially when the remainders have different error levels variances but also has a much lower computational complexity

strong solidity of free araki woods factors we show that shlyakhtenko s free araki woods factors are strongly solid meaning that for any diffuse amenable von neumann subalgebra that is the range of a normal conditional expectation the normalizer remains amenable this provides the first class of nonamenable strongly solid type iii factors

towards robustness in residue number systems the problem of robustly reconstructing a large number from its erroneous remainders with respect to several moduli namely the robust remaindering problem may occur in many applications including phase unwrapping frequency detection from several undersampled waveforms wireless sensor networks etc assuming that the dynamic range of the large number is the maximal possible one i e the least common multiple lcm of all the moduli a method called robust chinese remainder theorem for solving the robust remaindering problem has been recently proposed in this paper by relaxing the assumption that the dynamic range is fixed to be the lcm of all the moduli a tradeoff between the dynamic range and the robustness bound for two modular systems is studied it basically says that a decrease in the dynamic range may lead to an increase of the robustness bound we first obtain a general condition on the remainder errors and derive the exact dynamic range with a closed form formula for the robustness to hold we then propose simple closed form reconstruction algorithms furthermore the newly obtained two modular results are applied to the robust reconstruction for multimodular systems and generalized to real numbers finally some simulations are carried out to verify our proposed theoretical results

fisher equation with density dependent diffusion special solutions a special family of solutions explicit in the space and time variables is found for the fisher equation with density dependent diffusion the connection with the known travelling wave solution and the initial conditions from which that evolves is also shown