Large deviations of Rouse polymer chain: first passage problem

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations, and measure the mean first-passage time $\tau(z)$ for the free end to reach a certain distance $z$ away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of $\tau(z)$ are observed, with transition between them varying as a function of chain length. We use these simulations results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations lead us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0

IHRM and expatriation in Japanese MNCs: HRM practices and their impact on adjustment and job performance

Studies of international human resource management (IHRM) have pointed out that Japanese multinational companies (MNCs) tend to use more parent-country nationals (PCNs) than do western MNCs. The ethnocentric staffing policies imply that the management of expatriation has a greater influence on the success of Japanese MNCs. We use survey data from 149 Japanese repatriates to examine the relationship between IHRM practices – selection, preparation and corporate support – and expatriate adjustment and job performance, as well as identify differences by the location of assignment. We find that selection criteria, language ability and familiarity with local cultures are positively related to work adjustment, and that leadership and relational abilities are slightly associated with job performance though there were no significant relationships between considerations for family situations and adjustment or job performance. The results also reveal that HRM practices while abroad, in particular the interactive exchange of information between expatriates and the headquarters, have a significant influence. Pre-departure preparation programs are not related to the dependent variables. The data also suggests that living and working in China is a particular problem for Japanese expatriates.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Using problem-based learning in a chemistry practical class for pharmacy students and engaging them with feedback

Objective: To introduce a new approach to problem based learning (PBL) used in the context of medicinal chemistry practical class teaching pharmacy students. Design: The described chemistry practical is based on independent studies by small groups of undergraduate students (4-5), who design their own practical work taking relevant professional standards into account. Students are carefully guided by feedback and acquire a set of skills important to their future profession as healthcare professionals. This model has been tailored to the application of PBL in a chemistry practical class setting for a large student cohort (150 students). Assessment: The achievement of learning outcomes is based on the submission of relevant documentation including a certificate of analysis, in addition to peer assessment. Some of the learning outcomes are also assessed in the final written examination at the end of the academic year. Conclusion: The described design of a novel PBL chemistry laboratory course for pharmacy students has been found to be successful. Self-reflective learning and engagement with feedback were encouraged, and students enjoyed the challenging learning experience. Skills that are highly essential for the students’ future careers as healthcare professionals are promoted.

The multiple team formation problem using sociometry

The Team Formation problem (TFP) has become a well-known problem in the OR literature over the last few years. In this problem, the allocation of multiple individuals that match a required set of skills as a group must be chosen to maximise one or several social positive attributes. Speci�cally, the aim of the current research is two-fold. First, two new dimensions of the TFP are added by considering multiple projects and fractions of people's dedication. This new problem is named the Multiple Team Formation Problem (MTFP). Second, an optimization model consisting in a quadratic objective function, linear constraints and integer variables is proposed for the problem. The optimization model is solved by three algorithms: a Constraint Programming approach provided by a commercial solver, a Local Search heuristic and a Variable Neighbourhood Search metaheuristic. These three algorithms constitute the first attempt to solve the MTFP, being a variable neighbourhood local search metaheuristic the most effi�cient in almost all cases. Applications of this problem commonly appear in real-life situations, particularly with the current and ongoing development of social network analysis. Therefore, this work opens multiple paths for future research.

A PCR-RFLP assay for gender assignment in the three-toed sloths (Bradypus, Pilosa, Bradypodidae)

The three-toed sloths (Bradypus) are slow-moving arboreal neotropical mammals. Understanding demographic variables (such as sex ratio) of populations is a key for conservation purposes. Nevertheless, gender assignment of Bradypus is particularly challenging because of the lack of sexual dimorphism in infants and in adults, particularly B. torquatus, the most endangered of the three-toed sloths, in which sex is attributed by visual observation of the reproductively active males. Here, we standardized a method for sexing Bradypus individuals using PCR-RFLP of sex-linked genes ZFX/ZFY. This assay was validated with known-gender animals and proved accurate to assign gender on three Bradypus species.

Contributions to the taxonomy of the Normanellidae (Copepoda, Harpacticoida): description of a new genus from the Brazilian continental shelf and re-assignment of Pseudocletodes vararensis Scott & Scott, 1893 (ex Nannopodidae)

A new genus and species of Normanellidae (Copepoda, Harpacticoida), Paranaiara inajae gen. et sp. nov., is described from the continental shelf off the northern coast of Sao Paulo State, Brazil. The new genus differs from the type genus Normanella Brady, 1880 and Sagamiella Lee & Huys, 1999 in its presence of lamelliform caudal rami, a maxillulary endopod represented by 2 setae, an unarmed maxillipedal syncoxa, and reduced setation on P2 enp-2 (without outer spine) and P3 enp-2 (with only 2 inner setae). All these apomorphic character states are shared with the genus Pseudocletodes Scott & Scott, 1893, formerly placed in the family Nannopodidae (ex Huntemanniidae) and here assigned to the Normanellidae. Pseudocletodes can be differentiated from Paranaiara by the loss of the P1 endopod and of the inner seta on P2-P4 enp-1, the presence of only 2 inner setae on P2 enp-2 (instead of 3) and only 1 inner seta on P4 exp-3 (instead of 2), the presence of a second inner seta on P4 enp-2 (instead of 1), the morphology of the fifth pair of legs which are not medially fused and have only 3 endopodal elements (instead of 4) in the male, and the well developed caudal ramus seta V (instead of rudimentary). It is postulated that prehensility of the P1 endopod was secondarily lost in the common ancestor of Paranaiara and Pseudocletodes. An updated family diagnosis of the Normanellidae and a dichotomous identification key to the 22 currently valid species are presented.

ROOT PROBLEM FOR CONVENIENT MAPS

In this paper we study when the minimal number of roots of the so-called convenient maps horn two-dimensional CW complexes into closed surfaces is zero We present several necessary and sufficient conditions for such a map to be root free Among these conditions we have the existence of specific fittings for the homomorphism induced by the map on the fundamental groups, existence of the so-called mutation of a specific homomorphism also induced by the map, and existence of particular solutions of specific systems of equations on free groups over specific subgroups

Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved.

Dynamics in dumbbell domains II. The limiting problem

In this work we continue the analysis of the asymptotic dynamics of reaction-diffusion problems in a dumbbell domain started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2) (2006) 551-597]. Here we study the limiting problem, that is, an evolution problem in a ""domain"" which consists of an open, bounded and smooth set Omega subset of R(N) with a curve R(0) attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Omega the evolution is independent of the evolution in R(0) whereas in R(0) the evolution depends on the evolution in Omega through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors. (C) 2009 Elsevier Inc. All rights reserved.