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.

Robust multimodal face and fingerprint fusion in the presence of spoofing attacks

Anti-spoofing is attracting growing interest in biometrics, considering the variety of fake materials and new means to attack biometric recognition systems. New unseen materials continuously challenge state-of-the-art spoofing detectors, suggesting for additional systematic approaches to target anti-spoofing. By incorporating liveness scores into the biometric fusion process, recognition accuracy can be enhanced, but traditional sum-rule based fusion algorithms are known to be highly sensitive to single spoofed instances. This paper investigates 1-median filtering as a spoofing-resistant generalised alternative to the sum-rule targeting the problem of partial multibiometric spoofing where m out of n biometric sources to be combined are attacked. Augmenting previous work, this paper investigates the dynamic detection and rejection of livenessrecognition pair outliers for spoofed samples in true multi-modal configuration with its inherent challenge of normalisation. As a further contribution, bootstrap aggregating (bagging) classifiers for fingerprint spoof-detection algorithm is presented. Experiments on the latest face video databases (Idiap Replay- Attack Database and CASIA Face Anti-Spoofing Database), and fingerprint spoofing database (Fingerprint Liveness Detection Competition 2013) illustrate the efficiency of proposed techniques.

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

Biases in comparative analyses of extinction risk: mind the gap

1. Comparative analyses are used to address the key question of what makes a species more prone to extinction by exploring the links between vulnerability and intrinsic species’ traits and/or extrinsic factors. This approach requires comprehensive species data but information is rarely available for all species of interest. As a result comparative analyses often rely on subsets of relatively few species that are assumed to be representative samples of the overall studied group. 2. Our study challenges this assumption and quantifies the taxonomic, spatial, and data type biases associated with the quantity of data available for 5415 mammalian species using the freely available life-history database PanTHERIA. 3. Moreover, we explore how existing biases influence results of comparative analyses of extinction risk by using subsets of data that attempt to correct for detected biases. In particular, we focus on links between four species’ traits commonly linked to vulnerability (distribution range area, adult body mass, population density and gestation length) and conduct univariate and multivariate analyses to understand how biases affect model predictions. 4. Our results show important biases in data availability with c.22% of mammals completely lacking data. Missing data, which appear to be not missing at random, occur frequently in all traits (14–99% of cases missing). Data availability is explained by intrinsic traits, with larger mammals occupying bigger range areas being the best studied. Importantly, we find that existing biases affect the results of comparative analyses by overestimating the risk of extinction and changing which traits are identified as important predictors. 5. Our results raise concerns over our ability to draw general conclusions regarding what makes a species more prone to extinction. Missing data represent a prevalent problem in comparative analyses, and unfortunately, because data are not missing at random, conventional approaches to fill data gaps, are not valid or present important challenges. These results show the importance of making appropriate inferences from comparative analyses by focusing on the subset of species for which data are available. Ultimately, addressing the data bias problem requires greater investment in data collection and dissemination, as well as the development of methodological approaches to effectively correct existing biases.

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.

A constrained recursive least squares algorithm for adaptive combination of multiple models

In this paper, we develop a novel constrained recursive least squares algorithm for adaptively combining a set of given multiple models. With data available in an online fashion, the linear combination coefficients of submodels are adapted via the proposed algorithm.We propose to minimize the mean square error with a forgetting factor, and apply the sum to one constraint to the combination parameters. Moreover an l1-norm constraint to the combination parameters is also applied with the aim to achieve sparsity of multiple models so that only a subset of models may be selected into the final model. Then a weighted l2-norm is applied as an approximation to the l1-norm term. As such at each time step, a closed solution of the model combination parameters is available. The contribution of this paper is to derive the proposed constrained recursive least squares algorithm that is computational efficient by exploiting matrix theory. The effectiveness of the approach has been demonstrated using both simulated and real time series examples.

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.