Ergodic and Nonergodic Anomalous Diffusion in Coupled Stochastic Processes

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long time behaviour of the mean square displacement. Anomalous diffusion is found. Since the diffusion exponent can not be predicted using a simple scaling argument, anomalous scaling appears as well. We also find that the coupling can lead to ergodic or non-ergodic behaviour of the studied process. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems coupled with unobserved dynamical degrees of freedom by means of standard, diffusive Langevin descriptions

Methods of tropical optimization in rating alternatives based on pairwise comparisons

We apply methods of tropical optimization to handle problems of rating alternatives on the basis of the log-Chebyshev approximation of pairwise comparison matrices. We derive a direct solution in a closed form, and investigate the obtained solution when it is not unique. Provided the approximation problem yields a set of score vectors, rather than a unique (up to a constant factor) one, we find those vectors in the set, which least and most differentiate between the alternatives with the highest and lowest scores, and thus can be representative of the entire solution.Comment: 9 pages, presented at the Annual Intern. Conf. of the German Operations Research Society (GOR), Helmut Schmidt University Hamburg, Germany, August 30 - September 2, 201

Accurate Liability Estimation Improves Power in Ascertained Case Control Studies

Linear mixed models (LMMs) have emerged as the method of choice for confounded genome-wide association studies. However, the performance of LMMs in non-randomly ascertained case-control studies deteriorates with increasing sample size. We propose a framework called LEAP (Liability Estimator As a Phenotype, https://github.com/omerwe/LEAP) that tests for association with estimated latent values corresponding to severity of phenotype, and demonstrate that this can lead to a substantial power increase

Cyclic projectors and separation theorems in idempotent convex geometry

Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodules of the n-fold cartesian product of the max-plus semiring it is known that one can separate a vector from a closed subsemimodule that does not contain it. We establish here a more general separation theorem, which applies to any finite collection of closed semimodules with a trivial intersection. In order to prove this theorem, we investigate the spectral properties of certain nonlinear operators called here idempotent cyclic projectors. These are idempotent analogues of the cyclic nearest-point projections known in convex analysis. The spectrum of idempotent cyclic projectors is characterized in terms of a suitable extension of Hilbert's projective metric. We deduce as a corollary of our main results the idempotent analogue of Helly's theorem.Comment: 20 pages, 1 figur

Final State Interactions Effects in Neutrino-Nucleus Interactions

Final State Interactions effects are discussed in the context of Monte Carlo simulations of neutrino-nucleus interactions. A role of Formation Time is explained and several models describing this effect are compared. Various observables which are sensitive to FSI effects are reviewed including pion-nucleus interaction and hadron yields in backward hemisphere. NuWro Monte Carlo neutrino event generator is described and its ability to understand neutral current $\pi^0$ production data in $\sim 1$ GeV neutrino flux experiments is demonstrated.Comment: 13 pages, 16 figure

Designing a physical activity parenting course : parental views on recruitment, content and delivery

Background Many children do not engage in sufficient levels of physical activity (PA) and spend too much time screen-viewing (SV). High levels of SV (e.g. watching TV, playing video games and surfing the internet) and low levels of PA have been associated with adverse health outcomes. Parenting courses may hold promise as an intervention medium to change children’s PA and SV. The current study was formative work conducted to design a new parenting programme to increase children’s PA and reduce their SV. Specifically, we focussed on interest in a course, desired content and delivery style, barriers and facilitators to participation and opinions on control group provision. Methods In-depth telephone interviews were conducted with thirty two parents (29 female) of 6–8 year olds. Data were analysed thematically. An anonymous online survey was also completed by 750 parents of 6–8 year old children and descriptive statistics calculated. Results Interview participants were interested in a parenting course because they wanted general parenting advice and ideas to help their children be physically active. Parents indicated that they would benefit from knowing how to quantify their child’s PA and SV levels. Parents wanted practical ideas of alternatives to SV. Most parents would be unable to attend unless childcare was provided. Schools were perceived to be a trusted source of information about parenting courses and the optimal recruitment location. In terms of delivery style, the majority of parents stated they would prefer a group-based approach that provided opportunities for peer learning and support with professional input. Survey participants reported the timing of classes and the provision of childcare were essential factors that would affect participation. In terms of designing an intervention, the most preferred control group option was the opportunity to attend the same course at a later date. Conclusions Parents are interested in PA/SV parenting courses but the provision of child care is essential for attendance. Recruitment is likely to be facilitated via trusted sources. Parents want practical advice on how to overcome barriers and suggest advice is provided in a mutually supportive group experience with expert input

Semiring and semimodule issues in MV-algebras

In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings - such an approach naturally imposing the introduction and study of a suitable corresponding class of semimodules, called MV-semimodules. We present several results addressed toward a semiring theory for MV-algebras. In particular we show a representation of MV-algebras as a subsemiring of the endomorphism semiring of a semilattice, the construction of the Grothendieck group of a semiring and its functorial nature, and the effect of Mundici categorical equivalence between MV-algebras and lattice-ordered Abelian groups with a distinguished strong order unit upon the relationship between MV-semimodules and semimodules over idempotent semifields.Comment: This version contains some corrections to some results at the end of Section

Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing

We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$. We give a positive answer to the long-standing open question whether this problem is strongly $NP$-complete for $m=4$. As a second result, we improve the lower bound of $\frac{12}{11}$ for approximating pseudo-polynomial Strip Packing to $\frac{5}{4}$. Since the best known approximation algorithm for this problem has a ratio of $\frac{4}{3} + \varepsilon$, this result narrows the gap between approximation ratio and inapproximability result by a significant step. Both results are proven by a reduction from the strongly $NP$-complete problem 3-Partition