Percolation in suspensions of polydisperse hard rods : quasi-universality and finite-size effects

We present a study of connectivity percolation in suspensions of hard spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. We focus attention on polydispersity in the length, the diameter and the connectedness criterion, and invoke bimodal, Gaussian and Weibull distributions for these. The main finding from our simulations is that the percolation threshold shows quasi universal behaviour, i.e., to a good approximation it depends only on certain cumulants of the full size and connectivity distribution. Our connectedness percolation theory hinges on a Lee-Parsons type of closure recently put forward that improves upon the often-used second virial approximation [ArXiv e-prints, May 2015, 1505.07660]. The theory predicts exact universality. Theory and simulation agree quantitatively for aspect ratios in excess of 20, if we include the connectivity range in our definition of the aspect ratio of the particles. We further discuss the mechanism of cluster growth that, remarkably, differs between systems that are polydisperse in length and in width, and exhibits non-universal aspects.Comment: 7 figure

Osmotic compression of droplets of hard rods: A computer simulation study

By means of computer simulations we study how droplets of hard, rod-like particles optimize their shape and internal structure under the influence of the osmotic compression caused by the presence of spherical particles that act as depletion agents. At sufficiently high osmotic pressures the rods that make up the drops spontaneously align to turn them into uniaxial nematic liquid crystalline droplets. The nematic droplets or "tactoids" that are formed this way are not spherical but elongated, resulting from the competition between the anisotropic surface tension and the elastic deformation of the director field. In agreement with recent theoretical predictions we find that sufficiently small tactoids have a uniform director field, whilst large ones are characterized by a bipolar director field. From the shape and director-field transformation of the droplets we are able to estimate the surface anchoring strength and an average of the elastic constants of the hard-rod nematic

A Class of Convex Quadratic Nonseparable Resource Allocation Problems with Generalized Bound Constraints

We study a convex quadratic nonseparable resource allocation problem that arises in the area of decentralized energy management (DEM), where unbalance in electricity networks has to be minimized. In this problem, the given resource is allocated over a set of activities that is divided into subsets, and a cost is assigned to the overall allocated amount of resources to activities within the same subset. We derive two efficient algorithms with $O(n \log  n)$ worst-case time complexity to solve this problem. For the special case where all subsets have the same size, one of these algorithms even runs in linear time given the subset size. Both algorithms are inspired by well-studied breakpoint search methods for separable convex resource allocation problems. Numerical evaluations on both real and synthetic data confirm the theoretical efficiency of both algorithms and demonstrate their suitability for integration in DEM systems

On a reduction for a class of resource allocation problems

In the resource allocation problem (RAP), the goal is to divide a given amount of resource over a set of activities while minimizing the cost of this allocation and possibly satisfying constraints on allocations to subsets of the activities. Most solution approaches for the RAP and its extensions allow each activity to have its own cost function. However, in many applications, often the structure of the objective function is the same for each activity and the difference between the cost functions lies in different parameter choices such as, e.g., the multiplicative factors. In this article, we introduce a new class of objective functions that captures the majority of the objectives occurring in studied applications. These objectives are characterized by a shared structure of the cost function depending on two input parameters. We show that, given the two input parameters, there exists a solution to the RAP that is optimal for any choice of the shared structure. As a consequence, this problem reduces to the quadratic RAP, making available the vast amount of solution approaches and algorithms for the latter problem. We show the impact of our reduction result on several applications and, in particular, we improve the best known worst-case complexity bound of two important problems in vessel routing and processor scheduling from $O(n^2)$ to $O(n \log n)$

A fast algorithm for quadratic resource allocation problems with nested constraints

We study the quadratic resource allocation problem and its variant with lower and upper constraints on nested sums of variables. This problem occurs in many applications, in particular battery scheduling within decentralized energy management (DEM) for smart grids. We present an algorithm for this problem that runs in $O(n \log n)$ time and, in contrast to existing algorithms for this problem, achieves this time complexity using relatively simple and easy-to-implement subroutines and data structures. This makes our algorithm very attractive for real-life adaptation and implementation. Numerical comparisons of our algorithm with a subroutine for battery scheduling within an existing tool for DEM research indicates that our algorithm significantly reduces the overall execution time of the DEM system, especially when the battery is expected to be completely full or empty multiple times in the optimal schedule. Moreover, computational experiments with synthetic data show that our algorithm outperforms the currently most efficient algorithm by more than one order of magnitude. In particular, our algorithm is able to solves all considered instances with up to one million variables in less than 17 seconds on a personal computer

Quadratic nonseparable resource allocation problems with generalized bound constraints

We study a quadratic nonseparable resource allocation problem that arises in the area of decentralized energy management (DEM), where unbalance in electricity networks has to be minimized. In this problem, the given resource is allocated over a set of activities that is divided into subsets, and a cost is assigned to the overall allocated amount of resources to activities within the same subset. We derive two efficient algorithms with $O(n\log n)$ worst-case time complexity to solve this problem. For the special case where all subsets have the same size, one of these algorithms even runs in linear time given the subset size. Both algorithms are inspired by well-studied breakpoint search methods for separable convex resource allocation problems. Numerical evaluations on both real and synthetic data confirm the theoretical efficiency of both algorithms and demonstrate their suitability for integration in DEM systems

ODDO: Online Duality-Driven Optimization

Motivated by energy management for micro-grids, we study convex optimization problems with uncertainty in the objective function and sequential decision making. To solve these problems, we propose a new framework called ``Online Duality-Driven Optimization'' (ODDO). This framework distinguishes itself from existing paradigms for optimization under uncertainty in its efficiency, simplicity, and ability to solve problems without any quantitative assumptions on the uncertain data. The key idea in this framework is that we predict, instead of the actual uncertain data, the optimal Lagrange multipliers. Subsequently, we use these predictions to construct an online primal solution by exploiting strong duality of the problem. We show that the framework is robust against prediction errors in the optimal Lagrange multipliers both theoretically and in practice. In fact, evaluations of the framework on problems with both real and randomly generated input data show that ODDO can achieve near-optimal online solutions, even when we use only elementary statistics to predict the optimal Lagrange multipliers

Дії, що дезорганізують роботу установ виконання покарань: співрозмірність злочину та покарання

Досліджується співрозмірність покарання за дії, що дезорганізують роботу уста­нов виконання покарань (ст. 392 КК України), із характером та ступенем суспільної небезпеки цього злочину, а також співрозмірність покарання за злочин, що розгля­дається, із покараннями за окремі злочини із суміжними складами.Исследуется соразмерность наказания за действия, которые дезорганизуют рабо­ту учреждений исполнения наказаний (ст. 392 УК Украины), с характером и уровнем общественной опасности этого преступления, а также с соразмерность наказания за расматриваемое преступление с наказаними за отдельные преступления со смежными составами.The article contains the study of adequacy of punishment for actions disorganizing work of penitentiary institutions (art. 392 of Criminal Code of Ukraine) and public danger of this crime also punishments for other crimes

Direct aggression and generalized anxiety in adolescence:Heterogeneity in development and intra-individual change

Co-occurrence of aggression and anxiety might change during adolescence, or stay stable. We studied change and stability of four types of co-occurrence regarding direct aggression and anxiety in adolescence: an anxious and non-aggressive type, an aggressive and non-anxious type, a comorbid aggressive-anxious type and a no problems type. We applied a person-centered approach to assess increases and decreases of these types, and tested various models of intra-individual change of the types: the stability, acting out and failure models. We used data from a five-wave study of 923 early-to-middle and 390 middle-to-late adolescents (48.5 % male), thereby covering the ages of 12–20. We observed accelerated development in the older cohort: adolescents tended to grow faster out of the aggressive types in middle-to-late adolescence than in early-to-middle adolescence. We observed one other group-dependent pattern of heterogeneity in development, namely “gender differentiation”: gender differences in aggression and generalized anxiety became stronger over time. We found support for two perspectives on intra-individual change of the four types, namely the stability and the acting out perspective. The no problems—and to a lesser extent the anxious—type proved to be stable across time. Acting out was found in early-to-middle adolescents, males, and adolescents with poorer-quality friendships. In all three groups, there were substantial transitions from the anxious type to the aggressive type during 4 years (between 20 and 41 %). Remarkably, acting out was most prevalent in subgroups that, generally speaking, are more vulnerable for aggressive behavior, namely early-to-middle adolescents and males. We interpret acting out as the attempt of adolescents to switch from anxiety to instrumental aggression, in order to become more visible and obtain an autonomous position in the adolescent world. Acting out contributed to the explanation of accelerated development and gender differentiation. We also observed an increase of adolescents with no problems. These findings highlight that the co-occurrence of aggression and anxiety changes considerably during adolescence, but also that the anxious and no problems types are quite stable in this period. Keywords: Direct aggression Generalized anxiety Adolescence Longitudinal researc