<i>H</i>₂ and mixed <i>H</i>₂/<i>H</i>_∞ Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation

Mixed precision GMRES-based iterative refinement with recycling

summary:With the emergence of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes for solving linear systems $Ax=b$ have recently been developed. However, in certain settings, GMRES may require too many iterations per refinement step, making it potentially more expensive than the alternative of recomputing the LU factors in a higher precision. In this work, we incorporate the idea of Krylov subspace recycling, a well-known technique for reusing information across sequential invocations, of a Krylov subspace method into a mixed precision GMRES-based iterative refinement solver. The insight is that in each refinement step, we call preconditioned GMRES on a linear system with the same coefficient matrix $A$. In this way, the GMRES solves in subsequent refinement steps can be accelerated by recycling information obtained from previous steps. We perform numerical experiments on various random dense problems, Toeplitz problems, and problems from real applications, which confirm the benefits of the recycling approach

Nearly-Linear Time LP Solvers and Rounding Algorithms for Scheduling Problems

We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives such as makespan and weighted completion time. For many problems, we develop nearly-linear time approximation algorithms with approximation ratios matching the current best ones achieved in polynomial time. Our main technique is linear programming relaxation. For the unrelated machine setting, we formulate mixed packing and covering LP relaxations of nearly-linear size, and solve them approximately using the nearly-linear time solver of Young. For the makespan objective, we develop a rounding algorithm with (2+?)-approximation ratio. For the weighted completion time objective, we prove the LP is as strong as the rectangle LP used by Im and Li, leading to a nearly-linear time (1.45 + ?)-approximation for the problem. For problems in the identical machine with precedence constraints setting, the precedence constraints can not be formulated as packing or covering constraints. To achieve the nearly-linear running time, we define a polytope for the constraints, and leverage the multiplicative weight update (MWU) method with an oracle which always returns solutions in the polytope

Parameter Tuning for Optimization Software

Mixed integer programming (MIP) problems are highly parameterized, and finding parameter settings that achieve high performance for specific types of MIP instances is challenging. This paper presents a method to find the information about how CPLEX solver parameter settings perform for the different classes of mixed integer linear programs by using designed experiments and statistical models. Fitting a model through design of experiments helps in finding the optimal region across all combinations of parameter settings. The study involves recognizing the best parameter settings that results in the best performance for a specific class of instances. Choosing good setting has a large effect in minimizing the solution time and optimality gap

Nearly-Linear Time Approximate Scheduling Algorithms

We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting. The objectives we study include makespan, weighted completion time, and $L_q$ norm of machine loads. We develop nearly-linear time approximation algorithms for the studied problems with $O(1)$-approximation ratios, many of which match the correspondent best known ratios achievable in polynomial time. Our main technique is linear programming relaxation. For problems in the unrelated machine setting, we formulate mixed packing and covering LP relaxations of nearly-linear size, and solve them approximately using the nearly-linear time solver of Young. We show the LP solutions can be rounded within $O(1)$-factor loss. For problems in the identical machine with precedence constraints setting, the precedence constraints can not be formulated as packing or covering constraints. To achieve the claimed running time, we define a polytope for the constraints, and leverage the multiplicative weight update (MWU) method with an oracle which always returns solutions in the polytope. Along the way of designing the oracle, we encounter the single-commodity maximum flow problem over a directed acyclic graph $G = (V, E)$, where sources and sinks have limited supplies and demands, but edges have infinite capacities. We develop a $\frac{1}{1+\epsilon}$-approximation for the problem in time $O\left(\frac{|E|}{\epsilon}\log |V|\right)$, which may be of independent interest

Socioeconomic characteristics, family structure and trajectories of children's psychosocial problems in a period of social transition

Data from the Czech part of the European Longitudinal Study of Pregnancy and Childhood offer a unique opportunity to examine a period of changing socioeconomic structure of the country. Our aim was to analyse the association between socioeconomic status, family structure and children’s psychosocial problems at the age of 7, 11, 15 and 18 years in 3,261 subjects and compare our results with findings from western settings. The Strengths and Difficulties Questionnaire (SDQ) and its five subscales were used to assess individual problem areas (emotional symptoms, peer problems, hyperactivity, conduct problems) and prosocial behaviour. Socioeconomic status was represented by maternal education and three forms of family structure were identified: nuclear family, new partner family and single parent family. The SDQ subscale score over time was modelled as a quadratic growth curve using a linear mixed-effects model. Maternal university education was associated with a faster decline in problems over time for all five SDQ subscales. Problems in children from nuclear families were found to be significantly lower than in children from single parent families for all SDQ subscales with the exception of peer problems. Compared to nuclear families, children from new partner families scored significantly higher in hyperactivity and conduct problems subscales. The nuclear family structure and higher maternal education have been identified as protective factors for children’s psychosocial problems, in agreement with findings from western settings. Adopting a longitudinal perspective was shown as essential for providing a more complex view of children’s psychosocial problems over time

Socioeconomic characteristics, family structure and trajectories of children's psychosocial problems in a period of social transition

Data from the Czech part of the European Longitudinal Study of Pregnancy and Childhood offer a unique opportunity to examine a period of changing socioeconomic structure of the country. Our aim was to analyse the association between socioeconomic status, family structure and children's psychosocial problems at the age of 7, 11, 15 and 18 years in 3,261 subjects and compare our results with findings from western settings. The Strengths and Difficulties Questionnaire (SDQ) and its five subscales were used to assess individual problem areas (emotional symptoms, peer problems, hyperactivity, conduct problems) and prosocial behaviour. Socioeconomic status was represented by maternal education and three forms of family structure were identified: nuclear family, new partner family and single parent family. The SDQ subscale score over time was modelled as a quadratic growth curve using a linear mixed-effects model. Maternal university education was associated with a faster decline in problems over time for all five SDQ subscales. Problems in children from nuclear families were found to be significantly lower than in children from single parent families for all SDQ subscales with the exception of peer problems. Compared to nuclear families, children from new partner families scored significantly higher in hyperactivity and conduct problems subscales. The nuclear family structure and higher maternal education have been identified as protective factors for children's psychosocial problems, in agreement with findings from western settings. Adopting a longitudinal perspective was shown as essential for providing a more complex view of children's psychosocial problems over time

Improvements in naturalistic speech-in-noise comprehension in middle-aged and older adults after 3 weeks of computer-based speechreading training

Problems in understanding speech in noisy environments are characteristic for age-related hearing loss. Since hearing aids do not mitigate these communication problems in every case, potential alternatives in a clinical rehabilitation plan need to be explored. This study investigates whether a computer-based speechreading training improves audiovisual speech perception in noise in a sample of middle-aged and older adults (N = 62, 47–83 years) with 32 participants completing a speechreading training and 30 participants of an active control group completing a foreign language training. Before and after training participants performed a speech-in-noise task mimicking real-life communication settings with participants being required to answer a speaker’s questions. Using generalized linear mixed-effects models we found a significant improvement in audiovisual speech perception in noise in the speechreading training group. This is of great relevance as these results highlight the potential of a low-cost and easy-to-implement intervention for a profound and widespread problem as speech-in-noise comprehension impairment