Integrity Constraints Revisited: From Exact to Approximate Implication

Integrity constraints such as functional dependencies (FD) and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate probability distributions. The implication problem studies whether a set of constraints (antecedents) implies another constraint (consequent), and has been investigated in both the database and the AI literature, under the assumption that all constraints hold exactly. However, many applications today consider constraints that hold only approximately. In this paper we define an approximate implication as a linear inequality between the degree of satisfaction of the antecedents and consequent, and we study the relaxation problem: when does an exact implication relax to an approximate implication? We use information theory to define the degree of satisfaction, and prove several results. First, we show that any implication from a set of data dependencies (MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most quadratic in the number of variables; when the consequent is an FD, the factor can be reduced to 1. Second, we prove that there exists an implication between CIs that does not admit any relaxation; however, we prove that every implication between CIs relaxes "in the limit". Then, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Finally, we show how some of the results in the paper can be derived using the I-measure theory, which relates between information theoretic measures and set theory. Our results recover, and sometimes extend, previously known results about the implication problem: the implication of MVDs and FDs can be checked by considering only 2-tuple relations.

Rheological Relaxation of OSB Beams Reinforced with CFRP Composites

An experimental and analytical approach to the relaxation problem of wood-based materials—OSB (Oriented Strand Boards—pressed wood-based composite panels) beams, including beams with CFRP (Carbon fiber reinforced polymer) tape composite reinforcement, is presented. It is a relevant engineering and scientific problem due to the fact that wood and wood-based materials, as well as composite reinforcements, are widely used in building constructions. Their rheological properties are very important and complicated to estimate. A 10 day long relaxation test of thick OSB beams without reinforcement and with CFRP tape was performed. A four-point bending test with five different bending levels was performed, during which the reduction of the loading force was measured. A five-parameter rheological model was used to describe the rheology of the beams. The equations of this model were calculated with the use of Laplace transform, whereas the values of the parameters were calculated based on the experimental relaxation curves. A high correlation between experimental and theoretical results was obtained. A beam reinforced with CFRP tape was treated as a system with a viscoelastic element (OSB) and an elastic element (CFRP), joined together without the possibility of slipping. The equations of the mathematical model were calculated based on the assumptions of the linear theory of viscoelasticity and the convolution integral. A good correlation between experimental and theoretical results was obtained. A significant redistribution of stresses was observed during the relaxation of the reinforced beam. The reinforced beams show a higher stiffness of approximately 63% and carry proportionally higher loads than unreinforced beams at the same deflection values.

Implementation of neutralizing fields for particle–particle simulations using like charges

The particle–particle (PP) model has a growing number of applications in plasma simulations, because of its high accuracy of solving Coulomb collisions. One of the main issues restricting the practical use of the PP model is its large computational cost, which is now becoming acceptable thanks to state-of-art parallel computing techniques. Another issue is the singularity that occurs when two particles are too close. The most effective approach of avoiding the singularity would be to simulate particles with only like charges plus a neutralizing field, such that the short-range collisions are equivalent to those of using unlike charges. In this paper, we introduce a way of adding the neutralizing field by using the analytical solution of the electric field in the domain filled with uniformly distributed charges, for applications with homogeneous and quasi-neutral plasmas under a reflective boundary condition. Two most common Cartesian domain geometries, cubic and spherical, are considered. The model is verified by comparing simulation results with an analytical solution of an electron–ion temperature relaxation problem, and a corresponding simulation using unlike charges. In addition, it is found that a PP simulation using like charges can achieve a significant speed-up of 100 compared with a corresponding simulation using unlike charges, due to the capability of using larger time steps while maintaining the same energy conservation.

An asymptotic analysis for a generalized Cahn–Hilliard system with fractional operators

In the recent paper “Well-posedness and regularity for a generalized fractional Cahn–Hilliard system” (Colli et al. in Atti Accad Naz Lincei Rend Lincei Mat Appl 30:437–478, 2019), the same authors have studied viscous and nonviscous Cahn–Hilliard systems of two operator equations in which nonlinearities of double-well type, like regular or logarithmic potentials, as well as nonsmooth potentials with indicator functions, were admitted. The operators appearing in the system equations are fractional powers $$A^{2r}$$ A 2 r and $$B^{2\sigma }$$ B 2 σ (in the spectral sense) of general linear operators A and B, which are densely defined, unbounded, selfadjoint, and monotone in the Hilbert space $$L^2(\Omega )$$ L 2 ( Ω ) , for some bounded and smooth domain $$\Omega \subset {{\mathbb {R}}}^3$$ Ω ⊂ R 3 , and have compact resolvents. Existence, uniqueness, and regularity results have been proved in the quoted paper. Here, in the case of the viscous system, we analyze the asymptotic behavior of the solution as the parameter $$\sigma $$ σ appearing in the operator $$B^{2\sigma }$$ B 2 σ decreasingly tends to zero. We prove convergence to a phase relaxation problem at the limit, and we also investigate this limiting problem, in which an additional term containing the projection of the phase variable on the kernel of B appears.

A Linear Programming Relaxation DEA Model for Selecting a Single Efficient Unit with Variable RTS Technology

The selection-based problem is a type of decision-making issue which involves opting for a single option among a set of available alternatives. In order to address the selection-based problem in data envelopment analysis (DEA), various integrated mixed binary linear programming (MBLP) models have been developed. Recently, an MBLP model has been proposed to select a unit in DEA with variable returns-to-scale technology. This paper suggests utilizing the linear programming relaxation model rather than the MBLP model. The MBLP model is proved here to be equivalent to its linear programming relaxation problem. To the best of the authors’ knowledge, this is the first linear programming model suggested for selecting a single efficient unit in DEA under the VRS (Variable Returns to Scale) assumption. Two theorems and a numerical example are provided to validate the proposed LP model from both theoretical and practical perspectives.

Identifying Stressors and Coping Strategies of Elite Esports Competitors

Researchers have examined some of the psychological aspects of competing at a high level in esports. The present study aims to build on this literature by examining the various stressors faced and the associated coping strategies employed by seven esports competitors. The interviews were inductively analysed, and the findings illustrated a range of internal (e.g., communication issues, lack of shared team goals) and external (e.g., event audience, media interviews) stressors that the participants faced. Following this, the coping strategies used to deal with these stressors were deductively analysed. A number of emotion- (e.g., breathing, relaxation), problem- (e.g., intra-team communication after matches), and approach- (e.g., team camps, delegating roles) coping strategies were described by participants. Avoidance coping strategies were predominantly highlighted as being used during games. Results are considered in line with how applied practitioners might support players to develop strategies to deal with stressors, which might in turn lead to performance enhancements.

An Approach to Chance Constrained Problems Based on Huge Data Sets Using Weighted Stratified Sampling and Adaptive Differential Evolution

In this paper, a new approach to solve Chance Constrained Problems (CCPs) using huge data sets is proposed. Specifically, instead of the conventional mathematical model, a huge data set is used to formulate CCP. This is because such a large data set is available nowadays due to advanced information technologies. Since the data set is too large to evaluate the probabilistic constraint of CCP, a new data reduction method called Weighted Stratified Sampling (WSS) is proposed to describe a relaxation problem of CCP. An adaptive Differential Evolution combined with a pruning technique is also proposed to solve the relaxation problem of CCP efficiently. The performance of WSS is compared with a well known method, Simple Random Sampling. Then, the proposed approach is applied to a real-world application, namely the flood control planning formulated as CCP.

Comparing Information Metrics for a Coupled Ornstein–Uhlenbeck Process

It is often the case when studying complex dynamical systems that a statistical formulation can provide the greatest insight into the underlying dynamics. When discussing the behavior of such a system which is evolving in time, it is useful to have the notion of a metric between two given states. A popular measure of information change in a system under perturbation has been the relative entropy of the states, as this notion allows us to quantify the difference between states of a system at different times. In this paper, we investigate the relaxation problem given by a single and coupled Ornstein–Uhlenbeck (O-U) process and compare the information length with entropy-based metrics (relative entropy, Jensen divergence) as well as others. By measuring the total information length in the long time limit, we show that it is only the information length that preserves the linear geometry of the O-U process. In the coupled O-U process, the information length is shown to be capable of detecting changes in both components of the system even when other metrics would detect almost nothing in one of the components. We show in detail that the information length is sensitive to the evolution of subsystems.

Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation

The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

Identifying Stressors and Coping Strategies of Elite Esports Competitors

Researchers have examined some of the psychological aspects of competing at a high level in esports. The present study aims to build on this literature by examining the various stressors faced and the associated coping strategies employed by seven esports competitors. The interviews were inductively analysed, and the findings illustrated a range of internal (e.g., communication issues, lack of shared team goals) and external (e.g., event audience, media interviews) stressors that the participants faced. Following this, the coping strategies used to deal with these stressors were deductively analysed. A number of emotion- (e.g., breathing, relaxation), problem- (e.g., intra-team communication after matches), and approach- (e.g., team camps, delegating roles) coping strategies were described by participants. Avoidance coping strategies were predominantly highlighted as being used during games. Results are considered in line with how applied practitioners might support players to develop strategies to deal with stressors, which might in turn lead to performance enhancements.