Conservative compact finite difference scheme for the N‐coupled nonlinear Klein–Gordon equations

In this article, a compact finite difference method is developed for the periodic initial value problem of the N‐coupled nonlinear Klein–Gordon equations. The present scheme is proved to preserve the total energy in the discrete sense. Due to the difficulty in obtaining the priori estimate from the discrete energy conservation law, the cut‐off function technique is employed to prove the convergence, which shows the new scheme possesses second order accuracy in time and fourth order accuracy in space, respectively. Additionally, several numerical results are reported to confirm our theoretical analysis. Lastly, we apply the reliable method to simulate and study the collisions of solitary waves numerically.     

A comparative study of the leading machine learning techniques and two new optimization algorithms

We present here a computational study comparing the performance of leading machine learning techniques to that of recently developed graph-based combinatorial optimization algorithms (SNC and KSNC). The surprising result of this study is that SNC and KSNC consistently show the best or close to best performance in terms of their F₁-scores, accuracy, and recall. Furthermore, the performance of SNC and KSNC is considerably more robust than that of the other algorithms; the others may perform well on average but tend to vary greatly across data sets. This demonstrates that combinatorial optimization techniques can be competitive as compared to state-of-the-art machine learning techniques. The code developed for SNC and KSNC is publicly available.     

Characterization of Basil Volatile Fraction and Study of Its Agronomic Variation by ASCA

Basil is a plant known worldwide for its culinary and health attributes. It counts more than a hundred and fifty species and many more chemo-types due to its easy cross-breeds. Each species and each chemo-type have a typical aroma pattern and selecting the proper one is crucial for the food industry. Twelve basil varieties have been studied over three years (2018–2020), as have four different cuts. To characterize the aroma profile, nine typical basil flavour molecules have been selected using a gas chromatography–mass spectrometry coupled with an olfactometer (GC–MS/O). The concentrations of the nine selected molecules were measured by an ultra-fast CG e-nose and Principal Component Analysis (PCA) was applied to detect possible differences among the samples. The PCA results highlighted differences between harvesting years, mainly for 2018, whereas no observable clusters were found concerning varieties and cuts, probably due to the combined effects of the investigated factors. For this reason, the ANOVA Simultaneous Component Analysis (ASCA) methodology was applied on a balanced a posteriori designed dataset. All the considered factors and interactions were statistically significant (p < 0.05) in explaining differences between the basil aroma profiles, with more relevant effects of variety and year.     

The partition problem

In this paper we describe several forms of thek-partition problem and give integer programming formulations of each case. The dimension of the associated polytopes and some basic facets are identified. We also give several valid and facet defining inequalities for each of the polytopes.Partial Support from NSF Grants DMS 8606188 and ECS 8800281 is gratefully acknowledged.     

A unified theory for coherent systems in reliability II. A unified viewpoint on multinary coherent systems through monotone coherence and relevance

Binary coherent system theory has played an important part in reliability. Its extension to (‘degradable’ or ‘multistate’ or) multinary systems has recently been considered in various papers, through various definitions. This paper studies the most general model for multinary systems, proposes a unified viewpoint on multinary coherent systems and gives unified arguments to apply and to investigate further the binary and multinary cases. In a more detailed way, the ‘helpful bridge’ lately proposed by Block and Savits¹ between the binary and multinary cases is completed and multinary systems then can be studied in terms of monotone binary coherent systems, introduced in a companion paper.² Through various results, multinary systems are examined in terms of structure functions and of life functions; fundamental relations for their analysis are obtained with their set characterizations; the main axis that can be retained among the numerous types of coherence is emphasized, in a unified way, through relevance; reliability models are examined through performance processes, life lengths and performance functions; and Birnbaum's factors of importance are thoroughly extended to the multinary case. Fundamental results proposed in previous studies are thus completed with a shorter unified approach.     

Dynamic routing in open queueing networks: Brownian models,cut constraints and resource pooling

We present an introductory review of recent work on the control of open queueing networks. We assume that customers of different types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through the network is an ordered set of service stations: a customer queues for service at each station on its route and then leaves the system. The two methods of control we consider are the routing of customers through the network, and the sequencing of service at the stations, and our aim is to minimize the number of customers in the system. We concentrate especially on the insights which can be obtained from heavy traffic analysis, and in particular from Harrison's Brownian network models. Our main conclusion is that in many respects dynamic routingsimplifies the behaviour of networks, and that under good control policies it may well be possible to model the aggregate behaviour of a network quite straightforwardly.Supported by SERC grant GR/F 94194.     

T‐joins intersecting small edge‐cuts in graphs

In an earlier paper 3 , we studied cycles in graphs that intersect all edge‐cuts of prescribed sizes. Passing to a more general setting, we examine the existence of T‐joins in grafts that intersect all edge‐cuts whose size is in a given set A ?{1,2,3}. In particular, we characterize all the contraction‐minimal grafts admitting no T‐joins that intersect all edge‐cuts of size 1 and 2. We also show that every 3‐edge‐connected graft admits a T‐join intersecting all 3‐edge‐cuts. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 64–71, 2007     

A linear program for the two-hub location problem

This paper considers the discrete two-hub location problem. We need to choose two hubs from a set of nodes. The remaining nodes are to be connected to one of the two hubs which act as switching points for internodal flows. A configuration which minimizes the total flow cost needs to be found. We show that the problem can be solved in polynomial time when the hub locations are fixed. Since there are at most ways to choose the hub locations, the two-hub location problem can be solved in polynomial time. We transform the quadratic 0–1 integer program of the single allocation problem in the fixed two-hub system into a linear program and show that all extreme points of the polytope defined by the LP are integral. Also, the problem can be transformed into a minimum cut problem which can be solved efficiently by any polynomial time algorithm.     

Isolating block and existence of connecting orbits

Using the notion of an isolating block, some existence criteria of trajectories connecting two critical pints of planar dynaniiral systems are given. Project supported by the National Natural Science Foundation of China.     

Exact ground states of Ising spin glasses: New experimental results with a branch-and-cut algorithm

In this paper we study two-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100×100 can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than 20,000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other, more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determineda priori. Our ground-state energy estimation at zero field is –1.317.