Restricted Problem Research Articles

How the COVID-19 pandemic shaped Canadians' preferences for setting of dying: Comparison of two panel surveys.

The purpose of this article is to assess whether COVID-19 shaped Canadians' preferred settings of dying. We compared data collected using the same survey from two independent but comparable sets of panel respondents, prior to and after the onset of the pandemic. A vignette methodology was used to assess preferences for dying in each of four settings: home, acute/intensive care, palliative care, and long-term residential care. Although preferences for dying at home, in acute/intensive care and palliative care units did not change, preferences for dying in nursing homes significantly declined. In the pandemic's first and second waves, the spread of knowledge about problems of poor care, visitation restrictions, and fears of contagion in Canadian long-term residential care may have shaped public perceptions of and preferences for dying these settings. If this change persists, it may influence advance care planning decisions. That preferences for dying at home did not shift is, however, noteworthy.

A multi-level rescheduling approach for a dynamic remote operations scheduling problem

ABSTRACT In this paper, we tackle a dynamic scheduling problem faced by a large international company. The problem involves assigning installation projects arriving over time to specialised technicians who execute them remotely. Each project consists of several tasks having processing times, release dates, and execution deadlines. The company needs to assign projects to technicians and schedule tasks complying with technicians' skills, precedence constraints between tasks, and tasks requiring multiple technicians simultaneously. The problem is dynamic as new projects and tasks become available over time, requiring their allocation to technicians. We formulate the offline problem as a mixed integer linear program that minimises the makespan, and we address the dynamic version solving restricted problems within a rolling horizon framework. The approach systematically implements different levels of schedule adjustment to incorporate new information. To study scalability, we validate our algorithm by using both real-world and synthetic simulations demonstrating its efficiency and effectiveness. Additionally, we provide interesting managerial insights for the company.

The Lyapunov Stability of Central Configurations of the Planar Circular Restricted Four-Body Problem

The Lyapunov Stability of Central Configurations of the Planar Circular Restricted Four-Body Problem

Orthorexia as an Eating Disorder Spectrum-A Review of the Literature.

The purpose of this study is to compare and analyze research studies focused on orthorexia nervosa (ON) as a spectrum of eating disorders, and to summarize potential risk factors in different age and social groups. ON is characterized by an obsession with healthy eating, which leads to a restrictive diet and health problems. Due to a lack of comprehensive analyses, this review re-examined studies from 2006 to 2023, initially retrieving 53,134 articles. Upon refining the criteria and risk factors for eating disorders, 34 notable records were identified. These studies employed diagnostic tools such as ORTO and BOT, focusing on risk factors for ON. Results indicate that individuals suffering from eating disorders, losing weight, exercising heavily, developing relationship problems, and suffering from body dysmorphic disorder are at high risk of developing ON. A significant correlation was found between ON, BMI, and gender, but not between ON and OCD. Interestingly, ON symptoms appear to overlap with those of other eating disorders, such as anorexia and bulimia, especially in terms of obsessive control over dieting and fear of gaining weight, indicating a close relationship between the two. Interestingly, orthorexia nervosa may serve as a coping mechanism for anorexia, providing a sense of control. However, further research on its long-term effects is required.

Adults who Smoke Should Have Pulmonary Function Testing Before and After Coronary Artery Bypass Grafting (CABG)

Background: Recent research has shown that coronary artery bypass grafting (CABG) has a mortality rate of 0.6–3.0%, making it a popular and generally safe cardiac operation. The purpose of this study is to examine the relationship between sex, age, and diabetes in the early changes in lung volumes measured by pulmonary function tests before and after coronary artery bypass grafting (CABG) in individuals who smoke. Subjects and procedures: Elective coronary artery bypass surgery was the procedure of choice for 200 consecutive patients in this prospective controlled trial. Participants who were not part of the trial were those who were in an emergency or who had a valve operation done alongside a CABG procedure. Based on the data from the operation, the cardiopulmonary bypass time was 98.89 minutes with a standard deviation of 25.14 minutes. The average time for cardiac ischemia was 67.8 minutes with a standard deviation of 26.6 minutes and a range of 25 to 227 minutes. The total time spent in the intensive care unit was 53.54 hours with a standard deviation of 27.98 hours and a range of 4 to 102 hours. Thirteen patients, or 6.5%, were cold, while the remaining patients were warm. Thirteen patients, or 6.5%, used ice slush as a topical cooling method. The results of the pulmonary function tests taken before and after surgery were significantly different. Conclusion: Postoperative obstructive and restrictive breathing problems are associated with cigarette smoking's detrimental effects on pulmonary functioning. Patients with a smoking history who are scheduled for elective revascularization surgery should have their pulmonary status evaluated before surgery, and they should be strongly encouraged to quit smoking as soon as possible before surgery to minimize the risk of respiratory complications after surgery.

Interpolating Between Rényi Entanglement Entropies for Arbitrary Bipartitions via Operator Geometric Means

AbstractThe asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the flattening ranks. Over the complex numbers, a refinement of this problem, originating in the theory of quantum entanglement, is to find the optimal rate of entanglement transformations as a function of the error exponent. This trade-off can also be characterized in terms of the set of normalized, additive, multiplicative functionals that are monotone in a suitable sense, which includes the restriction-monotones as well. For example, the flattening ranks generalize to the (exponentiated) Rényi entanglement entropies of order $$\alpha \in [0,1]$$ α ∈ [ 0 , 1 ] . More complicated parameters of this type are known, which interpolate between the flattening ranks or Rényi entropies for special bipartitions, with one of the parts being a single tensor factor. We introduce a new construction of subadditive and submultiplicative monotones in terms of a regularized Rényi divergence between many copies of the pure state represented by the tensor and a suitable sequence of positive operators. We give explicit families of operators that correspond to the flattening-based functionals, and show that they can be combined in a nontrivial way using weighted operator geometric means. This leads to a new characterization of the previously known additive and multiplicative monotones, and gives new submultiplicative and subadditive monotones that interpolate between the Rényi entropies for all bipartitions. We show that for each such monotone there exist pointwise smaller multiplicative and additive ones as well. In addition, we find lower bounds on the new functionals that are superadditive and supermultiplicative.

Machine learning on quantum experimental data toward solving quantum many-body problems

Advancements in the implementation of quantum hardware have enabled the acquisition of data that are intractable for emulation with classical computers. The integration of classical machine learning (ML) algorithms with these data holds potential for unveiling obscure patterns. Although this hybrid approach extends the class of efficiently solvable problems compared to using only classical computers, this approach has been only realized for solving restricted problems because of the prevalence of noise in current quantum computers. Here, we extend the applicability of the hybrid approach to problems of interest in many-body physics, such as predicting the properties of the ground state of a given Hamiltonian and classifying quantum phases. By performing experiments with various error-reducing procedures on superconducting quantum hardware with 127 qubits, we managed to acquire refined data from the quantum computer. This enabled us to demonstrate the successful implementation of theoretically suggested classical ML algorithms for systems with up to 44 qubits. Our results verify the scalability and effectiveness of the classical ML algorithms for processing quantum experimental data.

Graph realization of distance sets

The Distance Realization problem is defined as follows. Given an n×n matrix D of nonnegative integers, interpreted as inter-vertex distances, find an n-vertex weighted or unweighted graph G realizing D, i.e., whose inter-vertex distances satisfy distG(i,j)=Di,j for every 1≤i<j≤n, or decide that no such realizing graph exists. The problem was studied for general weighted and unweighted graphs, as well as for cases where the realizing graph is restricted to a specific family of graphs (e.g., trees or bipartite graphs). An extension of Distance Realization that was studied in the past is where each entry in the matrix D may contain a range of consecutive permissible values. We refer to this extension as Range Distance Realization (or Range-DR). Restricting each range to at most k values yields the problem k-Range Distance Realization (or k-Range-DR). The current paper introduces a new extension of Distance Realization, in which each entry Di,j of the matrix may contain an arbitrary set of acceptable values for the distance between i and j, for every 1≤i<j≤n. We refer to this extension as Set Distance Realization (Set-DR), and to the restricted problem where each entry may contain at most k values as k-Set Distance Realization (or k-Set-DR).We first show that 2-Range-DR is NP-hard for unweighted graphs (implying the same for 2-Set-DR). Next we prove that 2-Set-DR is NP-hard for unweighted and weighted trees.Finally, we explore Set-DR where the realization is restricted to the families of stars, paths, cycles, or caterpillars. For the weighted case, our positive results are that there exist polynomial time algorithms for the 2-Set-DR problem on stars, paths and cycles, and for the 1-Set-DR problem on caterpillars. On the hardness side, we prove that 6-Set-DR is NP-hard for stars and 5-Set-DR is NP-hard for paths, cycles and caterpillars. For the unweighted case, our results are the same, except for the case of unweighted stars, for which k-Set-DR is polynomially solvable for any k.

Single machine scheduling with the total weighted late work and rejection cost

AbstractWe study a single machine scheduling problem with the total weighted late work and the total rejection cost. The late work of a job is the part of this job executed after its due date, and the rejection cost of a job is the fee of rejecting to process it. We consider a Pareto scheduling and two restricted scheduling problems. The Pareto scheduling problem aims to find all non‐dominated values of the total weighted late work and the total rejection cost. The restricted scheduling problems are dedicated to minimizing the total weighted late work with the total rejection cost not greater than a given threshold, and minimizing the total rejection cost with the total weighted late work not greater than a given threshold, respectively. For the Pareto scheduling problem, we prove that it is binary NP‐hard by providing a pseudo‐polynomial time algorithm, and give a fully polynomial time approximation scheme (FPTAS). For the restricted scheduling problems, we prove that there are no FPTASes unless , which answers an open problem. Moreover, we develop relaxed FPTASes for these two restricted scheduling problems.

Composite learning prescribed performance control of strict-feedback nonlinear systems with mismatched parametric uncertainties

A composite learning prescribed performance control (CLPPC) approach is presented for strict-feedback nonlinear systems with mismatched parametric uncertainties. A finite-time performance function based on polynomial is introduced to predefined a restriction region with respect to the tracking error. By introducing an error transformation function, the tracking error restriction problem of the original system is transformed into the stability problem of an equivalent transformation system. To guarantee the convergence of unknown parameters, online recording data and instantaneous are used to generate a prediction error, which is used together with filtered tracking errors to update parameter estimations under an interval excitation condition. All signals are proven to be ultimately uniformly stable under the proposed CLPPC strategy. Furthermore, the tracking error is limited within the predefined region after the predefined time. Simulation results verify the effectiveness of the proposed approach.

A bay design problem in less-than-unit-load production warehouse

In this paper, we consider a bay design problem in a less-than-unit-load production warehouse, which is motivated by a real-world problem in a semiconductor company. The objective is to maximize the utilization of the vertical space in bays by considering several practical storage requirements. To solve the problem, a non-linear integer programming model is first formulated. Since the problem is similar to a two-stage cutting stock problem (CSP), a column-and-row generation (CRG) method is developed, in which the original problem is decomposed into a restricted master problem and three subproblems, including two classical column generation subproblems and a row generation subproblem. The two former subproblems are solved as unbounded knapsack problems and for the latter, a two-stage approach is applied. The results of computational experiments on randomly generated instances show that the proposed CRG method is more efficient than the classic column-generation-based method, solving the non-linear model directly and solving a cut model in the literature directly. The results of a case study show that our strategy can improve the utilization of the existing warehouse storage space significantly by about 24%. The CRG method is also tested on basic two-stage two-dimensional CSP benchmarks and its performance is compared to those of other pattern-based methods. The results show its potential for effectively solving the basic two-stage two-dimensional CSPs.

Robust tracking via coarse-to-fine redetection and spatial–temporal reliability evaluation

Correlation-filter-based trackers still suffer from the problem of spatial restriction and have difficulty in handling unreliable tracking results. In this paper, we propose a robust correlation tracking method by integrating coarse-to-fine redetection scheme and spatial–temporal reliability evaluation strategy. Specifically, we first exploit an improved multi-region coarse estimation method to identify multiple possible candidate regions. Then, the dense search is performed in candidate regions and some candidate objects are obtained. Considering that a good sampling center can help obtain more reasonable response values for the target and other objects, the proposed redetection scheme jointly considers the sampling center quality and detection quality to determine the redetection result. To reduce the risk of drifting to similar distractors in the expanded search area, a novel reliability evaluation strategy is developed with spatial–temporal context to measure the sampling center quality and further elaborate the reliability scores of candidate objects. Furthermore, an effective output integration method is proposed to determine the final output by carefully checking the tracking result and redetection result with historical information and distance constraint. Extensive experimental results demonstrate that the proposed method can achieve favorable tracking performance compared with some state-of-the-art trackers.

FPWT: Filter pruning via wavelet transform for CNNs

The enormous data and computational resources required by Convolutional Neural Networks (CNNs) hinder the practical application on mobile devices. To solve this restrictive problem, filter pruning has become one of the practical approaches. At present, most existing pruning methods are currently developed and practiced with respect to the spatial domain, which ignores the potential interconnections in the model structure and the decentralized distribution of image energy in the spatial domain. The image frequency domain transform method can remove the correlation between image pixels and concentrate the image energy distribution, which results in lossy compression of images. In this study, we find that the frequency domain transform method is also applicable to the feature maps of CNNs. The filter pruning via wavelet transform (WT) is proposed in this paper (FPWT), which combines the frequency domain information of WT with the output feature map to more obviously find the correlation between feature maps and make the energy into a relatively concentrated distribution in the frequency domain. Moreover, the importance score of each feature map is calculated by the cosine similarity and the energy-weighted coefficients of the high and low frequency components, and prune the filter based on its importance score. Experiments on two image classification datasets validate the effectiveness of FPWT. For ResNet-110 on CIFAR-10, FPWT reduces FLOPs and parameters by more than 60.0 % with 0.53 % accuracy improvement. For ResNet-50 on ImageNet, FPWT reduces FLOPs by 53.8 % and removes parameters by 49.7 % with only 0.97 % loss of Top-1 accuracy.

Minimising the makespan on parallel identical machines with log-linear position-dependent processing times

This article studies the minimum makespan scheduling problem on parallel identical machines with the log-linear learning/ageing effect, also known as polynomial positional learning/ageing effect. To develop a Fully Polynomial Time Approximation Scheme to the problem, we start with an intermediate artificial variant that rounds the values to integers and restricts the solutions to instances sorted in the shortest/longest processing time order. To this end, we propose a dynamic programming algorithm and show that the difference between its returned value and the minimum makespan of the original problem is independent of the processing times. This then leads to an algorithm with provable guaranteed ϵ-additive approximation and pseudo-polynomial running time algorithm, resulting in the desired fully polynomial time approximation solution to the original, not restricted problem.

Dynamics of a restricted (6 + 1)-vortex problem

This paper investigates the dynamics of a restricted (6 + 1)-vortex problem. The existence of nested equilateral triangle configurations depends on the position of two triangles, which can be divided into two situations: staggered arrangement and symmetrical arrangement. Firstly, we provide the existence conditions for the configuration and further discuss the stability of the configuration numerically. Secondly, we have established the global dynamics of the restricted point-vortex problem with configurations under different arrangements, including the dynamic behavior of equilibrium points, periodic orbits, homoclinic orbits, and heteroclinic orbits.

Dynamics around the Earth–Moon triangular points in the Hill restricted 4-body problem

This paper investigates the motion of a small particle moving near the triangular points of the Earth–Moon system. The dynamics are modeled in the Hill restricted 4-body problem (HR4BP), which includes the effect of the Earth and Moon as in the circular restricted 3-body problem (CR3BP), as well as the direct and indirect effect of the Sun as a periodic time-dependent perturbation of the CR3BP. Due to the periodic perturbation, the triangular points of the CR3BP are no longer equilibrium solutions; rather, the triangular points are replaced by periodic orbits with the same period as the perturbation. Additionally, there is a 2:1 resonant periodic orbit that persists from the CR3BP into the HR4BP. In this work, we investigate the dynamics around these invariant objects by performing a center manifold reduction and computing families of 2-dimensional invariant tori and their linear normal behavior. We identify bifurcations and relationships between families. Mechanisms for transport between the Earth, L4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_4$$\\end{document}, and the Moon are discussed. Comparisons are made between the results presented here and in the bicircular problem (BCP).

Reconstructing Euler’s work on collinear solutions of the 3-body problem and identifying their corresponding Lagrange points

This paper presents a slightly different perspective on Euler solutions, which are well-known central configurations characterizing all collinear solutions of the 3-body problem. We then build upon this by introducing an additional body with zero mass and classifying the resulting central configurations of the circular restricted 4-body problem.

Energy-informed pathways: A fundamental approach to designing ballistic lunar transfers

Ballistic Lunar Transfers (BLTs) offer propellant-efficient paths to the Moon. The nature of such transfers relies on the combined gravitational influence of the Earth, Moon, and Sun to reach the lunar vicinity. These transfers are often constructed as point designs to deliver results for a specific application. This investigation focuses on a broader, more foundational approach to BLTs seeking general design characteristics. This investigation introduces dynamics-based approaches for characterizing low-energy cislunar transfers. Principles from dynamical systems theory are applied in the Earth-Moon-Sun Bicircular Restricted Four-body Problem to enable the construction of such paths. Structures such as the instantaneous equilibrium solutions and the evolution of the Hamiltonian offer a dynamical foundation for the mechanisms that govern low-energy transfers. A targeting framework enables the methodical construction of BLT families by applying dynamically informed initial conditions from perigee maps and equilibrium solutions. With solutions generated in the four-body model, several strategies are incorporated to transition the solutions into a higher-fidelity force model governed by the ephemerides of the celestial bodies. Incorporating transfer geometries from the Earth-Moon and Sun-B1 rotating frame offers an effective transition strategy for ballistic lunar transfers to such a higher-fidelity force model. Connections between the underlying dynamics that govern ballistic lunar transfers and the practical results in the mission design process are highlighted.

Study of Stokes Drag and Radiation Pressure in the Restricted Four-Body Problem with Variable Mass

Study of Stokes Drag and Radiation Pressure in the Restricted Four-Body Problem with Variable Mass

On the Restricted Steiner Multi Cycle Problem

We introduce a new problem, called Steiner Multi Cycle Problem, in which we are given a complete weighted graph G=(V,E), which respects the triangle inequality, a collection of terminal sets {T1,…,Tk}, where for each a in [k] we have a subset Ta of V and these terminal sets are pairwise disjoint. The goal is to find a set of disjoint cycles of minimum cost such that for each a in [k], all vertices of Ta belong to a same cycle. Our main interest is in a restricted case where |Ta|=2, for each a in [k], which models a collaborative problem with pickup and delivery. We show that even the restricted problem is NP-Hard, and present three heuristics to solve it: a dynamic programming algorithm called Refinement Search Heuristic, which explores geometric and laminar set properties; a heuristic based on the Gonzales Clustering algorithm; and a GRASP Heuristic with Path Relinking. We performed computational experiments with 525 instances to compare these methods, which achieved results close to the optimum, highlighting the performance of the Refinement Search Heuristic both in quality and time.