Hypercube Model Research Articles

Emergency service systems: The use of the hypercube queueing model in the solution of probabilistic location problems

AbstractProbabilistic location problems are surveyed from the perspective of their use in the design of emergency service systems, with special emphasis on emergency medical systems. Pioneering probabilistic models were defined in the 1980s, as a natural extension of deterministic covering models (first generation models) and backup models (second generation). These probabilistic models, however, adopted simplifying assumptions that in many cases do not correspond to real‐world situations, where servers usually cooperate and have specific individual workloads. Thus the idea of embedding the hypercube queueing model into these formulations is to make them more adherent to the real world. The hypercube model and its extensions are initially presented in some detail, which is followed by a brief review of exact and approximate methods for its solution. Probabilistic models for the design of emergency service systems are then reviewed. The pioneering models of Daskin and ReVelle and Hogan are extended by embedding the hypercube model into them. Solution methods for these models are surveyed next, with comments on specialized models for the design of emergency medical systems for urban areas and highways.

Analysis of E-learning innovation and core capability using a hypercube model

New information and communication technologies and emerging learning models have triggered a new wave of educational innovation-electronic learning (E-learning). This study utilizes a hypercube innovation model to analyze the differences in technology and learning models (instruction model/environment) used in traditional classroom learning versus E-learning environments. The results show that the innovation from traditional classroom learning to E-learning is radical for both the learner and instructor, leading to drastic changes in the technology and learning model. For educational institutions, the technology is a fundamental change, while the learning model is reinforced. From the dynamic capability perspectives, a set of core capabilities needed for successfully exploiting E-learning is identified. These results provide insight for learners, instructors and educational institutions for enhancing their understanding of E-learning innovation, and provide guidelines to help E-learning stakeholders adapt from the traditional classroom to E-learning environments.

Modelo hipercubo integrado a um algoritmo genético para análise de sistemas médicos emergenciais em rodovias

O modelo hipercubo, conhecido na literatura de problemas de localização de sistemas servidor para cliente, é um modelo baseado em teoria de filas espacialmente distribuídas e aproximações Markovianas. O modelo pode ser modificado para analisar os sistemas de atendimentos emergenciais (SAEs) em rodovias, considerando as particularidades da política de despacho destes sistemas. Neste estudo, combinou-se o modelo hipercubo com um algoritmo genético para otimizar a configuração e operação de SAEs em rodovias. A abordagem é efetiva para apoiar decisões relacionadas ao planejamento e operação destes sistemas, por exemplo, em determinar o tamanho ideal para as áreas de cobertura de cada ambulância, de forma a minimizar o tempo médio de resposta aos usuários e o desbalanceamento das cargas de trabalho das ambulâncias. Os resultados computacionais desta abordagem foram analisados utilizando dados reais do sistema Anjos do Asfalto (rodovia Presidente Dutra).

Computation of Adalines' Sensitivity to Weight Perturbation

In this paper, the sensitivity of Adalines to weight perturbation is discussed. According to the discrete feature of Adalines' input and output, the sensitivity is defined as the probability of an Adaline's erroneous outputs due to weight perturbation with respect to all possible inputs. By means of hypercube model and analytical geometry method, a heuristic algorithm is given to accurately compute the sensitivity. The accuracy of the algorithm is verified by computer simulations.

Mean-field theory description of structural phase transitions in a model ferroelectric with double Morse substrate potential

We investigate the general features of a ferroelectric D-dimensional hypercubic model, with a symmetric double Morse-type on-site potential and nearest-neighbour interaction, that exhibits structural phase transitions. The mean-field theory (MFT) is developed for this model where the anharmonicity is the main characteristic. It is based on making a Gaussian ansatz for the single-particle probability density function and helps us to make a more extensive survey of the order parameter. Two different cases are considered and analytical results analysed. Finally, we discuss the important features of the Hamiltonian, depending on the range of the force constant on the one hand and the strength of the anharmonicity on the other, which is responsible for these structural transitions (first order and second order).

Revolution or evolution? An analysis of E-health innovation and impact using a hypercube model

This study utilises a hypercube innovation model to analyse the changes in both healthcare informatics and medical related delivery models based on the innovations from Tele-healthcare, electronic healthcare (E-healthcare), to mobile healthcare (M-healthcare). Further, the critical impacts of these E-health innovations on the stakeholders: healthcare customers, hospitals, healthcare complementary providers and healthcare regulators are identified. Thereafter, the critical capabilities for adopting each innovation are discussed.

Topological conditions for discrete symmetry breaking and phase transitions

In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase transition are introduced and discussed. A very simple model, which we refer to as the hypercubic model, is introduced and solved. The main purpose of this model is that of illustrating the content of the sufficient conditions, but it is interesting also in itself due to its simplicity. Then some mean-field models already known in the literature are discussed in the light of the sufficient conditions introduced here.

Analysis of E-commerce innovation and impact: a hypercube model

Electronic commerce (E-commerce) innovating applications have posed novel, technical, organizational and commercial challenges. This study uses a hypercube model to investigate these innovative changes and focuses on their impacts on E-commerce stakeholders: providers, E-commerce companies, customers, and complementors. The results indicate that mobile commerce (M-commerce) differs substantially from Web-based commerce in some technological components, yet both share common business model. However, from Web-based to M-commerce, innovation is architectural for customers and E-commerce companies, but a radical change for complementors. From M-commerce to U-commerce, innovation is modular to customers, architectural to complementors and radical to E-commerce companies and providers. Thereafter, the critical impacts of E-commerce innovations on the stakeholders are identified.

A four-ligand hypercube model to quantify allosteric interactions within the GABA A receptor complex

The aim of this study was to investigate the couplings between various binding sites on the GABA A receptor complex. We investigated combinations of three test compounds: (1) GABA (γ-aminobutyric acid), (2) Org 20549 [(2β3α5α)-21hydroxy- 3Hydroxy-2(4morpholinyl)pregnan-20one methane-sulphonate)], a neuroactive steroid and (3) retigabine (D-23129, N-(2-amino-4-(4-fluorobenzylamino)-phenyl) carbamic acid ethyl ester), a new antiepileptic drug. Receptor-binding assays were conducted using rat brain membranes. [ 3H]TBOB ([ 3H]- t-butyl-bicyclo-ortho-benzoate) was the tracer ligand. All three test compounds inhibited the binding of [ 3H]TBOB with EC 50's of 4.0, 98 and 23 μM, respectively. Isobolic analysis of the combination data showed that the three compounds act in synergy in displacing [ 3H]TBOB. These interactions could be described and quantified by a hypercube model in which each of the three test compounds and [ 3H]TBOB bind to different, allosterically coupled sites such that each of the test compounds allosterically displaces the tracer [ 3H]TBOB and allosterically enhances the affinity of any other test compound by a factor 4.4. The simultaneous binding of any two ligands enhances the affinity of the third by a factor 9. These results may contribute to the understanding of individual variability in drug responses and to the discussion about rational polytherapy.

Towards unified formulations and extensions of two classical probabilistic location models

We give a unified view of Daskin's Maximum Expected Covering Location Problem (MEXCLP) and ReVelle and Hogan's Maximum Availability Location Problem (MALP), identifying similarities and dissimilarities between these models and showing how they relate to each other. These models arise in the location of servers in congested emergency systems. An existing extension of MEXCLP is reviewed; we then develop an extension of MALP and give the corresponding mathematical formulation. These two extensions are obtained when the simplifying assumptions of the original models are dropped and Larson's hypercube model is embedded into local search methods. In this paper these methods are further enhanced by the use of simulated annealing. Computational results are given for problems available in the literature.

Solução do problema de localização de máxima disponibolidade utilizando o modelo hipercubo

O Problema de Localização de Máxima Disponibilidade (PLMD) busca localizar m servidores tal que o máximo número de chamadas a um serviço de emergência tenha um servidor disponível a menos de uma distância crítica Spredefinida, com confiabilidadealfa . Neste artigo o PLMD é estendido para o caso em que as taxas de ocupação são calculadas individualmente, por servidor. Isto é conseguido através do uso do Modelo Hipercubo, embutido em uma heurística de substituição de vértices. Resultados computacionais são mostrados para redes de até 150 vértices disponíveis na literatura.

Generalized linear recursive networks: topological and routing properties

This paper presents a methodology for generalizing the class of linear recursive networks (LRN) reported by Hsu et al. [IEEE Trans Parallel Distrib Syst 1997; 8(7)]. The proposed generalization relaxes the restriction on the number of isomorphic subgraphs of LRNs, which is at most 1 by Hsu et al. [IEEE Trans Parallel Distrib Syst 1997; 8(7)]. Hence, our methodology permits the design of a communication topology of size n which satisfies the linear recurrence equation G n ( A)= a 1 G n−1 ( A)∪ a 2 G n−2 ( A)∪⋯∪ a k G n− k ( A), with a j being any non-negative integer for each j∈{1,2,…, k} and a 1>0. In addition, we address the problem of routing of messages in an generalized linear recursive network (GLRN). The paradigm of Fibonacci cubes (FCs) is used to demonstrate the proposed technique. FCs were introduced recently as an attractive alternative to the well-known hypercube model for interconnection networks. A generalized FC, referred to as a “Fibonacci graph” (FG) of size n, is composed of an arbitrary number of such graphs of size n−1 and size n−2. The structural advantage of GLRNs, in general, and FG, in particular, manifests itself in the following ways: 1. They allow more choices to construct systems of various sizes. 2. They emulate other topologies, such as hypercubes, trees, rings and meshes very efficiently. The results of this paper have important applications e.g. in multitasking and job scheduling where a job is decomposed into a set of tasks and assigned to a subset of processors with specified interconnection topology.

Accurate estimation of expected coverage: revisited

As noted in several studies (Batta et al., Transp. Sci. 23 (1989) 277), (Burwell et al., Comput. Opns. Res. 20 (1993) 113), (Daskin, Network and Discrete Location, Wiley, New York, 1995), (Marianov and ReVelle, Eur. J. Opns. Res. 93 (1996) 110), (Saydam et al., Socio-Econ. Plann. Sci. 28(2) (1994) 113), the accurate estimation of expected coverage is an important and open issue. Although the maximum expected coverage model is empirically shown to prescribe a robust set of “optimal” locations, earlier findings suggest that it could also over or underestimate the coverage by a significant margin. In this study, we present a genetic algorithm (GA) that combines the expected coverage approach with the hypercube model (Jarvis, Mgmt. Sci. 31 (1985) 235), (Larson, Comput. Opns. Res. 1 (1974) 67), (Larson, Opns. Res. 23 (1975) 845) to solve the maximum expected coverage location problem with increased accuracy and realism. Our findings suggest that the GA provides at least as good solutions 94% of the time making it a viable alternative to the two-step procedures stipulated earlier.

Critical behavior of certain antiferromagnets with complicated ordering: Four-loopɛ-expansion analysis

The critical behavior of a complex N-component order parameter Ginzburg-Landau model with isotropic and cubic interactions describing antiferromagnetic and structural phase transitions in certain crystals with complicated ordering is studied in the framework of the four-loop renormalization group (RG) approach in $(4-\ve)$ dimensions. By using dimensional regularization and the minimal subtraction scheme, the perturbative expansions for RG functions are deduced and resummed by the Borel-Leroy transformation combined with a conformal mapping. Investigation of the global structure of RG flows for the physically significant cases N=2 and N=3 shows that the model has an anisotropic stable fixed point governing the continuous phase transitions with new critical exponents. This is supported by the estimate of the critical dimensionality $N_c=1.445(20)$ obtained from six loops via the exact relation $N_c={1/2} n_c$ established for the complex and real hypercubic models.

On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Within the four-loop $\ve$ expansion, we study the critical behavior of certain antiferromagnets with complicated ordering. We show that an anisotropic stable fixed point governs the phase transitions with new critical exponents. This is supported by the estimate of critical dimensionality $N_c^C=1.445(20)$ obtained from six loops via the exact relation $N_c^C={1/2} N_c^R$ established for the real and complex hypercubic models.

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The objective of the present paper is to analyze the use and solution of the hypercube model for the case of non-homogeneous servers (servers with different mean service times). Systems with non-homogeneous servers can be found in several real world applications, such as for example in the provision of Emergency Medical Services (EMS) in some Brazilian cities. The importance of explicitly considering non-homogeneous servers in the hypercube model is initially demonstrated through an illustrative example. It is then shown that the solution for the non-homogeneous case can be advantageously obtained by the method of Gauss-Siedel. This method was tested for a network of 55 nodes, in models with between 10 and 17 servers, with the total system workload varying between 0.1 and 0.9. Finally, a regression model is proposed to estimate the computing time required to solve a specific problem

Critical thermodynamics of three-dimensionalMN-component field model with cubic anisotropy from higher-loop ε expansion

The critical thermodynamics of an $MN$-component field model with cubic anisotropy relevant to the phase transitions in certain crystals with complicated ordering is studied within the four-loop $\ve$ expansion using the minimal subtraction scheme. Investigation of the global structure of RG flows for the physically significant cases M=2, N=2 and M=2, N=3 shows that the model has an anisotropic stable fixed point with new critical exponents. The critical dimensionality of the order parameter is proved to be equal to $N_c^C=1.445(20)$, that is exactly half its counterpart in the real hypercubic model.

Analysing emergency medical service ambulance deployment on a Brazilian highway using the hypercube model

In this study we analyse the ambulance deployment of an emergency medical system on a Brazilian highway connecting the cities of São Paulo and Rio de Janeiro. Our focus is on the mean response time of the system to an emergency call, viewed as an important component of the user service. To evaluate the system performance we applied the hypercube model, a well-known tool for planning server-to-customer systems, which is based on spatially distributed queuing theory. The results showed that the model can be effective in supporting design and operational decisions, in particular to reduce the workload unbalancing among the ambulances.

Efficient lot-sizing under a differential transportation cost structure for serially distributed warehouses

A major cost element in the logistics of distributed warehousing is transportation cost. In most practical systems, the transportation costs are volume-dependent. The unit transportation costs are usually determined differentially among intervals of shipment volumes. While the unit cost is constant over an interval, it follows a stepwise declining pattern from an interval to the next higher interval of shipment volumes. This structure is analogous to that of quantity-discounted inventory systems. We consider a single-product, serial warehousing system operating under the differential transportation costs and the traditional holding and ordering costs. External demand occurs at the final stage at a constant continuous rate. Demand must be met on time over an infinite horizon under continuous review. The objective is to determine the ordering lot size for each warehouse such that the long-run average cost is minimized. We model the above problem and establish its structural properties. We first consider two-level differential transportation cost structures and develop efficient algorithms to obtain a best integer ratio and optimal powers-of-two policies. Next, we consider multilevel cost structures and develop a hypercube characterization of the solution space. Efficient algorithms to yield a best integer ratio and powers-of-two policies using the hypercube model and a relaxation approach using the two-level model are developed. Extensive computational studies with the algorithms reveal that the proposed modeling and algorithmic approach is both viable and efficient in solving practical distribution problems. Conclusions and direction for future research are presented.

O uso do modelo hipercubo na solução de problemas de localização probabilísticos

O modelo hipercubo é revisitado tendo em vista sua utilização em métodos de solução para problemas de localização probabilísticos. Este uso do modelo é de bastante relevância em situações em que a aleatoriedade na disponibilidade dos servidores é um fator importante a ser considerado; em algumas circunstâncias esta aleatoriedade só pode ser representada pela modelagem de filas espacialmente distribuídas.O modelo é apresentado com o auxílio de um exemplo ilustrativo, para o qual são derivadas as equações de equilíbrio; medidas de desempenho do modelo são também definidas. Isto é seguido pela descrição de um método exato e de outro aproximado para o cálculo destas medidas. Diversos modelos de localização probabilísticos são então estudados, o que é seguido pela análise de métodos de solução disponíveis para esses modelos, com ênfase especial nos métodos que incluem o uso do modelo hipercubo. Embora atualmente de uso incipiente em problemas de localização probabilísticos, o modelo tem grande potencial nesse contexto, por exemplo se integrado a metaheurísticas tais como simulated annealing e busca tabu.