Search results for: interval graph

Authors: Benny Benyamin Nasution, Rahmat Widia Sembiring, Abdul Rahman Dalimunthe, Nursiah Mustari, Nisfan Bahri, Berta br Ginting, Riadil Akhir Lubis, Rita Tavip Megawati, Indri Dithisari

Abstract:

The earth coordinate system is an important part of an attempt for earthquake forecasting, such as the one using Single Layer Hierarchical Graph Neuron (SLHGN). However, there are a number of problems that need to be worked out before the coordinate system can be utilized for the forecaster. One example of those is that SLHGN requires that the focused area of an earthquake must be constructed in a grid-like form. In fact, within the current earth coordinate system, the same longitude-difference would produce different distances. This can be observed at the distance on the Equator compared to distance at both poles. To deal with such a problem, a coordinate system has been developed, so that it can be used to support the ongoing earthquake forecasting using SLHGN. Two important issues have been developed in this system: 1) each location is not represented through two-value (longitude and latitude), but only a single value, 2) the conversion of the earth coordinate system to the x-y cartesian system requires no angular formulas, which is therefore fast. The accuracy and the performance have not been measured yet, since earthquake data is difficult to obtain. However, the characteristics of the SLHGN results show a very promising answer.

Keywords: hierarchical graph neuron, multidimensional hierarchical graph neuron, single layer hierarchical graph neuron, natural disaster forecasting, earthquake forecasting, earth coordinate system

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Authors: Lin Cheng, Zijiang Yang

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Program synthesis is the task to automatically generate programs based on user specification. In this paper, we present a framework that synthesizes programs from flow charts that serve as accurate and intuitive specification. In order doing so, we propose a deep neural network called GRCNN that recognizes graph structure from its image. GRCNN is trained end-to-end, which can predict edge and node information of the flow chart simultaneously. Experiments show that the accuracy rate to synthesize a program is 66.4%, and the accuracy rates to recognize edge and node are 94.1% and 67.9%, respectively. On average, it takes about 60 milliseconds to synthesize a program.

Keywords: program synthesis, flow chart, specification, graph recognition, CNN

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Authors: B. Roopa Sri, Y Lakshmi Naidu

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Chemical Graph Theory (CGT) is the branch of mathematical chemistry in which molecules are modeled to study their physicochemical properties using molecular descriptors. Amongst these descriptors, topological indices play a vital role in predicting the properties by defining the graph topology of the molecule. Recently, the bond-additive topological index known as the Mostar index has been proposed. In this paper, we compute the Mostar-type indices of octane isomers and use the data obtained to perform QSPR analysis. Furthermore, we show the correlation between the Mostar type indices and the properties.

Keywords: chemical graph theory, mostar type indices, octane isomers, qspr analysis, topological index

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Authors: Ali Golestani, Vahid Naseri, Hossein Taheri

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Recently, some of studies examined the effect of exercise on neurotrophic factors influencing the growth, protection, plasticity and function in central and peripheral nerve cells. The aim of this study was to investigate the effects of continuous and interval aerobic exercises with moderate intensity on serum levels of glial cell line-derived neurotrophic factor (GDNF) and aerobic capacity in obese children. 21 obese students with an average age of 13.6 ± 0.5 height 171 ± 5 and BMI 32 ± 1.2 were divided randomly to control, continuous aerobic and interval aerobic groups. Training protocol included continuous or interval aerobic exercises with moderate intensity 50-65%MHR, three times per week for 10 weeks. 48 hours before and after executing of protocol, blood samples were taken from the participants and their GDNF serum levels were measured by ELISA. Aerobic power was estimated using Shuttle-run test. T-test results indicated a small increase in their GDNF serum levels, which was not statistically significant (p =0.11). In addition, the results of ANOVA did not show any significant difference between continuous and interval aerobic training on the serum levels of their GDNF but their aerobic capacity significantly increased (p =0.012). Although continuous and interval aerobic exercise improves aerobic power in obese children, they had no significant effect on their serum levels of GDNF.

Keywords: aerobic power, continuous aerobic training, glial cell line-derived neurotrophic factor (GDNF), interval aerobic training, obese children

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Authors: Rashini Maduka, C. R. Wijesinghe, A. R. Weerasinghe

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Drug-drug interactions (DDIs) can happen when two or more drugs are taken together. Today DDIs have become a serious health issue due to adverse drug effects. In vivo and in vitro methods for identifying DDIs are time-consuming and costly. Therefore, in-silico-based approaches are preferred in DDI identification. Most machine learning models for DDI prediction are used chemical and biological drug properties as features. However, some drug features are not available and costly to extract. Therefore, it is better to make automatic feature engineering. Furthermore, people who have diabetes already suffer from other diseases and take more than one medicine together. Then adverse drug effects may happen to diabetic patients and cause unpleasant reactions in the body. In this study, we present a model with a graph convolutional autoencoder and a graph decoder using a dataset from DrugBank version 5.1.3. The main objective of the model is to identify unknown interactions between antidiabetic drugs and the drugs taken by diabetic patients for other diseases. We considered automatic feature engineering and used Known DDIs only as the input for the model. Our model has achieved 0.86 in AUC and 0.86 in AP.

Keywords: drug-drug interaction prediction, graph embedding, graph convolutional networks, adverse drug effects

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Authors: Masoumeh Ali Pouri, Hamid Haj Seyyed Javadi

Abstract:

Nowadays, cloud processing is one of the important issues in information technology. Since scheduling of tasks graph is an NP-hard problem, considering approaches based on undeterminisitic methods such as evolutionary processing, mostly genetic and cuckoo algorithms, will be effective. Therefore, an efficient algorithm has been proposed for scheduling of tasks graph to obtain an appropriate scheduling with minimum time. In this algorithm, the new approach is based on making the length of the critical path shorter and reducing the cost of communication. Finally, the results obtained from the implementation of the presented method show that this algorithm acts the same as other algorithms when it faces graphs without communication cost. It performs quicker and better than some algorithms like DSC and MCP algorithms when it faces the graphs involving communication cost.

Keywords: cloud computing, scheduling, tasks graph, chakoos algorithm

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Authors: Sonal Budhiraja, Biswabrata Pradhan

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This work considers statistical inference based on progressive Type-I interval censored data with random removal. The scheme of progressive Type-I interval censoring with random removal can be described as follows. Suppose n identical items are placed on a test at time T0 = 0 under k pre-fixed inspection times at pre-specified times T1 < T2 < . . . < Tk, where Tk is the scheduled termination time of the experiment. At inspection time Ti, Ri of the remaining surviving units Si, are randomly removed from the experiment. The removal follows a binomial distribution with parameters Si and pi for i = 1, . . . , k, with pk = 1. In this censoring scheme, the number of failures in different inspection intervals and the number of randomly removed items at pre-specified inspection times are observed. Asymptotic properties of the maximum likelihood estimators (MLEs) are established under some regularity conditions. A β-content γ-level tolerance interval (TI) is determined for two parameters Weibull lifetime model using the asymptotic properties of MLEs. The minimum sample size required to achieve the desired β-content γ-level TI is determined. The performance of the MLEs and TI is studied via simulation.

Keywords: asymptotic normality, consistency, regularity conditions, simulation study, tolerance interval

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Authors: Benniche Omar

Abstract:

We are concerned with abstract fully nonlinear differential equations having the form y’(t)=Ay(t)+f(t,y(t)) where A is an m—dissipative operator (possibly multi—valued) defined on a subset D(A) of a Banach space X with values in X and f is a given function defined on I×X with values in X. We consider a graph K in I×X. We recall that K is said to be viable with respect to the above abstract differential equation if for each initial data in K there exists at least one trajectory starting from that initial data and remaining in K at least for a short time. The viability problem has been studied by many authors by using various techniques and frames. If K is closed, it is shown that a tangency condition, which is mainly linked to the dynamic, is crucial for viability. In the case when X is infinite dimensional, compactness and convexity assumptions are needed. In this paper, we are concerned with the notion of near viability for a given graph K with respect to y’(t)=Ay(t)+f(t,y(t)). Roughly speaking, the graph K is said to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)), if for each initial data in K there exists at least one trajectory remaining arbitrary close to K at least for short time. It is interesting to note that the near viability is equivalent to an appropriate tangency condition under mild assumptions on the dynamic. Adding natural convexity and compactness assumptions on the dynamic, we may recover the (exact) viability. Here we investigate near viability for a graph K in I×X with respect to y’(t)=Ay(t)+f(t,y(t)) where A and f are as above. We emphasis that the t—dependence on the perturbation f leads us to introduce a new tangency concept. In the base of a tangency conditions expressed in terms of that tangency concept, we formulate criteria for K to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)). As application, an abstract null—controllability theorem is given.

Keywords: abstract differential equation, graph, tangency condition, viability

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Authors: Saha Naseri

Abstract:

Introduction/Objective: Son preference, a preference for sons over daughters, is a practice deeply-rooted in gender inequality that is widespread in many societies and across different religions and cultures. In this study, we are aiming to study the effects of son preference on fertility outcomes (birth interval and current contraceptive use) in Afghanistan, where have been perceived with high rates of son preference. The objectives of the study are to examine the association between the sex of the previous child and the duration of the subsequent birth interval and to evaluate the effect of son preference on current contraceptive use. Methodology: Afghanistan Demographic and Health Survey (DHS) (2015) was used to study the impact of son preference on fertility outcomes among married women. The data collected from 28,661 on currently-married women, aged between 15 and 49 years who have at least one child, have used to conduct this quantitative study. Outcomes of interest are birth interval and current contraceptive use. Simple and multiple regression analysis have been conducted to assess the effect of son preference on these fertility outcomes. Results: The present study has highlighted that son preference somehow exists among married women in Afghanistan. It is indicated that the sex of the first birth is significantly associated with the succeeding birth interval. Having a female child as the first baby was associated with a shorter average succeeding birth interval by 1.8 months compared to a baby boy (p-value = 0.000). For the second model, the results identified that women who desire for more sons have 7% higher odds to be current contraceptive user compared to those who have no preference (p-value = 0.03). The latter results do not indicate the son preference. However, one limitation for this result was the timeliness of the questions asked since contraceptive use in the current time was asked along with a question on ‘future’ desired sex composition. Moreover, women may have just given birth and want to reach a certain time span of birth interval before planning for another child, even if it was a boy, which might have affected the results. Conclusion: Overall, this study has demonstrated that there is a positive relationship between son preference and one main fertility behaviors, birth interval. The second fertility outcome, current contraceptive use, was not a good indicator to measure son preference. Based on the finding, recommendations will be made for appropriate interventions addressing gender norms and related fertility decisions.

Keywords: Afghanistan, birth interval, contraceptive, son preference

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Authors: M. Ghasemi, F. Eskandari, B. Hamzehei, A. R. Arshi

Abstract:

Bioelectric activity of nervous cells might be changed causing by various factors. This alteration can lead to unforeseen circumstances in other organs of the body. Therefore, the purpose of this study was to model a single neuron and its behavior under an initial stimulation. This study was developed based on cable theory by means of the Bond Graph method. The numerical values of the parameters were derived from empirical studies of cellular electrophysiology experiments. Initial excitation was applied through square current functions, and the resulted action potential was estimated along the neuron. The results revealed that the model was developed in this research adapted with the results of experimental studies and demonstrated the electrical behavior of nervous cells properly.

Keywords: bond graph, stimulation, nervous cells, modeling

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Authors: Benazzouz Djamel, Termeche Adel, Touati Youcef, Alem Said, Ouziala Mahdi

Abstract:

This paper presents an approach which detect and isolate efficiently a fault in a system. This approach avoids false alarms, non-detections and delays in detecting faults. A study case have been proposed to show the importance of taking into consideration the uncertainties in the decision-making procedure and their effect on the degradation diagnostic performance and advantage of using Bond Graph (BG) for such degradation. The use of BG in the Linear Fractional Transformation (LFT) form allows generating robust Analytical Redundancy Relations (ARR’s), where the uncertain part of ARR’s is used to generate the residuals adaptive thresholds. The study case concerns an electromechanical system composed of a motor, a reducer and an external load. The aim of this application is to show the effectiveness of the BG-LFT approach to robust fault detection.

Keywords: bond graph, LFT, uncertainties, detection and faults isolation, ARR

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Authors: Abdolrasoul Daneshjoo, Fatemeh Akbari Ghara

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Background and Purpose: Obesity is an increasing factor in cardiovascular disease and serum levels of cellular adhesion molecule. It plays an important role in predicting risk for coronary artery disease. The purpose of this research was to study the effect of eight weeks moderate intensity interval training and curcumin intake on ICAM-1 & VCAM-1 levels of menopausal fat rats. Materials and methods: in this study, 28 Wistar Menopausal fat rats aged 6-8 weeks with an average weight of 250-300 (gr) were randomly divided into four groups: control, curcumin supplement, moderate intensity interval training and moderate intensity interval training + curcumin supplement. (7 rats each group). The training program was planned as 8 weeks and 3 sessions per week. Each session consisted of 10 one-min sets with 50 percent intensity and the 2-minutes interval between sets in the first week. Subjects started with 14 meters per minute, and 2 (m/min) was added to increase their speed weekly until the speed of 28 (m/min) in the 8th week. Blood samples were taken 48 hours after the last training session, and ICAM-1 A and VCAM-1 levels were measured. SPSS software, one-way analysis of variance (ANOVA) and Pearson correlation coefficient were used to assess the results. Results: The results showed that eight weeks of training and taking curcumin had significant effects on ICAM-1 levels of the rats (p ≤ 0.05). However, it had no significant effect on VCAM-1 levels in menopausal obese rates (p ≥ 0.05). There was no significant correlation between the levels of ICAM-1 and VCAM-1 in eight weeks training and taking curcumin. Conclusion: Implementation of moderate intensity interval training and the use of curcumin decreased ICAM-1 significantly.

Keywords: curcumin, interval training , ICMA, VCAM

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Authors: Jake Gonzalez, Tommy Dang

Abstract:

This paper proposes a temporal graph approach to visualize and analyze the evolution of gene relationships and nomenclature over time. An interactive web-based tool implements this temporal graph, enabling researchers to traverse a timeline and observe coupled dynamics in network topology and naming conventions. Analysis of a real human genomic dataset reveals the emergence of densely interconnected functional modules over time, representing groups of genes involved in key biological processes. For example, the antimicrobial peptide DEFA1A3 shows increased connections to related alpha-defensins involved in infection response. Tracking degree and betweenness centrality shifts over timeline iterations also quantitatively highlight the reprioritization of certain genes’ topological importance as knowledge advances. Examination of the CNR1 gene encoding the cannabinoid receptor CB1 demonstrates changing synonymous relationships and consolidating naming patterns over time, reflecting its unique functional role discovery. The integrated framework interconnecting these topological and nomenclature dynamics provides richer contextual insights compared to isolated analysis methods. Overall, this temporal graph approach enables a more holistic study of knowledge evolution to elucidate complex biology.

Keywords: temporal graph, gene relationships, nomenclature evolution, interactive visualization, biological insights

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Authors: Nitaya Buntao

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This paper considers the problems of interval estimation for rainfall mean of the lognormal distribution and the delta-lognormal distribution in Northeastern Thailand. We present here the modified generalized pivotal approach (MGPA) compared to the modified method of variance estimates recovery (MMOVER). The performance of each method is examined in term of coverage probabilities and average lengths by Monte Carlo simulation. An extensive simulation study indicates that the MMOVER performs better than the MGPA approach in terms of the coverage probability; it results in highly accurate coverage probability.

Keywords: rainfall mean, interval estimation, lognormal distribution, delta-lognormal distribution

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Authors: Yaw-Ling Lin

Abstract:

A de Bruijn graph of order k is a graph whose vertices representing all length-k sequences with edges joining pairs of vertices whose sequences have maximum possible overlap (length k−1). Every Hamiltonian cycle of this graph defines a distinct, minimum length de Bruijn sequence containing all k-mers exactly once. A Kautz sequence is the minimal generating sequence so as the sequence of minimal length that produces all possible length-k sequences with the restriction that every two consecutive alphabets in the sequences must be different. A collection of de Bruijn/Kautz sequences are orthogonal if any two sequences are of maximally differ in sequence composition; that is, the maximum length of their common substring is k. In this paper, we discuss how such a collection of (maximal) orthogonal de Bruijn/Kautz sequences can be made and use the algorithm to build up a web application service for the synthesized DNA and other related biomolecular sequences.

Keywords: biomolecular sequence synthesis, de Bruijn sequences, Eulerian cycle, Hamiltonian cycle, Kautz sequences, orthogonal sequences

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Authors: Raghavi C. Janaswamy

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In the healthcare sector, heterogenous data elements such as patients, diagnosis, symptoms, conditions, observation text from physician notes, and prescriptions form the essentials of the Electronic Health Record (EHR). The data in the form of clear text and images are stored or processed in a relational format in most systems. However, the intrinsic structure restrictions and complex joins of relational databases limit the widespread utility. In this regard, the design and development of realistic mapping and deep connections as real-time objects offer unparallel advantages. Herein, a graph neural network-based classification of EHR data has been developed. The patient conditions have been predicted as a node classification task using a graph-based open source EHR data, Synthea Database, stored in Tigergraph. The Synthea DB dataset is leveraged due to its closer representation of the real-time data and being voluminous. The graph model is built from the EHR heterogeneous data using python modules, namely, pyTigerGraph to get nodes and edges from the Tigergraph database, PyTorch to tensorize the nodes and edges, PyTorch-Geometric (PyG) to train the Graph Neural Network (GNN) and adopt the self-supervised learning techniques with the AutoEncoders to generate the node embeddings and eventually perform the node classifications using the node embeddings. The model predicts patient conditions ranging from common to rare situations. The outcome is deemed to open up opportunities for data querying toward better predictions and accuracy.

Keywords: electronic health record, graph neural network, heterogeneous data, prediction

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Authors: Jiajun Wang, Xiaoge Li

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The purpose of the aspect-level sentiment analysis task is to identify the sentiment polarity of aspects in a sentence. Currently, most methods mainly focus on using neural networks and attention mechanisms to model the relationship between aspects and context, but they ignore the dependence of words in different ranges in the sentence, resulting in deviation when assigning relationship weight to other words other than aspect words. To solve these problems, we propose a new aspect-level sentiment analysis model that combines a multi-channel convolutional network and graph convolutional network (GCN). Firstly, the context and the degree of association between words are characterized by Long Short-Term Memory (LSTM) and self-attention mechanism. Besides, a multi-channel convolutional network is used to extract the features of words in different ranges. Finally, a convolutional graph network is used to associate the node information of the dependency tree structure. We conduct experiments on four benchmark datasets. The experimental results are compared with those of other models, which shows that our model is better and more effective.

Keywords: aspect-level sentiment analysis, attention, multi-channel convolution network, graph convolution network, dependency tree

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Authors: Ould Bouamama, M. Bressel, D. Hissel, M. Hilairet

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Fuel cell (FC) is one of the best alternatives of fossil energy. Recently, the research community of fuel cell has shown a considerable interest for diagnosis in view to ensure safety, security, and availability when faults occur in the process. The problematic for model based FC diagnosis consists in that the model is complex because of coupling of several kind of energies and the numerical values of parameters are not always known or are uncertain. The present paper deals with use of one tool: the Linear Fractional Transformation bond graph tool not only for uncertain modelling but also for monitorability (ability to detect and isolate faults) analysis and formal generation of robust fault indicators with respect to parameter uncertainties.The developed theory applied to a nonlinear FC system has proved its efficiency.

Keywords: bond graph, fuel cell, fault detection and isolation (FDI), robust diagnosis, structural analysis

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Authors: Prat Yotyawilai, Taratip Suwannasart

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Business Process Model and Notation (BPMN) is more important in the business process and creating functional models, and is a standard for OMG, which becomes popular in various organizations and in education. Researches related to software testing based on models are prominent. Although most researches use the UML model in software testing, not many researches use the BPMN Model in creating test cases. Therefore, this research proposes a design of a tool for generating test cases from the BPMN. The model is analyzed and the details of the various components are extracted before creating a flow graph. Both details of components and the flow graph are used in generating test cases.

Keywords: software testing, test case, BPMN, flow graph

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Authors: Yuntao Liu, Lei Wang, Haoran Xia

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Machine learning has shown extensive applications in the development of classification models for autism spectrum disorder (ASD) using neural image data. This paper proposes a fusion multi-modal classification network based on a graph neural network. First, the brain is segmented into 116 regions of interest using a medical segmentation template (AAL, Anatomical Automatic Labeling). The image features of sMRI and the signal features of fMRI are extracted, which build the node and edge embedding representations of the brain map. Then, we construct a dynamically updated brain map neural network and propose a method based on a dynamic brain map adjacency matrix update mechanism and learnable graph to further improve the accuracy of autism diagnosis and recognition results. Based on the Autism Brain Imaging Data Exchange I dataset(ABIDE I), we reached a prediction accuracy of 74% between ASD and TD subjects. Besides, to study the biomarkers that can help doctors analyze diseases and interpretability, we used the features by extracting the top five maximum and minimum ROI weights. This work provides a meaningful way for brain disorder identification.

Keywords: autism spectrum disorder, brain map, supervised machine learning, graph network, multimodal data, model interpretability

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Authors: Mahdi Jalili

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Functional connectivity in the human brain can be represented as a network using electroencephalography (EEG) signals. Network representation of EEG time series can be an efficient vehicle to understand the underlying mechanisms of brain function. Brain functional networks – whose nodes are brain regions and edges correspond to functional links between them – are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which graph theory metrics are sex dependent. To this end, EEGs from 24 healthy female subjects and 21 healthy male subjects were recorded in eyes-closed resting state conditions. The connectivity matrices were extracted using correlation analysis and were further binarized to obtain binary functional networks. Global and local efficiency measures – as graph theory metrics– were computed for the extracted networks. We found that male brains have a significantly greater global efficiency (i.e., global communicability of the network) across all frequency bands for a wide range of cost values in both hemispheres. Furthermore, for a range of cost values, female brains showed significantly greater right-hemispheric local efficiency (i.e., local connectivity) than male brains.

Keywords: EEG, brain, functional networks, network science, graph theory

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Authors: Hae-Yeoun Lee

Abstract:

Quantification of cardiac function is performed by calculating blood volume and ejection fraction in routine clinical practice. However, these works have been performed by manual contouring,which requires computational costs and varies on the observer. In this paper, an automatic left ventricle segmentation algorithm on cardiac magnetic resonance images (MRI) is presented. Using knowledge on cardiac MRI, a K-mean clustering technique is applied to segment blood region on a coil-sensitivity corrected image. Then, a graph searching technique is used to correct segmentation errors from coil distortion and noises. Finally, blood volume and ejection fraction are calculated. Using cardiac MRI from 15 subjects, the presented algorithm is tested and compared with manual contouring by experts to show outstanding performance.

Keywords: cardiac MRI, graph searching, left ventricle segmentation, K-means clustering

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Authors: Lavinia B. Dulla

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The exploration study of the fuzzy regression approach attempts to present that fuzzy regression can be used as a possible alternative to classical regression. It likewise seeks to assess the differences and characteristics of simple linear regression and fuzzy regression using the width of prediction interval, mean absolute deviation, and variance of residuals. Based on the simple linear regression model, the fuzzy regression approach is worth considering as an alternative to simple linear regression when the sample size is between 10 and 20. As the sample size increases, the fuzzy regression approach is not applicable to use since the assumption regarding large sample size is already operating within the framework of simple linear regression. Nonetheless, it can be suggested for a practical alternative when decisions often have to be made on the basis of small data.

Keywords: fuzzy regression approach, minimum fuzziness criterion, interval regression, prediction interval

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Authors: Subhash Chandra Sharma, Mohammad Soleimani

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Selection of the correct lubricant for the top of rail application is a complex process. In this paper, the selection of the proper lubricant for a Top-Of-Rail (TOR) lubrication system based on graph theory and matrix approach has been developed. Attributes influencing the selection process and their influence on each other has been represented through a digraph and an equivalent matrix. A matrix function which is called the Permanent Function is derived. By substituting the level of inherent contribution of the influencing parameters and their influence on each other qualitatively, a criterion called Suitability Index is derived. Based on these indices, lubricants can be ranked for their suitability. The proposed model can be useful for maintenance engineers in selecting the best lubricant for a TOR application. The proposed methodology is illustrated step–by-step through an example.

Keywords: lubricant selection, top of rail lubrication, graph-theory, Ranking of lubricants

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Authors: E. R. Swart, S. J. Gismondi, N. R. Swart, C. E. Bell

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We present an heuristic algorithm that decides graph non-Hamiltonicity. All graphs are directed, each undirected edge regarded as a pair of counter directed arcs. Each of the n! Hamilton cycles in a complete graph on n+1 vertices is mapped to an n-permutation matrix P where p(u,i)=1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n+1. We first create exclusion set E by noting all arcs (u, v) not in G, sufficient to code precisely all cycles excluded from G i.e. cycles not in G use at least one arc not in G. Members are pairs of components of P, {p(u,i),p(v,i+1)}, i=1, n-1. A doubly stochastic-like relaxed LP formulation of the Hamilton cycle decision problem is constructed. Each {p(u,i),p(v,i+1)} in E is coded as variable q(u,i,v,i+1)=0 i.e. shrinks the feasible region. We then implement the Weak Closure Algorithm (WCA) that tests necessary conditions of a matching, together with Boolean closure to decide 0/1 variable assignments. Each {p(u,i),p(v,j)} not in E is tested for membership in E, and if possible, added to E (q(u,i,v,j)=0) to iteratively maximize |E|. If the WCA constructs E to be maximal, the set of all {p(u,i),p(v,j)}, then G is decided non-Hamiltonian. Only non-Hamiltonian G share this maximal property. Ten non-Hamiltonian graphs (10 through 104 vertices) and 2000 randomized 31 vertex non-Hamiltonian graphs are tested and correctly decided non-Hamiltonian. For Hamiltonian G, the complement of E covers a matching, perhaps useful in searching for cycles. We also present an example where the WCA fails.

Keywords: Hamilton cycle decision problem, computational complexity theory, graph theory, theoretical computer science

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

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Authors: Ayşe Dilek Maden

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For a given a simple connected graph, we present some new bounds via a new approach for a special topological index given by the sum of the real number power of the non-zero normalized Laplacian eigenvalues. To use this approach presents an advantage not only to derive old and new bounds on this topic but also gives an idea how some previous results in similar area can be developed.

Keywords: degree Kirchhoff index, normalized Laplacian eigenvalue, spanning tree, simple connected graph

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Authors: Kreangkri Ratchagit

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This paper is concerned with exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, timevarying delays, Lyapunov-Krasovskii functional, Leibniz-Newton’s formula

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Authors: F. Hamidi, N. Amiri, H. Mishmast Nehi

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The Bilevel Programming (BP) model has been presented for a decision making process that consists of two decision makers in a hierarchical structure. In fact, BP is a model for a static two person game (the leader player in the upper level and the follower player in the lower level) wherein each player tries to optimize his/her personal objective function under dependent constraints; this game is sequential and non-cooperative. The decision making variables are divided between the two players and one’s choice affects the other’s benefit and choices. In other words, BP consists of two nested optimization problems with two objective functions (upper and lower) where the constraint region of the upper level problem is implicitly determined by the lower level problem. In real cases, the coefficients of an optimization problem may not be precise, i.e. they may be interval. In this paper we develop an algorithm for solving interval bilevel linear fractional programming problems. That is to say, bilevel problems in which both objective functions are linear fractional, the coefficients are interval and the common constraint region is a polyhedron. From the original problem, the best and the worst bilevel linear fractional problems have been derived and then, using the extended Charnes and Cooper transformation, each fractional problem can be reduced to a linear problem. Then we can find the best and the worst optimal values of the leader objective function by two algorithms.

Keywords: best and worst optimal solutions, bilevel programming, fractional, interval coefficients

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Authors: Boumesbah Asma, Chergui Mohamed El-amine

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Since it has been shown that the multi-objective minimum spanning tree problem (MOST) is NP-hard even with two criteria, we propose in this study a hybrid NSGA-II algorithm with an exact mutation operator, which is only used with low probability, to find an approximation to the Pareto front of the problem. In a connected graph G, a spanning tree T of G being a connected and cycle-free graph, if k edges of G\T are added to T, we obtain a partial graph H of G inducing a reduced size multi-objective spanning tree problem compared to the initial one. With a weak probability for the mutation operator, an exact method for solving the reduced MOST problem considering the graph H is then used to give birth to several mutated solutions from a spanning tree T. Then, the selection operator of NSGA-II is activated to obtain the Pareto front approximation. Finally, an adaptation of the VNS metaheuristic is called for further improvements on this front. It allows finding good individuals to counterbalance the diversification and the intensification during the optimization search process. Experimental comparison studies with an exact method show promising results and indicate that the proposed algorithm is efficient.

Keywords: minimum spanning tree, multiple objective linear optimization, combinatorial optimization, non-sorting genetic algorithm, variable neighborhood search

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