Search results for: anxious/depressed problem

Authors: Md. Ahsan Ayub, Kazi A. Kalpoma, Humaira Tasnim Proma, Syed Mehrab Kabir, Rakib Ibna Hamid Chowdhury

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Constraint Satisfaction Problem (CSP) is observed in various applications, i.e., scheduling problems, timetabling problems, assignment problems, etc. Researchers adopt a CSP technique to tackle a certain problem; however, each technique follows different approaches and ways to solve a problem network. In our exhaustive study, it has been possible to visualize the processes of essential CSP algorithms from a very concrete constraint satisfaction example, NQueens Problem, in order to possess a deep understanding about how a particular constraint satisfaction problem will be dealt with by our studied and implemented techniques. Besides, benchmark results - time vs. value of N in N-Queens - have been generated from our implemented approaches, which help understand at what factor each algorithm produces solutions; especially, in N-Queens puzzle. Thus, extended decisions can be made to instantiate a real life problem within CSP’s framework.

Keywords: arc consistency (AC), backjumping algorithm (BJ), backtracking algorithm (BT), constraint satisfaction problem (CSP), forward checking (FC), least constrained values (LCV), maintaining arc consistency (MAC), minimum remaining values (MRV), N-Queens problem

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Authors: Deyadeen Ali Alshibani

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In the literature, the multi-armed bandit problem as a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. There are several different algorithms models and their applications on this problem. In this paper, we evaluate the Regret-regression through comparing with Q-learning method. A simulation on determination of optimal treatment regime is presented in detail.

Keywords: optimal, bandit problem, optimization, dynamic programming

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Prasad Urvashi, Wynn Yezarni, Williams Shehan, Ravindran Arun

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Introduction: Primary health services are often the first point of contact that patients with mental illness have with the healthcare system. A number of tools have been developed to increase detection of depression in the context of primary care. However, one challenge amongst many includes utilizing these tools within the limited primary care consultation timeframe. Therefore, short questionnaires that screen for depression that are just as effective as more comprehensive diagnostic tools may be beneficial in improving detection rates of patients visiting a primary care setting. Objective: To develop and determine the sensitivity and specificity of a 2-Question Questionnaire (2-QQ) to screen for depression in in a suburban primary care clinic in Ragama, Sri Lanka. The purpose is to develop a short screening tool for depression that is culturally adapted in order to increase the detection of depression in the Sri Lankan patient population. Methods: This was a cross-sectional study involving two steps. Step one: verbal administration of 2-QQ to patients by their primary care physician. Step two: completion of the Peradeniya Depression Scale, a validated diagnostic tool for depression, the patient after their consultation with the primary care physician. The results from the PDS were then correlated to the results from the 2-QQ for each patient to determine sensitivity and specificity of the 2-QQ. Results: A score of 1/+ on the 2-QQ was most sensitive but least specific. Thus, setting the threshold at this level is effective for correctly identifying depressed patients, but also inaccurately captures patients who are not depressed. A score of 6 on the 2-QQ was most specific but least sensitive. Setting the threshold at this level is effective for correctly identifying patients without depression, but not very effective at capturing patients with depression. Discussion: In the context of primary care, it may be worthwhile setting the 2-QQ screen at a lower threshold for positivity (such as a score of 1 or above). This would generate a high test sensitivity and thus capture the majority of patients that have depression. On the other hand, by setting a low threshold for positivity, patients who do not have depression but score higher than 1 on the 2-QQ will also be falsely identified as testing positive for depression. However, the benefits of identifying patients who present with depression may outweigh the harms of falsely identifying a non-depressed patient. It is our hope that the 2-QQ will serve as a quick primary screen for depression in the primary care setting and serve as a catalyst to identify and treat individuals with depression.

Keywords: depression, primary care, screening tool, Sri Lanka

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem solves the problem of fitting 3 circles into a right triangle such that these 3 circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles inside the triangle with special tangency properties among circles and triangle sides; we call it extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving Tri(Tn) problem, n>2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary Carc. We call these problems the Carc(Tn) problems. The CPU time it takes for Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties, is less than one second.

Keywords: circle packing, computer-aided geometric design, geometric constraint solver, Malfatti’s problem

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Authors: Noppadon Phumeechanya, Panita Wannapiroon

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The purpose of this research is to design the ubiquitous scaffold learning environment using problem-based learning activities that enhance problem-solving skills and context awareness, and to evaluate the suitability of the ubiquitous scaffold learning environment using problem-based learning activities. We divide the research procedures into two phases. The first phase is to design the ubiquitous scaffold learning environment using problem-based learning activities, and the second is to evaluate the ubiquitous scaffold learning environment using problem-based learning activities. The sample group in this study consists of five experts selected using the purposive sampling method. We analyse data by arithmetic mean and standard deviation. The research findings are as follows; the ubiquitous scaffold learning environment using problem-based learning activities consists of three major steps, the first is preparation before learning. This prepares learners to acknowledge details and learn through u-LMS. The second is the learning process, where learning activities happen in the ubiquitous learning environment and learners learn online with scaffold systems for each step of problem solving. The third step is measurement and evaluation. The experts agree that the ubiquitous scaffold learning environment using problem-based learning activities is highly appropriate.

Keywords: ubiquitous learning environment scaffolding, learning activities, problem-based learning, problem-solving skills, context awareness

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Authors: Ming Yi Hsu, Hui Jung Chao

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The anxiety and depression adolescents in Taiwan experience can cause suicide attempts and result in unfortunate deaths. An effective method for relieving anxiety and depression is brisk walking; a moderate and low intensity aerobic exercise, which uses large muscle groups rhythmically. The research purpose was to investigate the effects of a 12-week, school-based, brisk-walking program in decreasing anxiety and depression, and in improving self-concept among high school students living in central Taiwan. A quasi-experiment using the time series design (T1 T2 X T3 T4) was conducted. The Beck Youth Inventories 2 (BYI-II) Chinese version was given four times: the first time T1 was in the 4th week prior to intervention, T2 was in the intervention week, T3 was in the 6th week after the start of the intervention period and T4 was in the 12th week post intervention. The baseline phase of the time series constituted T1 and T2. The intervention phase constituted T2, T3, and T4. The amounts of brisk walking were recorded by self-report The Generalized Estimating Equation (GEE) was used to examine the effects of brisk walking on anxiety, depression, and self-concept. The independent t-test was used to compare mean scores on three dependent variables between brisk walking over and less than 90-minutes per week. Findings revealed that levels of anxiety and self-concept had nonsignificant change during the baseline phase, while the level of depression increased significantly. In contrast, the study demonstrated significant decreases in anxiety and depression as well as increases in positive self-concept (p=.001, p<.001, p=.017) during the intervention phase. Furthermore, a subgroup analysis was completed on participants who demonstrated elevated anxiety (23.4%), and depression (29.7%), and below average self-concept (18.6%) at baseline (T2). The subgroup of anxious, depressed, or low self-concept participants who received the brisk-walking intervention demonstrated significant decreases in anxiety and depression, and significant increases in self-concept scores. Participants who engaged in brisk walking over 90 minutes per week reported decreased mean scores on anxiety (t=-2.395, p=.035) and depression (t=-2.142, p=.036) in contrast with those who engaged in brisk-walking time less than 90 minutes per week. Regarding the effects on participants whose anxiety, scores were within the normal range at baseline, there was demonstrated significant decrease in the level of anxiety when they increased their time on brisk walking before each term examination. Overall, the brisk-walking program was effective and feasible to promote adolescents’ mental health by decreasing anxiety and depression as well as elevating self-concept. It also helped adolescents from anxiety before term examinations.

Keywords: adolescents, anxiety, depression, self-concept

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Authors: Kamariah Abu Bakar, Jennifer Way

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This study investigated how young children (six years old) constructed and used representations in mathematics classroom; particularly in problem solving. The purpose of this study is to explore the ways children used representations in solving addition problems and to determine whether their representations can play a supportive role in understanding the problem situation and solving them correctly. Data collection includes observations, children’s artifact, photographs and conversation with children during task completion. The results revealed that children were able to construct and use various representations in solving problems. However, they have certain preferences in generating representations to support their problem solving.

Keywords: young children, representations, addition, problem solving

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Authors: Pei Chin Lim

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School of Mathematics and Science of Singapore Polytechnic offers a Basic Mathematics module to students who did not pass GCE O-Level Additional Mathematics. These students are weaker in Mathematics. In particular, they struggle with word problems and tend to leave them blank in tests and examinations. In order to improve students’ problem-solving skills, the school redesigned the Basic Mathematics module to incorporate Polya’s problem-solving methodology. During tutorial lessons, students have to work through learning activities designed to raise their metacognitive awareness by following Polya’s problem-solving process. To assess the effectiveness of the redesign, students’ working for a challenging word problem in the mid-semester test were analyzed. Sixty-five percent of students attempted to understand the problem by making sketches. Twenty-eight percent of students went on to devise a plan and implement it. Only five percent of the students still left the question blank. These preliminary results suggest that with regular exposure to an explicit and systematic problem-solving approach, weak students’ problem-solving skills can potentially be improved.

Keywords: mathematics education, metacognition, problem solving, weak students

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Authors: Derkaoui Orkia, Lehireche Ahmed

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The topic of this article is to exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for solving NP-hard problems. This approach provides tight relaxations of combinatorial and quadratic problems. In this work, we solve the maximum clique problem using this relaxation. The clique problem is the computational problem of finding cliques in a graph. It is widely acknowledged for its many applications in real-world problems. The numerical results show that it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming. We implement a primal-dual interior points algorithm to solve this problem based on semidefinite programming. The semidefinite relaxation of this problem can be solved in polynomial time.

Keywords: semidefinite programming, maximum clique problem, primal-dual interior point method, relaxation

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Authors: Mehmet Hakan Karaata

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In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring.

Keywords: algorithm, cycle, graph algorithm, graph theory, network structuring

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Authors: Hashini E. Mohottala

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We report the combine use of Wikispaces (WikiS) and Group Problem Solving (GPS) sessions conducted in the introductory level physics classes. As a part of this new teaching tool, some essay type problems were posted on the WikiS in weekly basis and students were encouraged to participate in problem solving without providing numerical final answers but the steps. Wikispace is used as a platform for students to meet online and create discussions. Each week students were further evaluated on problem solving skills opening up more opportunity for peer interaction through GPS. Each group was given a different problem to solve and the answers were graded. Students developed a set of skills in decision-making, problem solving, communication, negotiation, critical and independent thinking and teamwork through the combination of WikiS and GPS.

Keywords: group problem solving (GPS), wikispace (WikiS), physics education, learning

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Authors: Sourabh Joshi, Tarun Sharma, Anurag Sharma

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Ant Colony Optimization is heuristic Algorithm which has been proven a successful technique applied on number of combinatorial optimization problems. Two variants of Ant Colony Optimization algorithm named Ant System and Max-Min Ant System are implemented in MATLAB to solve travelling Salesman Problem and the results are compared. In, this paper both systems are analyzed by solving the some Travelling Salesman Problem and depict which system solve the problem better in term of cost and time.

Keywords: Ant Colony Optimization, Travelling Salesman Problem, Ant System, Max-Min Ant System

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Authors: Boris Melnikov, Dmitrii Chaikovskii, Elena Melnikova

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The traveling salesman problem (TSP) is a well-known optimization problem that seeks to find the shortest possible route that visits a set of points and returns to the starting point. In this paper, we apply some heuristics of the TSP for the task of restoring the DNA matrix. This restoration problem is often considered in biocybernetics. For it, we must recover the matrix of distances between DNA sequences if not all the elements of the matrix under consideration are known at the input. We consider the possibility of using this method in the testing of distance calculation algorithms between a pair of DNAs to restore the partially filled matrix.

Keywords: optimization problems, DNA matrix, partially filled matrix, traveling salesman problem, heuristic algorithms

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Authors: Ocotlán Díaz-Parra, Jorge A. Ruiz-Vanoye, Alejandro Fuentes-Penna, Beatriz Bernabe-Loranca, Patricia Ambrocio-Cruz, José J. Hernández-Flores

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The Maritime Platform Transport Problem of Solid, Special and Dangerous Waste consist of to minimize the monetary value of carry different types of waste from one location to another location using ships. We offer a novel mathematical, the characterization of the problem and the use CPLEX to find the optimal values to solve the Solid, Special and Hazardous Waste Transportation Problem of offshore platforms instances of Mexican state-owned petroleum company (PEMEX). The set of instances used are WTPLib real instances and the tool CPLEX solver to solve the MPTPSSDW problem.

Keywords: oil platform, transport problem, waste, solid waste

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Authors: Farzaneh Rajabighamchi, Stan van Hoesel, Christof Defryn

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The generalized traveling salesman problem (GTSP) is an extension of the traveling salesman problem (TSP) where the set of nodes is partitioned into clusters, and the salesman must visit exactly one node per cluster. In this research, we apply the definition of the GTSP to an order picker routing problem with multiple locations per product. As such, each product represents a cluster and its corresponding nodes are the locations at which the product can be retrieved. To pick a certain product item from the warehouse, the picker needs to visit one of these locations during its pick tour. As all products are scattered throughout the warehouse, the product clusters not separated geographically. We propose an exact LP model as well as heuristic and meta-heuristic solution algorithms for the order picking problem with multiple product locations.

Keywords: warehouse optimization, order picking problem, generalised travelling salesman problem, heuristic algorithm

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Authors: Ivan Baravy

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Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: Mohsen Ziaee

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Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

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Authors: Cagri Memis, Muzaffer Kapanoglu

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The school bus routing problem (SBRP) is a variant of the Vehicle Routing Problem (VRP) classified as a location-allocation-routing problem. In this study, the SBRP is decomposed into two sub-problems: (1) bus route generation and (2) bus stop selection to solve large instances of the SBRP in reasonable computational times. To solve the first sub-problem, we propose a genetic algorithm to generate bus routes. Once the routes have been fixed, a sub-problem remains of allocating students to stops considering the capacity of the buses and the walkability constraints of the students. While the exact method solves small-scale problems, treating large-scale problems with the exact method becomes complex due to computational problems, a deficiency that the genetic algorithm can overcome. Results obtained from the proposed approach on 150 instances up to 250 stops show that the matheuristic algorithm provides better solutions in reasonable computational times with respect to benchmark algorithms.

Keywords: genetic algorithm, matheuristic, school bus routing problem, vehicle routing problem

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Authors: Broderick Crawford, Ricardo Soto, Natalia Berrios, Eduardo Olguin

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In this paper, we present a binary cat swarm optimization for solving the Set covering problem. The set covering problem is a well-known NP-hard problem with many practical applications, including those involving scheduling, production planning and location problems. Binary cat swarm optimization is a recent swarm metaheuristic technique based on the behavior of discrete cats. Domestic cats show the ability to hunt and are curious about moving objects. The cats have two modes of behavior: seeking mode and tracing mode. We illustrate this approach with 65 instances of the problem from the OR-Library. Moreover, we solve this problem with 40 new binarization techniques and we select the technical with the best results obtained. Finally, we make a comparison between results obtained in previous studies and the new binarization technique, that is, with roulette wheel as transfer function and V3 as discretization technique.

Keywords: binary cat swarm optimization, binarization methods, metaheuristic, set covering problem

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Authors: Hernández Eva Selene, Reyna Mary Carmen, Rivera Héctor, Barragán Irving

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We propose an approach that jointly addresses the layout of a facility and the scheduling of a sequence of jobs. In real production, these two problems are interrelated. However, they are treated separately in the literature. Our approach is an extension of the job shop problem with transportation delay, where the location of the machines is selected among possible sites. The model minimizes the makespan, using the short processing times rule with two algorithms; the first one considers all the permutations for the location of machines, and the second only a heuristic to select some specific permutations that reduces computational time. Some instances are proved and compared with literature.

Keywords: layout problem, job shop scheduling problem, concurrent scheduling and layout problem, metaheuristic

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Authors: V. A. Doss, R. Sowndarya, K. Juila Rose Mary

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Objective: Amino acid neurotransmitter system dysfunction plays a major role in the pathophysiology of depression. The objective of the present study was to identify the amino acids as possible metabolite biomarkers for depression using GCMS (Gas Chromatography Mass Spectrometry) before and after exercise regimen in brain samples of depression induced animal models. Methods: Depression-like behaviour was induced by Chronic Unpredictable mild stress (CUMS). Severity of depression was measured by forced swim test (FST) and sucrose consumption test (SCT). Swimming protocol was followed for 4 weeks of exercise treatment. Brain obtained from depressed and exercise treated rats were used for the metabolite analysis by GCMS. Subsequent statistical analysis obtained by ANOVA followed by post hoc test revealed significant metabolic changes. Results: Amino acids such as alanine, glycine, serine, glutamate, homocysteine, proline and branched chain aminoacids (BCAs) Leucine, Isoleucine, Valine were determined in brain samples of control, depressed and exercised groups. Among these amino acids, the levels of D-Serine and branched chain amino acids were found to be decreased in depression induced rats. After four weeks of swimming exercise regimen, there were improvements in the levels of serine and Branched chain amino acids. Conclusion: We suggest that Serine and BCAs may be investigated as potential metabolite markers using GCMS and their beneficial metabolic changes in Exercise.

Keywords: metabolomics, depression, forced swim test, exercise, amino acid metabolites, GCMS, biomarker

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Authors: S. Nasri, H. Bouziri

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Disasters are quite experienced in our days. They are caused by floods, landslides, and building fires that is the main objective of this study. To cope with these unexpected events, precautions must be taken to protect human lives. The emphasis on disposal work focuses on the resolution of the evacuation problem in case of no-notice disaster. The problem of evacuation is listed as a dynamic network flow problem. Particularly, we model the evacuation problem as an earliest arrival flow problem with load dependent transit time. This problem is classified as NP-Hard. Our challenge here is to propose a metaheuristic solution for solving the evacuation problem. We define our objective as the maximization of evacuees during earliest periods of a time horizon T. The objective provides the evacuation of persons as soon as possible. We performed an experimental study on emergency evacuation from the tunisian children’s hospital. This work prompts us to look for evacuation plans corresponding to several situations where the network dynamically changes.

Keywords: dynamic network flow, load dependent transit time, evacuation strategy, earliest arrival flow problem, tabu search metaheuristic

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Authors: Elham Fathi, Seyed Mohammad Kalantarkousheh, Abolfazl Hatami Varzane

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The present study aimed to determine predict capacity of the relationship among attachment styles, humor styles and communication patterns in female married students. Statistical population consisted of female married students from Allameh Tabataba’i University. The research sample consisted of 104 married students selected through convenience sampling. They responded to study instruments that consisted of attachment styles, humor styles and Communication patterns questionnaires. Data was analyzed by means of correlation method. The results indicated significant positive relationship between secure attachment styles with adaptive humor styles, and anxious attachment styles with maladaptive humor styles. Also a negative relationship between avoidant attachment with affiliative humor, and anxious attachment with self-enhancing humor was found. Furthermore, a negative relationship between self- enhancing humor styles with demand – withdraw communication pattern, and between affiliative humor with mutual avoidant communication pattern and a positive relationship between affiliative humor with mutual constructive communication pattern was observed. The relationship between secure attachment with mutual constructive communication pattern was positive, while relationship between avoidant attachment to mutual constructive communication pattern was negative and significant and its relation with mutual avoidant communication pattern was significantly positive. The result of regression analysis indicated that affliative humor style and secure attachment style, positively predicted mutual constructive communication pattern. Avoidant attachment style positively and affliative humor style negatively predicted the mutual avoidant communication pattern. And self-enhancing humor style negatively predicted the demand – withdraw communication pattern style.

Keywords: attachment styles, communication patterns, humor styles, female married students

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Authors: Ramón Cruzat, Sergio F. Ochoa, Ignacio Casas, Luis A. Guerrero, José Bravo

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Patients under health treatments that involve long stays at a hospital or health centre (e.g. cancer, organ transplants and severe burns), tend to get bored or depressed because of the lack of social interaction with family and friends. Such a situation also affects the evolution and effectiveness of their treatments. In many cases, the solution to this problem involves extra challenges, since many patients need to rest quietly (or remain in bed) to their being contagious. Considering the weak health condition in which usually are these kinds, keeping them motivated and quiet represents an important challenge for nurses and caregivers. This article presents a mobile ubiquitous game called MagicRace, which allows hospitalized kinds to interact socially with one another without putting to risk their sensitive health conditions. The game does not require a communication infrastructure at the hospital, but instead, it uses a mobile ad hoc network composed of the handheld devices used by the kids to play. The usability and performance of this application was tested in two different sessions. The preliminary results show that users experienced positive feelings from this experience.

Keywords: ubiquitous game, children's emotional support, social isolation, mobile collaborative interactions

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Authors: Divyesh Patel, Tanuja Srivastava

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This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

Keywords: discrete tomography, exactly-1-4-adjacency, simulated annealing, binary matrices

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Authors: S. R. Santhanam

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A gifted child is one who gives evidence of creativity, good memory, rapid learning. In mathematics, a teacher often comes across some gifted children and they exhibit the following characteristics: unusual alertness, enjoying solving problems, getting bored on repetitions, self-taught, going beyond what teacher taught, ask probing questions, connecting unconnected concepts, vivid imagination, readiness for research work, perseverance of a topic. There are two main areas of research carried out on them: 1)identifying gifted children, 2) interacting and channelizing them. A lack of appropriate recognition will lead the gifted child demotivated. One of the main findings is if proper attention and nourishment are not given then it leads a gifted child to become depressed, underachieving, fail to reach their full potential and sometimes develop negative attitude towards school and study. After identifying them, a mathematics teacher has to develop them into a fall fledged achiever. The responsibility of the teacher is enormous. The teacher has to be resourceful and patient. But interacting with them one finds a lot of surprises and awesomeness. The elementary algebraic identities like (a+b)(a-b)=a²-b², expansion of like (a+b)²(a-b)² and others are taught to students, of age group 13-15 in India. An average child will be satisfied with a single proof and immediate application of these identities. But a gifted child expects more from the teacher and at one stage after a little training will surpass the teacher also. In this short paper, the author shares his experience regarding teaching algebraic identities to gifted children. The following problem was given to a set of 10 gifted children of the specified age group: If a natural number ‘n’ to expressed as the sum of the two squares, will 2n also be expressed as the sum of two squares? An investigation has been done on what multiples of n satisfying the criterion. The attempts of the gifted children were consolidated and conclusion was drawn. A second problem was given to them as: can two natural numbers be found such that the difference of their square is 3? After a successful solution, more situations were analysed. As a third question, the finding of the sign of an algebraic expression in three variables was analysed. As an example: if a,b,c are real and unequal what will be sign of a²+4b²+9c²-4ab-12bc-6ca? Apart from an expression as a perfect square what other methods can be employed to prove an algebraic expression as positive negative or non negative has been analysed. Expressions like 4x²+2y²+13y²-2xy-4yz-6zx were given, and the children were asked to find the sign of the expression for all real values of x,y and z. In all investigations, only basic algebraic identities were used. As a next probe, a divisibility problem was initiated. When a,b,c are natural numbers such that a+b+c is at least 6, and if a+b+c is divisible by 6 then will 6 divide a³+b³+c³. The gifted children solved it in two different ways.

Keywords: algebraic identities, gifted children, Indian scenario, research

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Authors: Chaghoub Soraya, Zhang Xiaoyan

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This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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