Tower Of Hanoi Research Articles

Home Program for Acquisition and Maintenance of Microsurgical Skills During the Coronavirus Disease 2019 Outbreak

BackgroundDuring the current global crisis unleashed by the severe acute respiratory syndrome coronavirus 2 outbreak, surgical departments have considerably reduced the amount of elective surgeries. This decrease leads to less time in the surgical room to develop and improve the surgical skills of residents. In this study, we developed a training program to obtain and maintain microsurgical skills at home, using a smartphone camera and low-cost materials, affordable for everyone.MethodsUsing a smartphone camera as a magnification device, 6 participants performed 5 exercises (coloring grids, grouping colors, unraveling of a gauze, knots with suture threads, and tower of Hanoi), both with the dominant and with the nondominant hand, for 4 weeks. We compared performance at the beginning and at the end of the training process. Each participant filled out an anonymous survey.ResultsWhen we compared the performance at the beginning and at the end of the training process, we found significant improvements (P = 0.05) with the dominant as well as the nondominant hand in all the exercises. All participants were satisfied or very satisfied with the definition of the objectives of the training process, material availability, the exercises performed, the choice of the time to train, and general satisfaction with the training program.ConclusionsWe developed a microsurgical skills training program to be performed at home, which can be easily reproduced. It allows residents to improve manual coordination skills and is regarded as a feasible adjunct for ongoing training for surgical residents.

User Experience Sensor for Man-Machine Interaction Modeled as an Analogy to the Tower of Hanoi.

This paper presents a novel user experience optimization concept and method, named User Experience Sensor, applied within the Hybrid Intelligence System (HINT). The HINT system, defined as a combination of an extensive AI system and the possibility of attaching a human expert, is designed to be used by relational agents, which may have a physical form, such as a robot, a kiosk, be embodied in an avatar, or may also exist as only software. The proposed method focuses on automatic process evaluation as a common sensor for optimization of the user experience for every process stage and the indicator for human-expert automatic session activation. This functionality is realized by the User Experience Sensor, which constitutes one of main elements of the self-optimizing interaction system. The authors present the optimization mechanism of the HINT system as an analogy to the process of building a Tower of Hanoi. The proposed sensor evaluates the user experience and measures the user/employee efficiency at every stage of a given process, offering the user to choose other forms of information, interaction, or expert support. The designed HINT system is able to learn and self-optimize, making the entire process more intuitive and easy for each and every user individually. The HINT system with the proposed sensor, implemented in a window assembly facility, successfully reduced assembly time, increased employees’ satisfaction, and assembly quality. The proposed approach can be implemented in numerous man–machine interaction applications.

Computing Molecular Topological Descriptors of Polymeric Networks Modeled by Sierpinski Networks

Sierpinski networks constitute an extensively studied class of graphs of fractal nature applicable in topology, mathematics of Tower of Hanoi, computer science, and Chemical graph theory. Recently the properties of Sierpinski networks have been studied like physico-chemical properties, thermodynamic properties, chemical activity, biological activity, metric dimension and degree based topological indices. In this paper, we further extend the study of Sierpinski networks and computed Zagreb types molecular descriptors (molecular topological indices) and their variants.

Long-Term Vipassana Meditation Enhances Executive Function in Adult Meditators

Objective: Vipassana meditation (VM) is a traditional Buddhist meditation practice that focuses on monitoring of clear awareness of oneself exactly what is happening as it happens, without judging. Executive functions (EF) are the high-level cognitive processes that facilitate goal-directed behaviors. It is well known that VM has significant effects on various affective states of the mind, such as relaxation, reduce stress and anxiety; however, less is known about the effect of VM on the executive function. This study aims to examine the effects of VM practice on the performance of the executive function in the adult meditators.Methods: Forty adult participants, age range between 25-50 year-olds, were recruited to this study. They were divided into three groups; the control group (N=20, mean age = 40.5 ± 5.8 years), Short-term VM group (N=6, mean age = 38.0±9.1 years), and Long-term VM group (N=14, mean age = 37.7±7.3 years). All participants were examined by 1) State-trait anxiety inventory (STAI); 2) Philadelphia mindfulness scale (PHLMS); 3) Digit span task of WAIS-IV, 4) Tower of Hanoi (ToH), and 5) Wisconsin Card Sorting Test (WCST-CV4). The mean scores of all task performance were statistically analyzed and compared between groups. Alpha values of .05 were considered significant throughout.Results: Both short-term and long-term VM has common benefits to decreased anxiety and increased mindfulness score as compared with the non-meditator group. Although short-term VM shows some benefits to the performance of several EF tasks, the discrepancy was not significant when compared with the control group. In contrast, long-term VM had a significant benefit to the performance of working memory, planning, and shift/cognitive flexibility, when compared with the non-meditator group. Our results indicated that long-term VM practice not only reduces anxiety and improves mindfulness, but the benefit also extends to improve the performance of the executive function in adult practitioners. Conclusion: In conclusion, our results suggest that continued practice of VM is highly effective for enhancing EF in healthy individuals. Long-term VM practice not only reduce stress and improve mindfulness but also enhance the performance of EF tasks of the practitioners.

Ego-depletion or invigoration in solving the tower of Hanoi? Action orientation helps overcome planning deficits

Personality systems interaction (PSI) theory postulates two executive control modes: Self-control and self-regulation. Self-control, typical of state oriented persons, should result in “ego depletion” whereas self-regulation, typical of action oriented persons, should result in invigoration. State- and action-oriented participants performed the Plan-a-Day and the 5-disk Tower-of-Hanoi tasks. There were no differences between them on the first task, but action had better performance than state oriented in terms of number of moves and solution time on the second task, independently of differences in self-determination. Better performance in the Tower of Hanoi correlated positively with activation, and negatively with apathy. We conclude that whereas self-control is associated with depletion, self-regulation is associated with invigoration in performing the Tower of Hanoi task.

Simple Variations on The Tower of Hanoi

The Tower of Hanoi problem was formulated in 1883 by mathematician Edouard Lucas. For over a century, this problem has become familiar to many of us in disciplines such as computer programming, algorithms, and discrete mathematics. Several variations to Lucas' original problem exist today, and interestingly some remain unsolved and continue to ignite research questions. Nevertheless, simple variations can still lead to interesting recurrences, which in turn are associated with exemplary proofs by induction. We explore this richness of the Tower of Hanoi beyond its classical setting to compliment the study of recurrences and proofs by induction, and clarify their pitfalls. Both topics are essential components of any typical introduction to algorithms or discrete mathematics.
 Subject Classification: A20, C30, D40, D50, E50, M10, N70, P20, Q30, R20

Child-Robot Collaborative Problem-Solving and the Importance of Child's Voluntary Interaction: A Developmental Perspective.

The emergence and development of cognitive strategies for the transition from exploratory actions towards intentional problem-solving in children is a key question for the understanding of the development of human cognition. Researchers in developmental psychology have studied cognitive strategies and have highlighted the catalytic role of the social environment. However, it is not yet adequately understood how this capacity emerges and develops in biological systems when they perform a problem-solving task in collaboration with a robotic social agent. This paper presents an empirical study in a human-robot interaction (HRI) setting which investigates children's problem-solving from a developmental perspective. In order to theoretically conceptualize children's developmental process of problem-solving in HRI context, we use principles based on the intuitive theory and we take into consideration existing research on executive functions with a focus on inhibitory control. We considered the paradigm of the Tower of Hanoi and we conducted an HRI behavioral experiment to evaluate task performance. We designed two types of robot interventions, “voluntary” and “turn-taking”—manipulating exclusively the timing of the intervention. Our results indicate that the children who participated in the voluntary interaction setting showed a better performance in the problem solving activity during the evaluation session despite their large variability in the frequency of self-initiated interactions with the robot. Additionally, we present a detailed description of the problem-solving trajectory for a representative single case-study, which reveals specific developmental patterns in the context of the specific task. Implications and future work are discussed regarding the development of intelligent robotic systems that allow child-initiated interaction as well as targeted and not constant robot interventions.

Sharp bounds on certain degree based topological indices for generalized Sierpiński graphs

Abstract Sierpinski graphs are broadly investigated graphs of fractal nature with applications in topology, computer science and mathematics of Tower of Hanoi. The generalized Sierpinski graphs are determined by reproduction of precisely the same graph, producing self-similar graph. Graph invariant referred to as topological index is used to predict physico-chemical properties, thermodynamic properties and biological activity of chemical. In QSAR/QSPR study, these graph invariants act a key role. In this article, we studied the first, second Zagreb and forgotten indices for generalized Sierpinski graph with arbitrary base graph G. Moreover, we obtained some sharp bounds with different parameters as order, size, maximum and minimum degree of G for these topological indices of generalized Sierpinski graph.

Trends in the process of engineering students collaborative solving problems of Tower of Hanoi

Trends in the process of engineering students collaborative solving problems of Tower of Hanoi

Discovering Fibonacci Numbers, Fibonacci Words, and a Fibonacci Fractal in the Tower of Hanoi

Discovering Fibonacci Numbers, Fibonacci Words, and a Fibonacci Fractal in the Tower of Hanoi

Children’s solving of ‘Tower of Hanoi’ tasks: dynamic testing with the help of a robot

The present study investigated the usefulness of a pre-programmed, teleoperated, socially assistive peer robot in dynamic testing of complex problem solving utilising the Tower of Hanoi. The robot, in a ‘Wizard of Oz’ setting, provided instructions and prompts during dynamic testing to children when they had to solve 3 D Tower of Hanoi puzzles. Participants were 37 second grade 8-year-old children, of whom half received graduated prompts training between pre-test and post-test, delivered by the robot, and half did not. It was found that children’s progression in task accuracy varied considerably, depending on whether or not children were trained in solving Tower puzzles. Trained children showed greater progression in the number of Tower problems that they could solve accurately, made considerably fewer steps, although the Tower puzzles increased quickly in difficulty level. The mean completion time of trained children decreased at a slower rate than that of the untrained children, but both groups of children took considerably more time to think and plan ahead before they started the solving process. Only moderate relations with planning behaviour were found. In general, the study revealed that computerised dynamic testing with a robot as assistant has much potential in unveiling children’s potential for learning and their ways of tackling complex problems. The advantages and challenges of using a robot in educational assessment were discussed.

The congruence subgroup problem for a family of branch groups

We construct a family of groups which generalize the Hanoi towers group and study the congruence subgroup problem for the groups in this family. We show that unlike the Hanoi towers group, the groups in this generalization are just infinite and have a trivial rigid kernel. We also put strict bounds on the branch kernel. Additionally, we show that these groups have subgroups of finite index with non-trivial rigid kernel. The only previously known group where this kernel is non-trivial is the Hanoi towers group and so this adds infinitely many new examples. Finally, we show that the topological closures of these groups have Hausdorff dimension arbitrarily close to 1.

Evaluación Neuropsicológica de Conmoción Cerebral: estudio de caso de un jugador de fútbol americano

La conmoción cerebral (CC) es la principal causa de lesión cerebral en deportistas de contacto siendo el fútbol americano (FA) uno de los más populares. La CC produce una amplia gama de síntomas físicos, cognitivos y emocionales que hasta el 36.1% de los jugadores desconocen. Los cambios cognitivos ocurren en la atención, memoria, flexibilidad mental, fluidez verbal, planeación, memoria de trabajo, inhibición y velocidad de procesamiento. El objetivo fue evaluar el rendimiento cognitivo de un jugador defensivo de FA categoría mayor, de 23 años de edad y 15 años de escolaridad, antes y después de presentar una CC. Se aplicaron los siguientes instrumentos: Cuestionario de Datos Generales, test de MoCA, Dígitos y Cubos en regresión, Detección Visual, Fluidez Verbal Semántica, test de Stroop, Torre de Hanoi y Wisconsin. Se estableció su perfil cognitivo basal en pretemporada y se reevaluó durante la temporada una semana posterior a una CC. En la evaluación pretemporada el jugador presentó un perfil cognitivo dentro de los rangos esperados para su edad y escolaridad. En la fase aguda de la CC, el jugador disminuyó su rendimiento en tareas de velocidad de procesamiento (pre: 26 seg; post:120 seg), atención sostenida (pre:7 puntos; post:6 puntos), inhibición (pre: 84 aciertos; post: 82 aciertos) y planeación (pre: 15 movimientos; post: 20 movimientos). La EN ha demostrado ser una herramienta sensible y confiable para la detección de los síntomas cognitivos en fase aguda y posterior a la CC.
 Palabras claves: neuropsicología, fútbol, cognición Cerebral Concussion (CC) is the main cause of brain injury in contact athletes, with American football (AF) being one of the most popular. The CC produces a wide range of physical, cognitive and emotional symptoms that most of the players (36,1%) do not know. Cognitive changes are observed in attention and memory processes, mental flexibility, verbal fluency, planning, working memory, inhibition and speed of processing. The Neuropsychological Assessment (NA) is fundamental for the detection and management of CC in the acute phase and its sequelae. The objective was to evaluate the cognitive performance of a defensive player of american football, major category, of 23 years of age and 15 years of schooling, before and after presenting a CC. Instruments were: General Data Questionnaire, MoCA test, Digits and Cubes in regression, Visual Detection, Semantic Verbal Fluency, Stroop test, Tower of Hanoi and Wisconsin Sorting Cards. Baseline cognitive profile was established and reevaluated during the season one week after a CC. In the pre-season evaluation the player presented a cognitive profile within the ranges expected. In the acute phase of CC, the player decreased his performance in processing speed tasks (pre: 26 sec, post: 120 sec), sustained attention (pre: 7 points, post: 6 points), inhibition (pre: 84) hits, post: 82 hits) and planning (pre: 15 movements, post: 20 movements). The NA has proven to be a sensitive and reliable tool for the detection of cognitive symptoms in the acute and post-CC phase.
 Key words: neuropsychology, football, cognition. A concussão (CC) é a principal causa de lesão cerebral em atletas de contato, sendo o futebol americano (AF) um dos mais populares. O CC produz uma ampla gama de sintomas físicos, cognitivos e emocionais que até 36,1% dos jogadores não conhecem. Mudanças cognitivas ocorrem na atenção, memória, flexibilidade mental, fluência verbal, planejamento, memória de trabalho, inibição e velocidade de processamento. Objetivou-se avaliar o desempenho cognitivo de um jogador defensivo da categoria sênior de AF, 23 anos de idade e 15 anos de escolaridade, antes e depois de apresentar um CC. Foram aplicados os seguintes instrumentos: Questionário de dados gerais, teste MoCA, Dígitos e regressão cubos, detecção visual, Fluência Verbal Semântica, teste Stroop, Torre de Hanói e Wisconsin. Seu perfil cognitivo basal foi estabelecido na pré-temporada e reavaliado durante a estação uma semana após o CC. Na avaliação neuropsicológica pré-temporada o jogador apresentou um perfil cognitivo dentro das faixas esperadas para sua idade e escolaridade. Na fase aguda da CC, o jogador diminuição do desempenho em tarefas velocidade de processamento (pré: 26 seg; coloca-120 seg), atenção sustentada (pré: 7 pontos; pós 6 pontos), a inibição (pré: 84 hits, post: 82 hits) e planejamento (pré: 15 movimentos, post: 20 movimentos). Na avaliação neuropsicológica provou ser uma ferramenta sensível e confiável para a detecção de sintomas cognitivos em fase aguda e subsequente CC.
 Palavras-chave: neuropsicologia, futebol, cognição.

Workshop Penggunaan Media Pembelajaran Berbasis Sampah dan Barang Bekas Bagi Guru MIN TTU

Permasalahan pokok di Madrasah Ibtidayah Negeri (MIN) TTU-Kefamenanu yang menjadi mitra pengabdian ini adalah: (i) belum tersedianya alat peraga matematika di sekolah mitra; (ii) belum pernah diselenggarakan kegiatan workshop tentang penggunaan alat peraga matematika di sekolah mitra. Metode pelaksanaan pengabdian ini adalah ceramah, demonstrasi, praktek langsung, diskusi dan penugasan. Adapun alat peraga yang digunakan antara lain: Mistar Bilangan, Kartu Positif Negatif, Puzzle FPB dan KPK, Magic Square, Perkalian Kanada, Congklak Penjumlahan, Tabel Cayley, Ular Tangga Aljabar, Menara Hanoi dan Tangram. Alat peraga matematika ini terbuat dari sampah dan barang bekas. Pelaksanaan pengabdian selama 3 hari dengan rincian satu hari workshop dengan peserta para guru dan dua hari praktek penggunaan alat peraga dengan peserta siswa kelas IV, V dan VI. Hasil evaluasi pengabdian menunjukkan bahwa i) 33,33% peserta sangat setuju dan 66,67% peserta workshop setuju bahwa materi workshop terorganisasi dengan baik dan alat peraga yang digunakan sesuai dengan materi pembelajaran di sekolah dasar, alat peraga menarik dan membantu siswa dalam belajar sambil bermain; ii) 80% peserta setuju dan 20% sangat setuju bahwa panduan praktik penggunaan alat peraga dengan LKS yang disediakan dapat dimengerti dengan baik.

Analysis and synthesis method for solving informatic problems

The article outlines the mail ideas of teaching methodology problem solving that formulated by G. Polya. It is shown how the skills to solve problems is associated with modern educational results. Examples of using analysis and synthesis method for drawing up plans for solving informatics problems (puzzles Transfusion and Tower of Hanoi, asks counting programs for a computer runner Evaluator, on counting number of paths in a graph, on building a winning strategy) are given.

4-Peg Hanoi Towers Algorithm Animation Demonstration System Based on Html5

Differing from the previous studies on demonstration Hanoi Tower algorithm based on desktop implementation, this paper adopts cross-platform HTML5 technology, drew on the references of three-peg Hanoi tower animation on the basis of fully study from the theory and realization of four-peg Hanoi tower, designed the animation implementation of four-peg Hanoi tower, simplified animation implementation and application popularized, intuitively expresses the relationship between the optimal number of moving steps and the section score in four-peg. The implementation method can also be applied to animation demonstration of other algorithm principles, and has a high reference value.

A note on the Frame–Stewart conjecture

Providing the example of a disc whose number of moves performed in some minimal solution for the Tower of Hanoi problem is not a power of 2, we show that the argument given in a paper by Demontis in this journal is false and the method incapable of solving the Frame–Stewart conjecture on the Tower of Hanoi with more than three pegs.

A Note on the Frame-Stewart Conjecture on the Generalized Tower of Hanoi Problem

The generalized Tower of Hanoi with p (≥ 3) pegs and n (≥ 1) discs, proposed by Stewart (1939) is well-known. To solve the problem, the scheme followed is : First, move the tower of the topmost i (smallest, consecutive) discs (optimally) to one of the auxiliary pegs in a tower, using the p pegs; next, move the remaining n – i (largest) discs (optimally) to the destination peg in a tower, using the p – 1 pegs available; and finally, transfer the discs on the auxiliary peg to the destination peg (optimally) in a tower. This is the so-called Frame-Stewart conjecture, which remains to be settled. The minimum number of moves under the scheme is denoted by SF(n, p). Chen and Shen (2004) have re-considered the Frame-Stewart conjecture in more detail, and claimed that SF(n, p) is of the order of 2 [ n ( p 2 )!] 1 / ( p 2 ). This paper gives a better lower bound of SF(n, p), which shows that the claim of Chen et al. (2004) is not correct.
 Journal of Bangladesh Academy of Sciences, Vol. 43, No. 1, 79-83, 2019

Differential Effects of Cognitive Reserve on the Neurocognitive Functioning of Polysubstance Users: an Exploratory Analysis Using Mixture Regression

We aimed to identify latent classes based on differential effects of cognitive reserve on neurocognitive variables, and to determine which variables of polysubstance use predict class membership. One hundred sixty-six male participants in residential treatment were recruited in Mexico City and evaluated with Montreal Cognitive Assessment, Tower of Hanoi, Cognitive Reserve Index Questionnaire, and a structured interview for substance use. We performed three independent mixture regression models with cognitive reserve as predictor and neurocognitive variables as outcomes, and we estimated covariate effects of age of onset, years of substance use, and past 30 days of use on class membership. Two class solutions for the three models, all demonstrating differential effects (e.g., for overall cognitive functioning, education seems to serve as a protective factor against impairment for most of the cases, whereas only for some few individuals both education and leisure may protect). No variable of substance use affected the probabilities of membership to latent classes. Individuals at risk of substance-induced neurocognitive impairment may be identified by the association between variables of cognitive performance and cognitive reserve.

Does Movement Matter? Prefrontal Cortex Activity During 2D vs. 3D Performance of the Tower of Hanoi Puzzle.

In the current study, we used functional near-infrared spectroscopy (fNIRS) to compare prefrontal cortex (PFC) activity in adults as they performed two conditions of the Tower of Hanoi (ToH) disk-transfer task that have equivalent executive function (EF) but different motor requirements. This study explored cognitive workload, here defined as the cognitive effort utilized while problem-solving by performance output. The first condition included a two-dimensional (2D) computerized ToH where participants completed trials using a computer mouse. In contrast, our second condition used a traditional, three-dimensional (3D) ToH that must be manually manipulated. Our aim was to better understand the role of the PFC in these two conditions to detect if PFC activity increases as a function of motor planning. Twenty right-handed, neurotypical adults (10M/10F, = 24.6, SD ± 2.8 years old) participated in two blocks (one per condition) of three 1-min trials where they were asked to solve as many puzzles as possible. These data were analyzed using a mixed effects ANOVA with participants nested within blocks for 2D vs. 3D conditions, presentation order (leading block), individual participants, and regions and additional follow-up statistics. Results showed that changes in oxygenated hemoglobin, ΔHbO, were significantly higher for 3D compared to 2D condition (p = 0.0211). Presentation order and condition interacted significantly (p = 0.0015). Notably, a strong correlation between performance and ΔHbO existed between blocks 1 and 2 (r = −0.69, r2 = 0.473, p < 0.01) when the 3D condition was initially performed, in contrast to the 2D condition where no significant correlation was seen. Findings also showed a significant decrease in ΔHbO between the first and second block (p = 0.0015) while performance increased significantly for both 3D and 2D conditions (p < 0.005). We plan to use this information in the future to narrow the potential points of impairment on the perception-cognition-action continuum in certain developmental disabilities.