Search results for: Pythagorean triples

Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation

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Authors: Anthony Overmars, Sitalakshmi Venkatraman

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This paper presents a method for determining all of the co-prime right angle triangles in the Euclidean field by looking at the intersection of the Pythagorean and Platonic right angle triangles and the corresponding lattice that this produces. The co-prime properties of each lattice point representing a unique right angle triangle are then considered. This paper proposes a conjunction between these two ancient disparaging theorists. This work has wide applications in information security where cryptography involves improved ways of finding tuples of prime numbers for secure communication systems. In particular, this paper has direct impact in enhancing the encryption and decryption algorithms in cryptography.

Keywords: Pythagorean triples, platonic triples, right angle triangles, co-prime numbers, cryptography

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Authors: Luiz G. Véras, Felipe L. Medeiros, Lamartine F. Guimarães

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This work approaches the automatic planning of paths for Unmanned Aerial Vehicles (UAVs) through the application of the Rapidly Exploring Random Tree Star-Smart (RRT*-Smart) algorithm. RRT*-Smart is a sampling process of positions of a navigation environment through a tree-type graph. The algorithm consists of randomly expanding a tree from an initial position (root node) until one of its branches reaches the final position of the path to be planned. The algorithm ensures the planning of the shortest path, considering the number of iterations tending to infinity. When a new node is inserted into the tree, each neighbor node of the new node is connected to it, if and only if the extension of the path between the root node and that neighbor node, with this new connection, is less than the current extension of the path between those two nodes. RRT*-smart uses an intelligent sampling strategy to plan less extensive routes by spending a smaller number of iterations. This strategy is based on the creation of samples/nodes near to the convex vertices of the navigation environment obstacles. The planned paths are smoothed through the application of the method called quintic pythagorean hodograph curves. The smoothing process converts a route into a dynamically-viable one based on the kinematic constraints of the vehicle. This smoothing method models the hodograph components of a curve with polynomials that obey the Pythagorean Theorem. Its advantage is that the obtained structure allows computation of the curve length in an exact way, without the need for quadratural techniques for the resolution of integrals.

Keywords: path planning, path smoothing, Pythagorean hodograph curve, RRT*-Smart

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Authors: Yassir I. Dinar

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We computed the weights of the adjoint action of distinguished sl2-triples in Lie algebra of type Dn using mathematical induction.

Keywords: lie algebra, root systems, representation theory, nilpotent orbits

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Authors: Amar Partap Singh Pharwaha, Balkrishan Jindal

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In this paper, a new method is developed for hiding image in a digital image with multilayer security. In the proposed method, the secret image is encrypted in the first instance using a flexible matrix based symmetric key to add first layer of security. Then another layer of security is added to the secret data by encrypting the ciphered data using Pythagorean Theorem method. The ciphered data bits (4 bits) produced after double encryption are then embedded within digital image in the spatial domain using Least Significant Bits (LSBs) substitution. To improve the image quality of the stego-image, an improved form of pixel adjustment process is proposed. To evaluate the effectiveness of the proposed method, image quality metrics including Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), entropy, correlation, mean value and Universal Image Quality Index (UIQI) are measured. It has been found experimentally that the proposed method provides higher security as well as robustness. In fact, the results of this study are quite promising.

Keywords: Pythagorean theorem, pixel adjustment, ciphered data, image hiding, least significant bit, flexible matrix

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Authors: Dumont Maxime, Correia Carlos, Sauvage Jean-François, Schwartz Noah, Gray Morgan

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Context: The concept of the segmented telescope is unavoidable to build extremely large telescopes (ELT) in the quest for spatial resolution, but it also allows one to fit a large telescope within a reduced volume of space (JWST) or into an even smaller volume (Standard Cubesat). Cubesats have tight constraints on the computational burden available and the small payload volume allowed. At the same time, they undergo thermal gradients leading to large and evolving optical aberrations. The pupil segmentation comes nevertheless with an obvious difficulty: to co-phase the different segments. The CubeSat constraints prevent the use of a dedicated wavefront sensor (WFS), making the focal-plane images acquired by the science detector the most practical alternative. Yet, one of the challenges for the wavefront sensing is the non-linearity between the image intensity and the phase aberrations. Plus, for Earth observation, the object is unknown and unrepeatable. Recently, several studies have suggested Neural Networks (NN) for wavefront sensing; especially convolutional NN, which are well known for being non-linear and image-friendly problem solvers. Aims: We study in this paper the prospect of using NN to measure the phasing aberrations of a segmented pupil from the focal-plane image directly without a dedicated wavefront sensing. Methods: In our application, we take the case of a deployable telescope fitting in a CubeSat for Earth observations which triples the aperture size (compared to the 10cm CubeSat standard) and therefore triples the angular resolution capacity. In order to reach the diffraction-limited regime in the visible wavelength, typically, a wavefront error below lambda/50 is required. The telescope focal-plane detector, used for imaging, will be used as a wavefront-sensor. In this work, we study a point source, i.e. the Point Spread Function [PSF] of the optical system as an input of a VGG-net neural network, an architecture designed for image regression/classification. Results: This approach shows some promising results (about 2nm RMS, which is sub lambda/50 of residual WFE with 40-100nm RMS of input WFE) using a relatively fast computational time less than 30 ms which translates a small computation burder. These results allow one further study for higher aberrations and noise.

Keywords: wavefront sensing, deep learning, deployable telescope, space telescope

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Authors: Peter M. Maurer Maurer

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DGL is a context free grammar-based tool for generating random data. Many types of simulator input data require some computation to be placed in the proper format. For example, it might be necessary to generate ordered triples in which the third element is the sum of the first two elements, or it might be necessary to generate random numbers in some sorted order. Although DGL is universal in computational power, generating these types of data is extremely difficult. To overcome this problem, we have enhanced DGL to include features that permit direct computation within the structure of a context free grammar. The features have been implemented as special types of productions, preserving the context free flavor of DGL specifications.

Keywords: DGL, Enhanced Context Free Grammars, Programming Constructs, Random Data Generation

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Authors: Yurii Bloshko, Oksana Olar

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This paper presents the analysis of 6 different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms

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Authors: Xuewen Yu, Danhui Dan

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The identification of impact load and some hard-to-obtain system parameters is crucial for the activities of analysis, validation, and evaluation in the engineering field. This paper proposes a method that utilizes neural networks based on 1D-CNN to identify the impact load and partial system parameters from measured responses. To this end, forward computations are conducted to provide datasets consisting of the triples (parameter θ, input u, output y). Then neural networks are trained to learn the mapping from input to output, fu|{θ} : y → u, as well as from input and output to parameter, fθ : (u, y) → θ. Afterward, feeding the trained neural networks the measured output response, the input impact load and system parameter can be calculated, respectively. The method is tested on two simulated examples and shows sound accuracy in estimating the impact load (waveform and location) and system parameters.

Keywords: convolutional neural network, impact load identification, system parameter identification, inverse problem

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Authors: Alan S. Weber

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This contribution reviews the current biomedical and qualitative arts research on arts-in-health interventions to improve both individual and population health outcomes. Arts therapies–for example, music therapy with roots in Aristoxenus’s Ἁρμονικὰ στοιχεῖα and the Pythagorean sect–have long been employed in therapeutic contexts. However, the 20th century witnessed the increasing use of the visual and plastic arts (drawing, painting, sculpting), performing arts (drama and dance), and other expressive arts modalities into occupational therapy, well-being medicine, and psychological and psychiatric counselling, diagnosis, and treatment. A significant body of peer-reviewed evidence in the medical and neurological sciences on the role of arts-in-health has developed, and specifically, research on music and art therapy has led to their inclusion within the current biomedical paradigm of evidence-based practice. The arts cannot only aid in public and population health promotion (promoting healthy behaviors and lifestyles, preventing disease onset) but also in addressing psychological issues (regulation of emotion; stress, anxiety, and depression reduction), behavioural issues (basic life skills, coping), and physiological response (immune system function, hormonal regulation, homeostatis). Working as a cross-disciplinary researcher in the arts in an American medical college, the author has developed several successful arts-in-health programs at the national and international level.

Keywords: arts-in-health, evidence based medicine, arts for health, expressive arts therapies

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Authors: Mayuko Matsuoka

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This presentation reports the relationships among EFL(English as a Foreign Language) students’ story comprehension in reading a story written in English and Japanese and empathic reactions. The main focus is put on their self-reflection on past study experiences, one of the empathic reactions after reading a story. One hundred fifty-five first-year university students in Japan read three SRL-themed stories written in English (their foreign language) and those written in Japanese (their mother tongue). The levels of the stories are equivalent, at CEFR(Common European Framework of Reference for Languages) B2 level. The result of categorical correlation analysis shows significant moderate correlations among three empathic reactions in a group reading English versions: having similar emotions as a protagonist, reflecting on their past study experiences, and getting lessons from a story. In addition, the result of logistic regression analysis for the data in a group reading English versions shows the chance of getting lessons from a story significantly approximately doubles if participants’ scores of a comprehension test increases by one, while it approximately triples if participants’ self-reflection occurs. These results do not appear in a group reading Japanese versions. The findings imply that self-reflection may support their comprehension of the English texts and leads to the participants’ getting lessons about SRL.

Keywords: comprehension, lesson, self-reflection, SRL

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Authors: Jutharat Attawet, Alex Y. Wang, Cindy M. Farquhar, Elizabeth A. Sullivan

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Background: Adverse maternal and perinatal outcomes of multiple pregnancies resulting from multiple embryo transfers (ET) has become significant concerns. This is particularly relevant for gestational carriers since they usually do not have infertility issues. Single embryo transfer (SET) therefore has been encouraged to assist reproductive technology (ART) practice in order to reduce multiple pregnancies. Objectives: This systematic review aims to investigate the pregnancy and birth outcomes of SET and multiple ET in surrogacy arrangements. Search methods: This study is a systematic review. Electronic databases were searched from CINAHL, Medline, Embase, Scopus and ProQuest for studies from 1980 to 2017. Cross-references and national ART reports were also manual searchings. Articles without restriction of English language and study types were accessed. Carrier cycles involving in SET and multiple ET were identified in database searching. The main outcome measures including clinical pregnancy, live delivery and multiple deliveries per gestational carrier cycle were compared between SET and multiple ET. Mantel-Haenzel risk ratios (RRs) with 95% confidence intervals (CIs), using the numbers of outcome events in SET and multiple ET of each study were calculated suing RevMan5.3. Outcomes: The search returned 97 articles of which 5 met the inclusion criteria. Approximately 50% of carrier cycles were transferred a single embryo and 50% were transferred more than one embryo. The clinical pregnancy rate (CPR) was 39% for SET and 53% for multiple ET, which was not significantly different with RR = 0.83 (95% CI: 0.67-1.03). The live delivery rate was 33% for SET and 57% for multiple ET which was not significantly different with RR = 0.78 (95% CI: 0.61-1.00). The multiple delivery rate per carrier was greater risks in the multiple ET carrier cycles (RR =0.4, 95% CI: 0.01-0.26). There were 104 sets of twins (including one set of twins selectively reduced from triplets to twins) and 1 set of triples in the multiple ET carrier cycle. In the SET carrier cycles, there were 2 sets of twins. Significance of the study: SET should be advocated among surrogate carriers to prevent multiple pregnancies and subsequent adverse outcomes for both carrier and baby. Surrogacy practice should be reviewed and surrogate carriers should be fully informed of the risk of adverse maternal and birth outcome of multiple pregnancies due to multiple embryo transfers.

Keywords: assisted reproduction, birth outcomes, carrier, gestational surrogacy, multiple embryo transfer, multiple pregnancy, pregnancy outcomes, single embryo transfer, surrogate mother, systematic review

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Authors: Paramita Banerjee, K. R. S. Chandrakumar, G. P. Das

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Bulk MgH2 has drawn much attention for the purpose of hydrogen storage because of its high hydrogen storage capacity (~7.7 wt %) as well as low cost and abundant availability. However, its practical usage has been hindered because of its high hydrogen desorption enthalpy (~0.8 eV/H2 molecule), which results in an undesirable desorption temperature of 3000C at 1 bar H2 pressure. To surmount the limitations of bulk MgH2 for the purpose of hydrogen storage, a detailed first-principles density functional theory (DFT) based study on the structure and stability of neutral (Mgm) and positively charged (Mgm+) Mg nanoclusters of different sizes (m = 2, 4, 8 and 12), as well as their interaction with molecular hydrogen (H2), is reported here. It has been found that due to the absence of d-electrons within the Mg atoms, hydrogen remained in molecular form even after its interaction with neutral and charged Mg nanoclusters. Interestingly, the H2 molecules do not enter into the interstitial positions of the nanoclusters. Rather, they remain on the surface by ornamenting these nanoclusters and forming new structures with a gravimetric density higher than 15 wt %. Our observation is that the inclusion of Grimme’s DFT-D3 dispersion correction in this weakly interacting system has a significant effect on binding of the H2 molecules with these nanoclusters. The dispersion corrected interaction energy (IE) values (0.1-0.14 eV/H2 molecule) fall in the right energy window, that is ideal for hydrogen storage. These IE values are further verified by using high-level coupled-cluster calculations with non-iterative triples corrections i.e. CCSD(T), (which has been considered to be a highly accurate quantum chemical method) and thereby confirming the accuracy of our ‘dispersion correction’ incorporated DFT calculations. The significance of the polarization and dispersion energy in binding of the H2 molecules are confirmed by performing energy decomposition analysis (EDA). A total of 16, 24, 32 and 36 H2 molecules can be attached to the neutral and charged nanoclusters of size m = 2, 4, 8 and 12 respectively. Ab-initio molecular dynamics (AIMD) simulation shows that the outermost H2 molecules are desorbed at a rather low temperature viz. 150 K (-1230C) which is expected. However, complete dehydrogenation of these nanoclusters occur at around 1000C. Most importantly, the host nanoclusters remain stable up to ~500 K (2270C). All these results on the adsorption and desorption of molecular hydrogen with neutral and charged Mg nanocluster systems indicate towards the possibility of reducing the dehydrogenation temperature of bulk MgH2 by designing new Mg-based nano materials which will be able to adsorb molecular hydrogen via this weak Mg-H2 interaction, rather than the strong Mg-H bonding. Notwithstanding the fact that in practical applications, these interactions will be further complicated by the effect of substrates as well as interactions with other clusters, the present study has implications on our fundamental understanding to this problem.

Keywords: density functional theory, DFT, hydrogen storage, molecular dynamics, molecular hydrogen adsorption, nanoclusters, physisorption

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Authors: Ahlam Ali, Katrina Lappin, Jaine Blayney, Ken Mills

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Leukaemia is the most frequently (30%) occurring type of paediatric cancer. Of these, approximately 80% are acute lymphoblastic leukaemia (ALL) with acute myeloid leukaemia (AML) cases making up the remaining 20% alongside other leukaemias. Unfortunately, children with AML do not have promising prognosis with only 60% surviving 5 years or longer. It has been highlighted recently the need for age-specific therapies for AML patients, with paediatric AML cases having a different mutational landscape compared with AML diagnosed in adult patients. Drug Repurposing is a recognized strategy in drug discovery and development where an already approved drug is used for diseases other than originally indicated. We aim to identify novel combination therapies with the promise of providing alternative more effective and less toxic induction therapy options. Our in-silico analysis highlighted ‘cell death and survival’ as an aberrant, potentially targetable pathway in paediatric AML patients. On this basis, 83 apoptotic inducing compounds were screened. A preliminary single agent screen was also performed to eliminate potentially toxic chemicals, then drugs were constructed into a pooled library with 10 drugs per well over 160 wells, with 45 possible pairs and 120 triples in each well. Seven cell lines were used during this study to represent the clonality of AML in paediatric patients (Kasumi-1, CMK, CMS, MV11-14, PL21, THP1, MOLM-13). Cytotoxicity was assessed up to 72 hours using CellTox™ Green reagent. Fluorescence readings were normalized to a DMSO control. Z-Score was assigned to each well based on the mean and standard deviation of all the data. Combinations with a Z-Score <2 were eliminated and the remaining wells were taken forward for further analysis. A well was considered ‘successful’ if each drug individually demonstrated a Z-Score <2, while the combination exhibited a Z-Score >2. Each of the ten compounds in one well (155) had minimal or no effect as single agents on cell viability however, a combination of two or more of the compounds resulted in a substantial increase in cell death, therefore the ten compounds were de-convoluted to identify a possible synergistic pair/triple combinations. The screen identified two possible ‘novel’ drug pairing, with BCL2 inhibitor ABT-737, combined with either a CDK inhibitor Purvalanol A, or AKT/ PI3K inhibitor LY294002. (ABT-737- 100 nM+ Purvalanol A- 1 µM) (ABT-737- 100 nM+ LY294002- 2 µM). Three possible triple combinations were identified (LY2409881+Akti-1/2+Purvalanol A, SU9516+Akti-1/2+Purvalanol A, and ABT-737+LY2409881+Purvalanol A), which will be taken forward for examining their efficacy at varying concentrations and dosing schedules, across multiple paediatric AML cell lines for optimisation of maximum synergy. We believe that our combination screening approach has potential for future use with a larger cohort of drugs including FDA approved compounds and patient material.

Keywords: AML, drug repurposing, ABT-737, apoptosis

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Authors: Soumava Boral, Sanjay K. Chaturvedi, Ian Howard, Kristoffer McKee, V. N. A. Naikan

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Due to strict regulations from government to enhance the possibilities of sustainability practices in industries, and noting the advances in sustainable manufacturing practices, it is necessary that the associated processes are also sustainable. Maintenance of large scale and complex machines is a pivotal task to maintain the uninterrupted flow of manufacturing processes. Appropriate maintenance practices can prolong the lifetime of machines, and prevent associated breakdowns, which subsequently reduces different cost heads. Selection of the best maintenance strategies for such machines are considered as a burdensome task, as they require the consideration of multiple technical criteria, complex mathematical calculations, previous fault data, maintenance records, etc. In the era of the fourth industrial revolution, organizations are rapidly changing their way of business, and they are giving their utmost importance to sensor technologies, artificial intelligence, data analytics, automations, etc. In this work, the effectiveness of several maintenance strategies (e.g., preventive, failure-based, reliability centered, condition based, total productive maintenance, etc.) related to a large scale and complex gearbox, operating in a steel processing plant is evaluated in terms of economic, social, environmental and technical criteria. As it is not possible to obtain/describe some criteria by exact numerical values, these criteria are evaluated linguistically by cross-functional experts. Fuzzy sets are potential soft-computing technique, which has been useful to deal with linguistic data and to provide inferences in many complex situations. To prioritize different maintenance practices based on the identified sustainable criteria, multi-criteria decision making (MCDM) approaches can be considered as potential tools. Multi-Attributive Ideal Real Comparative Analysis (MAIRCA) is a recent addition in the MCDM family and has proven its superiority over some well-known MCDM approaches, like TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and ELECTRE (ELimination Et Choix Traduisant la REalité). It has a simple but robust mathematical approach, which is easy to comprehend. On the other side, due to some inherent drawbacks of Intuitionistic Fuzzy Sets (IFS) and Pythagorean Fuzzy Sets (PFS), recently, the use of Fermatean Fuzzy Sets (FFSs) has been proposed. In this work, we propose the novel concept of FF-MAIRCA. We obtain the weights of the criteria by experts’ evaluation and use them to prioritize the different maintenance practices according to their suitability by FF-MAIRCA approach. Finally, a sensitivity analysis is carried out to highlight the robustness of the approach.

Keywords: Fermatean fuzzy sets, Fermatean fuzzy MAIRCA, maintenance strategy selection, sustainable manufacturing, MCDM

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