Search results for: Wajsberg algebra

Authors: Sonia Anand Knowlton

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With the rise of artificial intelligence, computer science is becoming increasingly integrated in virtually every area of life. Of course, the law is no exception. Through argumentation frameworks (AFs), computer scientists have used abstract algebra to structure the legal reasoning process in a way that allows conclusions to be drawn from a formalized system of arguments. In AFs, arguments compete against each other for logical success and are related to one another through the binary operation of the attack. The prevailing arguments make up the preferred extension of the given argumentation framework, telling us what set of arguments must be accepted from a logical standpoint. There have been several developments of AFs since its original conception in the early 90’s in efforts to make them more aligned with the human reasoning process. Generally, these developments have sought to add nuance to the factors that influence the logical success of competing arguments (e.g., giving an argument more logical strength based on the underlying value it promotes). The most cogent development was that of the Extended Argumentation Framework (EAF), in which attacks can themselves be attacked by other arguments, and the promotion of different competing values can be formalized within the system. This article applies the logical structure of EAFs to current theoretical understandings of judicial reasoning to contribute to theories of judging and to the evolution of AFs simultaneously. The argument is that the main limitation of EAFs, when applied to judicial reasoning, is that they require judges to themselves assign values to different arguments and then lexically order these values to determine the given framework’s preferred extension. Drawing on John Rawls’ Theory of Justice, the examination that follows is whether values are lexical and commensurable to this extent. The analysis that follows then suggests a potential extension of the EAF system with an approach that formalizes different “planes of attack” for competing arguments that promote lexically ordered values. This article concludes with a summary of how these insights contribute to theories of judging and of legal reasoning more broadly, specifically in indeterminate cases where judges must turn to value-based approaches.

Keywords: computer science, mathematics, law, legal theory, judging

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Authors: Urbánek Jiří J., Krahulec Josef, Urbánek Jiří F., Johanidesová Jitka

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These Computational assistance for the research and modelling of critical infrastructure subjects continuity deal with this paper. It enables us the using of prevailing operation system MS Office (SmartArt...) for mathematical models, using DYVELOP (Dynamic Vector Logistics of Processes) method. It serves for crisis situations investigation and modelling within the organizations of critical infrastructure. In the first part of the paper, it will be introduced entities, operators and actors of DYVELOP method. It uses just three operators of Boolean algebra and four types of the entities: the Environments, the Process Systems, the Cases and the Controlling. The Process Systems (PrS) have five “brothers”: Management PrS, Transformation PrS, Logistic PrS, Event PrS and Operation PrS. The Cases have three “sisters”: Process Cell Case, Use Case and Activity Case. They all need for the controlling of their functions special Ctrl actors, except ENV – it can do without Ctrl. Model´s maps are named the Blazons and they are able mathematically - graphically express the relationships among entities, actors and processes. In the second part of this paper, the rich blazons of DYVELOP method will be used for the discovering and modelling of the cycling cases and their phases. The blazons need live PowerPoint presentation for better comprehension of this paper mission. The crisis management of energetic crisis infrastructure organization is obliged to use the cycles for successful coping of crisis situations. Several times cycling of these cases is a necessary condition for the encompassment of the both the emergency event and the mitigation of organization´s damages. Uninterrupted and continuous cycling process bring for crisis management fruitfulness and it is a good indicator and controlling actor of organizational continuity and its sustainable development advanced possibilities. The research reliable rules are derived for the safety and reliable continuity of energetic critical infrastructure organization in the crisis situation.

Keywords: blazons, computational assistance, DYVELOP method, critical infrastructure

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Authors: Carmen Georgeta Dumitrache

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Measurements of terrestrial science aims to study the totality of operations and computing, which are carried out for the purposes of representation on the plan or map of the land surface in a specific cartographic projection and topographic scale. With the development of society, the metrics have evolved, and they land, being dependent on the achievement of a goal-bound utility of economic activity and of a scientific purpose related to determining the form and dimensions of the Earth. For measurements in the field, data processing and proper representation on drawings and maps of planimetry and landform of the land, using topographic and geodesic instruments, calculation and graphical reporting, which requires a knowledge of theoretical and practical concepts from different areas of science and technology. In order to use properly in practice, topographical and geodetic instruments designed to measure precise angles and distances are required knowledge of geometric optics, precision mechanics, the strength of materials, and more. For processing, the results from field measurements are necessary for calculation methods, based on notions of geometry, trigonometry, algebra, mathematical analysis and computer science. To be able to illustrate topographic measurements was established for the lifting of property located near the locality of Gircov, Romania. We determine this total surface of the plan (T30), parcel/plot, but also in the field trace the coordinates of a parcel. The purpose of the removal of the planimetric consisted of: the exact determination of the bounding surface; analytical calculation of the surface; comparing the surface determined with the one registered in the documents produced; drawing up a plan of location and delineation with closeness and distance contour, as well as highlighting the parcels comprising this property; drawing up a plan of location and delineation with closeness and distance contour for a parcel from Dave; in the field trace outline of plot points from the previous point. The ultimate goal of this work was to determine and represent the surface, but also to tear off a plot of the surface total, while respecting the first surface condition imposed by the Act of the beneficiary's property.

Keywords: topography, surface, coordinate, modeling

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Authors: Leon Mortari

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The Metropolitan East region of Rio de Janeiro state, Brazil, faces a historic water scarcity. Among the alternatives studied to solve this situation, the possibility of adduction of the available water in the reservoir Lagoa de Juturnaíba to supply the region's municipalities stands out. The allocation of a linear engineering project must occur through an evaluation of different aspects, such as altitude, slope, proximity to roads, distance from watercourses, land use and occupation, and physical and chemical features of the soil. This work aims to apply a multi-criteria model that combines geoprocessing techniques, decision-making, and geometric search algorithm to optimize a hypothetical adductor system in the scenario of expanding the water supply system that serves this region, known as Imunana-Laranjal, using the Lagoa de Juturnaíba as the source. It is proposed in this study, the construction of a spatial database related to the presented evaluation criteria, treatment and rasterization of these data, and standardization and reclassification of this information in a Geographic Information System (GIS) platform. The methodology involves the integrated analysis of these criteria, using their relative importance defined by weighting them based on expert consultations and the Analytic Hierarchy Process (AHP) method. Three approaches are defined for weighting the criteria by AHP: the first treats all criteria as equally important, the second considers weighting based on a pairwise comparison matrix, and the third establishes a hierarchy based on the priority of the criteria. For each approach, a distinct group of weightings is defined. In the next step, map algebra tools are used to overlay the layers and generate cost surfaces, that indicates the resistance to the passage of the adductor route, using the three groups of weightings. The Dijkstra algorithm, a geometric search algorithm, is then applied to these cost surfaces to find an optimized path within the geographical space, aiming to minimize resources, time, investment, maintenance, and environmental and social impacts.

Keywords: geometric search algorithm, GIS, pipeline, route optimization, spatial multi-criteria analysis model

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Authors: Peter Akayuure

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Geometry is considered an important strand in mathematics due to its wide-ranging utilitarian value and because it serves as a building block for understanding other aspects of undergraduate mathematics, including algebra and calculus. Matters regarding students’ geometric thinking have therefore long been pursued by mathematics researchers and educators globally via different theoretical lenses, curriculum reform efforts, and innovative instructional practices. However, so far, studies remain inconclusive about the instructional platforms that effectively promote geometric thinking. At the University of Education, Winneba, an undergraduate geometry course was designed and delivered on UEW Learning Management System (LMS) using Moodle platform. This study utilizes van Hiele’s theoretical lens to examine the entry and exit’s geometric thinking behaviours of prospective teachers who took the undergraduate geometry course in the LMS platform. The study was a descriptive survey that involved an intact class of 280 first-year students enrolled to pursue a bachelor's in mathematics education at the university. The van Hiele’s Geometric thinking test was used to assess participants’ entry and exit behaviours, while semi-structured interviews were used to obtain data for triangulation. Data were analysed descriptively and displayed in tables and charts. An Independent t-test was used to test for significant differences in geometric thinking behaviours between those who entered the university with a diploma certificate and with senior high certificate. The results show that on entry, more than 70% of the prospective teachers operated within the visualization level of van Hiele’s geometric thinking. Less than 20% reached analysis and abstraction levels, and no participant reached deduction and rigor levels. On exit, participants’ geometric thinking levels increased markedly across levels, but the difference from entry was not significant and might have occurred by chance. The geometric thinking behaviours of those enrolled with diploma certificates did not differ significant from those enrolled directly from senior high school. The study recommends that the design principles and delivery of undergraduate geometry course via LMS should be structured and tackled using van Hiele’s geometric thinking levels to serve as means of bridging the existing learning gaps of undergraduate students.

Keywords: geometric thinking, van Hiele’s, UEW learning management system, undergraduate geometry

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Authors: Marion G. Ben-Jacob, David Wang

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There is a mathematics requirement for entry level college and university students, especially those who plan to study STEM (Science, Technology, Engineering and Mathematics). Most of them take College Algebra, and to continue their studies, they need to succeed in this course. Different pedagogical strategies are employed to promote the success of our students. There is, of course, the Traditional Method of teaching- lecture, examples, problems for students to solve. The Emporium Model, another pedagogical approach, replaces traditional lectures with a learning resource center model featuring interactive software and on-demand personalized assistance. This presentation will compare these two methods of pedagogy and the study done with its results on this comparison. Math is the foundation for science, technology, and engineering. Its work is generally used in STEM to find patterns in data. These patterns can be used to test relationships, draw general conclusions about data, and model the real world. In STEM, solutions to problems are analyzed, reasoned, and interpreted using math abilities in a assortment of real-world scenarios. This presentation will examine specific examples of how math is used in the different STEM disciplines. Math becomes practical in science when it is used to model natural and artificial experiments to identify a problem and develop a solution for it. As we analyze data, we are using math to find the statistical correlation between the cause of an effect. Scientists who use math include the following: data scientists, scientists, biologists and geologists. Without math, most technology would not be possible. Math is the basis of binary, and without programming, you just have the hardware. Addition, subtraction, multiplication, and division is also used in almost every program written. Mathematical algorithms are inherent in software as well. Mechanical engineers analyze scientific data to design robots by applying math and using the software. Electrical engineers use math to help design and test electrical equipment. They also use math when creating computer simulations and designing new products. Chemical engineers often use mathematics in the lab. Advanced computer software is used to aid in their research and production processes to model theoretical synthesis techniques and properties of chemical compounds. Mathematics mastery is crucial for success in the STEM disciplines. Pedagogical research on formative strategies and necessary topics to be covered are essential.

Keywords: emporium model, mathematics, pedagogy, STEM

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Authors: Bastian Vollrath, Hartwig Hubel

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In case of over-elastic and cyclic loading, strain may accumulate due to a ratcheting mechanism until the state of shakedown is possibly achieved. Load history dependent numerical investigations by a step-by-step analysis are rather costly in terms of engineering time and numerical effort. In the case of multi-parameter loading, where various independent loadings affect the final state of shakedown, the computational effort becomes an additional challenge. Therefore, direct methods like the Simplified Theory of Plastic Zones (STPZ) are developed to solve the problem with a few linear elastic analyses. Post-shakedown quantities such as strain ranges and cyclic accumulated strains are calculated approximately by disregarding the load history. The STPZ is based on estimates of a transformed internal variable, which can be used to perform modified elastic analyses, where the elastic material parameters are modified, and initial strains are applied as modified loading, resulting in residual stresses and strains. The STPZ already turned out to work well with respect to cyclic loading between two states of loading. Usually, few linear elastic analyses are sufficient to obtain a good approximation to the post-shakedown quantities. In a multi-dimensional load domain, the approximation of the transformed internal variable transforms from a plane problem into a hyperspace problem, where time-consuming approximation methods need to be applied. Therefore, a solution restricted to structures with four stress components was developed to estimate the transformed internal variable by means of three-dimensional vector algebra. This paper presents the extension to cyclic multi-parameter loading so that an unlimited number of load cases can be taken into account. The theoretical basis and basic presumptions of the Simplified Theory of Plastic Zones are outlined for the case of elastic shakedown. The extension of the method to many load cases is explained, and a workflow of the procedure is illustrated. An example, adopting the FE-implementation of the method into ANSYS and considering multilinear hardening is given which highlights the advantages of the method compared to incremental, step-by-step analysis.

Keywords: cyclic loading, direct method, elastic shakedown, multi-parameter loading, STPZ

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Authors: Alice D. Dioquino, Olivia N. Buzon, Emilio F. Aguinaldo, Ruel Avila, Erwin R. Callo, Cristy Ocampo, Malvin R. Tabajen, Marla C. Papango, Marilou M. Ubina, Josephine Tondo, Cromwell L. Valeriano

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The main purpose of this study was to develop, evaluate and validate courseware on Selected Topics in Mathematics, Science, and the English Language. Specifically, it aimed to: 1. Identify the appropriate Instructional Systems Design (ISD) model in the development of the courseware material; 2. Assess the courseware material according to its: a. Content Characteristics; b. Instructional Characteristics; and c. Technical Characteristics 3. Find out if there is a significant difference in the performance of students before and after using the tutorial CAI. This research is developmental as well as a one group pretest-posttest design. The study had two phases. Phase I includes the needs analysis, writing of lessons and storyboard by the respective experts in each field. Phase II includes the digitization or the actual development of the courseware by the faculty of the ICT department. In this phase it adapted an instructional systems design (ISD) model which is the ADDIE model. ADDIE stands for Analysis, Design, Development, Implementation and Evaluation. Formative evaluation was conducted simultaneously with the different phases to detect and remedy any bugs in the courseware along the areas of content, instructional and technical characteristics. The expected output are the digitized lessons in Algebra, Biology, Chemistry, Physics and Communication Arts in English. Students and some IT experts validated the CAI material using the Evaluation Form by Wong & Wong. They validated the CAI materials as Highly Acceptable with an overall mean rating of 4.527and standard deviation of 0 which means that they were one in the ratings they have given the CAI materials. A mean gain was recorded and computing the t-test for dependent samples it showed that there were significant differences in the mean achievement of the students before and after the treatment (using CAI). The identified ISD model used in the development of the tutorial courseware was the ADDIE model. The quantitative analyses of data based on ratings given by the respondents’ shows that the tutorial courseware possess the characteristics and or qualities of a very good computer-based courseware. The ratings given by the different evaluators with regard to content, instructional, and technical aspects of the Tutorial Courseware are in conformity towards being excellent. Students performed better in mathematics, biology chemistry, physics and the English Communication Arts after they were exposed to the tutorial courseware.

Keywords: CAI, tutorial courseware, Instructional Systems Design (ISD) Model, education

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Authors: Michael Lousis

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This research study is concerned with learner’s errors on Arithmetic and Algebra. The data resulted from a broader international comparative research program called Kassel Project. However, its conceptualisation differed from and contrasted with that of the main program, which was mostly based on socio-demographic data. The way in which the research study was conducted, was not dependent on the researcher’s discretion, but was absolutely dictated by the nature of the problem under investigation. This is because the phenomenon of learners’ mathematical errors is due neither to the intentions of learners nor to institutional processes, rules and norms, nor to the educators’ intentions and goals; but rather to the way certain information is presented to learners and how their cognitive apparatus processes this information. Several approaches for the study of learners’ errors have been developed from the beginning of the 20th century, encompassing different belief systems. These approaches were based on the behaviourist theory, on the Piagetian- constructivist research framework, the perspective that followed the philosophy of science and the information-processing paradigm. The researcher of the present study was forced to disclose the learners’ course of thinking that led them in specific observable actions with the result of showing particular errors in specific problems, rather than analysing scripts with the students’ thoughts presented in a written form. This, in turn, entailed that the choice of methods would have to be appropriate and conducive to seeing and realising the learners’ errors from the perspective of the participants in the investigation. This particular fact determined important decisions to be made concerning the selection of an appropriate framework for analysing the mathematical errors and giving explanations. Thus the rejection of the belief systems concerning behaviourism, the Piagetian-constructivist, and philosophy of science perspectives took place, and the information-processing paradigm in conjunction with the philosophy of mind were adopted as a general account for the elaboration of data. This paper explains why these decisions were appropriate and beneficial for conducting the present study and for the establishment of the ensued thesis. Additionally, the reasons for the adoption of the information-processing paradigm in conjunction with the philosophy of mind give sound and legitimate bases for the development of future studies concerning mathematical error analysis are explained.

Keywords: advantages-disadvantages of theoretical prospects, behavioral prospect, critical evaluation of theoretical prospects, error analysis, information-processing paradigm, opting for the appropriate approach, philosophy of science prospect, Piagetian-constructivist research frameworks, review of research in mathematical errors

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Authors: Andrey Davydov, Konstantin Sveshnikov, Yulia Voronina

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There is now a lot of interest to the non-perturbative QED-effects, caused by diving of discrete levels into the negative continuum in the supercritical static or adiabatically slowly varying Coulomb fields, that are created by the localized extended sources with Z > Z_cr. Such effects have attracted a considerable amount of theoretical and experimental activity, since in 3+1 QED for Z > Z_cr,1 ≈ 170 a non-perturbative reconstruction of the vacuum state is predicted, which should be accompanied by a number of nontrivial effects, including the vacuum positron emission. Similar in essence effects should be expected also in both 2+1 D (planar graphene-based hetero-structures) and 1+1 D (one-dimensional ‘hydrogen ion’). This report is devoted to the study of such essentially non-perturbative vacuum effects for the supercritical Dirac-Coulomb systems in 1+1D and 2+1D, with the main attention drawn to the vacuum polarization energy. Although the most of works considers the vacuum charge density as the main polarization observable, vacuum energy turns out to be not less informative and in many respects complementary to the vacuum density. Moreover, the main non-perturbative effects, which appear in vacuum polarization for supercritical fields due to the levels diving into the lower continuum, show up in the behavior of vacuum energy even more clear, demonstrating explicitly their possible role in the supercritical region. Both in 1+1D and 2+1D, we explore firstly the renormalized vacuum density in the supercritical region using the Wichmann-Kroll method. Thereafter, taking into account the results for the vacuum density, we formulate the renormalization procedure for the vacuum energy. To evaluate the latter explicitly, an original technique, based on a special combination of analytical methods, computer algebra tools and numerical calculations, is applied. It is shown that, for a wide range of the external source parameters (the charge Z and size R), in the supercritical region the renormalized vacuum energy could significantly deviate from the perturbative quadratic growth up to pronouncedly decreasing behavior with jumps by (-2 x mc^2), which occur each time, when the next discrete level dives into the negative continuum. In the considered range of variation of Z and R, the vacuum energy behaves like ~ -Z^2/R in 1+1D and ~ -Z^3/R in 2+1D, exceeding deeply negative values. Such behavior confirms the assumption of the neutral vacuum transmutation into the charged one, and thereby of the spontaneous positron emission, accompanying the emergence of the next vacuum shell due to the total charge conservation. To the end, we also note that the methods, developed for the vacuum energy evaluation in 2+1 D, with minimal complements could be carried over to the three-dimensional case, where the vacuum energy is expected to be ~ -Z^4/R and so could be competitive with the classical electrostatic energy of the Coulomb source.

Keywords: non-perturbative QED-effects, one- and two-dimensional Dirac-Coulomb systems, supercritical fields, vacuum polarization

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Authors: M. Cardenas-Garcia, P. P. Gonzalez-Perez

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Intercellular communication is a necessary condition for cellular functions and it allows a group of cells to survive as a population. Throughout this interaction, the cells work in a coordinated and collaborative way which facilitates their survival. In the case of cancerous cells, these take advantage of intercellular communication to preserve their malignancy, since through these physical unions they can send signs of malignancy. The Wnt/β-catenin signaling pathway plays an important role in the formation of intercellular communications, being also involved in a large number of cellular processes such as proliferation, differentiation, adhesion, cell survival, and cell death. The modeling and simulation of cellular signaling systems have found valuable support in a wide range of modeling approaches, which cover a wide spectrum ranging from mathematical models; e.g., ordinary differential equations, statistical methods, and numerical methods– to computational models; e.g., process algebra for modeling behavior and variation in molecular systems. Based on these models, different simulation tools have been developed from mathematical ones to computational ones. Regarding cellular and molecular processes in cancer, its study has also found a valuable support in different simulation tools that, covering a spectrum as mentioned above, have allowed the in silico experimentation of this phenomenon at the cellular and molecular level. In this work, we simulate and explore the complex interaction patterns of intercellular communication in cancer cells using the Cellulat bioinformatics tool, a computational simulation tool developed by us and motivated by two key elements: 1) a biochemically inspired model of self-organizing coordination in tuple spaces, and 2) the Gillespie’s algorithm, a stochastic simulation algorithm typically used to mimic systems of chemical/biochemical reactions in an efficient and accurate way. The main idea behind the Cellulat simulation tool is to provide an in silico experimentation environment that complements and guides in vitro experimentation in intra and intercellular signaling networks. Unlike most of the cell signaling simulation tools, such as E-Cell, BetaWB and Cell Illustrator which provides abstractions to model only intracellular behavior, Cellulat is appropriate for modeling both intracellular signaling and intercellular communication, providing the abstractions required to model –and as a result, simulate– the interaction mechanisms that involve two or more cells, that is essential in the scenario discussed in this work. During the development of this work we made evident the application of our computational simulation tool (Cellulat) for the modeling and simulation of intercellular communication between normal and cancerous cells, and in this way, propose key molecules that may prevent the arrival of malignant signals to the cells that surround the tumor cells. In this manner, we could identify the significant role that has the Wnt/β-catenin signaling pathway in cellular communication, and therefore, in the dissemination of cancer cells. We verified, using in silico experiments, how the inhibition of this signaling pathway prevents that the cells that surround a cancerous cell are transformed.

Keywords: cancer cells, in silico approach, intercellular communication, key molecules, modeling and simulation

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Authors: Adriana Haulica

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Powered by Machine Learning, Precise medicine is tailored by now to use genetic and molecular profiling, with the aim of optimizing the therapeutic benefits for cohorts of patients. As the majority of Machine Language algorithms come from heuristics, the outputs have contextual validity. This is not very restrictive in the sense that medicine itself is not an exact science. Meanwhile, the progress made in Molecular Biology, Bioinformatics, Computational Biology, and Precise Medicine, correlated with the huge amount of human biology data and the increase in computational power, opens new healthcare challenges. A more accurate diagnosis is needed along with real-time treatments by processing as much as possible from the available information. The purpose of this paper is to present a deeper vision for the future of Artificial Intelligence in Precise medicine. In fact, actual Machine Learning algorithms use standard mathematical knowledge, mostly Euclidian metrics and standard computation rules. The loss of information arising from the classical methods prevents obtaining 100% evidence on the diagnosis process. To overcome these problems, we introduce MEDICOMPILLS, a new architectural concept tool of information processing in Precise medicine that delivers diagnosis and therapy advice. This tool processes poly-field digital resources: global knowledge related to biomedicine in a direct or indirect manner but also technical databases, Natural Language Processing algorithms, and strong class optimization functions. As the name suggests, the heart of this tool is a compiler. The approach is completely new, tailored for omics and clinical data. Firstly, the intrinsic biological intuition is different from the well-known “a needle in a haystack” approach usually used when Machine Learning algorithms have to process differential genomic or molecular data to find biomarkers. Also, even if the input is seized from various types of data, the working engine inside the MEDICOMPILLS does not search for patterns as an integrative tool. This approach deciphers the biological meaning of input data up to the metabolic and physiologic mechanisms, based on a compiler with grammars issued from bio-algebra-inspired mathematics. It translates input data into bio-semantic units with the help of contextual information iteratively until Bio-Logical operations can be performed on the base of the “common denominator “rule. The rigorousness of MEDICOMPILLS comes from the structure of the contextual information on functions, built to be analogous to mathematical “proofs”. The major impact of this architecture is expressed by the high accuracy of the diagnosis. Detected as a multiple conditions diagnostic, constituted by some main diseases along with unhealthy biological states, this format is highly suitable for therapy proposal and disease prevention. The use of MEDICOMPILLS architecture is highly beneficial for the healthcare industry. The expectation is to generate a strategic trend in Precise medicine, making medicine more like an exact science and reducing the considerable risk of errors in diagnostics and therapies. The tool can be used by pharmaceutical laboratories for the discovery of new cures. It will also contribute to better design of clinical trials and speed them up.

Keywords: bio-semantic units, multiple conditions diagnosis, NLP, omics

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Authors: A. Peyvan, D. Li, J. Komperda, F. Mashayek

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Turbulence can be observed in a variety fluid motions in nature and industrial applications. Recent investment in high-speed aircraft and propulsion systems has revitalized fundamental research on turbulent flows. In these systems, capturing chaotic fluid structures with different length and time scales is accomplished through the Direct Numerical Simulation (DNS) approach since it accurately simulates flows down to smallest dissipative scales, i.e., Kolmogorov’s scales. The discontinuous spectral element method (DSEM) is a high-order technique that uses spectral functions for approximating the solution. The DSEM code has been developed by our research group over the course of more than two decades. Recently, the code has been improved to run large cases in the order of billions of solution points. Running big simulations requires a considerable amount of RAM. Therefore, the DSEM code must be highly parallelized and able to start on multiple computational nodes on an HPC cluster with distributed memory. However, some pre-processing procedures, such as determining global element information, creating a global face list, and assigning global partitioning and element connection information of the domain for communication, must be done sequentially with a single processing core. A separate code has been written to perform the pre-processing procedures on a local machine. It stores the minimum amount of information that is required for the DSEM code to start in parallel, extracted from the mesh file, into text files (pre-files). It packs integer type information with a Stream Binary format in pre-files that are portable between machines. The files are generated to ensure fast read performance on different file-systems, such as Lustre and General Parallel File System (GPFS). A new subroutine has been added to the DSEM code to read the startup files using parallel MPI I/O, for Lustre, in a way that each MPI rank acquires its information from the file in parallel. In case of GPFS, in each computational node, a single MPI rank reads data from the file, which is specifically generated for the computational node, and send them to other ranks on the node using point to point non-blocking MPI communication. This way, communication takes place locally on each node and signals do not cross the switches of the cluster. The read subroutine has been tested on Argonne National Laboratory’s Mira (GPFS), National Center for Supercomputing Application’s Blue Waters (Lustre), San Diego Supercomputer Center’s Comet (Lustre), and UIC’s Extreme (Lustre). The tests showed that one file per node is suited for GPFS and parallel MPI I/O is the best choice for Lustre file system. The DSEM code relies on heavily optimized linear algebra operation such as matrix-matrix and matrix-vector products for calculation of the solution in every time-step. For this, the code can either make use of its matrix math library, BLAS, Intel MKL, or ATLAS. This fact and the discontinuous nature of the method makes the DSEM code run efficiently in parallel. The results of weak scaling tests performed on Blue Waters showed a scalable and efficient performance of the code in parallel computing.

Keywords: computational fluid dynamics, direct numerical simulation, spectral element, turbulent flow

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