Search results for: mathematical biology

Authors: Lulu Sun

Abstract:

In Addition is an after-school mathematics program in which students and their parents build mathematical confidence and competence by solving problems they curious about. It is a program consists of mix-grade from 4th to 6th grade of 10 to 20 students, including math problem solving and other activities. This partnership will focus on the relationship between the In-Addition and the parents’ engagement; in this kind of partnership, it has the In-Addition program teaching and the family engagement. This partnership is purpose to building cooperation between the program and parents, strengthening the links between the program and families.

Keywords: program-family, family engagement, positive bias, partnership

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Authors: Arunas Stirke, Neringa Bakute, Gatis Mozolevskis

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A technology of microfluidics is an emerging tool in the field of biology, medicine and chemistry. Microfluidic device is also known as ‘lab-on-a-chip’ technology [1]. In moving from macro- to microscale, there is unprecedented control over spatial and temporal gradients and patterns that cannot be captured in conventional Petri dishes and well plates [2]. However, there is not a single standard microfluidic chip designated for all purposes – every different field of studies needs a specific microchip with certain geometries, inlet/outlet, channel depth and other parameters to precisely regulate the required function. Since our group is studying an effect of pulsed electric field (PEF) to the cells, we have manufactured a microfluidic chip designated for high-throughput electroporation of cells. In our microchip, a cell culture chamber is divided into two parallel channels by a membrane, meanwhile electrodes for electroporation are attached to the wall of the channels. Both microchannels have their own inlet and outlet, enabling injection of transfection material separately. Our perspective is to perform electroporation of mammalian cells in two different ways: (1) plasmid and cells are injected in the same microchannel and (2) injected into separate microchannels. Moreover, oxygen and pH sensors are integrated on order to analyse cell viability parameters after PEF treatment.

Keywords: microfluidics, chip, fabrication, electroporation

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Authors: Jingyuan Hu, Zhandong Liu

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CRISPR genome editing technology has transformed molecular biology by accurately targeting and altering an organism’s DNA. Despite the state-of-art precision of CRISPR genome editing, the imprecise mutation outcome and off-target effects present considerable risk, potentially leading to unintended genetic changes. Targeted deep sequencing, combined with bioinformatics sequence alignment, can detect such unwanted mutations. Nevertheless, the classical method, Needleman-Wunsch (NW) algorithm may produce false alignment outcomes, resulting in inaccurate mutation identification. The key to precisely identifying CRISPR-induced mutations lies in determining optimal parameters for the sequence alignment algorithm. Hidden Markov models (HMM) are ideally suited for this task, offering flexibility across CRISPR systems by leveraging forward-backward algorithms for parameter estimation. In this study, we introduce CRISPR-HMM, a statistical software to precisely call CRISPR-induced mutations. We demonstrate that the software significantly improves precision in identifying CRISPR-induced mutations compared to NW-based alignment, thereby enhancing the overall understanding of the CRISPR gene-editing process.

Keywords: CRISPR, HMM, sequence alignment, gene editing

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Authors: Ahmed Madian, Muaz Aljarhi

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Coordinate Rotation Digital Computer (CORDIC) is a unique digital computing unit intended for the computation of mathematical operations and functions. This paper presents a multi-CORDIC processor that integrates different CORDIC architectures on a single FPGA chip and allows the user to select the CORDIC architecture to proceed with based on what he wants to calculate and his/her needs. Synthesis show that radix 2 CORDIC has the lowest clock delay, radix 8 CORDIC has the highest LUT usage and lowest register usage while Hybrid Radix 4 CORDIC had the highest clock delay.

Keywords: multi, CORDIC, FPGA, processor

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Authors: Jin Zhi

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This study focuses on a green screen keying method developed especially for film visual effects. There are a series of ways of using existing tools for creating mattes from green or blue screen plates. However, it is still a time-consuming process, and the results vary especially when it comes to retaining tiny details, such as hair and fur. This paper introduces an alternative concept and method for retaining edge details of characters on a green screen plate, also, a number of connected mathematical equations are explored. At the end of this study, a simplified process of applying this method in real productions is also introduced.

Keywords: green screen, visual effects, compositing, matte

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Authors: Z. Nougrara, J. Meunier

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In this paper, we present a new approach for extracting roads, there road network and its nodes from satellite image representing regions in Algeria. Our approach is related to our previous research work. It is founded on the information theory and the mathematical morphology. We therefore have to define objects as sets of pixels and to study the shape of these objects and the relations that exist between them. The main interest of this study is to solve the problem of the automatic mapping from satellite images. This study is thus applied for that the geographical representation of the images is as near as possible to the reality.

Keywords: nodes, road network, satellite image, updating a road map

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Authors: Shashi Sharma, V. K. Katiyar, Uaday Singh

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The ability to manipulate magnetic particles in fluid flows by means of inhomogeneous magnetic fields is used in a wide range of biomedical applications including magnetic drug targeting (MDT). In MDT, magnetic carrier particles bounded with drug molecules are injected into the vascular system up-stream from the malignant tissue and attracted or retained at the specific region in the body with the help of an external magnetic field. Although the concept of MDT has been around for many years, however, wide spread acceptance of the technique is still looming despite the fact that it has shown some promise in both in vivo and clinical studies. This is because traditional MDT has some inherent limitations. Typically, the magnetic force is not very strong and it is also very short ranged. Since the magnetic force must overcome rather large hydrodynamic forces in the body, MDT applications have been limited to sites located close to the surface of the skin. Even in this most favorable situation, studies have shown that it is difficult to collect appreciable amounts of the MDCPs at the target site. To overcome these limitations of the traditional MDT approach, Ritter and co-workers reported the implant assisted magnetic drug targeting (IA-MDT). In IA-MDT, the magnetic implants are placed strategically at the target site to greatly and locally increase the magnetic force on MDCPs and help to attract and retain the MDCPs at the targeted region. In the present work, we develop a mathematical model to study the capturing of magnetic nanoparticles flowing in a fluid in an implant assisted cylindrical channel under the magnetic field. A coil of ferromagnetic SS 430 has been implanted inside the cylindrical channel to enhance the capturing of magnetic nanoparticles under the magnetic field. The dominant magnetic and drag forces, which significantly affect the capturing of nanoparticles, are incorporated in the model. It is observed through model results that capture efficiency increases from 23 to 51 % as we increase the magnetic field from 0.1 to 0.5 T, respectively. The increase in capture efficiency by increase in magnetic field is because as the magnetic field increases, the magnetization force, which is attractive in nature and responsible to attract or capture the magnetic particles, increases and results the capturing of large number of magnetic particles due to high strength of attractive magnetic force.

Keywords: capture efficiency, implant assisted-magnetic drug targeting (IA-MDT), magnetic nanoparticles, modelling

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Authors: Mujde Turkkan, Nurkan Yagiz

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The vibrations, caused by the irregularities of the road surface, are to be suppressed via suspension systems. In this paper, sliding mode control for a half bus model with air suspension system is presented. The bus is modelled as five degrees of freedom (DoF) system. The mathematical model of the half bus is developed using Lagrange Equations. For time domain analysis, the bus model is assumed to travel at certain speed over the bump road. The numerical results of the analysis indicate that the sliding mode controllers can be effectively used to suppress the vibrations and to improve the ride comfort of the busses.

Keywords: active suspension system, air suspension, bus model, sliding mode control

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Authors: Valeria Minucciani, Maria Maddalena Margaria

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While mathematical tools that make digital architecture possible are very sophisticated and advanced, theoretical development of digital architecture (intended as a discipline that integrates or replaces the real architecture) is not. The fashion show, that involves interiors architecture, exhibit design and scenography, has been exploiting for ten years the opportunities offered by digital technologies. To gain greater visibility and to reach a wider audience, high-level experimentations have been performed. The aim of this paper is in investigating, through the analysis of some cases of virtual fashion shows, the 'architectural' impact of the virtual conception of interior space.

Keywords: digital interiors, exhibit, fashion catwalk, architectural theory

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Authors: Larry Wang

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The aim of this paper is to demonstrate how an online homework system is integrated in teaching and learning mathematics and how it improves the student success rates in some gateway mathematics courses. WeBWork provided by the Mathematical Association of America is adopted as the online homework system. During the period of 2010-2015, the system was implemented in classes of precalculus, calculus, probability and statistics, discrete mathematics, linear algebra, and differential equations. As a result, the passing rates of the sections with WeBWork are well above other sections without WeBWork (about 7-10% higher). The paper also shows how the WeBWork system was used.

Keywords: gateway mathematics, online grading, pass rate, WeBWorK

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Authors: Ahlam Inayatullah Badrul Munir, M. Husaini A. Rahman, Mohd Sukri Hassan

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Real-time PCR is a molecular biology technique that is currently being widely used for halal services to differentiating between porcine and bovine DNA. The useful of technique become very important for student or workers (who works in the laboratory) to learn how the technique could be run smoothly without fail. Same concept with conventional PCR, real-time PCR also needed DNA template, primer, enzyme polymerase, dNTP, and buffer. The difference is in real-time PCR, have additional component namely fluorescent dye. The most common use of fluorescent dye in real-time PCR is SYBR green. The purpose of this study was to find out how sensitive, specific and efficient real-time PCR technique was combined with SYBR green method and specific primers of CYT b. The results showed that real-time PCR technique using SYBR Green, capable of detecting porcine and bovine DNA concentrations up to 0.0001 µl/ng. The level of efficiency for both types of DNA was 91% (90-110). Not only that in specific primer CYT b bovine primer could detect only bovine DNA, and porcine primer could detect only porcine primer. So, from the study could be concluded that real-time PCR technique that was combined with specific primer CYT b and SYBR green method, was sensitive, specific and efficient to detect porcine and bovine DNA.

Keywords: sensitivity, specificity, efficiency, real-time PCR, SYBR green, Cytochrome b, porcine DNA, bovine DNA

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Authors: Wasif Mughees, Malik Al-Ahmad, Muhammad Naeem

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This research involves the design and analysis of pinch-based water/wastewater networks to minimize water utility in the petrochemical and petroleum industries. A study has been done on Tehran Oil Refinery to analyze feasibilities of regeneration, reuse and recycling of water network. COD is considered as a single key contaminant. Amount of freshwater was reduced about 149m3/h (43.8%) regarding COD. Re-design (or retrofitting) of water allocation in the networks was undertaken. The results were analyzed through graphical method and mathematical programming technique which clearly demonstrated that amount of required water would be determined by mass transfer of COD.

Keywords: minimization, water pinch, water management, pollution prevention

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Authors: M. Mousavi-Daramoroudi, H. Yousefnia, F. Abbasi-Davani, S. Zolghadri

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In this study, ¹⁷⁷Lu-DOTATOC was prepared under optimized conditions (radiochemical purity: > 99%, radionuclidic purity: > 99%). The percentage of injected dose per gram (%ID/g) was calculated for organs up to 168 h post injection. Compartmental model was applied to mathematical description of the drug behaviour in tissue at different times. The biodistribution data showed the significant excretion of the radioactivity from the kidneys. The adrenal and pancreas, as major expression sites for somatostatin receptor (SSTR), had significant uptake. A pharmacokinetic model of ¹⁷⁷Lu-DOTATOC was presented by compartmental analysis which demonstrates the behavior of the complex.

Keywords: biodistribution, compartmental modeling, ¹⁷⁷Lu, Octreotide

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Authors: R. Pargas, M. Reba

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Since 2006, the School of Computing and the Department of Mathematical Sciences have collaborated on several industry and NSF grants to develop new uses of technology in teaching and learning. Clemson University’s Creative Inquiry Program allowed computer science and mathematics students to earn credit each semester for participating in seminars which introduced them to new areas for independent research. We will discuss how the development of three interactive instructional apps for Calculus resulted not only in a useful product, but also in unique educational benefits for both the computer science students and the mathematics students, graduate and undergraduate, involved in the development process.

Keywords: calculus, apps, programming, mathematics

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Authors: Alexey Mustafin

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This paper explores the complex interplay between materialism, spiritualism, dualism, and non-dualism in the context of both Western and Eastern philosophical traditions. The research question is centered around understanding the implications of these perspectives on our comprehension of reality. The study employs a comparative analysis of worldviews, scientific perspectives, and case studies to achieve its objectives. The theoretical framework examines the critiques of materialism, spiritualism, dualism, and non-dualism, synthesizing different perspectives. A comparative analysis of Western (Greek, Christian, and Enlightenment) and Eastern (Hinduism, Buddhism, and Taoism) philosophical traditions provides a holistic understanding of diverse worldviews. The study further investigates scientific perspectives, including classical physics, quantum physics, biology, neuroscience, and their implications on the understanding of reality. Case studies on near-death experiences, meditation, healing, and parapsychology serve as practical examples of the interplay between these perspectives. The synthesis of findings offers insights into the implications for our understanding of reality and highlights future directions for research in this interdisciplinary field.

Keywords: biocentrism, quantum physics, neurosciense and consciousness, meditation and brain, religion experiences and scientific research, buddhism and science

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Authors: Shubham Tandon, Rajni Goel

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The prime objective of our review paper is to study the quantitative psychology impact on our daily life. Quantitative techniques have been studied with the aim of discovering solutions in an advanced way. To get the unbiased and correct results, statistics and other useful mathematical aspects have been reviewed. So, many psychologists use quantitative techniques while working in the area of psychology with the aim of discovering solutions in an advanced way. This ensures their accurate outcomes as those will make use of precise criteria in knowing the minds and conditions of any person. Also, proper experimentation and observational tools are taken care of to avoid some possibilities of invalid data.

Keywords: quantitative psychology, psychologists, statistics, person, results, minds

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Authors: Saeyoung Lee

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As the enthusiasm for education in Korea is too much high, it is well known by others that children in Korea get good scores in Mathematics. However, behind of this good reputation, children in Korea are easy to get lose self-confidence, tend to complaint and rarely participate in the class because of too much competition which leads to lack of competences. In this regard, the main goals of this paper are, by applying the programme based on peer-communication on Mathematics education field, it would like to improve self-managemental competence to make children gain self-confidence, communicative competence to make them deal with complaint and communitive competence to make them participated in the class for the age of 10 children to solve this problem. 14 children the age of 10 in one primary school in Gangnam, Seoul, Korea had participated in the research from March 2018 to October 2018. They were under the programme based on peer-communication during the period. Every Mathematics class maintained the same way. Firstly a problem was given to children. Secondly, children were asked to find many ways to solve the problem as much as they could by themselves. Thirdly all ways to solve the problem by children were posted on the board and three of the children made a group to distinguish the ways from valid to invalid. Lastly, all children made a discuss to find one way which is the most efficient among valid ways. Pre-test was carried out by the questionnaire based on Likert scale before applying the programme. The result of the pre-test was 3.89 for self-managemental competence, 3.91 for communicative competence and 4.19 for communitive competence. Post-test was carried out by the same questionnaire after applying the programme. The result of the post-test was 3.93 for self-managemental competence, 4.23 for communicative competence and 4.20 for communitive competence. That means by applying the programme based on peer-communication on Mathematics education field, the age of 10 children in Korea could improve self-managemental, communicative and communitive competence. Especially it works very well on communicative competence by increasing 0.32 points as it marked. Considering this research, Korean Mathematics education based on competition which leads to lack of competences should be changed to cooperative structure to make students more competent rather than just getting good scores. In conclusion, innovative teaching methods which are focused on improving competences such as the programme based on peer-communication which was applied in this research are strongly required to be studied and widely used.

Keywords: competences, mathematics education, peer-communication, primary education

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Authors: Cleiton Pons Ferreira, Diana Francisca Adamatti

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Advancements in computers technology have allowed to obtain information for research in biology and neuroscience. In order to transform the data from these surveys, networks have long been used to represent important biological processes, changing the use of this tools from purely illustrative and didactic to more analytic, even including interaction analysis and hypothesis formulation. Many studies have involved this application, but not directly for interpretation of data obtained from brain functions, asking for new perspectives of development in neuroinformatics using existent models of tools already disseminated by the bioinformatics. This study includes an analysis of neurological data through electroencephalogram (EEG) signals, using the Cytoscape, an open source software tool for visualizing complex networks in biological databases. The data were obtained from a comparative case study developed in a research from the University of Rio Grande (FURG), using the EEG signals from a Brain Computer Interface (BCI) with 32 eletrodes prepared in the brain of a blind and a sighted individuals during the execution of an activity that stimulated the spatial ability. This study intends to present results that lead to better ways for use and adapt techniques that support the data treatment of brain signals for elevate the understanding and learning in neuroscience.

Keywords: neuroinformatics, bioinformatics, network tools, brain mapping

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Authors: Shirin Jalili, Hadi Shirzad, Samaneh Nabavi, Somayeh Khanjani

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Forensic entomology is the science of study and analysis of insects evidences to aid in criminal investigation. Being aware of the distribution, biology, ecology and behavior of insects, which are founded at crime scene can provide information about when, where and how the crime has been committed. It has many application in criminal investigations. Its main use is estimation of the minimum time after death in suspicious death. The close association between insects and corpses and the use of insects in criminal investigations is the subject of forensic entomology. Because insects attack to the decomposing corpse and spawning on it from the initial stages. Forensic scientists can estimate the postmortem index by studying the insects population and the developing larval stages.In addition, toxicological and molecular studies of these insects can reveal the cause of death or even the identity of a victim. It also be used to detect drugs and poisons, and determination of incident location. Gathering robust entomological evidences is made possible for experts by recent Techniques. They can provide vital information about death, corpse movement or burial, submersion interval, time of decapitation, identification of specific sites of trauma, post-mortem artefacts on the body, use of drugs, linking a suspect to the scene of a crime, sexual molestations and the identification of suspects.

Keywords: Forensic entomology, post mortem interval, insects, larvae

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Authors: Beatriz Suárez López, Gabriela Forman

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Kombucha (a symbiotic culture of bacteria and yeast) produces material capable of acquiring multiple shapes and textures that change significantly under different environment or temperature variations (e.g., when it is exposed to wet conditions), properties that may be explored in the scenic industry. This paper presents an analysis of its specific characteristics, exploring them as a non-conventional material for arts and performance. Costume Design uses surfaces as a powerful way of expression to represent concepts and stories; it may apply the unique features of nano bacterial cellulose (NBC) as assets in this artistic context. A mix of qualitative and quantitative (interventionist) methodology approaches were used -review of relevant literature to deepen knowledge on the research topic (crossing bibliography from different fields of studies: Biology, Art, Costume Design, etc.); as well as descriptive methods: laboratorial experiments, document quantities, observation to identify material properties and possibilities used to express a multiple narrative ideas, concepts and feelings. The results confirmed that NBC is an interactive and versatile material viable to be used in an alternative scenic context; its unique aesthetic and performative qualities, which change in contact to moisture, is a resource that can be used to show a visual and poetic impact on stage.

Keywords: biotechnological materials, contemporary dance, costume design, nano bacterial cellulose, performing arts

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Authors: Karthik Mittal

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This study performs an unsupervised machine learning analysis to find clusters of related SNPs which highlight biological pathways that are important for the biological mechanisms of breast cancer. Studying genetic variations in isolation is illogical because these genetic variations are known to modulate protein production and function; the downstream effects of these modifications on biological outcomes are highly interconnected. After extracting the SNPs and their effect on different types of breast cancer using the MRBase library, two unsupervised machine learning clustering algorithms were implemented on the genetic variants: a k-means clustering algorithm and a hierarchical clustering algorithm; furthermore, principal component analysis was executed to visually represent the data. These algorithms specifically used the SNP’s beta value on the three different types of breast cancer tested in this project (estrogen-receptor positive breast cancer, estrogen-receptor negative breast cancer, and breast cancer in general) to perform this clustering. Two significant genetic pathways validated the clustering produced by this project: the MAPK signaling pathway and the connection between the BRCA2 gene and the ESR1 gene. This study provides the first proof of concept showing the importance of unsupervised machine learning in interpreting GWAS summary statistics.

Keywords: breast cancer, computational biology, unsupervised machine learning, k-means, PCA

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Authors: Ahmed Amin Mousa, Tamer M. Ismail, M. Abd El Salam

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This work presents a robot called Conceptual Robotic Cube, CR-Cube. The robot can be used as an educational tool for children from the age of three. It has a cube shape attached with a camera colours sensor. In addition, it contains four wheels to move smoothly. The researchers prepared a questionnaire to measure the efficiency of the robot. The design and the questionnaire was presented to 11 experts who agreed that the robot is appropriate for learning numbering and colours for preschool children.

Keywords: CR-Cube, robotic cube, conceptual robot, conceptual cube, colour concept, early childhood education

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Authors: Lamis Naddaf, Yuval Tabach

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In this research, we identified the missense genetic variants that have the potential to enhance resistance against cancer. Such field has not been widely explored, as researchers tend to investigate mutations that cause diseases, in response to the suffering of patients, rather than those mutations that protect from them. In conjunction with the genomic revolution, and the advances in genetic engineering and synthetic biology, identifying the protective variants will increase the power of genotype-phenotype predictions and can have significant implications on improved risk estimation, diagnostics, prognosis and even for personalized therapy and drug discovery. To approach our goal, we systematically investigated the sites of the coding genomes and picked up the alleles that showed a correlation with the species’ cancer resistance. We predicted 250 protecting variants (PVs) with a 0.01 false discovery rate and more than 20 thousand PVs with a 0.25 false discovery rate. Cancer resistance in Mammals and reptiles was significantly predicted by the number of PVs a species has. Moreover, Genes enriched with the protecting variants are enriched in pathways relevant to tumor suppression like pathways of Hedgehog signaling and silencing, which its improper activation is associated with the most common form of cancer malignancy. We also showed that the PVs are more abundant in healthy people compared to cancer patients within different human races.

Keywords: comparative genomics, machine learning, cancer resistance, cancer-protecting alleles

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Authors: Muhammad Rezal Kamel Ariffin, Muhammad Asyraf Asbullah

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The square root modulo problem is a known primitive in designing an asymmetric cryptosystem. It was first attempted by Rabin. Decryption failure of the Rabin cryptosystem caused by the 4-to-1 decryption output is overcome efficiently in this work. The proposed scheme to overcome the decryption failure issue (known as the AAβ-cryptosystem) is constructed using a simple mathematical structure, it has low computational requirements and would enable communication devices with low computing power to deploy secure communication procedures efficiently.

Keywords: Rabin cryptosystem, 4-to-1 decryption failure, square root modulo problem, integer factorization problem

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Authors: Ozlem Senyigit, Nur Yilmaz

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Throughout the architectural education, it is aimed to provide students with the ability to find original solutions to current problems. In this sense, workshops that provide creative thinking within the action, experiencing the environment, and finding instant solutions to problems have an important place in the education process. Parasitic architecture, which is a contemporary design approach in the architectural agenda, includes small scale designs integrated into the carrier system of existing structures in spaces of the existing urban fabric which resembles the host-parasite relationship in the biology field. The scope of this study consists of a 12-weeks long experimental workshop of the 'parasitic architecture', which was designed within the scope of Basic Design 2 course of the Department of Architecture of Çukurova University in the 2017-2018 academic year. In this study, parasitic architecture was discussed as a space design method. Students analyzed the campus of the Çukurova University and drew sketches to identify gaps in it. During the workshop, the function-form-context relationship was discussed. The output products were evaluated within the context of urban spaces/gaps, functional requirements, and students gained awareness not just about the urban occupancy but also gaps.

Keywords: design approach, parasitic architecture, experimental workshop, architectural education

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Authors: Mohammed R. Elkobaisi, Abdelsalam Maatuk

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The search engines are the large scale information retrieval tools from the Web that are currently freely available to all. This paper explains how to convert the raw resulted number of search engines into useful information. This represents a new method for data gathering comparing with traditional methods. When a query is submitted for a multiple numbers of keywords, this take a long time and effort, hence we develop a user interface program to automatic search by taking multi-keywords at the same time and leave this program to collect wanted data automatically. The collected raw data is processed using mathematical and statistical theories to eliminate unwanted data and converting it to usable data.

Keywords: search engines, information extraction, agent system

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Authors: Eze R. Onukwugha

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The presence of cyanide in wastewater is known to inhibit the normal functioning of bio-reactors since it has the tendency to poison reactor micro-organisms. Bench scale models of activated sludge reactors with varying aspect ratios were operated for the treatment of cassava wastewater at several values of hydraulic retention time (HRT). The different values of HRT were achieved by the use of a peristaltic pump to vary the rate of introduction of the wastewater into the reactor. The main parameters monitored are the cyanide concentration and respective COD values of the influent and effluent. These observed values were then transformed into a mathematical model for the prediction of treatment efficiency.

Keywords: wastewater, aspect ratio, cyanide-inhibited wastewater, modeling

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Authors: Valencia P. L. Rodrigo, Morita A. Adelina, Vargas V. Martin

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This proposal consists of an analysis of macro concepts involved within an organization growth using educational technologies, which will relate each concept, in a mathematical way with a vision of harmonic work. Working collaboratively, competitively and cooperatively so that this growth is harmonious and homogenous, coining a new term, Harmonic Work. The Harmonic Work ensures that the organization grows in all business directions, allowing managers to project a much more accurate growth, making clear the contribution of each department, resulting in an algorithm that analyzes each of the variables both endogenous and exogenous, establishing different performance indicators in its process of growth.

Keywords: business projection, collaboration, competitiveness, educational technology, harmonious growth

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Authors: Sami Ali Metwally, Bedour Helmy Abou-Leila, Hussien I.Abdel-Shafy

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The work was carried out at the greenhouse of National Research Centre, Pot experiment was carried out during of 2020 and 2021 seasons aimed to study the effect of two types of water (two recycling gray water treatments((SMR (Sequencing Batch Reactor) and MBR(Membrane Biology Reactor) and three watering intervals 15, 20 and 25 days on Syangonium plants growth. Examination of data cleared that, (MBR) recorded increase in vegetative growth parameters, osmotic pressure, transpiration rate chlorophyll a,b,carotenoids and carbohydrate)in compared with SBR.As for water, intervalsthe highest values of most growth parameters were obtained from plants irrigated with after (20 days) compared with other treatments.15 days irrigation intervals recorded significantly increased in osmotic pressure, transpiration rate and photosynthetic pigments, while carbohydrate values recorded decreased. Interaction between water type and water intervals(SBR) recorded the highest values of most growth parameters by irrigation after 20 days. While the treatment (MBR)and irrigated after 25 days showed the highest values on leaf area and leaves fresh weight compared with other treatments.

Keywords: grey water, water intervals, Syngonium plant, recycling water, vegetative growth

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Authors: Vandana N. Purav

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The Dynamical systems concept is a mathematical formalization for any fixed rule that describes the time dependence of a points position in its ambient space. e.g. pendulum of a clock, the number of fish each spring in a lake, the number of rabbits spring in an enclosure, etc. The Dynamical system theory used to describe the complex nature that is dynamical systems with differential equations called continuous dynamical system or dynamical system with difference equations called discrete dynamical system. The concept of dynamical system has its origin in Newtonian mechanics.

Keywords: dynamical systems, Fibonacci numbers, Newtonian mechanics, discrete dynamical system

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