Search results for: computational mathematics
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2460

Search results for: computational mathematics

480 Pibid and Experimentation: A High School Case Study

Authors: Chahad P. Alexandre

Abstract:

PIBID-Institutional Program of Scholarships to Encourage Teaching - is a Brazilian government program that counts today with 48.000 students. It's goal is to motivate the students to stay in the teaching undergraduate programs and to help fill the gap of 100.000 teachers that are needed today in the under graduated schools. The major lack of teachers today is in physics, chemistry, mathematics, and biology. At IFSP-Itapetininga we formatted our physics PIBID based on practical activities. Our students are divided in two São Paulo state government high schools in the same city. The project proposes class activities based on experimentation, observation and understanding of physical phenomena. The didactical experiments are always in relation with the content that the teacher is working, he is the supervisor of the program in the school. Always before an experiment is proposed a little questionnaire to learn about the students preconceptions and one is filled latter to evaluate if now concepts have been created. This procedure is made in order to compare their previous knowledge and how it changed after the experiment is developed. The primary goal of our project is to make the Physics class more attractive to the students and to develop in high school students the interest in learning physics and to show the relation of Physics to the day by day and to the technological world. The objective of the experimental activities is to facilitate the understanding of the concepts that are worked on classes because under experimentation the PIBID scholarship student stimulate the curiosity of the high school student and with this he can develop the capacity to understand and identify the physical phenomena with concrete examples. Knowing how to identify this phenomena and where they are present at the high school student life makes the learning process more significant and pleasant. This proposal make achievable to the students to practice science, to appropriate of complex, in the traditional classes, concepts and overcoming the common preconception that physics is something distant and that is present only on books. This preconception is extremely harmful in the process of scientific knowledge construction. This kind of learning – through experimentation – make the students not only accumulate knowledge but also appropriate it, also to appropriate experimental procedures and even the space that is provided by the school. The PIBID scholarship students, as future teachers also have the opportunity to try experimentation classes, to intervene in the classes and to have contact with their future career. This opportunity allows the students to make important reflection about the practices realized and consequently about the learning methods. Due to this project, we found out that the high school students stay more time focused in the experiment compared to the traditional explanation teachers´ class. As a result in a class, as a participative activity, the students got more involved and participative. We also found out that the physics under graduated students drop out percentage is smaller in our Institute than before the PIBID program started.

Keywords: innovation, projects, PIBID, physics, pre-service teacher experiences

Procedia PDF Downloads 332
479 Replicating Brain’s Resting State Functional Connectivity Network Using a Multi-Factor Hub-Based Model

Authors: B. L. Ho, L. Shi, D. F. Wang, V. C. T. Mok

Abstract:

The brain’s functional connectivity while temporally non-stationary does express consistency at a macro spatial level. The study of stable resting state connectivity patterns hence provides opportunities for identification of diseases if such stability is severely perturbed. A mathematical model replicating the brain’s spatial connections will be useful for understanding brain’s representative geometry and complements the empirical model where it falls short. Empirical computations tend to involve large matrices and become infeasible with fine parcellation. However, the proposed analytical model has no such computational problems. To improve replicability, 92 subject data are obtained from two open sources. The proposed methodology, inspired by financial theory, uses multivariate regression to find relationships of every cortical region of interest (ROI) with some pre-identified hubs. These hubs acted as representatives for the entire cortical surface. A variance-covariance framework of all ROIs is then built based on these relationships to link up all the ROIs. The result is a high level of match between model and empirical correlations in the range of 0.59 to 0.66 after adjusting for sample size; an increase of almost forty percent. More significantly, the model framework provides an intuitive way to delineate between systemic drivers and idiosyncratic noise while reducing dimensions by more than 30 folds, hence, providing a way to conduct attribution analysis. Due to its analytical nature and simple structure, the model is useful as a standalone toolkit for network dependency analysis or as a module for other mathematical models.

Keywords: functional magnetic resonance imaging, multivariate regression, network hubs, resting state functional connectivity

Procedia PDF Downloads 141
478 Fluid-Structure Interaction Analysis of a Vertical Axis Wind Turbine Blade Made with Natural Fiber Based Composite Material

Authors: Ivan D. Ortega, Juan D. Castro, Alberto Pertuz, Manuel Martinez

Abstract:

One of the problems considered when scientists talk about climate change is the necessity of utilizing renewable sources of energy, on this category there are many approaches to the problem, one of them is wind energy and wind turbines whose designs have frequently changed along many years trying to achieve a better overall performance on different conditions. From that situation, we get the two main types known today: Vertical and Horizontal axis wind turbines, which have acronyms VAWT and HAWT, respectively. This research aims to understand how well suited a composite material, which is still in development, made with natural origin fibers is for its implementation on vertical axis wind turbines blades under certain wind loads. The study consisted on acquiring the mechanical properties of the materials to be used which where bactris guineenis, also known as pama de lata in Colombia, and adhesive that acts as the matrix which had not been previously studied to the point required for this project. Then, a simplified 3D model of the airfoil was developed and tested under some preliminary loads using finite element analysis (FEA), these loads were acquired in the Colombian Chicamocha Canyon. Afterwards, a more realistic pressure profile was obtained using computational fluid dynamics which took into account the 3D shape of the complete blade and its rotation. Finally, the blade model was subjected to the wind loads using what is known as one way fluidstructure interaction (FSI) and its behavior analyzed to draw conclusions. The observed overall results were positive since the material behaved fairly as expected. Data suggests the material would be really useful in this kind of applications in small to medium size turbines if it is given more attention and time to develop.

Keywords: CFD, FEA, FSI, natural fiber, VAWT

Procedia PDF Downloads 211
477 Implementation of Free-Field Boundary Condition for 2D Site Response Analysis in OpenSees

Authors: M. Eskandarighadi, C. R. McGann

Abstract:

It is observed from past experiences of earthquakes that local site conditions can significantly affect the strong ground motion characteristics experience at the site. One-dimensional seismic site response analysis is the most common approach for investigating site response. This approach assumes that soil is homogeneous and infinitely extended in the horizontal direction. Therefore, tying side boundaries together is one way to model this behavior, as the wave passage is assumed to be only vertical. However, 1D analysis cannot capture the 2D nature of wave propagation, soil heterogeneity, and 2D soil profile with features such as inclined layer boundaries. In contrast, 2D seismic site response modeling can consider all of the mentioned factors to better understand local site effects on strong ground motions. 2D wave propagation and considering that the soil profile on the two sides of the model may not be identical clarifies the importance of a boundary condition on each side that can minimize the unwanted reflections from the edges of the model and input appropriate loading conditions. Ideally, the model size should be sufficiently large to minimize the wave reflection, however, due to computational limitations, increasing the model size is impractical in some cases. Another approach is to employ free-field boundary conditions that take into account the free-field motion that would exist far from the model domain and apply this to the sides of the model. This research focuses on implementing free-field boundary conditions in OpenSees for 2D site response analysisComparisons are made between 1D models and 2D models with various boundary conditions, and details and limitations of the developed free-field boundary modeling approach are discussed.

Keywords: boundary condition, free-field, opensees, site response analysis, wave propagation

Procedia PDF Downloads 138
476 Experimental and Numerical Studies of Droplet Formation

Authors: Khaled Al-Badani, James Ren, Lisa Li, David Allanson

Abstract:

Droplet formation is an important process in many engineering systems and manufacturing procedures, which includes welding, biotechnologies, 3D printing, biochemical, biomedical fields and many more. The volume and the characteristics of droplet formation are generally depended on various material properties, microfluidics and fluid mechanics considerations. Hence, a detailed investigation of this process, with the aid of numerical computational tools, are essential for future design optimization and process controls of many engineering systems. This will also improve the understanding of changes in the properties and the structures of materials, during the formation of the droplet, which is important for new material developments to achieve different functions, pending the requirements of the application. For example, the shape of the formed droplet is critical for the function of some final products, such as the welding nugget during Capacitor Discharge Welding process, or PLA 3D printing, etc. Although, most academic journals on droplet formation, focused on issued with material transfer rate, surface tension and residual stresses, the general emphasis on the characteristics of droplet shape has been overlooked. The proposed work for this project will examine theoretical methodologies, experimental techniques, and numerical modelling, using ANSYS FLUENT, to critically analyse and highlight optimization methods regarding the formation of pendant droplet. The project will also compare results from published data with experimental and numerical work, concerning the effects of key material parameters on the droplet shape. These effects include changes in heating/cooling rates, solidification/melting progression and separation/break-up times. From these tests, a set of objectives is prepared, with an intention of improving quality, stability and productivity in modelling metal welding and 3D printing.

Keywords: computer modelling, droplet formation, material distortion, materials forming, welding

Procedia PDF Downloads 275
475 A Formal Microlectic Framework for Biological Circularchy

Authors: Ellis D. Cooper

Abstract:

“Circularchy” is supposed to be an adjustable formal framework with enough expressive power to articulate biological theory about Earthly Life in the sense of multi-scale biological autonomy constrained by non-equilibrium thermodynamics. “Formal framework” means specifically a multi-sorted first-order-theorywithequality (for each sort). Philosophically, such a theory is one kind of “microlect,” which means a “way of speaking” (or, more generally, a “way of behaving”) for overtly expressing a “mental model” of some “referent.” Other kinds of microlect include “natural microlect,” “diagrammatic microlect,” and “behavioral microlect,” with examples such as “political theory,” “Euclidean geometry,” and “dance choreography,” respectively. These are all describable in terms of a vocabulary conforming to grammar. As aspects of human culture, they are possibly reminiscent of Ernst Cassirer’s idea of “symbolic form;” as vocabularies, they are akin to Richard Rorty’s idea of “final vocabulary” for expressing a mental model of one’s life. A formal microlect is presented by stipulating sorts, variables, calculations, predicates, and postulates. Calculations (a.k.a., “terms”) may be composed to form more complicated calculations; predicates (a.k.a., “relations”) may be logically combined to form more complicated predicates; and statements (a.k.a., “sentences”) are grammatically correct expressions which are true or false. Conclusions are statements derived using logical rules of deduction from postulates, other assumed statements, or previously derived conclusions. A circularchy is a formal microlect constituted by two or more sub-microlects, each with its distinct stipulations of sorts, variables, calculations, predicates, and postulates. Within a sub-microlect some postulates or conclusions are equations which are statements that declare equality of specified calculations. An equational bond between an equation in one sub-microlect and an equation in either the same sub-microlect or in another sub-microlect is a predicate that declares equality of symbols occurring in a side of one equation with symbols occurring in a side of the other equation. Briefly, a circularchy is a network of equational bonds between sub-microlects. A circularchy is solvable if there exist solutions for all equations that satisfy all equational bonds. If a circularchy is not solvable, then a challenge would be to discover the obstruction to solvability and then conjecture what adjustments might remove the obstruction. Adjustment means changes in stipulated ingredients (sorts, etc.) of sub-microlects, or changes in equational bonds between sub-microlects, or introduction of new sub-microlects and new equational bonds. A circularchy is modular insofar as each sub-microlect is a node in a network of equation bonds. Solvability of a circularchy may be conjectured. Efforts to prove solvability may be thwarted by a counter-example or may lead to the construction of a solution. An automated theorem-proof assistant would likely be necessary for investigating a substantial circularchy, such as one purported to represent Earthly Life. Such investigations (chains of statements) would be concurrent with and no substitute for simulations (chains of numbers).

Keywords: autonomy, first-order theory, mathematics, thermodynamics

Procedia PDF Downloads 209
474 Improving Patient-Care Services at an Oncology Center with a Flexible Adaptive Scheduling Procedure

Authors: P. Hooshangitabrizi, I. Contreras, N. Bhuiyan

Abstract:

This work presents an online scheduling problem which accommodates multiple requests of patients for chemotherapy treatments in a cancer center of a major metropolitan hospital in Canada. To solve the problem, an adaptive flexible approach is proposed which systematically combines two optimization models. The first model is intended to dynamically schedule arriving requests in the form of waiting lists whereas the second model is used to reschedule the already booked patients with the goal of finding better resource allocations when new information becomes available. Both models are created as mixed integer programming formulations. Various controllable and flexible parameters such as deviating the prescribed target dates by a pre-determined threshold, changing the start time of already booked appointments and the maximum number of appointments to move in the schedule are included in the proposed approach to have sufficient degrees of flexibility in handling arrival requests and unexpected changes. Several computational experiments are conducted to evaluate the performance of the proposed approach using historical data provided by the oncology clinic. Our approach achieves outstandingly better results as compared to those of the scheduling system being used in practice. Moreover, several analyses are conducted to evaluate the effect of considering different levels of flexibility on the obtained results and to assess the performance of the proposed approach in dealing with last-minute changes. We strongly believe that the proposed flexible adaptive approach is very well-suited for implementation at the clinic to provide better patient-care services and to utilize available resource more efficiently.

Keywords: chemotherapy scheduling, multi-appointment modeling, optimization of resources, satisfaction of patients, mixed integer programming

Procedia PDF Downloads 149
473 Self-Supervised Attributed Graph Clustering with Dual Contrastive Loss Constraints

Authors: Lijuan Zhou, Mengqi Wu, Changyong Niu

Abstract:

Attributed graph clustering can utilize the graph topology and node attributes to uncover hidden community structures and patterns in complex networks, aiding in the understanding and analysis of complex systems. Utilizing contrastive learning for attributed graph clustering can effectively exploit meaningful implicit relationships between data. However, existing attributed graph clustering methods based on contrastive learning suffer from the following drawbacks: 1) Complex data augmentation increases computational cost, and inappropriate data augmentation may lead to semantic drift. 2) The selection of positive and negative samples neglects the intrinsic cluster structure learned from graph topology and node attributes. Therefore, this paper proposes a method called self-supervised Attributed Graph Clustering with Dual Contrastive Loss constraints (AGC-DCL). Firstly, Siamese Multilayer Perceptron (MLP) encoders are employed to generate two views separately to avoid complex data augmentation. Secondly, the neighborhood contrastive loss is introduced to constrain node representation using local topological structure while effectively embedding attribute information through attribute reconstruction. Additionally, clustering-oriented contrastive loss is applied to fully utilize clustering information in global semantics for discriminative node representations, regarding the cluster centers from two views as negative samples to fully leverage effective clustering information from different views. Comparative clustering results with existing attributed graph clustering algorithms on six datasets demonstrate the superiority of the proposed method.

Keywords: attributed graph clustering, contrastive learning, clustering-oriented, self-supervised learning

Procedia PDF Downloads 31
472 Influence of Internal Topologies on Components Produced by Selective Laser Melting: Numerical Analysis

Authors: C. Malça, P. Gonçalves, N. Alves, A. Mateus

Abstract:

Regardless of the manufacturing process used, subtractive or additive, material, purpose and application, produced components are conventionally solid mass with more or less complex shape depending on the production technology selected. Aspects such as reducing the weight of components, associated with the low volume of material required and the almost non-existent material waste, speed and flexibility of production and, primarily, a high mechanical strength combined with high structural performance, are competitive advantages in any industrial sector, from automotive, molds, aviation, aerospace, construction, pharmaceuticals, medicine and more recently in human tissue engineering. Such features, properties and functionalities are attained in metal components produced using the additive technique of Rapid Prototyping from metal powders commonly known as Selective Laser Melting (SLM), with optimized internal topologies and varying densities. In order to produce components with high strength and high structural and functional performance, regardless of the type of application, three different internal topologies were developed and analyzed using numerical computational tools. The developed topologies were numerically submitted to mechanical compression and four point bending testing. Finite Element Analysis results demonstrate how different internal topologies can contribute to improve mechanical properties, even with a high degree of porosity relatively to fully dense components. Results are very promising not only from the point of view of mechanical resistance, but especially through the achievement of considerable variation in density without loss of structural and functional high performance.

Keywords: additive manufacturing, internal topologies, porosity, rapid prototyping, selective laser melting

Procedia PDF Downloads 322
471 Trajectory Optimization of Re-Entry Vehicle Using Evolutionary Algorithm

Authors: Muhammad Umar Kiani, Muhammad Shahbaz

Abstract:

Performance of any vehicle can be predicted by its design/modeling and optimization. Design optimization leads to efficient performance. Followed by horizontal launch, the air launch re-entry vehicle undergoes a launch maneuver by introducing a carefully selected angle of attack profile. This angle of attack profile is the basic element to complete a specified mission. Flight program of said vehicle is optimized under the constraints of the maximum allowed angle of attack, lateral and axial loads and with the objective of reaching maximum altitude. The main focus of this study is the endo-atmospheric phase of the ascent trajectory. A three degrees of freedom trajectory model is simulated in MATLAB. The optimization process uses evolutionary algorithm, because of its robustness and efficient capacity to explore the design space in search of the global optimum. Evolutionary Algorithm based trajectory optimization also offers the added benefit of being a generalized method that may work with continuous, discontinuous, linear, and non-linear performance matrix. It also eliminates the requirement of a starting solution. Optimization is particularly beneficial to achieve maximum advantage without increasing the computational cost and affecting the output of the system. For the case of launch vehicles we are immensely anxious to achieve maximum performance and efficiency under different constraints. In a launch vehicle, flight program means the prescribed variation of vehicle pitching angle during the flight which has substantial influence reachable altitude and accuracy of orbit insertion and aerodynamic loading. Results reveal that the angle of attack profile significantly affects the performance of the vehicle.

Keywords: endo-atmospheric, evolutionary algorithm, efficient performance, optimization process

Procedia PDF Downloads 396
470 STEM (Science–Technology–Engineering–Mathematics) Based Entrepreneurship Training, Within a Learning Company

Authors: Diana Mitova, Krassimir Mitrev

Abstract:

To prepare the current generation for the future, education systems need to change. It implies a way of learning that meets the demands of the times and the environment in which we live. Productive interaction in the educational process implies an interactive learning environment and the possibility of personal development of learners based on communication and mutual dialogue, cooperation and good partnership in decision-making. Students need not only theoretical knowledge, but transferable skills that will help them to become inventors and entrepreneurs, to implement ideas. STEM education , is now a real necessity for the modern school. Through learning in a "learning company", students master examples from classroom practice, simulate real life situations, group activities and apply basic interactive learning strategies and techniques. The learning company is the subject of this study, reduced to entrepreneurship training in STEM - technologies that encourage students to think outside the traditional box. STEM learning focuses the teacher's efforts on modeling entrepreneurial thinking and behavior in students and helping them solve problems in the world of business and entrepreneurship. Learning based on the implementation of various STEM projects in extracurricular activities, experiential learning, and an interdisciplinary approach are means by which educators better connect the local community and private businesses. Learners learn to be creative, experiment and take risks and work in teams - the leading characteristics of any innovator and future entrepreneur. This article presents some European policies on STEM and entrepreneurship education. It also shares best practices for training company training , with the integration of STEM in the learning company training environment. The main results boil down to identifying some advantages and problems in STEM entrepreneurship education. The benefits of using integrative approaches to teach STEM within a training company are identified, as well as the positive effects of project-based learning in a training company using STEM. Best practices for teaching entrepreneurship through extracurricular activities using STEM within a training company are shared. The following research methods are applied in this research paper: Theoretical and comparative analysis of principles and policies of European Union countries and Bulgaria in the field of entrepreneurship education through a training company. Experiences in entrepreneurship education through extracurricular activities with STEM application within a training company are shared. A questionnaire survey to investigate the motivation of secondary vocational school students to learn entrepreneurship through a training company and their readiness to start their own business after completing their education. Within the framework of learning through a "learning company" with the integration of STEM, the activity of the teacher-facilitator includes the methods: counseling, supervising and advising students during work. The expectation is that students acquire the key competence "initiative and entrepreneurship" and that the cooperation between the vocational education system and the business in Bulgaria is more effective.

Keywords: STEM, entrepreneurship, training company, extracurricular activities

Procedia PDF Downloads 87
469 In Silico Study of Antiviral Drugs Against Three Important Proteins of Sars-Cov-2 Using Molecular Docking Method

Authors: Alireza Jalalvand, Maryam Saleh, Somayeh Behjat Khatouni, Zahra Bahri Najafi, Foroozan Fatahinia, Narges Ismailzadeh, Behrokh Farahmand

Abstract:

Object: In the last two decades, the recent outbreak of Coronavirus (SARS-CoV-2) imposed a global pandemic in the world. Despite the increasing prevalence of the disease, there are no effective drugs to treat it. A suitable and rapid way to afford an effective drug and treat the global pandemic is a computational drug study. This study used molecular docking methods to examine the potential inhibition of over 50 antiviral drugs against three fundamental proteins of SARS-CoV-2. METHODS: Through a literature review, three important proteins (a key protease, RNA-dependent RNA polymerase (RdRp), and spike) were selected as drug targets. Three-dimensional (3D) structures of protease, spike, and RdRP proteins were obtained from the Protein Data Bank. Protein had minimal energy. Over 50 antiviral drugs were considered candidates for protein inhibition and their 3D structures were obtained from drug banks. The Autodock 4.2 software was used to define the molecular docking settings and run the algorithm. RESULTS: Five drugs, including indinavir, lopinavir, saquinavir, nelfinavir, and remdesivir, exhibited the highest inhibitory potency against all three proteins based on the binding energies and drug binding positions deduced from docking and hydrogen-bonding analysis. Conclusions: According to the results, among the drugs mentioned, saquinavir and lopinavir showed the highest inhibitory potency against all three proteins compared to other drugs. It may enter laboratory phase studies as a dual-drug treatment to inhibit SARS-CoV-2.

Keywords: covid-19, drug repositioning, molecular docking, lopinavir, saquinavir

Procedia PDF Downloads 75
468 3D Numerical Study of Tsunami Loading and Inundation in a Model Urban Area

Authors: A. Bahmanpour, I. Eames, C. Klettner, A. Dimakopoulos

Abstract:

We develop a new set of diagnostic tools to analyze inundation into a model district using three-dimensional CFD simulations, with a view to generating a database against which to test simpler models. A three-dimensional model of Oregon city with different-sized groups of building next to the coastline is used to run calculations of the movement of a long period wave on the shore. The initial and boundary conditions of the off-shore water are set using a nonlinear inverse method based on Eulerian spatial information matching experimental Eulerian time series measurements of water height. The water movement is followed in time, and this enables the pressure distribution on every surface of each building to be followed in a temporal manner. The three-dimensional numerical data set is validated against published experimental work. In the first instance, we use the dataset as a basis to understand the success of reduced models - including 2D shallow water model and reduced 1D models - to predict water heights, flow velocity and forces. This is because models based on the shallow water equations are known to underestimate drag forces after the initial surge of water. The second component is to identify critical flow features, such as hydraulic jumps and choked states, which are flow regions where dissipation occurs and drag forces are large. Finally, we describe how future tsunami inundation models should be modified to account for the complex effects of buildings through drag and blocking.Financial support from UCL and HR Wallingford is greatly appreciated. The authors would like to thank Professor Daniel Cox and Dr. Hyoungsu Park for providing the data on the Seaside Oregon experiment.

Keywords: computational fluid dynamics, extreme events, loading, tsunami

Procedia PDF Downloads 104
467 Optimal Emergency Shipment Policy for a Single-Echelon Periodic Review Inventory System

Authors: Saeed Poormoaied, Zumbul Atan

Abstract:

Emergency shipments provide a powerful mechanism to alleviate the risk of imminent stock-outs and can result in substantial benefits in an inventory system. Customer satisfaction and high service level are immediate consequences of utilizing emergency shipments. In this paper, we consider a single-echelon periodic review inventory system consisting of a single local warehouse, being replenished from a central warehouse with ample capacity in an infinite horizon setting. Since the structure of the optimal policy appears to be complicated, we analyze this problem under an order-up-to-S inventory control policy framework, the (S, T) policy, with the emergency shipment consideration. In each period of the periodic review policy, there is a single opportunity at any point of time for the emergency shipment so that in case of stock-outs, an emergency shipment is requested. The goal is to determine the timing and amount of the emergency shipment during a period (emergency shipment policy) as well as the base stock periodic review policy parameters (replenishment policy). We show that how taking advantage of having an emergency shipment during periods improves the performance of the classical (S, T) policy, especially when fixed and unit emergency shipment costs are small. Investigating the structure of the objective function, we develop an exact algorithm for finding the optimal solution. We also provide a heuristic and an approximation algorithm for the periodic review inventory system problem. The experimental analyses indicate that the heuristic algorithm is computationally more efficient than the approximation algorithm, but in terms of the solution efficiency, the approximation algorithm performs very well. We achieve up to 13% cost savings in the (S, T) policy if we apply the proposed emergency shipment policy. Moreover, our computational results reveal that the approximated solution is often within 0.21% of the globally optimal solution.

Keywords: emergency shipment, inventory, periodic review policy, approximation algorithm.

Procedia PDF Downloads 127
466 Fast Bayesian Inference of Multivariate Block-Nearest Neighbor Gaussian Process (NNGP) Models for Large Data

Authors: Carlos Gonzales, Zaida Quiroz, Marcos Prates

Abstract:

Several spatial variables collected at the same location that share a common spatial distribution can be modeled simultaneously through a multivariate geostatistical model that takes into account the correlation between these variables and the spatial autocorrelation. The main goal of this model is to perform spatial prediction of these variables in the region of study. Here we focus on a geostatistical multivariate formulation that relies on sharing common spatial random effect terms. In particular, the first response variable can be modeled by a mean that incorporates a shared random spatial effect, while the other response variables depend on this shared spatial term, in addition to specific random spatial effects. Each spatial random effect is defined through a Gaussian process with a valid covariance function, but in order to improve the computational efficiency when the data are large, each Gaussian process is approximated to a Gaussian random Markov field (GRMF), specifically to the block nearest neighbor Gaussian process (Block-NNGP). This approach involves dividing the spatial domain into several dependent blocks under certain constraints, where the cross blocks allow capturing the spatial dependence on a large scale, while each individual block captures the spatial dependence on a smaller scale. The multivariate geostatistical model belongs to the class of Latent Gaussian Models; thus, to achieve fast Bayesian inference, it is used the integrated nested Laplace approximation (INLA) method. The good performance of the proposed model is shown through simulations and applications for massive data.

Keywords: Block-NNGP, geostatistics, gaussian process, GRMF, INLA, multivariate models.

Procedia PDF Downloads 83
465 Scheduling Jobs with Stochastic Processing Times or Due Dates on a Server to Minimize the Number of Tardy Jobs

Authors: H. M. Soroush

Abstract:

The problem of scheduling products and services for on-time deliveries is of paramount importance in today’s competitive environments. It arises in many manufacturing and service organizations where it is desirable to complete jobs (products or services) with different weights (penalties) on or before their due dates. In such environments, schedules should frequently decide whether to schedule a job based on its processing time, due-date, and the penalty for tardy delivery to improve the system performance. For example, it is common to measure the weighted number of late jobs or the percentage of on-time shipments to evaluate the performance of a semiconductor production facility or an automobile assembly line. In this paper, we address the problem of scheduling a set of jobs on a server where processing times or due-dates of jobs are random variables and fixed weights (penalties) are imposed on the jobs’ late deliveries. The goal is to find the schedule that minimizes the expected weighted number of tardy jobs. The problem is NP-hard to solve; however, we explore three scenarios of the problem wherein: (i) both processing times and due-dates are stochastic; (ii) processing times are stochastic and due-dates are deterministic; and (iii) processing times are deterministic and due-dates are stochastic. We prove that special cases of these scenarios are solvable optimally in polynomial time, and introduce efficient heuristic methods for the general cases. Our computational results show that the heuristics perform well in yielding either optimal or near optimal sequences. The results also demonstrate that the stochasticity of processing times or due-dates can affect scheduling decisions. Moreover, the proposed problem is general in the sense that its special cases reduce to some new and some classical stochastic single machine models.

Keywords: number of late jobs, scheduling, single server, stochastic

Procedia PDF Downloads 485
464 Effects of the Air Supply Outlets Geometry on Human Comfort inside Living Rooms: CFD vs. ADPI

Authors: Taher M. Abou-deif, Esmail M. El-Bialy, Essam E. Khalil

Abstract:

The paper is devoted to numerically investigating the influence of the air supply outlets geometry on human comfort inside living looms. A computational fluid dynamics model is developed to examine the air flow characteristics of a room with different supply air diffusers. The work focuses on air flow patterns, thermal behavior in the room with few number of occupants. As an input to the full-scale 3-D room model, a 2-D air supply diffuser model that supplies direction and magnitude of air flow into the room is developed. Air distribution effect on thermal comfort parameters was investigated depending on changing the air supply diffusers type, angles and velocity. Air supply diffusers locations and numbers were also investigated. The pre-processor Gambit is used to create the geometric model with parametric features. Commercially available simulation software “Fluent 6.3” is incorporated to solve the differential equations governing the conservation of mass, three momentum and energy in the processing of air flow distribution. Turbulence effects of the flow are represented by the well-developed two equation turbulence model. In this work, the so-called standard k-ε turbulence model, one of the most widespread turbulence models for industrial applications, was utilized. Basic parameters included in this work are air dry bulb temperature, air velocity, relative humidity and turbulence parameters are used for numerical predictions of indoor air distribution and thermal comfort. The thermal comfort predictions through this work were based on ADPI (Air Diffusion Performance Index),the PMV (Predicted Mean Vote) model and the PPD (Percentage People Dissatisfied) model, the PMV and PPD were estimated using Fanger’s model.

Keywords: thermal comfort, Fanger's model, ADPI, energy effeciency

Procedia PDF Downloads 401
463 Teaching for Social Justice: Towards Education for Sustainable Development

Authors: Nashwa Moheyeldine

Abstract:

Education for sustainable development (ESD) aims to preserve the rights of the present and future generations as well as preserving the globe, both humans and nature. ESD should aim not only to bring about consciousness of the current and future issues, but also to foster student agency to bring about change at schools, communities and nations. According to the Freirian concept of conscientização, (conscientization) — “learning to perceive social, political, and economic contradictions, and to take action against the oppressive elements of reality”, education aims to liberate people to understand and act upon their worlds. Social justice is greatly intertwined with a nation’s social, political and economic rights, and thus, should be targeted through ESD. “Literacy researchers have found that K-12 students who engage in social justice inquiries develop vital academic knowledge and skills, critical understandings about oppression in the world, and strong dispositions to continue working toward social justice beyond the initial inquiries they conduct”. Education for social justice greatly equips students with the critical thinking skills and sense of agency, that are required for responsible decision making that would ensure a sustainable world. In fact teaching for social justice is intersecting with many of the pedagogies such as multicultural education, cultural relevant pedagogy, education for sustainable development, critical theory pedagogy, (local and global) citizenship education, all of which aim to prepare students for awareness, responsibility and agency. Social justice pedagogy has three specific goals, including helping students develop 1) a sociopolitical consciousness - an awareness of the symbiotic relationship between the social and political factors that affect society, 2) a sense of agency, the freedom to act on one’s behalf and to feel empowered as a change agent, and 3) positive social and cultural identities. The keyword to social justice education is to expose the realities to the students, and challenge the students not only to question , but also to change. Social justice has been usually discussed through the subjects of history and social sciences, however, an interdisciplinary approach is essential to enhance the students’ understanding of their world. Teaching social justice through various subjects is also important, as it make students’ learning relevant to their lives. The main question that this paper seeks to answer is ‘How could social justice be taught through different subjects and tools, such as mathematics, literature through story-telling, geography, and service learning will be shown in this paper. Also challenges to education for social justice will be described. Education is not a neutral endeavor, but is either oriented toward the cause of liberation or in support of domination. In fact , classrooms can be “a microcosm of the emancipatory societies we seek to encourage”, education for the 21st century should be relevant to students' lives where it exposes life's realities to them. Education should also provide students with the basics of school subjects with the bigger goal of helping them make the world a better, more just place to live in.

Keywords: teaching for social justice, student agency, citizenship education, education

Procedia PDF Downloads 395
462 Faster Pedestrian Recognition Using Deformable Part Models

Authors: Alessandro Preziosi, Antonio Prioletti, Luca Castangia

Abstract:

Deformable part models achieve high precision in pedestrian recognition, but all publicly available implementations are too slow for real-time applications. We implemented a deformable part model algorithm fast enough for real-time use by exploiting information about the camera position and orientation. This implementation is both faster and more precise than alternative DPM implementations. These results are obtained by computing convolutions in the frequency domain and using lookup tables to speed up feature computation. This approach is almost an order of magnitude faster than the reference DPM implementation, with no loss in precision. Knowing the position of the camera with respect to horizon it is also possible prune many hypotheses based on their size and location. The range of acceptable sizes and positions is set by looking at the statistical distribution of bounding boxes in labelled images. With this approach it is not needed to compute the entire feature pyramid: for example higher resolution features are only needed near the horizon. This results in an increase in mean average precision of 5% and an increase in speed by a factor of two. Furthermore, to reduce misdetections involving small pedestrians near the horizon, input images are supersampled near the horizon. Supersampling the image at 1.5 times the original scale, results in an increase in precision of about 4%. The implementation was tested against the public KITTI dataset, obtaining an 8% improvement in mean average precision over the best performing DPM-based method. By allowing for a small loss in precision computational time can be easily brought down to our target of 100ms per image, reaching a solution that is faster and still more precise than all publicly available DPM implementations.

Keywords: autonomous vehicles, deformable part model, dpm, pedestrian detection, real time

Procedia PDF Downloads 267
461 Improvement Performances of the Supersonic Nozzles at High Temperature Type Minimum Length Nozzle

Authors: W. Hamaidia, T. Zebbiche

Abstract:

This paper presents the design of axisymmetric supersonic nozzles, in order to accelerate a supersonic flow to the desired Mach number and that having a small weight, in the same time gives a high thrust. The concerned nozzle gives a parallel and uniform flow at the exit section. The nozzle is divided into subsonic and supersonic regions. The supersonic portion is independent to the upstream conditions of the sonic line. The subsonic portion is used to give a sonic flow at the throat. In this case, nozzle gives a uniform and parallel flow at the exit section. It’s named by minimum length Nozzle. The study is done at high temperature, lower than the dissociation threshold of the molecules, in order to improve the aerodynamic performances. Our aim consists of improving the performances both by the increase of exit Mach number and the thrust coefficient and by reduction of the nozzle's mass. The variation of the specific heats with the temperature is considered. The design is made by the Method of Characteristics. The finite differences method with predictor-corrector algorithm is used to make the numerical resolution of the obtained nonlinear algebraic equations. The application is for air. All the obtained results depend on three parameters which are exit Mach number, the stagnation temperature, the chosen mesh in characteristics. A numerical simulation of nozzle through Computational Fluid Dynamics-FASTRAN was done to determine and to confirm the necessary design parameters.

Keywords: flux supersonic flow, axisymmetric minimum length nozzle, high temperature, method of characteristics, calorically imperfect gas, finite difference method, trust coefficient, mass of the nozzle, specific heat at constant pressure, air, error

Procedia PDF Downloads 141
460 Performance Comparison of Deep Convolutional Neural Networks for Binary Classification of Fine-Grained Leaf Images

Authors: Kamal KC, Zhendong Yin, Dasen Li, Zhilu Wu

Abstract:

Intra-plant disease classification based on leaf images is a challenging computer vision task due to similarities in texture, color, and shape of leaves with a slight variation of leaf spot; and external environmental changes such as lighting and background noises. Deep convolutional neural network (DCNN) has proven to be an effective tool for binary classification. In this paper, two methods for binary classification of diseased plant leaves using DCNN are presented; model created from scratch and transfer learning. Our main contribution is a thorough evaluation of 4 networks created from scratch and transfer learning of 5 pre-trained models. Training and testing of these models were performed on a plant leaf images dataset belonging to 16 distinct classes, containing a total of 22,265 images from 8 different plants, consisting of a pair of healthy and diseased leaves. We introduce a deep CNN model, Optimized MobileNet. This model with depthwise separable CNN as a building block attained an average test accuracy of 99.77%. We also present a fine-tuning method by introducing the concept of a convolutional block, which is a collection of different deep neural layers. Fine-tuned models proved to be efficient in terms of accuracy and computational cost. Fine-tuned MobileNet achieved an average test accuracy of 99.89% on 8 pairs of [healthy, diseased] leaf ImageSet.

Keywords: deep convolution neural network, depthwise separable convolution, fine-grained classification, MobileNet, plant disease, transfer learning

Procedia PDF Downloads 171
459 Prompt Design for Code Generation in Data Analysis Using Large Language Models

Authors: Lu Song Ma Li Zhi

Abstract:

With the rapid advancement of artificial intelligence technology, large language models (LLMs) have become a milestone in the field of natural language processing, demonstrating remarkable capabilities in semantic understanding, intelligent question answering, and text generation. These models are gradually penetrating various industries, particularly showcasing significant application potential in the data analysis domain. However, retraining or fine-tuning these models requires substantial computational resources and ample downstream task datasets, which poses a significant challenge for many enterprises and research institutions. Without modifying the internal parameters of the large models, prompt engineering techniques can rapidly adapt these models to new domains. This paper proposes a prompt design strategy aimed at leveraging the capabilities of large language models to automate the generation of data analysis code. By carefully designing prompts, data analysis requirements can be described in natural language, which the large language model can then understand and convert into executable data analysis code, thereby greatly enhancing the efficiency and convenience of data analysis. This strategy not only lowers the threshold for using large models but also significantly improves the accuracy and efficiency of data analysis. Our approach includes requirements for the precision of natural language descriptions, coverage of diverse data analysis needs, and mechanisms for immediate feedback and adjustment. Experimental results show that with this prompt design strategy, large language models perform exceptionally well in multiple data analysis tasks, generating high-quality code and significantly shortening the data analysis cycle. This method provides an efficient and convenient tool for the data analysis field and demonstrates the enormous potential of large language models in practical applications.

Keywords: large language models, prompt design, data analysis, code generation

Procedia PDF Downloads 11
458 ADP Approach to Evaluate the Blood Supply Network of Ontario

Authors: Usama Abdulwahab, Mohammed Wahab

Abstract:

This paper presents the application of uncapacitated facility location problems (UFLP) and 1-median problems to support decision making in blood supply chain networks. A plethora of factors make blood supply-chain networks a complex, yet vital problem for the regional blood bank. These factors are rapidly increasing demand; criticality of the product; strict storage and handling requirements; and the vastness of the theater of operations. As in the UFLP, facilities can be opened at any of $m$ predefined locations with given fixed costs. Clients have to be allocated to the open facilities. In classical location models, the allocation cost is the distance between a client and an open facility. In this model, the costs are the allocation cost, transportation costs, and inventory costs. In order to address this problem the median algorithm is used to analyze inventory, evaluate supply chain status, monitor performance metrics at different levels of granularity, and detect potential problems and opportunities for improvement. The Euclidean distance data for some Ontario cities (demand nodes) are used to test the developed algorithm. Sitation software, lagrangian relaxation algorithm, and branch and bound heuristics are used to solve this model. Computational experiments confirm the efficiency of the proposed approach. Compared to the existing modeling and solution methods, the median algorithm approach not only provides a more general modeling framework but also leads to efficient solution times in general.

Keywords: approximate dynamic programming, facility location, perishable product, inventory model, blood platelet, P-median problem

Procedia PDF Downloads 494
457 TAXAPRO, A Streamlined Pipeline to Analyze Shotgun Metagenomes

Authors: Sofia Sehli, Zainab El Ouafi, Casey Eddington, Soumaya Jbara, Kasambula Arthur Shem, Islam El Jaddaoui, Ayorinde Afolayan, Olaitan I. Awe, Allissa Dillman, Hassan Ghazal

Abstract:

The ability to promptly sequence whole genomes at a relatively low cost has revolutionized the way we study the microbiome. Microbiologists are no longer limited to studying what can be grown in a laboratory and instead are given the opportunity to rapidly identify the makeup of microbial communities in a wide variety of environments. Analyzing whole genome sequencing (WGS) data is a complex process that involves multiple moving parts and might be rather unintuitive for scientists that don’t typically work with this type of data. Thus, to help lower the barrier for less-computationally inclined individuals, TAXAPRO was developed at the first Omics Codeathon held virtually by the African Society for Bioinformatics and Computational Biology (ASBCB) in June 2021. TAXAPRO is an advanced metagenomics pipeline that accurately assembles organelle genomes from whole-genome sequencing data. TAXAPRO seamlessly combines WGS analysis tools to create a pipeline that automatically processes raw WGS data and presents organism abundance information in both a tabular and graphical format. TAXAPRO was evaluated using COVID-19 patient gut microbiome data. Analysis performed by TAXAPRO demonstrated a high abundance of Clostridia and Bacteroidia genera and a low abundance of Proteobacteria genera relative to others in the gut microbiome of patients hospitalized with COVID-19, consistent with the original findings derived using a different analysis methodology. This provides crucial evidence that the TAXAPRO workflow dispenses reliable organism abundance information overnight without the hassle of performing the analysis manually.

Keywords: metagenomics, shotgun metagenomic sequence analysis, COVID-19, pipeline, bioinformatics

Procedia PDF Downloads 196
456 Computation of Residual Stresses in Human Face Due to Growth

Authors: M. A. Askari, M. A. Nazari, P. Perrier, Y. Payan

Abstract:

Growth and remodeling of biological structures have gained lots of attention over the past decades. Determining the response of the living tissues to the mechanical loads is necessary for a wide range of developing fields such as, designing of prosthetics and optimized surgery operations. It is a well-known fact that biological structures are never stress-free, even when externally unloaded. The exact origin of these residual stresses is not clear, but theoretically growth and remodeling is one of the main sources. Extracting body organs from medical imaging, does not produce any information regarding the existing residual stresses in that organ. The simplest cause of such stresses is the gravity since an organ grows under its influence from its birth. Ignoring such residual stresses might cause erroneous results in numerical simulations. Accounting for residual stresses due to tissue growth can improve the accuracy of mechanical analysis results. In this paper, we have implemented a computational framework based on fixed-point iteration to determine the residual stresses due to growth. Using nonlinear continuum mechanics and the concept of fictitious configuration we find the unknown stress-free reference configuration which is necessary for mechanical analysis. To illustrate the method, we apply it to a finite element model of healthy human face whose geometry has been extracted from medical images. We have computed the distribution of residual stress in facial tissues, which can overcome the effect of gravity and cause that tissues remain firm. Tissue wrinkles caused by aging could be a consequence of decreasing residual stress and not counteracting the gravity. Considering these stresses has important application in maxillofacial surgery. It helps the surgeons to predict the changes after surgical operations and their consequences.

Keywords: growth, soft tissue, residual stress, finite element method

Procedia PDF Downloads 342
455 Review of Strategies for Hybrid Energy Storage Management System in Electric Vehicle Application

Authors: Kayode A. Olaniyi, Adeola A. Ogunleye, Tola M. Osifeko

Abstract:

Electric Vehicles (EV) appear to be gaining increasing patronage as a feasible alternative to Internal Combustion Engine Vehicles (ICEVs) for having low emission and high operation efficiency. The EV energy storage systems are required to handle high energy and power density capacity constrained by limited space, operating temperature, weight and cost. The choice of strategies for energy storage evaluation, monitoring and control remains a challenging task. This paper presents review of various energy storage technologies and recent researches in battery evaluation techniques used in EV applications. It also underscores strategies for the hybrid energy storage management and control schemes for the improvement of EV stability and reliability. The study reveals that despite the advances recorded in battery technologies there is still no cell which possess both the optimum power and energy densities among other requirements, for EV application. However combination of two or more energy storages as hybrid and allowing the advantageous attributes from each device to be utilized is a promising solution. The review also reveals that State-of-Charge (SoC) is the most crucial method for battery estimation. The conventional method of SoC measurement is however questioned in the literature and adaptive algorithms that include all model of disturbances are being proposed. The review further suggests that heuristic-based approach is commonly adopted in the development of strategies for hybrid energy storage system management. The alternative approach which is optimization-based is found to be more accurate but is memory and computational intensive and as such not recommended in most real-time applications.

Keywords: battery state estimation, hybrid electric vehicle, hybrid energy storage, state of charge, state of health

Procedia PDF Downloads 220
454 Towards Designing of a Potential New HIV-1 Protease Inhibitor Using Quantitative Structure-Activity Relationship Study in Combination with Molecular Docking and Molecular Dynamics Simulations

Authors: Mouna Baassi, Mohamed Moussaoui, Hatim Soufi, Sanchaita RajkhowaI, Ashwani Sharma, Subrata Sinha, Said Belaaouad

Abstract:

Human Immunodeficiency Virus type 1 protease (HIV-1 PR) is one of the most challenging targets of antiretroviral therapy used in the treatment of AIDS-infected people. The performance of protease inhibitors (PIs) is limited by the development of protease mutations that can promote resistance to the treatment. The current study was carried out using statistics and bioinformatics tools. A series of thirty-three compounds with known enzymatic inhibitory activities against HIV-1 protease was used in this paper to build a mathematical model relating the structure to the biological activity. These compounds were designed by software; their descriptors were computed using various tools, such as Gaussian, Chem3D, ChemSketch and MarvinSketch. Computational methods generated the best model based on its statistical parameters. The model’s applicability domain (AD) was elaborated. Furthermore, one compound has been proposed as efficient against HIV-1 protease with comparable biological activity to the existing ones; this drug candidate was evaluated using ADMET properties and Lipinski’s rule. Molecular Docking performed on Wild Type and Mutant Type HIV-1 proteases allowed the investigation of the interaction types displayed between the proteases and the ligands, Darunavir (DRV) and the new drug (ND). Molecular dynamics simulation was also used in order to investigate the complexes’ stability, allowing a comparative study of the performance of both ligands (DRV & ND). Our study suggested that the new molecule showed comparable results to that of Darunavir and may be used for further experimental studies. Our study may also be used as a pipeline to search and design new potential inhibitors of HIV-1 proteases.

Keywords: QSAR, ADMET properties, molecular docking, molecular dynamics simulation.

Procedia PDF Downloads 17
453 Reduction of Plutonium Production in Heavy Water Research Reactor: A Feasibility Study through Neutronic Analysis Using MCNPX2.6 and CINDER90 Codes

Authors: H. Shamoradifar, B. Teimuri, P. Parvaresh, S. Mohammadi

Abstract:

One of the main characteristics of Heavy Water Moderated Reactors is their high production of plutonium. This article demonstrates the possibility of reduction of plutonium and other actinides in Heavy Water Research Reactor. Among the many ways for reducing plutonium production in a heavy water reactor, in this research, changing the fuel from natural Uranium fuel to Thorium-Uranium mixed fuel was focused. The main fissile nucleus in Thorium-Uranium fuels is U-233 which would be produced after neutron absorption by Th-232, so the Thorium-Uranium fuels have some known advantages compared to the Uranium fuels. Due to this fact, four Thorium-Uranium fuels with different compositions ratios were chosen in our simulations; a) 10% UO2-90% THO2 (enriched= 20%); b) 15% UO2-85% THO2 (enriched= 10%); c) 30% UO2-70% THO2 (enriched= 5%); d) 35% UO2-65% THO2 (enriched= 3.7%). The natural Uranium Oxide (UO2) is considered as the reference fuel, in other words all of the calculated data are compared with the related data from Uranium fuel. Neutronic parameters were calculated and used as the comparison parameters. All calculations were performed by Monte Carol (MCNPX2.6) steady state reaction rate calculation linked to a deterministic depletion calculation (CINDER90). The obtained computational data showed that Thorium-Uranium fuels with four different fissile compositions ratios can satisfy the safety and operating requirements for Heavy Water Research Reactor. Furthermore, Thorium-Uranium fuels have a very good proliferation resistance and consume less fissile material than uranium fuels at the same reactor operation time. Using mixed Thorium-Uranium fuels reduced the long-lived α emitter, high radiotoxic wastes and the radio toxicity level of spent fuel.

Keywords: Heavy Water Reactor, Burn up, Minor Actinides, Neutronic Calculation

Procedia PDF Downloads 236
452 A Framework for Auditing Multilevel Models Using Explainability Methods

Authors: Debarati Bhaumik, Diptish Dey

Abstract:

Multilevel models, increasingly deployed in industries such as insurance, food production, and entertainment within functions such as marketing and supply chain management, need to be transparent and ethical. Applications usually result in binary classification within groups or hierarchies based on a set of input features. Using open-source datasets, we demonstrate that popular explainability methods, such as SHAP and LIME, consistently underperform inaccuracy when interpreting these models. They fail to predict the order of feature importance, the magnitudes, and occasionally even the nature of the feature contribution (negative versus positive contribution to the outcome). Besides accuracy, the computational intractability of SHAP for binomial classification is a cause of concern. For transparent and ethical applications of these hierarchical statistical models, sound audit frameworks need to be developed. In this paper, we propose an audit framework for technical assessment of multilevel regression models focusing on three aspects: (i) model assumptions & statistical properties, (ii) model transparency using different explainability methods, and (iii) discrimination assessment. To this end, we undertake a quantitative approach and compare intrinsic model methods with SHAP and LIME. The framework comprises a shortlist of KPIs, such as PoCE (Percentage of Correct Explanations) and MDG (Mean Discriminatory Gap) per feature, for each of these three aspects. A traffic light risk assessment method is furthermore coupled to these KPIs. The audit framework will assist regulatory bodies in performing conformity assessments of AI systems using multilevel binomial classification models at businesses. It will also benefit businesses deploying multilevel models to be future-proof and aligned with the European Commission’s proposed Regulation on Artificial Intelligence.

Keywords: audit, multilevel model, model transparency, model explainability, discrimination, ethics

Procedia PDF Downloads 81
451 Search for APN Permutations in Rings ℤ_2×ℤ_2^k

Authors: Daniel Panario, Daniel Santana de Freitas, Brett Stevens

Abstract:

Almost Perfect Nonlinear (APN) permutations with optimal resistance against differential cryptanalysis can be found in several domains. The permutation used in the standard for symmetric cryptography (the AES), for example, is based on a special kind of inversion in GF(28). Although very close to APN (2-uniform), this permutation still contains one number 4 in its differential spectrum, which means that, rigorously, it must be classified as 4-uniform. This fact motivates the search for fully APN permutations in other domains of definition. The extremely high complexity associated to this kind of problem precludes an exhaustive search for an APN permutation with 256 elements to be performed without the support of a suitable mathematical structure. On the other hand, in principle, there is nothing to indicate which mathematically structured domains can effectively help the search, and it is necessary to test several domains. In this work, the search for APN permutations in rings ℤ2×ℤ2k is investigated. After a full, exhaustive search with k=2 and k=3, all possible APN permutations in those rings were recorded, together with their differential profiles. Some very promising heuristics in these cases were collected so that, when used as a basis to prune backtracking for the same search in ℤ2×ℤ8 (search space with size 16! ≅244), just a few tenths of a second were enough to produce an APN permutation in a single CPU. Those heuristics were empirically extrapolated so that they could be applied to a backtracking search for APNs over ℤ2×ℤ16 (search space with size 32! ≅2117). The best permutations found in this search were further refined through Simulated Annealing, with a definition of neighbors suitable to this domain. The best result produced with this scheme was a 3-uniform permutation over ℤ2×ℤ16 with only 24 values equal to 3 in the differential spectrum (all the other 968 values were less than or equal 2, as it should be the case for an APN permutation). Although far from being fully APN, this result is technically better than a 4-uniform permutation and demanded only a few seconds in a single CPU. This is a strong indication that the use of mathematically structured domains, like the rings described in this work, together with heuristics based on smaller cases, can lead to dramatic cuts in the computational resources involved in the complexity of the search for APN permutations in extremely large domains.

Keywords: APN permutations, heuristic searches, symmetric cryptography, S-box design

Procedia PDF Downloads 147