Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1070

World Academy of Science, Engineering and Technology

[Mathematical and Computational Sciences]

Online ISSN : 1307-6892

1070 Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease

Authors: Hamdy Agiza, Mohamed Elsohaly, Mohamed Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with a common age of onset, symptoms, and progression levels. In this paper we will solve analytically the Parkinson’s disease model as a non-linear delay differential equation using the steps method. The method of step transforms a system of DDEs into systems of ODEs. On some numerical example, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: parkinson's disease, delay differential equation, step method, two delays

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1069 Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model

Authors: H. C. Chinwenyi, H. D. Ibrahim, T. Danjuma

Abstract:

An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equations (PDEs) options price valuation formula for the Heston stochastic volatility model. We obtained the various PDEs option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem, respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Partial Differential Equations, option price valuation, Black-Scholes partial differential equations, Ito process

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1068 Using Nonhomogeneous Poisson Process with Compound Distribution to Price Catastrophe Options

Authors: Rong-Tsorng Wang

Abstract:

In this paper, we derive a pricing formula for catastrophe equity put options (or CatEPut) with non-homogeneous loss and approximated compound distributions. We assume that the loss claims arrival process is a nonhomogeneous Poisson process (NHPP) representing the clustering occurrences of loss claims, the size of loss claims is a sequence of independent and identically distributed random variables, and the accumulated loss distribution forms a compound distribution and is approximated by a heavy-tailed distribution. A numerical example is given to calibrate parameters, and we discuss how the value of CatEPut is affected by the changes of parameters in the pricing model we provided.

Keywords: pricing model, catastrophe equity put options, compound distributions, nonhomogeneous Poisson process

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1067 Robust Numerical Method for Singularly Perturbed Semilinear Boundary Value Problem with Nonlocal Boundary Condition

Authors: Habtamu Garoma Debela, Gemechis File Duressa

Abstract:

In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: singular perturbation, nonlocal boundary condition, nonstandard fitted operator, semilinear problem, uniformly convergent

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1066 Mathematical Analysis of Simple Supported Euler-Bernoulli Beam on a Variable Elastic Foundation under a Partially Distributed Moving Load.

Authors: I. A. Idowu, S. O. Sogunro, A. O. Atilade, T. A. Abozos

Abstract:

The dynamic responses of an elastically supported Euler- Bernoulli beam on variable elastic foundation under partially distributed moving loads were investigated. The governing equation is fourth order partial differential equation, which was reduced to second order ordinary differential equation by using analytical method in terms of series solution and solved by numerical method using mathematical software (Maple). The numerical analysis shows that the response amplitude of the moving mass and moving force for variable pre-stressed increase as mass of the load M increases. It was found that the response displacement of the beam decrease as the value of the elastic foundation K increases. Also, the response displacement of the beam decrease as the value of the pre-stressed N increase. Comparison of moving mass and moving force shown that moving mass is greater than that of moving force

Keywords: moving load, elastic foundation, Euler-Bernoulli beam, Variable pre-stressed, partially distributed, moving force

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1065 Numerical Investigation of Hybrid Ferrofluid Unsteady Flow through Porous Channel

Authors: M. Zubair Akbar Qureshi, Wajahat Hussain Khan

Abstract:

The viscous, two-dimensional, incompressible, and laminar time-dependent heat transfer flow through a ferromagnetic fluid is considered in this paper. Flow takes place in a channel between two porous walls under the influence of the magnetic field located beyond the channel. It is assumed that there are no electric field effects and the variation in the magnetic field vector that could occur within the F

Keywords: Heat Transfer, Magnetic Field, porous channel, hybrid ferrofluid

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1064 The Physical Impact of Nano-Layer Due to Dispersions of Carbon Nano-Tubes through an Absorbent Channel: A Numerical Nano-Fluid Flow Model

Authors: Muhammad Zubair Akbar Qureshi, Abdul Bari Farooq

Abstract:

The intention of the current study to analyze the significance of nano-layer in incompressible magneto-hydrodynamics (MHD) flow of a Newtonian nano-fluid consisting of carbon nano-materials has been considered through an absorbent channel with moving porous walls. Using applicable similarity transforms, the governing equations are converted into a system of nonlinear ordinary differential equations which are solved by using the 4th-order Runge-Kutta technique together with shooting methodology. The phenomena of nano-layer have also been modeled mathematically. The inspiration behind this segment is to reveal the behavior of involved parameters on velocity and temperature profiles. A detailed table is presented in which the effects of involved parameters on shear stress and heat transfer rate are discussed. Specially presented the impact of the thickness of the nano-layer and radius of the particle on the temperature profile. We observed that due to an increase in the thickness of the nano-layer, the heat transfer rate increases rapidly. The consequences of this research may be advantageous to the applications of biotechnology and industrial motive.

Keywords: carbon nano-tubes, Thermal Conductivity, magneto-hydrodynamics, nano-layer

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1063 Thermal Analysis for Darcy Forchheimer Effect with Hybrid Ferro Fluid Flow

Authors: M. Zubair Akbar Qureshi, Behzad Ali Khan

Abstract:

The article analyzes the Darcy Forchheimer 2D Hybrid ferrofluid. The flow of a Hybrid ferrofluid is made due to an unsteady porous channel. The classical liquid water is treated as a based liquid. The flow in the permeable region is characterized by the Darcy-Forchheimer relation. Heat transfer phenomena are studied during the flow. The transformation of a partial differential set of equations into a strong ordinary differential frame is formed through appropriate variables. The numerical Shooting Method is executed for solving the simplified set of equations. In addition, a numerical analysis (ND-Solve) is utilized for the convergence of the applied technique. The influence of some flow model quantities like Pr (Prandtle number), r (porous medium parameter), F (Darcy-porous medium parameter), Re (Reynolds number), Pe (Peclet number) on velocity and temperature field are scrutinized and studied through sketches. Certain physical factors like f ''(η) (skin friction coefficient) and θ^'(η) (rate of heat transfer) are first derived and then presented through tables.

Keywords: porous medium, porous channel, darcy forcheimer, hybrid ferro fluid

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1062 Numerical Study of Entropy Generation Due to Hybrid Nano-Fluid Flow through Coaxial Porous Disks

Authors: Muhammad Bilal Ameen, M. Zubair Akbar Qureshi

Abstract:

The current investigation of two-dimensional hybrid nanofluid flows with two coaxial parallel disks has been presented. Consider the hybrid nanofluid has been taken as steady-state. Consider the coaxial disks that have been porous. Consider the heat equation to examine joule heating and viscous dissipation effects. Nonlinear partial differential equations have been solved numerically. For shear stress and heat transfer, results are tabulated. Hybrid nanoparticles and Eckert numbers are increasing for heat transfer. Entropy generation is expanded with radiation parameters Eckert, Reynold, Prandtl, and Peclet numbers. A set of ordinary differential equations is obtained to utilize the capable transformation variables. The numerical solution of the continuity, momentum, energy, and entropy generation equations is obtaining using the command bvp4c of Matlab as a solver. To explore the impact of main parameters like suction/infusion, Prandtl, Reynold, Eckert, Peclet number, and volume fraction parameters, various graphs have been plotted and examined. It is concluded that a convectional nanofluid is highly compared by entropy generation with the boundary layer of hybrid nanofluid.

Keywords: Heat Transfer, entropy generation, hybrid nano fluid, porous disks

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1061 Economic Development Process: A Compartmental Analysis of a Model with Two Delays

Authors: Charles Awono Onana, Amadou Banda Ndione

Abstract:

In this paper the compartmental approach is applied to build a macroeconomic model characterized by countries. We consider a total of N countries that are subdivided into three compartments according to their economic status: D(t) denotes the compartment of developing countries at time t, E(t) stands for the compartment of emerging countries at time t while A(t) represents advanced countries at time t. The model describes the process of economic development and includes the notion of openness through collaborations between countries. Two delays appear in this model to describe the average time necessary for collaborations between countries to become efficient for their development process. Our model represents the different stages of development. It further gives the conditions under which a country can change its economic status and demonstrates the short-term positive effect of openness on economic growth. In addition, we investigate bifurcation by considering the delay as a bifurcation parameter and examine the onset and termination of Hopf bifurcations from a positive equilibrium. Numerical simulations are provided in order to illustrate the theoretical part and to support discussion.

Keywords: Economic Development, Hopf Bifurcation, Fiscal Policy, compartmental systems, delayed dynamical system

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1060 Jensen's Inequality and M-Convex Functions

Authors: Yamin Sayyari

Abstract:

In this paper, we generalized the Jensen's inequality for m-convex functions and also we present a correction of Jensen's inequality which is a better than the generalization of this inequality for m-convex functions. Finally, we have found new lower and new upper bounds for Jensen's discrete inequality.

Keywords: Inequality, Jensen's inequality, Convex function, m-convex function

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1059 Multiscale Simulation of Ink Seepage into Fibrous Structures through a Mesoscopic Variational Model

Authors: Athmane Bakhta, Sebastien Leclaire, David Vidal, Francois Bertrand, Mohamed Cheriet

Abstract:

This work presents a new three-dimensional variational model proposed for the simulation of ink seepage into paper sheets at the fiber level. The model, inspired by the Hising model, takes into account a finite volume of ink and describes the system state through gravity, cohesion, and adhesion force interactions. At the mesoscopic scale, the paper substrate is modeled using a discretized fiber structure generated using a numerical deposition procedure. A modified Monte Carlo method is introduced for the simulation of the ink dynamics. Besides, a multiphase lattice Boltzmann method is suggested to fine-tune the mesoscopic variational model parameters, and it is shown that the ink seepage behaviors predicted by the proposed model can resemble those predicted by a method relying on first principles.

Keywords: Modelling and simulation, Monte Carlo, fibrous media, lattice Boltzmann, variational model

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1058 Optimization of Coefficients of Fractional Order Proportional-Integrator-Derivative Controller on Permanent Magnet Synchronous Motors Using Particle Swarm Optimization

Authors: Ali Motalebi Saraji, Reza Zarei Lamuki

Abstract:

Speed control and behavior improvement of permanent magnet synchronous motors (PMSM) that have reliable performance, low loss, and high power density, especially in industrial drives, are of great importance for researchers. Because of its importance in this paper, coefficients optimization of proportional-integrator-derivative fractional order controller is presented using Particle Swarm Optimization (PSO) algorithm in order to improve the behavior of PMSM in its speed control loop. This improvement is simulated in MATLAB software for the proposed optimized proportional-integrator-derivative fractional order controller with a Genetic algorithm and compared with a full order controller with a classic optimization method. Simulation results show the performance improvement of the proposed controller with respect to two other controllers in terms of rising time, overshoot, and settling time.

Keywords: Particle Swarm Optimization, speed control loop of permanent magnet synchronous motor, fractional and full order proportional-integrator-derivative controller, coefficients optimization, improvement of behavior

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1057 A Topological Approach for Motion Track Discrimination

Authors: Tegan H. Emerson, Colin C. Olson, George Stantchev, Jason A. Edelberg, Michael Wilson

Abstract:

Detecting small targets at range is difficult because there is not enough spatial information present in an image sub-region containing the target to use correlation-based methods to differentiate it from dynamic confusers present in the scene. Moreover, this lack of spatial information also disqualifies the use of most state-of-the-art deep learning image-based classifiers. Here, we use characteristics of target tracks extracted from video sequences as data from which to derive distinguishing topological features that help robustly differentiate targets of interest from confusers. In particular, we calculate persistent homology from time-delayed embeddings of dynamic statistics calculated from motion tracks extracted from a wide field-of-view video stream. In short, we use topological methods to extract features related to target motion dynamics that are useful for classification and disambiguation and show that small targets can be detected at range with high probability.

Keywords: topological data analysis, motion tracks, persistence images, time-delay embedding

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1056 Distributed Minimum Spanning Forest

Authors: Ahmad Shahzad, Frans Coenen

Abstract:

Minimum spanning forest (MSF) is widely studied in graph related problems due to its importance in various applications from collaborative filtering as used in recommender engines to coarsening of graphs for Multilevel graph partitioning. However, with advent to data becoming larger enough to be handled in a single machine it has increasingly becoming important to distribute the data over a cluster of machine. That requires re-engineering and implementation of classical algorithms to be used in distributed environment and gain efficiency in terms of lower run time costs. In this paper a distributed approach of MSF is been presented which is based on classical algorithm of Kruskal to calculate Minimum Spanning Trees (MST). The presented approach is cross compared with current state of the art distributed algorithms and it has shown to outperform existing algorithms.

Keywords: Distributed Algorithms, minimum spanning tree, Distributed Kruskal’s Algorithm, Minimum Spanning Forest

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1055 Matching on Bipartite Graphs with Applications to School Course Registration Systems

Authors: Zhihan Li

Abstract:

Nowadays, most universities use the course enrollment system considering students’ registration orders. However, the students’ preference level to certain courses is also one important factor to consider. In this research, the possibility of applying a preference-first system has been discussed and analyzed compared to the order-first system. A bipartite graph is applied to resemble the relationship between students and courses they tend to register. With the graph set up, we apply Ford-Fulkerson (F.F.) Algorithm to maximize parings between two sets of nodes, in our case, students and courses. Two models are proposed in this paper: the one considered students’ order first, and the one considered students’ preference first. By comparing and contrasting the two models, we highlight the usability of models which potentially leads to better designs for school course registration systems.

Keywords: Graph Theory, bipartite graph, Ford-Fulkerson (F.F.) algorithm, maximum matching

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1054 Identifying Network Subgraph-associated Essential Genes in Molecular Networks

Authors: Chien-Hung Huang, Ka-Lok Ng, Efendi Zaenudin

Abstract:

Essential genes play an important role in the survival of an organism. It has been shown that cancer-associated essential genes are genes necessary for cancer cell proliferation, where these genes are potential therapeutic targets. Also, it was demonstrated that mutations of the cancer-associated essential genes give rise to the resistance of immunotherapy for patients with tumors. We noted that most of the studies are focus on collecting information and predictions of the essential genes, there is no or relatively few works on studying the biological effects of the essential genes from a network perspective. We hypothesize that one can analyze a biological molecular network by decomposing it into both three-node and four-node digraphs (subgraphs). These network subgraphs encode the regulatory interaction information among the network’s genetic elements. In this study, the frequency of occurrence of the subgraph-associated essential genes in a molecular network was quantified by using the statistical parameter, odds ratio. Biological effects of subgraph-associated essential genes are discussed. In summary, the subgraph approach provides a systematic method for analyzing molecular networks and it can capture useful biological information for biomedical research.

Keywords: Graph Theory, essential genes, biological molecular networks, network subgraphs

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1053 Pure and Mixed Nash Equilibria Domain of a Discrete Game Model with Dichotomous Strategy Space

Authors: A. S. Mousa, F. Shoman

Abstract:

We present a discrete game theoretical model with homogeneous individuals who make simultaneous decisions. In this model the strategy space of all individuals is a discrete and dichotomous set which consists of two strategies. We fully characterize the coherent, split and mixed strategies that form Nash equilibria and we determine the corresponding Nash domains for all individuals. We find all strategic thresholds in which individuals can change their mind if small perturbations in the parameters of the model occurs.

Keywords: Game theory, Nash Equilibrium, coherent strategy, split strategy, pure strategy, mixed strategy

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1052 Jacobson Semisimple Skew Inverse Laurent Series Rings

Authors: Ahmad Moussavi

Abstract:

In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided.

Keywords: skew polynomial rings, Laurent series, skew inverse Laurent series rings

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1051 Learning from Dendrites: Improving the Point Neuron Model

Authors: Alexander Vandesompele, Joni Dambre

Abstract:

The diversity in dendritic arborization, as first illustrated by Santiago Ramon y Cajal, has always suggested a role for dendrites in the functionality of neurons. In the past decades, thanks to new recording techniques and optical stimulation methods, it has become clear that dendrites are not merely passive electrical components. They are observed to integrate inputs in a non-linear fashion and actively participate in computations. Regardless, in simulations of neural networks dendritic structure and functionality are often overlooked. Especially in a machine learning context, when designing artificial neural networks, point neuron models such as the leaky-integrate-and-fire (LIF) model are dominant. These models mimic the integration of inputs at the neuron soma, and ignore the existence of dendrites. In this work, the LIF point neuron model is extended with a simple form of dendritic computation. This gives the LIF neuron increased capacity to discriminate spatiotemporal input sequences, a dendritic functionality as observed in another study. Simulations of the spiking neurons are performed using the Bindsnet framework. In the common LIF model, incoming synapses are independent. Here, we introduce a dependency between incoming synapses such that the post-synaptic impact of a spike is not only determined by the weight of the synapse, but also by the activity of other synapses. This is a form of short term plasticity where synapses are potentiated or depressed by the preceding activity of neighbouring synapses. This is a straightforward way to prevent inputs from simply summing linearly at the soma. To implement this, each pair of synapses on a neuron is assigned a variable,representing the synaptic relation. This variable determines the magnitude ofthe short term plasticity. These variables can be chosen randomly or, more interestingly, can be learned using a form of Hebbian learning. We use Spike-Time-Dependent-Plasticity (STDP), commonly used to learn synaptic strength magnitudes. If all neurons in a layer receive the same input, they tend to learn the same through STDP. Adding inhibitory connections between the neurons creates a winner-take-all (WTA) network. This causes the different neurons to learn different input sequences. To illustrate the impact of the proposed dendritic mechanism, even without learning, we attach five input neurons to two output neurons. One output neuron isa regular LIF neuron, the other output neuron is a LIF neuron with dendritic relationships. Then, the five input neurons are allowed to fire in a particular order. The membrane potentials are reset and subsequently the five input neurons are fired in the reversed order. As the regular LIF neuron linearly integrates its inputs at the soma, the membrane potential response to both sequences is similar in magnitude. In the other output neuron, due to the dendritic mechanism, the membrane potential response is different for both sequences. Hence, the dendritic mechanism improves the neuron’s capacity for discriminating spa-tiotemporal sequences. Dendritic computations improve LIF neurons even if the relationships between synapses are established randomly. Ideally however, a learning rule is used to improve the dendritic relationships based on input data. It is possible to learn synaptic strength with STDP, to make a neuron more sensitive to its input. Similarly, it is possible to learn dendritic relationships with STDP, to make the neuron more sensitive to spatiotemporal input sequences. Feeding structured data to a WTA network with dendritic computation leads to a significantly higher number of discriminated input patterns. Without the dendritic computation, output neurons are less specific and may, for instance, be activated by a sequence in reverse order.

Keywords: Spiking Neural Networks, dendritic computation, point neuron model

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1050 Chinese Remainder Theorem and Decidability

Authors: Zahra Sheikhaleslami

Abstract:

The Chinese remainder theorem deals with systems of modular equations. It has many applications. The Chinese remainder theorem requires that modules be pairwise coprime. In this paper, we discuss the general Chinese remainder theorem, which does not require this restriction on modules. We also show interesting applications of the general Chinese remainder theorem in proving decidability.

Keywords: Chinese Remainder Theorem, Decidability, general Chinese remainder theorem, quantifier-elimination

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1049 Hermite-Hadamard Type Integral Inequalities Involving k-Riemann-Liouville Fractional Integrals and Their Applications

Authors: A. Kashuri, R. Liko

Abstract:

In this paper, some generalization integral inequalities of Hermite-Hadamard type for functions whose derivatives are s-convex in modulus are given by using k-fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be view as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators, and interested readers can find new interesting results using our idea and technique as well.

Keywords: Hermite-Hadamard's inequalities, Hölder's inequality, k-Riemann-Liouville fractional integral, special means

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1048 Dual-Actuated Vibration Isolation Technology for Precise Motion Control of a Rotary System Mounted on an Oscillation-Transmitting Structure

Authors: Kamand Bagherian, Nariman Niknejad

Abstract:

A vibration isolation technology for precise position control of a rotary system powered by two permanent magnet DC (PMDC) motors, mounted on an oscillatory structure, is proposed. To achieve vibration isolation in these systems, active damping and disturbance rejection (ADDR) technology is presented, which introduces a cooperation of a main and an auxiliary actuator, controlled by discrete-time sliding mode control (DTSMC) based schemes. The controller of the main actuator tracks a desired position, and the auxiliary actuator simultaneously isolates the induced vibration, as its controller follows a torque trend. To determine this torque trend, a combination of two algorithms is introduced by ADDR technology. The first torque-trend producing algorithm rejects the disturbance by counteracting an estimation of the perturbation, derived from a model-based observer. The second applies active variable damping to minimize the oscillation of the output shaft. In this practice, the presented technology is implemented on a rotary system with a pendulum attached, mounted on a linear actuator simulating an oscillation-transmitting structure. In addition, the obtained results illustrate the functionality of the proposed technology.

Keywords: Vibration Isolation, Stability Robustness, Position Control, Active Damping, discrete-time nonlinear controller, disturbance tracking algorithm, oscillation transmitting support

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1047 On Lie-Central Derivations and Almost Inner Lie-Derivations of Leibniz Algebras

Authors: Natalia Pacheco Rego

Abstract:

The Liezation functor is a map from the category of Leibniz algebras to the category of Lie algebras, which assigns a Leibniz algebra to the Lie algebra given by the quotient of the Leibniz algebra by the ideal spanned by the square elements of the Leibniz algebra. This functor is left adjoint to the inclusion functor that considers a Lie algebra as a Leibniz algebra. This environment fits in the framework of central extensions and commutators in semi-abelian categories with respect to a Birkhoff subcategory, where classical or absolute notions are relative to the abelianization functor. Classical properties of Leibniz algebras (properties relative to the abelianization functor) were adapted to the relative setting (with respect to the Liezation functor); in general, absolute properties have the corresponding relative ones, but not all absolute properties immediately hold in the relative case, so new requirements are needed. Following this line of research, it was conducted an analysis of central derivations of Leibniz algebras relative to the Liezation functor, called as Lie-derivations, and a characterization of Lie-stem Leibniz algebras by their Lie-central derivations was obtained. In this paper, we present an overview of these results, and we analyze some new properties concerning Lie-central derivations and almost inner Lie-derivations. Namely, a Leibniz algebra is a vector space equipped with a bilinear bracket operation satisfying the Leibniz identity. We define the Lie-bracket by [x, y]lie = [x, y] + [y, x] , for all x, y . The Lie-center of a Leibniz algebra is the two-sided ideal of elements that annihilate all the elements in the Leibniz algebra through the Lie-bracket. A Lie-derivation is a linear map which acts as a derivative with respect to the Lie-bracket. Obviously, usual derivations are Lie-derivations, but the converse is not true in general. A Lie-derivation is called a Lie-central derivation if its image is contained in the Lie-center. A Lie-derivation is called an almost inner Lie-derivation if the image of an element x is contained in the Lie-commutator of x and the Leibniz algebra. The main results we present in this talk refer to the conditions under which Lie-central derivation and almost inner Lie-derivations coincide.

Keywords: almost inner Lie-derivation, Lie-center, Lie-central derivation, Lie-derivation

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1046 Market Solvency Capital Requirement Minimization: How Non-linear Solvers Provide Portfolios Complying with Solvency II Regulation

Authors: Abraham Castellanos, Christophe Durville, Sophie Echenim

Abstract:

In this article, a portfolio optimization problem is performed in a Solvency II context: it illustrates how advanced optimization techniques can help to tackle complex operational pain points around the monitoring, control, and stability of Solvency Capital Requirement (SCR). The market SCR of a portfolio is calculated as a combination of SCR sub-modules. These sub-modules are the results of stress-tests on interest rate, equity, property, credit and FX factors, as well as concentration on counter-parties. The market SCR is non convex and non differentiable, which does not make it a natural optimization criteria candidate. In the SCR formulation, correlations between sub-modules are fixed, whereas risk-driven portfolio allocation is usually driven by the dynamics of the actual correlations. Implementing a portfolio construction approach that is efficient on both a regulatory and economic standpoint is not straightforward. Moreover, the challenge for insurance portfolio managers is not only to achieve a minimal SCR to reduce non-invested capital but also to ensure stability of the SCR. Some optimizations have already been performed in the literature, simplifying the standard formula into a quadratic function. But to our knowledge, it is the first time that the standard formula of the market SCR is used in an optimization problem. Two solvers are combined: a bundle algorithm for convex non- differentiable problems, and a BFGS (Broyden-Fletcher-Goldfarb- Shanno)-SQP (Sequential Quadratic Programming) algorithm, to cope with non-convex cases. A market SCR minimization is then performed with historical data. This approach results in significant reduction of the capital requirement, compared to a classical Markowitz approach based on the historical volatility. A comparative analysis of different optimization models (equi-risk-contribution portfolio, minimizing volatility portfolio and minimizing value-at-risk portfolio) is performed and the impact of these strategies on risk measures including market SCR and its sub-modules is evaluated. A lack of diversification of market SCR is observed, specially for equities. This was expected since the market SCR strongly penalizes this type of financial instrument. It was shown that this direct effect of the regulation can be attenuated by implementing constraints in the optimization process or minimizing the market SCR together with the historical volatility, proving the interest of having a portfolio construction approach that can incorporate such features. The present results are further explained by the Market SCR modelling.

Keywords: Portfolio Management, Numerical Optimization, financial risk, solvency capital requirement

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1045 Continuous-Time and Discrete-Time Singular Value Decomposition of an Impulse Response Function

Authors: Yucheng Liu, Rogelio Luck

Abstract:

This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Keywords: Green’s Function, singular value decomposition, impulse response function, Hankel Matrix, Toeplitz matrix

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1044 Collective Strategies Dominate in Spatial Iterated Prisoners Dilemma

Authors: Jiawei Li

Abstract:

How cooperation emerges and persists in a population of selfish agents is a fundamental question in evolutionary game theory. Our research shows that Collective Strategies with Master-Slave Mechanism (CSMSM) defeat Tit-for-Tat and other well-known strategies in spatial iterated prisoner’s dilemma. A CSMSM identifies kin members by means of a handshaking mechanism. If the opponent is identified as non-kin, a CSMSM will always defect. Once two CSMSMs meet, they play master and slave roles. A mater defects and a slave cooperates in order to maximize the master’s payoff. CSMSM outperforms non-collective strategies in spatial IPD even if there is only a small cluster of CSMSMs in the population. The existence and performance of CSMSM in spatial iterated prisoner’s dilemma suggests that cooperation first appears and persists in a group of collective agents.

Keywords: Evolutionary game theory, spatial prisoners dilemma, collective strategy, master-slave mechanism

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1043 Pricing European Options under Jump Diffusion Models with Fast L-stable Padé Scheme

Authors: Salah Alrabeei, Mohammad Yousuf

Abstract:

The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: integral differential equations, jump–diffusion model, L-stable methods, pricing European options

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1042 Model of Optimal Centroids Approach for Multivariate Data Classification

Authors: Pham Van Nha, Cam Le Binh

Abstract:

Particle Swarm Optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO's ideas are simple and easy to understand, but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply it in the multivariate data classification. First, PSOs, the general mathematical model (MPSO), is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: Global optimization, analysis of optimization, artificial intelligence based optimization, optimization for learning and data analysis

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1041 Identification of Clinical Characteristics from Persistent Homology Applied to Tumor Imaging

Authors: Eashwar V. Somasundaram, Raoul R. Wadhwa, Jacob G. Scott

Abstract:

The use of radiomics in measuring geometric properties of tumor images such as size, surface area, and volume has been invaluable in assessing cancer diagnosis, treatment, and prognosis. In addition to analyzing geometric properties, radiomics would benefit from measuring topological properties using persistent homology. Intuitively, features uncovered by persistent homology may correlate to tumor structural features. One example is necrotic cavities (corresponding to 2D topological features), which are markers of very aggressive tumors. We develop a data pipeline in R that clusters tumors images based on persistent homology is used to identify meaningful clinical distinctions between tumors and possibly new relationships not captured by established clinical categorizations. A preliminary analysis was performed on 16 Magnetic Resonance Imaging (MRI) breast tissue segments downloaded from the 'Investigation of Serial Studies to Predict Your Therapeutic Response with Imaging and Molecular Analysis' (I-SPY TRIAL or ISPY1) collection in The Cancer Imaging Archive. Each segment represents a patient’s breast tumor prior to treatment. The ISPY1 dataset also provided the estrogen receptor (ER), progesterone receptor (PR), and human epidermal growth factor receptor 2 (HER2) status data. A persistent homology matrix up to 2-dimensional features was calculated for each of the MRI segmentation. Wasserstein distances were then calculated between all pairwise tumor image persistent homology matrices to create a distance matrix for each feature dimension. Since Wasserstein distances were calculated for 0, 1, and 2-dimensional features, three hierarchal clusters were constructed. The adjusted Rand Index was used to see how well the clusters corresponded to the ER/PR/HER2 status of the tumors. Triple-negative cancers (negative status for all three receptors) significantly clustered together in the 2-dimensional features dendrogram (Adjusted Rand Index of .35, p = .031). It is known that having a triple-negative breast tumor is associated with aggressive tumor growth and poor prognosis when compared to non-triple negative breast tumors. The aggressive tumor growth associated with triple-negative tumors may have a unique structure in an MRI segmentation, which persistent homology is able to identify. This preliminary analysis shows promising results in the use of persistent homology on tumor imaging to assess the severity of breast tumors. The next step is to apply this pipeline to other tumor segment images from The Cancer Imaging Archive at different sites such as the lung, kidney, and brain. In addition, whether other clinical parameters, such as overall survival, tumor stage, and tumor genotype data are captured well in persistent homology clusters will be assessed. If analyzing tumor MRI segments using persistent homology consistently identifies clinical relationships, this could enable clinicians to use persistent homology data as a noninvasive way to inform clinical decision making in oncology.

Keywords: Oncology, Cancer Biology, Persistent Homology, radiomics, topological data analysis, tumor imaging

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