Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1046

World Academy of Science, Engineering and Technology

[Mathematical and Computational Sciences]

Online ISSN : 1307-6892

1046 Pure and Mixed Nash Equilibria Domain of a Discrete Game Model with Dichotomous Strategy Space

Authors: A. S. Mousa, F. Shoman

Abstract:

We introduce 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 occur.

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

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1045 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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1044 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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1043 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:

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1042 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 the 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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1041 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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1040 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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1039 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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1038 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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1037 An Optimized Approach to Generate the Possible States of Football Tournaments Final Table

Authors: Mouslem Damkhi

Abstract:

This paper focuses on possible states of a football tournament final table according to the number of participating teams. Each team holds a position in the table with which it is possible to determine the highest and lowest points for that team. This paper proposes an optimized search space based on the minimum and maximum number of points which can be gained by each team to produce and enumerate the possible states for a football tournament final table. The proposed search space minimizes producing the invalid states which cannot occur during a football tournament. The generated states are filtered by a validity checking algorithm which seeks to reach a tournament graph based on a generated state. Thus, the algorithm provides a way to determine which team’s wins, draws and loses values guarantee a particular table position. The paper also presents and discusses the experimental results of the approach on the tournaments with up to eight teams. Comparing with a blind search algorithm, our proposed approach reduces generating the invalid states up to 99.99%, which results in a considerable optimization in term of the execution time.

Keywords: Combinatorics, Enumeration, graph, tournament

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1036 A Methodology for Characterising the Tail Behaviour of a Distribution

Authors: Serge Provost, Yishan Zang

Abstract:

Following a review of various approaches that are utilized for classifying the tail behavior of a distribution, an easily implementable methodology that relies on an arctangent transformation is presented. The classification criterion is actually based on the difference between two specific quantiles of the transformed distribution. The resulting categories enable one to classify distributional tails as distinctly short, short, nearly medium, medium, extended medium and somewhat long, providing that at least two moments exist. Distributions possessing a single moment are said to be long tailed while those failing to have any finite moments are classified as having an extremely long tail. Several illustrative examples will be presented.

Keywords: distributional moments, heavy-tailed distributions, arctangent transformation, tail classification

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1035 Time Series Analysis on the Production of Fruit Juice: A Case Study of National Horticultural Research Institute (Nihort) Ibadan, Oyo State

Authors: Abiodun Ayodele Sanyaolu

Abstract:

The research was carried out to investigate the time series analysis on quarterly production of fruit juice at the National Horticultural Research Institute Ibadan from 2010 to 2018. Documentary method of data collection was used, and the method of least square and moving average were used in the analysis. From the calculation and the graph, it was glaring that there was increase, decrease, and uniform movements in both the graph of the original data and the tabulated quarter values of the original data. Time series analysis was used to detect the trend in the highest number of fruit juice and it appears to be good over a period of time and the methods used to forecast are additive and multiplicative models. Since it was observed that the production of fruit juice is usually high in January of every year, it is strongly advised that National Horticultural Research Institute should make more provision for fruit juice storage outside this period of the year.

Keywords: Time series, least square, fruit juice, multiplicative models

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1034 A New Approach for Solving Fractional Coupled Pdes

Authors: Prashant Pandey

Abstract:

In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: Diffusion Equation, spectral method, Laguerre polynomials, fractional coupled PDE, stability and convergence analysis

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1033 Operational Matrix Method for Fuzzy Fractional Reaction Diffusion Equation

Authors: SACHIN KUMAR

Abstract:

Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: Diffusion Equation, spectral method, legendre polynomial, fractional PDE, fuzzy valued function

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1032 Robust Numerical Scheme for Pricing American Options under Jump Diffusion Models

Authors: Salah Alrabeei, Mohammad Yousuf

Abstract:

We evaluate the American option price with jump diffusion models by using efficient time-dependent numerical methods. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M²) into O(M logM). Partial fraction forms of rational approximation schemes are used to overcome the complexity of inverting polynomial of matrices. Fourth-order and second-order convergence are numerically proved.

Keywords: integral differential equations, jump–diffusion model, American options, rational approximation

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1031 Inverse Scattering for a Second-Order Discrete System via Transmission Eigenvalues

Authors: Abdon Choque-Rivero

Abstract:

The Jacobi system with the Dirichlet boundary condition is considered on a half-line lattice when the coefficients are real valued. The inverse problem of recovery of the coefficients from various data sets containing the so-called transmission eigenvalues is analyzed. The Marchenko method is utilized to solve the corresponding inverse problem.

Keywords: discrete system, Inverse Scattering, transmission eigenvalues, Marchenko method

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1030 The Structure of Invariant Manifolds after a Supercritical Hamiltonian Hopf Bifurcation

Authors: Matthaios Katsanikas

Abstract:

We study the structure of the invariant manifolds of complex unstable periodic orbits of a family of periodic orbits, in a 3D autonomous Hamiltonian system of galactic type, after a transition of this family from stability to complex instability (Hamiltonian Hopf bifurcation). We consider the case of a supercritical Hamiltonian Hopf bifurcation. The invariant manifolds of complex unstable periodic orbits have two kinds of structures. The first kind is represented by a disk confined structure on the 4D space of section. The second kind is represented by a complicated central tube structure that is associated with an extended network of tube structures, strips and flat structures of sheet type on the 4D space of section.

Keywords: Chaos, Dynamical systems, Galactic Dynamics, phase space

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1029 A Coupled System of Caputo-Type Katugampola Fractional Differential Equations with Integral Boundary Conditions

Authors: Yacine Arioua

Abstract:

In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: Fractional Differential Equations, Uniqueness, existence, coupled system, Caputo-Katugampola derivative, fixed point theorems

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1028 Algebraic Characterization of Sheaves over Boolean Spaces

Authors: U. M. Swamy

Abstract:

A compact Hausdorff and totally disconnected topological space are known as Boolean space in view of the stone duality between Boolean algebras and such topological spaces. A sheaf over X is a triple (S, p, X) where S and X are topological spaces and p is a local homeomorphism of S onto X (that is, for each element s in S, there exist open sets U and G containing s and p(s) in S and X respectively such that the restriction of p to U is a homeomorphism of U onto G). Here we mainly concern on sheaves over Boolean spaces. From a given sheaf over a Boolean space, we obtain an algebraic structure in such a way that there is a one-to-one correspondence between these algebraic structures and sheaves over Boolean spaces.

Keywords: Boolean algebra, Boolean space, sheaf, stone duality

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1027 Impact Evaluation of Vaccination against Eight-Child-Killer Diseases on under-Five Children Mortality at Mbale District, Uganda

Authors: Lukman Abiodun Nafiu

Abstract:

This study examines the impact evaluation of vaccination against eight-child-killer diseases on under-five children mortality at Mbale District. It was driven by three specific objectives which are to determine the proportion of under-five children mortality due to the eight-child-killer diseases to the total under-five children mortality; establish the cause-effect relationship between the eight-child-killer diseases and under-five children mortality; as well as establish the dependence of under-five children mortality in the location at Mbale District. A community based cross-sectional and longitudinal (panel) study design involving both quantitative and qualitative (focus group discussion and in-depth interview) approaches was employed over a period of 36 months. Multi-stage cluster design involving Health Sub-District (HSD), Forms of Ownership (FOO) and Health Facilities Centres (HFC) as the first, second and third stages respectively was used. Data was collected regarding the eight-child-killer diseases namely: measles, pneumonia, pertussis (whooping cough), diphtheria, poliomyelitis (polio), tetanus, haemophilus influenza, rotavirus gastroenteritis and mortality regarding immunized and non-immunized children aged 0-59 months. We monitored the children over a period of 24 months. The study used a sample of 384 children out of all the registered children for each year at Mbale Referral Hospital and other Primary Health Care Centres (HCIV, HCIII and HCII) at Mbale District between 2015 and 2019. These children were followed from birth to their current state (living or dead). The data collected in this study was analysed using cross tabulation and the chi-square test. The study concluded that majority of mothers at Mbale district took their children for immunization and thus reducing the occurrence of under-five children mortality. Overall, 2.3%, 4.6%, 3.1%, 5.4%, 1.5%, 3.8%, 0.0% and 0.0% of under-five children had polio, tetanus, diphtheria, measles, pertussis, pneumonia, haemophilus influenzae and rotavirus gastroenteritis respectively across all the sub counties at Mbale district during the period considered. Also, different locations (sub counties) do not have significant influence on the occurrence of these eight-child-killer diseases among the under-five children at Mbale district. Therefore, the study recommended that government and agencies should continue to work together to implement measures of vaccination programs and increasing access to basic health care with a continuous improvement on the social interventions to progress child survival.

Keywords: Diseases, Children, Vaccination, Mortality

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1026 Inverse Source Problems for Wave Propagation

Authors: Mozhgan Nora Entekhabi

Abstract:

Source problems play an important and unique role in PDEs. More specifically, inverse source scattering problem arises in many areas of science. It has numerous applications to medical imaging and geophysics, acoustical and bio-medical industries, antenna synthesis, and material science. In particular, inverse source problem seeks the radiating source which produces the measured wave field. This research aims to provide a technique for recovering the source function of the Helmholtz equation and some classical system of PDEs from boundary data at multiple wave numbers when the source is compactly sup- ported in an arbitrary bounded C2− boundary domain, establish uniqueness for the source from the Cauchy data on any open non empty part of the boundary for arbitrary positive K, and increasing stability when wave number K is getting large for a 2 and 3 dimensional general domain. Various studies showed that the uniqueness can be regained by taking multifrequency boundary measurement in a non-empty frequency interval (0,K).

Keywords: Helmholtz equation, Inverse Scattering Theory, Elasticity System, Infinite Plate

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1025 A Note on Decidability of the Theory of Natural Numbers

Authors: Zahra Sheikhaleslami

Abstract:

The additive theory or (the multiplication theory) of a set of natural numbers is the first theory of the structure of that set with the addition or (multiplication) operation that set is taken be additive(multiplicative),i.e., closed under addition or (multiplication). In this paper, decidability (i.e.,there exists an algorithm that decides whether a given sentence is derivable from the theory )of the structures of natural numbers study in different languages and introduce ways that it allows quantifier elimination (for the theory ) and review some classical theorems and will give new proofs for old results.

Keywords: incompleteness, Decidability, Number Structure, First Order Logic

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1024 Spatial-Temporal Awareness Approach for Extensive Re-Identification

Authors: Tyng-Rong Roan, Fuji Foo, Wenwey Hseush

Abstract:

In today's security industry, data generated by CCTV, IoT sensors, edge devices, or social media are the key elements for many security-critical applications. Recent development of AI and edge computing plays a critical role to capture single-sourced sensory events (e.g., detecting an unattended suitcase from one single CCTV), which, nevertheless, tells partial and probably imprecise information, rather than the whole truth. Putting together multiple streams of events in one space for cross examination is the way to figure out what actually happened in the field. One of the most essential problems is re-identification (i.e., tracking persons) across a large number of CCTVs over a vast area. As an industrial practitioner, we have developed a human-like Long-Short-Term Memory (LSTM) framework to capture sensory events from the edge. It reconstructs the pictures of what happened and when/where in a vast, persistent memory space, similar to a mind map. LSTM contains five levels: (1) sensory event capture for perception, (2) sensory memory for attention, (3) working memory for awareness, (4) long-term memory system 1 (fast thinking) for prediction and (5) long-term memory system 2 (slow thinking) for reasoning. The core of LSTM is the working memory, which handles visions, sounds, and episodes, and understands the concepts of time and space. It functions as a mind map to show relationships among pieces of the whole in time and in space, supporting spatial-temporal awareness and manipulation. Extensive re-identification incurs difficulties in performing real-time and achieving high accuracy, even across a couple of CCTVs. Imagine, for example, the challenges to track and trace daily 300 thousand passengers by two thousand CCTVs at 99% accuracy. Two approaches, spatial-temporal-awareness approach and feature-based approach were established to address these issues. The spatial-temporal-awareness approach serves as the major method for re-identification, and another approach is minor one, based on commonly used features, such as colors, poses, and wearables for auxiliary information. This study employs temporal and spatial information and relations to determine whether any individual is the same person captured by multiple CCTVs according to the Exclusion Principle (i.e., the locations of two distinct persons cannot be overlapped) and projected movement (i.e., probability of persons showing up from the neighbor CCTVs). Once persons' identifications cannot be connected, feature-based algorithm is then activated for further determination. Part of this study is to conduct a proof-of-concept (POC) demonstration using the re-identification algorithms to solve the problem of unattended suitcase detection in a public place (around 20x30 square meters) with six CCTVs. Three questions are answered in the POC: (1) what happened and when/where, (2) who dropped the suitcase, and (3) where is the person now. The POC demonstrates that the solution with spatial-temporal awareness and commonly used feature detection achieves a high degree of accuracy in real time to support a security-critical application.

Keywords: long-short-term memory, re-identification, security critical application, spatial-temporal awareness

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1023 Finite Element and Split Bregman Methods for Solving a Family of Optimal Control Problem with Partial Differential Equation Constraint

Authors: Mahmoud Lot

Abstract:

In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Finite Element Method, Split Bregman Method, optimal control with elliptic partial differential equation constraint

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1022 Evaluation of a Piecewise Linear Mixed-Effects Model in the Analysis of Randomized Cross-over Trial

Authors: Moses Mwangi, Geert Verbeke, Geert Molenberghs

Abstract:

Cross-over designs are commonly used in randomized clinical trials to estimate efficacy of a new treatment with respect to a reference treatment (placebo or standard). The main advantage of using cross-over design over conventional parallel design is its flexibility, where every subject become its own control, thereby reducing confounding effect. Jones & Kenward, discuss in detail more recent developments in the analysis of cross-over trials. We revisit the simple piecewise linear mixed-effects model, proposed by Mwangi et. al, (in press) for its first application in the analysis of cross-over trials. We compared performance of the proposed piecewise linear mixed-effects model with two commonly cited statistical models namely, (1) Grizzle model; and (2) Jones & Kenward model, used in estimation of the treatment effect, in the analysis of randomized cross-over trial. We estimate two performance measurements (mean square error (MSE) and coverage probability) for the three methods, using data simulated from the proposed piecewise linear mixed-effects model. Piecewise linear mixed-effects model yielded lowest MSE estimates compared to Grizzle and Jones & Kenward models for both small (Nobs=20) and large (Nobs=600) sample sizes. It’s coverage probability were highest compared to Grizzle and Jones & Kenward models for both small and large sample sizes. A piecewise linear mixed-effects model is a better estimator of treatment effect than its two competing estimators (Grizzle and Jones & Kenward models) in the analysis of cross-over trials. The data generating mechanism used in this paper captures two time periods for a simple 2-Treatments x 2-Periods cross-over design. Its application is extendible to more complex cross-over designs with multiple treatments and periods. In addition, it is important to note that, even for single response models, adding more random effects increases the complexity of the model and thus may be difficult or impossible to fit in some cases.

Keywords: Simulation, Evaluation, performance measures, Grizzle model, Jones & Kenward model

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1021 Integrated Nested Laplace Approximations For Quantile Regression

Authors: Kajingulu Malandala, Ranganai Edmore

Abstract:

The asymmetric Laplace distribution (ADL) is commonly used as the likelihood function of the Bayesian quantile regression, and it offers different families of likelihood method for quantile regression. Notwithstanding their popularity and practicality, ADL is not smooth and thus making it difficult to maximize its likelihood. Furthermore, Bayesian inference is time consuming and the selection of likelihood may mislead the inference, as the Bayes theorem does not automatically establish the posterior inference. Furthermore, ADL does not account for greater skewness and Kurtosis. This paper develops a new aspect of quantile regression approach for count data based on inverse of the cumulative density function of the Poisson, binomial and Delaporte distributions using the integrated nested Laplace Approximations. Our result validates the benefit of using the integrated nested Laplace Approximations and support the approach for count data.

Keywords: Quantile regression, count data, Delaporte distribution, integrated nested Laplace approximation

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1020 Using Linear Logistic Regression to Evaluation the Patient and System Delay and Effective Factors in Mortality of Patients with Acute Myocardial Infarction

Authors: Firouz Amani, Adalat Hoseinian, Sajjad Hakimian

Abstract:

Background: The mortality due to Myocardial Infarction (MI) is often occur during the first hours after onset of symptom. So, for taking the necessary treatment and decreasing the mortality rate, timely visited of the hospital could be effective in this regard. The aim of this study was to investigate the impact of effective factors in mortality of MI patients by using Linear Logistic Regression. Materials and Methods: In this case-control study, all patients with Acute MI who referred to the Ardabil city hospital were studied. All of died patients were considered as the case group (n=27) and we select 27 matched patients without Acute MI as a control group. Data collected for all patients in two groups by a same checklist and then analyzed by SPSS version 24 software using statistical methods. We used the linear logistic regression model to determine the effective factors on mortality of MI patients. Results: The mean age of patients in case group was significantly higher than control group (75.1±11.7 vs. 63.1±11.6, p=0.001).The history of non-cardinal diseases in case group with 44.4% significantly higher than control group with 7.4% (p=0.002).The number of performed PCIs in case group with 40.7% significantly lower than control group with 74.1% (P=0.013). The time distance between hospital admission and performed PCI in case group with 110.9 min was significantly upper than control group with 56 min (P=0.001). The mean of delay time from Onset of symptom to hospital admission (patient delay) and the mean of delay time from hospital admissions to receive treatment (system delay) was similar between two groups. By using logistic regression model we revealed that history of non-cardinal diseases (OR=283) and the number of performed PCIs (OR=24.5) had significant impact on mortality of MI patients in compare to other factors. Conclusion: Results of this study showed that of all studied factors, the number of performed PCIs, history of non-cardinal illness and the interval between onset of symptoms and performed PCI have significant relation with morality of MI patients and other factors were not meaningful. So, doing more studies with a large sample and investigated other involved factors such as smoking, weather and etc. is recommended in future.

Keywords: Heart Failure, Mortality, arrhythmia, Acute MI

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1019 Rayleigh Wave Propagation in an Orthotropic Medium under the Influence of Exponentially Varying Inhomogeneities

Authors: Sumit Kumar Vishwakarma

Abstract:

The aim of the paper is to investigate the influence of inhomogeneity associated with the elastic constants and density of the orthotropic medium. The inhomogeneity is considered as exponential function of depth. The impact of gravity had been discussed. Using the concept of separation of variables, the system of a partial differential equation (equation of motion) has been converted into ordinary differential equation, which is coupled in nature. It further reduces to a biquadratic equation whose roots were found by using MATLAB. A suitable boundary condition is employed to derive the dispersion equation in a closed-form. Numerical simulations had been performed to show the influence of the inhomogeneity parameter. It was observed that as the numerical values of increases, the phase velocity of Rayleigh waves decreases at a particular wavenumber. Graphical illustrations were drawn to visualize the effect of the increasing and decreasing values of the inhomogeneity parameter. It can be concluded that it has a remarkable bearing on the phase velocity as well as damping velocity.

Keywords: inhomogeneity, Rayleigh waves, orthotropic medium, gravity field

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1018 Forecasting Amman Stock Market Data Using a Hybrid Method

Authors: Ahmad Awajan, Sadam Al Wadi

Abstract:

In this study, a hybrid method based on Empirical Mode Decomposition and Holt-Winter (EMD-HW) is used to forecast Amman stock market data. First, the data are decomposed by EMD method into Intrinsic Mode Functions (IMFs) and residual components. Then, all components are forecasted by HW technique. Finally, forecasting values are aggregated together to get the forecasting value of stock market data. Empirical results showed that the EMD- HW outperform individual forecasting models. The strength of this EMD-HW lies in its ability to forecast non-stationary and non- linear time series without a need to use any transformation method. Moreover, EMD-HW has a relatively high accuracy comparing with eight existing forecasting methods based on the five forecast error measures.

Keywords: Forecasting, Time series, empirical mode decomposition, Holt-Winter method

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1017 An Improved Approach to Solve Two-Level Hierarchical Time Minimization Transportation Problem

Authors: Kalpana Dahiya

Abstract:

This paper discusses a two-level hierarchical time minimization transportation problem, which is an important class of transportation problems arising in industries. This problem has been studied by various researchers, and a number of polynomial time iterative algorithms are available to find its solution. All the existing algorithms, though efficient, have some shortcomings. The current study proposes an alternate solution algorithm for the problem that is more efficient in terms of computational time than the existing algorithms. The results justifying the underlying theory of the proposed algorithm are given. Further, a detailed comparison of the computational behaviour of all the algorithms for randomly generated instances of this problem of different sizes validates the efficiency of the proposed algorithm.

Keywords: Global optimization, transportation problem, hierarchical optimization, concave minimization

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