Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 658

Search results for: generalized Boolean sum

658 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

Procedia PDF Downloads 75
657 Durrmeyer Type Modification of q-Generalized Bernstein Operators

Authors: Ruchi, A. M. Acu, Purshottam N. Agrawal

Abstract:

The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, Peetre’s K-functional, Lipschitz class, mixed modulus of smoothness

Procedia PDF Downloads 112
656 Bivariate Generalization of q-α-Bernstein Polynomials

Authors: Tarul Garg, P. N. Agrawal

Abstract:

We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

Procedia PDF Downloads 289
655 Cubical Representation of Prime and Essential Prime Implicants of Boolean Functions

Authors: Saurabh Rawat, Anushree Sah

Abstract:

K Maps are generally and ideally, thought to be simplest form for obtaining solution of Boolean equations. Cubical Representation of Boolean equations is an alternate pick to incur a solution, otherwise to be meted out with Truth Tables, Boolean Laws, and different traits of Karnaugh Maps. Largest possible k- cubes that exist for a given function are equivalent to its prime implicants. A technique of minimization of Logic functions is tried to be achieved through cubical methods. The main purpose is to make aware and utilise the advantages of cubical techniques in minimization of Logic functions. All this is done with an aim to achieve minimal cost solution.r

Keywords: K-maps, don’t care conditions, Boolean equations, cubes

Procedia PDF Downloads 313
654 Problems of Boolean Reasoning Based Biclustering Parallelization

Authors: Marcin Michalak

Abstract:

Biclustering is the way of two-dimensional data analysis. For several years it became possible to express such issue in terms of Boolean reasoning, for processing continuous, discrete and binary data. The mathematical backgrounds of such approach — proved ability of induction of exact and inclusion–maximal biclusters fulfilling assumed criteria — are strong advantages of the method. Unfortunately, the core of the method has quite high computational complexity. In the paper the basics of Boolean reasoning approach for biclustering are presented. In such context the problems of computation parallelization are risen.

Keywords: Boolean reasoning, biclustering, parallelization, prime implicant

Procedia PDF Downloads 51
653 Practical Methods for Automatic MC/DC Test Cases Generation of Boolean Expressions

Authors: Sekou Kangoye, Alexis Todoskoff, Mihaela Barreau

Abstract:

Modified Condition/Decision Coverage (MC/DC) is a structural coverage criterion that aims to prove that all conditions involved in a Boolean expression can influence the result of that expression. In the context of automotive, MC/DC is highly recommended and even required for most security and safety applications testing. However, due to complex Boolean expressions that often embedded in those applications, generating a set of MC/DC compliant test cases for any of these expressions is a nontrivial task and can be time consuming for testers. In this paper we present an approach to automatically generate MC/DC test cases for any Boolean expression. We introduce novel techniques, essentially based on binary trees to quickly and optimally generate MC/DC test cases for the expressions. Thus, the approach can be used to reduce the manual testing effort of testers.

Keywords: binary trees, MC/DC, test case generation, nontrivial task

Procedia PDF Downloads 316
652 On the Fractional Integration of Generalized Mittag-Leffler Type Functions

Authors: Christian Lavault

Abstract:

In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

Procedia PDF Downloads 325
651 Not Three Gods but One: Why Reductionism Does Not Serve Our Theological Discourse

Authors: Finley Lawson

Abstract:

The triune nature of God is one of the most complex doctrines of Christianity, and its complexity is further compounded when one considers the incarnation. However, many of the difficulties and paradoxes associated with our idea of the divine arise from our adherence to reductionist ontology. In order to move our theological discourse forward, in respect to divine and human nature, a holistic interpretation of our profession of faith is necessary. The challenge of a holistic interpretation is that it questions our ability to make any statement about the genuine, ontological individuation of persons (both divine and human), and in doing so raises the issue of whether we are, ontologically, bound to descend in to a form of pan(en)theism. In order to address the ‘inevitable’ slide in to pan(en)theism. The impact of two forms of holistic interpretation, Boolean and Non-Boolean, on our concept of personhood will be examined. Whilst a Boolean interpretation allows for a greater understanding of the relational nature of the Trinity, it is the Non-Boolean interpretation which has greater ontological significance. A Non-Boolean ontology, grounded in our scientific understanding of the nature of the world, shows our quest for individuation rests not in ontological fact but in epistemic need, and that it is our limited epistemology that drives our need to divide that which is ontologically indivisible. This discussion takes place within a ‘methodological’, rather than ‘doctrinal’ approach to science and religion - examining assumptions and methods that have shaped our language and beliefs about key doctrines, rather than seeking to reconcile particular Christian doctrines with particular scientific theories. Concluding that Non-Boolean holism is the more significant for our doctrine is, in itself, not enough. A world without division appears much removed from the distinct place of man and divine as espoused in our creedal affirmation, to this end, several possible interpretations for understanding Non-Boolean human – divine relations are tentatively put forward for consideration.

Keywords: holism, individuation, ontology, Trinitarian relations

Procedia PDF Downloads 172
650 Pushing the Boundary of Parallel Tractability for Ontology Materialization via Boolean Circuits

Authors: Zhangquan Zhou, Guilin Qi

Abstract:

Materialization is an important reasoning service for applications built on the Web Ontology Language (OWL). To make materialization efficient in practice, current research focuses on deciding tractability of an ontology language and designing parallel reasoning algorithms. However, some well-known large-scale ontologies, such as YAGO, have been shown to have good performance for parallel reasoning, but they are expressed in ontology languages that are not parallelly tractable, i.e., the reasoning is inherently sequential in the worst case. This motivates us to study the problem of parallel tractability of ontology materialization from a theoretical perspective. That is we aim to identify the ontologies for which materialization is parallelly tractable, i.e., in the NC complexity. Since the NC complexity is defined based on Boolean circuit that is widely used to investigate parallel computing problems, we first transform the problem of materialization to evaluation of Boolean circuits, and then study the problem of parallel tractability based on circuits. In this work, we focus on datalog rewritable ontology languages. We use Boolean circuits to identify two classes of datalog rewritable ontologies (called parallelly tractable classes) such that materialization over them is parallelly tractable. We further investigate the parallel tractability of materialization of a datalog rewritable OWL fragment DHL (Description Horn Logic). Based on the above results, we analyze real-world datasets and show that many ontologies expressed in DHL belong to the parallelly tractable classes.

Keywords: ontology materialization, parallel reasoning, datalog, Boolean circuit

Procedia PDF Downloads 191
649 Method of Synthesis of Controlled Generators Balanced a Strictly Avalanche Criteria-Functions

Authors: Ali Khwaldeh, Nimer Adwan

Abstract:

In this paper, a method for constructing a controlled balanced Boolean function satisfying the criterion of a Strictly Avalanche Criteria (SAC) effect is proposed. The proposed method is based on the use of three orthogonal nonlinear components which is unlike the high-order SAC functions. So, the generator synthesized by the proposed method has separate sets of control and information inputs. The proposed method proves its simplicity and the implementation ability. The proposed method allows synthesizing a SAC function generator with fixed control and information inputs. This ensures greater efficiency of the built-in oscillator compared to high-order SAC functions that can be used as a generator. Accordingly, the method is completely formalized and implemented as a software product.

Keywords: boolean function, controlled balanced boolean function, strictly avalanche criteria, orthogonal nonlinear

Procedia PDF Downloads 75
648 The Impact of Socialization Preferences on Perceptions of Generalized Social Trust in China

Authors: Menghzheng Yao

Abstract:

Generalized social trust among Chinese has been declining in the past few decades, making the search for its causes necessary. Drawing on the symbolic interaction theory and the 2012 Chinese General Social Survey data, this research investigated the impact of people’s socialization preferences and frequencies on their perceptions of generalized social trust in China. This research also took a preliminary step towards understanding the spatial differences of the generalized social trust using the ArcGIS software. The results show that respondents who interacted with their neighbors more frequently were more likely to have higher levels of perceptions of generalized social trust. Several demographics were also significantly related to perception of generalized social trust. Elderly and better educated Chinese and people with higher self-perceived social status were associated with greater levels of generalized social trust perception, while urban dwellers and religious respondents expressed lower levels of such perception. Implications for future research and policy are discussed.

Keywords: China, generalized social trust, symbolic interaction, ArcGIS

Procedia PDF Downloads 277
647 Nano Generalized Topology

Authors: M. Y. Bakeir

Abstract:

Rough set theory is a recent approach for reasoning about data. It has achieved a large amount of applications in various real-life fields. The main idea of rough sets corresponds to the lower and upper set approximations. These two approximations are exactly the interior and the closure of the set with respect to a certain topology on a collection U of imprecise data acquired from any real-life field. The base of the topology is formed by equivalence classes of an equivalence relation E defined on U using the available information about data. The theory of generalized topology was studied by Cs´asz´ar. It is well known that generalized topology in the sense of Cs´asz´ar is a generalization of the topology on a set. On the other hand, many important collections of sets related with the topology on a set form a generalized topology. The notion of Nano topology was introduced by Lellis Thivagar, which was defined in terms of approximations and boundary region of a subset of an universe using an equivalence relation on it. The purpose of this paper is to introduce a new generalized topology in terms of rough set called nano generalized topology

Keywords: rough sets, topological space, generalized topology, nano topology

Procedia PDF Downloads 336
646 Generalized Central Paths for Convex Programming

Authors: Li-Zhi Liao

Abstract:

The central path has played the key role in the interior point method. However, the convergence of the central path may not be true even in some convex programming problems with linear constraints. In this paper, the generalized central paths are introduced for convex programming. One advantage of the generalized central paths is that the paths will always converge to some optimal solutions of the convex programming problem for any initial interior point. Some additional theoretical properties for the generalized central paths will be also reported.

Keywords: central path, convex programming, generalized central path, interior point method

Procedia PDF Downloads 220
645 Upper Bound of the Generalized P-Value for the Difference between Two Future Population Means

Authors: Rada Somkhuean, Sa-aat Niwitpong, Suparat Niwitpong

Abstract:

This paper presents the generalized p-values for testing the difference between two future population means when the variances are unknown, in both cases for when the variances are equal and unequal. We also derive a closed form expression of the upper bound of the proposed generalized p-value.

Keywords: generalized p-value, two future population means, upper bound, variances

Procedia PDF Downloads 318
644 Generalized Chaplygin Gas and Varying Bulk Viscosity in Lyra Geometry

Authors: A. K. Sethi, R. N. Patra, B. Nayak

Abstract:

In this paper, we have considered Friedmann-Robertson-Walker (FRW) metric with generalized Chaplygin gas which has viscosity in the context of Lyra geometry. The viscosity is considered in two different ways (i.e. zero viscosity, non-constant r (rho)-dependent bulk viscosity) using constant deceleration parameter which concluded that, for a special case, the viscous generalized Chaplygin gas reduces to modified Chaplygin gas. The represented model indicates on the presence of Chaplygin gas in the Universe. Observational constraints are applied and discussed on the physical and geometrical nature of the Universe.

Keywords: bulk viscosity, lyra geometry, generalized chaplygin gas, cosmology

Procedia PDF Downloads 77
643 Weyl Type Theorem and the Fuglede Property

Authors: M. H. M. Rashid

Abstract:

Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.

Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge transform

Procedia PDF Downloads 60
642 Local Homology Modules

Authors: Fatemeh Mohammadi Aghjeh Mashhad

Abstract:

In this paper, we give several ways for computing generalized local homology modules by using Gorenstein flat resolutions. Also, we find some bounds for vanishing of generalized local homology modules.

Keywords: a-adic completion functor, generalized local homology modules, Gorenstein flat modules

Procedia PDF Downloads 319
641 On the Analysis of Strategies of Buechi Games

Authors: Ahmad Termimi Ab Ghani, Kojiro Higuchi

Abstract:

In this paper, we present some results of simultaneous infinite games. We mainly work with generalized reachability games and Buechi games. These games are two-player concurrent games where each player chooses simultaneously their moves at each step. Our goal is to give simple expressions of values for each game. Moreover, we are interested in the question of what type of optimal (ε-optimal) strategy exists for both players depending on the type of games. We first show the determinacy (optimal value) and optimal (ε-optimal) strategies in generalized reachability games. We provide a simple expressions of value of this game and prove the existence of memoryless randomized ε-optimal strategy for Player I in any generalized reachability games. We then observe games with more complex objectives, games with Buechi objectives. We present how to compute an ε-optimal strategies and approximate a value of game in some way. Specifically, the results of generalized reachability games are used to show the value of Buechi games can be approximated as values of some generalized reachability games.

Keywords: optimal Strategies, generalized reachability games, Buechi games

Procedia PDF Downloads 479
640 On Fourier Type Integral Transform for a Class of Generalized Quotients

Authors: A. S. Issa, S. K. Q. AL-Omari

Abstract:

In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Boehmian, Fourier integral, Fourier type integral, generalized quotient

Procedia PDF Downloads 235
639 Spectral Clustering from the Discrepancy View and Generalized Quasirandomness

Authors: Marianna Bolla

Abstract:

The aim of this paper is to compare spectral, discrepancy, and degree properties of expanding graph sequences. As we can prove equivalences and implications between them and the definition of the generalized (multiclass) quasirandomness of Lovasz–Sos (2008), they can be regarded as generalized quasirandom properties akin to the equivalent quasirandom properties of the seminal Chung-Graham-Wilson paper (1989) in the one-class scenario. Since these properties are valid for deterministic graph sequences, irrespective of stochastic models, the partial implications also justify for low-dimensional embedding of large-scale graphs and for discrepancy minimizing spectral clustering.

Keywords: generalized random graphs, multiway discrepancy, normalized modularity spectra, spectral clustering

Procedia PDF Downloads 113
638 Point Estimation for the Type II Generalized Logistic Distribution Based on Progressively Censored Data

Authors: Rana Rimawi, Ayman Baklizi

Abstract:

Skewed distributions are important models that are frequently used in applications. Generalized distributions form a class of skewed distributions and gain widespread use in applications because of their flexibility in data analysis. More specifically, the Generalized Logistic Distribution with its different types has received considerable attention recently. In this study, based on progressively type-II censored data, we will consider point estimation in type II Generalized Logistic Distribution (Type II GLD). We will develop several estimators for its unknown parameters, including maximum likelihood estimators (MLE), Bayes estimators and linear estimators (BLUE). The estimators will be compared using simulation based on the criteria of bias and Mean square error (MSE). An illustrative example of a real data set will be given.

Keywords: point estimation, type II generalized logistic distribution, progressive censoring, maximum likelihood estimation

Procedia PDF Downloads 99
637 An Extension of the Generalized Extreme Value Distribution

Authors: Serge Provost, Abdous Saboor

Abstract:

A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

Procedia PDF Downloads 254
636 Convergence of Generalized Jacobi, Gauss-Seidel and Successive Overrelaxation Methods for Various Classes of Matrices

Authors: Manideepa Saha, Jahnavi Chakrabarty

Abstract:

Generalized Jacobi (GJ) and Generalized Gauss-Seidel (GGS) methods are most effective than conventional Jacobi and Gauss-Seidel methods for solving linear system of equations. It is known that GJ and GGS methods converge for strictly diagonally dominant (SDD) and for M-matrices. In this paper, we study the convergence of GJ and GGS converge for symmetric positive definite (SPD) matrices, L-matrices and H-matrices. We introduce a generalization of successive overrelaxation (SOR) method for solving linear systems and discuss its convergence for the classes of SDD matrices, SPD matrices, M-matrices, L-matrices and for H-matrices. Advantages of generalized SOR method are established through numerical experiments over GJ, GGS, and SOR methods.

Keywords: convergence, Gauss-Seidel, iterative method, Jacobi, SOR

Procedia PDF Downloads 91
635 Characterization of Probability Distributions through Conditional Expectation of Pair of Generalized Order Statistics

Authors: Zubdahe Noor, Haseeb Athar

Abstract:

In this article, first a relation for conditional expectation is developed and then is used to characterize a general class of distributions F(x) = 1-e^(-ah(x)) through conditional expectation of difference of pair of generalized order statistics. Some results are reduced for particular cases. In the end, a list of distributions is presented in the form of table that are compatible with the given general class.

Keywords: generalized order statistics, order statistics, record values, conditional expectation, characterization

Procedia PDF Downloads 379
634 A Case of Generalized Anxiety Disorder (GAD)

Authors: Muhammad Zeeshan

Abstract:

This case study is about a 54 years man named Mr. U, referred to Capital Hospital, Islamabad, with the presenting complaints of Generalized Anxiety Disorder (GAD). Contrary to his complaints, the client reported psychological symptoms such as restlessness, low mood and fear of darkness and fear from closed places from the last 30 days. He also had a fear of death and his existence in the grave. His sleep was also disturbed due to excessive urination due to diabetes. He was also suffering from semantic symptoms such as headache, numbness of feet and pain in the chest and blockage of the nose. A complete history was taken and informal assessment (clinical interview and MSE) and formal testing (BAI) was applied that showed the clear diagnosis of Generalized Anxiety Disorder. CBT, relaxation techniques, prayer chart and behavioural techniques were applied for the treatment purposes.

Keywords: generalized anxiety disorder, presenting complaints, formal and informal assessment, diagnosis

Procedia PDF Downloads 59
633 The Intersection/Union Region Computation for Drosophila Brain Images Using Encoding Schemes Based on Multi-Core CPUs

Authors: Ming-Yang Guo, Cheng-Xian Wu, Wei-Xiang Chen, Chun-Yuan Lin, Yen-Jen Lin, Ann-Shyn Chiang

Abstract:

With more and more Drosophila Driver and Neuron images, it is an important work to find the similarity relationships among them as the functional inference. There is a general problem that how to find a Drosophila Driver image, which can cover a set of Drosophila Driver/Neuron images. In order to solve this problem, the intersection/union region for a set of images should be computed at first, then a comparison work is used to calculate the similarities between the region and other images. In this paper, three encoding schemes, namely Integer, Boolean, Decimal, are proposed to encode each image as a one-dimensional structure. Then, the intersection/union region from these images can be computed by using the compare operations, Boolean operators and lookup table method. Finally, the comparison work is done as the union region computation, and the similarity score can be calculated by the definition of Tanimoto coefficient. The above methods for the region computation are also implemented in the multi-core CPUs environment with the OpenMP. From the experimental results, in the encoding phase, the performance by the Boolean scheme is the best than that by others; in the region computation phase, the performance by Decimal is the best when the number of images is large. The speedup ratio can achieve 12 based on 16 CPUs. This work was supported by the Ministry of Science and Technology under the grant MOST 106-2221-E-182-070.

Keywords: Drosophila driver image, Drosophila neuron images, intersection/union computation, parallel processing, OpenMP

Procedia PDF Downloads 130
632 Generalized Dirac oscillators Associated to Non-Hermitian Quantum Mechanical Systems

Authors: Debjit Dutta, P. Roy, O. Panella

Abstract:

In recent years, non Hermitian interaction in non relativistic as well as relativistic quantum mechanics have been examined from various aspect. We can observe interesting fact that for such systems a class of potentials, namely the PT symmetric and η-pseudo Hermitian admit real eigenvalues despite being non Hermitian and analogues of those system have been experimentally verified. Point to be noted that relativistic non Hermitian (PT symmetric) interactions can be realized in optical structures and also there exists photonic realization of the (1 + 1) dimensional Dirac oscillator. We have thoroughly studied generalized Dirac oscillators with non Hermitian interactions in (1 + 1) dimensions. To be more specific, we have examined η pseudo Hermitian interactions within the framework of generalized Dirac oscillator in (1 + 1) dimensions. In particular, we have obtained a class of interactions which are η-pseudo Hermitian and the metric operator η could have been also found explicitly. It is possible to have exact solutions of the generalized Dirac oscillator for some choices of the interactions. Subsequently we have employed the mapping between the generalized Dirac oscillator and the Jaynes Cummings (JC) model by spin flip to obtain a class of exactly solvable non Hermitian JC as well as anti Jaynes Cummings (AJC) type models.

Keywords: Dirac oscillator, non-Hermitian quantum system, Hermitian, relativistic

Procedia PDF Downloads 351
631 Modeling of Maximum Rainfall Using Poisson-Generalized Pareto Distribution in Kigali, Rwanda

Authors: Emmanuel Iyamuremye

Abstract:

Extreme rainfall events have caused significant damage to agriculture, ecology, and infrastructure, disruption of human activities, injury, and loss of life. They also have significant social, economic, and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur, hence mitigating the consequences. Extreme value theory has been used widely in modeling extreme rainfall and in various disciplines, such as financial markets, the insurance industry, failure cases. Climatic extremes have been analyzed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions, which provides evidence of the importance of modeling extreme rainfall from different regions of the world. In this paper, we focused on Peak Over Thresholds approach, where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research also considers the use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Kigali. The results indicate that the proposed Poisson-GP distribution provides a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. The research also found a slow increase in return levels for maximum monthly rainfall for higher return periods, and further, the intervals are increasingly wider as the return period is increasing.

Keywords: exceedances, extreme value theory, generalized Pareto distribution, Poisson generalized Pareto distribution

Procedia PDF Downloads 53
630 VaR or TCE: Explaining the Preferences of Regulators

Authors: Silvia Faroni, Olivier Le Courtois, Krzysztof Ostaszewski

Abstract:

While a lot of research concentrates on the merits of VaR and TCE, which are the two most classic risk indicators used by financial institutions, little has been written on explaining why regulators favor the choice of VaR or TCE in their set of rules. In this paper, we investigate the preferences of regulators with the aim of understanding why, for instance, a VaR with a given confidence level is ultimately retained. Further, this paper provides equivalence rules that explain how a given choice of VaR can be equivalent to a given choice of TCE. Then, we introduce a new risk indicator that extends TCE by providing a more versatile weighting of the constituents of probability distribution tails. All of our results are illustrated using the generalized Pareto distribution.

Keywords: generalized pareto distribution, generalized tail conditional expectation, regulator preferences, risk measure

Procedia PDF Downloads 35
629 A Fast Version of the Generalized Multi-Directional Radon Transform

Authors: Ines Elouedi, Atef Hammouda

Abstract:

This paper presents a new fast version of the generalized Multi-Directional Radon Transform method. The new method uses the inverse Fast Fourier Transform to lead to a faster Generalized Radon projections. We prove in this paper that the fast algorithm leads to almost the same results of the eldest one but with a considerable lower time computation cost. The projection end result of the fast method is a parameterized Radon space where a high valued pixel allows the detection of a curve from the original image. The proposed fast inversion algorithm leads to an exact reconstruction of the initial image from the Radon space. We show examples of the impact of this algorithm on the pattern recognition domain.

Keywords: fast generalized multi-directional Radon transform, curve, exact reconstruction, pattern recognition

Procedia PDF Downloads 195