Search results for: weighted manifolds

Authors: M. Abdelmalek

Abstract:

In this work, we study the hypersurfaces of constant weighted mean curvature embedded in weighted manifolds. We give a condition about these hypersurfaces to be minimal. This condition is given by the ellipticity of the weighted Newton transformations. We especially prove that two compact hypersurfaces of constant weighted mean curvature embedded in space forms and with the intersection in at least a point of the boundary must be transverse. The method is based on the calculus of the matrix of the second fundamental form in a boundary point and then the matrix associated with the Newton transformations. By equality, we find the weighted elementary symmetric function on the boundary of the hypersurface. We give in the end some examples and applications. Especially in Euclidean space, we use the above result to prove the Alexandrov spherical caps conjecture for the weighted case.

Keywords: weighted mean curvature, weighted manifolds, ellipticity, Newton transformations

Procedia PDF Downloads 90

Authors: Zainab Al-Maamari, Yassir Dinar

Abstract:

The orbit space of an irreducible representation of a finite group is a variety with the ring of invariant polynomials as a coordinate ring. The invariant ring is a polynomial ring if and only if the representation is a reflection representation. Boris Dubrovin shows that the orbits spaces of irreducible real reflection representations acquire the structure of polynomial Frobenius manifolds. Dubrovin's method was also used to construct different examples of Frobenius manifolds on certain reflection representations. By successfully applying Dubrovin’s method on non-polynomial invariant rings of linear representations of dicyclic groups, it gives some results that magnify the relation between invariant theory and Frobenius manifolds.

Keywords: invariant ring, Frobenius manifold, inversion, representation theory

Procedia PDF Downloads 97

Authors: Seyedehsomayeh Hosseini

Abstract:

Much attention has been paid over centuries to understanding and solving the problem of minimization of functions. Compared to linear programming and nonlinear unconstrained optimization problems, nonlinear constrained optimization problems are much more difficult. Since the procedure of finding an optimizer is a search based on the local information of the constraints and the objective function, it is very important to develop techniques using geometric properties of the constraints and the objective function. In fact, differential geometry provides a powerful tool to characterize and analyze these geometric properties. Thus, there is clearly a link between the techniques of optimization on manifolds and standard constrained optimization approaches. Furthermore, there are manifolds that are not defined as constrained sets in R^n an important example is the Grassmann manifolds. Hence, to solve optimization problems on these spaces, intrinsic methods are used. In a nondifferentiable problem, the gradient information of the objective function generally cannot be used to determine the direction in which the function is decreasing. Therefore, techniques of nonsmooth analysis are needed to deal with such a problem. As a manifold, in general, does not have a linear structure, the usual techniques, which are often used in nonsmooth analysis on linear spaces, cannot be applied and new techniques need to be developed. This paper presents necessary and sufficient conditions for a strict local minimum of extended real-valued, nonsmooth functions defined on Riemannian manifolds.

Keywords: Riemannian manifolds, nonsmooth optimization, lower semicontinuous functions, subdifferential

Procedia PDF Downloads 359

Authors: Mancho Manev

Abstract:

The concept of almost paracontact Riemannian manifolds (abbr., apcR manifolds) was introduced by I. Sato in 1976 as an analogue of almost contact Riemannian manifolds. The notion of an apcR manifold of type (p,q) was defined by S. Sasaki in 1980, where p and q are respectively the numbers of the multiplicity of the structure eigenvalues 1 and -1. It also has a simple eigenvalue of 0. In our work, we consider (2n+1)-dimensional apcR manifolds of type (n,n), i.e., the paracontact distribution of the studied manifold can be considered as a 2n-dimensional almost paracomplex Riemannian distribution with almost paracomplex structure and structure group O(n) × O(n). The aim of the present study is to introduce a new class of apcR manifolds. Such a manifold is obtained using the construction of a certain Riemannian cone over it, and the resulting manifold is a paraholomorphic paracomplex Riemannian manifold (abbr., phpcR manifold). We call it a para-Sasaki-like Riemannian manifold (abbr., pSlR manifold) and give some explicit examples. We study the structure of pSlR spaces and find that the paracontact form η is closed and each pSlR manifold locally can be considered as a certain product of the real line with a phpcR manifold, which is locally a Riemannian product of two equidimensional Riemannian spaces. We also obtain that the curvature of the pSlR manifolds is completely determined by the curvature of the underlying local phpcR manifold. Moreover, the ξ-directed Ricci curvature is equal to -2n, while in the Sasaki case, it is 2n. Accordingly, the pSlR manifolds can be interpreted as the counterpart of the Sasaki manifolds; the skew-symmetric part of ∇η vanishes, while in the Sasaki case, the symmetric part vanishes. We define a hyperbolic extension of a (complete) phpcR manifold that resembles a certain warped product, and we indicate that it is a (complete) pSlR manifold. In addition, we consider the hyperbolic extension of a phpcR manifold and prove that if the initial manifold is a complete Einstein manifold with negative scalar curvature, then the resulting manifold is a complete Einstein pSlR manifold with negative scalar curvature. In this way, we produce new examples of a complete Einstein Riemannian manifold with negative scalar curvature. Finally, we define and study para contact conformal/homothetic deformations by deriving a subclass that preserves the para-Sasaki-like condition. We then find that if we apply a paracontact homothetic deformation of a pSlR space, we obtain that the Ricci tensor is invariant.

Keywords: almost paracontact Riemannian manifolds, Einstein manifolds, holomorphic product manifold, warped product manifold

Procedia PDF Downloads 205

Authors: Bhavini Pandya

Abstract:

This paper considers Hη: T2 → T2 the Perturbed Cerbelli-Giona map. That is a family of 2-dimensional nonlinear area-preserving transformations on the torus T2=[0,1]×[0,1]= ℝ2/ ℤ2. A single parameter η varies between 0 and 1, taking the transformation from a hyperbolic toral automorphism to the “Cerbelli-Giona” map, a system known to exhibit multifractal properties. Here we study the multifractal properties of the family of maps. We apply a box-counting method by defining a grid of boxes Bi(δ), where i is the index and δ is the size of the boxes, to quantify the distribution of stable and unstable manifolds of the map. When the parameter is in the range 0.51< η <0.58 and 0.68< η <1 the map is ergodic; i.e., the unstable and stable manifolds eventually cover the whole torus, although not in a uniform distribution. For accurate numerical results we require correspondingly accurate construction of the stable and unstable manifolds. Here we use the piecewise linearity of the map to achieve this, by computing the endpoints of line segments which define the global stable and unstable manifolds. This allows the generalized fractal dimension Dq, and spectrum of dimensions f(α), to be computed with accuracy. Finally, the intersection of the unstable and stable manifold of the map will be investigated, and compared with the distribution of periodic points of the system.

Keywords: feed forward, gradient descent, neural network, integral equation

Procedia PDF Downloads 187

Authors: Ibrahim Alsendid, Rob Sturman, Benjamin Sharp

Abstract:

In this paper, we consider a family of 2-dimensional nonlinear area-preserving transformations on the torus. A single parameter η varies between 0 and 1, taking the transformation from a hyperbolic toral automorphism to the “Cerbelli-Giona” map, a system known to exhibit multifractal properties. Here we study the multifractal properties of the family of maps. We apply a box-counting method by defining a grid of boxes Bi(δ), where i is the index and δ is the size of the boxes, to quantify the distribution of stable and unstable manifolds of the map. When the parameter is in the range 0.51< η <0.58 and 0.68< η <1 the map is ergodic; i.e., the unstable and stable manifolds eventually cover the whole torus, although not in a uniform distribution. For accurate numerical results, we require correspondingly accurate construction of the stable and unstable manifolds. Here we use the piecewise linearity of the map to achieve this, by computing the endpoints of line segments that define the global stable and unstable manifolds. This allows the generalized fractal dimension Dq, and spectrum of dimensions f(α), to be computed with accuracy. Finally, the intersection of the unstable and stable manifold of the map will be investigated and compared with the distribution of periodic points of the system.

Keywords: Discrete-time dynamical systems, Fractal geometry, Multifractal behaviour of the Perturbed map, Multifractal of Dynamical systems

Procedia PDF Downloads 210

Authors: Shams Alyusof

Abstract:

This work is to enrich the studies of the frames due to their prominent role in pure mathematics as well as in applied mathematics and many applications in computer science and engineering. Recently, there are remarkable studies of operators that preserve frames on some spaces, and this research could be considered as an extension of such studies. Indeed, this paper is to we characterize weighted composition operators that preserve frames in weighted Hardy spaces on the open unit disk. Moreover, it shows that this characterization does not apply to generalized weighted composition operators on such spaces. Nevertheless, this study could be extended to provide more specific characterizations.

Keywords: frames, generalized weighted composition operators, weighted Hardy spaces, analytic functions

Procedia PDF Downloads 120

Authors: Jay Prakash Singh

Abstract:

The aim of the present paper is to study properties of Quasi conformally flat LP-Sasakian manifolds with a coefficient α. In this paper, we prove that a Quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α is an η−Einstein and in a quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α if the scalar curvature tensor is constant then M is of constant curvature.

Keywords: LP-Sasakian manifolds, quasi-conformal curvature tensor, concircular vector field, torse forming vector field, Einstein manifold

Procedia PDF Downloads 790

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: dynamical systems, galactic dynamics, chaos, phase space

Procedia PDF Downloads 135

Authors: Lina Wu, Ye Li, Jia Liu

Abstract:

We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in L^q space to infinite in non-L^q space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

Keywords: differential forms, holder inequality, Liouville-type problems, p-balanced growth, p-harmonic maps, q-energy growth, tests for series

Procedia PDF Downloads 233

Authors: M. Zamurad Shah, M. Kemal Ozgoren, Raza Samar

Abstract:

This paper presents a 3D guidance scheme for Unmanned Aerial Vehicles (UAVs). The proposed guidance scheme is based on the sliding mode approach using nonlinear sliding manifolds. Generalized 3D kinematic equations are considered here during the design process to cater for the coupling between longitudinal and lateral motions. Sliding mode based guidance scheme is then derived for the multiple-input multiple-output (MIMO) system using the proposed nonlinear manifolds. Instead of traditional sliding surfaces, nonlinear sliding surfaces are proposed here for performance and stability in all flight conditions. In the reaching phase control inputs, the bang-bang terms with signum functions are accompanied with proportional terms in order to reduce the chattering amplitudes. The Proposed 3D guidance scheme is implemented on a 6-degrees-of-freedom (6-dof) simulation of a UAV and simulation results are presented here for different 3D trajectories with and without disturbances.

Keywords: unmanned aerial vehicles, sliding mode control, 3D guidance, nonlinear sliding manifolds

Procedia PDF Downloads 450

Authors: Sujith Rajashekar Swamy, Meghana Rajashekara Swamy

Abstract:

Although T1-weighted gadolinium-enhanced imaging (T1-Gd) has its established clinical role in diagnosing brain lesions of infectious and metastatic origins, the use of post-contrast susceptibility-weighted imaging (SWI) has been understudied. This observational study aims to explore and compare the prominence of brain parenchymal lesions between T1-Gd and SWI-Gd images. A cross-sectional study design was utilized to analyze 58 patients with brain parenchymal lesions using T1-Gd and SWI-Gd scanning techniques. Our results indicated that SWI-Gd enhanced the conspicuity of metastatic as well as infectious brain lesions when compared to T1-Gd. Consequently, it can be used as an adjunct to T1-Gd for post-contrast imaging, thereby avoiding additional contrast administration. Improved conspicuity of brain lesions translates directly to enhanced patient outcomes, and hence SWI-Gd imaging proves useful to meet that endpoint.

Keywords: susceptibility weighted, T1 weighted, brain lesions, gadolinium contrast

Procedia PDF Downloads 125

Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

Abstract:

Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: non-linear wilcoxon, robust estimation, variogram estimation, wilcoxon norm

Procedia PDF Downloads 457

Authors: Santu Dey, Arindam Bhattacharyya

Abstract:

The object of the present paper is to study a quarter-symmetric metric connection in a Lorentzian α-Sasakian manifold. We study some curvature properties of Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. We investigate quasi-projectively at, Φ-symmetric, Φ-projectively at Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection. We also discuss Lorentzian α-Sasakian manifold admitting quartersymmetric metric connection satisfying P.S = 0, where P denote the projective curvature tensor with respect to quarter-symmetric metric connection.

Keywords: quarter-symmetric metric connection, Lorentzian alpha-Sasakian manifold, quasi-projectively flat Lorentzian alpha-Sasakian manifold, phi-symmetric manifold

Procedia PDF Downloads 237

Authors: Rob Gesley Capistrano, Jasper James Isaac, Rose Mae Moralda, Therese Anne Peleo, Danica Rillo, Maria Virginia Santillian

Abstract:

One of the valuable things that shows the intelligence among individuals is the academic background specifically their Grade Weighted Average and the significant result of the Comprehensive Examination. The general objective of the researchers to this study is to determine if there is a significant difference between General Weighted Average and Comprehensive Examination Result of Psychometrician Board Passers and Non-Board Passers. The respondents of this study composed of board passers and non-board passers. The researchers used purposive sampling technique. The result utilized by using T-test Independent Sample to determine the comparison of General Weighted Average and Comprehensive Examination Result of Board Passers and Non Board Passers. At the end, it concluded that the General Weighted Average of Board Passers and Non-Board Passers shows that there is no significant difference, but the average showed a minimal variation. The Comprehensive Examination Result of Board Passers and Non-Board Passers result revealed that there is a significant difference. The performance of comprehensive examination that will test the overall knowledge of an individual and will determine whose more proficient will likely to have a higher score. The result of the comprehensive examination had an impact in the passing performance of board examination.

Keywords: board passers, comprehensive examination result, grade weighted average, non board passers

Procedia PDF Downloads 184

Authors: Salisu ibrahim, Abdalla Rababah

Abstract:

In this research, we use Weighted G2-Multi-degree reduction of Bezier curve of degree n to a Bezier curve of degree m, m < n. The degree reduction of Bezier curves is used to represent a given Bezier curve of n by a Bezier curve of degree m, m < n. Exact degree reduction is not possible, and degree reduction is approximate process in nature. We derive a weighted degree reducing method that is geometrically continuous at the end points. Different norms will be considered, several error minimizations will be given. The proposed methods produce error function that are less than the errors of existing methods.

Keywords: Bezier curves, multiple degree reduction, geometric continuity, error function

Procedia PDF Downloads 479

Authors: Riaz Ahmad, Jiazhong Zhang, Asma Farooqi

Abstract:

In this study, mass transport between separation bubbles and the flow around a two-dimensional airfoil are numerically investigated using Lagrangian Coherent Structures (LCSs). Finite Time Lyapunov Exponent (FTLE) technique is used for the computation to identify invariant manifolds and LCSs. Moreover, the Characteristic Base Split (CBS) scheme combined with dual time stepping technique is applied to simulate such transient flow at low Reynolds number. We then investigate the evolution of vortex structures during the transport process with the aid of LCSs. To explore the vortex formation at the surface of the airfoil, the dynamics of separatrix is also taken into account which is formed by the combination of stable-unstable manifolds. The Lagrangian analysis gives a detailed understanding of vortex dynamics and separation bubbles which plays a significant role to explore the performance of the unsteady flow generated by the airfoil. Transport process and flow separation phenomena are studied extensively to analyze the flow pattern by Lagrangian point of view.

Keywords: transport phenomena, CBS Method, vortex formation, Lagrangian Coherent Structures

Procedia PDF Downloads 137

Authors: Halil Ibrahim Demir, Abdullah Hulusi Kokcam, Fuat Simsir, Özer Uygun

Abstract:

Traditionally, three important manufacturing functions which are process planning, scheduling and due-date assignment are performed sequentially and separately. Although there are numerous works on the integration of process planning and scheduling and plenty of works focusing on scheduling with due date assignment, there are only a few works on integrated process planning, scheduling and due-date assignment. Although due-dates are determined without taking into account of weights of the customers in the literature, here weighted due-date assignment is employed to get better performance. Jobs are scheduled according to weighted earliest due date dispatching rule and due dates are determined according to some popular due date assignment methods by taking into account of the weights of each job. Simulated Annealing, Evolutionary Strategies, Random Search, hybrid of Random Search and Simulated Annealing, and hybrid of Random Search and Evolutionary Strategies, are applied as solution techniques. Three important manufacturing functions are integrated step-by-step and higher integration levels are found better. Search meta-heuristics are found to be very useful while improving performance measure.

Keywords: process planning, weighted scheduling, weighted due-date assignment, simulated annealing, evolutionary strategies, hybrid searches

Procedia PDF Downloads 461

Authors: Zhe Xu, Jian Li, Lvping Li, Zezheng Dong

Abstract:

This work is to study an optimized transfer strategy of connecting Earth and Mars via the vicinity of libration points, which have been playing an increasingly important role in trajectory designing on a deep space mission, and can be used as an effective alternative solution for Earth-Mars direct transfer mission in some unusual cases. The use of vicinity of libration points of the sun-planet body system is becoming potential gateways for future interplanetary transfer missions. By adding fuel to cargo spaceships located in spaceports, the interplanetary round-trip exploration shuttle mission of such a system facility can also be a reusable transportation system. In addition, in some cases, when the S/C cruising through invariant manifolds, it can also save a large amount of fuel. Therefore, it is necessary to make an effort on looking for efficient transfer strategies using variant manifold about libration points. It was found that Earth L1/L2 Halo/Lyapunov orbits and Mars L2/L1 Halo/Lyapunov orbits could be connected with reasonable fuel consumption and flight duration with appropriate design. In the paper, the halo hopping method and coplanar circular method are briefly introduced. The former used differential corrections to systematically generate low ΔV transfer trajectories between interplanetary manifolds, while the latter discussed escape and capture trajectories to and from Halo orbits by using impulsive maneuvers at periapsis of the manifolds about libration points. In the following, designs of transfer strategies of the two methods are shown here. A comparative performance analysis of interplanetary transfer strategies of the two methods is carried out accordingly. Comparison of strategies is based on two main criteria: the total fuel consumption required to perform the transfer and the time of flight, as mentioned above. The numeric results showed that the coplanar circular method procedure has certain advantages in cost or duration. Finally, optimized transfer strategy with engineering constraints is searched out and examined to be an effective alternative solution for a given direct transfer mission. This paper investigated main methods and gave out an optimized solution in interplanetary transfer via the vicinity of libration points. Although most of Earth-Mars mission planners prefer to build up a direct transfer strategy for the mission due to its advantage in relatively short time of flight, the strategies given in the paper could still be regard as effective alternative solutions since the advantages mentioned above and longer departure window than direct transfer.

Keywords: circular restricted three-body problem, halo/Lyapunov orbit, invariant manifolds, libration points

Procedia PDF Downloads 242

Authors: Halil Ibrahim Demir, Caner Erden, Abdullah Hulusi Kokcam, Mumtaz Ipek

Abstract:

Process planning, scheduling, and due date assignment are three important manufacturing functions which are studied independently in literature. There are hundreds of works on IPPS and SWDDA problems but a few works on IPPSDDA problem. Integrating these three functions is very crucial due to the high relationship between them. Since the scheduling problem is in the NP-Hard problem class without any integration, an integrated problem is even harder to solve. This study focuses on the integration of these functions. Sum of weighted tardiness, earliness, and due date related costs are used as a penalty function. Random search and hybrid metaheuristics are used to solve the integrated problem. Marginal improvement in random search is very high in the early iterations and reduces enormously in later iterations. At that point directed search contribute to marginal improvement more than random search. In this study, random and genetic search methods are combined to find better solutions. Results show that overall performance becomes better as the integration level increases.

Keywords: process planning, genetic algorithm, hybrid search, random search, weighted due-date assignment, weighted scheduling

Procedia PDF Downloads 360

Authors: Preeti Sharma

Abstract:

This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied.

Keywords: Lupas-Durrmeyer operators, polya distribution, weighted approximation, rate of convergence, modulus of continuity

Procedia PDF Downloads 343

Authors: Halil Ibrahim Demir, Tarık Cakar, Ibrahim Cil, Muharrem Dugenci, Caner Erden

Abstract:

Conventionally, process planning, scheduling, and due-date assignment functions are performed separately and sequentially. The interdependence of these functions requires integration. Although integrated process planning and scheduling, and scheduling with due date assignment problems are popular research topics, only a few works address the integration of these three functions. This work focuses on the integration of process planning, WMS scheduling, and WPPW due date assignment. Another novelty of this work is the use of a weighted due date assignment. In the literature, due dates are generally assigned without considering the importance of customers. However, in this study, more important customers get closer due dates. Typically, only tardiness is punished, but the JIT philosophy punishes both earliness and tardiness. In this study, all weighted earliness, tardiness, and due date related costs are penalized. As no customer desires distant due dates, such distant due dates should be penalized. In this study, various levels of integration of these three functions are tested and genetic search and random search are compared both with each other and with ordinary solutions. Higher integration levels are superior, while search is always useful. Genetic searches outperformed random searches.

Keywords: process planning, weighted scheduling, weighted due-date assignment, genetic algorithm, random search

Procedia PDF Downloads 392

Authors: Halil Ibrahim Demir, Caner Erden, Mumtaz Ipek, Ozer Uygun

Abstract:

Traditionally, the three important manufacturing functions, which are process planning, scheduling and due-date assignment, are performed separately and sequentially. For couple of decades, hundreds of studies are done on integrated process planning and scheduling problems and numerous researches are performed on scheduling with due date assignment problem, but unfortunately the integration of these three important functions are not adequately addressed. Here, the integration of these three important functions is studied by using genetic, random-genetic hybrid, simulated annealing, random-simulated annealing hybrid and random search techniques. As well, the importance of the integration of these three functions and the power of meta-heuristics and of hybrid heuristics are studied.

Keywords: process planning, weighted scheduling, weighted due-date assignment, genetic search, simulated annealing, hybrid meta-heuristics

Procedia PDF Downloads 468

Authors: Kang-Mo Jung

Abstract:

The use of regularization for statistical methods has become popular. The least absolute shrinkage and selection operator (LASSO) framework has become the standard tool for sparse regression. However, it is well known that the LASSO is sensitive to outliers or leverage points. We consider a new robust estimation which is composed of the weighted loss function of the pairwise difference of residuals and the adaptive penalty function regulating the tuning parameter for each variable. Rank regression is resistant to regression outliers, but not to leverage points. By adopting a weighted loss function, the proposed method is robust to leverage points of the predictor variable. Furthermore, the adaptive penalty function gives us good statistical properties in variable selection such as oracle property and consistency. We develop an efficient algorithm to compute the proposed estimator using basic functions in program R. We used an optimal tuning parameter based on the Bayesian information criterion (BIC). Numerical simulation shows that the proposed estimator is effective for analyzing real data set and contaminated data.

Keywords: adaptive penalty function, robust penalized regression, variable selection, weighted rank regression

Procedia PDF Downloads 470

Authors: Fatma Abdedayem

Abstract:

The most effective and efficient methods in image categorization are almost based on bag-of-words (BOW) which presents image by a histogram of occurrence of visual words. In this paper, we propose a novel extension to this method. Firstly, we extract features in multi-scales by applying a color local descriptor named opponent-SIFT. Secondly, in order to represent image we use Spatial Pyramid Representation (SPR) and an extension to the BOW method which based on weighting visual words. Typically, the visual words are weighted during histogram assignment by computing the ratio of their occurrences in the image to the occurrences in the background. Finally, according to classical BOW retrieval framework, only a few words of the vocabulary is useful for image representation. Therefore, we select the useful weighted visual words that respect the threshold value. Experimentally, the algorithm is tested by using different image classes of PASCAL VOC 2007 and is compared against the classical bag-of-visual-words algorithm.

Keywords: BOW, useful visual words, weighted visual words, bag of visual words

Procedia PDF Downloads 434

Authors: Morteza Faghfouri

Abstract:

In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold.

Keywords: integral submanifolds, S-space forms, doubly warped product, inequality

Procedia PDF Downloads 286

Authors: Seema Vaidya

Abstract:

Mining association rule is a key issue in data mining. In any case, the standard models ignore the distinction among the exchanges, and the weighted association rule mining does not transform on databases with just binary attributes. This paper proposes a novel continuous example and executes a tree (FP-tree) structure, which is an increased prefix-tree structure for securing compacted, discriminating data about examples, and makes a fit FP-tree-based mining system, FP enhanced capacity algorithm is used, for mining the complete game plan of examples by illustration incessant development. Here, this paper handles the motivation behind making remarkable and weighted item sets, i.e. rare weighted item set mining issue. The two novel brightness measures are proposed for figuring the infrequent weighted item set mining issue. Also, the algorithm are handled which perform IWI which is more insignificant IWI mining. Moreover we utilized the rare item set for choice based structure. The general issue of the start of reliable definite rules is troublesome for the grounds that hypothetically no inciting technique with no other person can promise the rightness of influenced theories. In this way, this framework expects the disorder with the uncommon signs. Usage study demonstrates that proposed algorithm upgrades the structure which is successful and versatile for mining both long and short diagnostics rules. Structure upgrades aftereffects of foreseeing rare diseases of patient.

Keywords: association rule, data mining, IWI mining, infrequent item set, frequent pattern growth

Procedia PDF Downloads 396

Authors: I. Nižetić Kosović, T. Jagušt

Abstract:

Lately, with the increasing number of location-based applications, demand for highly accurate and reliable indoor localization became urgent. This is a challenging problem, due to the measurement variance which is the consequence of various factors like obstacles, equipment properties and environmental changes in complex nature of indoor environments. In this paper we propose low-cost custom-setup infrastructure solution and localization algorithm based on the Weighted Centroid Localization (WCL) method. Localization accuracy is increased by several enhancements: calibration of RSSI values gained from wireless nodes, repetitive measurements of RSSI to exclude deviating values from the position estimation, and by considering orientation of the device according to the wireless nodes. We conducted several experiments to evaluate the proposed algorithm. High accuracy of ~1m was achieved.

Keywords: indoor environment, received signal strength indicator, weighted centroid localization, wireless localization

Procedia PDF Downloads 230

Authors: Tapas Acharya, Monalisa Mitra

Abstract:

Overlay modeling is the most widely used conventional analysis for spatial decision support system. Overlay modeling requires a set of themes with different weightage computed in varied manners, which gives a resultant input for further integrated analysis. In spite of the popularity and most widely used technique; it gives inconsistent and erroneous results for similar inputs while processed in various GIS overlay techniques. This study is an attempt to compare and analyse the differences in the outputs of different overlay methods using GIS platform with same set of themes of the Precambrian metamorphic to obtain groundwater prospecting in Precambrian metamorphic rocks. The objective of the study is to emphasize the most suitable overlay method for groundwater prospecting in older Precambrian metamorphics. Seven input thematic layers like slope, Digital Elevation Model (DEM), soil thickness, lineament intersection density, average groundwater table fluctuation, stream density and lithology have been used in the spatial overlay models of fuzzy overlay, weighted overlay and weighted sum overlay methods to yield the suitable groundwater prospective zones. Spatial concurrence analysis with high yielding wells of the study area and the statistical comparative studies among the outputs of various overlay models using RStudio reveal that the Weighted Overlay model is the most efficient GIS overlay model to delineate the groundwater prospecting zones in the Precambrian metamorphic rocks.

Keywords: fuzzy overlay, GIS overlay model, groundwater prospecting, Precambrian metamorphics, weighted overlay, weighted sum overlay

Procedia PDF Downloads 123

Authors: Aysun Sezer

Abstract:

Magnetic Resonance Imaging (MRI) is one of the advanced diagnostic tools for evaluating shoulder pathologies. Proton Density (PD)-weighted MRI sequences prove highly effective in detecting edema. However, they are deficient in the anatomical identification of bones due to a trauma-induced decrease in signal-to-noise ratio and blur in the traumatized cortices. Computer-based diagnostic systems require precise segmentation, identification, and localization of anatomical regions in medical imagery. Deep learning-based object detection algorithms exhibit remarkable proficiency in real-time object identification and localization. In this study, the YOLOv8 model was employed to detect humeral head and scapular regions in 665 axial PD-weighted MR images. The YOLOv8 configuration achieved an overall success rate of 99.60% and 89.90% for detecting the humeral head and scapula, respectively, with an intersection over union (IoU) of 0.5. Our findings indicate a significant promise of employing YOLOv8-based detection for the humerus and scapula regions, particularly in the context of PD-weighted images affected by both noise and intensity inhomogeneity.

Keywords: YOLOv8, object detection, humerus, scapula, IRM

Procedia PDF Downloads 64