Monopoles on S-F(2) from the fuzzy conifold

The intersection of the conifold z(1)(2) + z(2)(2) + z(3)(2) = 0 and S-5 is a compact 3-dimensional manifold X-3. We review the description of X-3 as a principal U(1) bundle over S-2 and construct the associated monopole line bundles. These monopoles can have only even integers as their charge. We also show the Kaluza-Klein reduction of X-3 to S-2 provides an easy construction of these monopoles. Using the analogue of the Jordan-Schwinger map, our techniques are readily adapted to give the fuzzy version of the fibration X-3 -> S-2 and the associated line bundles. This is an alternative new realization of the fuzzy sphere S-F(2) and monopoles OH it.

Integrated sustainable irrigation planning with multiobjective Fuzzy optimization approach

Multiobjective fuzzy methodology is applied to a case study of Khadakwasla complex irrigation project located near Pune city of Maharashtra State, India. Three objectives, namely, maximization of net benefits, crop production and labour employment are considered. Effect of reuse of wastewater on the planning scenario is also studied. Three membership functions, namely, nonlinear, hyperbolic and exponential are analyzed for multiobjective fuzzy optimization. In the present study, objective functions are considered as fuzzy in nature whereas inflows are considered as dependable. It is concluded that exponential and hyperbolic membership functions provided similar cropping pattern for most of the situations whereas nonlinear membership functions provided different cropping pattern. However, in all the three cases, irrigation intensities are more than the existing irrigation intensity.

FUZZY CONIFOLD Y-F(6) AND MONOPOLES ON S-F(2) x S-F(2)

In this paper, we construct the fuzzy (finite-dimensional) analogs of the conifold Y-6 and its base X-5. We show that fuzzy X-5 is (the analog of) a principal U(1) bundle over fuzzy spheres S-F(2) x S-F(2) and explicitly construct the associated monopole bundles. In particular, our construction provides an explicit discretization of the spaces T-k,T-k and T-k,T-0.

Active yaw control of a vehicle using a Fuzzy logic algorithm

Yaw rate of a vehicle is highly influenced by the lateral forces generated at the tire contact patch to attain the desired lateral acceleration, and/or by external disturbances resulting from factors such as crosswinds, flat tire or, split-μ braking. The presence of the latter and the insufficiency of the former may lead to undesired yaw motion of a vehicle. This paper proposes a steer-by-wire system based on fuzzy logic as yaw-stability controller for a four-wheeled road vehicle with active front steering. The dynamics governing the yaw behavior of the vehicle has been modeled in MATLAB/Simulink. The fuzzy controller receives the yaw rate error of the vehicle and the steering signal given by the driver as inputs and generates an additional steering angle as output which provides the corrective yaw moment. The results of simulations with various drive input signals show that the yaw stability controller using fuzzy logic proposed in the current study has a good performance in situations involving unexpected yaw motion. The yaw rate errors of a vehicle having the proposed controller are notably smaller than an uncontrolled vehicle's, and the vehicle having the yaw stability controller recovers lateral distance and desired yaw rate more quickly than the uncontrolled vehicle.

Multi Label Classification of Discrete Data

The paper describes an algorithm for multi-label classification. Since a pattern can belong to more than one class, the task of classifying a test pattern is a challenging one. We propose a new algorithm to carry out multi-label classification which works for discrete data. We have implemented the algorithm and presented the results for different multi-label data sets. The results have been compared with the algorithm multi-label KNN or ML-KNN and found to give good results.

Fuzzy Classification of Time Series Data

The problem of classification of time series data is an interesting problem in the field of data mining. Even though several algorithms have been proposed for the problem of time series classification we have developed an innovative algorithm which is computationally fast and accurate in several cases when compared with 1NN classifier. In our method we are calculating the fuzzy membership of each test pattern to be classified to each class. We have experimented with 6 benchmark datasets and compared our method with 1NN classifier.

Regional flood frequency analysis using kernel- based fuzzy clustering approach

Regionalization approaches are widely used in water resources engineering to identify hydrologically homogeneous groups of watersheds that are referred to as regions. Pooled information from sites (depicting watersheds) in a region forms the basis to estimate quantiles associated with hydrological extreme events at ungauged/sparsely gauged sites in the region. Conventional regionalization approaches can be effective when watersheds (data points) corresponding to different regions can be separated using straight lines or linear planes in the space of watershed related attributes. In this paper, a kernel-based Fuzzy c-means (KFCM) clustering approach is presented for use in situations where such linear separation of regions cannot be accomplished. The approach uses kernel-based functions to map the data points from the attribute space to a higher-dimensional space where they can be separated into regions by linear planes. A procedure to determine optimal number of regions with the KFCM approach is suggested. Further, formulations to estimate flood quantiles at ungauged sites with the approach are developed. Effectiveness of the approach is demonstrated through Monte-Carlo simulation experiments and a case study on watersheds in United States. Comparison of results with those based on conventional Fuzzy c-means clustering, Region-of-influence approach and a prior study indicate that KFCM approach outperforms the other approaches in forming regions that are closer to being statistically homogeneous and in estimating flood quantiles at ungauged sites. Key Points Kernel-based regionalization approach is presented for flood frequency analysis Kernel procedure to estimate flood quantiles at ungauged sites is developed A set of fuzzy regions is delineated in Ohio, USA

Fixed-orientation equilateral triangle matching of point sets

Given a point set P and a class C of geometric objects, G(C)(P) is a geometric graph with vertex set P such that any two vertices p and q are adjacent if and only if there is some C is an element of C containing both p and q but no other points from P. We study G(del)(P) graphs where del is the class of downward equilateral triangles (i.e., equilateral triangles with one of their sides parallel to the x-axis and the corner opposite to this side below that side). For point sets in general position, these graphs have been shown to be equivalent to half-Theta(6) graphs and TD-Delaunay graphs. The main result in our paper is that for point sets P in general position, G(del)(P) always contains a matching of size at least vertical bar P vertical bar-1/3] and this bound is tight. We also give some structural properties of G(star)(P) graphs, where is the class which contains both upward and downward equilateral triangles. We show that for point sets in general position, the block cut point graph of G(star)(P) is simply a path. Through the equivalence of G(star)(P) graphs with Theta(6) graphs, we also derive that any Theta(6) graph can have at most 5n-11 edges, for point sets in general position. (C) 2013 Elsevier B.V. All rights reserved.

Spectrum of the three-dimensional fuzzy well

We develop the formalism of quantum mechanics on three-dimensional fuzzy space and solve the Schrodinger equation for the free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits. A high energy cut-off is found for the free particle spectrum, which also results in the modification of the high energy dispersion relation. An ultra-violet/infra-red duality is manifest in the free particle spectrum. The finite well also has an upper bound on the possible energy eigenvalues. The phase shifts due to scattering around the finite fuzzy potential well are calculated.

Quantum entropy for the fuzzy sphere and its monopoles

Using generalized bosons, we construct the fuzzy sphere S-F(2) and monopoles on S-F(2) in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.

Combining data sets of satellite-retrieved products for basin-scale water balance study: 2. Evaluation on the Mississippi Basin and closure correction model

In this study, we applied the integration methodology developed in the companion paper by Aires (2014) by using real satellite observations over the Mississippi Basin. The methodology provides basin-scale estimates of the four water budget components (precipitation P, evapotranspiration E, water storage change Delta S, and runoff R) in a two-step process: the Simple Weighting (SW) integration and a Postprocessing Filtering (PF) that imposes the water budget closure. A comparison with in situ observations of P and E demonstrated that PF improved the estimation of both components. A Closure Correction Model (CCM) has been derived from the integrated product (SW+PF) that allows to correct each observation data set independently, unlike the SW+PF method which requires simultaneous estimates of the four components. The CCM allows to standardize the various data sets for each component and highly decrease the budget residual (P - E - Delta S - R). As a direct application, the CCM was combined with the water budget equation to reconstruct missing values in any component. Results of a Monte Carlo experiment with synthetic gaps demonstrated the good performances of the method, except for the runoff data that has a variability of the same order of magnitude as the budget residual. Similarly, we proposed a reconstruction of Delta S between 1990 and 2002 where no Gravity Recovery and Climate Experiment data are available. Unlike most of the studies dealing with the water budget closure at the basin scale, only satellite observations and in situ runoff measurements are used. Consequently, the integrated data sets are model independent and can be used for model calibration or validation.

Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on M-F(6) from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

LANDSCAPE DYNAMICS MODELING THROUGH INTEGRATED MARKOV, FUZZY-AHP AND CELLULAR AUTOMATA

Multi temporal land use information were derived using two decades remote sensing data and simulated for 2012 and 2020 with Cellular Automata (CA) considering scenarios, change probabilities (through Markov chain) and Multi Criteria Evaluation (MCE). Agents and constraints were considered for modeling the urbanization process. Agents were nornmlized through fiizzyfication and priority weights were assigned through Analytical Hierarchical Process (AHP) pairwise comparison for each factor (in MCE) to derive behavior-oriented rules of transition for each land use class. Simulation shows a good agreement with the classified data. Fuzzy and AHP helped in analyzing the effects of agents of growth clearly and CA-Markov proved as a powerful tool in modelling and helped in capturing and visualizing the spatiotemporal patterns of urbanization. This provided rapid land evaluation framework with the essential insights of the urban trajectory for effective sustainable city planning.

Analytical approach to quantile estimation in regional frequency analysis based on fuzzy framework

Regional frequency analysis is widely used for estimating quantiles of hydrological extreme events at sparsely gauged/ungauged target sites in river basins. It involves identification of a region (group of watersheds) resembling watershed of the target site, and use of information pooled from the region to estimate quantile for the target site. In the analysis, watershed of the target site is assumed to completely resemble watersheds in the identified region in terms of mechanism underlying generation of extreme event. In reality, it is rare to find watersheds that completely resemble each other. Fuzzy clustering approach can account for partial resemblance of watersheds and yield region(s) for the target site. Formation of regions and quantile estimation requires discerning information from fuzzy-membership matrix obtained based on the approach. Practitioners often defuzzify the matrix to form disjoint clusters (regions) and use them as the basis for quantile estimation. The defuzzification approach (DFA) results in loss of information discerned on partial resemblance of watersheds. The lost information cannot be utilized in quantile estimation, owing to which the estimates could have significant error. To avert the loss of information, a threshold strategy (TS) was considered in some prior studies. In this study, it is analytically shown that the strategy results in under-prediction of quantiles. To address this, a mathematical approach is proposed in this study and its effectiveness in estimating flood quantiles relative to DFA and TS is demonstrated through Monte-Carlo simulation experiments and case study on Mid-Atlantic water resources region, USA. (C) 2015 Elsevier B.V. All rights reserved.

Construction of Singer Subgroup Orbit Codes Based on Cyclic Difference Sets

A recent approach for the construction of constant dimension subspace codes, designed for error correction in random networks, is to consider the codes as orbits of suitable subgroups of the general linear group. In particular, a cyclic orbit code is the orbit of a cyclic subgroup. Hence a possible method to construct large cyclic orbit codes with a given minimum subspace distance is to select a subspace such that the orbit of the Singer subgroup satisfies the distance constraint. In this paper we propose a method where some basic properties of difference sets are employed to select such a subspace, thereby providing a systematic way of constructing cyclic orbit codes with specified parameters. We also present an explicit example of such a construction.