Rough sets in graphs using similarity relations

<abstract><p>In this paper, we investigate the theory of rough set to study graphs using the concept of orbits. Rough sets are based on a clustering criterion and we use the idea of similarity of vertices under automorphism as a criterion. We introduce indiscernibility relation in terms of orbits and prove necessary and sufficient conditions under which the indiscernibility partitions remain the same when associated with different attribute sets. We show that automorphisms of the graph $ \mathcal{G} $ preserve the indiscernibility partitions. Further, we prove that for any graph $ \mathcal{G} $ with $ k $ orbits, any reduct $ \mathcal{R} $ consists of one element from $ k-1 $ orbits of the graph. We also study the rough membership functions for paths, cycles, complete and complete bipartite graphs. Moreover, we introduce essential sets and discernibility matrices induced by orbits of graphs and study their relationship. We also prove that every essential set consists of union of any two orbits of the graph.</p></abstract>

Clustering by Errors: A Self-Organized Multitask Learning Method for Acoustic Scene Classification

Acoustic scene classification (ASC) tries to inference information about the environment using audio segments. The inter-class similarity is a significant issue in ASC as acoustic scenes with different labels may sound quite similar. In this paper, the similarity relations amongst scenes are correlated with the classification error. A class hierarchy construction method by using classification error is then proposed and integrated into a multitask learning framework. The experiments have shown that the proposed multitask learning method improves the performance of ASC. On the TUT Acoustic Scene 2017 dataset, we obtain the ensemble fine-grained accuracy of 81.4%, which is better than the state-of-the-art. By using multitask learning, the basic Convolutional Neural Network (CNN) model can be improved by about 2.0 to 3.5 percent according to different spectrograms. The coarse category accuracies (for two to six super-classes) range from 77.0% to 96.2% by single models. On the revised version of the LITIS Rouen dataset, we achieve the ensemble fine-grained accuracy of 83.9%. The multitask learning models obtain an improvement of 1.6% to 1.8% compared to their basic models. The coarse category accuracies range from 94.9% to 97.9% for two to six super-classes with single models.

Turbulent kinetic energy balance in the atmospheric surface layer over a tropical region

ABSTRACT. The various tenns of the turbulent kinetic energy budget in the surface layer over Jodhpur, India have been worked out and compared with established similarity relations. The turbulent production and dissipation tend to balance under moderately unstable conditions for most of the runs considered for investigation.

Estimation of surface parameters from a 30 metre micro-meteorological tower over a deep moist convective region

The estimation of u*, 0*, q*. and Obukov-length In the surface layer from micro-meteorological tower data still poses an important challange. In the present study a procedure for the parametric estimation has been developed which is consistent both with the similarity relation and the profile relation. The study has been done using both fast response and slow response tower data. Since similarity relations involve a particular level z. so inspite of starting from a layer, the parameters should be attributed to a relations involve a particular level only, It has been suggested that the convenient level is geometric mean height of the layer. The ratio of eddy diffusivities (KhKm.) has been estimated both for stable and unstable situation and this ratio is presented by a single expression which incidentally yields a new value of a constant involved.

Homotopic Solution for 3D Darcy–Forchheimer Flow of Prandtl Fluid through Bidirectional Extending Surface with Cattaneo–Christov Heat and Mass Flux Model

The 3D Prandtl fluid flow through a bidirectional extending surface is analytically investigated. Cattaneo–Christov fluid model is employed to govern the heat and mass flux during fluid motion. The Prandtl fluid motion is mathematically modeled using the law of conservations of mass, momentum, and energy. The set of coupled nonlinear PDEs is converted to ODEs by employing appropriate similarity relations. The system of coupled ODEs is analytically solved using the well-established mathematical technique of HAM. The impacts of various physical parameters over the fluid state variables are investigated by displaying their corresponding plots. The augmenting Prandtl parameter enhances the fluid velocity and reduces the temperature and concentration of the fluid. The momentum boundary layer boosts while the thermal boundary layer mitigates with the rising elastic parameter ( α 2 ) strength. Furthermore, the enhancing thermal relaxation parameter ( γ e )) reduces the temperature distribution, whereas the augmenting concentration parameter ( γ c ) drops the strength of the concentration profile. The increasing Prandtl parameter declines the fluid temperature while the augmenting Schmidt number drops the fluid concentration. The comparison of the HAM technique with the numerical solution shows an excellent agreement and hence ascertains the accuracy of the applied analytical technique. This work finds applications in numerous fields involving the flow of non-Newtonian fluids.

On the scaling laws for low-temperature plasmas at macro and micro scales

The theoretical background and historical development of the similarity theory during the past decades are reviewed. We demonstrate similar discharges in local and nonlocal kinetic regimes, taking the low-pressure capacitive radio frequency (rf) discharges and microdischarges as examples. By using fully kinetic particle-in-cell simulations, we verify the similarity law (SL) and show a violation of frequency scaling (f-scaling) in the low-pressure capacitive rf plasmas. The similarity relations for electron density and electron power absorption are confirmed in similar rf discharges. With only the driving frequency varied, the f-scaling for electron density is also validated, showing almost the same trend as the similarity scaling, across most of the frequency regime. However, violations of the f-scaling are observed at lower frequencies, which are found to be relevant to the electron heating mode transition from stochastic to Ohmic heating. The scaling characteristics have also been comprehensively studied for microdischarges with dimensions from hundreds to several microns, with transition from secondary electron dominated regime to field emission regime. Finally, practical applications of the similarity and scaling laws are summarized.

Discrete Two-Step Cross-Modal Hashing through the Exploitation of Pairwise Relations

The cross-modal hashing method can map heterogeneous multimodal data into a compact binary code that preserves semantic similarity, which can significantly enhance the convenience of cross-modal retrieval. However, the currently available supervised cross-modal hashing methods generally only factorize the label matrix and do not fully exploit the supervised information. Furthermore, these methods often only use one-directional mapping, which results in an unstable hash learning process. To address these problems, we propose a new supervised cross-modal hash learning method called Discrete Two-step Cross-modal Hashing (DTCH) through the exploitation of pairwise relations. Specifically, this method fully exploits the pairwise similarity relations contained in the supervision information: for the label matrix, the hash learning process is stabilized by combining matrix factorization and label regression; for the pairwise similarity matrix, a semirelaxed and semidiscrete strategy is adopted to potentially reduce the cumulative quantization errors while improving the retrieval efficiency and accuracy. The approach further combines an exploration of fine-grained features in the objective function with a novel out-of-sample extension strategy to enable the implicit preservation of consistency between the different modal distributions of samples and the pairwise similarity relations. The superiority of our method was verified through extensive experiments using two widely used datasets.

Multiple Solutions for Stagnation-Point Flow of Unsteady Carreau Fluid along a Permeable Stretching/Shrinking Sheet with Non-Uniform Heat Generation

The aim of the present study was to explore the effect of a non-uniform heat source/sink on the unsteady stagnation point flow of Carreau fluid past a permeable stretching/shrinking sheet. The novelty of the flow model was enhanced with additional effects of magnetohydrodynamics, joule heating, and viscous dissipation. The nonlinear partial differential equations were converted into ordinary differential equations with the assistance of appropriate similarity relations and were then tackled by employing the Runge-Kutta-Fehlberg technique with the shooting method. The impacts of pertinent parameters on the dimensionless velocity and temperature profiles along with the friction factor and local Nusselt number were extensively discussed by means of graphical depictions and tables. The current results were compared to the previous findings under certain conditions to determine the precision and validity of the present study. The fluid flow velocity of Carreau fluid increased with the value of the magnetic parameter in the case of the first solution, and the opposite behavior was noticed for the second solution. It was seen that temperature of the Carreau fluid expanded with the higher values of unsteadiness and magnetic parameters. It was visualized from multiple branches that the local Nusselt number declined with the Eckert number parameter for both the upper and lower branch.