Similarity Properties Research Articles

The Funk and Hilbert geometries for spaces of constant curvature

The goal of this paper is to introduce and to study analogues of the Euclidean Funk and Hilbert metrics on open convex subsets of the hyperbolic space \(\mathbb H ^n\) and of the sphere \(S^n\). We highlight some striking similarities among the three cases (Euclidean, spherical and hyperbolic) which hold at least at a formal level. The proofs of the basic properties of the classical Funk metric on subsets of \(\mathbb R ^n\) use similarity properties of Euclidean triangles which of course do not hold in the non-Euclidean cases. Transforming the side lengths of triangles using hyperbolic and circular functions and using some non-Euclidean trigonometric formulae, the Euclidean similarity techniques are transported into the non-Euclidean worlds. We start by giving three representations of the Funk metric in each of the non-Euclidean cases, which parallel known representations for the Euclidean case. The non-Euclidean Funk metrics are shown to be Finslerian, and the associated Finsler norms are described. We then study their geodesics. The Hilbert geometry of convex sets in the non-Euclidean constant curvature spaces \(S^n\) and \(\mathbb H ^n\) is then developed by using the properties of the Funk metric and by introducing a non-Euclidean cross ratio. In the case of Euclidean (respectively spherical, hyperbolic) geometry, the Euclidean (respectively spherical, hyperbolic) geodesics are Funk and Hilbert geodesics. This leads to a formulation and a discussion of Hilbert’s Problem IV in the non-Euclidean settings. Projection maps between the spaces \(\mathbb R ^n, \mathbb H ^n\) and the upper hemisphere establish equivalences between the Hilbert geometries of convex sets in the three spaces of constant curvature, but such an equivalence does not hold for Funk geometries.

Elastic Wave Localization in Layered Phononic Crystals With Fractal Superlattices

In this paper, localization phenomena of in-plane time-harmonic elastic waves propagating in layered phononic crystals (PNCs) with different fractal superlattices are studied. For this purpose, oblique wave propagation in layered structures is considered. To describe wave localization phenomena, the localization factor is applied and computed by the transfer matrix method. Three typical fractal superlattices are considered, namely, the Cantorlike fractal superlattice (CLFSL), the golden-section fractal superlattice (GSFSL), and the Fibonacci fractal superlattice (FFSL). Numerical results for the localization factors of CLFSL, GSFSL, and FFSL are presented and analyzed. The results show that the localization factor of a CLFSL exhibits an approximate similarity and band-splitting properties. The number of decomposed bandgaps of the GSFSL and FFSL follows the composition of the special fractal structures. In addition, with increasing fractal series, the value of the localization factor is enlarged. These results are of great importance for structure design of fractal PNCs.

Radiative reverse shock laser experiments relevant to accretion processes in cataclysmic variables

We discuss the production of radiative reverse shocks in experiments at the Omega-60 laser facility. The ability of this high-intensity laser to impart large energy densities on micron-thin foils makes it feasible to create supersonic plasma flows. Obtaining a radiative reverse shock in the laboratory requires a sufficiently fast flow (∼100 km/s) of a material whose opacity is large enough to produce energetically significant emission from experimentally achievable shocked layers. The reverse shock forms in the flow once it is impeded. This paper presents the first radiographic data of normal incidence, reverse shockwaves. These experiments are primarily motivated by the contribution of radiative reverse shock waves to the evolving dynamics of the cataclysmic variable (CV) system in which they reside. We show similarity properties to suggest that the experimental production of radiative reserve shocks in the laboratory may be scalable to such astrophysical systems.

A general framework for analyzing beta diversity, nestedness and related community-level phenomena based on abundance data

We describe a procedure for evaluating the relative importance of beta diversity, nestedness, and similarity properties of ecological data matrices containing density, cover or biomass scores of species. Our goals are achieved by extension of the simplex approach – originally proposed for presence–absence data – to abundances. Basically, the method involves decomposition of the Marczewski–Steinhaus coefficient of dissimilarity between pairs of sites into two fractions, one derived from differences between total abundance and the other from differences due to abundance replacement. These are contrasted by the similarity function counterpart, known as the Ruzicka coefficient, and are displayed graphically using ternary (or 2D simplex) plots. Interpretation is aided by calculating percentage contributions from these components to the (dis)similarity structure. Measures of replacement and nestedness are new for abundance data; these are considered complementary phenomena reflecting antithetic ecological processes that are analogous to those operating at the presence–absence level. The method is illustrated by artificial data and a range of actual ecological data sets representing different groups of organisms, different scales and different types of data. While the simplex diagrams and associated coefficients are meaningful by themselves, their comparison with presence–absence based results gives additional insight into data structure and background factors.

Detecting video frame-rate up-conversion based on periodic properties of inter-frame similarity

Video frame-rate up-conversion is one of the common operations for tampering digital videos in the temporal domain, such as creating fake high-quality videos and splicing two video clips with different frame rates. However, few existing works have been proposed for detecting this form of tampering operation. Based on the analysis of extensive experiments, we found that frame-rate up-conversion algorithms employed in most current video editing softwares will inevitably introduce some periodic artifacts into inter-frame similarity in the resulting video frame sequence. By analyzing such artifacts, we propose a simple yet very effective method to expose video after frame-rate up-conversion, and further estimate its original frame rate. The experimental results evaluated on 100 original videos at different frame rates have shown the effectiveness of the proposed method. The average detection accuracy can achieve as high as 99 % on noise-free videos in uncompressed and H.264/AVC formats. Besides, the proposed method is robust to noise as the detection accuracy could reach over 85 % and 95 % on noised videos with Gaussian white noise when SNR is 33 db and 36 db respectively.

A novel complexity reduction using similarity property in ML-ZF detection for MIMO systems

A novel complexity reduction using similarity property in ML-ZF detection for MIMO systems

Investigation of Mutual Coupling Effects in Conventional and Fractal Capacitive Coupled Suspended RMSAs

An array of coplanar capacitive coupled suspended microstrip antenna has been investigated to study the mutual coupling effect between its elements. Also, the work is extended to study the mutual coupling effect in Koch shaped coplanar capacitive coupled suspended fractal microstrip antenna. From the investigations it is observed that less coupling effect occurs between the elements in fractal array. This study reveals the use of fractal geometries in place of conventional (regular) shapes because of their numerous advantages like self similarity property, ability to excite multiple resonant modes etc. Antenna arrays are simulated using IE3D software from Zeland which is based on Method of Moments (MoM).

Numerical Study of the Effect of Parietal Suction and Injection on Momentum and Heat Transfer of Laminar and Turbulent External Flow

The present study is focused on the effect of parietal suction and injection on the hydrodynamic and thermal behavior of external flow. Injection is produced by imposing inward parietal velocity, which corresponds to negative values of stream function. While suction is produced by imposing outward parietal velocity which corresponds to positive values of stream function. External flow is assumed two- dimensional boundary-layer where laminar, transitional and turbulent flow region are considered. Turbulence is modeled by algebraic eddy viscosity approach of Cebeci and Smith. Numerical procedure, based on an implicit finite difference box method with non-uniform grid is employed for the solution of the coupled governing conservation equations of mass, momentum, enthalpy and boundary conditions. It can be shown that wall conditions affect significantly the momentum and heat transfer. For laminar flow, imposed stream function condition confers the property of flow similarity for both situations of suction and injection. In contrast, non-similarity for turbulent flow parameters is observed. The increase of injection velocity causes an increase of flow shape factor and decreases the shear coefficient and the Nusselt number. Turbulence amplifies parietal shear stress, which delays the flow separation.

Implementation of Gabor Filter on ARM9 Processor

This work implements gabor filter on ARM9 board.Gabor filters are widely used as band pass filters in image processing for texture analysis,feature extraction ,edge detection etc.They have frequency and orientation representation similar to human visual system.They have the property of self similarity that is every filter can be generated from mother wavelet.ARM9 processors have v4t architecture .It has strong arithametical capability.Since the ARM9 has features like camera interface,AHB,Enhanced DSP instruction,the filter imple mented on ARM9 can be used for realtime image processing.This implementation uses Opencv functions

Position-Specific Analysis and Prediction for Protein Lysine Acetylation Based on Multiple Features

Protein lysine acetylation is a type of reversible post-translational modification that plays a vital role in many cellular processes, such as transcriptional regulation, apoptosis and cytokine signaling. To fully decipher the molecular mechanisms of acetylation-related biological processes, an initial but crucial step is the recognition of acetylated substrates and the corresponding acetylation sites. In this study, we developed a position-specific method named PSKAcePred for lysine acetylation prediction based on support vector machines. The residues around the acetylation sites were selected or excluded based on their entropy values. We incorporated features of amino acid composition information, evolutionary similarity and physicochemical properties to predict lysine acetylation sites. The prediction model achieved an accuracy of 79.84% and a Matthews correlation coefficient of 59.72% using the 10-fold cross-validation on balanced positive and negative samples. A feature analysis showed that all features applied in this method contributed to the acetylation process. A position-specific analysis showed that the features derived from the critical neighboring residues contributed profoundly to the acetylation site determination. The detailed analysis in this paper can help us to understand more of the acetylation mechanism and can provide guidance for the related experimental validation.

Optimizing Predictive Performance of CASE Ultra Expert System Models Using the Applicability Domains of Individual Toxicity Alerts

Fragment based expert system models of toxicological end points are primarily comprised of a set of substructures that are statistically related to the toxic property in question. These special substructures are often referred to as toxicity alerts, toxicophores, or biophores. They are the main building blocks/classifying units of the model, and it is important to define the chemical structural space within which the alerts are expected to produce reliable predictions. Furthermore, defining an appropriate applicability domain is required as part of the OECD guidelines for the validation of quantitative structure-activity relationships (QSARs). In this respect, this paper describes a method to construct applicability domains for individual toxicity alerts that are part of the CASE Ultra expert system models. Defining applicability domain for individual alerts was necessary because each CASE Ultra model is comprised of multiple alerts, and different alerts of a model usually represent different toxicity mechanisms and cover different structural space; the use of an applicability domain for the overall model is often not adequate. The domain for each alert was constructed using a set of fragments that were found to be statistically related to the end point in question as opposed to using overall structural similarity or physicochemical properties. Use of the applicability domains in reducing false positive predictions is demonstrated. It is now possible to obtain ROC (receiver operating characteristic) profiles of CASE Ultra models by applying domain adherence cutoffs on the alerts identified in test chemicals. This helps in optimizing the performance of a model based on their true positive-false positive prediction trade-offs and reduce drastic effects on the predictive performance caused by the active/inactive ratio of the model's training set. None of the major currently available commercial expert systems for toxicity prediction offer the possibility to explore a model's full range of sensitivity-specificity spectrum, and therefore, the methodology developed in this study can be of benefit in improving the predictive ability of the alert based expert systems.

Performance evaluation of data clustering techniques using KDD Cup-99 Intrusion detection data set

Intrusion-detection systems aim at detecting attacks against computer systems and networks or, in general, against information systems. A number of techniques are available for intrusion detection. Data mining is the one of the efficient technique among them. Intrusion detection and clustering have forever been hot topics in the area of machine learning. Data clustering is a procedure of putting related data into groups. Clustering procedure clusters the data into groups with the property of inter-group similarity and intra-group dissimilarity. A clustering technique partitions a data-set into several groups such that the likeness within a group is larger than amongst groups. Clustering as an intrusion detection technique has long before proved to be beneficial. This paper evaluate four most representative off-line clustering techniques: k-means clustering, fuzzy c-means clustering, Mountain clustering, and Subtractive clustering. These techniques are implemented and tested against KDD cup-99 data set, which is used as a standard benchmark data set for intrusion detection. Performance and accuracy of the four techniques are presented and compared in this paper. The experimental outcomes obtained by applying these algorithms on KDD cup-99 data set demonstrate that k-means and fuzzy c-means clustering algorithms perform well in terms of accuracy and computation time.

Tick-borne Nyamanini virus replicates in the nucleus and exhibits unusual genome and matrix protein properties.

Tick-borne Nyamanini virus (NYMV) is the prototypic member of a recently discovered genus in the order Mononegavirales, designated Nyavirus. The NYMV genome codes for six distinct genes. Sequence similarity and structural properties suggest that genes 1, 5, and 6 encode the nucleoprotein (N), the glycoprotein (G), and the viral polymerase (L), respectively. The function of the other viral genes has been unknown to date. We found that the third NYMV gene codes for a protein which, when coexpressed with N and L, can reconstitute viral polymerase activity, suggesting that it represents a polymerase cofactor. The second viral gene codes for a small protein that inhibits viral polymerase activity and further strongly enhances the formation of virus-like particles when coexpressed with gene 4 and the viral glycoprotein G. This suggests that two distinct proteins serve a matrix protein function in NYMV as previously described for members of the family Filoviridae. We further found that NYMV replicates in the nucleus of infected cells like members of the family Bornaviridae. NYMV is a poor inducer of beta interferon, presumably because the viral genome is 5' monophosphorylated and has a protruding 3' terminus as observed for bornaviruses. Taken together, our results demonstrate that NYMV possesses biological properties previously regarded as typical for filoviruses and bornaviruses, respectively.

Increasing clone maintenance support by unifying clone detection and refactoring activities

ContextClone detection tools provide an automated mechanism to discover clones in source code. On the other side, refactoring capabilities within integrated development environments provide the necessary functionality to assist programmers in refactoring. However, we have observed a gap between the processes of clone detection and refactoring. ObjectiveIn this paper, we describe our work on unifying the code clone maintenance process by bridging the gap between clone detection and refactoring. MethodThrough an Eclipse plug-in called CeDAR (Clone Detection, Analysis, and Refactoring), we forward clone detection results to the refactoring engine in Eclipse. In this case, the refactoring engine is supplied with information about the detected clones to which it can then determine those clones that can be refactored. We describe the extensions to Eclipse’s refactoring engine to allow clones with additional similarity properties to be refactored. ResultsOur evaluation of open source artifacts shows that this process yields considerable increases in the instances of clone groups that may be suggested to the programmer for refactoring within Eclipse. ConclusionBy unifying the processes of clone detection and refactoring, in addition to providing extensions to the refactoring engine of an IDE, the strengths of both processes (i.e., more significant detection capabilities and an established framework for refactoring) can be garnered.

Analysis of the designs of iraca hats made in Colón - Genova, Nariño

This document presents an analysis of the interlaces used in the configuration of nine straw hat styles produced by the Colon - Genova community, Narino, Colombia. These hats are known under the names of Comun, Pintao, Gallineto- Granizo, Fino, Cuadros, Calado or Huecos, Costeno or Vueltiao, Bandera and Bird's-Eye. The interpretation of the geometric thought employed in the design of these hats had like reference, between other authors, the methodologies proposed by Gerdes (1999) and Aroca (2009), that have been applied in the African continent and in South America. Besides, the existence of a logic of the construction became established, based in count strategies and organization that become evident in the crossed of the iracas or chullas. The evolution techniques were evidenced, which imply modifications in the basic fabric bearing to changes in the logic of the construction, resulting in the generation of new designs that search to fulfill to the needs of the present-day society. Craftsmen discuss the symmetry in their designs applying complex processes of estimate and count, which are tried to show. The symmetric figures correspond to triangles, quadrilateral and hexagons organized in stripes that fulfill properties of congruence, similarity and parallelism, being this a language of the researchers interpretation validated upon showing the results to academic communities.

Similarity analysis of a glottal-like jet

This work discloses similarity properties of a high-aspect-ratio pulsating jet with lateral confinement exhibiting axis switching in a region close to the jet exit. The analysis is conducted separately within the major and minor planes of the jet source. The similarity relations derived from the in-plane flow equations are combined with experimental data collected in a recent three-dimensional velocimetry study of a glottal-like jet. Empirically, non-collapsing profiles are shown to rescale as collapsing profiles in the similarity variables within ranges of the streamwise coordinate, which are determined by the analysis. The similarity properties are shown to be useful to make predictions on the jet axis-switching characteristics.

The similarity problem for Z―-stable C*-algebras

We show that the tensor product of two unital C* -algebras, one of which is nuclear and admits a unital *-homomorphism from (the building blocks of) the Jiang–Su algebra, has Kadison's similarity property. As a consequence, we obtain that a unital C* -algebra that absorbs the Jiang–Su algebra tensorially also has this property.

Sparse regularization for precipitation downscaling

Downscaling of remotely sensed precipitation images and outputs of general circulation models has been a subject of intense interest in hydrometeorology. The problem of downscaling is basically one of resolution enhancement, that is, appropriately adding details or high frequency features onto a low‐resolution observation or simulated rainfall field. Invoking the property of rainfall self similarity, this mathematically ill‐posed problem has been approached in the past within a stochastic framework resulting in ensemble of possible high‐resolution realizations. In this work, we recast the rainfall downscaling into an ill‐posed inverse problem and introduce a class of nonlinear estimators to properly regularize it and obtain the best high‐resolution estimate in an optimal sense. This regularization capitalizes on two main observations: (1) precipitation fields are sparse when transformed into an appropriately chosen domain (e.g., wavelet), and (2) small‐scale organized precipitation features tend to recur within and across different storm environments. We demonstrate the promise of the proposed methodology through downscaling and error analysis of level III precipitation reflectivity snapshots provided by the ground‐based next generation Doppler weather radars in a ground validation sites of the Tropical Rainfall Measuring Mission.

Comparison of scattering by different nonspherical, wavelength-scale particles

It is well established that spherical and nonspherical particles scatter light differently. There are a large number of studies where scattering properties of different nonspherical particles are studied. Here we study to what degree scattering matrices of different nonspherical particles resemble each other, and whether there are significant correlations between morphological similarity and similar single-scattering properties. Altogether 15 different shapes are considered, including both irregular and regular shapes as well as homogeneous and inhomogeneous particles. For all nonspherical particles, orientation- and ensemble-averaged scattering properties are considered, and variability within each ensemble is ignored. The results reveal that different nonspherical shapes have surprisingly similar phase functions. An analysis of the asymmetry parameter reveals that the resemblance is, however, only qualitative: the phase functions are featureless and predominantly flat at side scattering, but they are nevertheless different. The degree of linear polarization for unpolarized incident light shows much larger differences among the shapes, albeit it is much more positive for all nonspherical targets than for Mie spheres. Similar to the phase function, the depolarization ratio tends to be similar among the nonspherical particle types, implying that the strength of depolarization cannot be used as a measure for the type of nonsphericity. In general, it is found that there does not seem to be a clear correlation between particle morphology and scattering properties.

The relation between linguistic categories and cognition: The case of numeral classifiers

The classifier grammar system categorises things in the world in a way that is drastically different from the way nouns do. Previous research revealed amplified similarity among objects belonging to the same classifier category in Chinese speakers, but how this amplified classifier similarity effect arises was still an open question. The present research was conducted to address this question. For this purpose, we compared speakers of Chinese, Japanese (classifier languages), and German (nonclassifier language) on a range of cognitive tasks including similarity judgements, property induction, and fast-speed word-picture matching. Although Chinese and Japanese classifier systems are similar in their semantic structures, classifier classes for nouns are marked more systematically in Chinese than in Japanese. The amplified classifier similarity effect was found in Chinese but not in Japanese speakers. We explore the nature of the amplified classifier similarity effect and propose an explanation for how it may arise.