Exact Similarity Research Articles

Exact Solution for a Magnetogasdynamical Cylindrical Shock Wave in a Self-Gravitating Rotating Perfect Gas with Radiation Heat Flux and Variable Density

An exact similarity solution for a magnetoradiative cylindrical shock wave in a self-gravitating rotating perfect gas is obtained. The density, azimuthal velocity, and magnetic field strength are assumed to vary in an undisturbed medium. It is shown that the flow variables, namely, the radial velocity, pressure, magnetic field strength, azimuthal velocity, mass, and the radiation flux, decrease from the highest values at the shock front to zero; however, the density tends to infinity as the symmetry axis is approached. The effects of variation in the magnetic field strength, gravitational parameter, rotational parameter, and in the adiabatic exponent on the flow variables and shock strength are discussed. The solutions obtained for self-gravitating and nongravitating media are compared. The total energy of the shock wave is shown to be not constant.

Scalable, variable-length similarity search in data series

Data series similarity search is an important operation and at the core of several analysis tasks and applications related to data series collections. Despite the fact that data series indexes enable fast similarity search, all existing indexes can only answer queries of a single length (fixed at index construction time), which is a severe limitation. In this work, we propose ULISSE, the first data series index structure designed for answering similarity search queries of variable length. Our contribution is two-fold. First, we introduce a novel representation technique, which effectively and succinctly summarizes multiple sequences of different length (irrespective of Z-normalization). Based on the proposed index, we describe efficient algorithms for approximate and exact similarity search, combining disk based index visits and in-memory sequential scans. We experimentally evaluate our approach using several synthetic and real datasets. The results show that ULISSE is several times (and up to orders of magnitude) more efficient in terms of both space and time cost, when compared to competing approaches.

Similarity solution and Runge Kutta method to a thermal boundary layer model at the entrance region of a circular tube

PurposeThe purpose of this paper is to re-examine the assumptions implicit in Leveque’s approximation, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge–Kutta fourth-order (RK4) method. Finally, other important thermal results obtained from this analysis, such as approximate Nusselt number in the thermal entrance region, was discussed in detail. After that, the analytical results of the present paper are validated with certain previous investigations which were found in the specialized literature.Design/methodology/approachBy defining a similarity variable, the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This paper gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form and presents a similarity solution. The calculation methodology for numerical resolution is based on the RK4 technique.FindingsThe profiles of the solutions are provided from which the authors infer that the numerical and exact solutions agreed very well. Another result that the authors obtained from this paper is the number of Nusselt in the thermal entrance region for which a parametric study was carried out and discussed well for the impact of scientific contribution.Originality/valueThe novelty of this paper is the application of the RK4 with a step size control, as a sequential numerical method of a ODEs system compared with the exact similarity solution of the thermal boundary layer problem.

Numerical investigation of MHD stagnation-point flow and heat transfer of sodium alginate non-Newtonian nanofluid

Abstract A rigorous analysis of unsteady magnetohydrodynamic mixed convection and electrically conducting nanofluid model with a stretching/shrinking wedge is presented. First, the governing partial differential equations for momentum and energy conservation are converted to coupled nonlinear ordinary differential equations by means of exact similarity transformation. The homotopy analysis method (HAM) is employed to obtain the analytical approximations for flow velocity and temperature distributions of alumina-sodium alginate naofluid. The solution is found to be dependent on some parameters including the nanoparticle volume fraction, unsteadiness parameter, magnetic parameter, mixed convection parameter and the generalized prandtl number. A systematic study is carried out to illustrate the effects of these parameters on the velocity and temperature distributions. Also, the value of skin friction coefficient and local Nusselt number are compared with copper-sodium alginate and titania-sodium alginate nanofluids.

Spatio-textual user matching and clustering based on set similarity joins

This paper addresses the problem of matching and clustering users based on their geolocated posts. Individual posts are matched according to spatial distance and textual similarity thresholds. Then, user similarity is defined as the ratio of their posts that match each other. Based on these criteria, we introduce efficient algorithms for identifying pairs of matching users in a large dataset, as well as for computing the top-k matching pairs. We then proceed to identify spatio-textual user clusters. For this purpose, we use the Louvain method for community detection. Our algorithms operate on a user graph where edge weights represent spatio-textual user similarities. Since the exact user similarity graph can be prohibitively expensive to compute, we exploit our previous algorithms to derive efficient methods that reduce execution time both by avoiding to compute exact similarity scores and by reducing the number of similarity calculations performed. The presented solution allows a trade-off between computation time and quality of detected clusters. The proposed algorithms are evaluated using three real-world datasets.

Index Structures for Fast Similarity Search for Real Vectors. II*

This survey article considers index structures for fast similarity search for objects represented by real-valued vectors. Structures for both exact and faster but approximate similarity search are considered. Index structures based on partitioning into regions (including hierarchical ones) and on proximity graphs are mainly presented. The acceleration of similarity search using the transformation of initial data is also discussed. The ideas of concrete algorithms including recently proposed ones are outlined. The approaches to the acceleration of similarity search in index structures of the considered types and also on the basis of similarity-preserving hashing are discussed and compared.

Using computed similarity of distinctive digital traces to evaluate non-obvious links and repetitions in cyber-investigations

This work addresses the challenge of discerning non-exact or non-obvious similarities between cybercrimes, proposing a new approach to finding linkages and repetitions across cases in a cyber-investigation context using near similarity calculation of distinctive digital traces. A prototype system was developed to test the proposed approach, and the system was evaluated using digital traces collected during actual cyber-investigations. The prototype system also links cases on the basis of exact similarity between technical characteristics. This work found that the introduction of near similarity helps to confirm already existing links, and exposes additional linkages between cases. Automatic detection of near similarities across cybercrimes gives digital investigators a better understanding of the criminal context and the actual phenomenon, and can reveal a series of related offenses. Using case data from 207 cyber-investigations, this study evaluated the effectiveness of computing similarity between cases by applying string similarity algorithms to email addresses. The Levenshtein algorithm was selected as the best algorithm to segregate similar email addresses from non-similar ones. This work can be extended to other digital traces common in cybercrimes such as URLs and domain names. In addition to finding linkages between related cybercrime at a technical level, similarities in patterns across cases provided insights at a behavioral level such as modus operandi (MO). This work also addresses the step that comes after the similarity computation, which is the linkage verification and the hypothesis formation. For forensic purposes, it is necessary to confirm that a near match with the similarity algorithm actually corresponds to a real relation between observed characteristics, and it is important to evaluate the likelihood that the disclosed similarity supports the hypothesis of the link between cases. This work recommends additional information, including certain technical, contextual and behavioral characteristics that could be collected routinely in cyber-investigations to support similarity computation and link evaluation.

Exact similarity and traveling wave solutions to an integrable evolution equation for surface waves in deep water

In this paper, the Lie symmetry analysis and the dynamical system method are performed on an integrable evolution equation for surface waves in deep water $$\begin{aligned} 2\sqrt{\frac{k}{g}}u_{xxt}=k^2u_x-\frac{3}{2}k(uu_x)_{xx}. \end{aligned}$$ All of the geometric vector fields of the equation are presented, as well as some exact similarity solutions with an arbitrary function of t are obtained by using a special symmetry reduction and the dynamical system method. Different kinds of traveling wave solutions also be found by selecting the function appropriately.

A New Framework of Frequent Uncertain Subgraph Mining

Nowadays, frequent graph mining approaches are very popular in several applications and big data domains. However, some problems are still not solved and need more attention from researchers such as inexact subgraph matching when similarity among subgraphs is not totally proved. Furthermore, many research works dealt with structural graph matching, but a little attention was paid to semantic graph matching when graph vertices and/or edges are attributed and typed. Therefore, this paper proposes a new possibilistic flexible graph mining approach to discover similar subgraphs, by applying possibilistic similarity rather than using hard structural exact similarity. This novel approach is hybrid and uses two similarity measures. An approximate structural similarity function of graph edit distance function and a semantic vertices similarity function based on possibilistic information affinity function. Experimental evaluation was conducted on real datasets borrowed from various domains and tests have shown a highly superiority of our hybrid frequent subgraph mining approach by achieving a good time processing performance and simultaneously discovering more similar subgraphs.

Quantity Tropes and Internal Relations

In this article, we present a new conception of internal relations between quantity tropes falling under determinates and determinables. We begin by providing a novel characterization of the necessary relations between these tropes as basic internal relations. The core ideas here are that the existence of the relata is sufficient for their being internally related, and that their being related does not require the existence of any specific entities distinct from the relata. We argue that quantity tropes are, as determinate particular natures, internally related by certain relations of proportion and order. By being determined by the nature of tropes, the relations of proportion and order remain invariant in conventional choice of unit for any quantity and give rise to natural divisions among tropes. As a consequence, tropes fall under distinct determinables and determinates. Our conception provides an accurate account of quantitative distances between tropes but avoids commitment to determinable universals. In this important respect, it compares favorably with the standard conception taking exact similarity and quantitative distances as primitive internal relations. Moreover, we argue for the superiority of our approach in comparison with two additional recent accounts of the similarity of quantity tropes.

MHD mixed convection oblique stagnation-point flow on a vertical plate

Purpose This paper aims to study the problem of the steady plane oblique stagnation-point flow of an electrically conducting Newtonian fluid impinging on a heated vertical sheet. The temperature of the plate varies linearly with the distance from the stagnation point. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB. Findings An exact similarity solution of the magnetohydrodynamic (MHD) Navier–Stokes equations under the Boussinesq approximation is obtained. Numerical solutions of the relevant functions and the structure of the flow field are presented and discussed for several values of the parameters which influence the motion: the Hartmann number, the parameter describing the oblique part of the motion, the Prandtl number (Pr) and the Richardson numbers. Dual solutions exist for several values of the parameters. Originality value The present results are original and new for the problem of MHD mixed convection oblique stagnation-point flow of a Newtonian fluid over a vertical flat plate, with the effect of induced magnetic field and temperature.

The New Life of the Good Souls in Josephus: Resurrection or Reincarnation?

AbstractThis study examines four Josephan passages discussing souls entering a new body or life. It argues that research on this issue can be advanced from the conclusion by several scholars that despite the language of reincarnation it is really the belief in resurrection that underlies Josephus’s accounts. The key findings include: Josephus does not directly characterize the new life as a reward, and the fact that its recipients are good souls does not contradict reincarnation. The descriptions of the new body inb.j.are in all respects easier to reconcile with reincarnation than resurrection. The expression ἐκ περιτροπῆς (αἰώνων) is best understood as referring to (cyclical) recurrence. The Josephan version of re-embodiment that emerges has many exact similarities with accounts of reincarnation but only a few general ones with resurrection. The thesis that Josephus’s real referent is resurrection is implausible.

Mixing Length Scales of Low Temperature Spin Plaquettes Models

Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we perform a rigorous study of the thermodynamic properties of two dimensional plaquette models, the square and triangular plaquette models. We prove that for any positive temperature both models have a unique infinite volume Gibbs measure with exponentially decaying correlations. We analyse the scaling of three a priori different static correlation lengths in the small temperature regime, the mixing, cavity and multispin correlation lengths. Finally, using the symmetries of the model we determine an exact self similarity property for the infinite volume Gibbs measure.

Exact similarity solutions for forced convection flow over horizontal plate in saturated porous medium with temperature-dependent viscosity

In this paper, we revisit a mathematical model representing a two-dimensional forced convection boundary-layer flow over a horizontal impermeable plate with a variable heat flux and viscosity. It is assumed that the fluid viscosity varies as an inverse linear function of temperature, the free stream velocity varies as an inverse linear of x and the wall heat flux varies with x as $x^{\lambda}$ ; where $\lambda > -1$ and x measures the distance along the surface. Analytical local similarity solutions are presented which reveal that there are two competing effects: $\lambda$ and $\theta_{e}$ ; where $\theta_{e}$ is the variable viscosity parameter. It has been shown that for $\theta_{e} > 0$ dual solutions exist and boundary separation occurs, while a unique local similarity solution exists for any $\theta_{e} < 0$ .

Heat transfer scaling analysis of the single-phase natural circulation flow system

In this study, the heating power in the heat source or the core decay power is proposed as the reference parameter for the scaling analyses. From the scaling analyses assuming quasi-steady state flow, three system-level dimensionless numbers for the thermal heat transfer were obtained: the dimensionless power rate number, the dimensionless HX heat transfer number, and the dimensionless heat loss number. Based on the three local heat transfer processes, the dimensionless HX heat transfer number is further broken down into three dimensionless local heat transfer numbers: the dimensionless HX tube internal convective heat transfer number, the dimensionless HX tube conductive heat transfer number, and the dimensionless HX tube external convective heat transfer number, with each representing local heat transfer similarity. Analogically, three dimensionless local heat loss numbers were also derived. With the obtained dimensionless numbers, the scaling criteria for exact HX heat transfer similarity were derived. It was found the tube inner diameter should be scaled down in terms of the tube length scaling ratio for exact heat transfer similarity. In addition, three sets of scaling criteria for a full-pressure model, the new scaling criteria (general), the new scaling criteria (ideal), and the new scaling criteria (practical), were proposed.

Time series joins, motifs, discords and shapelets: a unifying view that exploits the matrix profile

The last decade has seen a flurry of research on all-pairs-similarity-search (or similarity joins) for text, DNA and a handful of other datatypes, and these systems have been applied to many diverse data mining problems. However, there has been surprisingly little progress made on similarity joins for time series subsequences. The lack of progress probably stems from the daunting nature of the problem. For even modest sized datasets the obvious nested-loop algorithm can take months, and the typical speed-up techniques in this domain (i.e., indexing, lower-bounding, triangular-inequality pruning and early abandoning) at best produce only one or two orders of magnitude speedup. In this work we introduce a novel scalable algorithm for time series subsequence all-pairs-similarity-search. For exceptionally large datasets, the algorithm can be trivially cast as an anytime algorithm and produce high-quality approximate solutions in reasonable time and/or be accelerated by a trivial porting to a GPU framework. The exact similarity join algorithm computes the answer to the time series motif and time series discord problem as a side-effect, and our algorithm incidentally provides the fastest known algorithm for both these extensively-studied problems. We demonstrate the utility of our ideas for many time series data mining problems, including motif discovery, novelty discovery, shapelet discovery, semantic segmentation, density estimation, and contrast set mining. Moreover, we demonstrate the utility of our ideas on domains as diverse as seismology, music processing, bioinformatics, human activity monitoring, electrical power-demand monitoring and medicine.

Leveraging set relations in exact set similarity join

Exact set similarity join, which finds all the similar set pairs from two collections of sets, is a fundamental problem with a wide range of applications. The existing solutions for set similarity join follow a filtering-verification framework, which generates a list of candidate pairs through scanning indexes in the filtering phase, and reports those similar pairs in the verification phase. Though much research has been conducted on this problem, set relations, which we find out is quite effective on improving the algorithm efficiency through computational cost sharing, have never been studied. Therefore, in this paper, instead of considering each set individually, we explore the set relations in different levels to reduce the overall computational costs. First, it has been shown that most of the computational time is spent on the filtering phase, which can be quadratic to the number of sets in the worst case for the existing solutions. Thus we explore index-level set relations to reduce the filtering cost to be linear to the size of the input while keeping the same filtering power. We achieve this by grouping related sets into blocks in the index and skipping useless index probes in joins. Second, we explore answer-level set relations to further improve the algorithm based on the intuition that if two sets are similar, their answers may have a large overlap. We derive an algorithm which incrementally generates the answer of one set from an already computed answer of another similar set rather than compute the answer from scratch to reduce the computational cost. Finally, we conduct extensive performance studies using 21 real datasets with various data properties from a wide range of domains. The experimental results demonstrate that our algorithm outperforms all the existing algorithms across all datasets and can achieve more than an order of magnitude speedup against the state- of-the-art algorithms.

Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model

A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, which it is modelled through a convective condition (Robin condition). The interface between the two phases is idealized as a mushy region and it is represented following the model of Solomon, Wilson, and Alexiades. An exact similarity solution is obtained when a restriction on data is verified, and it is analysed the relation between the problem considered here and the problem with a temperature condition at the fixed boundary. Moreover, it is proved that the solution to the problem with the convective boundary condition converges to the solution to a problem with a temperature condition when the heat transfer coefficient at the fixed boundary goes to infinity, and it is given an estimation of the difference between these two solutions. Results in this article complete and improve the ones obtained in Tarzia (Comput Appl Math 9:201–211, 1990).

The exact probability law for the approximated similarity from the Minhashing method

We propose a probabilistic setting in which we study the probability law of the Rajaraman and Ullman \textit{RU} algorithm and a modified version of it denoted by \textit{RUM}. These algorithms aim at estimating the similarity index between huge texts in the context of the web. We give a foundation of this method by showing, in the ideal case of carefully chosen probability laws, the exact similarity is the mathematical expectation of the random similarity provided by the algorithm. Some extensions are given. \noindent \textbf{R\'{e}sum\'{e}.} Nous proposons un cadre probabilistique dans lequel nous \'{e}tudions la loi de probabilit\'{e} de l'algorithme de Rajaraman et Ullman \textit{RU} ainsi qu'une version modifi\'{e}e de cet algorithme not\'{e}e \textit{RUM}. Ces alogrithmes visent \`{a} estimer l'indice de la similarit\'{e} entre des textes de grandes tailles dans le contexte du Web. Nous donnons une base de validit\'e de cette m\'{e}thode en montrant que pour des lois de probabilit\'{e}s minutieusement choisies, la similarit\'{e} exacte est l'esp\'{e}rance math\'{e}matique de la similarit\'{e} al\'{e}atoire donn\'{e}e par l'algorithme \textit{RUM}. Des g\'en\'eralisations sont abord\'ees.

Entropy Generation on MHD Flow of Powell-Eyring Fluid Between Radially Stretching Rotating Disk with Diffusion-Thermo and Thermo-Diffusion Effects

AbstractAn investigation is performed for an alyzing the effect of entropy generation on the steady, laminar, axisymmetric flow of an incompressible Powell-Eyring fluid. The flow is considered in the presence of vertically applied magnetic field between radially stretching rotating disks. The Energy and concentration equation is taking into account to investigate the heat dissipation, Soret, Dufour and Joule heating effects. To describe the considered flow non-dimensionalized equations, an exact similarity function is used to reduce a set of the partial differential equation into a system of non-linear coupled ordinary differential equation with the associated boundary conditions. Using homotopy analysis method (HAM), an analytic solution for velocity, temperature and concentration profiles are obtained over the entire range of the imperative parameters. The velocity components, concentration and temperature field are used to determine the entropy generation. Plots illustrate important results on the effect of physical flow parameters. Results obtained by means of HAM are then compared with the results obtained by using optimized homotopy analysis method (OHAM). They are in very good agreement.