Similarity Type Research Articles

An analysis of alignment and integral based kernels for machine learning from vessel trajectories

In this paper we present an analysis of the application of the two most important types of similarity measures for moving object trajectories in machine learning from vessel movement data. These similarities are applied in the tasks of clustering, classification and outlier detection. The first similarity type are alignment measures, such as dynamic time warping and edit distance. The second type are based on the integral over time between two trajectories. Following earlier work we define these measures in the context of kernel methods, which provide state-of-the-art, robust algorithms for the tasks studied. Furthermore, we include the influence of applying piecewise linear segmentation as pre-processing to the vessel trajectories when computing alignment measures, since this has been shown to give a positive effect in computation time and performance.In our experiments the alignment based measures show the best performance. Regular versions of edit distance give the best performance in clustering and classification, whereas the softmax variant of dynamic time warping works best in outlier detection. Moreover, piecewise linear segmentation has a positive effect on alignments, due to the fact that salient points in a trajectory, especially important in clustering and outlier detection, are highlighted by the segmentation and have a large influence in the alignments. Based on our experiments, integral over time based similarity measures are not well-suited for learning from vessel trajectories.

One-Dimensional Nonlinear Stefan Problems in Storm’s Materials

We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material x > 0; with phase change temperature Tf : We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. In the first case, we assume a heat flux boundary condition of the type q(t) = q 0 t , and in the second case, we assume a temperature boundary condition T = Ts < Tf at the fixed face. Solutions of similarity type are obtained in both cases, and the equivalence of the two problems is demonstrated. We also give procedures in order to compute the explicit solution.

The simplest protoalgebraic logic

The logic is the sentential logic defined in the language with just implication → by the axiom of reflexivity or identity “” and the rule of Modus Ponens “from φ and to infer ψ”. The theorems of this logic are exactly all formulas of the form . We argue that this is the simplest protoalgebraic logic, and that in it every set of assumptions encodes in itself not only all its consequences but also their proofs. In this paper we study this logic from the point of view of abstract algebraic logic, and in particular we use it as a relatively natural counterexample to settle some open problems in this theory. It appears that this logic has almost no properties: it is neither equivalential nor weakly algebraizable; it does not have an algebraic semantics; it does not satisfy any form of the Deduction Theorem, other than the most general parameterized and local one that all protoalgebraic logics satisfy; it is not filter-distributive; and so on. It satisfies some forms of the interpolation property but in a rather trivial way. Very few things are known about its algebraic counterpart, save that its intrinsic variety is the class of all algebras of the similarity type.

Categorical Abstract Algebraic Logic: Referential Algebraic Semantics

Wojcicki has provided a characterization of selfextensional logics as those that can be endowed with a complete local referential semantics. His result was extended by Jansana and Palmigiano, who developed a duality between the category of reduced congruential atlases and that of reduced referential algebras over a fixed similarity type. This duality restricts to one between reduced atlas models and reduced referential algebra models of selfextensional logics. In this paper referential algebraic systems and congruential atlas systems are introduced, which abstract referential algebras and congruential atlases, respectively. This enables the formulation of an analog of Wojcicki's Theorem for logics formalized as ?-institutions. Moreover, the results of Jansana and Palmigiano are generalized to obtain a duality between congruential atlas systems and referential algebraic systems over a fixed categorical algebraic signature. In future work, the duality obtained in this paper will be used to obtain one between atlas system models and referential algebraic system models of an arbitrary selfextensional ?-institution. Using this latter duality, the characterization of fully selfextensional deductive systems among the selfextensional ones, that was obtained by Jansana and Palmigiano, can be extended to a similar characterization of fully selfextensional ?-institutions among appropriately chosen classes of selfextensional ones.

Boolean-like algebras

Using Vaggione’s concept of central element in a double-pointed algebra, we introduce the notion of Boolean-like variety as a generalisation of Boolean algebras to an arbitrary similarity type. Appropriately relaxing the requirement that every element be central in any member of the variety, we obtain the more general class of semi-Boolean-like varieties, which still retain many of the pleasing properties of Boolean algebras. We prove that a double-pointed variety is discriminator if and only if it is semi-Boolean-like, idempotent, and 0-regular. This theorem yields a new Maltsev-style characterisation of double-pointed discriminator varieties.

Image based measurements for evaluation of pelvic organ prolapse

Magnetic resonance imaging (MRI) measurements are essential for the diagnosis of pelvic organ prolapse given the inaccuracy of clinical examination. However, MRI pelvic floor measurements are currently performed manually and can be inconsistent and time-consuming. In this paper, we present a scheme for semi-automatic measurement modeling on MRI based on image segmentation and intersecting point identification methods. The segmentation algorithm is a multi-stage mechanism based on block grouping, support vector machine classification, morphological operation and prior shape information. Block grouping is achieved by classifying blocks as bone or background based on image texture features. The classified blocks are then used to find the initial segmentation by the first phase morphological opening. Prior shape information is incorporated into the initial segmentation to obtain the final segmentation using registration with the similarity type transformation. After segmentation, points of reference that are used for pelvic floor measurements are identified using morphological skeleton operation. The experiments on the MRI images show that the presented scheme can detect the points of reference on the pelvic floor structure to determine the reference lines needed for the assessment of pelvic organ prolapse. This will lead towards more consistent and faster pelvic organ prolapse diagnosis on dynamic MRI studies, and possible screening procedures for predicting predisposition to pelvic organ prolapse by radiologic evaluation of pelvic floor measurements.

Satellite Image Retrieval using Modified Block Truncation Coding and Kekre Transform Patterns

Satellite images and Content Based Image Retrieval are interesting topics of research since years. Specifically, CBIR is on developing technologies for bridging the semantic gap that currently prevents wide-deployment of image content-based search engines. Image search engines currently in use are mostly rely on human generated data, such as text. Annotation of an image is totally depend on the person’s perception who is going to store it into database. It is time-consuming as well as error prone. Therefore search engine using text input results in various non-relevant images. To overcome drawbacks of text based image retrieval, Content based image retrieval is introduced where retrieval of images is totally depend on the features of images. Mostly, content-based methods are based on low-level descriptions, while high-level or semantic descriptions are beyond current capabilities. In this paper, we will try to implement the technique to fill this gap. This technique can eventually be extended to allow for content-based similarity type of search, to find out different query blocks from satellite image. We will fire an object as a query and most similar blocks will get retrieved. This will help out to trace particular object from large satellite image.

Is every matrix similar to a polynomial in a companion matrix?

Given a field F, an integer n⩾1, and a matrix A∈Mn(F), are there polynomials f,g∈F[X], with f monic of degree n, such that A is similar to g(Cf), where Cf is the companion matrix of f? For infinite fields the answer is easily seen to positive, so we concentrate on finite fields. In this case we give an affirmative answer, provided |F|⩾n-2. Moreover, for any finite field F, with |F|=m, we construct a matrix A∈Mm+3(F) that is not similar to any matrix of the form g(Cf).Of use above, but also of independent interest, is a constructive procedure to determine the similarity type of any given matrix g(Cf) purely in terms of f and g, without resorting to polynomial roots in F or in any extension thereof. This, in turn, yields an algorithm that, given g and the invariant factors of any A, returns the elementary divisors of g(A). It is a rational procedure, as opposed to the classical method that uses the Jordan decomposition of A to find that of g(A).Finally, extending prior results by the authors, we show that for an integrally closed ring R with field of fractions F and companion matrices C,D the subalgebra R〈C,D〉 of Mn(R) is a free R-module of rank n+(n-m)(n-1), where m is the degree of gcd(f,g)∈F[X], and a presentation for R〈C,D〉 is given in terms of C and D. A counterexample is furnished to show that R〈C,D〉 need not be a free R-module if R is not integrally closed. The preceding information is used to study Mn(R), and others, as R[X]-modules.

ON SEMILATTICE-BASED LOGICS WITH AN ALGEBRAIZABLE ASSERTIONAL COMPANION

This paper studies some properties of the so-called semilattice-based logics (which are dened in a standard way using only the order relation from a variety of algebras that have a semilattice reduct with maximum) under the assumption that its companion assertional logic (dened from the same variety of algebras using the top element as representing truth) is algebraizable. This describes a very common situation, and the conclusion of the paper is that these semilattice-based logics exhibit some of the good behaviour of protoalgebraic logics, without being necessarily so. The main result is that all these logics have enough Leibniz lters, a fact previously known in the literature to occur only for protoalgebraic logics. Another signicant result is that the two companion logics coincide if and only if one of them enjoys the characteristic property of the other, that is, if and only if the semilattice-based logic is algebraizable, and if and only if its assertional companion is selfextensional. When these conditions are met, then the (unique) logic is nitely, regularly and strongly algebraizable and fully Fregean; this places it at some of the highest ranks in both the Leibniz hierarchy and the Frege hierarchy. Let K be a class of algebras of the same (arbitrary) similarity type. The class K is said to be semilattice-based when each algebra in K has a semilattice reduct uniformly dened

Long Nonlinear Surface Waves in the Presence of a Variable Current

We investigate the eigenvalue problem governing the propagation of long nonlinear surface waves when there is a current beneath the surface, y being the vertical coordinate. The amplitude of such waves evolves according to the KdV equation and it was proved by Burns [1] that their speed of propagation c is such that there is no critical layer (i.e., c lies outside the range of ). If, however, the critical layer is nonlinear, the result of Burns does not necessarily apply because the phase change of linear theory then vanishes. In this paper, we consider specific velocity profiles and determine c as a function of Froude number for modes with nonlinear critical layers. Such modes do not always exist, the case of the asymptotic suction profile being a notable example. We find, however, that singular modes can be obtained for boundary layer profiles of the Falkner–Skan similarity type, including the Blasius case. These and other examples are treated and we examine singular solutions of the Rayleigh equation to gain insight about the long wave limit of such solutions.

Weak homomorphisms between functorial algebras

AbstractIn universal algebra, homomorphisms are usually considered between algebras of the same similarity type. Different from that, the notion of a weak homomorphism, as introduced by E. Marczewski in 1961, does not depend on a signature, but only on the clones of term operations generated by the examined algebras. We generalize this idea by defining weak homomorphisms between

Explicit solution for a Stefan problem with variable latent heat and constant heat flux boundary conditions

In Voller, Swenson and Paola [V.R. Voller, J.B. Swenson, C. Paola, An analytical solution for a Stefan problem with variable latent heat, Int. J. Heat Mass Transfer 47 (2004) 5387–5390], and Lorenzo-Trueba and Voller [J. Lorenzo-Trueba, V.R. Voller, Analytical and numerical solution of a generalized Stefan problem exhibiting two moving boundaries with application to ocean delta formation, J. Math. Anal. Appl. 366 (2010) 538–549], a model associated with the formation of sedimentary ocean deltas is studied through a one-phase Stefan-like problem with variable latent heat. Motivated by these works, we consider a two-phase Stefan problem with variable latent of fusion and initial temperature, and constant heat flux boundary conditions. We obtain the sufficient condition on the data in order to have an explicit solution of a similarity type of the corresponding free boundary problem for a semi-infinite material. Moreover, the explicit solution given in the first quoted paper can be recovered for a particular case by taking a null heat flux condition at the infinity.

POSITIVE FRAGMENTS OF RELEVANCE LOGIC AND ALGEBRAS OF BINARY RELATIONS

We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.

The Stefan problem with temperature-dependent thermal conductivity and a convective term with a convective condition at the fixed face

We study a one-phase Stefan problem for a semi-infinitematerial with temperature-dependent thermal conductivity and aconvective term with a convective boundary condition at the fixedface $x=0$. We obtain sufficient conditions for data in orderto have a parametric representationof the solution of the similarity type for $t \geq t_0 > 0$ with $t_0 $ an arbitrary positive time. We obtain explicitsolutions through the unique solution of a Cauchy problem with thetime as a parameter and we also give an algorithm in order tocompute the explicit solution.

Exact Solutions for Nonclassical Stefan Problems

We consider one‐phase nonclassical unidimensional Stefan problems for a source function F which depends on the heat flux, or the temperature on the fixed face x = 0. In the first case, we assume a temperature boundary condition, and in the second case we assume a heat flux boundary condition or a convective boundary condition at the fixed face. Exact solutions of a similarity type are obtained in all cases.

Explicit solutions for one-dimensional two-phase free boundary problems with either shrinkage or expansion

Abstract We consider a one-dimensional solidification of a pure substance which is initially in liquid state in a bounded interval [ 0 , l ] . Initially, the liquid is above the freezing temperature, and cooling is applied at x = 0 while the other end x = l is kept adiabatic. At the time t = 0 , the temperature of the liquid at x = 0 comes down to the freezing point and solidification begins, where x = s ( t ) is the position of the solid–liquid interface. As the liquid solidifies, it shrinks ( 0 r 1 ) or expands ( r 0 ) and appears a region between x = 0 and x = r s ( t ) , with r 1 . Temperature distributions of the solid and liquid phases and the position of the two free boundaries ( x = r s ( t ) and x = s ( t ) ) in the solidification process are studied. For three different cases, changing the condition on the free boundary x = r s ( t ) (temperature boundary condition, heat flux boundary condition and convective boundary condition) an explicit solution is obtained. Moreover, the solution of each problem is given as a function of a parameter which is the unique solution of a transcendental equation and for two of the three cases a condition on the parameter must be verified by data of the problem in order to have an instantaneous phase-change process. In all the cases, the explicit solution is given by a representation of the similarity type.

Double Basic Algebras

To any bounded lattice with section antitone bijections can be assigned an algebra with two binary, two unary and a nullary operations satisfying similar axioms as a basic algebra. Due to the doubled similarity type, this algebra is called a double basic algebra. Also conversely, every double basic algebra induces a bounded lattice equipped with antitone bijections in every section. We study properties of double basic algebras, their interval algebras and several conclusions of the so-called pseudo-commutativity.

Computing congruences efficiently

For a fixed similarity type which is at least binary, we show there is a linear time algorithm for computing the principal congruence generated by a pair of elements.

Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids

We study varieties with a term-definable poset structure, po-groupoids. It is known that connected posets have the strict refinement property (SRP). In [arXiv:0808.1860v1 [math.LO]] it is proved that semidegenerate varieties with the SRP have definable factor congruences and if the similarity type is finite, directly indecomposables are axiomatizable by a set of first-order sentences. We obtain such a set for semidegenerate varieties of connected po-groupoids and show its quantifier complexity is bounded in general.

Algebras of Relations and Relevance Logic

We prove that algebras of binary relations whose similarity type includes intersection, composition, converse negation and the identity constant form a non-finitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of relevant logic with respect to binary relations.