A New Method on Measure of Similarity between Interval-Valued Intuitionistic Fuzzy Sets for Pattern Recognition

The theory of fuzzy sets, proposed by Zadeh, has gained successful applications in various fields. Measures of similarity between fuzzy sets have gained attention from researchers for their wide applications in real world. Similarity measures are very useful in some areas, such as pattern recognition, machine learning, decision making and market prediction etc. Many measures of similarity between fuzzy sets have been proposed.

Atanassov presented intuitionistic fuzzy sets which are very effective to deal with vagueness. Gau and Buehere researched vague sets. Bustince and Burillo pointed out that the notion of vague sets is same as that of interval-valued intuitionistic fuzzy sets. Chen and Tan proposed two similarity measures for measuring the degree of similarity between vague sets. De et al. defined some operations on intuitionistic fuzzy sets. Szmidt and Kacprzyk introduced the Hamming distance between intuitionistic fuzzy sets and proposed a similarity measure between intuitionistic fuzzy sets based on the distance.

Modeling the Log Density Distribution with Orthogonal Polynomials

Density estimation is one of the most important and difficult statistical problems. There exists a vast literature on the topic and this is not the goal of the paper to provide an overview of all existing approaches. Mainly three methodologies have been developed: First, a non parametric approach can be used, such as kernel density estimation, penalized maximum likelihood or spline density smoothing. Second, finite mixture can be applied to model multi model distributions. Third, polynomials can be used for the log density modelling and estimation. The latter approach, taken in the present paper, is the simplest and can be used at a preliminary stage of density estimation.

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Identification of optimal topography of the barotropic ocean model in the North Atlantic by variational data assimilation

The use of the data assimilation technique to identify optimal topography is discussed in frames of time-dependent motion governed by nonlinear barotropic ocean model. Assimilation of artificially generated data allows to measure the influence of various error sources and to classify the impact of noise that is present in observational data and model parameters. The choice of length of the assimilation window in 4DVar is discussed. It is shown that using longer window lengths would provide more accurate ocean topography. The topography defined using this technique can be further used in other model runs that start from other initial conditions and are situated in other parts of the model’s attractor.

On irreducible weight representations of a new deformation Uq (sl2) of U (sl2)

Starting from a Hecke R-matrix, Jing and Zhang constructed a new deformation Uq(sl2) of U(sl2) and studied its finite dimensional representations in [Pacific J. Math., 171 (1995), 437-454]. In this note, more irreducible representations for this algebra are constructed. At first, by using methods in non commutative algebraic geometry the points of the spectrum of the category of representations over this new deformation are studied. The construction recovers all finite dimensional irreducible representations classified by Jing and Zhang, and yields new families of infinite dimensional irreducible weight representations.

Spectral theory of abelian categories was first initiated by Gabriel in. In particular, Gabriel defined the injective spectrum of any noetherian Grothendieck category. The injective spectrum consists of isomorphism classes of in decomposable injective objects inthe category endowed with the Zariski topology. If R is a commutative noetherian ring, then the injective spectrum of the category of all R-modules is homeomorphic to the prime spectrum of R. This homeomorphism is a part (and the main step in the argument) of the Gabriel’s reconstruction Theorem, according to which any noetherian commutative scheme can be uniquely reconstructed up to isomorphism from the category of quasi-coherent sheaves on it.

Assessing the Lifestyle of an Extinct Animal Studying its Automatic Nervous System

The titannosaurs became extinct 66 million years ago. Their size restricted their mobility, thermo regulation and blood supply to the organs. The study deployed modeling techniques and statistics to assess the prehistoric physiology, size, metabolism and organ function. 

The Automatic nervous system ensured blood flow to the brain through muscle contraction and special boney structures in the neck called cervical ribs. In order to keep face with the huge metabolic needs of the body, the animal could sleep for only 3 hrs a day and had very high body temperatures which increased with activity. There was an in-built cooling mechanism in their carotid arteries to preserve the brain function. This study identified that growth-lines in osteons in the anterior process of the rib grew faster than dense bone and juveniles grew faster than adults Power spectral analyses of growth intervals in osteons showed a ratio of 1.3 (LF/HF) and for bone 1.4 (LF/HF) NS.The life span of the animal was 100 years.

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Dilatation structures I. Fundamentals

A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is apart of a series of papers which show that such a structure allows to do non-commutative analysis, in the sense of differential calculus, on a large class of metric spaces, some of them fractals. We also describe a formal, universal calculus with binary decorated planar trees, which underlies any dilatation structure.

The purpose of this paper is to introduce dilatation structures on metric spaces. A dilatation structure is a concept in between a group and a differential structure. Any metric space (X,d) endowed with a dilatation structure has an associated tangent bundle. The tangent space at a point is a conical group that is the tangent space has a group structure together with a one-parameter group of auto morphisms. Conical groups generalize Carnot groups, i.e nilpotent groups endowed with a graduation. Each dilatation structure leads to a non-commutative differential calculus on the metric space (X, d).

Conformal Geometry in Engineering and Medicine

With the development of 3D geometric acquisition technologies, massive 3D geometric data are ubiquitous today. It is of great challenges to process and analyze 3D geometric data efficiently and accurately. Computational conformal geometry is an emerging inter-disciplinary field, which combines modern geometry with computer science and offers rigorous and practical tools for tackling massive geometric data processing problems. The concepts and methods in conformal geometry play fundamental roles in many fields in engineering and medicine.

Conformal geometry studies the invariants under the conformal transformation (angle preserving mapping) group. Conformal geometry is more flexible than Riemannian geometry, and more rigid than topology. Conformal geometry is capable of unifying all shapes in real world to one of three canonical shapes, the sphere, the plane, or the hyperbolic disk; conformal geometric algorithms convert 3D geometric processing problems to 2D image processing problems; furthermore, all surfaces in real life have conformal structures, therefore conformal geometric methods are general. These merits make conformal geometry a powerful tool for real applications.

Power of Permutation Tests Using Generalized Additive Models with Bivariate Smoothers

In spatial epidemiology, when applying Generalized Additive Models (GAMs) with a bivariate locally weighted regression smooth over longitude and latitude, a natural hypothesis is whether location is associated with an outcome, i.e. whether the smoothing term is necessary. An approximate chi-square test (ACST) is available but has aninflated type I error rate. Permutation tests can provide appropriately sized alternatives. This research evaluated powers of ACST and four permutation tests: the conditional (CPT), fixed span (FSPT) and fixed multiple span (FMSPT) and unconditional (UPT) permutation tests. 

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On Non ergodic Property of Bose Gas with Weak Pair Interaction

In this paper we prove that Bose gas with weak pair interaction is non ergodic system. In order to prove this fact we consider the divergences in some non equilibrium diagram technique. These divergences are analogous to the divergences in the kinetic equations discovered by Cohen and Dorfman. We develop the general theory of re-normalization of such divergences and illustrate it with some simple examples. The fact that the system is nonergodic leads to the following consequence: to prove that the system tends to the thermal equilibrium we should take into account its behavior on its boundary. In this paper we illustrate this thesis with the Bogoliubov derivation of the kinetic equations.

Invitation to operadic dynamics

In 1963, Gerstenhaber invented an operad calculus in the Hochschild complex of an associative algebra; operads were introduced under the name of pre-Lie systems. In the same year, Stasheff constructed quite an original geometrical operad, which nowadays is called an associahedra. The notion of an operad was further formalised by May as a tool for iterated loop spaces. The main principles of the operad calculus (brace algebra) were presented by Gerstenhaber and Voronov. Some quite remarkable research activity in the operad theory and its applications can be observed in the last decade. It may be said that operads are also becoming an important tool for Quantum Field Theory and deformation quantization.

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Particle-Based or Field-Based Models for Polymer Systems?

Compared to the systems which are composed of simple atoms or molecules, the structures of polymer systems in equilibrium are richer. The main reason is that a polymer molecule is composed of many monomers with the same or different chemical property. 

Take AB di block co polymers as an example. Each molecule has a form AA• • •ABB• ••B where the monomer A and B have different chemical properties. The equilibrium structures for di block co polymer, e.g., lamellar, hexagonal cylinder, bicontinuous gyroidand bcc sphere, etc., have been found for different composition of monomer B through computation and experiments. This equilibrium structures (A-rich and B-rich phase domain) with a length scale of 10-100 nm, is the result of competition of two factors: the repulsion of two chemically distinct monomer A and B, and the conformal entropy penalty. Since monomers A and B are connected in each molecule, monomer A and B are only be separated microscopically. Thus it is called micro separation.

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Bayesian Analysis Using Power Priors with Application to Pediatric Quality of Care

Investigators conducting new research often have access to data from previous studies, and in such cases it is not only scientifically reasonable but also statistically advantageous to incorporate this information into the current analysis.

Consider, for example, the common scenario in which a funding agency finances research incrementally, first requiring a small pilot or feasibility study before funding a more elaborate trial. In such cases, it can be beneficial to incorporate the pilot data into the subsequent analysis to increase the power to detect treatment effects. One strategy for synthesizing results across studies is through a Bayesian modeling approach. Because Bayesian methods can incorporate historical information through a prior distribution, they provide a natural framework for updating information across studies.

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Newton’s laws for a biquaternionic model of the electro-gravimagnetic field, charges, currents, and their interactions

In the present paper, a biquaternionic model of the electro-gravimagnetic (EGM) field is considered, which is called energetic. For this, a complex Hamiltonian form of Maxwell equations (MEs) is used, which allows to get the biquaternionic form of these equations. Note that Maxwell gave his equations in quaternionic form, but the modern form belongs to Heaviside. 

Quaternionic forms of MEs were used by some authors for their solving. Kassandrov applied similar forms for building a unified field model. Here we use the scalar-vector form of biquaternion, which is very impressive and can be adapted for writing the physical variables and equations. Based on Newton’s laws, the biquaternionic transformation equations of charges and currents at the presence of the EGM fields are constructed. The relation of these equations to hydrodynamics equations is considered. The energy conservation law at the presence of the field interaction is found.

Deformations of ternary algebras

The aim of this paper is to extend to ternary algebras the classical theory of formal deformations of algebras introduced by Gerstenhaber. The associativity of ternary algebras is available in two forms, totally associative case or partially associative case. To any partially associative algebra corresponds by anti-commutation a ternary Lie algebra. In this work, we summarize the principal definitions and properties as well as classification in dimension 2 of these algebras. Then we focuss ourselves on the partially associative ternary algebras, we construct the first groups of a cohomolgy adapted to formal deformations and then we work out a theory of formal deformation in a way similar to the binary algebras.

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Mathematical Approaches to the NMR Peak-Picking Problem

Nuclear magnetic resonance (NMR) spectroscopy and X-ray crystallography are two experimental techniques used to determine the three-dimensional structures of proteins. 

NMR spectroscopy has the unique ability to capture proteins in vivo. Currently, protein structure determination by NMR follows the procedure proposed by Kurt Wüth rich in 1986. This procedure consists of peak picking, resonance assignment, nuclear overhauser effect (NOE) assignment and structure calculation steps. Among the four steps, peak picking is time consuming and requires extensive expert knowledge. Computational methods designed to automate and improve this step are still needed. The inputs to the peak picking problem are an NMR spectrum or a set of spectra, whereas the outputs are the lists of peaks (signals) identified from these spectra.

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On compact realifications of exceptional simple Kantor triple systems

Let A be the realification of the matrix algebra determined by Jordan algebra of hermitian matrices of order three over complex composition algebra. We define an in volutive auto morphism on A with a certain action on the triple system obtained from A which give models of simple compact Kantor triple systems. In addition, we give an explicit formula for the canonical trace form and the classification for these triples and their corresponding exceptional real simple Lie algebras. Moreover, we present all realifications of complex exceptional simple Lie algebras as Kantor algebras for a compact simple Kantor triple system defined on a structurable algebra of skew-dimension one.

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In search of a Mathematical Theory Using Space-Time

Two types of matter namely observable subluminal matter called tardyon (locality) and the unobservable superluminal matter called tachyon (non-locality) co-exist in a motion. While the Tardyon can be converted as Tachyon, Tachyon alters itself as Tardyon.  The Tardyonic rotating motion produces the centrifugal force, and tachyonic rotating motion produces the centripetal force, that is gravity. By applying the tardyonic and tachyonic coexistence principle, this study tries to prepare a new gravitational formula to establish the mathematical theory of Space Time.

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