Search results for "Graph theory"
showing 10 items of 784 documents
Counting and equidistribution in quaternionic Heisenberg groups
2020
AbstractWe develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.
Mappings of finite distortion: the degree of regularity
2005
This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)⩾1 be a measurable function defined on a domain Ω⊂Rn,n⩾2, and such that exp(βK(x))∈Lloc1(Ω), β>0. We show that there exist two universal constants c1(n),c2(n) with the following property: Let f be a mapping in Wloc1,1(Ω,Rn) with |Df(x)|n⩽K(x)J(x,f) for a.e. x∈Ω and such that the Jacobian determinant J(x,f) is locally in L1log−c1(n)βL. Then automatically J(x,f) is locally in L1logc2(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite disto…
Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains
2019
AbstractThe conformal mapping $$f(z)=(z+1)^2 $$ f ( z ) = ( z + 1 ) 2 from $${\mathbb {D}}$$ D onto the standard cardioid has a homeomorphic extension of finite distortion to entire $${\mathbb {R}}^2 .$$ R 2 . We study the optimal regularity of such extensions, in terms of the integrability degree of the distortion and of the derivatives, and these for the inverse. We generalize all outcomes to the case of conformal mappings from $${\mathbb {D}}$$ D onto cardioid-type domains.
Free Minor Closed Classes and the Kuratowski theorem
2009
Free-minor closed classes [2] and free-planar graphs [3] are considered. Versions of Kuratowski-like theorem for free-planar graphs and Kuratowski theorem for planar graphs are considered.
Calculating minimum discrepancy to assess the nestedness of species assemblages
2009
Nestedness is a pattern whereby species-poor assemblages are composed of subsets of the species occurring in richer assemblages. One of the most commonly used measures of the degree of nestedness for presence-absence matrices is the ‘discrepancy’ metric. A hitherto neglected property of that metric is that it may take several values for a given site-by-species matrix in the presence of ties in the marginal totals. This complicates the quantification of nestedness for the observed presence-absence matrix, as well as the assessment of statistical significance, which is typically achieved through Monte Carlo simulations. A solution to the problem is to calculate the minimum discrepancy using a…
ChemInform Abstract: LOCATION OF TRANSITION STATES AND STABLE INTERMEDIATES BY MINIMAX/MINIMI OPTIMIZATION OF SYNCHRONOUS TRANSIT PATHWAYS
1983
The MINIMAX/MINIMI concept for the location of transition states and/or stable intermediates of chemical reactions is introduced, based on the synchronous transit method. According to this strategy, minimization of quadratic synchronous transit path maxima or minima is achieved by constrained exhaustive optimization of internal coordinates. The method and its efficiency are demonstrated for two-dimensional model surfaces as well as for thermally allowed electrocyclic interconversions of cyclopropyl-/allyl-cation and cyclobutene-/butadiene (gauche) within the framework of MNDO-SCF calculations. Thus, in both cases a direct comparison with the exact solution determined by minimization of the …
Impact of physicians’ participation in non-interventional post-marketing studies on their prescription habits: A retrospective 2-armed cohort study i…
2020
Background Non-interventional post-marketing studies (NIPMSs) sponsored by pharmaceutical companies are controversial because, while they are theoretically useful instruments for pharmacovigilance, some authors have hypothesized that they are merely marketing instruments used to influence physicians’ prescription behavior. So far, it has not been shown, to our knowledge, whether NIPMSs actually do have an influence on prescription behavior. The objective of this study was therefore to investigate whether physicians’ participation in NIPMSs initiated by pharmaceutical companies has an impact on their prescription behavior. In addition, we wanted to analyze whether specific characteristics of…
Computational Analysis Workshop: Comparing Four Approaches to Melodic Analysis
2009
We compare four computational approaches of melodic analysis according to diverse approach aspects: input type (monophonic or polyphonic), pattern identification type (strict or similar), analysis segmentation, aim of approach, motivic pattern representation, and type of result representations. The considered four computational approaches are the following: a similarity neighbourhood approach by Adiloglu (Adiloglu and Obermayer 2006a, b), a multiple viewpoint representation and discovery approach by Anagnostopoulou (Anagnostopoulou, Share and Conklin 2006), a topological approach by Buteau (2005), and an approach based on multidimensional closed pattern mining by Lartillot (Lartillot and To…
A Fuzzy-Clustering Based Approach for Measuring Similarity Between Melodies
2017
Symbolic melodic similarity aims to evaluate the degree of likeness of two or more sequences of notes. In this work, we propose the use of fuzzy c-means clustering as a tool for the measurement of the similarity between two melodies with a different number of notes. Moreover, we present an algorithm, FOCM, implemented in a computer program written in C\(\sharp \) able to read two melodies from files with MusicXML format and to perform the clustering to calculate the dissimilarity between any two melodies. In addition, for each iteration step in the convergence process of the algorithm, a family of intermediate states (transition melodies) are obtained that can be used as new thematic materi…
Graph Topology Learning and Signal Recovery Via Bayesian Inference
2019
The estimation of a meaningful affinity graph has become a crucial task for representation of data, since the underlying structure is not readily available in many applications. In this paper, a topology inference framework, called Bayesian Topology Learning, is proposed to estimate the underlying graph topology from a given set of noisy measurements of signals. It is assumed that the graph signals are generated from Gaussian Markov Random Field processes. First, using a factor analysis model, the noisy measured data is represented in a latent space and its posterior probability density function is found. Thereafter, by utilizing the minimum mean square error estimator and the Expectation M…