Geodesic congruences and inhomogeneous heisenberg ferromagnet

A geometric method to find exact solutions to the one-dimensional classical non-homogeneous Heisenberg ferromagnet model is proposed. By constructing a one-parameter family of geodesics on an arbitrary surface in E3 we are able to find both the coupling function of the model and the particular solution to this model

Triangulating the Real Projective Plane

We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general position, i.e., no three of them are collinear. We also design an algorithm for triangulating P2 if this necessary condition holds. As far as we know, this is the first computational result on the real projective plane

AVEID: Automatic Video System for Measuring Engagement In Dementia

Engagement in dementia is typically measured using behavior observational scales (BOS) that are tedious and involve intensive manual labor to annotate, and are therefore not easily scalable. We propose AVEID, a low cost and easy-to-use video-based engagement measurement tool to determine the engagement level of a person with dementia (PwD) during digital interaction. We show that the objective behavioral measures computed via AVEID correlate well with subjective expert impressions for the popular MPES and OME BOS, confirming its viability and effectiveness. Moreover, AVEID measures can be obtained for a variety of engagement designs, thereby facilitating large-scale studies with PwD populations

An Upper Bound on the Average Size of Silhouettes

It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides, for the first time, theoretical evidence supporting this for a large class of objects, namely for polyhedra that approximate surfaces in some reasonable way; the surfaces may be non-convex and non-differentiable and they may have boundaries. We prove that such polyhedra have silhouettes of expected size $O(\sqrt{n})$ where the average is taken over all points of view and n is the complexity of the polyhedron

Interaction Grammars

Interaction Grammar (IG) is a grammatical formalism based on the notion of polarity. Polarities express the resource sensitivity of natural languages by modelling the distinction between saturated and unsaturated syntactic structures. Syntactic composition is represented as a chemical reaction guided by the saturation of polarities. It is expressed in a model-theoretic framework where grammars are constraint systems using the notion of tree description and parsing appears as a process of building tree description models satisfying criteria of saturation and minimality

Chromista

The concept of chromists, at its most expansive, includes the heterokonts (stramenopiles), alveolates, rhizarians, heliozoans, telonemians, haptophytes and cryptophytes. There is mounting evidence that this grouping is not valid. Even in the narrowest sense (the heterokonts), chromists include very diverse forms, exhibiting a great variety of trophic mechanisms. This great diversity in form and feeding make it difficult to identify any unifying features, but molecular phylogenetic studies have shown that this group of organisms is indeed monophyletic. The distribution of morphological characters over reconstructed trees allows for the identification of potential synapomorphic characters that have been secondarily lost or modified across the group. These include a combination of mitochondria with tubular cristae; the biflagellate heterokont condition; and, if photosynthetic, then with chlorophyll c, girdle lamellae and four membranes around the chloroplast, the outer continuous with the nuclear envelope. Heterotrophy appears to be ancestral but is also occasionally a derived state from autotrophic forms.Web of Scienc

Time- and Space-Efficient Evaluation of Some Hypergeometric Constants

The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $\zeta(3)$ to $d$ decimal digits have time complexity $O(M(d) \log^2 d)$ and space complexity of $O(d \log d)$ or $O(d)$. Following work from Cheng, Gergel, Kim and Zima, we present a new algorithm with the same asymptotic complexity, but more efficient in practice. Our implementation of this algorithm improves slightly over existing programs for the computation of $\pi$, and we announce a new record of 2 billion digits for $\zeta(3)$

Links between different analytic descriptions of constant mean curvature surfaces

Transformations between different analytic descriptions of constant mean curvature (CMC) surfaces are established. In particular, it is demonstrated that the system $$\begin{split} &\partial \psi_{1} = (|\psi_{1}|^{2} + |\psi_{2}|^{2}) \psi_{2} \\ &\bar{\partial} \psi_{2} =- (|\psi_{1}|^{2} + |\psi_{2}|^{2}) \psi_{1} \end{split}$$ descriptive of CMC surfaces within the framework of the generalized Weierstrass representation, decouples into a direct sum of the elliptic Sh-Gordon and Laplace equations. Connections of this system with the sigma model equations are established. It is pointed out, that the instanton solutions correspond to different Weierstrass parametrizations of the standard sphere $S^{2} \subset E^{3}$