purpose : to assess the results of 1-minute and 5-minute schirmer's test (st) when the eyes are open (sto) and closed (stc) in normal participants. methods : in a comparative, observational case series study, 34 normal volunteers were included in the study. inclusion criteria were normal ophthalmologic findings except for refractive errors, no use of contact lenses, no history of previous ...

Contour detection may be mediated by lateral interactions between neighboring cortical neurons whose receptive fields have collinear axes of preferred orientation. This hypothesis was tested in psychophysical experiments and computer simulations using a contour detection task in which observers searched for groups of Gabor patches that followed spatially extended contour paths embedded in noise...

We construct the first examples of manifolds, the simplest one being S3×S4×R5, which admit infinitely many complete nonnegatively curved metrics with pairwise nonhomeomorphic souls. According to the soul theorem of J. Cheeger and D. Gromoll [CG72], a complete open manifold of nonnegative sectional curvature is diffeomorphic to the total space of the normal bundle of a compact totally geodesic s...

A Heegaard diagram for a 3-manifold is regarded as a pair of simplexes in the complex of curves on a surface and a Heegaard splitting as a pair of subcomplexes generated by the equivalent diagrams. We relate geometric and combinatorial properties of these subcomplexes with topological properties of the manifold and/or the associated splitting. For example we show that for any splitting of a 3-m...

In this section, we derive in detail the closed form solution of problem (12) for binary pairwise factors (Sect. 4.1). Recall that the marginal polytope M(G a) is given by:

In the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive resul...

At every point, a smooth plane curve can be approximated, to second order, by circle; this circle is called osculating. One may think of the osculating as passing through three infinitesimally close points curve. A vertex point at which hyper-osculates: it approximates third order. Equivalently, critical curvature function. Consider (necessarily non-closed) curve, free from vertices. The classi...

Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise th...

In this section, we give a brief review of the measure theory which will be used in later sections. We use [R, Chapters 1 and 2] as our main resource. A σ-algebra on a set X is a collectionM of subsets of X such that ∅ ∈M, if S ∈M, then X \ S ∈ M, and if a countable collection S1, S2, . . . ∈ M, then ∪i=1Si ∈ M. That is, M is closed under complements and countable unions, and contains the empty...

In this letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations (DDE), which shows excellent agreement with results based on explicit stochastic simulations of non-Markovian epidemics on networks. Furthermore, we analytically compu...