Making an extensive use of small transfinite topological dimension trind, we ascribe to every metric space X an ordinal number (or −1 or Ω) tHD(X), and we call it the transfinite Hausdorff dimension of X. This ordinal number shares many common features with Hausdorff dimension. It is monotone with respect to subspaces, it is invariant under bi-Lipschitz maps (but in general not under homeomorph...

Given a Galois covering of complete spin manifolds where the base metric has PSC near infinity, we prove that for small enough epsilon > 0, spectral projection Dirac operator finite trace in Atiyah von Neumann algebra. This allows us to define L2 index even case and its compatibility with Xie-Yu higher index. We also deduce versions classical Gromov-Lawson relative theorems. Finally, briefly di...

Four synthetic peptides (Peptidyl MIMs; Demeter Biotechnologies, Inc.) were evaluated for their in vitro activity against Acholeplasma laidlawii. Fifty percent effective concentration values ranged from 1 to 15 microM. Three of these compounds are more lethal than cecropin B against A. laidlawii.

A tandem solar cell device whose sub-cells are fabricated exclusively from small molecules (SMs) through both solution-processed and vacuum-processed deposition techniques is described. The front sub-cell's active layer consists of a bulk heterojunction (BHJ) DPP(TBFu)2:PC70BM device while the back cell has a typical bilayer structure employing a 2,4-bis[4-(N,N-diisobutylamino)-2,6-dihydroxyphe...

This paper studies the problem of k-optimal-location-selection (kOLS) retrieval in metric spaces. Given a set DA of customers, a set DB of locations, a constrained region R, and a critical distance dc , a metric kOLS (MkOLS) query retrieves k locations in DB that are outside R but have the maximal optimality scores. Here, the optimality score of a location l 2 DB located outside R is defined as...

This paper focuses on the study of open curves in a Riemannian manifold M , and proposes a reparametrization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. in [13] to define a Riemannian metric on the space of immersions M = Imm([0, 1],M) by pullback of a natural metric on the tangent bundle TM. This induces a first-o...

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The metrization of the space of neural responses is an ongoing research program seeking to find natural ways to describe, in geometrical terms, the sets of possible activities in the brain. One component of this program are the spike metrics, notions of distance between two spike trains recorded from a neuron. Alignment spike metrics work by identifying “equivalent” spikes in one train and the ...

Learning a typical image enhancement pipeline involves minimization of a loss function between enhanced and reference images. While L1 and L2 losses are perhaps the most widely used functions for this purpose, they do not necessarily lead to perceptually compelling results. In this paper, we show that adding a learned no-reference image quality metric to the loss can significantly improve enhan...

Abstract. Histograms are commonly used for representing summaries of observed data and they can be considered non parametric estimates of probability distributions. Symbolic Data Analysis formalized the concept of histogram symbolic variable, as a variable which allows to describe statistical units by histograms instead of single values. In this paper we present a linear regression model for mu...