45 research outputs found
Performance of Hyperbolic Geometry Models on Top-N Recommendation Tasks
We introduce a simple autoencoder based on hyperbolic geometry for solving
standard collaborative filtering problem. In contrast to many modern deep
learning techniques, we build our solution using only a single hidden layer.
Remarkably, even with such a minimalistic approach, we not only outperform the
Euclidean counterpart but also achieve a competitive performance with respect
to the current state-of-the-art. We additionally explore the effects of space
curvature on the quality of hyperbolic models and propose an efficient
data-driven method for estimating its optimal value.Comment: Accepted at ACM RecSys 2020; 7 page
Auger feed mixer with perforated winding
The article presents the results of an analysis of existing feed mixers and feed mixer patents. Disadvantages such as high power consumption, low uniformity of mixed feed, and high metal consumption have been identified. We have presented the design of a screw feed mixer
Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators
We study the relation between vertex operators in AdS_5 x S^5 and classical
spinning string solutions. In the limit of large quantum numbers the treatment
of vertex operators becomes semiclassical. In this regime, a given vertex
operator carrying a certain set of quantum numbers defines a singular solution.
We show in a number of examples that this solution coincides with the classical
string solution with the same quantum numbers but written in a different
two-dimensional coordinate system. The marginality condition imposed on an
operator yields a relation between the energy and the other quantum numbers
which is shown to coincide with that of the corresponding classical string
solution. We also argue that in some cases vertex operators in AdS_5 x S^5
cannot be given by expressions similar to the ones in flat space and a more
involved consideration is required.Comment: 23 pages, 1 Figur
Caged Black Holes: Black Holes in Compactified Spacetimes I -- Theory
In backgrounds with compact dimensions there may exist several phases of
black objects including the black-hole and the black-string. The phase
transition between them raises puzzles and touches fundamental issues such as
topology change, uniqueness and Cosmic Censorship. No analytic solution is
known for the black hole, and moreover, one can expect approximate solutions
only for very small black holes, while the phase transition physics happens
when the black hole is large. Hence we turn to numerical solutions. Here some
theoretical background to the numerical analysis is given, while the results
will appear in a forthcoming paper. Goals for a numerical analysis are set. The
scalar charge and tension along the compact dimension are defined and used as
improved order parameters which put both the black hole and the black string at
finite values on the phase diagram. Predictions for small black holes are
presented. The differential and the integrated forms of the first law are
derived, and the latter (Smarr's formula) can be used to estimate the ``overall
numerical error''. Field asymptotics and expressions for physical quantities in
terms of the numerical ones are supplied. Techniques include ``method of
equivalent charges'', free energy, dimensional reduction, and analytic
perturbation for small black holes.Comment: 23 pages. v3: version to be published in PRD, 3 references adde