3,611 research outputs found
On Maximal Unbordered Factors
Given a string of length , its maximal unbordered factor is the
longest factor which does not have a border. In this work we investigate the
relationship between and the length of the maximal unbordered factor of
. We prove that for the alphabet of size the expected length
of the maximal unbordered factor of a string of length~ is at least
(for sufficiently large values of ). As an application of this result, we
propose a new algorithm for computing the maximal unbordered factor of a
string.Comment: Accepted to the 26th Annual Symposium on Combinatorial Pattern
Matching (CPM 2015
Visualizing recommendations to support exploration, transparency and controllability
Research on recommender systems has traditionally focused on the development of algorithms to improve accuracy of recommendations. So far, little research has been done to enable user interaction with such systems as a basis to support exploration and control by end users. In this paper, we present our research on the use of information visualization techniques to interact with recommender systems. We investigated how information visualization can improve user understanding of the typically black-box rationale behind recommendations in order to increase their perceived relevance and meaning and to support exploration and user involvement in the recommendation process. Our study has been performed using TalkExplorer, an interactive visualization tool developed for attendees of academic conferences. The results of user studies performed at two conferences allowed us to obtain interesting insights to enhance user interfaces that integrate recommendation technology. More specifically, effectiveness and probability of item selection both increase when users are able to explore and interrelate multiple entities - i.e. items bookmarked by users, recommendations and tags. Copyright © 2013 ACM
Non-Commutative Corrections to the MIC-Kepler Hamiltonian
Non-commutative corrections to the MIC-Kepler System (i.e. hydrogen atom in
the presence of a magnetic monopole) are computed in Cartesian and parabolic
coordinates. Despite the fact that there is no simple analytic expression for
non-commutative perturbative corrections to the MIC-Kepler spectrum, there is a
term that gives rise to the linear Stark effect which didn't exist in the
standard hydrogen model.Comment: 5 page
Twist Deformation of Rotationally Invariant Quantum Mechanics
Non-commutative Quantum Mechanics in 3D is investigated in the framework of
the abelian Drinfeld twist which deforms a given Hopf algebra while preserving
its Hopf algebra structure. Composite operators (of coordinates and momenta)
entering the Hamiltonian have to be reinterpreted as primitive elements of a
dynamical Lie algebra which could be either finite (for the harmonic
oscillator) or infinite (in the general case). The deformed brackets of the
deformed angular momenta close the so(3) algebra. On the other hand, undeformed
rotationally invariant operators can become, under deformation, anomalous (the
anomaly vanishes when the deformation parameter goes to zero). The deformed
operators, Taylor-expanded in the deformation parameter, can be selected to
minimize the anomaly. We present the deformations (and their anomalies) of
undeformed rotationally-invariant operators corresponding to the harmonic
oscillator (quadratic potential), the anharmonic oscillator (quartic potential)
and the Coulomb potential.Comment: 20 page
Novel inferences of ionisation & recombination for particle/power balance during detached discharges using deuterium Balmer line spectroscopy
The physics of divertor detachment is determined by divertor power, particle
and momentum balance. This work provides a novel analysis technique of the
Balmer line series to obtain a full particle/power balance measurement of the
divertor. This supplies new information to understand what controls the
divertor target ion flux during detachment.
Atomic deuterium excitation emission is separated from recombination
quantitatively using Balmer series line ratios. This enables analysing those
two components individually, providing ionisation/recombination source/sinks
and hydrogenic power loss measurements. Probabilistic Monte Carlo techniques
were employed to obtain full error propagation - eventually resulting in
probability density functions for each output variable. Both local and overall
particle and power balance in the divertor are then obtained. These techniques
and their assumptions have been verified by comparing the analysed synthetic
diagnostic 'measurements' obtained from SOLPS simulation results for the same
discharge. Power/particle balance measurements have been obtained during
attached and detached conditions on the TCV tokamak.Comment: The analysis results of this paper were formerly in arXiv:1810.0496
Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect
Our previous ``exotic'' particle, together with the more recent anomalous
anyon model (which has arbitrary gyromagnetic factor ) are reviewed. The
non-relativistic limit of the anyon generalizes the exotic particle which has
to any .When put into planar electric and magnetic fields, the Hall
effect becomes mandatory for all , when the field takes some critical
value.Comment: A new reference added. Talk given by P. Horvathy at the International
Workshop "Nonlinear Physics: Theory and Experiment. III. July'04, Gallipoli
(Lecce, Italy). To be published in Theor. Math. Phys. Latex 9 pages, no
figure
On sl(2)-equivariant quantizations
By computing certain cohomology of Vect(M) of smooth vector fields we prove
that on 1-dimensional manifolds M there is no quantization map intertwining the
action of non-projective embeddings of the Lie algebra sl(2) into the Lie
algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant
quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear
Mathematical Physic
On the Schrödinger-Newton equation and its symmetries: a geometric view
LaTeX 29 pages; minor correctionsInternational audienceThe \SN (SN) equation is recast on purely geometrical grounds, namely in terms of Bargmann structures over (\d+1)-dimensional Newton-Cartan (NC) spacetimes. Its maximal group of invariance, which we call the SN group, is determined as the group of conformal Bargmann automorphisms that preserve the coupled Schr\"odinger and NC gravitational field equations. Canonical unitary representations of the SN group are worked out, helping us recover, in particular, a very specific occurrence of dilations with dynamical exponent z=(\d+2)/3
Studies on the reactivity of a tertiary allylic alcohol in an acetophenonic series, a model for natural products synthesis
The synthesis of benzopyranic simplified analogues of dibenzopyranic natural compounds is described, together with the access to a precursor of a new furobenzopyranic natural product. These natural products have anti-cancer activity. The 1,3-diacetoxy-2-acetyl-4-(3-hydroxy-3-methylbut-1-enyl)benzene synthone is used as a common precursor to these structures
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