5,976 research outputs found
Toric rings, inseparability and rigidity
This article provides the basic algebraic background on infinitesimal
deformations and presents the proof of the well-known fact that the non-trivial
infinitesimal deformations of a -algebra are parameterized by the
elements of cotangent module of . In this article we focus on
deformations of toric rings, and give an explicit description of in
the case that is a toric ring.
In particular, we are interested in unobstructed deformations which preserve
the toric structure. Such deformations we call separations. Toric rings which
do not admit any separation are called inseparable. We apply the theory to the
edge ring of a finite graph. The coordinate ring of a convex polyomino may be
viewed as the edge ring of a special class of bipartite graphs. It is shown
that the coordinate ring of any convex polyomino is inseparable. We introduce
the concept of semi-rigidity, and give a combinatorial description of the
graphs whose edge ring is semi-rigid. The results are applied to show that for
, is not rigid while for , is
rigid. Here is the complete bipartite graph with one
edge removed.Comment: 33 pages, chapter 2 of the Book << Multigraded Algebra and
Applications>> 2018, Springer International Publishing AG, part of Springer
Natur
Chaotic Explosions
We investigate chaotic dynamical systems for which the intensity of
trajectories might grow unlimited in time. We show that (i) the intensity grows
exponentially in time and is distributed spatially according to a fractal
measure with an information dimension smaller than that of the phase space,(ii)
such exploding cases can be described by an operator formalism similar to the
one applied to chaotic systems with absorption (decaying intensities), but
(iii) the invariant quantities characterizing explosion and absorption are
typically not directly related to each other, e.g., the decay rate and fractal
dimensions of absorbing maps typically differ from the ones computed in the
corresponding inverse (exploding) maps. We illustrate our general results
through numerical simulation in the cardioid billiard mimicking a lasing
optical cavity, and through analytical calculations in the baker map.Comment: 7 pages, 5 figure
Robust Bayesian target detection algorithm for depth imaging from sparse single-photon data
This paper presents a new Bayesian model and associated algorithm for depth
and intensity profiling using full waveforms from time-correlated single-photon
counting (TCSPC) measurements in the limit of very low photon counts (i.e.,
typically less than 20 photons per pixel). The model represents each Lidar
waveform as an unknown constant background level, which is combined in the
presence of a target, to a known impulse response weighted by the target
intensity and finally corrupted by Poisson noise. The joint target detection
and depth imaging problem is expressed as a pixel-wise model selection and
estimation problem which is solved using Bayesian inference. Prior knowledge
about the problem is embedded in a hierarchical model that describes the
dependence structure between the model parameters while accounting for their
constraints. In particular, Markov random fields (MRFs) are used to model the
joint distribution of the background levels and of the target presence labels,
which are both expected to exhibit significant spatial correlations. An
adaptive Markov chain Monte Carlo algorithm including reversible-jump updates
is then proposed to compute the Bayesian estimates of interest. This algorithm
is equipped with a stochastic optimization adaptation mechanism that
automatically adjusts the parameters of the MRFs by maximum marginal likelihood
estimation. Finally, the benefits of the proposed methodology are demonstrated
through a series of experiments using real data.Comment: arXiv admin note: text overlap with arXiv:1507.0251
Lidar waveform based analysis of depth images constructed using sparse single-photon data
This paper presents a new Bayesian model and algorithm used for depth and
intensity profiling using full waveforms from the time-correlated single photon
counting (TCSPC) measurement in the limit of very low photon counts. The model
proposed represents each Lidar waveform as a combination of a known impulse
response, weighted by the target intensity, and an unknown constant background,
corrupted by Poisson noise. Prior knowledge about the problem is embedded in a
hierarchical model that describes the dependence structure between the model
parameters and their constraints. In particular, a gamma Markov random field
(MRF) is used to model the joint distribution of the target intensity, and a
second MRF is used to model the distribution of the target depth, which are
both expected to exhibit significant spatial correlations. An adaptive Markov
chain Monte Carlo algorithm is then proposed to compute the Bayesian estimates
of interest and perform Bayesian inference. This algorithm is equipped with a
stochastic optimization adaptation mechanism that automatically adjusts the
parameters of the MRFs by maximum marginal likelihood estimation. Finally, the
benefits of the proposed methodology are demonstrated through a serie of
experiments using real data
Knowledge of packaging waste among czech university students
Received: February 1st, 2023 ; Accepted: June 16th, 2023 ; Published: June 28th, 2023 ; Correspondence: Ing. Shuran Zhao, [email protected] residential sector generates around 14% of the overall waste production in the
Czech Republic. This essential share requires special attention to analyze with particular
emphasis for citizen education, especially on young people. Thus, this research is dedicated to
citizens' awareness about packaging waste to increase their knowledge. The experiment was
conducted in the form of a survey, and students from a Czech university were asked to estimate
the weight of the packaging waste presented to them in term to verify their knowledge about
packaging waste. This experiment featured different groups of students over time. The result
showed no difference in knowledge between these student groups over time. The long-term home
study caused by COVID-19 did not appear to have affected students' knowledge of packaging
waste. This study showed students' actual knowledge about packaging waste and highlighted the
gap and importance of education in waste management
Electron-vibration coupling constants in positively charged fullerene
Recent experiments have shown that C60 can be positively field-doped. In that
state, fullerene exhibits a higher resistivity and a higher superconducting
temperature than the corresponding negatively doped state. A strong
intramolecular hole-phonon coupling, connected with the Jahn-Teller effect of
the isolated positive ion, is expected to be important for both properties, but
the actual coupling strengths are so far unknown. Based on density functional
calculations, we determine the linear couplings of the two a_g, six g_g, and
eight h_g vibrational modes to the H_u HOMO level of the C60 molecule. The
couplings predict a D_5 distortion, and an H_u vibronic ground state for C60^+.
They are also used to generate the dimensionless coupling constant
which controls the superconductivity and the phonon contribution to the
electrical resistivity in the crystalline phase. We find that is 1.4
times larger in positively-charged C60 than in the negatively-doped case. These
results are discussed in the context of the available transport data and
superconducting temperatures. The role of higher orbital degeneracy in
superconductivity is also addressed.Comment: 22 pages - 3 figures. This revision includes few punctuation
corrections from proofreadin
Nonequilibrium electron spin polarization in a double quantum dot. Lande mechanism
In moderately strong magnetic fields, the difference in Lande g-factors in
each of the dots of a coupled double quantum dot device may induce oscillations
between singlet and triplet states of the entangled electron pair and lead to a
nonequilibrium electron spin polarization. We will show that this polarization
may partially survive the rapid inhomogeneous decoherence due to random nuclear
magnetic fields.Comment: New version contains figures. New title better reflects the content
of the pape
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