17,567 research outputs found
Categorification of quantum symmetric pairs I
We categorify a coideal subalgebra of the quantum group of
by introducing a -category \`a la
Khovanov-Lauda-Rouquier, and show that self-dual indecomposable -morphisms
categorify the canonical basis of this algebra. This allows us to define a
categorical action of this coideal algebra on the categories of modules over
cohomology rings of partial flag varieties and on the BGG category
of type B/C.Comment: final version, to appear in Quantum Topolog
Takens-Bogdanov bifurcation of travelling wave solutions in pipe flow
The appearance of travelling-wave-type solutions in pipe Poiseuille flow that
are disconnected from the basic parabolic profile is numerically studied in
detail. We focus on solutions in the 2-fold azimuthally-periodic subspace
because of their special stability properties, but relate our findings to other
solutions as well. Using time-stepping, an adapted Krylov-Newton method and
Arnoldi iteration for the computation and stability analysis of relative
equilibria, and a robust pseudo-arclength continuation scheme we unfold a
double-zero (Takens-Bogdanov) bifurcating scenario as a function of Reynolds
number (Re) and wavenumber (k). This scenario is extended, by the inclusion of
higher order terms in the normal form, to account for the appearance of
supercritical modulated waves emanating from the upper branch of solutions at a
degenerate Hopf bifurcation. These waves are expected to disappear in
saddle-loop bifurcations upon collision with lower-branch solutions, thereby
leaving stable upper-branch solutions whose subsequent secondary bifurcations
could contribute to the formation of the phase space structures that are
required for turbulent dynamics at higher Re.Comment: 26 pages, 15 figures (pdf and png). Submitted to J. Fluid Mec
Network calculus for parallel processing
In this note, we present preliminary results on the use of "network calculus"
for parallel processing systems, specifically MapReduce
Biomedical Informatics Applications for Precision Management of Neurodegenerative Diseases
Modern medicine is in the midst of a revolution driven by “big data,” rapidly advancing computing power, and broader integration of technology into healthcare. Highly detailed and individualized profiles of both health and disease states are now possible, including biomarkers, genomic profiles, cognitive and behavioral phenotypes, high-frequency assessments, and medical imaging. Although these data are incredibly complex, they can potentially be used to understand multi-determinant causal relationships, elucidate modifiable factors, and ultimately customize treatments based on individual parameters. Especially for neurodegenerative diseases, where an effective therapeutic agent has yet to be discovered, there remains a critical need for an interdisciplinary perspective on data and information management due to the number of unanswered questions. Biomedical informatics is a multidisciplinary field that falls at the intersection of information technology, computer and data science, engineering, and healthcare that will be instrumental for uncovering novel insights into neurodegenerative disease research, including both causal relationships and therapeutic targets and maximizing the utility of both clinical and research data. The present study aims to provide a brief overview of biomedical informatics and how clinical data applications such as clinical decision support tools can be developed to derive new knowledge from the wealth of available data to advance clinical care and scientific research of neurodegenerative diseases in the era of precision medicine
Properties of the ground F state and the excited P state of atomic thorium in cold collisions with He
We measure inelastic collisional cross sections for the ground F
state and the excited P state of atomic thorium in cold collisions with
He. We determine for Th (F) at 800 mK the ratio of the momentum-transfer to Zeeman relaxation cross sections for
collisions with He. For Th (P), we study electronic inelastic
processes and find no quenching even after collisions. We also determine
the radiative lifetime of Th (P) to be ms. This great
stability of the metastable state opens up the possibility for further study,
including trapping
Vibrational quenching of the electronic ground state in ThO in cold collisions with He
We measure the ratio of the momentum-transfer to the vibrational
quenching cross section for the X (), , state
of molecular thorium monoxide (ThO) in collisions with atomic He between
800 mK and 2.4 K. We observe indirect evidence for ThO--He van der Waals'
complex formation, which has been predicted by theory. We determine the 3-body
recombination rate constant at 2.4 K, and establish that the binding
energy E 4 K
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