Categorification of quantum symmetric pairs I

We categorify a coideal subalgebra of the quantum group of $\mathfrak{sl}_{2r+1}$ by introducing a $2$-category \`a la Khovanov-Lauda-Rouquier, and show that self-dual indecomposable $1$-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 $\mathcal{O}$ 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 3^3F2_2 state and the excited 3^3P0_0 state of atomic thorium in cold collisions with 3^3He

We measure inelastic collisional cross sections for the ground $^3$F$_2$ state and the excited $^3$P$_0$ state of atomic thorium in cold collisions with $^3$He. We determine for Th ($^3$F$_2$) at 800 mK the ratio $\gamma \approx 500$ of the momentum-transfer to Zeeman relaxation cross sections for collisions with $^3$He. For Th ($^3$P$_0$), we study electronic inelastic processes and find no quenching even after $10^6$ collisions. We also determine the radiative lifetime of Th ($^3$P$_0$) to be $\tau > 130$ 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 3^3He

We measure the ratio $\gamma$ of the momentum-transfer to the vibrational quenching cross section for the X ($^1\Sigma^+$), $\nu=1$, $\mathrm{J=0}$ state of molecular thorium monoxide (ThO) in collisions with atomic $^3$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 $\Gamma_3$ at 2.4 K, and establish that the binding energy E$_b >$ 4 K