Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO(nn)

Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. We develop necessary means to determine the homotopy class of a given loop in this space. Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] to the complex Hamiltonian case does not provide any new information.Comment: Minor changes, journal reference adde

Detonation wave diffraction in H₂-O₂-Ar mixtures

In the present study, we have examined the diffraction of detonation in weakly unstable hydrogen–oxygen–argon mixtures. High accuracy and computational efficiency are obtained using a high-order WENO scheme together with adaptive mesh refinement, which enables handling realistic geometries with resolution at the micrometer level. Both detailed chemistry and spectroscopic models of laser induced fluorescence and chemiluminescence were included to enable a direct comparison with experimental data. Agreement was found between the experiments and the simulations in terms of detonation diffraction structure both for sub-critical and super-critical regimes. The predicted wall reflection distance is about 12–14 cell widths, in accordance with previous experimental studies. Computations show that the re-initiation distance is relatively constant, at about 12–15 cell widths, slightly above the experimental value of 11 cell widths. The predicted critical channel height is 10–11 cell widths, which differs from experiments in circular tubes but is consistent with rectangular channel results

A Computation of the Maximal Order Type of the Term Ordering on Finite Multisets

We give a sharpening of a recent result of Aschenbrenner and Pong about the maximal order type of the term ordering on the finite multisets over a wpo. Moreover we discuss an approach to compute maximal order types of well-partial orders which are related to tree embeddings

On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

A Datasheet for the INSIGHT Birmingham, Solihull, and Black Country Diabetic Retinopathy Screening Dataset

Purpose: Diabetic retinopathy (DR) is the most common microvascular complication associated with diabetes mellitus (DM), affecting approximately 40% of this patient population. Early detection of DR is vital to ensure monitoring of disease progression and prompt sight saving treatments as required. This article describes the data contained within the INSIGHT Birmingham, Solihull, and Black Country Diabetic Retinopathy Dataset. / Design: Dataset descriptor for routinely collected eye screening data. / Participants: All diabetic patients aged 12 years and older, attending annual digital retinal photography-based screening within the Birmingham, Solihull, and Black Country Eye Screening Programme. / Methods: The INSIGHT Health Data Research Hub for Eye Health is a National Health Service (NHS)–led ophthalmic bioresource that provides researchers with safe access to anonymized, routinely collected data from contributing NHS hospitals to advance research for patient benefit. This report describes the INSIGHT Birmingham, Solihull, and Black Country DR Screening Dataset, a dataset of anonymized images and linked screening data derived from the United Kingdom's largest regional DR screening program. / Main Outcome Measures: This dataset consists of routinely collected data from the eye screening program. The data primarily include retinal photographs with the associated DR grading data. Additional data such as corresponding demographic details, information regarding patients’ diabetic status, and visual acuity data are also available. Further details regarding available data points are available in the supplementary information, in addition to the INSIGHT webpage included below. / Results: At the time point of this analysis (December 31, 2019), the dataset comprised 6 202 161 images from 246 180 patients, with a dataset inception date of January 1, 2007. The dataset includes 1 360 547 grading episodes between R0M0 and R3M1. / Conclusions: This dataset descriptor article summarizes the content of the dataset, how it has been curated, and what its potential uses are. Data are available through a structured application process for research studies that support discovery, clinical evidence analyses, and innovation in artificial intelligence technologies for patient benefit. Further information regarding the data repository and contact details can be found at https://www.insight.hdrhub.org/

Soundness and completeness proofs by coinductive methods

We show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. For the classical completeness result, we first establish an abstract property of possibly infinite derivation trees. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems for various flavors of first-order logic. Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. This forms the subject of several cyclic proof systems for first-order logic augmented with inductive predicate definitions studied in the literature. All the discussed results are formalized using Isabelle/HOL’s recently introduced support for codatatypes and corecursion. The development illustrates some unique features of Isabelle/HOL’s new coinductive specification language such as nesting through non-free types and mixed recursion–corecursion

Structural Insights into the Inhibition of Cytosolic 5′-Nucleotidase II (cN-II) by Ribonucleoside 5′-Monophosphate Analogues

Cytosolic 5′-nucleotidase II (cN-II) regulates the intracellular nucleotide pools within the cell by catalyzing the dephosphorylation of 6-hydroxypurine nucleoside 5′-monophosphates. Beside this physiological function, high level of cN-II expression is correlated with abnormal patient outcome when treated with cytotoxic nucleoside analogues. To identify its specific role in the resistance phenomenon observed during cancer therapy, we screened a particular class of chemical compounds, namely ribonucleoside phosphonates to predict them as potential cN-II inhibitors. These compounds incorporate a chemically and enzymatically stable phosphorus-carbon linkage instead of a regular phosphoester bond. Amongst them, six compounds were predicted as better ligands than the natural substrate of cN-II, inosine 5′-monophosphate (IMP). The study of purine and pyrimidine containing analogues and the introduction of chemical modifications within the phosphonate chain has allowed us to define general rules governing the theoretical affinity of such ligands. The binding strength of these compounds was scrutinized in silico and explained by an impressive number of van der Waals contacts, highlighting the decisive role of three cN-II residues that are Phe 157, His 209 and Tyr 210. Docking predictions were confirmed by experimental measurements of the nucleotidase activity in the presence of the three best available phosphonate analogues. These compounds were shown to induce a total inhibition of the cN-II activity at 2 mM. Altogether, this study emphasizes the importance of the non-hydrolysable phosphonate bond in the design of new competitive cN-II inhibitors and the crucial hydrophobic stacking promoted by three protein residues

Vortex nozzle interaction in solid rocket motors: A scaling law for upstream acoustic response

In solid rocket motors, vortex nozzle interactions can be a source of large-amplitude pressure pulsations. Using a two-dimensional frictionless flow model, a scaling law is deduced, which describes the magnitude of a pressure pulsation as being proportional to the product of the dynamic pressure of the upstream main flow and of vortex circu- lation. The scaling law was found to be valid for both an integrated noz- zle with surrounding cavity and a nozzle geometry without surrounding cavity that forms a right angle with the combustion chamber side wall. Deviations from the scaling law only occur when unrealistically strong circulations are considered