Complementary vertices and adjacency testing in polytopes

Our main theoretical result is that, if a simple polytope has a pair of complementary vertices (i.e., two vertices with no facets in common), then it has at least two such pairs, which can be chosen to be disjoint. Using this result, we improve adjacency testing for vertices in both simple and non-simple polytopes: given a polytope in the standard form {x \in R^n | Ax = b and x \geq 0} and a list of its V vertices, we describe an O(n) test to identify whether any two given vertices are adjacent. For simple polytopes this test is perfect; for non-simple polytopes it may be indeterminate, and instead acts as a filter to identify non-adjacent pairs. Our test requires an O(n^2 V + n V^2) precomputation, which is acceptable in settings such as all-pairs adjacency testing. These results improve upon the more general O(nV) combinatorial and O(n^3) algebraic adjacency tests from the literature.Comment: 14 pages, 5 figures. v1: published in COCOON 2012. v2: full journal version, which strengthens and extends the results in Section 2 (see p1 of the paper for details

Proteinopathies as hallmarks of impaired gene expression, proteostasis and mitochondrial function in amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) is a fatal adult-onset neurodegenerative disease characterized by progressive degeneration of upper and lower motor neurons. As with the majority of neurodegenerative diseases, the pathological hallmarks of ALS involve proteinopathies which lead to the formation of various polyubiquitylated protein aggregates in neurons and glia. ALS is a highly heterogeneous disease, with both familial and sporadic forms arising from the convergence of multiple disease mechanisms, many of which remain elusive. There has been considerable research effort invested into exploring these disease mechanisms and in recent years dysregulation of RNA metabolism and mitochondrial function have emerged as of crucial importance to the onset and development of ALS proteinopathies. Widespread alterations of the RNA metabolism and post-translational processing of proteins lead to the disruption of multiple biological pathways. Abnormal mitochondrial structure, impaired ATP production, dysregulation of energy metabolism and calcium homeostasis as well as apoptosis have been implicated in the neurodegenerative process. Dysfunctional mitochondria further accumulate in ALS motor neurons and reflect a wider failure of cellular quality control systems, including mitophagy and other autophagic processes. Here, we review the evidence for RNA and mitochondrial dysfunction as some of the earliest critical pathophysiological events leading to the development of ALS proteinopathies, explore their relative pathological contributions and their points of convergence with other key disease mechanisms. This review will focus primarily on mutations in genes causing four major types of ALS (C9ORF72, SOD1, TARDBP/TDP-43, and FUS) and in protein homeostasis genes (SQSTM1, OPTN, VCP, and UBQLN2) as well as sporadic forms of the disease. Finally, we will look to the future of ALS research and how an improved understanding of central mechanisms underpinning proteinopathies might inform research directions and have implications for the development of novel therapeutic approaches

Restrictions on the lifetime of sterile neutrinos from primordial nucleosynthesis

We analyze the influence of decaying sterile neutrinos with the masses in the range 1-140 MeV on the primordial Helium-4 abundance, explicitly solving the Boltzmann equations for all particle species, taking into account neutrino flavour oscillations, and paying special attention to systematic uncertainties. We show that the Helium abundance depends only on the sterile neutrino lifetime and not on the way the active-sterile mixing is distributed between flavours, and derive an upper bound on the lifetime. We also demonstrate that the recent results of Izotov & Thuan [arXiv:1001.4440], who find 2sigma higher than predicted by the standard primordial nucleosynthesis value of Helium-4 abundance, are consistent with the presence in the plasma of sterile neutrinos with the lifetime 0.01-2 seconds. The decay of these particles perturbs the spectra of (decoupled) neutrinos and heats photons, changing the ratio of neutrino to photon energy density, that can be interpreted as extra neutrino species at the recombination epoch.Comment: 17 pp. + Appendices. Analysis of deuterium bounds and more accurate account of CMB bounds on Helium-4 is added. Final version to appear in JCA

Eligibility for vericiguat in a real-world heart failure population according to trial, guideline and label criteria:Data from the Swedish Heart Failure Registry

Aim: We investigated the eligibility for vericiguat in a real-world heart failure (HF) population based on trial, guideline and label criteria. Methods and results: From the Swedish HF registry, 23 573 patients with HF with reduced ejection fraction (HFrEF) enrolled between 2000 and 2018, with a HF duration ≥6 months, were considered. Eligibility for vericiguat was calculated based on criteria from (i) the Vericiguat Global Study in Subjects with Heart Failure and Reduced Ejection Fraction (VICTORIA) trial; (ii) European and American guidelines on HF; (iii) product labelling according to the Food and Drug Administration and European Medicines Agency. Estimated eligibility for vericiguat in the trial, guidelines, and label scenarios was 21.4%, 47.4%, and 47.4%, respectively. Prior HF hospitalization within 6 months was the criterion limiting eligibility the most in all scenarios (met by 49.1% of the population). In the trial scenario, other criteria meaningfully limiting eligibility were elevated N-terminal pro-B-type natriuretic peptide levels and nitrate use. In all scenarios, eligibility was higher among patients hospitalized for HF at baseline (44.3% vs. 21.4% [trial scenario] and 97.3% vs. 47.4% [guideline/label scenarios] for hospitalized vs. non-hospitalized patients). Overall, eligible patients were older, had more severe HF, more comorbidities, and consequently higher cardiovascular mortality and HF hospitalization rates compared with ineligible patients across all scenarios. Conclusion: In a large and contemporary real-world HFrEF cohort, we estimated that 21.4% of patients would be eligible for vericiguat according to the VICTORIA trial selection criteria, 47.4% based on guidelines and labelling. Eligibility for vericiguat translated into the selection of a population at high risk of morbidity/mortality.</p

Correlation Functions for Diffusion-Limited Annihilation, A + A -> 0

The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A + A -> 0, is obtained analytically and explicitly, following the method of intervals. In the long time asymptotic limit, the correlation functions of annihilation are identical to those of coalescence, A + A -> A, despite differences between the two models in other statistical measures, such as the interparticle distribution function

Duration and severity of Medieval drought in the Lake Tahoe Basin

This paper is not subject to U.S. copyright. The definitive version was published in Quaternary Science Reviews 30 (2011): 3269-3279, doi:10.1016/j.quascirev.2011.08.015.Droughts in the western U.S. in the past 200 years are small compared to several megadroughts that occurred during Medieval times. We reconstruct duration and magnitude of extreme droughts in the northern Sierra Nevada from hydroclimatic conditions in Fallen Leaf Lake, California. Stands of submerged trees rooted in situ below the lake surface were imaged with sidescan sonar and radiocarbon analysis yields an age estimate of ∼1250 AD. Tree-ring records and submerged paleoshoreline geomorphology suggest a Medieval low-stand of Fallen Leaf Lake lasted more than 220 years. Over eighty more trees were found lying on the lake floor at various elevations above the paleoshoreline. Water-balance calculations suggest annual precipitation was less than 60% normal from late 10th century to early 13th century AD. Hence, the lake’s shoreline dropped 40–60 m below its modern elevation. Stands of pre-Medieval trees in this lake and in Lake Tahoe suggest the region experienced severe drought at least every 650–1150 years during the mid- and late-Holocene. These observations quantify paleo-precipitation and recurrence of prolonged drought in the northern Sierra Nevada.Support for this work was provided by US Geological Survey/ Desert Research Institute under Project ID# 2003NV39B, a Geological Society of America graduate research grant and the IRIS undergraduate internship program. F. Biondiwas supported, in part by NSF Cooperative Agreement EPS-0814372 to the Nevada System of Higher Education. N. Driscoll was supported in part by a grant from CA DWR

The delivery of personalised, precision medicines via synthetic proteins

Introduction: The design of advanced drug delivery systems based on synthetic and su-pramolecular chemistry has been very successful. Liposomal doxorubicin (Caelyx®), and liposomal daunorubicin (DaunoXome®), estradiol topical emulsion (EstrasorbTM) as well as soluble or erodible polymer systems such as pegaspargase (Oncaspar®) or goserelin acetate (Zoladex®) represent considerable achievements. The Problem: As deliverables have evolved from low molecular weight drugs to biologics (currently representing approximately 30% of the market), so too have the demands made of advanced drug delivery technology. In parallel, the field of membrane trafficking (and endocytosis) has also matured. The trafficking of specific receptors i.e. material to be recycled or destroyed, as well as the trafficking of protein toxins has been well characterized. This, in conjunction with an ability to engineer synthetic, recombinant proteins provides several possibilities. The Solution: The first is using recombinant proteins as drugs i.e. denileukin diftitox (Ontak®) or agalsidase beta (Fabrazyme®). The second is the opportunity to use protein toxin architecture to reach targets that are not normally accessible. This may be achieved by grafting regulatory domains from multiple species to form synthetic proteins, engineered to do multiple jobs. Examples include access to the nucleocytosolic compartment. Herein the use of synthetic proteins for drug delivery has been reviewed

A quantitative systems pharmacology consortium approach to managing immunogenicity of therapeutic proteins

Immunogenicity is a major challenge in drug development and patient care. Currently, most efforts are dedicated to the elimination of the unwanted immune responses through T‐cell epitope prediction and protein engineering. However, because it is unlikely that this approach will lead to complete eradication of immunogenicity, we propose that quantitative systems pharmacology models should be developed to predict and manage immunogenicity. The potential impact of such a mechanistic model‐based approach is precedented by applications of physiologically‐based pharmacokinetics

Gaia Early Data Release 3: The celestial reference frame (Gaia-CRF3)

Context. Gaia-CRF3 is the celestial reference frame for positions and proper motions in the third release of data from the Gaia mission, Gaia DR3 (and for the early third release, Gaia EDR3, which contains identical astrometric results). The reference frame is defined by the positions and proper motions at epoch 2016.0 for a specific set of extragalactic sources in the (E)DR3 catalogue. Aims. We describe the construction of Gaia-CRF3 and its properties in terms of the distributions in magnitude, colour, and astrometric quality. Methods. Compact extragalactic sources in Gaia DR3 were identified by positional cross-matching with 17 external catalogues of quasi-stellar objects (QSO) and active galactic nuclei (AGN), followed by astrometric filtering designed to remove stellar contaminants. Selecting a clean sample was favoured over including a higher number of extragalactic sources. For the final sample, the random and systematic errors in the proper motions are analysed, as well as the radio-optical offsets in position for sources in the third realisation of the International Celestial Reference Frame (ICRF3). Results. Gaia-CRF3 comprises about 1.6 million QSO-like sources, of which 1.2 million have five-parameter astrometric solutions in Gaia DR3 and 0.4 million have six-parameter solutions. The sources span the magnitude range G = 13-21 with a peak density at 20.6 mag, at which the typical positional uncertainty is about 1 mas. The proper motions show systematic errors on the level of 12 μas yr-1 on angular scales greater than 15 deg. For the 3142 optical counterparts of ICRF3 sources in the S/X frequency bands, the median offset from the radio positions is about 0.5 mas, but it exceeds 4 mas in either coordinate for 127 sources. We outline the future of Gaia-CRF in the next Gaia data releases. Appendices give further details on the external catalogues used, how to extract information about the Gaia-CRF3 sources, potential (Galactic) confusion sources, and the estimation of the spin and orientation of an astrometric solution