An explicit counterexample to the Lagarias-Wang finiteness conjecture

The joint spectral radius of a finite set of real $d \times d$ matrices is defined to be the maximum possible exponential rate of growth of long products of matrices drawn from that set. A set of matrices is said to have the \emph{finiteness property} if there exists a periodic product which achieves this maximal rate of growth. J.C. Lagarias and Y. Wang conjectured in 1995 that every finite set of real $d \times d$ matrices satisfies the finiteness property. However, T. Bousch and J. Mairesse proved in 2002 that counterexamples to the finiteness conjecture exist, showing in particular that there exists a family of pairs of $2 \times 2$ matrices which contains a counterexample. Similar results were subsequently given by V.D. Blondel, J. Theys and A.A. Vladimirov and by V.S. Kozyakin, but no explicit counterexample to the finiteness conjecture has so far been given. The purpose of this paper is to resolve this issue by giving the first completely explicit description of a counterexample to the Lagarias-Wang finiteness conjecture. Namely, for the set \mathsf{A}_{\alpha_*}:= \{({cc}1&1\\0&1), \alpha_*({cc}1&0\\1&1)\} we give an explicit value of \alpha_* \simeq 0.749326546330367557943961948091344672091327370236064317358024...] such that $\mathsf{A}_{\alpha_*}$ does not satisfy the finiteness property.Comment: 27 pages, 2 figure

Ring Formation from an Oscillating Black Hole

Massive black hole (BH) mergers can result in the merger remnant receiving a "kick", of order 200 km s$^{-1}$ or more, which will cause the remnant to oscillate about the galaxy centre. Here we analyze the case where the BH oscillates through the galaxy centre perpendicular or parallel to the plane of the galaxy for a model galaxy consisting of an exponential disk, a Plummer model bulge, and an isothermal dark matter halo. For the perpendicular motion we find that there is a strong resonant forcing of the disk radial motion near but somewhat less than the "resonant radii" $r_R$ where the BH oscillation frequency is equal one-half, one-fourth, (1/6, etc.) of the radial epicyclic frequency in the plane of the disk. Near the resonant radii there can be a strong enhancement of the radial flow and disk density which can lead to shock formation. In turn the shock may trigger the formation of a ring of stars near $r_R$. As an example, for a BH mass of $10^8 M_\odot$ and a kick velocity of 150 km s$^{-1}$, we find that the resonant radii lie between 0.2 and 1 kpc. For BH motion parallel to the plane of the galaxy we find that the BH leaves behind it a supersonic wake where star formation may be triggered. The shape of the wake is calculated as well as the slow-down time of the BH. The differential rotation of the disk stretches the wake into ring-like segments.Comment: 7 pages, 7 figure

Modeling the β-secretase cleavage site and humanizing amyloid-beta precursor protein in rat and mouse to study Alzheimer's disease

BACKGROUND: Three amino acid differences between rodent and human APP affect medically important features, including β-secretase cleavage of APP and Aβ peptide aggregation (De Strooper et al., EMBO J 14:4932-38, 1995; Ueno et al., Biochemistry 53:7523-30, 2014; Bush, 2003, Trends Neurosci 26:207-14). Most rodent models for Alzheimer's disease (AD) are, therefore, based on the human APP sequence, expressed from artificial mini-genes randomly inserted in the rodent genome. While these models mimic rather well various biochemical aspects of the disease, such as Aβ-aggregation, they are also prone to overexpression artifacts and to complex phenotypical alterations, due to genes affected in or close to the insertion site(s) of the mini-genes (Sasaguri et al., EMBO J 36:2473-87, 2017; Goodwin et al., Genome Res 29:494-505, 2019). Knock-in strategies which introduce clinical mutants in a humanized endogenous rodent APP sequence (Saito et al., Nat Neurosci 17:661-3, 2014) represent useful improvements, but need to be compared with appropriate humanized wildtype (WT) mice. METHODS: Computational modelling of the human β-CTF bound to BACE1 was used to study the differential processing of rodent and human APP. We humanized the three pivotal residues we identified G676R, F681Y and R684H (labeled according to the human APP770 isoform) in the mouse and rat genomes using a CRISPR-Cas9 approach. These new models, termed mouse and rat Apphu/hu, express APP from the endogenous promotor. We also introduced the early-onset familial Alzheimer's disease (FAD) mutation M139T into the endogenous Rat Psen1 gene. RESULTS: We show that introducing these three amino acid substitutions into the rodent sequence lowers the affinity of the APP substrate for BACE1 cleavage. The effect on β-secretase processing was confirmed as both humanized rodent models produce three times more (human) Aβ compared to the original WT strain. These models represent suitable controls, or starting points, for studying the effect of transgenes or knock-in mutations on APP processing (Saito et al., Nat Neurosci 17:661-3, 2014). We introduced the early-onset familial Alzheimer's disease (FAD) mutation M139T into the endogenous Rat Psen1 gene and provide an initial characterization of Aβ processing in this novel rat AD model. CONCLUSION: The different humanized APP models (rat and mouse) expressing human Aβ and PSEN1 M139T are valuable controls to study APP processing in vivo allowing the use of a human Aβ ELISA which is more sensitive than the equivalent system for rodents. These animals will be made available to the research community

Understanding Uncertainty

A way to assess the information decrease uncertainty and project risk was described. Incorporating the method into real-time evaluation programs allowed continual updating of prognoses, such as the distance to a drilling target. Three case studies showed uncertainty analysis for geosteering into a thin pay section, a shaly-sand petrophysical analysis and a walkaway vertical seismic profile (VSP)

Dicarbon­yl(η5-cyclo­penta­dien­yl)[2-(phenyl­sulfan­yl)eth­yl]iron(II)

The title compound, [Fe(C5H5)(C8H9S)(CO)2], is a three-legged piano-stool iron(II) complex that is characterized by a thio­ethyl-linked phenyl ring and a cyclo­penta­dienyl moiety that occupies the apical coordination site. The two aromatic rings are essentially planar with the same maximum deviation of 0.009 Å. The mean planes of the phenyl and cyclo­penta­dienyl rings bis­ect at an acute angle of 50.08°

Analytical Potential-Density Pairs for Flat Rings and Toroidal Structures

The Kuzmin-Toomre family of discs is used to construct potential-density pairs that represent flat ring structures in terms of elementary functions. Systems composed of two concentric flat rings, a central disc surrounded by one ring and a ring with a centre of attraction are also presented. The circular velocity of test particles and the epicyclic frequency of small oscillations about circular orbits are calculated for these structures. A few examples of three-dimensional potential-density pairs of "inflated" flat rings (toroidal mass distributions) are presented.Comment: 25 pages, 11 figures, accepted for publication in MNRA

Intercomparison of Metop-A SO2 measurements during the 2010- 2011 Icelandic eruptions

The European Space Agency project Satellite Monitoring of Ash and Sulphur Dioxide for the mitigation of Aviation Hazards, was introduced after the eruption of the Icelandic volcano Eyjafjallajökull in the spring of 2010 to facilitate the development of an optimal EndtoEnd System for Volcanic Ash Plume Monitoring and Prediction. The Eyjafjallajökull plume drifted towards Europe and caused major disruptions of European air traffic for several weeks affecting the everyday life of millions of people. The limitations in volcanic plume monitoring and prediction capabilities gave birth to this observational system which is based on comprehensive satellitederived ash plume and sulphur dioxide [SO2] level estimates, as well as a widespread validation using supplementary satellite, aircraft and groundbased measurements. Intercomparison of the volcanic total SO2 column and plume height observed by GOME2/ MetopA and IASI/MetopA are shown before, during and after the Eyjafjallajökull 2010 eruptions as well as for the 2011 Grímsvötn eruption. Colocated groundbased Brewer Spectrophotometer data extracted from the World Ozone and Ultraviolet Radiation Data Centre for de Bilt, the Netherlands, are also compared to the different satellite estimates. Promising agreement is found for the two different types of instrument for the SO2 columns with linear regression coefficients ranging around from 0.64 when comparing the different instruments and 0.85 when comparing the two different IASI algorithms. The agreement for the plume height is lower, possibly due to the major differences between the height retrieval part of the GOME2 and IASI algorithms. The comparisons with the Brewer groundbased station in de Bilt, The Netherlands show good qualitative agreement for the peak of the event however stronger eruptive signals are required for a longer quantitative comparison

A global catalogue of large SO \u3c inf\u3e 2 sources and emissions derived from the Ozone Monitoring Instrument

Sulfur dioxide (SO2) measurements from the Ozone Monitoring Instrument (OMI) satellite sensor processed with the new principal component analysis (PCA) algorithm were used to detect large point emission sources or clusters of sources. The total of 491 continuously emitting point sources releasing from about 30 kt yr-1 to more than 4000 kt yr-1 of SO2 per year have been identified and grouped by country and by primary source origin: volcanoes (76 sources); power plants (297); smelters (53); and sources related to the oil and gas industry (65). The sources were identified using different methods, including through OMI measurements themselves applied to a new emission detection algorithm, and their evolution during the 2005-2014 period was traced by estimating annual emissions from each source. For volcanic sources, the study focused on continuous degassing, and emissions from explosive eruptions were excluded. Emissions from degassing volcanic sources were measured, many for the first time, and collectively they account for about 30 % of total SO2 emissions estimated from OMI measurements, but that fraction has increased in recent years given that cumulative global emissions from power plants and smelters are declining while emissions from oil and gas industry remained nearly constant. Anthropogenic emissions from the USA declined by 80 % over the 2005-2014 period as did emissions from western and central Europe, whereas emissions from India nearly doubled, and emissions from other large SO2-emitting regions (South Africa, Russia, Mexico, and the Middle East) remained fairly constant. In total, OMI-based estimates account for about a half of total reported anthropogenic SO2 emissions; the remaining half is likely related to sources emitting less than 30 kt yr-1 and not detected by OMI

A Comparison Study of Eleven Static Heuristics for Mapping a Class of Independent Tasks onto Ileterogeneous Distributed Computing Systems

ABSTRACT Il\u27lixed-machine heterogeneous computing (HC) environments utilize a distributed suite of different high-performance machines, interconnected with high-speed links to perform different computationally intensive applications that have diverse comput ational requirements. HC environments are well suited to meet thl: computational dell-tands of large, diverse groups of tasks. The problem of mapping (defined as matching and scheduling) these tasks onto the machines of a distributed HC environment has been shown, in general, to be NP-complete, requiring the development of heuristic techniques. Selecting the best heuristic to use in a given enviroi~menth, owever, remains a difficult problem, because comparisons are often clouded by different underlying assumptions in the original studies of each heuristic. There~fore; a collection of eleven heuristics from the literature has been selected: a,dapted, in~plementeda, nd anaiyzed under one set of common assumptions. It is assumed that the heuristics derive a, mapping statically (i.e., off-line). It is also assumed that a meta-task (i.e., a set of independent, non-communicating tasks) is being mapped, and that the goal is to minimize the total execution time of the metla-task. The eleven heuristics examined are Opportunistic Load Balancing, Minimum Execution Time, MininLlum Clompletion Time, Min-min, hllax-min, Duplex? Genetic i-Ilgorithm, Simulated Annealing, Genetic Simulat.ed .Annealing, Tabu, and Ax. This study provides one even basis for comparisor] and insights into circumstances where one technique will out perform another. The evaluation procedure is specified, the heuristics are defined, and then comparison results are discussed. It is shown that for the ca.ses studied here, the relat,ively simple Min-min heuristic performs well in comparison to the other techniques

The Demise of Multidrug-Resistant HIV-1: the National Time Trend in Portugal

OBJECTIVES: Despite a decreasing mortality and morbidity in treated HIV-1 patients, highly active antiretroviral treatment (HAART) can still fail due to the development of drug resistance. Especially, multidrug-resistant viruses pose a threat to efficient therapy. We studied the changing prevalence of multidrug resistance (MDR) over time in a cohort of HIV-1-infected patients in Portugal. PATIENTS AND METHODS: We used data of 8065 HIV-1-infected patients followed from July 2001 up to April 2012 in 22 hospitals located in Portugal. MDR at a specific date of sampling was defined as no more than one fully active drug (excluding integrase and entry inhibitors) at that time authorized by the Portuguese National Authority of Medicines and Health Products (INFARMED), as interpreted with the Rega algorithm version 8.0.2. A generalized linear mixed model was used to study the time trend of the prevalence of MDR. RESULTS: We observed a statistically significant decrease in the prevalence of MDR over the last decade, from 6.9% (95% CI: 5.7-8.4) in 2001-03, 6.0% (95% CI: 4.9-7.2) in 2003-05, 3.7% (95% CI: 2.8-4.8) in 2005-07 and 1.6% (95% CI: 1.1-2.2) in 2007-09 down to 0.6% (95% CI: 0.3-0.9) in 2009-12 [OR=0.80 (95% CI: 0.75-0.86); P<0.001]. In July 2011 the last new case of MDR was seen. CONCLUSIONS: The prevalence of multidrug-resistant HIV-1 is decreasing over time in Portugal, reflecting the increasing efficiency of HAART and the availability of new drugs. Therefore, in designing a new drug, safety and practical aspects, e.g. less toxicity and ease of use, may need more attention than focusing mainly on efficacy against resistant strains.info:eu-repo/semantics/publishedVersio