Rank of divisors on tropical curves

We investigate, using purely combinatorial methods, structural and algorithmic properties of linear equivalence classes of divisors on tropical curves. In particular, an elementary proof of the Riemann-Roch theorem for tropical curves, similar to the recent proof of the Riemann-Roch theorem for graphs by Baker and Norine, is presented. In addition, a conjecture of Baker asserting that the rank of a divisor D on a (non-metric) graph is equal to the rank of D on the corresponding metric graph is confirmed, and an algorithm for computing the rank of a divisor on a tropical curve is constructed

Geometric Tomography With Topological Guarantees

We consider the problem of reconstructing a compact 3-manifold (with boundary) embedded in $\mathbb{R}^3$ from its cross-sections with a given set of cutting planes having arbitrary orientations. Under appropriate sampling conditions that are satisfied when the set of cutting planes is dense enough, we prove that the algorithm presented by Liu et al. in [1] preserves the homotopy type of the object. Using the homotopy equivalence, we also show that the reconstructed object is homeomorphic (and isotopic) to the original object. This is the first time that 3D shape reconstruction from cross-sections comes with such theoretical guarantees. [1] L. Liu, C.L. Bajaj, J.O. Deasy, D.A. Low, and T. Ju. Surface reconstruction from non-parallel curve networks. Computer Graphics Forum, 27:155-163, 2008

Geometric Tomography With Topological Guarantees

research report in http://hal.archives-ouvertes.fr/inria-00440322/International audienceWe consider the problem of reconstructing a compact 3-manifold (with boundary) embedded in R3 from its cross- sections with a given set of cutting planes having arbitrary orientations. Under appropriate sampling conditions that are satisfied when the set of cutting planes is dense enough, we prove that the algorithm presented by Liu et al. preserves the homotopy type of the original object. Using the homotopy equivalence, we also show that the reconstructed object is homeomorphic (and isotopic) to the original object. This is the first time that shape reconstruction from cross-sections comes with such theoretical guarantees

Delayed elasticity of metallic glasses: Loading time and temperature dependences of the anelastic relaxation

One of the hallmarks of disordered matter is the large amplitude of the anelastic deformation, i.e., the fraction of reversible deformation that is not instantaneously recovered after the release of load but is delayed in time. In this paper, this delayed elasticity is studied for the glass-forming Zr46.25Ti8.25Cu7.5Ni10Be27.5 alloy by means of stress step and recovery experiments. Even at high temperatures, not far from the glass transition, the delayed elasticity can recover an important fraction of the deformation and endure for a long time. Analyzing the effects of loading time and waiting time on the strain evolution, we reveal the presence of an anelastic response with a timescale dependent on loading time and an invariant shape, which indicates the presence of a distribution of reversible relaxation modes following a t-n law with exponent n between 0.5 and 1. The underlying distribution of energy barriers activated at different temperatures is accordingly shape invariant. Moreover, we found that a distribution of reversible modes corresponding to the high-frequency side of the a-relaxation peak can reproduce the experimental results. The results establish a direct link between the dynamical spectrum and the distribution of activation energies, revealing the origin of the transient creep and anelastic recovery behaviors of metallic glasses.Peer ReviewedPostprint (published version

Banana pest risk assessment along banana trade axes running from low to high altitude sites, in the Eastern DR Congo and in Burundi

Pests and diseases greatly contribute to the decline in banana yields, food and income insecurity in the Great Lakes region of Africa. Understanding people’s role in pest and disease spread at landscape level is crucial for effective pest and disease management. To determine this, focus group discussions (FGDs) targeting 10 experienced farmers (50% female and 50% male) were conducted in 27 villages along four banana trade routes in western Burundi and eastern DR Congo. FGDs determined the presence and risk of spread of key banana pests and diseases via the movement of banana bunches, planting material and other products, labourers, traders and farm tools. Black leaf streak (BLS), Fusarium wilt and banana bunchy top disease (BBTD) were reported to have been in the landscape for over 40 years while Xanthomonas wilt (XW) was a more recent introduction (1-7 years). BBTD, XW and weevils were the most prevalent constraints. BBTD was observed at previously unsuitable high-altitude zones, which should be a cause of concern, especially with the current risk of climate change. Climate change, and linked temperature increases, could also worsen the prevalence of XW, weevils, nematodes and BLS. Movement of farming tools by labourers and traders, of planting material/suckers and banana bunches emerged as the most common human practices potentially responsible for the spread and/or build-up of banana pests/diseases. Strengthening farmer’s knowledge and institutional capacities of actors on these different modes of disease spread in banana value chains in the region is recommended

Demonstration of integrated microscale optics in surface-electrode ion traps

In ion trap quantum information processing, efficient fluorescence collection is critical for fast, high-fidelity qubit detection and ion-photon entanglement. The expected size of future many-ion processors require scalable light collection systems. We report on the development and testing of a microfabricated surface-electrode ion trap with an integrated high numerical aperture (NA) micromirror for fluorescence collection. When coupled to a low NA lens, the optical system is inherently scalable to large arrays of mirrors in a single device. We demonstrate stable trapping and transport of 40Ca+ ions over a 0.63 NA micromirror and observe a factor of 1.9 enhancement in photon collection compared to the planar region of the trap.Comment: 15 pages, 8 figure

Social determinants of spatial inequalities in COVID-19 outcomes across England: A multiscale geographically weighted regression analysis.

A variety of factors are associated with greater COVID-19 morbidity or mortality, due to how these factors influence exposure to (in the case of morbidity) or severity of (in the case of mortality) COVID-19 infections. We use multiscale geographically weighted regression to study spatial variation in the factors associated with COVID-19 morbidity and mortality rates at the local authority level across England (UK). We investigate the period between March 2020 and March 2021, prior to the rollout of the COVID-19 vaccination program. We consider a variety of factors including demographic (e.g. age, gender, and ethnicity), health (e.g. rates of smoking, obesity, and diabetes), social (e.g. Index of Multiple Deprivation), and economic (e.g. the Gini coefficient and economic complexity index) factors that have previously been found to impact COVID-19 morbidity and mortality. The Index of Multiple Deprivation has a significant impact on COVID-19 cases and deaths in all local authorities, although the effect is the strongest in the south of England. Higher proportions of ethnic minorities are associated with higher levels of COVID-19 mortality, with the strongest effect being found in the west of England. There is again a similar pattern in terms of cases, but strongest in the north of the country. Other factors including age and gender are also found to have significant effects on COVID-19 morbidity and mortality, with differential spatial effects across the country. The results provide insights into how national and local policymakers can take account of localized factors to address spatial health inequalities and address future infectious disease pandemics. [Abstract copyright: © 2024 The Authors.