Two-band random matrices

Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of spectra are directly reconstructed from the recurrence equation for orthogonal polynomials associated with a given random matrix ensemble. It is established that an eigenvalue gap does not affect the local eigenvalue correlations which follow the universal sine and the universal multicritical laws in the bulk and soft-edge scaling limits, respectively. By contrast, global smoothed eigenvalue correlations do reflect the presence of a gap, and are shown to satisfy a new universal law exhibiting a sharp dependence on the odd/even dimension of random matrices whose spectra are bounded. In the case of unbounded spectrum, the corresponding universal `density-density' correlator is conjectured to be generic for chaotic systems with a forbidden gap and broken time reversal symmetry.Comment: 12 pages (latex), references added, discussion enlarge

Composition algebras and the two faces of G2G_{2}

We consider composition and division algebras over the real numbers: We note two r\^oles for the group $G_{2}$: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are equivalent, by means of a regular metric. We express in some diagrams the relation between some pertinent groups, most of them related to the octonions. Some applications to physics are also discussed.Comment: 11 pages, 3 figure

Climate Change Impacts on Freshwater Wetland Hydrology and Vegetation Cover Cycling Along a Regional Aridity Gradient

Global mean temperature may increase up to 6°C by the end of this century and together with precipitation change may steepen regional aridity gradients. The hydrology, productivity, and ecosystem services from freshwater wetlands depend on their future water balance. We simulated the hydrology and vegetation dynamics of wetland complexes in the North American Prairie Pothole Region with the WETLANDSCAPE model. Simulations for 63 precipitation × temperature combinations spanning 6°C warming and −20% to +20% annual precipitation change at 19 locations along a mid-continental aridity gradient showed that aridity explained up to 99% of the variation in wetland stage and hydroperiod for all wetland permanence types, and in vegetation cycling for semipermanent wetlands. The magnitude and direction of hydrologic responses depended on whether climate changes increased or decreased water deficits. Warming to 6°C and 20% less precipitation increased wetland water deficits and more strongly decreased wetland stage and hydroperiod from historic levels at low aridity, especially in semipermanent wetlands, where peak vegetation cycling (Cover Cycle Index, CCI) also shifted to lower aridity. In contrast, 20% more precipitation decreased water deficits, increasing wetland stage and hydroperiod most strongly in shallow wetlands at high aridity, but filling semipermanent wetlands and reducing CCI at low aridity. All climate changes narrowed the range of aridity favorable to high productivity. Climate changes that reduce water deficits may help maintain wetlands at high aridity at the expense of those at low aridity, but with warming certain, increased deficits are more likely and will help maintain wetlands at lower aridity but exacerbate loss of wetlands at high aridity. Thus, there is likely not a universally applicable approach to mitigating climate change impacts on freshwater wetlands across regional aridity gradients. Conservation strategies need to account for aridity-specific effects of climate change on freshwater wetland ecosystems

Plant-based protein sources applied as ingredients in meat analogues sustainable production.

Abstract:Though obtained from vegetable ingredients, meat analogues are replacers of traditional meat products. They mimic the flavor, juiciness, and texture and look similar to their counterparts. The innovation relies on addressing nutrition, wellness, environmental, and social issues. Plant-based sources are seen as healthier and environmentally friendly for some people. Therefore, this review summarizes nutritious vegetable sources as alternative protein-based ingredients in meat analogues for sustainable development in the food production chain. A survey was conducted from January 2019 to December 2023 in three databases to find out the most used vegetable sources rich in protein, scientific journals, gaps, and legislation on this topic. The main protein-rich ingredients in the timeline publications were soybean, pea, chickpea, peanuts, oat, and isolates from these sources, besides microalgae extrudates. These raw materials add up the nutritional value and technological properties to meat analogues. Much was done in the later years concerning technology, although there are still gaps on specific legislations for plant-based products worldwide, investments in segregated plants within a meat industry and marketing, so people are more open and aware of the benefits. Concerning the outcomes of this research, it is possible to conclude that meat analogues will remain a focus, and more ingredients are prone to meet consumer demands of innovative and healthy products that go beyond the purpose of just nourishing but indeed offering extra benefits, and opening new possibilities of marketed products. Resumo: Os análogos cárneos são substitutos dos produtos cárneos tradicionais, embora obtidos a partir de ingredientes vegetais. Eles imitam o sabor, a suculência, a textura e são semelhantes aos seus equivalentes. A inovação está em combinar nutrição, bem-estar, questões ambientais e sociais. Fontes vegetais são vistas como mais saudáveis e ecologicamente corretas por algumas pessoas. Portanto, esta revisão resume fontes vegetais nutritivas como ingredientes alternativos proteicos para análogos cárneos visando desenvolvimento sustentável na cadeia produtiva alimentícia. Foi realizada uma pesquisa de Janeiro de 2019 a Dezembro de 2023 em três bases de dados para se descobrir as principais fontes vegetais proteicas, periódicos científicos, lacunas e legislações sobre o tema. Os principais ingredientes proteicos encontrados na linha do tempo estipulada referem-se a soja, ervilha, grão de bico, amendoim, aveia e isolados dessas fontes, além de extrusados de microalgas. Essas matérias-primas agregam valor nutricional e propriedades tecnológicas aos análogos cárneos. Muito foi feito nos últimos anos em relação à tecnologia, embora ainda existam lacunas que dependem de legislações específicas para produtos vegetais mundialmente, investimentos em fábricas segregadas dentro de uma indústria de carne e marketing, para que as pessoas estejam mais abertas e conscientes dos benefícios. Como resultados desta pesquisa é possível concluir que os análogos cárneos continuarão em foco e mais ingredientes tendem a surgir para atender às demandas dos consumidores por produtos inovadores e saudáveis que vão além da nutrição, oferecendo benefícios extras e abrindo novas possibilidades de produtos comercializados.Título em português: Fontes de proteína vegetal aplicadas como ingredientes na produção sustentável de análogos de carne

Active Amplification of the Terrestrial Albedo to Mitigate Climate Change: An Exploratory Study

This study explores the potential to enhance the reflectance of solar insolation by the human settlement and grassland components of the Earth's terrestrial surface as a climate change mitigation measure. Preliminary estimates derived using a static radiative transfer model indicate that such efforts could amplify the planetary albedo enough to offset the current global annual average level of radiative forcing caused by anthropogenic greenhouse gases by as much as 30 percent or 0.76 W/m2. Terrestrial albedo amplification may thus extend, by about 25 years, the time available to advance the development and use of low-emission energy conversion technologies which ultimately remain essential to mitigate long-term climate change. However, additional study is needed to confirm the estimates reported here and to assess the economic and environmental impacts of active land-surface albedo amplification as a climate change mitigation measure.Comment: 21 pages, 3 figures. In press with Mitigation and Adaptation Strategies for Global Change, Springer, N

Self-Duality in D <= 8-dimensional Euclidean Gravity

In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Riemannian manifold. Solutions to these self-duality equations are provided by manifolds of SU(2), SU(3), G_2 and Spin(7) holonomy. The equations in eight dimensions are a master set for those in lower dimensions. By considering gauge fields propagating on these self-dual manifolds and embedding the spin connection in the gauge connection, solutions to the D-dimensional equations for self-dual Yang-Mills fields are found. We show that the Yang-Mills action on such manifolds is topologically bounded from below, with the bound saturated precisely when the Yang-Mills field is self-dual. These results have a natural interpretation in supersymmetric string theory.Comment: 9 pages, Latex, factors in eqn. (6) corrected, acknowledgement and reference added, typos fixe

The PDEs of biorthogonal polynomials arising in the two-matrix model

The two-matrix model can be solved by introducing bi-orthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of bi-orthogonal polynomials (called "windows") satisfy polynomial ODEs as well as deformation equations (PDEs) and finite difference equations (Delta-E) which are all Frobenius compatible and define discrete and continuous isomonodromic deformations for the irregular ODE, as shown in previous works of ours. In the one matrix model an explicit and concise expression for the coefficients of these systems is known and it allows to relate the partition function with the isomonodromic tau-function of the overdetermined system. Here, we provide the generalization of those expressions to the case of bi-orthogonal polynomials, which enables us to compute the determinant of the fundamental solution of the overdetermined system of ODE+PDEs+Delta-E.Comment: 20 pages v1 18 Nov 2003; v2 9 Jan 2004: trivial Latex mistake correcte