New Bounds and Computations on Prime-Indexed Primes

In a 2009 article, Barnett and Broughan considered the set of prime-index primes. If the prime numbers are listed in increasing order (2, 3, 5, 7, 11, 13, 17, . . .), then the prime-index primes are those which occur in a prime-numbered position in the list (3, 5, 11, 17, . . .). Barnett and Broughan established a prime-indexed prime number theorem analogous to the standard prime number theorem and gave an asymptotic for the size of the n-th prime-indexed prime. We give explicit upper and lower bounds for π2(x), the number of prime-indexed primes up to x, as well as upper and lower bounds on the n-th prime-indexed prime, all improvements on the bounds from 2009. We also prove analogous results for higher iterates of the sequence of primes. We present empirical results on large gaps between prime-index primes, the sum of inverses of the prime-index primes, and an analog of Goldbach’s conjecture for prime-index primes

Examining the Effect of Charged Lipids on Mitochondrial Outer Membrane Dynamics Using Atomistic Simulations

The outer mitochondrial membrane (OMM) is involved in multiple cellular functions such as apoptosis, inflammation and signaling via its membrane-associated and -embedded proteins. Despite the central role of the OMM in these vital phenomena, the structure and dynamics of the membrane have regularly been investigated in silico using simple two-component models. Accordingly, the aim was to generate the realistic multi-component model of the OMM and inspect its properties using atomistic molecular dynamics (MD) simulations. All major lipid components, phosphatidylinositol (PI), phosphatidylcholine (PC), phosphatidylethanolamine (PE), and phosphatidylserine (PS), were included in the probed OMM models. Because increased levels of anionic PS lipids have potential effects on schizophrenia and, more specifically, on monoamine oxidase B enzyme activity, the effect of varying the PS concentration was explored. The MD simulations indicate that the complex membrane lipid composition (MLC) behavior is notably different from the two-component PC-PE model. The MLC changes caused relatively minor effects on the membrane structural properties such as membrane thickness or area per lipid; however, notable effects could be seen with the dynamical parameters at the water-membrane interface. Increase of PS levels appears to slow down lateral diffusion of all lipids and, in general, the presence of anionic lipids reduced hydration and slowed down the PE headgroup rotation. In addition, sodium ions could neutralize the membrane surface, when PI was the main anionic component; however, a similar effect was not seen for high PS levels. Based on these results, it is advisable for future studies on the OMM and its protein or ligand partners, especially when wanting to replicate the correct properties on the water-membrane interface, to use models that are sufficiently complex, containing anionic lipid types, PI in particular

Corredores de biodiversidade na Bacia do Alto Paraguai: modelagem, mapeamento e aplicação em políticas públicas para sustentabilidade.

Os resultados apresentados neste Documento, portanto, vêm convergir com a necessidade de construção de estratégias de planejamento territorial e uso da terra, uma vez que abordam um dos pontos fundamentais para a conservação da biodiversidade, que é a conectividade das paisagens para a flora e a fauna. A conservação da biodiversidade, além de uma necessidade estratégica para a humanidade, está entre os pilares do desenvolvimento sustentável, ou ainda do uso ecologicamente sustentável de recursos naturais e de uso da terra

Effects of Brazil's political crisis on the science needed for biodiversity conservation.

The effects of Brazil's political crisis on science funding necessary for biodiversity conservation are likely to be global. Brazil is not only the world?s most biodiverse nation, it is responsible for the greater part of the Amazon forest, which regulates the climate and provides rain to much of southern South America. Brazil was a world leader in satellite monitoring of land-use change, in-situ biodiversity monitoring, reduction in tropical-forest deforestation, protection of indigenous lands, and a model for other developing nations. Coordinated public responses will be necessary to prevent special-interest groups from using the political crisis to weaken science funding, environmental legislation and law enforcement

Effects of Brazil's political crisis on the science needed for biodiversity conservation

The effects of Brazil’s political crisis on science funding necessary for biodiversity conservation are likely to be global. Brazil is not only the world’s most biodiverse nation, it is responsible for the greater part of the Amazon forest, which regulates the climate and provides rain to much of southern South America. Brazil was a world leader in satellite monitoring of land-use change, in-situ biodiversity monitoring, reduction in tropical-forest deforestation, protection of indigenous lands, and a model for other developing nations. Coordinated public responses will be necessary to prevent special-interest groups from using the political crisis to weaken science funding, environmental legislation and law enforcement. Keywords: Brazil, biodiversity, climate change, governance, fundin

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear un derstanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5–7 vast areas of the tropics remain understudied.8–11 In the American tropics, Amazonia stands out as the world’s most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepre sented in biodiversity databases.13–15 To worsen this situation, human-induced modifications16,17 may elim inate pieces of the Amazon’s biodiversity puzzle before we can use them to understand how ecological com munities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple or ganism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region’s vulnerability to environmental change. 15%–18% of the most ne glected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lostinfo:eu-repo/semantics/publishedVersio

Some recent progress on sharp Fourier restriction theory

The purpose of this note is to discuss several results that have been obtained in the last decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than aiming at full generality, we focus on several concrete examples of underlying manifolds with large groups of symmetries, which sometimes allow for simple geometric proofs. We mention several open problems along the way, and include an appendix on integration on manifolds using delta calculus