Topological properties of semigroup primes of a commutative ring

A semigroup prime of a commutative ring $R$ is a prime ideal of the semigroup $(R,\cdot)$. One of the purposes of this paper is to study, from a topological point of view, the space \scal(R) of prime semigroups of $R$. We show that, under a natural topology introduced by B. Olberding in 2010, \scal(R) is a spectral space (after Hochster), spectral extension of \Spec(R), and that the assignment R\mapsto\scal(R) induces a contravariant functor. We then relate -- in the case $R$ is an integral domain -- the topology on \scal(R) with the Zariski topology on the set of overrings of $R$. Furthermore, we investigate the relationship between \scal(R) and the space $\boldsymbol{\mathcal{X}}(R)$ consisting of all nonempty inverse-closed subspaces of \spec(R), which has been introduced and studied in C.A. Finocchiaro, M. Fontana and D. Spirito, "The space of inverse-closed subsets of a spectral space is spectral" (submitted). In this context, we show that \scal( R) is a spectral retract of $\boldsymbol{\mathcal{X}}(R)$ and we characterize when \scal( R) is canonically homeomorphic to $\boldsymbol{\mathcal{X}}(R)$, both in general and when \spec(R) is a Noetherian space. In particular, we obtain that, when $R$ is a B\'ezout domain, \scal( R) is canonically homeomorphic both to $\boldsymbol{\mathcal{X}}(R)$ and to the space \overr(R) of the overrings of $R$ (endowed with the Zariski topology). Finally, we compare the space $\boldsymbol{\mathcal{X}}(R)$ with the space \scal(R(T)) of semigroup primes of the Nagata ring $R(T)$, providing a canonical spectral embedding \xcal(R)\hookrightarrow\scal(R(T)) which makes \xcal(R) a spectral retract of \scal(R(T)).Comment: 21 page

A topological version of Hilbert's Nullstellensatz

We prove that the space of radical ideals of a ring $R$, endowed with the hull-kernel topology, is a spectral space, and that it is canonically homeomorphic to the space of the nonempty Zariski closed subspaces of Spec$(R)$, endowed with a Zariski-like topology.Comment: J. Algebra (to appear

Electron-hole pairing in graphene-GaAs heterostructures

Vertical heterostructures combining different layered materials offer novel opportunities for applications and fundamental studies of collective behavior driven by inter-layer Coulomb coupling. Here we report heterostructures comprising a single-layer (or bilayer) graphene carrying a fluid of massless (massive) chiral carriers, and a quantum well created in GaAs 31.5 nm below the surface, supporting a high-mobility two-dimensional electron gas. These are a new class of double-layer devices composed of spatially-separated electron and hole fluids. We find that the Coulomb drag resistivity significantly increases for temperatures below 5-10 K, following a logarithmic law. This anomalous behavior is a signature of the onset of strong inter-layer correlations, compatible with the formation of a condensate of permanent excitons. The ability to induce strongly-correlated electron-hole states paves the way for the realization of coherent circuits with minimal dissipation and nanodevices including analog-to-digital converters and topologically protected quantum bits.Comment: 9 pages, 9 figures, 72 reference

INSIDIA:a FIJI macro delivering high-throughput and high-content spheroid invasion analysis

Time-series image capture of in vitro 3D spheroidal cancer models embedded within an extracellular matrix affords examination of spheroid growth and cancer cell invasion. However, a customizable, comprehensive and open source solution for the quantitative analysis of such spheroid images is lacking. Here, the authors describe INSIDIA (INvasion SpheroID ImageJ Analysis), an open-source macro implemented as a customizable software algorithm running on the FIJI platform, that enables high-throughput high-content quantitative analysis of spheroid images (both bright-field gray and fluorescent images) with the output of a range of parameters defining the spheroid “tumor” core and its invasive characteristics

The Thermal Structural Transition of Alpha-Crystallin Modulates Subunit Interactions and Increases Protein Solubility

Background: Alpha crystallin is an oligomer composed of two types of subunits, alpha-A and alpha-B crystallin, and is the major constituent of human lens. The temperature induced condensation of alpha-crystallin, the main cause for eye lens opacification (cataract), is a two step-process, a nucleation followed by an aggregation phase, and a protective effect towards the aggregation is exhibited over the alpha crystallin phase transition temperature (Tc = 318.16 K). Methods/Results: To investigate if a modulation of the subunit interactions over Tc could trigger the protective mechanism towards the aggregation, we followed, by using simultaneously static and dynamic light scattering, the temperature induced condensation of alpha-crystallin. By developing a mathematical model able to uncouple the nucleation and aggregation processes, we find a previously unobserved transition in the nucleation rate constant. Its temperature dependence allows to determine fundamental structural parameters, the chemical potential (Dm) and the interfacial tension (c) of the aggregating phase, that characterize subunit interactions. Conclusions/General Significance: The decrease of both Dm and c at Tc, and a relative increase in solubility, reveal a significative decrease in the strenght of alpha-crystallin subunits interactions, which protects from supramolecolar condensation in hypertermic conditions. On the whole, we suggest a general approach able to understand the structural and kinetic mechanisms involved in aggregation-related diseases and in drugs development and testing

Face masks and nanotechnology: Keep the blue side up

Coronavirus Disease 2019 (COVID-19) is one of the biggest challenges of the 21st century. While researchers are working on vaccine development and elucidating the mechanism of action and evolution of the harmful SARS-CoV-2, the current most important public health measure, second only to social distancing, is the obligatory wearing of facial protection. The Centers for Disease Control and Prevention recommended in April 2020 that the public wear face coverings in areas with high rates of transmission based on epidemiological evidence on the strong relationship between mask wearing and pandemic control. This protection against SARS-CoV-2 and other airborne pathogens, boost the design and production of innovative solutions by industry stakeholders. Nanoparticles, nanofibers, and other pioneering technologies based on nanomaterials have been introduced in mask production chains to improve performance and confer antiviral properties. During an emergency like COVID-19, these products directly available to the public should be carefully analyzed in terms of efficacy and possible long-term effects on the wearers’ skin and lungs as well as on the environment. This opinion paper provides a wealth of information on the role of nanotechnologies in improving the performance of facial masks and on possible future consequences caused by a poorly regulated use of nanotechnology in textiles

Effects of Spatial Food Distribution on Search Behavior in Rats (Rattus norvegicus)

To analyze how search strategies are adapted according to the geometric distribution of food sources, the authors submitted rats to a search task in which they had to explore 9 food trays in an open field and avoid visiting already-depleted trays. Trays were spatially arranged in 4 independent configurations: a cross, a 3 × 3 matrix, 3 clusters of 3 trays each, and a random configuration. Rats exhibited differential search efficiency as a specific effect of the susceptibility of the configurations to being explored in a principled way: Crosses were first, matrices or clusters were in the middle, and random configurations were last. Although no exhaustive searches or highly principled patterns were observed in any of the configurations, performances improved as the sessions went by. Thus, structural affordances of the environment influence the construction not only of search strategies but also of information linked to where the reward is. © 2007 American Psychological Association