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Let (Mⁿ,g) be a complete simply connectedn-dimensional Riemannian manifold with curvature bounds Sect_g≤ κ for κ ≤ 0 and Ric_g≥ (n− 1)KgforK≤ 0. We prove that for any bounded domain Ω ⊂Mⁿwith diameterdand Lipschitz boundary, if Ω* is a geodesic ball in the simply connected space form with constant sectional curvature κ enclosing the same volume as Ω, then σ₁(Ω) ≤Cσ₁(Ω*), where σ₁(Ω) and σ₁(Ω*) denote the first nonzero Steklov eigenvalues of Ω and Ω* respectively, andC=C(n, κ,K,d) is an explicit constant. When κ =K, we haveC= 1 and recover the Brock–Weinstock inequality, asserting that geodesic balls uniquely maximize the first nonzero Steklov eigenvalue among domains of the same volume, in Euclidean space and the hyperbolic space. 

The abrupt drop of resistance to zero at a critical temperature is a key signature of the current paradigm of the metal–superconductor transition. However, the emergence of an intermediate bosonic insulating state characterized by a resistance peak preceding the onset of the superconducting transition has challenged this traditional understanding. Notably, this phenomenon has been predominantly observed in disordered or chemically doped low-dimensional systems, raising intriguing questions about the generality of the effect and its underlying fundamental physics. Here, we present a systematic experimental study of compressed elemental sulfur, an undoped three-dimensional (3D) high-pressure superconductor, with detailed measurements of electrical resistance as a function of temperature, magnetic field, and current. The anomalous resistance peak observed in this 3D system is interpreted based on an empirical model of a metal–bosonic insulator–superconductor transition, potentially driven by vortex dynamics under magnetic field and energy dissipation processes. These findings offer a fresh platform for theoretical analysis of the decades-long enigmatic of the underlying mechanism of this phenomenon. 

Disordered linkers (DLs) are intrinsically disordered regions that facilitate movement between adjacent functional regions/domains, contributing to many key cellular functions. The recently completed second Critical Assessments of protein Intrinsic Disorder prediction (CAID2) experiment evaluated DL predictions by considering a rather narrow scenario when predicting 40 proteins that are already known to have DLs. We expand this evaluation by using a much larger set of nearly 350 test proteins from CAID2 and by investigating three distinct scenarios: (1) prediction residues in DLs vs. in non-DL regions (typical use of DL predictors); (2) prediction of residues in DLs vs. other disordered residues (to evaluate whether predictors can differentiate residues in DLs from other types of intrinsically disordered residues); and (3) prediction of proteins harboring DLs. We find that several methods provide relatively accurate predictions of DLs in the first scenario. However, only one method, APOD, accurately identifies DLs among other types of disordered residues (scenario 2) and predicts proteins harboring DLs (scenario 3). We also find that APOD’s predictive performance is modest, motivating further research into the development of new and more accurate DL predictors. We note that these efforts will benefit from a growing amount of training data and the availability of sophisticated deep network models and emphasize that future methods should provide accurate results across the three scenarios. 

Abstract The DescribePROT database of amino acid-level descriptors of protein structures and functions was substantially expanded since its release in 2020. This expansion includes substantial increase in the size, scope, and quality of the underlying data, the addition of experimental structural information, the inclusion of new data download options, and an upgraded graphical interface. DescribePROT currently covers 19 structural and functional descriptors for proteins in 273 reference proteomes generated by 11 accurate and complementary predictive tools. Users can search our resource in multiple ways, interact with the data using the graphical interface, and download data at various scales including individual proteins, entire proteomes, and whole database. The annotations in DescribePROT are useful for a broad spectrum of studies that include investigations of protein structure and function, development and validation of predictive tools, and to support efforts in understanding molecular underpinnings of diseases and development of therapeutics. DescribePROT can be freely accessed at http://biomine.cs.vcu.edu/servers/DESCRIBEPROT/.