Sign regularity preserving linear operators

A matrix A?Rm�n is strictly sign regular/SSR (or sign regular/SR) if for each 1?k?min{m,n}, all k�k minors of A (or non-zero k�k minors of A) have the same sign. This class of matrices contains the totally positive matrices, and was first studied by Schoenberg (1930) to characterize Variation Diminution (VD), a fundamental property in total positivity theory. In this note, we classify all surjective linear mappings L:Rm�n?Rm�n that preserve: (i) sign regularity and (ii) sign regularity with a given sign pattern, as well as (iii) strict versions of these

Mapping the Hierarchical Environmental Transformations of Nanoscale UiO-66 Metal–organic Framework

Metal–organic frameworks (MOFs) hold immense potential for applications from separations to catalysis, yet their long-term behavior across real-world environments remains unclear. Here we introduce a hierarchical exposure framework that tracks the structural and chemical transformations in the archetypal zirconium MOF UiO-66 across sequential compartments─atmospheric gases, air, aqueous media and a biological host─and resolves how prior exposures condition or prime subsequent transformations. Using synchrotron-based spectroscopy, we find that oxidative/reactive gases leave the Zr-carboxylate nodes essentially intact, whereas exposure to environmentally relevant aqueous media initiates partial shifts in local Zr coordination and introduces oxygen into the pores─with transformation extent governed by the chemistry of the environmental matrices. Strikingly, acute exposure (24 h) to the water flea Daphnia magna drives profound framework degradation and respeciation to Zr hydroxide species. Microfocus XRF maps show that Zr is highly localized in the animal’s digestive tract, and region-specific XANES confirms uniform speciation across its tissues. Our findings establish a paradigm shifting cross-compartment transformation hierarchy in which biological processes can dominate the fate of stable MOFs even when abiotic exposures appear benign. Thus, organism-level biotransformation should be performed as a necessary part of environmental safety assessments and materials design

Fourier Domain Gradient Descent Total Least Square/Fourth Algorithm for Efficient Adaptive Direction of Arrival Estimation

Direction-of-arrival (DOA) estimation is formulated within an adaptive-filtering framework that partitions the sensor array into a reference element and an auxiliary array. The auxiliary-array signal is filtered and subtracted from the reference to produce an error, minimized by the complex least-mean-square (LMS) algorithm. Although LMS converges rapidly with a large step size, it exhibits degraded steady-state performance; conversely, the complex least-mean-fourth (LMF) algorithm yields better steady-state accuracy but slower convergence. To combine their strengths, we propose two algorithms: complex LMS/F, which adaptively switches between LMS and LMF algorithms according to a threshold parameter; and complex GD-TLS/F, which employs a gradient-descent total-least-squares criterion to enhance robustness against noisy inputs. We derive the cost functions and weight update rules for both algorithms and introduce a novel computationally efficient Fourier domain approach for DOA estimation from the adaptive filter weights. A comprehensive theoretical analysis that includes a global optimal solution, mean stability, steady-state mean-square performance, and mean-square convergence is presented. Extensive simulation results demonstrate that the proposed algorithms achieve lower estimation error compared to existing adaptive algorithms

Surface functionalization of Polypropylene using Sulfhydrated supercharged green fluorescent proteins

Polypropylene (PP) is widely used in medical packaging and filtration applications for its stability, strength, and low cost. However, its inert and hydrophobic surface limits broader functionality, necessitating surface modification to enhance its properties, such as durability, environmental resistance, and biocompatibility. While traditional coating materials offer improvements, their nonrenewable origins and associated environmental concerns have prompted a growing interest in sustainable alternatives. As a sustainable alternative, protein-based coatings offer inherent biodegradability and tunable functionality. Here, we report a simple, one-step, activation-free method for surface modification of PP using sulfhydrated green fluorescent proteins (GFPs). The approach involves reacting highly cationic GFP with 2-iminothiolane (Traut’s reagent), which targets surface-exposed primary amines and enables the conversion of amino to sulfhydryl group. The modified protein spontaneously adhered to the PP surfaces, forming a stable coating. The influence of surface charge and primary amines on the coating efficiency was evaluated using GFP variants with differing ratios of basic to acidic residues. We also monitored the coating efficiency under a range of physicochemical conditions, including varying the pH, ionic strength, reducing agents, and metal ion chelators. Surface morphology and property were characterized by atomic force microscopy, scanning electron microscopy, X-ray photoelectron spectroscopy, and contact angle measurements. Finally, the protein-coated surface was functionalized with citrate-capped gold nanoparticles, which catalyzed the reduction of p-nitrophenol to p-aminophenol. We anticipate that this protein-based strategy will offer a sustainable and versatile platform for functionalizing polypropylene using intrinsic protein chemistry with potential applications in catalysis

From nature to engineering: translational progress in biological, biomimetic, and bioinspired nanomaterials for next-generation technologies

Nature provides a rich source of design principles for the development of advanced micro- and nanostructured materials with functionalities that are difficult to achieve through conventional engineering alone. This review analyzes the translational progression from biological nanomaterials (NMs) derived directly from natural components, through biomimetic systems that replicate hierarchical structure and function, to bioinspired materials that abstract and re-engineer biological design logic. Emphasis is placed on synthesis methodologies, hierarchical organization, and structure-property correlations that govern macroscopic performance. The review critically examines representative material classes, including protein and polysaccharide assemblies, polymer nanocomposites, carbon-based nanostructures, hybrid scaffolds, and dynamic polymer networks with particular attention to biomedical applications such as tissue regeneration, wound healing, drug and gene delivery, and biointerfacing devices. Broader translational relevance is discussed across biotechnology, agriculture, energy, environmental remediation, and surface engineering, highlighting shared functional requirements and constraints. By integrating quantitative structure-property relationships with cross-domain analysis, this review identifies recurring technical bottlenecks related to interfacial stability, functional integration, and manufacturability. Common design rules governing successful translation are distilled, emphasizing hierarchical integration, interface-dominated behaviour, and scalability-aware fabrication. Together, these insights provide a critical framework for advancing biological, biomimetic, and bioinspired NMs from laboratory studies toward robust, application-relevant technologies

How good are inducing points for dataset distillation?

Dataset distillation methods learn a representative summary of the full dataset such that training on the distilled data is more efficient in terms of time and space. The current state-of-the-art methods exploit the correspondence between infinitely wide neural networks (NNs) and kernel ridge regression to design distillation methods that result in high-quality summaries of the data. In this work, we leverage the correspondence between infinitely wide networks and Gaussian Processes(GPs) for learning a distilled dataset. We investigate the feasibility of using the inducing points method for Gaussian Processes, as a data distillation method. While most of the existing dataset distillation methods are based on loss or gradient matching, our method looks at the function space approximation, facilitated by the NN-GP correspondence. Additionally, using recent theoretical results on GP regression and neural tangent kernels(NTKs), we also provide an upper bound on the size of the distilled data. We demonstrate the utility of inducing points as distilled data on a set of datasets empirically

Explaining 95 GeV anomalies in the 2-Higgs doublet model type-I

We show how the 2-Higgs Doublet Model (2HDM) Type-I can explain some excesses recently seen at the Large Hadron Collider (LHC) in γγ and τ+τ− final states in turn matching Large Electron Positron (LEP) data in bb¯ signatures, all anomalies residing around 95 GeV. The explanation to such anomalous data is found in the aforementioned scenario when in inverted mass hierarchy, in two configurations: i) when the lightest CP-even Higgs state is alone capable of reproducing the excesses; ii) when a combination of such a state and the CP-odd Higgs boson is able to do so. To test further this scenario, we present some Benchmark Points (BPs) of it amenable to phenomenological investigation

The Genius of Koshliakov and his indomitable spirit

From a Soviet labor camp, Nikolai Koshliakov developed a striking generalization of the Riemann zeta function under conditions that defy imagination. This article traces the origins of his work on transcendental functions arising from a generalized Riemann equation. Along the way, it reveals how profound mathematics can emerge even in the most hostile environments