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This paper investigates the integration of multiple geometries present within a ReLU-based neural network. A ReLU neural network determines a piecewise affine linear continuous map, M , from an input space ℝ m to an output space ℝ n . The piecewise behavior corresponds to a polyhedral decomposition of ℝ m . Each polyhedron in the decomposition can be labeled with a binary vector (whose length equals the number of ReLU nodes in the network) and with an affine linear function (which agrees with M when restricted to points in the polyhedron). We develop a toolbox that calculates the binary vector for a polyhedra containing a given data point with respect to a given ReLU FFNN. We utilize this binary vector to derive bounding facets for the corresponding polyhedron, extraction of "active" bits within the binary vector, enumeration of neighboring binary vectors, and visualization of the polyhedral decomposition (Python code is available at https://github.com/cglrtrgy/GoL_Toolbox). Polyhedra in the polyhedral decomposition of ℝ m are neighbors if they share a facet. Binary vectors for neighboring polyhedra differ in exactly 1 bit. Using the toolbox, we analyze the Hamming distance between the binary vectors for polyhedra containing points from adversarial/nonadversarial datasets revealing distinct geometric properties. A bisection method is employed to identify sample points with a Hamming distance of 1 along the shortest Euclidean distance path, facilitating the analysis of local geometric interplay between Euclidean geometry and the polyhedral decomposition along the path. Additionally, we study the distribution of Chebyshev centers and related radii across different polyhedra, shedding light on the polyhedral shape, size, clustering, and aiding in the understanding of decision boundaries., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Liu, Caglar, Peterson and Kirby.)

The three-dimensional arrangement of atoms in molecules is essential for understanding their properties and behavior. Traditional 2D representations and digital 3D models presented on 2D media often fall short in conveying the complexity of molecular structures. Autostereoscopic displays, often marketed as "holographic" displays, pose a potential solution to this challenge. These displays, with their multi-view and single-view configurations, promise to advance chemistry education and research by offering accurate 3D representations with depth and parallax. In this perspective, I delve into the possibilities and limitations of autostereoscopic displays in chemistry, discussing the underlying technology and potential applications, from research to teaching and science communication. Multi-view autostereoscopic displays excel in facilitating collaborative work by enabling multiple viewers to simultaneously perceive the same 3D structure from different angles. However, they currently suffer from low resolution and high cost, which could limit their immediate widespread adoption. Conversely, single-view autostereoscopic displays with eye-tracking, while limited to one viewer at a time, provide higher resolution at a lower cost, thus suggesting that they might become the technology of the future given the balance of price to performance. Despite current limitations, autostereoscopic displays possess undeniable potential for shaping the future of chemistry education and research., (© 2023 The Authors. Chemistry - A European Journal published by Wiley-VCH GmbH.)

The junChS-F12 composite method has been improved by means of the latest implementation of the CCSD(F12*)(T+) ansatz and validated for the thermochemistry of molecules containing atoms of the first three rows of the periodic table. A thorough benchmark showed that this model, in conjunction with cost-effective revDSD-PBEP86-D3(BJ) reference geometries, offers an optimal compromise between accuracy and computational cost. If improved geometries are sought, the most effective option is to add MP2-F12 core-valence correlation corrections to CCSD(T)-F12b/jun-cc-pVTZ geometries without the need of performing any extrapolation to the complete basis set limit. In the same vein, CCSD(T)-F12b/jun-cc-pVTZ harmonic frequencies are remarkably accurate without any additional contribution. Pilot applications to noncovalent intermolecular interactions, conformational landscapes, and tautomeric equilibria confirm the effectiveness and reliability of the model., (© 2023 The Authors. Journal of Computational Chemistry published by Wiley Periodicals LLC.)

Within certain categories of geometric shapes, prototypical exemplars that best characterize the category have been evidenced. These geometric prototypes are classically identified through the visual and haptic perception or motor production and are usually characterized by their spatial dimension. However, whether prototypes can be recalled through the auditory channel has not been formally investigated. Here we address this question by using auditory cues issued from timbre-modulated friction sounds evoking human drawing elliptic movements. Since non-spatial auditory cues were previously found useful for discriminating distinct geometric shapes such as circles or ellipses, it is hypothesized that sound dynamics alone can evoke shapes such as an exemplary ellipse. Four experiments were conducted and altogether revealed that a common elliptic prototype emerges from auditory, visual, and motor modalities. This finding supports the hypothesis of a common coding of geometric shapes according to biological rules with a prominent role of sensory-motor contingencies in the emergence of such prototypical geometry., Competing Interests: Declaration of Competing Interest The authors declare no competing interests., (Copyright © 2023 Elsevier B.V. All rights reserved.)

In this paper, for a highly coupled two-stage ejector-based cooling cycle, the optimization of primary nozzle length and angle of the second-stage ejector under varied primary nozzle diameters of the second stage was conducted first. Next, the evaluation for the influence of variable back pressure on ER of the two-stage ejector was performed. Last, the identification of the effect of the variable back pressure on the key geometries of the two-stage ejector was carried out. The results revealed that: (1) with the increase of the nozzle diameter at the second stage, the ER of both stages decreased with the increases of the length and angle of the converging section of the second-stage primary nozzle; (2) the pressure lift ratio range of the second-stage ejector in the critical mode gradually increased with the increase of the nozzle diameter of the second-stage; (3) when the pressure lift ratio increased from 102% to 106%, the peak ER of the second-stage decreased, and the influence of the area ratio and nozzle exit position of the second-stage ejector on its ER was reduced; (4) with the increase of nozzle diameter of the second-stage, the influence of area ratio and nozzle exit position of the second-stage on the second-stage performance decreased; and (5) the optimal AR of the second stage decreased but the optimal nozzle exit position of the second stage kept constant with the pressure lift ratio of the two-stage ejector.

Cold Spray Additive Manufacturing (CSAM) is an emergent technique to produce parts by the additive method, and, like other technologies, it has pros and cons. Some advantages are using oxygen-sensitive materials to make parts, such as Ti alloys, with fast production due to the high deposition rate, and lower harmful residual stress levels. However, the limitation in the range of the parts' geometries is a huge CSAM con. This work presents a new conceptual strategy for CSAM spraying. The controlled manipulation of the robot arm combined with the proper spraying parameters aims to optimize the deposition efficiency and the adhesion of particles on the part sidewalls, resulting in geometries from thin straight walls, less than 5 mm thick, up to large bulks. This new strategy, Metal Knitting, is presented regarding its fundamentals and by comparing the parts' geometries produced by Metal Knitting with the traditional strategy. The Metal Knitting described here made parts with vertical sidewalls, in contrast to the 40 degrees of inclination obtained by the traditional strategy. Their mechanical properties, microstructures, hardness, and porosity are also compared for Cu, Ti, Ti6Al4V, 316L stainless steel, and Al.

Micrometer-sized hydrogels are cross-linked three-dimensional network matrices with high-water contents and dimensions ranging from several to hundreds of micrometers. Due to their excellent biocompatibility and capability to mimic physiological microenvironments in vivo, micrometer-sized hydrogels have attracted much attention in the biomedical engineering field. Their biological properties and applications are primarily influenced by their chemical compositions and geometries. However, inhomogeneous morphologies and uncontrollable geometries limit traditional micrometer-sized hydrogels obtained by bulk mixing. In contrast, microfluidic technology holds great potential for the fabrication of micrometer-sized hydrogels since their geometries, sizes, structures, compositions, and physicochemical properties can be precisely manipulated on demand based on the excellent control over fluids. Therefore, micrometer-sized hydrogels fabricated by microfluidic technology have been applied in the biomedical field, including drug encapsulation, cell encapsulation, and tissue engineering. This review introduces micrometer-sized hydrogels with various geometries synthesized by different microfluidic devices, highlighting their advantages in various biomedical applications over those from traditional approaches. Overall, emerging microfluidic technologies enrich the geometries and morphologies of hydrogels and accelerate translation for industrial production and clinical applications., (© 2022 The Authors. Advanced Healthcare Materials published by Wiley-VCH GmbH.)

TiO 2 nanotubes (TiO 2 NTs) are beneficial for photogenerated electron separation in photocatalysis. In order to improve the utilization rate of TiO 2 NTs in the visible light region, an effective method is to use Au n cluster deposition-modified TiO 2 NTs. It is of great significance to investigate the mechanism of Au n clusters supported on TiO 2 NTs to strengthen its visible-light response. In this work, the structures, electronic properties, Mulliken atomic charge, density of states, band structure, and deformation density of Au n ( n = 1, 8, 13) clusters supported on TiO 2 NTs were investigated by DMOL3. Based on published research results, the most stable adsorption configurations of Au n ( n = 1, 8, 13) clusters supported with TiO 2 NTs were obtained. The adsorption energy increased as the number of Au adatoms increased linearly. The Au n clusters supported on TiO 2 NTs carry a negative charge. The band gaps of the three most stable structures of each adsorption system decreased compared to TiO 2 NTs; the valence top and the conduction bottom of the Fermi level come mainly from the contribution of 5 d and 6 s -Au. The electronic properties of the 5 d and 6 s impurity orbitals cause valence widening and band gap narrowing.

Computationally obtaining structural parameters along a reaction coordinate is commonly performed with Kohn-Sham density functional theory which generally provides a good balance between speed and accuracy. However, CPU times still range from inconvenient to prohibitive, depending on the size of the system under study. Herein, the tight binding GFN2-xTB method [C. Bannwarth, S. Ehlert, S. Grimme, J. Chem. Theory Comput. 2019, 15, 1652] is investigated as an alternative to produce reasonable geometries along a reaction path, that is, reactant, product and transition state structures for a series of transformations involving gold complexes. A small mean error (1 kcal/mol) was found, with respect to an efficient composite hybrid-GGA exchange-correlation functional (PBEh-3c) paired with a double-ζ basis set, which is 2-3 orders of magnitude slower. The outlined protocol may serve as a rapid tool to probe the viability of proposed mechanistic pathways in the field of gold catalysis., (© 2021 The Authors. ChemPhysChem published by Wiley-VCH GmbH.)

The shape of nanoparticles is known recently as an important design parameter influencing considerably the fate of nanoparticles with and in biological systems. Several manufacturing techniques to generate nonspherical nanoparticles as well as studies on in vitro and in vivo effects thereof have been described. However, nonspherical nanoparticle shape stability in physiological-related conditions and the impact of formulation parameters on nonspherical nanoparticle resistance still need to be investigated. To address these issues, different nanoparticle fabrication methods using biodegradable polymers are explored to produce nonspherical nanoparticles via the prevailing film-stretching method. In addition, systematic comparisons to other nanoparticle systems prepared by different manufacturing techniques and less biodegradable materials (but still commonly utilized for drug delivery and targeting) are conducted. The study evinces that the strong interplay from multiple nanoparticle properties (i.e., internal structure, Young's modulus, surface roughness, liquefaction temperature [glass transition (T g ) or melting (T m )], porosity, and surface hydrophobicity) is present. It is not possible to predict the nonsphericity longevity by merely one or two factor(s). The most influential features in preserving the nonsphericity of nanoparticles are existence of internal structure and low surface hydrophobicity (i.e., surface-free energy (SFE) > ≈55 mN m -1 , material-water interfacial tension <6 mN m -1 ), especially if the nanoparticles are soft (<1 GPa), rough (R rms > 10 nm), porous (>1 m 2 g -1 ), and in possession of low bulk liquefaction temperature (<100 °C). Interestingly, low surface hydrophobicity of nanoparticles can be obtained indirectly by the significant presence of residual stabilizers. Therefore, it is strongly suggested that nonsphericity of particle systems is highly dependent on surface chemistry but cannot be appraised separately from other factors. These results and reviews allot valuable guidelines for the design and manufacturing of nonspherical nanoparticles having adequate shape stability, thereby appropriate with their usage purposes. Furthermore, they can assist in understanding and explaining the possible mechanisms of nonspherical nanoparticles effectivity loss and distinctive material behavior at the nanoscale., (© 2019 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)