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This research investigates the dynamic behavior of functionally graded graphene platelet honeycomb sandwich (FG-GPLHS) plates coupled with stiffeners under moving loads, a critical area lacking in current research. Utilizing sandwich equivalence theory, a model of the FG-GPLHS plate is constructed, and the coupling of stiffeners is achieved through displacement continuity conditions combined with displacement coordinate transformation. Artificial virtual spring methods are employed to simulate boundary conditions and establish the force matrix for moving loads. The spectral geometry method (SGM)-Chebyshev method is employed to solve for the model, yielding insights into its dynamic behavior. This research takes into account a number of factors such as honeycomb parameters, boundary conditions, loading velocities, stiffeners cross-section properties, graphene platelet (GPL) distribution pattern and mass fraction to evaluate their effects on the vibration damping effectiveness of the structure. In particular, the effect of honeycomb dimensions and GPL parameters on the vibration resistance and stability of the model under moving loads, which can realize a wider range of application values for this structure in engineering. [ABSTRACT FROM AUTHOR]

Objectives: Understanding human tooth structure fluorescence aids clinical and forensic dentistry, enabling tissue/material differentiation and the creation of esthetic restorative materials. Material manufacturers seek to replicate natural tooth fluorescence, necessitating the development of novel techniques to detect them. Procuring human teeth for research is challenging due to ethical and infection control standards, prompting a search for alternative models. Material and Methods: This study compares visible light‐induced fluorescence of porcine and human teeth to assess the value of porcine teeth as human analogs. Using a pulsed laser, an optimal fluorescence‐inducing wavelength was determined, followed by comparing fluorescence spectra between species. Results: Luminescence sensitivity and lifetimes were comparable between species, but spectral geometry differed. Conclusion: Porcine teeth, commonly used for dental material investigations, may not be suitable for dental fluorescence studies due to spectral differences. Accurately mimicking human tooth fluorescence remains complex. Further research is needed to develop reliable alternatives for dental fluorescence investigations that will advance clinical and forensic dentistry. [ABSTRACT FROM AUTHOR]

The study of protein molecular surfaces enables to better understand and predict protein interactions. Different methods have been developed in computer vision to compare surfaces that can be applied to protein molecular surfaces. The present work proposes a method using the Wave Kernel Signature: Protein LOcal Surficial Similarity Screening (PLO3S). The descriptor of the PLO3S method is a local surface shape descriptor projected on a unit sphere mapped onto a 2D plane and called Surface Wave Interpolated Maps (SWIM). PLO3S allows to rapidly compare protein surface shapes through local comparisons to filter large protein surfaces datasets in protein structures virtual screening protocols.

This paper presents a semi-analytical approach to analyze the dynamic response characteristics of lattice composite sandwich plates with varying lattice truss cores. Under the premise of satisfying the classical laminate theory assumptions of Allen, the lattice truss core is considered an equivalent homogenized structure. Then, the displacement equations for the sandwich plate utilize the first-order shear deformation theory (FSDT). The energy equation for the sandwich plate is constructed using the Lagrange energy method and solved through the Rayleigh–Ritz method. To mimic arbitrary boundary conditions, artificial boundary spring techniques are utilized. The spectral geometry method (SGM) is utilized to describe the displacement field of dynamic equations and boundary conditions. Legendre polynomials are chosen to construct admissible displacement functions for the structure, supplemented by auxiliary polynomials to eliminate discontinuities at the boundaries. The method’s validity is verified through comparisons with relevant literature and finite element method (FEM). Based on free vibration analysis, both steady-state and transient displacement responses of laminated composite sandwich plates are examined, considering the influences of structural parameters and boundary conditions on dynamic response characteristics. These works can provide suitable theoretical references for the engineering field. [ABSTRACT FROM AUTHOR]

We realize that a Sierpiński arrowhead curve (SAC) fills a Sierpiński gasket (SG) in the same manner as a Peano curve fills a square. Namely, in the limit of an infinite number of iterations, the fractal SAC remains self-avoiding, such that S A C ⊂ S G . Therefore, SAC differs from SG in the same sense as the self-avoiding Peano curve P C ⊂ 0,1 2 differs from the square. In particular, the SG has three-line segments constituting a regular triangle as its border, whereas the border of SAC has the structure of a totally disconnected fat Cantor set. Thus, in contrast to the SG, which has loops at all scales, the SAC is loopless. Consequently, although both patterns have the same similarity dimension D = ln ⁡ 3 / ln ⁡ 2 , their connectivity dimensions are different. Specifically, the connectivity dimension of the self-avoiding SAC is equal to its topological dimension d l S A C = d = 1 , whereas the connectivity dimension of the SG is equal to its similarity dimension, that is, d l S G = D . Therefore, the dynamic properties of SG and SAC are also different. Some other noteworthy features of the Sierpiński triangle are also highlighted. [ABSTRACT FROM AUTHOR]

Our research explores the application of Riemannian geometry and spectral embedding in the context of electroencephalogram (EEG) signal analysis for cognitive state classification. Leveraging the PyRiemann library and the AlphaWaves dataset, our study employs covariance estimation and the minimum distance to mean (MDM) classifier within a machine learning pipeline. The classification accuracy is assessed through stratified k-fold cross-validation. Furthermore, we introduce a novel visualization approach by calculating the spectral embedding of covariance matrices, providing insights into the underlying structure of the EEG epochs. Our findings showcase the potential of Riemannian geometry and spectral embedding as powerful tools in the domain of EEG-based cognitive state classification, contributing to the broader field of brain signal analysis and paving the way for automated and advanced neurocognitive studies. [ABSTRACT FROM AUTHOR]

This study conducts an in-depth analysis of clustering small molecules using spectral geometry and deep learning techniques. We applied a spectral geometric approach to convert molecular structures into triangulated meshes and used the Laplace–Beltrami operator to derive significant geometric features. By examining the eigenvectors of these operators, we captured the intrinsic geometric properties of the molecules, aiding their classification and clustering. The research utilized four deep learning methods: Deep Belief Network, Convolutional Autoencoder, Variational Autoencoder, and Adversarial Autoencoder, each paired with k-means clustering at different cluster sizes. Clustering quality was evaluated using the Calinski–Harabasz and Davies–Bouldin indices, Silhouette Score, and standard deviation. Nonparametric tests were used to assess the impact of topological descriptors on clustering outcomes. Our results show that the DBN + k-means combination is the most effective, particularly at lower cluster counts, demonstrating significant sensitivity to structural variations. This study highlights the potential of integrating spectral geometry with deep learning for precise and efficient molecular clustering. [ABSTRACT FROM AUTHOR]

This paper aims to establish a comprehensive model for evaluating the response characteristics of functionally graded graphene platelet-reinforced composite (FG-GPLRC) rectangular plates under stationary random acceleration excitation. Utilizing the first-order shear deformation theory (FSDT) and Halpin–Tsai assumptions, a dynamic model for the rectangular plate is derived, followed by obtaining the variational solution using the Rayleigh–Ritz method. To describe displacement components associated with dynamic equations and boundary conditions, a spectral geometry method (SGM) is employed. Additionally, a pseudo-excitation method (PEM) is utilized for the analysis of stationary random vibration. The proposed calculation method is validated through convergence analysis and comparative evaluation with existing literature and finite element models. Furthermore, the study investigates the influence of various factors, such as boundary conditions, the number and size of functionally graded rectangular plate layers, GPL distribution types, and material parameters, on the stationary random response attributes of FG rectangular plates. This research contributes to a deeper understanding of the dynamic response of functionally graded materials in structural configurations and offers a valuable analytical approach for researchers in this field. [ABSTRACT FROM AUTHOR]

The dynamic behavior of a physical system often originates from its spectral properties. In open systems, where the effective non-Hermitian description enables a wealth of spectral structures in the complex plane, the concomitant dynamics are significantly enriched, whereas the identification and comprehension of the underlying connections are challenging. Here we experimentally demonstrate the correspondence between the transient self-acceleration of local excitations and the non-Hermitian spectral topology using lossy photonic quantum walks. Focusing first on one-dimensional quantum walks, we show that the measured short-time acceleration of the wave function is proportional to the area enclosed by the eigenspectrum. We then reveal a similar correspondence in two-dimension quantum walks, where the self-acceleration is proportional to the volume enclosed by the eigenspectrum in the complex parameter space. In both dimensions, the transient self-acceleration crosses over to a long-time behavior dominated by a constant flow at the drift velocity. Our results unveil the universal correspondence between spectral topology and transient dynamics, and offer a sensitive probe for phenomena in non-Hermitian systems that originate from spectral geometry. The strong connection between the dynamics of a physical system and its Hamiltonian's spectrum has scarcely been applied in the non-Hermitian case. Here, the authors use a photonic quantum walk to confirm and expand previous theoretical analyses connecting self-acceleration dynamics with non-trivial point-gap topology. [ABSTRACT FROM AUTHOR]

In 1996 Erdös showed that among planar domains of fixed area, the smallest principal eigenvalue of the Dirichlet Laplacian with a constant magnetic field is uniquely achieved on the disk. We establish a quantitative version of this inequality, with an explicit remainder term depending on the field strength that measures how much the domain deviates from the disk. [ABSTRACT FROM AUTHOR]

We are concerned with a coupled-physics spectral problem arising in the coupled propagation of acoustic and elastic waves, which is referred to as the acoustic-elastic transmission eigenvalue problem. There are two major contributions in this work which are new to the literature. First, under a mild condition on the medium parameters, we prove the existence of an acoustic-elastic transmission eigenvalue. Second, we establish a geometric rigidity result of the transmission eigenfunctions by showing that they tend to localize on the boundary of the underlying domain. Moreover, we also consider interesting implications of the obtained results to the effective construction of metamaterials by using bubbly elastic structures and to the inverse problem associated with the fluid-structure interaction. [ABSTRACT FROM AUTHOR]

By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an idealized celestial sphere and then define the metric in terms of optimal transport in two dimensions. In this paper, we advocate for representing events in terms of a spectral function that encodes pairwise particle angles and products of particle energies, which enables a metric distance defined in terms of one-dimensional optimal transport. This approach has the advantage of automatically incorporating obvious isometries of the data, like rotations about the colliding beam axis. It also facilitates first-principles calculations, since there are simple closed-form expressions for optimal transport in one dimension. Up to isometries and event sets of measure zero, the spectral representation is unique, so the metric on the space of spectral functions is a metric on the space of events. At lowest order in perturbation theory in electron-positron collisions, our metric is simply the summed squared invariant masses of the two event hemispheres. Going to higher orders, we present predictions for the distribution of metric distances between jets in fixed-order and resummed perturbation theory as well as in parton-shower generators. Finally, we speculate on whether the spectral approach could furnish a useful metric on the space of quantum field theories. [ABSTRACT FROM AUTHOR]

This paper establishes several results for coalgebraic structure in 8-categories, specifically with connections to the spectral noncommutative geometry of cobordism theories. We prove that the categories of comodules and modules over a bialgebra always admit suitably structured monoidal structures in which the tensor product is taken in the ambient category (as opposed to a relative (co)tensor product over the underlying algebra or coalgebra of the bialgebra). We give two examples of higher coalgebraic structure: first, following Hess we show that for a map of En-ring spectra: A B, the associated 8-category of descent data is equivalent to the 8-category of comodules over BA B, the so-called descent coring; secondly, we show that Thom spectra are canonically equipped with a highly structured comodule structure which is equivalent to the 8-categorical Thom diagonal of Ando, Blumberg, Gepner, Hopkins and Rezk (which we describe explicitly) and that this highly structured diagonal decomposes the Thom isomorphism for an oriented Thom spectrum in the expected way indicating that Thom spectra are good examples of spectral noncommutative torsors. [ABSTRACT FROM AUTHOR]

A complete representation of 3D objects requires characterizing the space of deformations in an interpretable manner, from articulations of a single instance to changes in shape across categories. In this work, we improve on a prior generative model of geometric disentanglement for 3D shapes, wherein the space of object geometry is factorized into rigid orientation, non-rigid pose, and intrinsic shape. The resulting model can be trained from raw 3D shapes, without correspondences, labels, or even rigid alignment, using a combination of classical spectral geometry and probabilistic disentanglement of a structured latent representation space. Our improvements include more sophisticated handling of rotational invariance and the use of a diffeomorphic flow network to bridge latent and spectral space. The geometric structuring of the latent space imparts an interpretable characterization of the deformation space of an object. Furthermore, it enables tasks like pose transfer and pose-aware retrieval without requiring supervision. We evaluate our model on its generative modelling, representation learning, and disentanglement performance, showing improved rotation invariance and intrinsic-extrinsic factorization quality over the prior model. [ABSTRACT FROM AUTHOR]

Ocean wave climate, including wind waves and swells, is essential to human marine activities and global or regional climate systems, and is highly related to harnessing wave energy resources. In this study, a global 3-hourly instantaneous wave dataset was established with the third-generation wave model MASNUM-WAM and wind forcings derived from the products of the First Institute of Oceanography-Earth System Model version 2.0, the climate model coupled with wave model, under the unified framework of the Coupled Model Intercomparison Project phase 6. This dataset contains 17 wave parameters, including the information associated with wave energy and spectral shape geometries, from one historical (1950–2014) simulation and three future (2015–2100) scenario experiments (ssp125, ssp245, and ssp585). Moreover, all the parameters can be accessed separately in the form of wind waves and swells. The historical results show that the simulated wave characteristics agree well with satellite observations and the ERA5 reanalysis products. This dataset can provide the community with a unique and informative data source for wave climate and wave energy resource research. [ABSTRACT FROM AUTHOR]

We investigate the existence or non-existence of spectral minimal partitions of unbounded metric graphs, where the operator applied to each of the partition elements is a Schrödinger operator of the form -Δ + V with suitable (electric) potential V, which is taken as a fixed, underlying function on the whole graph. We show that there is a strong link between spectral minimal partitions and infimal partition energies on the one hand, and the infimum Σ of the essential spectrum of the corresponding Schrödinger operator on the whole graph on the other. Namely, we show that for any k ∈ ..., the infimal energy among all admissible k-partitions is bounded from above by Σ, and if it is strictly below Σ, then a spectral minimal k-partition exists. We illustrate our results with several examples of existence and non-existence of minimal partitions of unbounded and infinite graphs, with and without potentials. The nature of the proofs, a key ingredient of which is a version of the characterization of the infimum of the essential spectrum known as Persson's theorem for quantum graphs, strongly suggests that corresponding results should hold for Schrödinger operator-based partitions of unbounded domains in Euclidean space. [ABSTRACT FROM AUTHOR]

The use of one theorem of spectral analysis proved by Bordoni on a model of linear anisotropic beam proposed by the author allows the determination of the variation range of vibration frequencies of a beam in two typical restraint conditions. The proposed method is very general and allows its use on a very wide set of problems of engineering practice and mathematical physics. [ABSTRACT FROM AUTHOR]

In this work we study statistical properties of graph-based algorithms for multi-manifold clustering (MMC). In MMC the goal is to retrieve the multi-manifold structure underlying a given Euclidean data set when this one is assumed to be obtained by sampling a distribution on a union of manifolds M = M1 ∪ ⋯ ∪ MN that may intersect with each other and that may have different dimensions. We investigate sufficient conditions that similarity graphs on data sets must satisfy in order for their corresponding graph Laplacians to capture the right geometric information to solve the MMC problem. Precisely, we provide high probability error bounds for the spectral approximation of a tensorized Laplacian on M with a suitable graph Laplacian built from the observations; the recovered tensorized Laplacian contains all geometric information of all the individual underlying manifolds. We provide an example of a family of similarity graphs, which we call annular proximity graphs with angle constraints, satisfying these sufficient conditions. We contrast our family of graphs with other constructions in the literature based on the alignment of tangent planes. Extensive numerical experiments expand the insights that our theory provides on the MMC problem. [ABSTRACT FROM AUTHOR]

A new class of pharmacologically active mixed-ligand complexes (1a-2a) [MII(L)2 (bpy)], where L = 2-(4-morpholinobenzylideneamino)phenol), bpy = 2,2′-bipyridine, MII = Cu (1a), and Zn (2a), were assigned an octahedral geometry by analytical and spectral measurements. Gel electrophoresis showed that complex (1a) demonstrated the complete DNA cleavage mediated by H2O2. The overall DNA-binding constants observed from UV-vis, fluorometric, hydrodynamic, and electrochemical titrations were in the following sequence: (1a) > (2a) > (HL), which suggests that the complexes might intercalate DNA, a possibility that is further supported by the biothermodynamic characteristics. The binding constant results of BSA by electronic absorption and fluorometric titration demonstrate that complex (1a) exhibits the highest binding effectiveness among others, which means that all compounds could interact with BSA through a static approach, additionally supported by FRET measurements. Density FunctionalTheory (DFT) and molecular docking calculations were relied on to unveil the electronic structure, reactivity, and interacting capability of all substances with DNA, BSA, and SARS-CoV-2 main protease (Mpro). These observed binding energies fell within the following ranges: −7.7 to −8.6, −7.2 to −10.2, and −6.7 to −8.2 kcal/mol, respectively. The higher reactivity of the complexes compared to free ligand is supported by the Frontier MolecularOrbital (FMO) theory. The in vitro antibacterial, cytotoxic, and radical scavenging characteristics revealed that complex (1a) has the best biological efficacy compared to others. This is encouraged because all experimental findings are closely correlated with the theoretical measurements. [ABSTRACT FROM AUTHOR]

A fuzzy geometry is a certain type of spectral triple whose Dirac operator crucially turns out to be a finite matrix. This notion incorporates familiar examples like fuzzy spheres and fuzzy tori. In the framework of random noncommutative geometry, we use Barrett's characterization of Dirac operators of fuzzy geometries in order to systematically compute the spectral action S.D/ D Tr f .D/ for 2n-dimensional fuzzy geometries. In contrast to the original Chamseddine-- Connes spectral action, we take a polynomial f with f .x/ ! 1 as jxj ! 1 in order to obtain a well-defined path integral that can be stated as a random matrix model with action of the type S.D/ D N tr F CPi tr Ai tr Bi, being F, Ai and Bi noncommutative polynomials in 22n are obtained via chord diagrams and satisfy: independence of N; self-adjointness of the main polynomial F (modulo cyclic reordering of each monomial); also up to cyclicity, either self-adjointness or anti-self-adjointness of Ai and Bi simultaneously, for fixed i . Collectively, this favors a free probabilistic perspective for the large-N limit we elaborate on. [ABSTRACT FROM AUTHOR]

An intrinsic characteristic of musical sounds is the qualitative evolution of their timbre (tone colour). In this paper, we interpret each qualitative change by a bifurcation. We employ spectral and temporal envelopes as two of the most salient features of tone colour. Fourier analysis of a note generates its n -leading harmonic partials and an amplitude spectral n-vector A for n ≥ 2. We introduce harmonic manifolds associated with amplitude spectral vectors. This is to accommodate the n -leading harmonic partials of the note. Then, harmonic partials are modelled by solutions of a radial coupling of n -tuple parametric Hopf oscillators. We use one bifurcation parameter and interpolate the qualitative evolution of temporal envelope over a set of consecutive time-intervals via bifurcation analysis and control. Bifurcation scenarios involve harmonic asymptotic sets as time-asymptotic limits of harmonic partials. Each harmonic asymptotic set is homeomorphic to a k -tori, where k ≤ n is the number of contributing harmonic partials. Bifurcation classification of tone colour is then drawn up by encoding the spectral geometry of acoustic signals into harmonic manifolds and harmonic asymptotic sets. For instance, we treat audio C ♯ 4 files obtained from piano and violin. Different bifurcation scenarios distinguish temporal amplitude bifurcations of these sounds. A complete hysteresis cycle is observed within the temporal amplitude bifurcations of C ♯ 4 note played by violin. [ABSTRACT FROM AUTHOR]

We apply Geometric Arbitrage Theory (GAT) to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. The remarkable aspect of the GAT is the gauge symmetry, which can be translated to the financial context, by packaging all of the asset model information into a (stochastic) principal fiber bundle. We obtain closed-form equations involving default intensities and loss-given defaults characterizing the no-free-lunch-with-vanishing-risk condition for government and corporate bond markets while relying on the spread-term structure with default intensity and loss-given default. Moreover, we provide a sufficient condition equivalent to the Novikov condition implying the absence of arbitrage. Furthermore, the generic dynamics for an isolated credit market allowing for arbitrage possibilities (and minimizing the total quantity of potential arbitrage) are derived, and arbitrage credit bubbles for both base credit assets and credit derivatives are explicitly computed. The existence of an approximated risk-neutral measure allowing the definition of fundamental values for the assets is inferred through spectral theory. We show that instantaneous bond returns are serially uncorrelated and centered, that the expected value of credit bubbles remains constant for future times where no coupons are paid, and that the variance of the market portfolio nominals is concurrent with that of the corresponding bond deflators. [ABSTRACT FROM AUTHOR]

The main focus of this paper is concern to the study on the point-wise Osserman structure on 4-dimensional Lorentzian Lie group. In this paper we study on the spectrum of the Jacobi operator and spectrum of the skew-symmetric curvature operator on the non-abelian 4-dimensional Lie group G, whenever G equipped with an orthonormal left invariant pseudo-Riemannian metric g of signature (¡;+;+; +), i.e, Lorentzian metric, where e1 is a unit time-like vector. The Lie algebra structure in dimension four has key role in our investigation, also in this case we study on the classification of 1-Stein and mixed IP spaces. At the end we show that G does not admit any space form and Einstein structures. [ABSTRACT FROM AUTHOR]

Distributed Bragg Reflectors are optical structures capable of manipulating light behaviour, which are formed by stacking layers of thin-film materials. The inverse design of such structures is desirable, but not straightforward using conventional numerical methods. This study explores the application of Deep Learning to the design of a six-layer system, through the implementation of a Tandem Neural Network. The challenge is split into three sections: the generation of training data using the Transfer Matrix method, the design of a Simulation Neural Network (SNN) which maps structural geometry to spectral output, and finally an Inverse Design Neural Network (IDNN) which predicts the geometry required to produce target spectra. The latter enables the designer to develop custom multilayer systems with desired reflection properties. The SNN achieved an average accuracy of 97% across the dataset, with the IDNN achieving 94%. By using this inverse design method, custom-made reflectors can be manufactured in milliseconds, significantly reducing the cost of generating photonic devices and thin-film optics. [ABSTRACT FROM AUTHOR]

The Zhurong rover successfully landed in southern Utopia Planitia as part of the Tianwen-1 mission on 15 May 2021. One of the objectives of the Mars Surface Composition Detector (MarSCoDe) onboard the rover is to investigate mineral compositions on the Martian surface by measuring the near-infrared reflectance spectra. Before conducting spectral interpretation, in-flight data calibration is a crucial step due to the significant differences between the laboratory and the Martian environment. The work of the MarSCoDe spectrometer is based on an acousto-optic tunable filter (AOTF). The temperature variation of the AOTF could induce wavelength offset, making mineral identification uncertain. We first analyzed the viewing geometry of the spectral measurements of the calibration targets on the Mars rover according to its attitude to identify the anomalous data. The wavelength offsets were then determined by fitting the absorption positions of CO2 at ~1400 and ~2000 nm, representing the primary composition of the Martian atmosphere. The results showed 2–8 nm wavelength offsets, which correlated well with AOTF temperatures. The artifacts were removed in the wavelength-corrected reflectance spectra, which is critical to identify the material types on Mars, especially water-related minerals. [ABSTRACT FROM AUTHOR]

We show how the twisting of spectral triples induces a transition from a Euclidean to a Lorentzian noncommutative geometry at the level of the fermionic action. More specifically, we compute the fermionic action for the twisting of a closed Euclidean manifold, then that of a two-sheet Euclidean manifold, and finally the twisting of the spectral triple of electrodynamics in Euclidean signature. We obtain the Weyl and the Dirac equations in Lorentzian signature (and in the temporal gauge). The twisted fermionic action is then shown to be invariant under an action of the Lorentz group. This permits us to interpret the field of 1-form that parametrises the twisted fluctuation of a manifold as the (dual) of the energy-momentum 4-vector. [ABSTRACT FROM AUTHOR]

In this paper we study the spectral geometry of a 4-dimensional Lie group. The main focus of this paper is to study the 2-Stein and 2-Osserman structures on a 4-dimensional Riemannian Lie group. In this paper, we study the spectrum and trace of Jacobi operator and also we study the characteristic polynomial of generalized Jacobi operator on the non-abelian 4-dimensional Lie group G, whenever G is equipped with an orthonormal left invariant Riemannian metric g. The Lie algebra structures in dimension four have key role in this paper. It is known that in the classification of 4-dimensional non-abelian Lie algebras there are nineteen classes of Lie algebras up to isomorphism [12]. We consider these classes and study all of them. Finally, we study the space form problem and spectral properties of Szabo operator on G. [ABSTRACT FROM AUTHOR]

We introduce a novel learning-based method to recover shapes from their Laplacian spectra, based on establishing and exploring connections in a learned latent space. The core of our approach consists in a cycle-consistent module that maps between a learned latent space and sequences of eigenvalues. This module provides an efficient and effective link between the shape geometry, encoded in a latent vector, and its Laplacian spectrum. Our proposed data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost. Moreover, these latent space connections enable novel applications for both analyzing and controlling the spectral properties of deformable shapes, especially in the context of a shape collection. Our learning model and the associated analysis apply without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), nature of the latent space (generated by an auto-encoder or a parametric model), as well as across different shape classes, and admits arbitrary resolution of the input spectrum without affecting complexity. The increased flexibility allows us to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, latent space exploration and analysis, mesh super-resolution, shape exploration, style transfer, spectrum estimation for point clouds, segmentation transfer and non-rigid shape matching. [ABSTRACT FROM AUTHOR]

We obtain a complete asymptotic expansion for the eigenvalues of the Dirichlet-to-Neumann maps associated with Schrödinger operators on compact Riemannian surfaces with boundary. For the zero potential, we recover the well-known spectral asymptotics for the Steklov problem. For non-zero potentials, we obtain new geometric invariants determined by the spectrum of what we call the parametric Steklov problem. In particular, for constant potentials parametric Steklov problem, the total geodesic curvature on each connected component of the boundary is a spectral invariant. Under the constant curvature assumption, this allows us to obtain some interior information from the spectrum of these boundary operators. [ABSTRACT FROM AUTHOR]

We derive upper bounds for the eigenvalues of the Kirchhoff Laplacian on a compact metric graph depending on the graph's genus g. These bounds can be further improved if g = 0, i.e., if the metric graph is planar. Our results are based on a spectral correspondence between the Kirchhoff Laplacian and a particular combinatorial weighted Laplacian. In order to take advantage of this correspondence, we also prove new estimates for the eigenvalues of the weighted combinatorial Laplacians that were previously known only in the unweighted case. [ABSTRACT FROM AUTHOR]

The present Special Issue of Designs, Codes and Cryptography is dedicated to Aart Blokhuis, one of the leading mathematicians in finite geometry and combinatorics. References 1 Ball S, Blokhuis A, Mazzocca F. Maximal arcs in Desarguesian planes of odd order do not exist. The third editor of this special issue, Michel Lavrauw, was a PhD student of Aart between 1997 and 2001. Another challenging problem at the time was to prove the non-existence of maximal arcs in Galois planes of odd order; this was achieved by Aart and his coauthors Simeon Ball and Francesco Mazzocca in [[1]]. [Extracted from the article]

• Spectral basis functions as solutions to PDEs induced by the Laplace-Beltrami operator. • Spectral functions efficiently computed as solutions to sparse linear systems. • Smooth, local, multi-scale, intrinsic and data-driven basis functions. • Applications to signal approximation, smoothing, compression, and shape correspondence. [Display omitted] Basis functions provide a simple and effective way to interpolate signals on a surface with an arbitrary dimension, topology, and discretisation. However, the definition of local and shape-aware basis functions is still an open problem, which has been addressed through optimisation methods that are time-consuming, over-constrained, or admit more than one solution. In this context, we review the definition, properties, computation, and applications of the class of Laplacian spectral basis functions, which are defined as solutions to the harmonic equation, the diffusion equation, and PDEs involving the Laplace–Beltrami operator. The resulting functions are efficiently computed through the solution of sparse linear systems and satisfy different properties, such as smoothness, locality, and multi-scale shape encoding. Finally, the discussion of the properties of the Laplacian spectral basis functions is integrated with an analysis of their behaviour with respect to different measures (i.e., conformal and area-preserving metrics, transformation distance) and of their applications to spectral geometry processing and shape analysis. [ABSTRACT FROM AUTHOR]

Spacetime is conventionally viewed as a stage on which actors, in the form of massive and massless matter, move. In this study, we explore what may lie beyond this picture. The starting point is the observation that quantum field fluctuations are the more strongly correlated the shorter their spacetime distance. The notion of spacetime distance can, therefore, be replaced by the notion of correlation strength. This suggests a new picture in which the abstract 2-point and multi-point correlations are the primary structure, a picture which is essentially information-theoretic. In the low energy regime, the secondary notions of spacetime and of matter would then emerge as approximate representations of the abstract correlators, namely, in the form of Feynman rules on curved spacetime.

NGC 2617 attracted a lot of attention after the detection of changes in its spectral type; the geometry and kinematics of the broad-line region (BLR) are still ambiguous. In this paper, we present the high cadence (∼2 days) reverberation mapping campaign of NGC 2617 from 2019 October to 2020 May undertaken at the Lijiang 2.4 m telescope. For the first time, the velocity-resolved reverberation signature of the object was successfully detected. Both Hα and Hβ show an asymmetrical profile with a peak in the velocity-resolved time lags. For both of the lines, the lag of the line core is longer than those of the relevant wings, and the peak of the velocity-resolved lags is slightly blueshifted. These characteristics are not consistent with the theoretical prediction of the inflow, outflow or Keplerian disk model. Our observations give the time lags of Hα, Hβ, Hγ, and He i , with a ratio of τHα: τHβ: τHγ: τHe I = 1.27:1.00:0.89:0.20, which indicates a stratified structure in the BLR of the object. It is the first time that the lags of Hα and He i are obtained. Assuming a virial factor of f = 5.5 for the dispersion width of the line, the masses of the black holes derived from Hα and Hβ are and , respectively. Our observed results indicate the complexity of the BLR of NGC 2617. [ABSTRACT FROM AUTHOR]

The occurrence of rogue waves is closely related to the non-Gaussianity of sea states, and the non-Gaussianity is sensitive to the combination of three spectral geometries: wave steepness, bandwidth, and directional spreading. This paper presents a set of non- Gaussianity references that allow quantitative comparison of the non-Gaussianity of sea states with various combinations of the three geometries. In addition, an approach to introduce arbitrary 2D wave spectra into the references is presented, which allows quantitative investigation of the non-Gaussianity and the corresponding geometries in given sea states. Application in relation to certain rogue waves that occurred in wind-sea dominated sea states showed that the non-Gaussianity of skewness presented high values when those events occurred. However, abnormal values of kurtosis could not be found within the same period, indicating that third-order modulational instabilities were inactive in those events. Quantitative analyses based on the newly presented references revealed that the rogue waves that occurred in wind-sea dominated sea states, and presented extreme height and extreme destructive power, could hardly be formed from the modulational instabilities. This was because of not only the broad energy distribution in terms of direction, but also the broad bandwidth attributable to the developed wind-sea state. [ABSTRACT FROM AUTHOR]

It is well known that the automorphism group Aut(H) of the algebra of real quaternions H consists entirely of inner automorphisms iq : p → q ·p·q-1 for invertible q ∈ H and is isomorphic to the group of rotations SO(3). Hence, H has only inner derivations D = ad(x), x ∈ H. See [4] for derivations of various types of quaternions over the reals. Unlike real quaternions, the algebra Hd of dual quaternions has no nontrivial inner derivation. Inspired from almost inner derivations for Lie algebras, which were first introduced in [3] in their study of spectral geometry, we introduce coset invariant derivations for dual quaternion algebra being a derivation that simply keeps every dual quaternion in its coset space. We begin with finding conditions for a linear map on Hd become a derivation and show that the dual quaternion algebra Hd consists of only central derivations. We also show how a coset invariant central derivation of Hd is closely related with its spectrum. [ABSTRACT FROM AUTHOR]

The visible and near‐infrared imaging spectrometer on board the Yutu‐2 rover of Chang'E‐4 mission has conducted 2 sets of spectrophotometric measurements at two sites on its 10th lunar day. At each site, the reflectance spectra were measured on the same lunar regolith at different geometric configurations. The experiments reveal an increasing trend of the spectral reddening effect with the increasing phase angles, which may cause significant uncertainties on interpreting the maturity of the lunar regolith. Furthermore, the phase angles have significant effects on the 2‐μm band center and the 1‐μm band depth of the spectra, consequently on the estimation of mineral composition of the regolith. Finally, the derived average Hapke parameters using the in situ spectrophotometric measurements provide important ground‐truth for remote sensing observations. Plain Language Summary: Olivine, pyroxenes and plagioclase, the major constituent minerals of the surface of the Moon, have diagnostic absorption features in their visible and near‐infrared reflectance spectra. These features, including the wavelength position of the absorption band center and the depth of the absorption band, can be used to identify the mineralogy of the observed surface. The slope of the reflectance spectral curve is another feature that can be used to describe the degree of how the surface materials interact with space environment. The Yutu‐2 rover on board the China's Chang'E‐4 mission has been equipped with a visible to near‐infrared spectrometer, to carry out in situ spectral measurements at varied illumination and azimuth angles. These measurements provided us an excellent chance to study the effects of measurement angles on these spectral features, which can help us better understand the mineralogical information of lunar surface. Key Points: In situ spectrophotometric measurements by Chang'E‐4 Yutu‐2 rover show viewing geometry may affect band centers and depth of the spectraPhase reddening coupled with space weathering effects on the spectra may cause significant uncertainties on interpreting the maturity of lunar regolithThe derived Hapke parameters from the in situ spectrophotometric measurements provide ground truth for both in situ and orbital observations [ABSTRACT FROM AUTHOR]

In a smoky plasma, crystal-like structures (clusters) are formed which contain less than $10^{3}$ particles and are characterized by significant anisotropy of thermodynamic characteristics. Here, the influence of the clusters’ size on their melting temperature is studied. It was revealed that the phonon spectrum density of a nanometer-sized cluster cannot be represented by the classical Debye model. Therefore, to describe the real phonon spectrum of nanoclusters, two control parameters are introduced: the fractal dimension and the scale parameters. Based on the fractal shape of the phonon spectrum density, a method has been developed for calculating the relative melting temperature of clusters in the most real parameter range: $N = $ 100–500, $D = $ 2.4–2.8 where $N$ is the number of particles in the cluster and $D$ is its fractal dimension. [ABSTRACT FROM AUTHOR]

Given the adjacency matrix A of a digraph, the eigenvalues of the matrix AAT constitute the so-called non-negative spectrum of this digraph. We investigate the relation between the structure of digraphs and their non-negative spectra and associated eigenvectors. In particular, it turns out that the non-negative spectrum of a digraph can be derived from the traditional (adjacency) spectrum of certain undirected bipartite graphs. [ABSTRACT FROM AUTHOR]

This study deals with sound radiation from a thin clamped annular plate. The fluid loading effect is included. Although it is a classical problem, using direct numerical integration to solve such a problem is usually troublesome and time consuming since the coupling integrals have certain singularities. Therefore, this study applies radial polynomials to improve the time efficiency of numerical calculations with no loss of accuracy. As radial polynomials are usually used for circular geometry, spectral mapping has been proposed to perform the necessary conversion from circular to annular geometry. The conversion is performed in the wavenumber domain. Spectral mapping makes it possible to efficiently obtain a number of numerical results for the acoustic power and acoustic field generated. [ABSTRACT FROM AUTHOR]

Highlights • A multimodal distance measure based on the commutativity of image graph Laplacians. • Assumption: eigenvectors of image graph Laplacian capture structural information. • Use relation between joint diagonalization and matrix commutativity to compare images. • Performance is tested for multimodal image registration and is compared to NMI. • Results show that approach can deal with multiple and challenging mul- timodal datasets. Abstract The fusion and combination of images from multiple modalities is important in many applications. Typically, this process consists of the alignment of the images and the combination of the complementary information. In this work, we focused on the former part and propose a multimodal image distance measure based on the commutativity of graph Laplacians. The eigenvectors of the image graph Laplacian, and thus the graph Laplacian itself, capture the intrinsic structure of the image's modality. Using Laplacian commutativity as a criterion of image structure preservation, we adapt the problem of finding the closest commuting operators to multimodal image registration. Hence, by using the relation between simultaneous diagonalization and commutativity of matrices, we compare multimodal image structures by means of the commutativity of their graph Laplacians. In this way, we avoid spectrum reordering schemes or additional manifold alignment steps which are necessary to ensure the comparability of eigenspaces across modalities. We show on synthetic and real datasets that this approach is applicable to dense rigid and non-rigid image registration. Results demonstrated that the proposed measure is able to deal with very challenging multimodal datasets and compares favorably to normalized mutual information, a de facto similarity measure for multimodal image registration. [ABSTRACT FROM AUTHOR]

The copper(II) complexes of 1,4 diazepane based 3N-ligands have been synthesized and characterized as the novel models for lytic polysaccharides monooxygenases (LPMOs). They catalyze the oxidative cleavage of model substrate p -nitrophenyl-β-D-glucopyranoside into p -nitrophenol with higher yield (78.4%) and TON (300) in water. • Bioinspired copper(II) complexes are reported as LPMOs models. • The complexes provide structural resemblances to 'histidine brace' of LPMOs. • They showed oxidative C-O bond breakage with higher yield (78.4%) and TON (300). • The oxidative cleavage reactions occur via key intermediate CuII-OOH. Lytic polysaccharide monooxygenases (LPMOs) are copper-containing monooxygenase and catalyzing the oxidative cleavage of recalcitrant polysaccharides using dioxygen. The copper(II) complexes [Cu(L1)(H 2 O)ClO 4 ]ClO 4 1 , [L1 = 4-methyl-1-[(pyridin-2-yl-methyl)]-1,4-diazepane]; [Cu(L2)(H 2 O)ClO 4 ]ClO 4 2 , [L2 = 4-methyl-1-[(2-(pyridine-2-yl)ethyl]-1,4-diazepane] and [Cu(L3)(H 2 O)ClO 4 ]ClO 4 3 , [L3 = 1-(4-methoxy-3,5-dimethyl-pyridin-2-yl)methyl)-4-methyl-1,4-diazepane] have been synthesized and characterized as the novel models for LPMOs. The molecular structures exhibit distorted square pyramidal geometry (τ, 0.183–0.388) as similar to LPMOs. The Cu N (1.99–2.02 Å) bond distances of the model complexes are almost identical to those of native LPMOs enzyme (1.9–2.2 Å). The 1, 4-diazepane backbone and pyridine unit of complexes provide reasonable structural resemblances to 'histidine brace' and histidine residues of LPMOs respectively. The spectral, redox and kinetic studies were performed in water to mimic accurate enzymatic reaction conditions. The well-defined Cu(II)/Cu(I) reduction couples were observed around 8–112 mV versus NHE, which is lower than that of LPMOs. The electronic spectra of the complexes showed the d-d transitions around 600–635 nm and axial EPR parameter (g || , 2.28–2.29; A ||, 160–168 × 10−4 cm−1), which are almost identical to that of LPMOs. The model complexes were catalyzed oxidative cleavage of model substrate p -nitrophenyl- β -D-glucopyranoside into p -nitrophenol and D-allose with a maximum yield up to 78.4% and TON, 300. The kinetics of reaction monitored by following the formation of an absorption band around at 400 nm corresponds to p -nitrophenol, showed the rate of 3.19–5.26 × 10−3 s−1. The oxidative cleavage reaction may occur via CuII-OOH intermediate, whose formation accompanied by an electronic spectral signature around 375 nm with the rate of 1.61–9.06 × 10−3 s−1. The CuII-OOH intermediate was characterized by spectral methods and its geometry was optimized by DFT calculations. [ABSTRACT FROM AUTHOR]

Abstract The spectral conjugate gradient method is an effective method for large-scale unconstrained optimization problems. In this paper, based on Quasi-Newton direction and Quasi-Newton equation, a new spectral conjugate gradient method is proposed. This method is motivated by the three-term modified Polak-Ribiyre-Polyak (PRP) method and spectral parameters. The global convergence of algorithm is proved for general functions under a strong Wolfe line search. Numerical results show that the new algorithm is superior to the three-term modified PRP method. [ABSTRACT FROM AUTHOR]

Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering--clustering the vertices of a graph based on their spectral embedding--is commonly approached via K-means (or, more generally, Gaussian mixture model) clustering composed with either Laplacian spectral embedding (LSE) or adjacency spectral embedding (ASE). Recent theoretical results provide deeper understanding of the problem and solutions and lead us to a "two-truths" LSE vs. ASE spectral graph clustering phenomenon convincingly illustrated here via a diffusion MRI connectome dataset: The different embedding methods yield different clustering results, with LSE capturing left hemisphere/right hemisphere affinity structure and ASE capturing gray matter/white matter core-periphery structure. [ABSTRACT FROM AUTHOR]

In this work we show that the area of the event horizon of the Chong–Cvetic–Lu–Pope black hole can be reconstructed in terms of the spectra of the Laplacian on the event horizon. This result, which extends previous works regarding the de Sitter–Kerr–Newman case, points towards a possible description of the black hole degrees of freedom in terms of the spectra of canonical operators defined on the event horizon.

• Effect of arbitrary stiffness profile on track geometry degradation is investigated. • Individual support stiffness harmonics induce extra resonance velocities. • Shorter wavelength and larger standard deviation increase degradation rate. • Varying stiffness influence converges for wavelengths around 16 sleeper bays. This work addresses the contribution of the wavelength composition of the spectrum of the rail support stiffness profile to the expected long-term settlement. To that aim, purely harmonic stiffness variations of different wavelength are studied. The frequency-domain model with a double periodicity level previously developed by the first and last authors is adopted to embed the stiffness profile in one of the periodicity layers. Additional resonance velocities at which the resonance frequency of the track system coincides with the support-passing frequency or its multiples are found. The susceptibility to degradation is assessed both by quantifying the mechanical energy dissipated in the substructure under a moving train axle within one wavelength of the support stiffness variation, and the work performed by the wheel-rail contact force. It is shown that shorter wavelengths and larger standard deviations of varying ballast/subgrade stiffness result in an increasing energy dissipation in the substructure, and increase the work performed by the wheel-rail contact force, therefore leading to a reduced lifetime of the track. The energetic quantities increase for lower mean values of the stiffness profile, confirming the proneness of tracks on soft soils to degradation. The influence of varying stiffness vanishes for wavelengths of approximately 16 times the sleeper span, which is equivalent to a track length of about 10 m. High railpad stiffness values result in increased energy dissipation but the influence is limited. In general, an increasing train velocity amplifies the rate of track degradation, with no stabilizing trend in the high-speed regime (300 km/h). [ABSTRACT FROM AUTHOR]