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This work introduces a novel numerical method that relaxes the minimal configuration requirements for joint sensors and sources localization (JSSL) in 3D space using time of arrival (TOA) measurements. Traditionally, the principle requires that the number of valid equations (TOA measurements) must be equal to or greater than the number of unknown variables (sensor and source locations). State-of-the-art literature suggests that the minimum numbers of sensors and sources needed for localization are four to six and six to four, respectively. However, these stringent configurations limit the application of JSSL in scenarios with an insufficient number of sensors and sources. To overcome this limitation, we propose a numerical method that reduces the required number of sensors and sources, enabling more flexible JSSL configurations. First, we formulate the JSSL task as a series of triangles and apply the law of cosines to determine four unknown distances associated with one pair of sensors and three pairs of sources. Next, by utilizing triangle inequalities, we establish the lower and upper boundaries for these unknowns based on the known TOA measurements. The numerical method then searches within these boundaries to find the global optimal solutions, demonstrating that JSSL in 3D space is achievable with only four sensors and four sources, thus significantly relaxing the minimal configuration requirements. Theoretical proofs and simulation results confirm the feasibility and effectiveness of the proposed method., Comment: 13 pages, 6 figures

This paper deals with the problem of detecting maritime targets embedded in nonhomogeneous sea clutter, where limited number of secondary data is available due to the heterogeneity of sea clutter. A class of linear discriminant analysis (LDA)-based matrix information geometry (MIG) detectors is proposed in the supervised scenario. As customary, Hermitian positive-definite (HPD) matrices are used to model the observational sample data, and the clutter covariance matrix of received dataset is estimated as geometric mean of the secondary HPD matrices. Given a set of training HPD matrices with class labels, that are elements of a higher-dimensional HPD matrix manifold, the LDA manifold projection learns a mapping from the higher-dimensional HPD matrix manifold to a lower-dimensional one subject to maximum discrimination. In the current study, the LDA manifold projection, with the cost function maximizing between-class distance while minimizing within-class distance, is formulated as an optimization problem in the Stiefel manifold. Four robust LDA-MIG detectors corresponding to different geometric measures are proposed. Numerical results based on both simulated radar clutter with interferences and real IPIX radar data show the advantage of the proposed LDA-MIG detectors against their counterparts without using LDA as well as the state-of-art maritime target detection methods in nonhomogeneous sea clutter., Comment: 15 pages, 9 figures

Billions of organic molecules are known, but only a tiny fraction of the functional inorganic materials have been discovered, a particularly relevant problem to the community searching for new quantum materials. Recent advancements in machine-learning-based generative models, particularly diffusion models, show great promise for generating new, stable materials. However, integrating geometric patterns into materials generation remains a challenge. Here, we introduce Structural Constraint Integration in the GENerative model (SCIGEN). Our approach can modify any trained generative diffusion model by strategic masking of the denoised structure with a diffused constrained structure prior to each diffusion step to steer the generation toward constrained outputs. Furthermore, we mathematically prove that SCIGEN effectively performs conditional sampling from the original distribution, which is crucial for generating stable constrained materials. We generate eight million compounds using Archimedean lattices as prototype constraints, with over 10% surviving a multi-staged stability pre-screening. High-throughput density functional theory (DFT) on 26,000 survived compounds shows that over 50% passed structural optimization at the DFT level. Since the properties of quantum materials are closely related to geometric patterns, our results indicate that SCIGEN provides a general framework for generating quantum materials candidates., Comment: 512 pages total, 4 main figures + 218 supplementary figures

Ion transport across solid solid interfaces is often slower than through the bulk of a material, impeding the charge and discharge rate of batteries. Designing highly conductive interfaces is challenging due to the need to probe ion conduction at individual interfaces and correlate it with the local structure. In this study, we address this challenge by enabling the simultaneous measurements of local Li-dominated optical phonons and ion distributions, using high-energy and high-spatial-resolution spectroscopy in a scanning transmission electron microscope (STEM). Further, this method allows for a direct correlation of ion conduction with interfacial structures identified by STEM imaging. By examining diverse individual interfaces of LiCoO2, we reveal the sensitivity of ion conduction to interface atomic-scale structure and chemistry. Our method enables correlative analysis of ion transport behavior, and atomic and band structures, and can serve as a robust experimental approach for identifying interface structures that offer high conductivity and cyclability for batteries.

Uncertainty in timing information pertaining to the start time of microphone recordings and sources' emission time pose significant challenges in various applications, such as joint microphones and sources localization. Traditional optimization methods, which directly estimate this unknown timing information (UTIm), often fall short compared to approaches exploiting the low-rank property (LRP). LRP encompasses an additional low-rank structure, facilitating a linear constraint on UTIm to help formulate related low-rank structure information. This method allows us to attain globally optimal solutions for UTIm, given proper initialization. However, the initialization process often involves randomness, leading to suboptimal, local minimum values. This paper presents a novel, combined low-rank approximation (CLRA) method designed to mitigate the effects of this random initialization. We introduce three new LRP variants, underpinned by mathematical proof, which allow the UTIm to draw on a richer pool of low-rank structural information. Utilizing this augmented low-rank structural information from both LRP and the proposed variants, we formulate four linear constraints on the UTIm. Employing the proposed CLRA algorithm, we derive global optimal solutions for the UTIm via these four linear constraints.Experimental results highlight the superior performance of our method over existing state-of-the-art approaches, measured in terms of both the recovery number and reduced estimation errors of UTIm., Comment: 13 pages for main content; 9 pages for proof of proposed low rank properties; 13 figures

In an era where asynchronous environments pose challenges to traditional self-positioning methods, we propose a new transformation to the existing paradigm. Traditionally, time of arrival (TOA) measurements require both microphone and source signals, limiting their applicability in environments with unknown emission time of human voices or sources and unknown recording start time of independent microphones. To address this issue, our research pioneers a mapping function capable of transforming both TOA and time difference of arrival (TDOA) formulas, demonstrating, for the first time, that they can be identical to one another. This implies that microphone signals alone are sufficient for self-positioning without the need for source signal waveforms, a groundbreaking advancement in the field that carries the potential to revolutionize self-positioning techniques, expanding their applicability in challenging environments. Supported by a robust mathematical proof and compelling experimental results, this research represents a timely and significant contribution to the current discourse in signal, and audio processing., Comment: 1 figure, including 3 sub-figures

This study comes as a timely response to mounting criticism of the information bottleneck (IB) theory, injecting fresh perspectives to rectify misconceptions and reaffirm its validity. Firstly, we introduce an auxiliary function to reinterpret the maximal coding rate reduction method as a special yet local optimal case of IB theory. Through this auxiliary function, we clarify the paradox of decreasing mutual information during the application of ReLU activation in deep learning (DL) networks. Secondly, we challenge the doubts about IB theory's applicability by demonstrating its capacity to explain the absence of a compression phase with linear activation functions in hidden layers, when viewed through the lens of the auxiliary function. Lastly, by taking a novel theoretical stance, we provide a new way to interpret the inner organizations of DL networks by using IB theory, aligning them with recent experimental evidence. Thus, this paper serves as an act of justice for IB theory, potentially reinvigorating its standing and application in DL and other fields such as communications and biomedical research., Comment: 9 pages, 1 figures (4 subfigures)

This article describes a mean-field theoretical model for Spin-Crossover (SCO) materials and explores its implications. It is based on a simple Hamiltonian that yields the high spin molar fraction as a function of temperature and pressure, as well as a temperature-pressure phase diagram for the SCO transition. In order to test the model, we apply it to the giant Barocaloric Effect (BCE) of the SCO material [FeL$_2$][BF$_4$]$_2$ and comprehensively analyse its behavior. We found that optical phonons are responsible for 92\% of the total barocaloric entropy change. DFT calculations show that these optical phonons are mainly assigned to the low frequencies modes of vibration ($<400$ cm$^{-1}$), being associated to the Fe coordination., Comment: 6 figures

Topological quantum magnets FeSn and Fe$_{3}$Sn$_{2}$ were studied using neutron scattering and first-principles calculations. Both materials are metallic but host dispersionless flat bands with Dirac nodes at the $K$ point in reciprocal space. The local structure determined from the pair density function analysis of the neutron diffraction data provided no evidence for electron localization in both compounds, consistent with their metallic nature. At the same time, in FeSn, an anomalous suppression in the $c$-axis lattice constant coupled with changes in the phonon spectra were observed across T$_{N}$ indicating the presence of magneto-elastic coupling and spin-phonon interactions. In addition, it was observed that spin waves persisted well above T$_{N}$, suggesting that the in-plane ferromagnetic spin correlations survive at high temperatures. In contrast, no lattice anomaly was observed in Fe$_{3}$Sn$_{2}$. The inelastic signal could be mostly accounted for by phonons, determined from density functional theory, showing typical softening on warming., Comment: 10 pages, 7 figures

The structure-property relationship plays a central role in materials science. Understanding the structure-property relationship in solid-state materials is crucial for structure design with optimized properties. The past few years witnessed remarkable progress in correlating structures with properties in crystalline materials, such as machine learning methods and particularly graph neural networks as a natural representation of crystal structures. However, significant challenges remain, including predicting properties with complex unit cells input and material-dependent, variable-length output. Here we present the virtual node graph neural network to address the challenges. By developing three types of virtual node approaches - the vector, matrix, and momentum-dependent matrix virtual nodes, we achieve direct prediction of $\Gamma$-phonon spectra and full dispersion only using atomic coordinates as input. We validate the phonon bandstructures on various alloy systems, and further build a $\Gamma$-phonon database containing over 146,000 materials in the Materials Project. Our work provides an avenue for rapid and high-quality prediction of phonon spectra and bandstructures in complex materials, and enables materials design with superior phonon properties for energy applications. The virtual node augmentation of graph neural networks also sheds light on designing other functional properties with a new level of flexibility., Comment: 40 pages total, 4 main figures + 25 supplementary figures

Recently, an innovative matrix CFAR detection scheme based on information geometry, also referred to as the geometric detector, has been developed speedily and exhibits distinct advantages in several practical applications. These advantages benefit from the geometry of the Toeplitz Hermitian positive definite (HPD) manifold $\mathcal{M}_{\mathcal{T}H_{++}}$, but the sophisticated geometry also results in some challenges for geometric detectors, such as the implementation of the enhanced detector to improve the SCR (signal-to-clutter ratio) and the analysis of the detection performance. To meet these challenges, this paper develops the dual power spectrum manifold $\mathcal{M}_{\text{P}}$ as the dual space of $\mathcal{M}_{\mathcal{T}H_{++}}$. For each affine invariant geometric measure on $\mathcal{M}_{\mathcal{T}H_{++}}$, we show that there exists an equivalent function named induced potential function on $\mathcal{M}_{\text{P}}$. By the induced potential function, the measurements of the dissimilarity between two matrices can be implemented on $\mathcal{M}_{\text{P}}$, and the geometric detectors can be reformulated as the form related to the power spectrum. The induced potential function leads to two contributions: 1) The enhancement of the geometric detector, which is formulated as an optimization problem concerning $\mathcal{M}_{\mathcal{T}H_{++}}$, is transformed to an equivalent and simpler optimization on $\mathcal{M}_{\text{P}}$. In the presented example of the enhancement, the closed-form solution, instead of the gradient descent method, is provided through the equivalent optimization. 2) The detection performance is analyzed based on $\mathcal{M}_{\text{P}}$, and the advantageous characteristics, which benefit the detection performance, can be deduced by analyzing the corresponding power spectrum to the maximal point of the induced potential function., Comment: Submitted to IEEE Transactions on Information Theory

Cubic energy materials such as thermoelectrics or hybrid perovskite materials are often understood to be highly disordered. In GeTe and related IV-VI compounds, this is thought to provide the low thermal conductivities needed for thermoelectric applications. Since conventional crystallography cannot distinguish between static disorder and atomic motions, we develop the energy-resolved variable-shutter pair distribution function technique. This collects structural snapshots with varying exposure times, on timescales relevant for atomic motions. In disagreement with previous interpretations, we find the time-averaged structure of GeTe to be crystalline at all temperatures, but with anisotropic anharmonic dynamics at higher temperatures that resemble static disorder at fast shutter speeds, with correlated ferroelectric fluctuations along the $<$100$>$c direction. We show that this anisotropy naturally emerges from a Ginzburg-Landau model that couples polarization fluctuations through long-range elastic interactions. By accessing time-dependent atomic correlations in energy materials, we resolve the long-standing disagreement between local and average structure probes, and show that spontaneous anisotropy is ubiquitous in cubic IV-VI materials., Comment: Published version, substantial changes, many references removed due to journal limits :-( Please see the supporting information online. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format (see conditions)

Fe3-xGeTe2 is a layered magnetic van der Waals material of interest for both fundamental and applied research. Despite the observation of intriguing physical properties, open questions exist even on the basic features related to magnetism: is it a simple ferromagnet or are there antiferromagnetic regimes and are the moments local or itinerant. Here, we demonstrate that antiferromagnetic spin fluctuations coexist with the ferromagnetism through comprehensive elastic and inelastic neutron scattering and thermodynamic measurements. Our realistic dynamical mean-field theory calculations reveal that the competing magnetic fluctuations are driven by an orbital selective Mott transition, where only the plane-perpendicular a1g orbital of the Fe(3d) manifold remains itinerant. Our results highlight the multi-orbital character in Fe3-xGeTe2 that supports a rare coexistence of local and itinerant physics within this material., Comment: 16 pages, 3 main figures

Understanding phonons in $\alpha$-RuCl$_3$ is critical to analyze the controversy around the observation of the half-integer thermal quantum Hall effect. While many studies have focused on the magnetic excitations in $\alpha$-RuCl$_3$, its vibrational excitation spectrum has remained relatively unexplored. We investigate the phonon structure of $\alpha$-RuCl$_3$ via inelastic neutron scattering experiments and density functional theory calculations. Our results show excellent agreement between experiment and first principles calculations. After validating our theoretical model, we extrapolate the low energy phonon properties. We find that the phonons in $\alpha$-RuCl$_3$ that either propagate or vibrate in the out-of-plane direction have significantly reduced velocities, and therefore have the potential to dominate the observability of the elusive half integer plateaus in the thermal Hall conductance. In addition, we use low-energy interlayer phonons to resolve the low temperature stacking structure of our large crystal of $\alpha$-RuCl$_3$, which we find to be consistent with that of the $R\bar{3}$ space group, in agreement with neutron diffraction., Comment: The first two authors contributed equally

Bosonic Dirac materials are testbeds for dissipationless spin-based electronics. In the quasi two-dimensional honeycomb lattice of CrX$_{3}$ (X=Cl, Br, I), Dirac magnons have been predicted at the crossing of acoustical and optical spin waves, analogous to Dirac fermions in graphene. Here we show that, distinct from CrBr$_{3}$ and CrI$_{3}$, gapless Dirac magnons are present in bulk CrCl$_{3}$, with inelastic neutron scattering intensity at low temperatures approaching zero at the Dirac $K$ point. Upon warming, magnon-magnon interactions induce strong renormalization and decreased lifetimes, with a ~25% softening of the upper magnon branch intensity from 5 to 50 K, though magnon features persist well above T$_{N}$. Moreover, an unusual negative thermal expansion (NTE) of the $a$-axis lattice constant and anomalous phonon behavior are observed below 50 K, indicating magnetoelastic and spin-phonon coupling arising from an increase in the in-plane spin correlations that begins tens of Kelvin above T$_{N}$., Comment: Files include supplement