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We propose a novel design paradigm for arbitrarily capable deep photonic networks of cascaded Mach-Zehnder Interferometers (MZIs) for on-chip universal polarization handling. Using a device architecture made of cascaded Mach-Zehnder interferometers, we modify and train the phase difference between interferometer arms for both polarizations through wide operation bandwidths. Three proof-of-concept polarization handling devices are illustrated using a software-defined, physics-informed neural framework, to achieve user-specified target device responses as functions of polarization and wavelength. These devices include a polarization splitter, a polarization-independent power splitter, and an arbitrary polarization-dependent splitter to illustrate the capabilities of the design framework. The performance for all three devices is optimized using transfer matrix calculations; and their final responses are verified through 3D-FDTD simulations. All devices demonstrate state-of-the-art performance metrics with over 20 dB extinction, and flat-top transmission bands through bandwidths of 120 nm. In addition to the functional diversity enabled, the optimization for each device is completed in under a minute, highlighting the computational efficiency of the design paradigm presented. These results demonstrate the versatility of the deep photonic network design ecosystem in polarization management, unveiling promising prospects for advanced on-chip applications in optical communications, sensing, and computing.

This study highlights the importance of satisfying the eddy viscosity equivalence below the logarithmic layer, to deriving accurate compressibility transformations. First, we analyze the ability of known transformations to satisfy the eddy viscosity equivalence and show that the accuracy of these transformation is strongly dependent on this ability. Secondly, in a step-by-step manner, we devise new transformations that satisfy this hypothesis. An approach based on curve fitting of the incompressible Direct Numerical Simulation data for eddy viscosity profiles below the logarithmic layer provides an extremely accurate transformation. That motivates self-contained methods, making use of mixing length formulas, in the inner region. It is shown that the accuracy of existing transformations can be significantly improved by applying these ideas, below the logarithmic layer. Motivated by the effectiveness of the formulations derived from eddy viscosity equivalence, we introduce a new integral transformation based on Reynolds number equivalence between compressible and incompressible flow. This approach is based on defining a new compressible velocity scale, which affects the accuracy of transformations. Several choices for the velocity scale are tested, and in each attempt, it is shown that the eddy viscosity equivalence plays a very important role for the accuracy of compressibility transformations.

In this paper, we introduce a high-order tensor-train (TT) finite volume method for the Shallow Water Equations (SWEs). We present the implementation of the $3^{rd}$ order Upwind and the $5^{th}$ order Upwind and WENO reconstruction schemes in the TT format. It is shown in detail that the linear upwind schemes can be implemented by directly manipulating the TT cores while the WENO scheme requires the use of TT cross interpolation for the nonlinear reconstruction. In the development of numerical fluxes, we directly compute the flux for the linear SWEs without using TT rounding or cross interpolation. For the nonlinear SWEs where the TT reciprocal of the shallow water layer thickness is needed for fluxes, we develop an approximation algorithm using Taylor series to compute the TT reciprocal. The performance of the TT finite volume solver with linear and nonlinear reconstruction options is investigated under a physically relevant set of validation problems. In all test cases, the TT finite volume method maintains the formal high-order accuracy of the corresponding traditional finite volume method. In terms of speed, the TT solver achieves up to 124x acceleration of the traditional full-tensor scheme.

The presence of spin-polarized charge carriers in metallic magnets provides a mechanism for spin-lattice interactions mediated by electron-phonon coupling. Here, we present a theory of this mechanism used to estimate its effect on the exchange interactions in 2D magnets. Starting from a square lattice model at half filling, we show that the presence of electron-phonon coupling with equilibrium phonon distribution leads to a notable suppression of exchange interactions with temperature. We then apply our approach to the prototypical 2D metallic ferromagnet, Fe$_3$GeTe$_2$, with moderate electron-phonon coupling. We find that the exchange interactions undergo a renormalization, leading to a softening of the magnon modes, and suppression of the Curie temperature by $\sim$10\%. We expect that this effect can be further enhanced in systems with strong electron-phonon coupling, as well as for non-equilibrium distribution of phonons induced by strong laser fields or charge currents., Comment: 6 pages, 3 figures

Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention has been on low-order finite difference schemes for time discretization and spectral element schemes for spatial variables. However, our recent developments have resulted in the application of spectral methods to both space and time variables, preserving spectral convergence in both domains. Leveraging Tensor Train techniques, our approach tackles the curse of dimensionality inherent in space-time methods. Here, we extend this methodology to the nonlinear time-dependent convection-diffusion equation. Our discretization scheme exhibits a low-rank structure, facilitating translation to tensor-train (TT) format. Nevertheless, controlling the TT-rank across Newton's iterations, needed to deal with the nonlinearity, poses a challenge, leading us to devise the "Step Truncation TT-Newton" method. We demonstrate the exponential convergence of our methods through various benchmark examples. Importantly, our scheme offers significantly reduced memory requirement compared to the full-grid scheme.

In this study, we introduce a tensor-train (TT) finite difference WENO method for solving compressible Euler equations. In a step-by-step manner, the tensorization of the governing equations is demonstrated. We also introduce \emph{LF-cross} and \emph{WENO-cross} methods to compute numerical fluxes and the WENO reconstruction using the cross interpolation technique. A tensor-train approach is developed for boundary condition types commonly encountered in Computational Fluid Dynamics (CFD). The performance of the proposed WENO-TT solver is investigated in a rich set of numerical experiments. We demonstrate that the WENO-TT method achieves the theoretical $\text{5}^{\text{th}}$-order accuracy of the classical WENO scheme in smooth problems while successfully capturing complicated shock structures. In an effort to avoid the growth of TT ranks, we propose a dynamic method to estimate the TT approximation error that governs the ranks and overall truncation error of the WENO-TT scheme. Finally, we show that the traditional WENO scheme can be accelerated up to 1000 times in the TT format, and the memory requirements can be significantly decreased for low-rank problems, demonstrating the potential of tensor-train approach for future CFD application. This paper is the first study that develops a finite difference WENO scheme using the tensor-train approach for compressible flows. It is also the first comprehensive work that provides a detailed perspective into the relationship between rank, truncation error, and the TT approximation error for compressible WENO solvers.

One of the ways to make artificial intelligence more natural is to give it some room for doubt. Two main questions should be resolved in that way. First, how to train a model to estimate uncertainties of its own predictions? And then, what to do with the uncertain predictions if they appear? First, we proposed an uncertainty-aware negative log-likelihood loss for the case of N-dimensional multivariate normal distribution with spherical variance matrix to the solution of N-classes classification tasks. The loss is similar to the heteroscedastic regression loss. The proposed model regularizes uncertain predictions, and trains to calculate both the predictions and their uncertainty estimations. The model fits well with the label smoothing technique. Second, we expanded the limits of data augmentation at the training and test stages, and made the trained model to give multiple predictions for a given number of augmented versions of each test sample. Given the multi-view predictions together with their uncertainties and confidences, we proposed several methods to calculate final predictions, including mode values and bin counts with soft and hard weights. For the latter method, we formalized the model tuning task in the form of multimodal optimization with non-differentiable criteria of maximum accuracy, and applied particle swarm optimization to solve the tuning task. The proposed methodology was tested using CIFAR-10 dataset with clean and noisy labels and demonstrated good results in comparison with other uncertainty estimation methods related to sample selection, co-teaching, and label smoothing.

Today, machine learning tools, particularly artificial neural networks, have become crucial for diverse applications. However, current digital computing tools to train and deploy artificial neural networks often struggle with massive data sizes and high power consumptions. Optical computing provides inherent parallelism and perform fundamental operations with passive optical components. However, most of the optical computing platforms suffer from relatively low accuracies for machine learning tasks due to fixed connections while avoiding complex and sensitive techniques. Here, we demonstrate a genetically programmable yet simple optical neural network to achieve high performances with optical random projection. By genetically programming the orientation of the scattering medium which acts as a random projection kernel and only using 1% of the search space, our novel technique finds an optimum kernel and improves its initial test accuracies 7-22% for various machine learning tasks. Our optical computing method presents a promising approach to achieve high performance in optical neural networks with a simple and scalable design., Comment: Manuscript: 11 pages, 5 Figures. Supplementary material: 8 pages, 6 Figures, 2 Tables

Concept Bottleneck Models (CBMs) assume that training examples (e.g., x-ray images) are annotated with high-level concepts (e.g., types of abnormalities), and perform classification by first predicting the concepts, followed by predicting the label relying on these concepts. The main difficulty in using CBMs comes from having to choose concepts that are predictive of the label and then having to label training examples with these concepts. In our approach, we adopt a more moderate assumption and instead use text descriptions (e.g., radiology reports), accompanying the images in training, to guide the induction of concepts. Our cross-modal approach treats concepts as discrete latent variables and promotes concepts that (1) are predictive of the label, and (2) can be predicted reliably from both the image and text. Through experiments conducted on datasets ranging from synthetic datasets (e.g., synthetic images with generated descriptions) to realistic medical imaging datasets, we demonstrate that cross-modal learning encourages the induction of interpretable concepts while also facilitating disentanglement. Our results also suggest that this guidance leads to increased robustness by suppressing the reliance on shortcut features., Comment: Accepted at EMNLP 2023; camera-ready version

C$_3$N$_4$ is a recently discovered phase of carbon nitrides with the tetragonal crystal structure [D.Laniel $\textit{et al.}$, Adv. Mater. 2023, 2308030] that is stable at ambient conditions. C$_3$N$_4$ is a semiconductor exhibiting flat-band anomalies in the valence band, suggesting the emergence of many-body instabilities upon hole doping. Here, using state-of-the-art first-principles calculations we show that hole-doped C$_3$N$_4$ reveals strong electron-phonon coupling, leading to the formation of a gapped superconducting state. The phase transition temperatures turn out to be strongly dependent on the hole concentration. We propose that holes could be injected into C$_3$N$_4$ via boron doping which induces, according to our results, a rigid shift of the Fermi energy without significant modification of the electronic structure. Based on the electron-phonon coupling and Coulomb pseudopotential calculated from first principles, we conclude that the boron concentration of 6 atoms per nm$^3$ would be required to reach the critical temperature of $\sim$36 K at ambient pressure., Comment: Calculation of the Coulomb pseudopotential revised, which lowered the predicted Tc. Final version: 10 pages incl. Supplemental Material, 10 figures, and 2 tables

A key advantage of utilizing van der Waals materials as defect-hosting platforms for quantum applications is the controllable proximity of the defect to the surface or the substrate for improved light extraction, enhanced coupling with photonic elements, or more sensitive metrology. However, this aspect results in a significant challenge for defect identification and characterization, as the defect's optoelectronic properties depend on the specifics of the atomic environment. Here we explore the mechanisms by which the environment can influence the properties of carbon impurity centres in hexagonal boron nitride (hBN). We compare the optical and electronic properties of such defects between bulk-like and few-layer films, showing alteration of the zero-phonon line energies, modifications to their phonon sidebands, and enhancements of their inhomogeneous broadenings. To disentangle the various mechanisms responsible for these changes, including the atomic structure, electronic wavefunctions, and dielectric screening environment of the defect center, we combine ab-initio calculations based on a density-functional theory with a quantum embedding approach. By studying a variety of carbon-based defects embedded in monolayer and bulk hBN, we demonstrate that the dominant effect of the change in the environment is the screening of the density-density Coulomb interactions within and between the defect orbitals. Our comparative analysis of the experimental and theoretical findings paves the way for improved identification of defects in low-dimensional materials and the development of atomic scale sensors of dielectric environments., Comment: 38 pages, 7 figures

Fe$_3$GeTe$_2$ attracts significant attention due to technological perspectives of realizing room temperature ferromagnetism in two-dimensional materials. Here we show that due to structural peculiarities of the Fe$_3$GeTe$_2$ monolayer, short distance between the neighboring iron atoms induces a strong exchange coupling. This strong coupling allows us to consider them as an effective cluster with a magnetic moment $\sim$5 $\mu_B$, giving rise to a simplified spin model on a bipartite honeycomb lattice with the reduced number of long-range interactions. The simplified model perfectly reproduces the results of the conventional spin model, but allows for a more tractable description of the magnetic properties of Fe$_3$GeTe$_2$, which is important, e.g., for large-scale simulations. Also, we discuss the role of biaxial strain in the stabilization of ferromagnetic ordering in Fe$_3$GeTe$_2$., Comment: 7 pages, 7 figures

We study intrinsic charge-carrier scattering mechanisms and determine their contribution to the transport properties of the two-dimensional ferromagnet Fe$_3$GeTe$_2$. We use state-of-the-art first-principles calculations combined with the model approaches to elucidate the role of the electron-phonon and electron-magnon interactions in the electronic transport. Our findings show that the charge carrier scattering in Fe$_3$GeTe$_2$ is dominated by the electron-phonon interaction, while the role of magnetic excitations is marginal. At the same time, the magnetic ordering is shown to effect essentially on the electron-phonon coupling and its temperature dependence. This leads to a sublinear temperature dependence of the electrical resistivity near the Curie temperature, which is in line with experimental observations. The room temperature resistivity is estimated to be $\sim$35 $\mu \Omega \cdot$cm which may be considered as an intrinsic limit for monolayer Fe$_3$GeTe$_2$., Comment: 10 pages, 8 figures

In this study, we propose a unified, general framework for the direct discontinuous Galerkin methods. In the new framework, the antiderivative of the nonlinear diffusion matrix is not needed. This allows a simple definition of the numerical flux, which can be used for general diffusion equations with no further modification. We also present the nonlinear stability analyses of the new direct discontinuous Galerkin methods and perform several numerical experiments to evaluate their performance. The numerical tests show that the symmetric and the interface correction versions of the method achieve optimal convergence and are superior to the nonsymmetric version, which demonstrates optimal convergence only for problems with diagonal diffusion matrices but loses order for even degree polynomials with a non-diagonal diffusion matrix. Singular or blow-up solutions are also well captured with the new direct discontinuous Galerkin methods., Comment: 22 pages, 4 figures

We introduce a novel technique and an associated high resolution dataset that aims to precisely evaluate wireless signal based indoor positioning algorithms. The technique implements an augmented reality (AR) based positioning system that is used to annotate the wireless signal parameter data samples with high precision position data. We track the position of a practical and low cost navigable setup of cameras and a Bluetooth Low Energy (BLE) beacon in an area decorated with AR markers. We maximize the performance of the AR-based localization by using a redundant number of markers. Video streams captured by the cameras are subjected to a series of marker recognition, subset selection and filtering operations to yield highly precise pose estimations. Our results show that we can reduce the positional error of the AR localization system to a rate under 0.05 meters. The position data are then used to annotate the BLE data that are captured simultaneously by the sensors stationed in the environment, hence, constructing a wireless signal data set with the ground truth, which allows a wireless signal based localization system to be evaluated accurately., Comment: 30 pages

The term "sector" in professional business life is a vague concept since companies tend to identify themselves as operating in multiple sectors simultaneously. This ambiguity poses problems in recommending jobs to job seekers or finding suitable candidates for open positions. The latter holds significant importance when available candidates in a specific sector are also scarce; hence, finding candidates from similar sectors becomes crucial. This work focuses on discovering possible sector similarities through relational analysis. We employ several algorithms from the frequent pattern mining and collaborative filtering domains, namely negFIN, Alternating Least Squares, Bilateral Variational Autoencoder, and Collaborative Filtering based on Pearson's Correlation, Kendall and Spearman's Rank Correlation coefficients. The algorithms are compared on a real-world dataset supplied by a major recruitment company, Kariyer.net, from Turkey. The insights and methods gained through this work are expected to increase the efficiency and accuracy of various methods, such as recommending jobs or finding suitable candidates for open positions., Comment: 13 pages and 3 figures

Robotic ultrasound (US) imaging has been seen as a promising solution to overcome the limitations of free-hand US examinations, i.e., inter-operator variability. However, the fact that robotic US systems cannot react to subject movements during scans limits their clinical acceptance. Regarding human sonographers, they often react to patient movements by repositioning the probe or even restarting the acquisition, in particular for the scans of anatomies with long structures like limb arteries. To realize this characteristic, we proposed a vision-based system to monitor the subject's movement and automatically update the scan trajectory thus seamlessly obtaining a complete 3D image of the target anatomy. The motion monitoring module is developed using the segmented object masks from RGB images. Once the subject is moved, the robot will stop and recompute a suitable trajectory by registering the surface point clouds of the object obtained before and after the movement using the iterative closest point algorithm. Afterward, to ensure optimal contact conditions after repositioning US probe, a confidence-based fine-tuning process is used to avoid potential gaps between the probe and contact surface. Finally, the whole system is validated on a human-like arm phantom with an uneven surface, while the object segmentation network is also validated on volunteers. The results demonstrate that the presented system can react to object movements and reliably provide accurate 3D images., Comment: The paper has been accepted by IEEE TIM. Video: https://www.youtube.com/watch?v=MUtgSXS7EZI