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Anisotropy of local pressure distribution and dissipation are essential in understanding the evolution of the internal structure of compact objects and their observable characteristics. In this work, we reinterpret local pressure anisotropy in relativistic stellar structures as a contribution to the energy density. This approach allows the modelling of any anisotropic equation of state in self-gravitating systems by treating anisotropy as a contribution. We demonstrate that this approach provides more realistic stellar models that meet essential physical criteria, such as mass-radius relationships and stability conditions. The results are compared to observational data, particularly the inferred compactness values for pulsars PSR J0740+6620 and PSR J0030+0451, showing that anisotropic and isotropic models can represent these objects. We further explore how dissipation, such as temperature gradients, influences radial pressure and show that it can be modelled similarly to anisotropy., Comment: 18 pages, 2 figures

Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this reason, many alternative robust techniques have been studied in literature. In these terms, the Least Squares Quantile (LQS), and in particular the Least Squares Median, are among the regression estimators that exhibit better robustness properties. However, the accurate computation of this estimators is computationally demanding, resulting in a difficult estimator to obtain. In this paper, new novel approaches to compute a global optimal solution for the LQS estimator based on single-level and bilevel optimization methods are proposed. An extensive computational study is provided to support the efficiency of the methods considered, and an ad hoc procedure to address the scalability of the problem to larger instances is proposed.

In this paper, we introduce the Fixed Topology Minimum-Length Tree with Neighborhood Problem, which aims to embed a rooted tree-shaped graph into a $d$-dimensional metric space while minimizing its total length provided that the nodes must be embedded to some restricted areas. This problem has significant applications in efficiently routing cables or pipelines in engineering designs. We propose novel mathematical optimization-based approaches to solve different versions of the problem based on the domain for the embedding. In cases where the embedding maps to a continuous space, we provide several Mixed Integer Nonlinear Optimization formulations. If the embedding is to a network, we derive a mixed integer linear programming formulation as well as a dimensionality reduction methodology that allows for solving larger problems in less CPU time. A data-driven methodology is also proposed to construct a proper network based on the instance of the problem. We report the results of a battery of computational experiments that validate our proposal., Comment: 18 pages, 10 figures

Few-shot knowledge distillation recently emerged as a viable approach to harness the knowledge of large-scale pre-trained models, using limited data and computational resources. In this paper, we propose a novel few-shot feature distillation approach for vision transformers. Our approach is based on two key steps. Leveraging the fact that vision transformers have a consistent depth-wise structure, we first copy the weights from intermittent layers of existing pre-trained vision transformers (teachers) into shallower architectures (students), where the intermittence factor controls the complexity of the student transformer with respect to its teacher. Next, we employ an enhanced version of Low-Rank Adaptation (LoRA) to distill knowledge into the student in a few-shot scenario, aiming to recover the information processing carried out by the skipped teacher layers. We present comprehensive experiments with supervised and self-supervised transformers as teachers, on six data sets from various domains (natural, medical and satellite images) and tasks (classification and segmentation). The empirical results confirm the superiority of our approach over state-of-the-art competitors. Moreover, the ablation results demonstrate the usefulness of each component of the proposed pipeline. We release our code at https://github.com/dianagrigore/WeCoLoRA., Comment: Accepted at WACV 2025

Recent advancements in deep learning techniques have spurred considerable interest in their application to hyperspectral imagery processing. This paper provides a comprehensive review of the latest developments in this field, focusing on methodologies, challenges, and emerging trends. Deep learning architectures such as Convolutional Neural Networks (CNNs), Autoencoders, Deep Belief Networks (DBNs), Generative Adversarial Networks (GANs), and Recurrent Neural Networks (RNNs) are examined for their suitability in processing hyperspectral data. Key challenges, including limited training data and computational constraints, are identified, along with strategies such as data augmentation and noise reduction using GANs. The paper discusses the efficacy of different network architectures, highlighting the advantages of lightweight CNN models and 1D CNNs for onboard processing. Moreover, the potential of hardware accelerators, particularly Field Programmable Gate Arrays (FPGAs), for enhancing processing efficiency is explored. The review concludes with insights into ongoing research trends, including the integration of deep learning techniques into Earth observation missions such as the CHIME mission, and emphasizes the need for further exploration and refinement of deep learning methodologies to address the evolving demands of hyperspectral image processing., Comment: Hyperspectral, Deep Learning, Neural Networks, Image Processing, Classification, Segmentation, Hardware Accelerators, CHIME Mission

This paper compares different exact approaches to solve the Discrete Ordered Median Problem (DOMP). In recent years, DOMP has been formulated using set packing constraints giving rise to one of its most promising formulations. The use of this family of constraints, known as strong order constraints (SOC), has been validated in the literature by its theoretical properties and because their linear relaxation provides very good lower bounds. Furthermore, embedded in branch-and-cut or branch-price-and-cut procedures as valid inequalities, they allow one to improve computational aspects of solution methods such as CPU time and use of memory. In spite of that, the above mentioned formulations require to include another family of order constraints, e.g., the weak order constraints (WOC), which leads to coefficient matrices with elements other than {0,1}. In this work, we develop a new approach that does not consider extra families of order constraints and furthermore relaxes SOC -- in a branch-and-cut procedure that does not start with a complete formulation -- to add them iteratively using row generation techniques to certify feasibility and optimality. Exhaustive computational experiments show that it is advisable to use row generation techniques in order to only consider {0,1}-coefficient matrices modeling the DOMP. Moreover, we test how to exploit the problem structure. Implementing an efficient separation of SOC using callbacks improves the solution performance. This allows us to deal with bigger instances than using fixed cuts/constraints pools automatically added by the solver in the branch-and-cut for SOC, concerning both the formulation based on WOC and the row generation procedure.

This article explores the latest Convolutional Neural Networks (CNNs) for cloud detection aboard hyperspectral satellites. The performance of the latest 1D CNN (1D-Justo-LiuNet) and two recent 2D CNNs (nnU-net and 2D-Justo-UNet-Simple) for cloud segmentation and classification is assessed. Evaluation criteria include precision and computational efficiency for in-orbit deployment. Experiments utilize NASA's EO-1 Hyperion data, with varying spectral channel numbers after Principal Component Analysis. Results indicate that 1D-Justo-LiuNet achieves the highest accuracy, outperforming 2D CNNs, while maintaining compactness with larger spectral channel sets, albeit with increased inference times. However, the performance of 1D CNN degrades with significant channel reduction. In this context, the 2D-Justo-UNet-Simple offers the best balance for in-orbit deployment, considering precision, memory, and time costs. While nnU-net is suitable for on-ground processing, deployment of lightweight 1D-Justo-LiuNet is recommended for high-precision applications. Alternatively, lightweight 2D-Justo-UNet-Simple is recommended for balanced costs between timing and precision in orbit., Comment: Hyperspectral Satellite Data, Cloud Segmentation, Classification, Convolutional Neural Networks, Principal Component Analysis

In this paper we introduce a new class of cooperative games that arise from production-inventory problems. Several agents have to cover their demand over a finite time horizon and shortages are allowed. Each agent has its own unit production, inventory-holding and backlogging cost. Cooperation among agents is given by sharing production processes and warehouse facilities: agents in a coalition produce with \ the cheapest production cost and store with the cheapest inventory cost. We prove that the resulting cooperative game is totally balanced and the Owen set reduces to a singleton: the Owen point. Based on this type of allocation we find a population monotonic allocation scheme for this class of games. Finally, we point out the relationship of the Owen point with other well-known allocation rules such as the nucleolus and the Shapley value.

Production-inventory games were introduced in Guardiola et al. (2007) as a new class of totally balanced combinatorial optimization games. From among all core-allocations, the Owen point was proposed as a specifically appealing solution. In this paper we study some relationships of the class of production-inventory games and other classes of new and known games. In addition, we propose three axiomatic characterizations of the Owen point. We use eight axioms for these characterizations, among those, inessentiality and additivity of players' demands are used for the first time in this paper.

Consider a set N of n (>1) stores with single-item and single-period nondeterministic demands like in a classic newsvendor setting with holding and penalty costs only. Assume a risk-pooling single-warehouse centralized inventory ordering option. Allocation of costs in the centralized inventory ordering corresponds to modelling it as a cooperative cost game whose players are the stores. It has been shown that when holding and penalty costs are identical for all subsets of stores, the game based on optimal expected costs has a non empty core (Hartman et. al., 2000, Muller \textit{et. al.}, 2002). In this paper we examine a related inventory centralization game based on demand realizations that has, in general, an empty core even with identical penalty and holding costs (Hartman and Dror, 2005). We propose a repeated cost allocation scheme for dynamic realization games based on allocation processes introduced by Lehrer (2002a). We prove that the cost subsequences of the dynamic realization game process, based on Lehrer's rules, converge almost surely to either a least square value or the core of the expected game. We extend the above results to more general dynamic cost games and relax the independence hypothesis of the sequence of players' demands at different stages.

The electrical conductivity of magnesium silicate MgSiO3 has been studied, using the framework of the first-principles density functional theory and the Boltzmann transport theory, under the thermodynamic conditions of the Earth's lower mantle. We find that the conductivity of pristine MgSiO3 depends strongly on the structural phase of the material, as well as on temperature and pressure. The conductivity of the perovskite phase increases with increasing pressure (depth of the lower mantle) up to 90 GPa, then decreases at higher pressures due to a change in the material's band gap transition from direct to indirect. Finally, the structural phase transition that MgSiO3 undergoes near the bottom of the lower mantle, from perovskite to post-perovskite, causes an increase in the conductivity of MgSiO3, which should contribute to the increase in the electrical conductivity of the Earth's mantle under the thermodynamic conditions of the Earth's D" layer., Comment: 16 pages, 4 figures, 2 tables

Cooperative lot-sizing models with backlogging and heterogeneous costs are studied in Guardiola et al. (2020). In this model several firms participate in a consortium aiming at satisfying their demand over the planing horizon with minimal operation cost. Each firm uses the best ordering channel and holding technology provided by the participants in the consortium. The authors show that there are always fair allocations of the overall operation cost among the firms so that no group of agents profit from leaving the consortium. This paper revisits those cooperative lot-sizing models and presents a new family of cost allocations, the unitary Owen points. This family is an extension of the Owen set which enjoys very good properties in production-inventory proble, introduced by Guardiola et al. (2008). Necessary and sufficient conditions are provided for the unitary Owen points to be fair allocations. In addition, we provide empirical evidence, throughout simulation, showing that the above condition is fulfilled in most cases. Additionally, a relationship between lot-sizing games and a certain family of production-inventory games, through Owen's points of the latter, is described. This interesting relationship enables to easily construct a variety of fair allocations for cooperative lot-sizing models.

Results are presented from several samples taken from leaves of the Pardon Portico of Mosque-Cathedral of Cordoba, where an alteration on their surface was detected. Metal samples analyzed using X-ray microanalysis and powder x-ray diffraction were predominantly constituted by copper with some amounts of zinc attributed to brass, whereas other samples were also constituted by copper, tin and lead attributed to bronze. Surface samples were analyzed using the same techniques. In addition Fourier transform infrared spectroscopy was also used.The main compound identified in all the surface of the leaves is copper chloride hydroxide (atacamite). Lead chlorides have also been found. These data show that the sudden alteration that appears may be attributed to the use of some cleaning product containing chloride. Other compounds detected in the surface were gypsum, quartz and oxalates coming from environmental contamination.

Hyperspectral Imaging (HSI) is used in a wide range of applications such as remote sensing, yet the transmission of the HS images by communication data links becomes challenging due to the large number of spectral bands that the HS images contain together with the limited data bandwidth available in real applications. Compressive Sensing reduces the images by randomly subsampling the spectral bands of each spatial pixel and then it performs the image reconstruction of all the bands using recovery algorithms which impose sparsity in a certain transform domain. Since the image pixels are not strictly sparse, this work studies a data sparsification pre-processing stage prior to compression to ensure the sparsity of the pixels. The sparsified images are compressed $2.5\times$ and then recovered using the Generalized Orthogonal Matching Pursuit algorithm (gOMP) characterized by high accuracy, low computational requirements and fast convergence. The experiments are performed in five conventional hyperspectral images where the effect of different sparsification levels in the quality of the uncompressed as well as the recovered images is studied. It is concluded that the gOMP algorithm reconstructs the hyperspectral images with higher accuracy as well as faster convergence when the pixels are highly sparsified and hence at the expense of reducing the quality of the recovered images with respect to the original images., Comment: Hyperspectral Imaging, Compressive Sensing, Greedy Algorithms, Generalized Orthogonal Matching Pursuit (gOMP), Sparsity, Sparsification, IEEE-copyrighted material (2022), WHISPERS Workshop (13-16 September 2022)

Hyperspectral Imaging comprises excessive data consequently leading to significant challenges for data processing, storage and transmission. Compressive Sensing has been used in the field of Hyperspectral Imaging as a technique to compress the large amount of data. This work addresses the recovery of hyperspectral images 2.5x compressed. A comparative study in terms of the accuracy and the performance of the convex FISTA/ADMM in addition to the greedy gOMP/BIHT/CoSaMP recovery algorithms is presented. The results indicate that the algorithms recover successfully the compressed data, yet the gOMP algorithm achieves superior accuracy and faster recovery in comparison to the other algorithms at the expense of high dependence on unknown sparsity level of the data to recover., Comment: Hyperspectral Imaging, Compressive Sensing, Convex Algorithms, Greedy Algorithms, FISTA, ADMM, gOMP, BIHT, CoSaMP, IEEE-copyrighted material (2022), IVMSP Workshop (26-29 June 2022)

In this paper, we discuss portfolio selection strategies for Enhanced Indexation (EI), which are based on stochastic dominance relations. The goal is to select portfolios that stochastically dominate a given benchmark but that, at the same time, must generate some excess return with respect to a benchmark index. To achieve this goal, we propose a new methodology that selects portfolios using the ordered weighted average (OWA) operator, which generalizes previous approaches based on minimax selection rules and still leads to solving linear programming models. We also introduce a new type of approximate stochastic dominance rule and show that it implies the almost Second-order Stochastic Dominance (SSD) criterion proposed by Lizyayev and Ruszczynski (2012). We prove that our EI model based on OWA selects portfolios that dominate a given benchmark through this new form of stochastic dominance criterion. We test the performance of the obtained portfolios in an extensive empirical analysis based on real-world datasets. The computational results show that our proposed approach outperforms several SSD-based strategies widely used in the literature, as well as the global minimum variance portfolio.

Most advances in metaoptics have been made at visible wavelengths and above; in contrast, the vacuum ultraviolet (VUV) has barely been explored despite numerous scientific and technological opportunities. Creating metaoptic elements at this short wavelength is challenging due to the scarcity of VUV transparent materials and the small sizes of the required nanostructures. Here, we present the first transmissive VUV (175 nm) metalens. By using UV-grade silica and trading-off the Nyquist requirement for subwavelength structures against feasibility of the fabrication process, we achieve a step-change in diffraction efficiencies for wavelengths shorter than 300 nm. Our large numerical aperture (NA = 0.5) metalens shows an average diffraction efficiency of (53.3 +- 1.4)%. This demonstration opens up new avenues for compact flat optic systems operating in the VUV range.

In this Master Thesis, we use a technique to shift and stack the X-Ray spectra of 1138 galaxy clusters from the eRASS-1 survey, totalling 430649 counts. In comparison with previous stacking techniques, the method presented here introduces proper normalization of the shifted redistribution matrix file (RMF), which allows to recover the physical temperature and metallicity of the stacked spectra. Using this technique, we can obtain constraints in the stacked spectra for the individual abundances of O, Ne, Mg, Si, Ar, Ca, and Fe. Additionally, we study the possible detection of the previously reported 3.5keV unidentified line emission; however, the residuals barely exceed $\pm 2 \sigma$ in the [3-4]keV range. On the other hand, although residuals in the [3.4-3.55]keV band are compatible with charge exchange emission from SXVI (bare sulphur ions), charge exchange emission from OVII at 0.56keV should also be present, since it is 200 orders of magnitude higher than charge emission from SXVI in the [3.4-3.55]keV band; however, it is unfortunately not detected.

The EMPATHIC project aimed to design an emotionally expressive virtual coach capable of engaging healthy seniors to improve well-being and promote independent aging. One of the core aspects of the system is its human sensing capabilities, allowing for the perception of emotional states to provide a personalized experience. This paper outlines the development of the emotion expression recognition module of the virtual coach, encompassing data collection, annotation design, and a first methodological approach, all tailored to the project requirements. With the latter, we investigate the role of various modalities, individually and combined, for discrete emotion expression recognition in this context: speech from audio, and facial expressions, gaze, and head dynamics from video. The collected corpus includes users from Spain, France, and Norway, and was annotated separately for the audio and video channels with distinct emotional labels, allowing for a performance comparison across cultures and label types. Results confirm the informative power of the modalities studied for the emotional categories considered, with multimodal methods generally outperforming others (around 68% accuracy with audio labels and 72-74% with video labels). The findings are expected to contribute to the limited literature on emotion recognition applied to older adults in conversational human-machine interaction., Comment: This work has been submitted to the IEEE for possible publication

Optical frequency combs (FCs), that establish a rigid phase-coherent link between the microwave and optical domains of the electromagnetic spectrum, are emerging as a key high-precision tools for the development of quantum technology platforms. These include potential applications for communication, computation, information, sensing and metrology, and can extend from the near-infrared with micro-resonator combs, up to the technologically attractive terahertz (THz) frequency range, with powerful and miniaturized quantum cascade laser (QCL) FCs. The recently discovered ability of the QCLs to produce a harmonic frequency comb (HFC), a FC with large intermodal spacings, has attracted new interest in these devices for both applications and fundamental physics, particularly for the generation of THz tones of high spectral purity for high data rate wireless communication networks, for radiofrequency arbitrary waveform synthesis, and for the development of quantum key distributions. The controlled generation of harmonic states of a specific order remains, however, elusive in THz QCLs. Here we devise a strategy to obtain broadband HFC emission of a pre-defined order in QCL, by design. By patterning n regularly spaced defects on the top-surface of a double-metal Fabry-Perot QCL, we demonstrate harmonic comb emission with modes spaced by (n+1) free spectral range and with a record optical power/mode of ~270 $\mu W$.

Metalenses are composed of nanostructures for focusing light and have been widely explored in many exciting applications. However, their expanding dimensions pose simulation challenges. We propose a method to simulate metalenses in a timely manner using vectorial wave and ray tracing models. We sample the metalens' radial phase gradient and locally approximate it by a linear phase response. Each sampling point is modeled as a binary blazed grating, employing the chosen nanostructure, to build a transfer function set. The metalens transmission or reflection is then obtained by applying the corresponding transfer function to the incoming field on the regions surrounding each sampling point. Fourier optics is used to calculate the scattered fields under arbitrary illumination for the vectorial wave method and a Monte Carlo algorithm is used in the ray tracing formalism. We validated our method against finite difference time domain simulations at 632 nm and we were able to simulate metalenses larger than 3000lambda0 in diameter on a personal computer., Comment: 10 pages

Satellites are increasingly adopting on-board AI to optimize operations and increase autonomy through in-orbit inference. The use of Deep Learning (DL) models for segmentation in hyperspectral imagery offers advantages for remote sensing applications. In this work, we train and test 20 models for multi-class segmentation in hyperspectral imagery, selected for their potential in future space deployment. These models include 1D and 2D Convolutional Neural Networks (CNNs) and the latest vision transformers (ViTs). We propose a lightweight 1D-CNN model, 1D-Justo-LiuNet, which outperforms state-of-the-art models in the hypespectral domain. 1D-Justo-LiuNet exceeds the performance of 2D-CNN UNets and outperforms Apple's lightweight vision transformers designed for mobile inference. 1D-Justo-LiuNet achieves the highest accuracy (0.93) with the smallest model size (4,563 parameters) among all tested models, while maintaining fast inference. Unlike 2D-CNNs and ViTs, which encode both spectral and spatial information, 1D-Justo-LiuNet focuses solely on the rich spectral features in hyperspectral data, benefitting from the high-dimensional feature space. Our findings are validated across various satellite datasets, with the HYPSO-1 mission serving as the primary case study for sea, land, and cloud segmentation. We further confirm our conclusions through generalization tests on other hyperspectral missions, such as NASA's EO-1. Based on its superior performance and compact size, we conclude that 1D-Justo-LiuNet is highly suitable for in-orbit deployment, providing an effective solution for optimizing and automating satellite operations at edge., Comment: Remote Sensing, Satellite Hyperspectral Imagery, Segmentation, Deep Learning, 1D-CNNs, 2D-CNNs, ViTs

Long-lived particles (LLPs) arise in many theories beyond the Standard Model. These may be copiously produced from meson decays (or through their mixing with the LLP) at neutrino facilities and leave a visible decay signal in nearby neutrino detectors. We compute the expected sensitivity of the DUNE liquid argon (LAr) and gaseous argon (GAr) near detectors (ND) to light LLP decays. In doing so, we determine the expected backgrounds for both detectors, which have been largely overlooked in the literature, taking into account their angular and energy resolution. We show that searches for LLP decays into muon pairs, or into three pions, would be extremely clean. Conversely, decays into two photons would be affected by large backgrounds from neutrino interactions for both near detectors; finally, the reduced signal efficiency for $e^+ e^-$ pairs leads to a reduced sensitivity for ND-LAr. Our results are first presented in a model-independent way, as a function of the mass of the new state and its lifetime. We also provide detailed calculations for several phenomenological models with axion-like particles (coupled to gluons, to electroweak bosons, or to quark currents). Some of our results may also be of interest for other neutrino facilities using a similar detector technology (e.g. MicroBooNE, SBND, ICARUS, or the T2K Near Detector)., Comment: 35 pages, 11 Figures. v3: typos fixed, results unchanged

Hyperspectral Imaging, employed in satellites for space remote sensing, like HYPSO-1, faces constraints due to few labeled data sets, affecting the training of AI models demanding these ground-truth annotations. In this work, we introduce The HYPSO-1 Sea-Land-Cloud-Labeled Dataset, an open dataset with 200 diverse hyperspectral images from the HYPSO-1 mission, available in both raw and calibrated forms for scientific research in Earth observation. Moreover, 38 of these images from different countries include ground-truth labels at pixel-level totaling about 25 million spectral signatures labeled for sea/land/cloud categories. To demonstrate the potential of the dataset and its labeled subset, we have additionally optimized a deep learning model (1D Fully Convolutional Network), achieving superior performance to the current state of the art. The complete dataset, ground-truth labels, deep learning model, and software code are openly accessible for download at the website https://ntnu-smallsat-lab.github.io/hypso1_sea_land_clouds_dataset/ ., Comment: Computer Vision, Artificial Intelligence, Remote Sensing, Earth Observation, Hyperspectral Imaging, Classification, Labeled Data

The minimum and maximum cuts of an undirected edge-weighted graph are classic problems in graph theory. While the Min-Cut Problem can be solved in P, the Max-Cut Problem is NP-Complete. Exact and heuristic methods have been developed for solving them. For both problems, we introduce a natural extension in which cutting an edge induces a cost. Our goal is to find a cut that minimizes the sum of the cut weights but, at the same time, restricts its total cut cost to a given budget. We prove that both restricted problems are NPComplete and we also study some of its properties. Finally, we develop exact algorithms to solve both as well as a non-exact algorithm for the min-cut case based on a Lagreangean relaxation that generally provides optimal solutions. Their performance is reported by an extensive computational experience., Comment: 21 pages, 6 figures, 11 tables

In the present paper, we investigate the structural, thermodynamic, dynamic, elastic, and electronic properties of doped 2D diamond C$_4$X$_2$ (X = B or N) nanosheets in both AA$'$A$''$ and ABC stacking configurations, by first-principles calculations. Those systems are composed of 3 diamond-like graphene sheets, with an undoped graphene layer between two 50% doped ones. Our results, based on the analysis of ab-initio molecular dynamics simulations, phonon dispersion spectra, and Born's criteria for mechanical stability, revealed that all four structures are stable. Additionally, their standard enthalpy of formation values are similar to the one of pristine 2D diamond, recently synthesized by compressing three graphene layers. The C$_4$X$_2$ (X = B or N) systems exhibit high elastic constant values and stiffness comparable to the diamond. The C$_4$N$_2$ nanosheets present wide indirect band gaps that could be advantageous for applications similar to the ones of the hexagonal boron nitride (h-BN), such as a substrate for high-mobility 2D devices. On the other hand, the C$_4$B$_2$ systems are semiconductors with direct band gaps, in the 1.6 - 2.0 eV range, and small effective masses, which are characteristics that may be favorable to high carrier mobility and optoelectronics applications.

We notice an analogy between the motion of a relativistic particle with external homogeneous and time-dependent electromagnetic fields and the Dik'ii-Eilenberger equation for the Bogoliubov-de Gennes equation. By means of the integrable defocusing nonlinear Schr\"odinger hierarchy and their solitons appearing in the Gross-Neveu and Nambu-Jona-Lasinio models, we construct an infinite family of solutions of the Lorentz equation with non-vanishing curvature and torsion., Comment: 5 pages, 4 figures