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In this note, we characterise the existence of non-trivial invariant spinors on maximal flag manifolds associated to complex simple Lie algebras. This characterisation is based on the combinatorial properties of their set of positive roots., Comment: 11 pages

In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spin$^r$ context. We find new invariant spin$^r$ spinors on the projective spaces $\mathbb{CP}^n$, $\mathbb{HP}^n$, and the Cayley plane $\mathbb{OP}^2$ for all their homogeneous realisations. Specifically, for each of these realisations, we provide a complete description of the space of invariant spin$^r$ for the minimum value of $r$ for which this space is non-zero. Additionally, we demonstrate some geometric implications of the existence of special spin$^r$ spinors on these spaces., Comment: 41 pages; v2: solved some technical issues with tex (there were duplicate sections in v1)

In this work, we present a methodology for devising forward-backward methods for finding zeros in the sum of a finite number of maximally monotone operators. We extend the framework and techniques from [SIAM J. Optim., 34 (2024), pp. 1569-1594] to cover the case involving a finite number of cocoercive operators, which should be directly evaluated instead of computing their resolvent. The algorithms are induced by three graphs that determine how the algorithm variables interact with each other and how they are combined to compute each resolvent. The hypotheses on these graphs ensure that the algorithms obtained have minimal lifting and are frugal, meaning that the ambient space of the underlying fixed point operator has minimal dimension and that each resolvent and each cocoercive operator is evaluated only once per iteration. This framework not only allows to recover some known methods, but also to generate new ones, as the forward-backward algorithm induced by a complete graph. We conclude with a numerical experiment showing how the choice of graphs influences the performance of the algorithms.

In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with variables coupling, we consider a situation where straightforward translation to a fixed point problem is not possible because the operators that represent the relevant systems of nonlinear equations are not self-mappings, i.e., they operate between spaces of different dimensions. To overcome this difficulty we suggest an "alternating common fixed points algorithm" that acts alternatingly on the different vector variables. This approach translates the original problem to a common fixed point problem for which iterative algorithms are abound and exhibits a viable alternative to translation to an optimization problem, which usually requires derivatives information. However, to apply any of these iterative algorithms requires to ascertain the conditions that appear in their convergence theorems. To circumvent the need to verify conditions for convergence, we propose and motivate a derivative-free algorithm that better suits the tomographic absorption spectroscopy problem at hand and is even further improved by applying to it the superiorization approach. This is presented along with experimental results that demonstrate our approach., Comment: Accepted for publication in the journal: Communications in Optimization Theory

For each $n\in\mathbb{N}$, we construct a Riemannian spin manifold carrying a generalised Killing spinor with $n$ distinct eigenvalues, providing the first known examples of such objects for $n>4$. For each left-invariant metric on a three-dimensional Lie group, we explicitly find all invariant generalised Killing spinors. We find many new examples with three distinct eigenvalues, and we prove that, in some cases, this is the generic situation., Comment: 17 pages

In spite of the interest in the two-dimensional electron gases (2DEGs) experimentally found at surfaces and interfaces, important uncertainties remain about the observed insulator--metal transitions (IMTs). Here we show how an explicit improper coupling of carrier sources with a relevant soft mode significantly affects the transition. The analysis presented here for 2DEGs at polar interfaces is based on group theory, Landau-Ginzburg theory, and illustrated with first-principles calculations for the prototypical case of the LaAlO$_3$/SrTiO$_3$ interface, for which such a structural transition has recently been observed. This direct coupling implies that the appearance of the soft mode is always accompanied by carriers. For sufficiently strong coupling an avalanche-like first-order IMT is predicted.

Triangulenes are open-shell triangular graphene flakes with total spin increasing with their size. In the last years, on-surface-synthesis strategies have permitted fabricating and engineering triangulenes of various sizes and structures with atomic precision. However, direct proof of the increasing total spin with their size remains elusive. In this work, we report the combined in-solution and on-surface synthesis of a large nitrogen-doped triangulene (aza-[5]-triangulene) and the detection of its high spin ground state on a Au(111) surface. Bond-resolved scanning tunneling microscopy images uncovered radical states distributed along the zigzag edges, which were detected as weak zero-bias resonances in scanning tunneling spectra. These spectral features reveal the partial Kondo screening of a high spin state. Through a combination of several simulation tools, we find that the observed distribution of radical states is explained by a quintet ground state (S = 2), instead of the expected quartet state (S = 3/2), confirming the positively charged state of the molecule on the surface. We further provide a qualitative description of the change of (anti)aromaticity introduced by N-substitution, and its role in the charge stabilization on a surface, resulting in a S = 2 aza-[5]-triangulene on Au(111)., Comment: 8 pages with 4 figures

In this paper we introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of composite functions. BDSA exploits the combined nature of subgradients from the data and proximal steps, and integrates a line-search procedure to enhance its performance. While BDSA encompasses existing schemes proposed in the literature, it extends its applicability to more diverse problem domains. We establish the convergence of BDSA under the Kurdyka--Lojasiewicz property and provide an analysis of its convergence rate. To evaluate the effectiveness of BDSA, we introduce a novel family of challenging test functions with an abundance of critical points. We conduct comparative evaluations demonstrating its ability to effectively escape non-optimal critical points. Additionally, we present two practical applications of BDSA for testing its efficacy, namely, a constrained minimum-sum-of-squares clustering problem and a nonconvex generalization of Heron's problem.

Traditionally, it has been assumed that the stopping of a swift ion travelling through matter can be understood in terms of two essentially independent components, i.e. electronic vs. nuclear. Performing extensive Ehrenfest MD simulations of the process of proton irradiation of water ice that accurately describe not only the non-adiabatic dynamics of the electrons but also of the nuclei, we have found a stopping mechanism involving the interplay of the electronic and nuclear subsystems. This effect, which consists in a kinetic energy transfer from the projectile to the target nuclei thanks to the perturbations of the electronic density caused by the irradiation, is fundamentally different from the atomic displacements and collision cascades characteristic of nuclear stopping. Moreover, it shows a marked isotopic effect depending on the composition of the target, being relevant mostly for light water as opposed to heavy water. This result is consistent with long-standing experimental results which remained unexplained so far.

Spinorial methods have proven to be a powerful tool to study geometric properties of spin manifolds. Our aim is to continue the spinorial study of manifolds that are not necessarily spin. We introduce and study the notion of $G$-invariance of spin$^r$ structures on a manifold $M$ equipped with an action of a Lie group $G$. For the case when $M$ is a homogeneous $G$-space, we prove a classification result of these invariant structures in terms of the isotropy representation. As an example, we study the invariant spin$^r$ structures for all the homogeneous realisations of the spheres., Comment: 22 pages

When developing tools for automated cortical segmentation, the ability to produce topologically correct segmentations is important in order to compute geometrically valid morphometry measures. In practice, accurate cortical segmentation is challenged by image artifacts and the highly convoluted anatomy of the cortex itself. To address this, we propose a novel deep learning-based cortical segmentation method in which prior knowledge about the geometry of the cortex is incorporated into the network during the training process. We design a loss function which uses the theory of Laplace's equation applied to the cortex to locally penalize unresolved boundaries between tightly folded sulci. Using an ex vivo MRI dataset of human medial temporal lobe specimens, we demonstrate that our approach outperforms baseline segmentation networks, both quantitatively and qualitatively., Comment: Accepted at the 28th biennial international conference on Information Processing in Medical Imaging (IPMI 2023)

Understanding the generation and evolution of defects induced in matter by ion irradiation is of fundamental importance to estimate the degradation of functional properties of materials. Computational approaches used in dierent communities, from space radiation eects to nuclear energy experiments, are based on a number of approximations that, among others, traditionally neglect the coupling between electronic and ionic degrees of freedom in the description of displacements. In this work, we study collision cascades in GaAs, including the electronic stopping power for selfprojectiles in dierent directions obtained via real time Time Dependent Density Functional Theory in Molecular Dynamics simulations of collision cascades, using the recent electron-phonon model and the previously developed two-temperature model. We show that the former can be well applied to describe the eects of electronic stopping in molecular dynamics simulations of collision cascades in a multielement semiconductor and that the number of defects is considerably aected by electronic stopping eects. The results are also discussed in the wider context of the commonly used non-ionizing energy loss model to estimate degradation of materials by cumulative displacements.

We present real-time time-dependent density-functional-theory calculations of the electronic stopping power for negative and positive projectiles (electrons, protons, antiprotons and muons) moving through liquid water. After correction for finite mass effects, the nonlinear stopping power obtained in this work is significantly different from the previously known results from semi-empirical calculations based on the dielectric response formalism. Linear-nonlinear discrepancies are found both in the maximum value of the stopping power and the Bragg peak's position. Our results indicate the importance of the nonlinear description of electronic processes, particularly for electron projectiles, which are modeled here as classical point charges. Our findings also confirm the expectation that the quantum nature of the electron projectile should substantially influence the stopping power around the Bragg peak and below., Comment: 6 pages, 4 figures

By harvesting a wider range of the solar spectrum, intermediate band solar cells (IBSCs) can achieve efficiencies 50% higher than conventional single-junction solar cells. For this, additional requirements are imposed to the light-absorbing semiconductor, which must contain a collection of in-gap levels, called intermediate band (IB), optically coupled to but thermally decoupled from the valence and conduction bands (VB and CB). Quantum-dot-in-perovskite (QDiP) solids, where inorganic quantum dots (QDs) are embedded in a halide perovskite matrix, have been recently suggested as a promising material platform for developing IBSCs. In this work, QDiP solids with excellent morphological and structural quality and strong absorption and emission related to the presence of in-gap QD levels are synthesized. With them, QDiP-based IBSCs are fabricated and, by means of temperature-dependent photocurrent measurements, it is shown that the IB is strongly thermally decoupled from the valence and conduction bands. The activation energy of the IB$\rightarrow$CB thermal escape of electrons is measured to be 204 meV, resulting in the mitigation of this detrimental process even under room-temperature operation, thus fulfilling the first mandatory requisite to enable high-efficiency IBSCs.

This paper addresses the study of a new class of nonsmooth optimization problems, where the objective is represented as a difference of two generally nonconvex functions. We propose and develop a novel Newton-type algorithm to solving such problems, which is based on the coderivative generated second-order subdifferential (generalized Hessian) and employs advanced tools of variational analysis. Well-posedness properties of the proposed algorithm are derived under fairly general requirements, while constructive convergence rates are established by using additional assumptions including the Kurdyka--{\L}ojasiewicz condition. We provide applications of the main algorithm to solving a general class of nonsmooth nonconvex problems of structured optimization that encompasses, in particular, optimization problems with explicit constraints. Finally, applications and numerical experiments are given for solving practical problems that arise in biochemical models, constrained quadratic programming, etc., where advantages of our algorithms are demonstrated in comparison with some known techniques and results., Comment: 38 pages

We generalise the notion of translating solitons in Generalised Robertson-Walker sapcetimes, which come equipped with a natural conformal Killing time-like vector field. We single out three one-parameter families of warping functions for which these objects exist, and we fully classify the corresponding Grim Reapers -- translation-invariant solitons -- for a large family of Riemannian fibres., Comment: 24 pages

A standardized method for measuring thermophotovoltaic (TPV) efficiency has not been yet established, which makes the reported results difficult to compare. Besides, most of the TPV efficiencies reported to date have been obtained using small view factors, i.e., large cell-to-emitter distances, so the impact of the series resistance is usually underestimated, and the optical cavity effects, i.e., the multiple reflections taking place between the emitter and the cell, are not accounted for experimentally. In this work, we present an experimental setup able to measure the TPV efficiency under high view factors (up to 0.98), by using small emitter-to-cell distances (< 1 mm). This allows a more accurate direct measurement of the TPV efficiency at higher power densities than previous works. As a result, a TPV efficiency of 26.4+-0.1 % and a power density of 4.3+-0.8 W/cm2 have been obtained for an InGaAs TPV cell with a back surface reflector irradiated by a graphite thermal emitter at 1592 C.

We present a code modularization approach to design efficient and massively parallel cubic and linear-scaling solvers for electronic structure calculations using atomic orbitals. The modular implementation of the orbital minimization method, in which linear algebra and parallelization issues are handled via external libraries, is demonstrated in the SIESTA code. The DBCSR and ScaLAPACK libraries are used for algebraic operations with sparse and dense matrices, respectively. The MatrixSwitch and libOMM libraries, recently developed within the Electronic Structure Library, facilitate switching between different matrix formats and implement the energy minimization. We show results comparing the performance of several cubic-scaling algorithms, and also demonstrate the parallel performance of the linear-scaling solvers, and their supremacy over the cubic-scaling solvers for insulating systems with sizes of several hundreds of atoms., Comment: 13 pages, 10 figures

FePS$_3$ is a prototype van der Waals layered antiferromagnet and a Mott insulator under ambient conditions, which has been recently reported to go through a pressure-induced dimensionality crossover and an insulator-to-metal transition. These transitions also lead to the appearance of a novel magnetic metallic state. To further understand these emergent structural and physical properties, we have performed a first-principles study using van der Waals and Hubbard $U$ corrected density functional theory including a random structure search. Our computational study attempts to interpret the experimental coexistence of the low- and intermediate-pressure phases and we predict a novel high-pressure phase with distinctive dimensionality and different possible origins of metallicity., Comment: Re-Submission to SciPost

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning., Comment: Revised version, May 03, 2024; corrected a typographical error concerning the formula for the projection onto $\mathbf{V}$ on line 11 of page 13

The phenomenological theory for the polar instability giving rise to a two-dimensional electron gas at perovskite interfaces is hereby extended to include the coupling to perovskite tilts. A Landau theory for homogeneous tilts is first explored, setting the scene for the further, more realistic Landau-Ginzburg theory describing varying tilt amplitudes across a thin film. The theory is also generalized to account for the response to an applied electric field normal to the interface, which allows a finer control on phase transitions. The conventionally described physics of a single metal-insulator transition is substantially enriched by the coupling, the model describing various scenarios with one or two transitions, possibly continuous or discontinuous. First-principles calculations permit the estimation of the parameters defining the model, which have been calculated for the interface between lanthanum aluminate and strontium titanate., Comment: Accepted version

The process by which a nuclear projectile is decelerated by the electrons of the condensed matter it traverses is currently being studied by following the explicit dynamics of projectile and electrons from first principles in a simulation box with a sample of the host matter in periodic boundary conditions. The approach has been quite successful for diverse systems even in the strong-coupling regime of maximal dissipation. This technique is here revisited for periodic solids in the light of the Floquet theory of stopping, a time-periodic scattering framework characterizing the stationary dynamicalsolutions for a constant velocity projectile in an infinite solid. The effect of proton projectiles in diamond is studied under that light, using time-dependent density-functional theory in real time. The Floquet quasi-energy conserving stationary scattering regime, characterized by time-periodic properties such as particle density and the time derivative of energy, is obtained for a converged system size of one thousand atoms. The validity of the customary calculation of electronic stopping power from the average slope of the density-functional total energy is discussed. Quasi-energy conservation, as well as the implied fundamental approximations, are critically reviewed., Comment: Version accepted in Phys. Rev. Research. 12 pages, 7 figures

In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators. Our main contribution is establishing the first primal-dual splitting algorithm for composite monotone inclusions with minimal lifting. Specifically, the proposed scheme reduces the dimension of the product space where the underlying fixed point operator is defined, in comparison to other algorithms, without requiring additional evaluations of the resolvent operators. We prove the convergence of this new algorithm and analyze its performance in a problem arising in image deblurring and denoising. This work also contributes to the theory of resolvent splitting algorithms by extending the minimal lifting theorem recently proved by Malitsky and Tam to schemes with resolvent parameters.