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This paper considers the problem of finding the nearest $\Omega$-stable pencil to a given square pencil $A+xB \in \mathbb{C}^{n \times n}$, where a pencil is called $\Omega$-stable if it is regular and all of its eigenvalues belong to the closed set $\Omega$. We propose a new method, based on the Schur form of a matrix pair and Riemannian optimization over the manifold $U(n) \times U(n)$, that is, the Cartesian product of the unitary group with itself. While the developed theory holds for any closed set $\Omega$, we focus on two cases that are the most common in applications: Hurwitz stability and Schur stability. For these cases, we develop publicly available efficient implementations. Numerical experiments show that the resulting algorithm outperforms existing methods.

Stack canaries and shadow stacks are widely deployed mitigations to memory-safety vulnerabilities. While stack canaries are introduced by the compiler and rely on sentry values placed between variables and control data, shadow stack implementations protect return addresses explicitly and rely on hardware features available in modern processor designs for efficiency. In this paper we hypothesize that stack canaries and shadow stacks provide similar levels of protections against sequential stack-based overflows. Based on the Juliet test suite, we evaluate whether 64-bit x86 (x86-64) systems benefit from enabling stack canaries in addition to the x86-64 shadow stack enforcement. We observe divergence in overflow detection rates between the GCC and Clang compilers and across optimization levels, which we attribute to differences in stack layouts generated by the compilers. We also find that x86-64 shadow stack implementations are more effective and outperform stack canaries when combined with a stack-protector-like stack layout. We implement and evaluate an enhancement to the Clang x86-64 shadow stack instrumentation that improves the shadow stack detection accuracy based on this observation.

Context. Cosmic dust is ubiquitous in astrophysical environments, where it significantly influences the chemistry and the spectra. Dust grains are likely to grow through the accretion of atoms and molecules from the gas-phase onto them. Despite their importance, only a few studies compute sticking coefficients for relevant temperatures and species, and their direct impact on grain growth. Overall, the formation of dust and its growth are processes not well understood. Aims. To calculate sticking coefficients, binding energies, and grain growth rates over a wide range of temperatures, for various gas species interacting with carbonaceous dust grains. Methods. We perform molecular dynamics simulations with a reactive force field algorithm to compute accurate sticking coefficients and obtain binding energies. The results are included in an astrophysical model of nucleation regions to study dust growth. Results. We present, for the first time, sticking coefficients of H, H2, C, O, and CO on amorphous carbon structures for temperatures ranging from 50 K to 2250 K. In addition, we estimate the binding energies of H, C, and O in carbonaceous dust to calculate the thermal desorption rates. Combining accretion and desorption allows us to determine an effective accretion rate and sublimation temperature for carbonaceous dust. Conclusions. We find that sticking coefficients can differ substantially from what is commonly used in astrophysical models and this gives new insight on carbonaceous dust grain growth via accretion in dust-forming regions., Comment: Accepted for publication in Astronomy & Astrophysics (A&A)

Maximizing the power conversion efficiency of solar cells plays a crucial role in upscaling solar energy production. Combining two or more solar cells with different bandgaps into a multi-junction tandem solar cells lowers thermalization losses and increases the power conversion efficiency. Whilst the best efficiencies have been achieved by vertically stacking solar cells, the fabrication process is technologically demanding and leads to high production costs. Novel photovoltaic materials such as organic photovoltaics allow solution processing, which enables the cost effective production of lateral multijunctions, where the single subcells are aligned side by side. To fully unlock their optimal performance, lateral tandems require careful light management, redirecting different spectral bands to the corresponding solar cell. So far, solar spectral splitters suffered from a strong angle dependency, which caused a degradation in performance at the slightest deviation from normal incidence. In this contribution, we reduce this limitation and achieve an enhancement in the conversion efficiency across a wide range of incident angles by inverse designing a solar spectral splitter comprised of two free-form microstructured surfaces on the top and bottom of a supporting glass substrate. Moreover, thanks to the versatility of our methodology, we can tailor the angle-dependent functionality of our device. As such, we also design devices that are optimized to provide enhanced performance at certain oblique angles, which correspond to different times of the day, e.g., when the unit price of energy is higher.

Brain tumors are the most common solid tumors in children and young adults, but the scarcity of large histopathology datasets has limited the application of computational pathology in this group. This study implements two weakly supervised multiple-instance learning (MIL) approaches on patch-features obtained from state-of-the-art histology-specific foundation models to classify pediatric brain tumors in hematoxylin and eosin whole slide images (WSIs) from a multi-center Swedish cohort. WSIs from 540 subjects (age 8.5$\pm$4.9 years) diagnosed with brain tumor were gathered from the six Swedish university hospitals. Instance (patch)-level features were obtained from WSIs using three pre-trained feature extractors: ResNet50, UNI and CONCH. Instances were aggregated using attention-based MIL (ABMIL) or clustering-constrained attention MIL (CLAM) for patient-level classification. Models were evaluated on three classification tasks based on the hierarchical classification of pediatric brain tumors: tumor category, family and type. Model generalization was assessed by training on data from two of the centers and testing on data from four other centers. Model interpretability was evaluated through attention-mapping. The highest classification performance was achieved using UNI features and AMBIL aggregation, with Matthew's correlation coefficient of 0.86$\pm$0.04, 0.63$\pm$0.04, and 0.53$\pm$0.05, for tumor category, family and type classification, respectively. When evaluating generalization, models utilizing UNI and CONCH features outperformed those using ResNet50. However, the drop in performance from the in-site to out-of-site testing was similar across feature extractors. These results show the potential of state-of-the-art computational pathology methods in diagnosing pediatric brain tumors at different hierarchical levels with fair generalizability on a multi-center national dataset.

Up to 10% of memory-safety vulnerabilities in languages like C and C++ stem from uninitialized variables. This work addresses the prevalence and lack of adequate software mitigations for uninitialized memory issues, proposing architectural protections in hardware. Capability-based addressing, such as the University of Cambridge's CHERI, mitigates many memory defects, including spatial and temporal safety violations at an architectural level. However, current CHERI designs do not handle undefined behavior from uninitialized variables. We extend the CHERI capability model to include "conditional capabilities", enabling memory-access policies based on prior operations. This allows enforcement of policies that satisfy memory safety objectives such as "no reads to memory without at least one prior write" (Write-before-Read). We present our architecture extension, compiler support, and a detailed evaluation of our approach using the QEMU full-system simulator and our modified FPGA-based CHERI-RISCV softcore. Our evaluation shows Write-before-Read conditional capabilities are practical, with high detection accuracy while adding a small (~3.5%) overhead to the existing CHERI architecture.

In optical imaging, achieving high resolution often comes at the expense of a shallow depth of field. This means that when using a standard microscope, any minor movement of the object along the optical axis can cause the image to become blurry. To address this issue, we exploit inverse design techniques to optimise a phase mask which, when inserted into a standard microscope, extends the depth of field by a factor of approximately four without compromising the microscope's resolution. Differentiable Fourier optics simulations allow us to rapidly iterate towards an optimised design in a hybrid fashion, starting with gradient-free Bayesian optimisation and proceeding to a local gradient-based optimisation. To fabricate the device, a commercial two-photon 3D laser nanoprinter is used, in combination with a two-step pre-compensation routine, providing high fabrication speed and much better than subwavelength accuracy. We find excellent agreement between our numerical predictions and the measurements upon integrating the phase mask into a microscope and optically characterising selected samples. The phase mask enables us to conduct simultaneous multiplane imaging of objects separated by distances that cannot be achieved with the original microscope.

Deep learning has been used extensively for medical image analysis applications, assuming the training and test data adhere to the same probability distributions. However, a common challenge arises when dealing with medical images generated by different systems or even the same system with varying parameter settings. Such images often contain diverse textures and noise patterns, violating the assumption. Consequently, models trained on data from one machine or setting usually struggle to perform effectively on data from another. To address this issue in ultrasound images, we proposed a Generative Adversarial Network (GAN) based model in this paper. We formulated image harmonization and denoising tasks as an image-to-image translation task, wherein we modified the texture pattern and reduced noise in Carotid ultrasound images while keeping the image content (the anatomy) unchanged. The performance was evaluated using feature distribution and pixel-space similarity metrics. In addition, blood-to-tissue contrast and influence on computed risk markers (Gray scale median, GSM) were evaluated. The results showed that domain adaptation was achieved in both tasks (histogram correlation 0.920 and 0.844), as compared to no adaptation (0.890 and 0.707), and that the anatomy of the images was retained (structure similarity index measure of the arterial wall 0.71 and 0.80). In addition, the image noise level (contrast) did not change in the image harmonization task (-34.1 vs 35.2 dB) but was improved in the noise reduction task (-23.5 vs -46.7 dB). The model outperformed the CycleGAN in both tasks. Finally, the risk marker GSM increased by 7.6 (p<0.001) in task 1 but not in task 2. We conclude that domain translation models are powerful tools for ultrasound image improvement while retaining the underlying anatomy but that downstream calculations of risk markers may be affected., Comment: 17 pages, 7 figures, 7 tables

We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems, of which the inner one can be solved either exactly or cheaply, while the outer one can be recast as an unconstrained optimization task over a smooth real Riemannian manifold. We observe that this paradigm applies to many matrix nearness problems of practical interest appearing in the literature, thus revealing that they are equivalent in this sense to a Riemannian optimization problem. We also show that the objective function to be minimized on the Riemannian manifold can be discontinuous, thus requiring regularization techniques, and we give conditions for this to happen. Finally, we demonstrate the practical applicability of our method by implementing it for a number of matrix nearness problems that are relevant for applications and are currently considered very demanding in practice. Extensive numerical experiments demonstrate that our method often greatly outperforms its predecessors, including algorithms specifically designed for those particular problems., Comment: 31 pages, 7 figures, 3 tables

Pathology is the study of microscopic inspection of tissue, and a pathology diagnosis is often the medical gold standard to diagnose disease. Pathology images provide a unique challenge for computer-vision-based analysis: a single pathology Whole Slide Image (WSI) is gigapixel-sized and often contains hundreds of thousands to millions of objects of interest across multiple resolutions. In this work, we propose PathoLogy Universal TransfOrmer (PLUTO): a light-weight pathology FM that is pre-trained on a diverse dataset of 195 million image tiles collected from multiple sites and extracts meaningful representations across multiple WSI scales that enable a large variety of downstream pathology tasks. In particular, we design task-specific adaptation heads that utilize PLUTO's output embeddings for tasks which span pathology scales ranging from subcellular to slide-scale, including instance segmentation, tile classification, and slide-level prediction. We compare PLUTO's performance to other state-of-the-art methods on a diverse set of external and internal benchmarks covering multiple biologically relevant tasks, tissue types, resolutions, stains, and scanners. We find that PLUTO matches or outperforms existing task-specific baselines and pathology-specific foundation models, some of which use orders-of-magnitude larger datasets and model sizes when compared to PLUTO. Our findings present a path towards a universal embedding to power pathology image analysis, and motivate further exploration around pathology foundation models in terms of data diversity, architectural improvements, sample efficiency, and practical deployability in real-world applications.

The control of thermal radiation by means of micro-structured materials is an active area of research with applications such as thermophotovoltaics and radiative cooling. The original theories of thermal radiation were derived for electromagnetically large objects, and predict unpolarized, omnidirectional, and uncorrelated radiation. Microstructures, however, exhibit thermal emissions that can be polarized, highly directional, and spatially and temporally correlated. The original theories are also restricted to thermal equilibrium situations and do not apply to steady-state emissions of electromagnetically small objects under a stationary illumination. In here, we establish a polychromatic framework to predict thermal radiation in the stationary regime, which includes thermal equilibrium. After identifying an object--adapted set of independent polychromatic absorption modes, we assume that the emission also occurs independently through the outgoing versions of each polychromatic mode. Energy conservation leads then to a Kirchhoff-like law for each polychromatic mode. The salient properties of the polychromatic theory are: Emission in frequencies that are absent in the illumination, change in the number of photons, and applicability to both thermal radiation and luminescence upon illumination with a continuous wave laser, as long as the emitted power depends linearly on the input intensity. These properties are independent of the chosen set of polychromatic modes. In this work, we chose the absorption modes derived from the scattering operator of a given object, and use the T-matrix formalism for computations, which applies to general objects, including microscopic ones. Some counter-intuitive results motivate the future search for a different set of modes.

In the last years, Infrared Reflection-Absorption Spectroscopy (IRRAS) became a standard technique to study vibrational excitations of molecules. These investigations are strongly motivated by perspective applications in monitoring chemical processes. For a better understanding of the adsorption mechanism of molecules on dielectrics, the polarization-dependence of an interaction of infrared light with adsorbates at dielectric surfaces is commonly used. Thus, the peak positions in absorption spectra could be different for s- and p-polarized light. This shift between the peak positions depends on both the molecule itself and the dielectric substrate. While the origin of this shift is well understood for infinite two-dimensional adsorbate layers, finite-size samples, which consist of 2D islands of a small number of molecules, have never been considered. Here, we present a study on polarization-dependent finite-size effects in the optical response of such islands on dielectric substrates. The study uses a multi-scale modeling approach that connects quantum chemistry calculations to Maxwell scattering simulations. We distinguish the optical response of a single molecule, a finite number of molecules, and a two-dimensional adsorbate layer. We analyze CO and CO$_2$ molecules deposited on CeO$_2$ and Al$_2$O$_3$ substrates. The evolution of the shift between the polarization-dependent absorbance peaks is firstly studied for a single molecule, which it does not exhibit for at all, and for finite molecular islands, which it increases with increasing island size for, as well as for an infinite two-dimensional adsorbate layer. In the latter case, the agreement between the obtained results and the experimental IRRAS data and more traditional three/four-layer-model theoretical studies supports the predictive power of the multi-scale approach.

The mass loss experienced on the asymptotic giant branch (AGB) at the end of the lives of low- and intermediate-mass stars is widely accepted to rely on radiation pressure acting on dust grains formed in the extended AGB atmospheres. The interaction of convection, stellar pulsation, and heating and cooling processes cause the density, velocity and temperature distributions in the inner regions of the envelope to be complex, making the dust-formation process difficult to calculate. Hence, characterising the extended atmospheres and inner outflow empirically is paramount to advance our understanding of the dust-formation and wind-driving processes. To this end, we observe the AGB star R Dor using ALMA and modelled the $^{12}$CO $v=0, J=2-1$, $v=1, J=2-1$ and $3-2$ and $^{13}$CO $v=0, J=3-2$ lines using the 3D radiative transfer code LIME up to a distance of $\sim 4$ times the radius of the star at sub-mm wavelengths. We find a complex velocity field with structure down to scales at least equal to the resolution of the observations. The observed maps are well reproduced assuming spherical symmetry for the gas temperature and density distributions. We find the radial profiles of these two quantities to be very steep close to the star and shallower for radii larger than $\sim 1.6$ times the stellar sub-mm radius. This change is consistent with the transition between extended atmosphere and outflow. We constrain the standard deviation of the stochastic velocity distribution in the large-scale outflow to be $\lesssim 0.4$ km/s. We observe two emission blobs in the CO $v=0, J=2-1$ line and find their gas densities and radial velocities to be substantially larger than those of the surrounding gas. Monitoring the evolution of these blobs will lead to a better understanding of the role of these structures in the mass-loss process of R Dor.

AGB stars are major contributors to the chemical enrichment of the ISM through nucleosynthesis and extensive mass loss. Most of our current knowledge of AGB atmospheric and circumstellar chemistry, in particular in a C-rich environment, is based on observations of the carbon star IRC+10216. We aim to obtain a more generalised understanding of the chemistry in C-rich AGB CSEs by studying a sample of three carbon stars, IRAS15194-5115, IRAS15082-4808, and IRAS07454-7112, and test the archetypal status often attributed to IRC+10216. We performed spatially resolved, unbiased spectral surveys in ALMA Band 3. We identify a total of 132 rotational transitions from 49 molecular species. There are two main morphologies of the brightness distributions: centrally-peaked (e.g. HCN) and shell-like (e.g. C$_2$H). We estimated the sizes of the molecular emitting regions using azimuthally-averaged radial profiles of the line brightness distributions, and derived abundance estimates. Of the shell distributions, the cyanopolyynes peak at slightly smaller radii than the hydrocarbons, and CN and HNC show the most extended emission. The emitting regions for each species are the smallest for IRAS07454-7112. We find that, within the uncertainties of the analysis, the three stars present similar abundances for most species, also compared to IRC+10216. We find that SiO is more abundant in our three stars compared to IRC+10216. Our estimated isotopic ratios match well the literature values for the sources. The observed circumstellar chemistry appears very similar across our sample and compared to that of IRC+10216, both in terms of the relative location of the emitting regions and molecular abundances. This implies that, to a first approximation, the chemical models tailored to IRC+10216 are able to reproduce the observed chemistry in C-rich envelopes across roughly an order of magnitude in wind density., Comment: 21 pages. 13 figures and 8 tables in the main text. 5 appendices contain additional figures and tables. Appendix tables are available in electronic form at the CDS, along with the reprocessed ALMA cubes and spectra, at http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/ or via anonymous ftp to cdsarc.u-strasbg.fr(130.79.128.5). Accepted for publication in Astronomy & Astrophysics

The study of temporal coherence in a Bose-Einstein condensate of photons can be challenging, especially in the presence of correlations between the photonic modes. In this work, we use a microscopic, multimode model of photonic condensation inside a dye-filled microcavity and the quantum regression theorem, to derive an analytical expression for the equation of motion of the photon-photon correlation function. This allows us to derive the coherence time of the photonic modes and identify a nonmonotonic dependence of the temporal coherence of the condensed light with the cutoff frequency of the microcavity., Comment: 12 pages, 5 figures

The temporal coherence of an ideal Bose gas increases as the system approaches the Bose-Einstein condensation threshold from below, with coherence time diverging at the critical point. However, counter-examples have been observed for condensates of photons formed in an externally pumped, dye-filled microcavity, wherein the coherence time decreases rapidly for increasing particle number above threshold. This paper establishes intermode correlations as the central explanation for the experimentally observed dramatic decrease in the coherence time beyond critical pump power., Comment: 5 pages, 4 figures

Spinel (MgAl$_{2}$O$_{4}$) and krotite (CaAl$_{2}$O$_{4}$) are alternative candidates to alumina (Al$_2$O$_3$) as primary dust condensates in the atmospheres of oxygen-rich evolved stars. Moreover, spinel was proposed as a potential carrier of the circumstellar 13 $\mu$m feature. However, the formation of nucleating spinel clusters is challenging; in particular, the inclusion of Mg constitutes a kinetic bottleneck. We aim to understand the initial steps of cosmic dust formation (i.e. nucleation) in oxygen-rich environments using a quantum-chemical bottom-up approach. Starting with an elemental gas-phase composition, we constructed a detailed chemical-kinetic network that describes the formation and destruction of magnesium-, calcium-, and aluminium-bearing molecules as well as the smallest dust-forming (MgAl$_{2}$O$_{4}$)$_1$ and (CaAl$_{2}$O$_{4}$)$_1$ monomer clusters. Different formation scenarios with exothermic pathways were explored, including the alumina (Al$_2$O$_3$) cluster chemistry studied in Paper I of this series. The resulting extensive network was applied to two model stars, a semi-regular variable and a Mira-type star, and to different circumstellar gas trajectories, including a non-pulsating outflow and a pulsating model. We employed global optimisation techniques to find the most favourable (MgAl$_2$O$_4$)$_n$, (CaAl$_2$O$_4$)$_n$, and mixed (Mg$_x$Ca$_{(1-x)}$Al$_2$O$_4$)$_n$ isomers, with $n$=1$-$7 and x$\in$[0..1], and we used high level quantum-chemical methods to determine their potential energies. The growth of larger clusters with $n$=2$-$7 is described by the temperature-dependent Gibbs free energies.In the considered stellar outflow models, spinel clusters do not form in significant amounts. However, we find that in the Mira-type non-pulsating model CaAl$_2$O$_3$(OH)$_2$, a hydroxylated form of the calcium aluminate krotite monomer forms ..., Comment: 20 pages, 25 figures, accepted for publication in A&A

Nanophotonic concepts can improve many measurement techniques by enhancing and tailoring the light-matter interaction. However, the optical response of devices that implement such techniques can be intricate, depending on the sample under investigation. That combination of a promise and a challenge makes nanophotonics a ripe field for applying the concept of a digital twin: a digital representation of an entire real-world device. In this work, we detail the concept of a digital twin with the example of a nanophotonically-enhanced chiral sensing platform. In that platform, helicity-preserving cavities with diffractive mirrors enhance the light-matter interaction between chiral molecules and circularly polarized light, allowing a faster measurement of the circular dichroism of the molecules. However, the sheer presence of the molecules affects the cavity's functionality, demanding a holistic treatment to understand the device's performance. In our digital twin, optical and quantum chemistry simulations are fused to provide a comprehensive description of the device with the molecules across all length scales and predict the circular dichroism spectrum of the device containing molecules to be sensed. Performing simulations in lockstep with the experiment will allow a clear interpretation of the results of complex measurements. We also demonstrate how to design a cavity-enhanced circular dichroism spectrometer by utilizing our digital twin. The digital twin can be used to guide experiments and analyze results, and its underlying concept can be translated to many other optical experiments., Comment: 17 pages, 6 figures

Given a square pencil $A+ \lambda B$, where $A$ and $B$ are $n\times n$ complex (resp. real) matrices, we consider the problem of finding the singular complex (resp. real) pencil nearest to it in the Frobenius distance. This problem is known to be very difficult, and the few algorithms available in the literature can only deal efficiently with pencils of very small size. We show that the problem is equivalent to minimizing a certain objective function $f$ over the Riemannian manifold $SU(n) \times SU(n)$ (resp. $SO(n) \times SO(n)$ if the nearest real singular pencil is sought), where $SU(n)$ denotes the special unitary group (resp. $SO(n)$ denotes the special orthogonal group). This novel perspective is based on the generalized Schur form of pencils, and yields competitive numerical methods, by pairing it with { algorithms} capable of doing optimization on { Riemannian manifolds. We propose one algorithm that directly minimizes the (almost everywhere, but not everywhere, differentiable) function $f$, as well as a smoothed alternative and a third algorithm that is smooth and can also solve the problem} of finding a nearest singular pencil with a specified minimal index. We provide numerical experiments that show that the resulting methods allow us to deal with pencils of much larger size than alternative techniques, yielding candidate minimizers of comparable or better quality. In the course of our analysis, we also obtain a number of new theoretical results related to the generalized Schur form of a (regular or singular) square pencil and to the minimal index of a singular square pencil whose nullity is $1$.

In this paper, we study a generalization of the notion of AS-regularity for connected $\mathbb{Z}$-algebras. Our main result is a characterization of those categories equivalent to noncommutative projective schemes associated to right coherent regular $\mathbb{Z}$-algebras, which we call quantum projective $\mathbb{Z}$-spaces in this paper. As an application, we show that smooth quadric hypersurfaces and the standard noncommutative smooth quadric surfaces have right noetherian AS-regular $\mathbb{Z}$-algebras as homogeneous coordinate algebras. In particular, the latter are thus noncommutative $\mathbb{P}^1\times \mathbb{P}^1$.