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The Majorana tetron is a prototypical topological qubit stemming from the ground state degeneracy of a superconducting island hosting four Majorana modes. This degeneracy manifests as an effective non-local spin degree of freedom, whose most paradigmatic signature is the topological Kondo effect. Degeneracies of states with different fermionic parities characterize also minimal Kitaev chains which have lately emerged as a platform to realize and study unprotected versions of Majorana modes, dubbed poor man's Majorana modes. Here, we introduce the ``poor man's Majorana tetron'', comprising four quantum dots coupled via a floating superconducting island. Its charging energy yields non-trivial correlations among the dots, although, unlike a standard tetron, it is not directly determined by the fermionic parity of the Majorana modes. The poor man's tetron displays parameter regions with a two-fold degenerate ground state with odd fermionic parity, that gives rise to an effective Anderson impurity model when coupled to external leads. We show that this system can approach a regime featuring the topological Kondo effect under a suitable tuning of experimental parameters. Therefore, the poor man's tetron is a promising device to observe the non-locality of Majorana modes and their related fractional conductance., Comment: 28 pages, 9 figures

By the end of 2023, renewable sources cover 63.4% of the total electric power demand of Chile, and in line with the global trend, photovoltaic (PV) power shows the most dynamic increase. Although Chile's Atacama Desert is considered the sunniest place on Earth, PV power production, even in this area, can be highly volatile. Successful integration of PV energy into the country's power grid requires accurate short-term PV power forecasts, which can be obtained from predictions of solar irradiance and related weather quantities. Nowadays, in weather forecasting, the state-of-the-art approach is the use of ensemble forecasts based on multiple runs of numerical weather prediction models. However, ensemble forecasts still tend to be uncalibrated or biased, thus requiring some form of post-processing. The present work investigates probabilistic forecasts of solar irradiance for Regions III and IV in Chile. For this reason, 8-member short-term ensemble forecasts of solar irradiance for calendar year 2021 are generated using the Weather Research and Forecasting (WRF) model, which are then calibrated using the benchmark ensemble model output statistics (EMOS) method based on a censored Gaussian law, and its machine learning-based distributional regression network (DRN) counterpart. Furthermore, we also propose a neural network-based post-processing method resulting in improved 8-member ensemble predictions. All forecasts are evaluated against station observations for 30 locations, and the skill of post-processed predictions is compared to the raw WRF ensemble. Our case study confirms that all studied post-processing methods substantially improve both the calibration of probabilistic- and the accuracy of point forecasts. Among the methods tested, the corrected ensemble exhibits the best overall performance. Additionally, the DRN model generally outperforms the corresponding EMOS approach., Comment: 25 pages; 9 figures; 4 tables

Majorana modes can be engineered in arrays where quantum dots (QDs) are coupled via grounded superconductors, effectively realizing an artificial Kitaev chain. Minimal Kitaev chains, composed by two QDs, can host fully-localized Majorana modes at discrete points in parameter space, known as Majorana sweet spots. Here, we extend previous works by theoretically investigating a setup with two QDs coupled via a floating superconducting island. We study the effects of the charging energy of the island and the properties of the resulting minimal Kitaev chain. We initially employ a minimal perturbative model, valid in the weak QD-island coupling regime, to derive analytic expressions for the Majorana sweet spots and the splitting of the ground state degeneracy as a function of tunable physical parameters. The conclusions from this perturbative approximation are then benchmarked using a microscopic model that explicitly describes the internal degrees of freedom of the island. Our work shows the existence of Majorana sweet spots, even when the island is not tuned at a charge-degeneracy point. In contrast to the Kitaev chains in grounded superconductors, these sweet spots involve a degeneracy between states with a well-defined number of particles., Comment: 13 pages, 9 figures

In this work, we perform a systematic computer simulation study of ice premelting, and explore the thickness and structure of quasi-liquid layers formed at the interface of ice with substrates of different hydrophilicity. Our study shows that interfacial premelting occurs on neutral substrates of whatever hydrophilicity, forming films of limited thickness for substrates with contact angles larger than ca. 50$^\circ$ but exhibiting complete interfacial premelting at smaller contact angles. Contrary to most experimental studies, we focus not only on the premelting behavior with temperature, but also with pressure, which is a matter of relevance in important situations such as ice friction. Our study is guided within a rigorous framework of surface thermodynamics, demonstrating that the premelting film structure is a function of a single thermodynamic variable. By this token we are able to relate properties measured along an isobar, with premelting films at arbitrary temperature and pressure. We also find that adhesion strength in atomically smooth surfaces is one to two orders of magnitude larger than those found in experiments, and conjecture that the reason is substrate roughness and the presence of organic adsorbents. Our theoretical framework also allows us to exploit our results on interfacial premelting in order to gain insight into heterogeneous ice nucleation. We show that apolar smooth substrates of whatever hydrophilicity are unlikely nucleators, and that too large hydrophilicity conspires also against ice nucleation. Furthermore, we exploit statistical-thermodynamic framework to shed light into the nature of the surface intermolecular forces promoting interfacial premelting, and provide a model to predict quasi-liquid layer thickness as a function of the substrate's hydrophilicity with great potential applications in fields ranging from earth sciences to aircraft engineering.

In the evolving landscape of deep learning, there is a pressing need for more comprehensive datasets capable of training models across multiple modalities. Concurrently, in digital humanities, there is a growing demand to leverage technology for diverse media adaptation and creation, yet limited by sparse datasets due to copyright and stylistic constraints. Addressing this gap, our paper presents a novel dataset comprising Franco-Belgian comics from the 1950s annotated for tasks including depth estimation, semantic segmentation, saliency detection, and character identification. It consists of two distinct and consistent styles and incorporates object concepts and labels taken from natural images. By including such diverse information across styles, this dataset not only holds promise for computational creativity but also offers avenues for the digitization of art and storytelling innovation. This dataset is a crucial component of the AI4VA Workshop Challenges~\url{https://sites.google.com/view/ai4vaeccv2024}, where we specifically explore depth and saliency. Dataset details at \url{https://github.com/IVRL/AI4VA}., Comment: ECCV 2024 Workshop Proceedings

We consider the contextual combinatorial bandit setting where in each round, the learning agent, e.g., a recommender system, selects a subset of "arms," e.g., products, and observes rewards for both the individual base arms, which are a function of known features (called "context"), and the super arm (the subset of arms), which is a function of the base arm rewards. The agent's goal is to simultaneously learn the unknown reward functions and choose the highest-reward arms. For example, the "reward" may represent a user's probability of clicking on one of the recommended products. Conventional bandit models, however, employ restrictive reward function models in order to obtain performance guarantees. We make use of deep neural networks to estimate and learn the unknown reward functions and propose Neural UCB Clustering (NeUClust), which adopts a clustering approach to select the super arm in every round by exploiting underlying structure in the context space. Unlike prior neural bandit works, NeUClust uses a neural network to estimate the super arm reward and select the super arm, thus eliminating the need for a known optimization oracle. We non-trivially extend prior neural combinatorial bandit works to prove that NeUClust achieves $\widetilde{O}\left(\widetilde{d}\sqrt{T}\right)$ regret, where $\widetilde{d}$ is the effective dimension of a neural tangent kernel matrix, $T$ the number of rounds. Experiments on real world recommendation datasets show that NeUClust achieves better regret and reward than other contextual combinatorial and neural bandit algorithms.

We consider random walks on $\mathbb{Z}^8$ indexed by the infinite invariant tree, which consists of an infinite spine and finite random trees attached to it on both sides. We establish the precise order of the non-intersection probability between one walk indexed by one side of the tree, and an independent one indexed by both sides of an independent tree. This is analogous to the result by Lawler from the '90s for two independent simple random walks on $\mathbb{Z}^4$. We also prove a weak law of large numbers for the branching capacity of the range of a branching random walk.

Feature selection is an essential process in machine learning, especially when dealing with high-dimensional datasets. It helps reduce the complexity of machine learning models, improve performance, mitigate overfitting, and decrease computation time. This paper presents a novel feature selection framework, shap-select. The framework conducts a linear or logistic regression of the target on the Shapley values of the features, on the validation set, and uses the signs and significance levels of the regression coefficients to implement an efficient heuristic for feature selection in tabular regression and classification tasks. We evaluate shap-select on the Kaggle credit card fraud dataset, demonstrating its effectiveness compared to established methods such as Recursive Feature Elimination (RFE), HISEL (a mutual information-based feature selection method), Boruta and a simpler Shapley value-based method. Our findings show that shap-select combines interpretability, computational efficiency, and performance, offering a robust solution for feature selection., Comment: 13 pages, 1 figure

In positron emission tomography acquisition (PET), sensitivity along a line of response can vary due to crystal geometrical arrangements in the scanner and/or detector inefficiencies, leading to severe artefacts in the reconstructed image. To mitigate these effects, data must be corrected by a set of normalization coefficients applied to each line of response. The J-PET Modular scanner is a PET device made of 50 cm long plastic strips arranged axially, currently in operation at the Jagiellonian University in Krak\'ow (Poland). We have implemented a normalization method for the large field-of-view plastic-based J-PET Modular scanner using the component-based approach. We estimated the geometric normalization factors for the J-PET Modular scanner using Monte Carlo simulations. We also analysed the effects of variations in detection efficiency. A dedicated cylindrical phantom was simulated to investigate the impact of various factors on image quality. The image quality was quantified in terms of radial and axial uniformity metrics, and the standard deviation to mean intensity ratio, determined for a set of image slices. Without normalization, reconstructions of a uniform cylinder exhibit artefacts. These artefacts were satisfactorily compensated using the normalization factors. Applying geometrical corrections lowers the non-uniformity of the image expressed as a standard deviation-to-mean ratio to a range between 5.5 % to 8.5 %. Computationally, the technique is straightforward to parallelize, making it time-efficient. Preliminary estimates suggest that the method is appropriate for use with long axial field-of-view scanners, such as the total-body J-PET, currently under development at the Jagiellonian University., Comment: 36 pages, 16 figures, 4 tables

Molecular arrangement in the chiral smectic phases of the glassforming (S)-4'-(1-methylheptylcarbonyl)biphenyl-4-yl 4-[7-(2,2,3,3,4,4,4-heptafluorobutoxy) heptyl-1-oxy]benzoate is investigated by X-ray diffraction. An increased correlation length of the positional short-range order in the supercooled state agrees with the previous assumption of the hexatic smectic phase. However, the registered X-ray diffraction patterns are not typical for the hexatic phases. Comparison of the smectic layer spacing and optical tilt angle indicates a strongly non-linear shape of molecules, which enables choice of the molecular models obtained by DFT calculations, used subsequently to interpret the infra-red spectra. The presumption of the hexatic smectic FA* or IA* phase is supported by the splitting of the absorption bands related to the C=O stretching in the supercooled state, which is absent in the smectic CA* phase above the melting temperature. The glass transition affects the temperature dependence of the smectic layer spacing but only subtly impacts the infra-red spectra. Application of the k-means cluster analysis enables distinction between the infra-red spectra below and above the glass transition temperature, but only for certain spectral ranges., Comment: 33 pages, 12 figures

Convolutional Neural Networks (CNNs) have made remarkable strides; however, they remain susceptible to vulnerabilities, particularly in the face of minor image perturbations that humans can easily recognize. This weakness, often termed as 'attacks', underscores the limited robustness of CNNs and the need for research into fortifying their resistance against such manipulations. This study introduces a novel Non-Uniform Illumination (NUI) attack technique, where images are subtly altered using varying NUI masks. Extensive experiments are conducted on widely-accepted datasets including CIFAR10, TinyImageNet, and CalTech256, focusing on image classification with 12 different NUI attack models. The resilience of VGG, ResNet, MobilenetV3-small and InceptionV3 models against NUI attacks are evaluated. Our results show a substantial decline in the CNN models' classification accuracy when subjected to NUI attacks, indicating their vulnerability under non-uniform illumination. To mitigate this, a defense strategy is proposed, including NUI-attacked images, generated through the new NUI transformation, into the training set. The results demonstrate a significant enhancement in CNN model performance when confronted with perturbed images affected by NUI attacks. This strategy seeks to bolster CNN models' resilience against NUI attacks.

We present the Python pipeline that was developed to simulate the high contrast mode images of the MICADO instrument. This mode will comprise three classical Lyot coronagraphs with different occulting spot sizes, one vector apodized phase plate, and two sparse aperture masks. One critical aspect of these modes lies in their sensitivity to aberrations, requiring careful integration of non common path aberrations, as well as turbulent adaptive optics (AO) residuals. Besides, they will be operated following a specific observing strategy based on pupil tracking mode. For these reasons, we have developed the MICADO SimulaTor for HIgh Contrast (MISTHIC) pipeline to simulate realistic image cubes and derive the expected performance of these modes. Several sources of aberrations can be included: turbulent AO residuals, but also static or rotating aberrations, amplitude aberrations, simple Zernike screens... Including MICADO's specific features, such as the absence of atmospheric dispersion prior to the coronagraphic focal plane mask, our intent is to make this pipeline available to the community. This tool can be used to prepare scientific observations with the high contrast mode of MICADO, by predicting the performance to be expected within the most realistic assumptions., Comment: 8 pages, 7 figures

How can Transformers model and learn enumerative geometry? What is a robust procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a new paradigm in computational enumerative geometry in analyzing the $\psi$-class intersection numbers on the moduli space of curves. By formulating the enumerative problem as a continuous optimization task, we develop a Transformer-based model for computing $\psi$-class intersection numbers based on the underlying quantum Airy structure. For a finite range of genera, our model is capable of regressing intersection numbers that span an extremely wide range of values, from $10^{-45}$ to $10^{45}$. To provide a proper inductive bias for capturing the recursive behavior of intersection numbers, we propose a new activation function, Dynamic Range Activator (DRA). Moreover, given the severe heteroscedasticity of $\psi$-class intersections and the required precision, we quantify the uncertainty of the predictions using Conformal Prediction with a dynamic sliding window that is aware of the number of marked points. Next, we go beyond merely computing intersection numbers and explore the enumerative "world-model" of the Transformers. Through a series of causal inference and correlational interpretability analyses, we demonstrate that Transformers are actually modeling Virasoro constraints in a purely data-driven manner. Additionally, we provide evidence for the comprehension of several values appearing in the large genus asymptotic of $\psi$-class intersection numbers through abductive hypothesis testing.

Stroke remains a leading cause of global morbidity and mortality, placing a heavy socioeconomic burden. Over the past decade, advances in endovascular reperfusion therapy and the use of CT and MRI imaging for treatment guidance have significantly improved patient outcomes and are now standard in clinical practice. To develop machine learning algorithms that can extract meaningful and reproducible models of brain function for both clinical and research purposes from stroke images - particularly for lesion identification, brain health quantification, and prognosis - large, diverse, and well-annotated public datasets are essential. While only a few datasets with (sub-)acute stroke data were previously available, several large, high-quality datasets have recently been made publicly accessible. However, these existing datasets include only MRI data. In contrast, our dataset is the first to offer comprehensive longitudinal stroke data, including acute CT imaging with angiography and perfusion, follow-up MRI at 2-9 days, as well as acute and longitudinal clinical data up to a three-month outcome. The dataset includes a training dataset of n = 150 and a test dataset of n = 100 scans. Training data is publicly available, while test data will be used exclusively for model validation. We are making this dataset available as part of the 2024 edition of the Ischemic Stroke Lesion Segmentation (ISLES) challenge (https://www.isles-challenge.org/), which continuously aims to establish benchmark methods for acute and sub-acute ischemic stroke lesion segmentation, aiding in creating open stroke imaging datasets and evaluating cutting-edge image processing algorithms.

We present a study of the scattering of a monochromatic helical laser beam, described by a Laguerre-Gauss solution of the Maxwell equations, on an electron sheet, initially at rest in the focal plane of the laser; the interaction is described in the framework of a local plane wave approximation. We calculate the scattered electromagnetic field observed in an arbitrary point at a large distance from the laser focal spot, by adding coherently the contributions of each electron in the electron sheet. Due to the interference effects, the radiation is emitted only into the forward direction, within a narrow cone, and it has a spatial structure that we analyze theoretically and numerically. For circularly polarized incident fields, the structure is also helical, with a helical index which depends on the helical index of the incident radiation and the harmonic order. These structures can be observed experimentally, as each harmonic order is emitted with a different frequency, and within cones of different opening angles. Our findings are in agreement with experimental results in the literature which demonstrate the generation of OAM carrying photons by radiation scattering on electrons.

The growing interest in human-grade total body positron emission tomography (PET) systems has also application in small animal research. Due to the existing limitations in human-based studies involving drug development and novel treatment monitoring, animal-based research became a necessary step for testing and protocol preparation. In this simulation-based study two unconventional, cost-effective small animal total body PET scanners (for mouse and rat studies) have been investigated in order to inspect their feasibility for preclinical research. They were designed with the novel technology explored by the Jagiellonian-PET (J-PET) Collaboration. Two main PET characteristics: sensitivity and spatial resolution were mainly inspected to evaluate their performance. Moreover, the impact of the scintillator dimension and time-of-flight on the latter parameter was examined in order to design the most efficient tomographs. The presented results show that for mouse TB J-PET the achievable system sensitivity is equal to 2.35% and volumetric spatial resolution to 9.46 +- 0.54 mm3, while for rat TB J-PET they are equal to 2.6% and 14.11 +- 0.80 mm3, respectively. Furthermore, it was shown that the designed tomographs are almost parallax-free systems, hence, they resolve the problem of the acceptance criterion tradeoff between enhancing spatial resolution and reducing sensitivity.

Due to their inherent capabilities of capturing non-local dependencies, Transformer neural networks have quickly been established as the paradigmatic architecture for large language models and image processing. Next to these traditional applications, machine learning methods have also been demonstrated to be versatile tools in the analysis of image-like data of quantum phases of matter, e.g. given snapshots of many-body wave functions obtained in ultracold atom experiments. While local correlation structures in image-like data of physical systems can reliably be detected, identifying phases of matter characterized by global, non-local structures with interpretable machine learning methods remains a challenge. Here, we introduce the correlator Transformer (CoTra), which classifies different phases of matter while at the same time yielding full interpretability in terms of physical correlation functions. The network's underlying structure is a tailored attention mechanism, which learns efficient ways to weigh local and non-local correlations for a successful classification. We demonstrate the versatility of the CoTra by detecting local order in the Heisenberg antiferromagnet, and show that local gauge constraints in one- and two-dimensional lattice gauge theories can be identified. Furthermore, we establish that the CoTra reliably detects non-local structures in images of correlated fermions in momentum space (Cooper pairs) and that it can distinguish percolating from non-percolating images.

Plastic scintillator strips are considered as one of the promising solutions for the cost-effective construction of total-body positron emission tomography, (PET) system. The purpose of the performed measurements is to compare the transparency of long plastic scintillators with dimensions 6 mm x 24 mm x 1000 mm and with all surfaces polished. Six different types of commercial, general purpose, blue-emitting plastic scintillators with low attenuation of visible light were tested, namely: polyvinyl toluene-based BC-408, EJ-200, RP-408, and polystyrene-based Epic, SP32 and UPS-923A. For determination of the best type of plastic scintillator for totalbody Jagiellonian positron emission tomograph (TB-J-PET) construction, emission and transmission spectra, and technical attenuation length (TAL) of blue light-emitting by the scintillators were measured and compared. The TAL values were determined with the use of UV lamp as excitation source, and photodiode as light detector. Emission spectra of investigated scintillators have maxima in the range from 420 nm to 429 nm. The BC-408 and EJ-200 have the highest transmittance values of about 90% at the maximum emission wavelength measured through a 6 mm thick scintillator strip and the highest technical attenuation length reaching about 2000 mm, allowing assembly of long detection modules for time-of-flight (TOF) J-PET scanners. Influence of the 6 mm x 6 mm, 12 mm x 6 mm, 24 mm x 6 mm cross-sections of the 1000 mm long EJ-200 plastic scintillator on the TAL and signal intensity was measured. The highest TAL value was determined for samples with 24 mm x 6 mm cross-section., Comment: 10 pages, 5 figures

Despite progress towards achieving low error rates with superconducting qubits, error-prone two-qubit gates remain a bottleneck for realizing large-scale quantum computers. Therefore, a systematic framework to design high-fidelity gates becomes imperative. One type of two-qubit gate in superconducting qubits is the controlled-phase (CPHASE) gate, which utilizes a conditional interaction between higher energy levels of the qubits controlled by a baseband flux pulse on one of the qubits or a tunable coupler. In this work, we study an adiabatic implementation of CPHASE gates and formulate the design of the control trajectory for the gate as a pulse-design problem. We show in simulation that the Chebyshev-based trajectory can, in certain cases, enable gates with leakage error lower by an average of roughly 6% when compared to the widely used Slepian-based trajectory.

A widely accepted phenomenological rule states that solids with free surfaces cannot be overheated. In this work we discuss this statement critically under the light of the statistical thermodynamics of interfacial roughening transitions. Our results show that the basal face of ice as described by the TIP4P/Ice model can remain mechanically stable for more than one hundred nanoseconds when overheated by 1 K, and for several hundreds of nanoseconds at smaller overheating despite the presence of a significant quasi-liquid layer at the surface. Such time scales, which are often of little experimental significance, can become a concern for the determination of melting points by computer simulations using the direct coexistence method. In the light of this observation, we reinterpret computer simulations of ice premelting and show that current results for the TIP4P/Ice model all imply a scenario of incomplete surface melting. Using a thermodynamic integration path, we reassess our own estimates for the Laplace pressure difference between water and vapor. These calculations are used to measure the disjoining pressure of premelting liquid films and allow us to confirm a minimum of the interfacial free energy at finite premelting thickness of about one nanometer., Comment: Manuscript as version of record except for minor edits

In our contemporary era, meteorological weather forecasts increasingly incorporate ensemble predictions of visibility - a parameter of great importance in aviation, maritime navigation, and air quality assessment, with direct implications for public health. However, this weather variable falls short of the predictive accuracy achieved for other quantities issued by meteorological centers. Therefore, statistical post-processing is recommended to enhance the reliability and accuracy of predictions. By estimating the predictive distributions of the variables with the aid of historical observations and forecasts, one can achieve statistical consistency between true observations and ensemble predictions. Visibility observations, following the recommendation of the World Meteorological Organization, are typically reported in discrete values; hence, the predictive distribution of the weather quantity takes the form of a discrete parametric law. Recent studies demonstrated that the application of classification algorithms can successfully improve the skill of such discrete forecasts; however, a frequently emerging issue is that certain spatial and/or temporal dependencies could be lost between marginals. Based on visibility ensemble forecasts of the European Centre for Medium-Range Weather Forecasts for 30 locations in Central Europe, we investigate whether the inclusion of Copernicus Atmosphere Monitoring Service (CAMS) predictions of the same weather quantity as an additional covariate could enhance the skill of the post-processing methods and whether it contributes to the successful integration of spatial dependence between marginals. Our study confirms that post-processed forecasts are substantially superior to raw and climatological predictions, and the utilization of CAMS forecasts provides a further significant enhancement both in the univariate and multivariate setup., Comment: 23 pages, 10 figures

Hydrogen is a promising energy carrier for replacing fossil fuels, and hydrogen production via hydrogen evolution reaction (HER) is an environmentally friendly option if electrocatalysts with low overpotentials and long-term stability are used. In this work, the electrocatalytic performance of $\mathrm{Pt_{57.5}Cu_{14.7}Ni_{5.3}P_{22.5}}$ bulk metallic glass (BMG) with flat, micro-patterned, and nano-patterned surfaces for HER in 0.5 M H2SO4 is studied. The nano-patterned Pt-BMG demonstrates outstanding long-term stability and self-improving behavior with a final overpotential of 150 mV and a Tafel slope of 42 $\mathrm{mV dec^{-1}}$ after 1000 linear sweep voltammetry (LSV) cycles, which is respectively 42% and 37% lower than in the first LSV cycle. X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) indicate the formation of a layer of CuO/Cu2O foam deposited on top of the nano-patterned surface during the stability test of 1000 LSV cycles. A three-step process is proposed to explain the formation of CuxO foam via dynamic hydrogen bubble templating (DHBT) electrodeposition from Cu dissolution of the Pt-BMG without using copper salt. This work provides a method to create CuxO foams that could be used for various applications. Moreover, nano-patterned BMGs with DHBT deposition offer a feasible strategy to synthesize metal or metal-oxide foams., Comment: 28 pages, 9 figures (including supplementary information)

This article investigates the exceptional set of the boundary for the following problem: \begin{equation*} \begin{aligned} -\frac{\partial u}{\partial t} + \mathcal{M}_{\lambda,\Lambda}^+(D^2u) + b(x,t)\cdot Du + c(x,t)u =0 \quad \rm{in} ~ \Omega_{T}, \end{aligned} \end{equation*} We provide a sufficient condition on the exceptional set in terms of the bound of the Hausdorff measure of this boundary portion. This condition ensures that even if the boundary values are not nonnegative on this portion, the supersolution remains nonnegative.

Multivariate probabilistic verification is concerned with the evaluation of joint probability distributions of vector quantities such as a weather variable at multiple locations or a wind vector for instance. The logarithmic score is a proper score that is useful in this context. In order to apply this score to ensemble forecasts, a choice for the density is required. Here, we are interested in the specific case when the density is multivariate normal with mean and covariance given by the ensemble mean and ensemble covariance, respectively. Under the assumptions of multivariate normality and exchangeability of the ensemble members, a relationship is derived which describes how the logarithmic score depends on ensemble size. It permits to estimate the score in the limit of infinite ensemble size from a small ensemble and thus produces a fair logarithmic score for multivariate ensemble forecasts under the assumption of normality. This generalises a study from 2018 which derived the ensemble size adjustment of the logarithmic score in the univariate case. An application to medium-range forecasts examines the usefulness of the ensemble size adjustments when multivariate normality is only an approximation. Predictions of vectors consisting of several different combinations of upper air variables are considered. Logarithmic scores are calculated for these vectors using ECMWF's daily extended-range forecasts which consist of a 100-member ensemble. The probabilistic forecasts of these vectors are verified against operational ECMWF analyses in the Northern mid-latitudes in autumn 2023. Scores are computed for ensemble sizes from 8 to 100. The fair logarithmic scores of ensembles with different cardinalities are very close, in contrast to the unadjusted scores which decrease considerably with ensemble size. This provides evidence for the practical usefulness of the derived relationships., Comment: 24 pages; 7 figures; 4 tables

Output thresholding is the technique to search for the best threshold to be used during inference for any classifiers that can produce probability estimates on train and testing datasets. It is particularly useful in high imbalance classification problems where the default threshold is not able to refer to imbalance in class distributions and fail to give the best performance. This paper proposes OTLP, a thresholding framework using mixed integer linear programming which is model agnostic, can support different objective functions and different set of constraints for a diverse set of problems including both balanced and imbalanced classification problems. It is particularly useful in real world applications where the theoretical thresholding techniques are not able to address to product related requirements and complexity of the applications which utilize machine learning models. Through the use of Credit Card Fraud Detection Dataset, we evaluate the usefulness of the framework., Comment: 15 pages, 8 figures

Achieving the formation of target open crystalline lattices from colloidal particles is of paramount importance for their potential application in photonics. Examples of such desired structures are the diamond, tetrastack, and pyrochlore lattices. Here, we demonstrate that the self-assembly of tetravalent patchy particles results in the selective formation of cubic tetrastack crystals, both in the bulk and in the systems subjected to external fields exerted by the solid substrate. It is demonstrated that the presence of an external field allows for the formation of well-defined single crystals with a low density of defects. Moreover, depending on the strength of the applied external field, the mechanism of epitaxial growth changes. For weakly attractive external fields, the crystallization occurs in a similar manner as in the bulk, since the fluid does not wet the substrate. Nonetheless, the formed crystal is considerably better ordered than the crystals formed in bulk, since the surface induces the ordering in the first layer. On the other hand, it is demonstrated that the formation of well-ordered cubic tetrastack crystals is considerably enhanced by the increase in external field strength, and the formation of the thick crystalline film occurs via a series of layering transitions.

In this article we consider the following boundary value problem \begin{equation*}\label{abs} \left\{ \begin{aligned} F(x,u,Du,D^{2}u)+c(x)u+ p(x)u^{-\alpha}&=0~\text{in}~\Omega\\ u&=0~~\text{on}~~\partial\Omega, \end{aligned} \right. \end{equation*} where $\Omega$ is a bounded and $C^{2}$ smooth domain in $\mathbb{R}^N$ and $F$ has superlinear growth in gradient and $c(c)<-c_{0}$ for some positive constant $c_{0}.$ Here, we studies the boundary behaviour of the solutions to above equation and establishes the global regularity result similar to one established in [12,16] with linear growth in gradient.

We present the list of variable stars we found in the \kep\ superstamp data covering approximately nine arcminutes from the central region of NGC6819. This is a continuation of our work presented by Sanjayan et al.(2022a). We classified the variable stars based on the variability type and we established their cluster membership based on the available Gaia Data Release 3 astrometry. Our search revealed 385 variable stars but only 128 were found to be cluster members. In the case of eclipsing and contact binaries we calculated the mid-times of eclipses and derived ephemerides. We searched for eclipse timing variation using the observed minus calculated diagrams. Only five objects show significant orbital period variation. We used isochrones calculated within the MESA Isochrones and Stellar Tracks project and derived the average age (2.54 Gyr), average distance (2.3 kpc) and iron content [Fe/H] = -0.01(2), of NGC6819. We confirm this distance by the one derived from Gaia astrometry of the cluster members with membership probabilities greater than 0.9.

In this paper, we prove a theorem concerning the existence of three solutions for the following boundary value problem: \begin{equation*} -\mathcal{M}_{\lambda,\Lambda}^+(D^2u)-\Gamma|Du|^2=f(u)~~~\text{in}\ \Omega, u=0~~~\text{on}\ \partial\Omega, \end{equation*} where $f:[0,\infty]\to[0,\infty]$ is a $C^{\alpha}$ function and $\Omega$ denotes a bounded, smooth domain in $\mathbb{R}^N$. By constructing two ordered pairs of sub and supersolutions for a specific class of $f$ exhibiting sublinear growth, we further establish the existence of three positive solutions to the aforementioned boundary value problem.

Remote direct memory access (RDMA) networks are being rapidly adopted into industry for their high speed, low latency, and reduced CPU overheads compared to traditional kernel-based TCP/IP networks. RDMA enables threads to access remote memory without interacting with another process. However, atomicity between local accesses and remote accesses is not guaranteed by the technology, hence complicating synchronization significantly. The current solution is to require threads wanting to access local memory in an RDMA-accessible region to pass through the RDMA card using a mechanism known as loopback, but this can quickly degrade performance. In this paper, we introduce ALock, a novel locking primitive designed for RDMA-based systems. ALock allows programmers to synchronize local and remote accesses without using loopback or remote procedure calls (RPCs). We draw inspiration from the classic Peterson's algorithm to create a hierarchical design that includes embedded MCS locks for two cohorts, remote and local. To evaluate the ALock we implement a distributed lock table, measuring throughput and latency in various cluster configurations and workloads. In workloads with a majority of local operations, the ALock outperforms competitors up to 29x and achieves a latency up to 20x faster., Comment: 13 pages, 6 figures, SPAA '24

We theoretically explore the possibility of realizing the symmetry-protected topological Haldane phase of spin-1 chains in a tunable hybrid platform of superconducting islands (SIs) and quantum dots (QDs). Inspired by recent findings suggesting that an appropriately tuned QD-SI-QD block may behave as a robust spin-1 unit, we study the behavior of many such units tunnel-coupled into linear chains. Our efficient and fully microscopic modeling of long chains with several tens of units is enabled by the use of the surrogate model solver [Phys. Rev. B 108, L220506 (2023); arXiv:2402.18357]. Our numerical findings indicate that the QD-SI-QD chains exhibit emblematic features of the Haldane phase, such as fractional spin-1/2 edge states and non-vanishing string order parameters, and that these persist over a sizeable region of parameter space., Comment: 12 pages, 11 figures

Preceding a core-collapse supernova, various processes produce an increasing amount of neutrinos of all flavors characterized by mounting energies from the interior of massive stars. Among them, the electron antineutrinos are potentially detectable by terrestrial neutrino experiments such as KamLAND and Super-Kamiokande via inverse beta decay interactions. Once these pre-supernova neutrinos are observed, an early warning of the upcoming core-collapse supernova can be provided. In light of this, KamLAND and Super-Kamiokande, both located in the Kamioka mine in Japan, have been monitoring pre-supernova neutrinos since 2015 and 2021, respectively. Recently, we performed a joint study between KamLAND and Super-Kamiokande on pre-supernova neutrino detection. A pre-supernova alert system combining the KamLAND detector and the Super-Kamiokande detector was developed and put into operation, which can provide a supernova alert to the astrophysics community. Fully leveraging the complementary properties of these two detectors, the combined alert is expected to resolve a pre-supernova neutrino signal from a 15 M$_{\odot}$ star within 510 pc of the Earth, at a significance level corresponding to a false alarm rate of no more than 1 per century. For a Betelgeuse-like model with optimistic parameters, it can provide early warnings up to 12 hours in advance., Comment: Resubmitted to ApJ. 22 pages, 16 figures, for more information about the combined pre-supernova alert system, see https://www.lowbg.org/presnalarm/

High-speed interconnects, such as NVLink, are integral to modern multi-GPU systems, acting as a vital link between CPUs and GPUs. This study highlights the vulnerability of multi-GPU systems to covert and side channel attacks due to congestion on interconnects. An adversary can infer private information about a victim's activities by monitoring NVLink congestion without needing special permissions. Leveraging this insight, we develop a covert channel attack across two GPUs with a bandwidth of 45.5 kbps and a low error rate, and introduce a side channel attack enabling attackers to fingerprint applications through the shared NVLink interconnect., Comment: Accepted to SEED 2024

Recently, the rings whose injective right modules are R-projective (respectively, max-projective) were investigated and studied in [2]. Such ring are called right almost-QF (respectively, max-QF). In this paper, our aim is to give some further characterization of these rings over more general classes of rings, and address several questions about these rings. We obtain characterizations of max-QF rings over several classes of rings including local, semilocal right semihereditary, right nonsingular right noetherian and right nonsingular right finite dimensional rings. We prove that for a ring R being right almost-QF and right max-QF are not left-right symmetric. We also show that right almost-QF and right max-QF rings are not closed under factor rings. This leads to consider the rings all of whose factor rings are almost-QF and max-QF.

Strongly correlated electron systems with a kagome lattice can host abundant exotic quantum states such as superconductivity and spin/charge density waves (CDW) due to the complicated interactions between different degrees of freedoms in the framework of a unique two-dimensional geometrically frustrated lattice structure. Recently, successive orders of A-type antiferromagnetism (AFM), $2\times2\times2$ CDW and canted double-cone AFM have been manifested upon cooling in magnetic kagome FeGe. However, the mechanism of the CDW order and its interaction with magnetism are presently enigmatic at best. Here we investigate the evolution of CDW order with temperature across the spin canting transition in FeGe by single-crystal x-ray diffraction. Refinements of its modulated structure are presented using the superspace approach. Interestingly, the superlattice reflections originating from CDW-induced long-range structural modulation become extremely weak after the system enters the canted AFM while a $2\times2$ CDW in the $ab$ plane persists as a long-range order demonstrated by strong electronic modulation in the d$I$/d$V$ map of scanning tunneling spectroscopy. We discovered a novel CDW order without long-range structural modulation in FeGe probably because of the competition between CDW and canted AFM in determining the underlying crystal structure. In addition, occupational modulations of Ge1 atoms located in the kagome plane and displacive modulations of all the atoms were extracted from the refinements, confirming the existence of Ge atom dimerization along the $c$ axis as the major distortion and indicating a dynamic transformation between different CDW domains., Comment: 22 pages, 6 figures. Comments on the manuscript are welcome