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Run-by-run variability in parallel programs caused by floating-point non-associativity (FPNA) has been known to significantly affect reproducibility in iterative algorithms, due to accumulating errors. Non-reproducibility negatively affects efficiency and effectiveness of correctness testing for stochastic programs. Recently, the sensitivity of deep learning (DL) training and inference pipelines to FPNA have been found to be extreme, and can prevent certification for commercial applications, accurate assessment of robustness and sensitivity, and bug detection. New approaches in scientific computing applications have coupled DL models with high-performance computing (HPC) simulations, leading to an aggravation of debugging and testing challenges. Here we perform an investigation of the statistical properties of FPNA within modern parallel programming models, analyze performance and productivity impacts of replacing atomic operations with deterministic alternatives on GPUs, and examine the recently-added deterministic options within the PyTorch framework within the context of GPU deployment, uncovering and quantifying the impacts of input parameters triggering run-by-run variability and reporting on the reliability and completeness of the documentation. Finally, we evaluate the strategy of exploiting automatic determinism provided by deterministic hardware, using the Groq LPU$^{TM}$ accelerator for inference portions of the DL pipeline. We demonstrate the benefits that this strategy can provide within reproducibility and correctness efforts.

We introduce a non-Markovian rumor model in the complete graph on $n$ vertices inspired by Daley and Kendall's model. For this model, we prove a functional law of large numbers (FLLN) and a functional central limit theorem (FCLT). We apply these results to a non-Markovian version of the rumor model introduced by Lebensztayn, Machado and Rodr\'{i}guez.

Nickel nanoparticles (Ni NPs), thanks to their peculiar properties, are interesting materials for many applications including catalysis, hydrogen storage, and sensors. In this work, Ni NPs are synthesized in aqueous solution by a simple and rapid procedure with cetyltrimethylammonium bromide (CTAB) as a capping agent, and are extensively characterized by dynamic light scattering (DLS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). We investigated their shape, dimension, and their distribution on the surfaces of SiO2 and epitaxial graphene (EG) samples. Ni NPs have an average diameter of ~11 nm, with a narrow size dispersion, and their arrangement on the surface is strongly dependent on the substrate. EG samples functionalized with Ni NPs are further characterized by X-ray photoelectron spectroscopy (XPS), as made and after thermal annealing above 350{\deg}C to confirm the degradation of CTAB and the presence of metallic Ni(0). Moreover, high resolution scanning tunneling microscopy (STM) topographies reveal the structural stability of the NPs up to 550 {\deg}C.

We investigate the turbulence below a quasi-flat free surface, focusing on the energy transport in space and across scales. We leverage a large zero-mean-flow tank where homogeneous turbulence is generated by randomly actuated jets. A wide range of Reynolds number is spanned, reaching sufficient scale separation for the emergence of an inertial sub-range. Unlike previous studies, the forcing extends through the source layer, though the surface deformation remains millimetric. Particle image velocimetry along a surface-normal plane resolves from the dissipative to the integral scales. Both vertical and horizontal components of the turbulent kinetic energy approach the prediction based on rapid distortion theory as the Reynolds number is increased, indicating that discrepancies among previous studies are likely due to differences in the forcing. At odds with the theory, however, the integral scale of the horizontal fluctuations grows as the surface is approached. This is rooted in the profound influence exerted by the surface on the inter-scale energy transfer: along horizontal separations, the direct cascade of horizontal energy is hindered, while an inverse cascade of vertical energy is established. This is connected to the structure of upwellings and downwellings. The former, characterized by somewhat larger spatial extent and stronger intensity, are associated to extensional surface-parallel motions. They thus transfer energy to the larger horizontal scales, prevailing over downwellings which favour the compression (and concurrent vertical stretching) of the eddies. Both types of structures extend to depths between the integral and Taylor microscales.

Atomically thin materials offer multiple opportunities for layer-by-layer control of their electronic properties. While monolayer graphene (MLG) is a zero-gap system, Bernal-stacked bilayer graphene (BLG) acquires a finite band gap when the symmetry between the layers' potential energy is broken, usually, via a large electric field applied in double-gate devices. Here, we introduce an asymmetric twistronic stack comprising both MLG and BLG, synthesized via low-pressure chemical vapor deposition (LP-CVD) on Cu. Although a large ($\sim30^{\circ}$) twist angle decouples the MLG and BLG electronic bands near Fermi level, we find that the layer degeneracy in the BLG subsystem is lifted, producing a gap in the absence of external fields. The built-in interlayer asymmetry originates from proximity-induced energy shifts in the outermost layers and requires a displacement field of $0.14$ V/nm to be compensated. The latter corresponds to a $\sim10$ meV intrinsic BLG gap, a value confirmed by our thermal-activation measurements. The present results highlight the role of structural asymmetry and encapsulating environment, expanding the engineering toolbox for monolithically-grown graphene multilayers., Comment: 23 pages, 4 figures and supporting information

Intercalation of epitaxial graphene on SiC(0001) with Sn results in a well-ordered 2D metallic Sn phase with a $(1\times1)$ structure at the interface between SiC substrate and quasi-freestanding graphene. The 2D\,Sn phase exhibits exotic electronic properties with Dirac-like and flat bands coexisting close to the Fermi level that exhibit both Zeeman- and Rashba-type spin splittings. Possible inter-layer interactions between the 2D\,Sn layer and graphene that may result in emerging electronic properties remain unexplored. We use time- and angle-resolved photoemission spectroscopy to reveal a surprisingly short-lived non-equilibrium carrier distribution inside the Dirac cone of graphene. Further, we find that the graphene $\pi$-band exhibits a transient down-shift that we attribute to charging of the graphene layer with holes. We interpret our results with support from density functional theory calculations of the graphene - 2D\,Sn heterostructure that reveal a substantial hybridization between graphene $\pi$-band and Sn $p_z$-states that opens up a $\sim230$\,meV band gap inside the Dirac cone and delocalizes the charge carriers over both the graphene and 2D\,Sn layers. Our results have important implications for the design of future ultrafast optoelectronic devices that may find applications in the fields of light harvesting and detection, as supercapacitors, or in novel quantum computing technologies., Comment: 19 pages, 5 figures

Understanding and controlling the electronic properties of two-dimensional materials is crucial for their potential applications in nano- and optoelectronics. Monolayer transition metal dichalcogenides such as WS$_2$ have garnered significant interest due to their strong light-matter interaction and extreme sensitivity of the band structure to the presence of photogenerated electron-hole pairs. In this study, we investigate the transient electronic structure of monolayer WS$_2$ on a graphene substrate after resonant excitation of the A-exciton using time- and angle-resolved photoemission spectroscopy. We observe a pronounced band structure renormalization including a substantial reduction of the transient band gap that is in good quantitative agreement with our {\it ab initio} theory that reveals the importance of both intrinsic WS$_2$ and extrinsic substrate contributions to the transient band structure of monolayer WS$_2$. Our findings not only deepen the fundamental understanding of band structure dynamics in two-dimensional materials but also offer valuable insights for the development of novel electronic and optoelectronic devices based on monolayer TMDs and their heterostructures with graphene., Comment: 17 pages, 4 figures

We discuss a complementary asymptotic analysis of the so called minimal random walk. More precisely, we present a version of the almost sure central limit theorem as well as a generalization of the recently proposed quadratic strong laws. In addition, alternative demonstrations of the functional limit theorems will be supplied based on a P\'olya urn scheme instead of a martingale approach.

In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive solution, and we study its regularity. We study the persistence and extinction regimes, and we give sufficient conditions under which the disease-free equilibrium point is an asymptotically stable equilibrium point with probability one. We provide sufficient conditions under which the model admits a unique stationary measure. Finally, we illustrate our findings using simulations.

The widespread adoption of quadrotors for diverse applications, from agriculture to public safety, necessitates an understanding of the aerodynamic disturbances they create. This paper introduces a computationally lightweight model for estimating the time-averaged magnitude of the induced flow below quadrotors in hover. Unlike related approaches that rely on expensive computational fluid dynamics (CFD) simulations or time-consuming empirical measurements, our method leverages classical theory from turbulent flows. By analyzing over 9 hours of flight data from drones of varying sizes within a large motion capture system, we show that the combined flow from all propellers of the drone is well-approximated by a turbulent jet. Through the use of a novel normalization and scaling, we have developed and experimentally validated a unified model that describes the mean velocity field of the induced flow for different drone sizes. The model accurately describes the far-field airflow in a very large volume below the drone which is difficult to simulate in CFD. Our model, which requires only the drone's mass, propeller size, and drone size for calculations, offers a practical tool for dynamic planning in multi-agent scenarios, ensuring safer operations near humans and optimizing sensor placements., Comment: 7+1 pages

We use video footage of a water tunnel experiment to construct a two-dimensional reduced-order model of the flapping dynamics of an inverted flag in uniform flow. The model is obtained as the reduced dynamics on an attracting spectral submanifold (SSM) that emanates from the two slowest modes of the unstable fixed point of the flag. Beyond an unstable fixed point and a limit cycle expected from observations, our SSM-reduced model also confirms the existence of two unstable fixed points for the flag, which were found by previous studies. Importantly, the model correctly reconstructs the dynamics from a small number of general trajectories and no further information on the system. In the chaotic flapping regime, we construct a 4D SSM-reduced model that captures the system's chaotic attractor.

Within the nucleus, structural maintenance of chromosome protein complexes, namely condensin and cohesin, create an architecture to facilitate the organization and proper function of the genome. Condensin, in addition to performing loop extrusion, creates localized clusters of chromatin in the nucleolus through transient crosslinks. Large-scale simulations revealed three different dynamic behaviors as a function of timescale: slow crosslinking leads to no clusters, fast crosslinking produces rigid slowly changing clusters, while intermediate timescales produce flexible clusters that mediate gene interaction. By mathematically analyzing different relative scalings of the two sources of stochasticity, thermal fluctuations and the force induced by the transient crosslinks, we predict these three distinct regimes of cluster behavior. Standard time-averaging that takes the fluctuations of the transient crosslink force to zero predicts the existence of rigid clusters. Accounting for the interaction of both fluctuations from the crosslinks and thermal noise with an effective energy landscape predicts the timescale-dependent lifetimes of flexible clusters. No clusters are predicted when the fluctuations of the transient crosslink force are taken to be large relative to thermal fluctuations. This mathematical perturbation analysis illuminates the importance of accounting for stochasticity in local incoherent transient forces to predict emergent complex biological behavior., Comment: 9 pages, 6 figures

This study delves into the exploration of the limiting shape theorem for subadditive processes on finitely generated groups with polynomial growth, commonly referred to as virtually nilpotent groups. Investigating the algebraic structures underlying these processes, we present a generalized form of the asymptotic shape theorem within this framework. Extending subadditive ergodic theory in this context, we consider processes which exhibit both at most and at least linear random growth. We conclude with applications and illustrative examples., Comment: 36 pages, 1 figure; typos corrected, some lemmas revised

This rejoinder responds to discussions by of Caimo, Niezink, and Schweinberger and Fritz of ''A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks'' by Krivitsky, Coletti, and Hens, all published in the Journal of the American Statistical Association in 2023., Comment: 10 pages, 3 figures, 3 tables

Consider the following simple parking process on $\Lambda_n := \{-n, \ldots, n\}^d,d\ge1$: at each step, a site $i$ is chosen at random in $\Lambda_n$ and if $i$ and all its nearest neighbor sites are empty, $i$ is occupied. Once occupied, a site remains so forever. The process continues until all sites in $\Lambda_n$ are either occupied or have at least one of their nearest neighbors occupied. The final configuration (occupancy) of $\Lambda_n$ is called the jamming limit and is denoted by $X_{\Lambda_n}$. Ritchie (2006) constructed a stationary random field on $\mathbb Z^d$ obtained as a (thermodynamic) limit of the $X_{\Lambda_n}$'s as $n$ tends to infinity. As a consequence of his construction, he proved a strong law of large numbers for the proportion of occupied sites in the box $\Lambda_n$ for the random field $X$. Here we prove the central limit theorem, the law of iterated logarithm, and a gaussian concentration inequality for the same statistics. A particular attention will be given to the case $d=1$, in which we also obtain new asymptotic properties for the sequence $X_{\Lambda_n},n\ge1$ as well as a new proof to the closed-form formula for the occupation density of the parking process., Comment: 19 pages, 1 figure

Two-dimensional (2D) materials have received extensive research attentions over the past two decades due to their intriguing physical properties (such as the ultrahigh mobility and strong light-matter interaction at atomic thickness) and a broad range of potential applications (especially in the fields of electronics and optoelectronics). The growth of single-crystal 2D materials is the prerequisite to realize 2D-based high-performance applications. In this review, we aim to provide an in-depth analysis of the state-of-the-art technology for the growth and applications of 2D materials, with particular emphasis on single crystals. We first summarize the major growth strategies for monolayer 2D single crystals. Following that, we discuss the growth of multilayer single crystals, including the control of thickness, stacking sequence, and heterostructure composition. Then we highlight the exploration of 2D single crystals in electronic and optoelectronic devices. Finally, a perspective is given to outline the research opportunities and the remaining challenges in this field.

The potential of graphene for hydrogen storage, coupled with the established role of Platinum as a catalyst for the hydrogen evolution reaction and the spillover effect, makes Pt-functionalized graphene a promising candidate for near-ambient hydrogen storage. This paper focuses on examining the process of Pt cluster formation on epitaxial graphene and assesses the suitability of the system as hydrogen storage material. Scanning tunneling microscopy unveils two primary pathways for Pt cluster growth. In the initial phase, up to ~1 ML of Pt coverage, Pt tends to randomly disperse and cover the graphene surface, while the cluster height remains essentially unchanged. Beyond a coverage of 3 ML, the nucleation of new layers on existing clusters becomes predominant. Then, the clusters mainly grow in height. Thermal desorption spectroscopy on hydrogenated Pt-decorated graphene reveals the presence of multiple hydrogen adsorption mechanisms, manifested as two Gaussian peaks superimposed on a linearly increasing background. We attribute the first peak at 150{\deg}C to hydrogen physisorbed on the surface of Pt clusters. The second peak at 430{\deg}C is attributed to chemisorption of hydrogen on the surface of the clusters, while the linearly increasing background is assigned to hydrogen bonded in the bulk of the Pt clusters. These measurements demonstrate the ability of Pt-functionalized graphene to store molecular hydrogen at temperatures that are high enough for stable hydrogen binding at room temperature.

Graphene-hexagonal boron nitride (hBN) scalable heterostructures are pivotal for the development of graphene-based high-tech applications. In this work, we demonstrate the realization of high-quality graphene-hBN heterostructures entirely obtained with scalable approaches. hBN continuous films were grown via ion beam-assisted physical vapor deposition directly on commercially available $SiO_2/Si$ and used as receiving substrates for graphene single-crystal matrixes grown by chemical vapor deposition on copper. The structural, chemical, and electronic properties of the heterostructure were investigated by atomic force microscopy, Raman spectroscopy, and electrical transport measurements. We demonstrate graphene carrier mobilities exceeding $10,000 cm^2/Vs$ in ambient conditions, 30% higher than those directly measured on $SiO_{2}/Si$. We prove the scalability of our approach by measuring more than 100 transfer length method devices over a centimeter scale, which present an average carrier mobility of $7500 \pm 850 cm^{2}/Vs$. The reported high-quality all-scalable heterostructures are of relevance for the development of graphene-based high-performing electronic and optoelectronic applications.

The accurate prediction of the two-phase heat transfer coefficient (HTC) as a function of working fluids, channel geometries and process conditions is key to the optimal design and operation of compact heat exchangers. Advances in artificial intelligence research have recently boosted the application of machine learning (ML) algorithms to obtain data-driven surrogate models for the HTC. For most supervised learning algorithms, the task is that of a nonlinear regression problem. Despite the fact that these models have been proven capable of outperforming traditional empirical correlations, they have key limitations such as overfitting the data, the lack of uncertainty estimation, and interpretability of the results. To address these limitations, in this paper, we use a multi-output Gaussian process regression (GPR) to estimate the HTC in microchannels as a function of the mass flow rate, heat flux, system pressure and channel diameter and length. The model is trained using the Brunel Two-Phase Flow database of high-fidelity experimental data. The advantages of GPR are data efficiency, the small number of hyperparameters to be trained (typically of the same order of the number of input dimensions), and the automatic trade-off between data fit and model complexity guaranteed by the maximization of the marginal likelihood (Bayesian approach). Our paper proposes research directions to improve the performance of the GPR-based model in extrapolation., Comment: 7 pages, 2 figures, to be published in the proceedings of the 17th International Heat Transfer Conference 2023 (IHTC-17)

The quantum Hall effect is widely used for the investigation of fundamental phenomena, ranging from topological phases to composite fermions. In particular, the discovery of a room temperature resistance quantum in graphene is significant for compact resistance standards that can operate above cryogenic temperatures. However, this requires large magnetic fields that are accessible only in a few high magnetic field facilities. Here, we report on the quantum Hall effect in graphene encapsulated by the ferroelectric insulator CuInP2S6. Electrostatic gating of the graphene channel enables the Fermi energy to be tuned so that electrons in the localized states of the insulator are in equilibrium with the current-carrying, delocalized states of graphene. Due to the presence of strongly bound states in this hybrid system, a quantum Hall plateau can be achieved at room temperature in relatively modest magnetic fields. This phenomenon offers the prospect for the controlled manipulation of the quantum Hall effect at room temperature., Comment: 24 pages, 6 figures

Tumor heterogeneity is a challenge to designing effective and targeted therapies. Glioma-type identification depends on specific molecular and histological features, which are defined by the official WHO classification CNS. These guidelines are constantly updated to support the diagnosis process, which affects all the successive clinical decisions. In this context, the search for new potential diagnostic and prognostic targets, characteristic of each glioma type, is crucial to support the development of novel therapies. Based on a TCGA glioma RNA-sequencing dataset updated according to the 2016 and 2021 WHO guidelines, we proposed a two-step variable selection approach for biomarker discovery. Our framework encompasses the graphical lasso algorithm to estimate sparse networks of genes carrying diagnostic information. These networks are then used as input for regularised Cox survival regression model, allowing the identification of a smaller subset of genes with prognostic value. In each step, the results derived from the 2016 and 2021 classes were discussed and compared. For both WHO glioma classifications, our analysis identifies potential biomarkers, characteristic of each glioma type. Yet, better results were obtained for the WHO CNS classification in 2021, thereby supporting recent efforts to include molecular data on glioma classification.

The inverse-square law states that the effect a source has on its surroundings is inversely proportional to the square of the Euclidean distance from that source. Its applicability spans multiple fields including physics, engineering, and computer science. We study the combined effect of multiple point sources surrounding a closed region in multidimensional space. We determine that the maximum effect in D dimensions is on the region's boundary if $D \leq 4$, and the minimum is on the boundary if $D \geq 4$., Comment: 8 pages, 0 figures

In many neuromorphic workflows, simulators play a vital role for important tasks such as training spiking neural networks (SNNs), running neuroscience simulations, and designing, implementing and testing neuromorphic algorithms. Currently available simulators are catered to either neuroscience workflows (such as NEST and Brian2) or deep learning workflows (such as BindsNET). While the neuroscience-based simulators are slow and not very scalable, the deep learning-based simulators do not support certain functionalities such as synaptic delay that are typical of neuromorphic workloads. In this paper, we address this gap in the literature and present SuperNeuro, which is a fast and scalable simulator for neuromorphic computing, capable of both homogeneous and heterogeneous simulations as well as GPU acceleration. We also present preliminary results comparing SuperNeuro to widely used neuromorphic simulators such as NEST, Brian2 and BindsNET in terms of computation times. We demonstrate that SuperNeuro can be approximately 10--300 times faster than some of the other simulators for small sparse networks. On large sparse and large dense networks, SuperNeuro can be approximately 2.2 and 3.4 times faster than the other simulators respectively.

Today digital revolution is having a dramatic impact on the pharmaceutical industry and the entire healthcare system. The implementation of machine learning, extreme-scale computer simulations, and big data analytics in the drug design and development process offers an excellent opportunity to lower the risk of investment and reduce the time to the patient. Within the LIGATE project, we aim to integrate, extend, and co-design best-in-class European components to design Computer-Aided Drug Design (CADD) solutions exploiting today's high-end supercomputers and tomorrow's Exascale resources, fostering European competitiveness in the field. The proposed LIGATE solution is a fully integrated workflow that enables to deliver the result of a virtual screening campaign for drug discovery with the highest speed along with the highest accuracy. The full automation of the solution and the possibility to run it on multiple supercomputing centers at once permit to run an extreme scale in silico drug discovery campaign in few days to respond promptly for example to a worldwide pandemic crisis., Comment: Paper Accepted to the 20th ACM International Conference on Computing Frontiers (CF'23)

Ultrafast charge separation after photoexcitation is a common phenomenon in various van-der-Waals (vdW) heterostructures with great relevance for future applications in light harvesting and detection. Theoretical understanding of this phenomenon converges towards a coherent mechanism through charge transfer states accompanied by energy dissipation into strongly coupled phonons. The detailed microscopic pathways are material specific as they sensitively depend on the band structures of the individual layers, the relative band alignment in the heterostructure, the twist angle between the layers, and interlayer interactions resulting in hybridization. We used time- and angle-resolved photoemission spectroscopy combined with tight binding and density functional theory electronic structure calculations to investigate ultrafast charge separation and recombination in WS$_2$-graphene vdW heterostructures. We identify several avoided crossings in the band structure and discuss their relevance for ultrafast charge transfer. We relate our own observations to existing theoretical models and propose a unified picture for ultrafast charge transfer in vdW heterostructures where band alignment and twist angle emerge as the most important control parameters., Comment: 8 pages, 5 figures

The coupling of the electron system to lattice vibrations and their time-dependent control and detection provides unique insight into the non-equilibrium physics of semiconductors. Here, we investigate the ultrafast transient response of semiconducting monolayer 2$H$-MoTe$_2$ encapsulated with $h$BN using broadband optical pump-probe microscopy. The sub-40-fs pump pulse triggers extremely intense and long-lived coherent oscillations in the spectral region of the A' and B' exciton resonances, up to $\sim$20% of the maximum transient signal, due to the displacive excitation of the out-of-plane $A_{1g}$ phonon. Ab-initio calculations reveal a dramatic rearrangement of the optical absorption of monolayer MoTe$_2$ induced by an out-of-plane stretching and compression of the crystal lattice, consistent with an $A_{1g}$-type oscillation. Our results highlight the extreme sensitivity of the optical properties of monolayer TMDs to small structural modifications and their manipulation with light., Comment: 27 pages, 4 figures, supporting information

Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields. Here, we consider that the algebras are determined by configurations of finite spins on a countable set with their associated Gibbs distributions. The model preserves properties of the finite-dimensional Gibbs algebras found in the literature and extend their results. We introduce infertility in the genetic dynamics when the configurations differ macroscopically. It induces a decomposition of the algebra into a direct sum of fertile ideals with genetic realization. The proposed infinite-dimensional algebras are commutative, non-associative, with uncountable basis and zero divisors. The properties of Gibbs measures allow us to deal with the difficulties arising from the algebraic structure and obtain the results presented in this article., Comment: 26 pages, 4 figures; typos corrected, references added

We report on resonance Raman spectroscopy measurements with excitation photon energy down to 1.16 eV on graphene, to study how low-energy carriers interact with lattice vibrations. Thanks to the excitation energy close to the Dirac point at $\mathbf{K}$, we unveil a giant increase of the intensity ratio between the double-resonant 2D and 2D$^\prime$ peaks with respect to that measured in graphite. Comparing with fully \textit{ab initio} theoretical calculations, we conclude that the observation is explained by an enhanced, momentum-dependent coupling between electrons and Brillouin zone-boundary optical phonons. This finding applies to two dimensional Dirac systems and has important consequences for the modeling of transport in graphene devices operating at room temperature., Comment: 6 pages, 3 figures