Search

Scheduling languages express to a compiler a sequence of optimizations to apply. Compilers that support a scheduling language interface allow exploration of compiler optimizations, i.e., exploratory compilers. While scheduling languages have become a common feature of tools for expert users, the proliferation of these languages without unifying common features may be confusing to users. Moreover, we recognize a need to organize the compiler developer community around common exploratory compiler infrastructure, and future advances to address, for example, data layout and data movement. To support a broader set of users may require raising the level of abstraction. This paper provides a taxonomy of scheduling languages, first discussing their origins in iterative compilation and autotuning, noting the common features and how they are used in existing frameworks, and then calling for changes to increase their utility and portability.

The TraX Engine is an advanced data processing tool developed by ADVACAM in collaboration with the European Space Agency (ESA), specifically designed for analyzing data from Timepix detectors equipped with various sensor materials (Si, CdTe, GaAs, SiC). TraX Engine can process large datasets across various scientific and medical applications, including space radiation monitoring, particle therapy, and imaging. In space applications, the TraX Engine has been used to process data from satellites like OneWeb JoeySat deployed in LEO orbit, where it continuously monitors space radiation environments measuring flux, dose, and dose rate in real-time. In medical applications, particularly in particle therapy, the TraX Engine is used to process data to characterize radiation fields in terms of particle flux, Linear Energy Transfer, and spatial distribution of the radiation dose. The TraX Engine can identify and classify scattered particles, such as secondary protons and electrons, and estimate their contribution to out-of-field doses. In imaging applications, the TraX Engine is integrated into Compton cameras, where it supports photon source localization through directional reconstruction of photons. The system ability to identify gamma radiation source with high precision makes it suitable for medical imaging tasks, such as tracking I-131 used in thyroid cancer treatment or localizing radiation sources. This paper presents the architecture and capabilities of the newly developed software TraX Engine, alongside results from various applications, demonstrating its role in particle tracking, radiation monitoring, imaging, and others. With its modular architecture, the TraX Engine offers multiple interfaces, including a command-line tool, an API, a web portal, and a graphical user interface, ensuring usability across different fields and user expertise levels., Comment: 14 pages, 7 figures

This study investigates the response of Timepix3 semiconductor pixel detectors in proton beams of varying intensities, with a focus on FLASH proton therapy. Using the Timepix3 ASIC chip, we measured the spatial and spectral characteristics of 220 MeV proton beams delivered in short pulses. The experimental setup involved Minipix readout electronics integrated with a Timepix3 chipboard in a flexible architecture, and an Advapix Timepix3 with a silicon sensor. Measurements were carried out with Timepix3 detectors equipped with GaAs and silicon Si sensors. We also investigated the response of a bare Timepix3 ASIC chip (without a sensor). The detectors were placed within a waterproof holder attached to the IBA Blue water phantom, with additional measurements performed in air behind a 2 cm-thick solid phantom. The results demonstrated the capability of the Timepix3 detectors to measure time-over-threshold (ToT) and count rate (number of events) in both conventional and ultra-high-dose-rates proton beams. The bare ASIC chip configuration sustained up to a dose rate (DR) of 270 Gy/s, although it exhibited limited spatial resolution due to low detection efficiency. In contrast, Minipix Timepix3 with experimental GaAs sensors showed saturation at low DR=5 Gy/s. Furthermore, the Advapix Timepix3 detector was used in standard and customized configurations. In the standard configuration (Ikrum =5), the detector showed saturation at DR=5 Gy/s. But, in the customized configuration when the per-pixel discharging signal (Ikrum) was increased to 80, the detector demonstrated enhanced performance by reducing the duration of the ToT signal, allowing beam spot imaging up to DR=28 Gy/s in the plateau region of the Bragg curve. For such DR, the frame acquisition time was reduced to the order of microseconds, meaning only a fraction of the pulse (with pulse lengths on the order of milliseconds) was captured., Comment: 9 pages, 6 figures, JINST

This study experimentally examines the effect and changes in the delivered fields, using water-equivalent phantoms with and without titanium (Ti) dental implants positioned along the primary beam path. We measure in detail the composition and spectral-tracking characterization of particles generated in the entrance region of the Bragg curve using high-spatial resolution, spectral and time-sensitive imaging detectors with a pixelated array provided by the ASIC chip Timepix3. A 170 MeV proton beam was collimated and modulated in a polymethyl methacrylate (PMMA). Placing two dental implants at the end of the protons range in the phantom, the radiation was measured using two pixeled detectors with Si sensors. The Timepix3 (TPX3) detectors equipped with silicon sensors measure in detail particle fluxes, dose rates (DR) and linear energy transfer (LET) spectra for resolved particle types. Artificial intelligence (AI) based-trained neural networks (NN) calibrated in well-defined radiation fields were used to analyze and identify particles based on morphology and characteristic spectral-tracking response. The beam was characterized and single-particle tracks were registered and decomposed into particle-type groups. The resulting particle fluxes in both setups are resolved into three main classes of particles: i) protons, ii) electrons and photons iii) ions. Protons are the main particle component responsible for dose deposition. High-energy transfer particles (HETP), namely ions exhibited differences in both dosimetric aspects that were investigated: DR and particle fluxes, when the Ti implants were placed in the setup. The detailed multi-parametric information of the secondary radiation field provides a comprehensive understanding of the impact of Ti materials in proton therapy., Comment: 8 pages, 4 figures, IWORID Conference

This work investigates the operational acquisition time limits of Timepix3 and Timepix2 detectors operated in frame mode for high-count rate of high deposited energy transfer particles. Measurements were performed using alpha particles from a 241Am laboratory source and proton and carbon ion beams from a synchrotron accelerator. The particle count rate upper limit is determined by overlapping per-pixel particle signals, identifiable by the hits per pixel counter > 2, indicating the need to decrease acquisition time. On the other hand, the lower limit is the time required to collect the particle deposited charge while maintaining spectral properties. Different acquisition times were evaluated for an AdvaPIX Timepix3 detector (500 um Silicon sensor) with standard per-pixel DAC settings and a Minipix Timepix2 detector (300 um Silicon sensor) with standard and customized settings the pulse shaping parameter and threshold. For AdvaPIX Timepix3, spectra remained accurate down to 100 us frame acquisition time; at 10 us, loss of collected charge occurred, suggesting either avoiding this acquisition time or applying a correction. Timepix2 allowed acquisition times down to 100 ns for single particle track measurements even for high energy loss, enabled by a new Timepix2 feature delaying shutter closure until full particle charge collection. This work represents the first measurement utilizing Timepix-chips pixel detectors in an accelerator beam of clinical energy and intensity without the need to decrease the beam current. This is made possible by exploiting the short shutter feature in Timepix2 and a customized per-pixel energy calibration of the Timepix2 detector with a larger discharging signal value which allowed for a shorter time-over-threshold (ToT) signal. These customized settings extend the operation of the pixel detectors to higher event rates up to 10^9 particles/cm^2/s., Comment: 8 pages, 6 figures, IWORID conference

We show that the category of linearly topologized vector spaces over discrete fields constitutes the correct framework for algebraic structures on Floer homologies with field coefficients. Our case in point is the Poincar\'e duality theorem for Rabinowitz Floer homology. We prove that Rabinowitz Floer homology is a locally linearly compact vector space in the sense of Lefschetz, or, equivalently, a Tate vector space in the sense of Beilinson-Feigin-Mazur. Poincar\'e duality and the graded Frobenius algebra structure on Rabinowitz Floer homology then hold in the topological sense. Along the way, we develop in a largely self-contained manner the theory of linearly topologized vector spaces, with special emphasis on duality and completed tensor products, complementing results of Beilinson-Drinfeld, Beilinson, Rojas, Positselski, and Esposito-Penkov., Comment: 57 pages

Gravitational wave memory is said to arise when a gravitational wave burst produces changes in a physical system that persist even after that wave has passed. This paper analyzes gravitational wave bursts in plane wave spacetimes, deriving memory effects on timelike and null geodesics, massless scalar fields, and massless spinning particles whose motion is described by the spin Hall equations. All associated memory effects are found to be characterized by four ``memory tensors,'' three of which are independent. These tensors form a scattering matrix for the transverse components of geodesics. However, unlike for the ``classical'' memory effect involving initially comoving pairs of timelike geodesics, one of our results is that memory effects for null geodesics can have strong longitudinal components. When considering massless particles with spin, we solve the spin Hall equations analytically by showing that there exists a conservation law associated with each conformal Killing vector field. These solutions depend only on the same four memory tensors that control geodesic scattering. For massless scalar fields, we show that given any solution in flat spacetime, a weak-field solution in a plane wave spacetime can be generated just by differentiation. Precisely which derivatives are involved depend on the same four memory tensors. These effects are illustrated for scalar plane waves and higher-order Gaussian beams. Furthermore, we also present a numerical comparison between the dynamics of localized wave packets carrying angular momentum and the spin Hall equations.

The term of big data was used since 1990s, but it became very popular around 2012. A recent definition of this term says that big data are information assets characterized by high volume, velocity, variety and veracity that need special analytical methods and software technologies to extract value form them. While big data was used at the beginning mostly in information technology field, now it can be found in every area of activity: in governmental decision-making processes, manufacturing, education, healthcare, economics, engineering, natural sciences, sociology. The rise of Internet, mobile phones, social media networks, different types of sensors or satellites provide enormous quantities of data that can have profound effects on economic research. The data revolution that we are facing transformed the way we measure the human behavior and economic activities. Unemployment, consumer price index, population mobility, financial transactions are only few examples of economic phenomena that can be analyzed using big data sources. In this paper we will start with a taxonomy of big data sources and show how these new data sources can be used in empirical analyses and to build economic indicators very fast and with reduced costs., Comment: Knowledge for the market use, Conference Proceedings, 2018, Olomouc, Czech Republic

This paper explores practical aspects of using a high-level functional language for GPU-based arithmetic on ``midsize'' integers. By this we mean integers of up to about a quarter million bits, which is sufficient for most practical purposes. The goal is to understand whether it is possible to support efficient nested-parallel programs with a small, flexible code base. We report on GPU implementations for addition and multiplication of integers that fit in one CUDA block, thus leveraging temporal reuse from scratchpad memories. Our key contribution resides in the simplicity of the proposed solutions: We recognize that addition is a straightforward application of scan, which is known to allow efficient GPU implementation. For quadratic multiplication we employ a simple work-partitioning strategy that offers good temporal locality. For FFT multiplication, we efficiently map the computation in the domain of integral fields by finding ``good'' primes that enable almost-full utilization of machine words. In comparison, related work uses complex tiling strategies -- which feel too big a hammer for the job -- or uses the computational domain of reals, which may degrade the magnitude of the base in which the computation is carried. We evaluate the performance in comparison to the state-of-the-art CGBN library, authored by NvidiaLab, and report that our CUDA prototype outperforms CGBN for integer sizes higher than 32K bits, while offering comparable performance for smaller sizes. Moreover, we are, to our knowledge, the first to report that FFT multiplication outperforms the classical one on the larger sizes that still fit in a CUDA block. Finally, we examine Futhark's strengths and weaknesses for efficiently supporting such computations and find out that a compiler pass aimed at efficient sequentialization of excess parallelism would significantly improve performance.

FLASH radiotherapy necessitates the development of advanced Quality Assurance methods and detectors for accurate and online monitoring of the radiation field. This study introduces enhanced time-resolution detection systems and methods tailored for single-pulse detection. The goal of this work was to measure the delivered number of pulses, investigate temporal structure of individual pulses, and to develop a method for dose-per-pulse (DPP) monitoring based on secondary radiation particles produced in the experimental room. A 20 MeV electron beam generated from a linear accelerator (LINAC) was delivered to a water phantom. Ultra-high dose-per-pulse (UHDPP) electron beams were used with a dose per pulse ranging from 1 Gy to over 7 Gy. The pulse lengths ranged from 1.18 us to 2.88 us at a pulse rate frequency of 5 Hz. A semiconductor pixel detector Timepix3 (TPX3) was used to track direct interactions in the Silicon sensor created by single secondary particles. Measurements were performed in the air, while the detector was positioned out-of-field at a lateral distance of 200 cm parallel with the LINAC exit window. The dose deposited in the silicon was measured along with the pulse length and the nanostructure of the pulse. Simultaneously deposited energy and time of arrival of single particles were measured with a precision of 1.56 ns. The measured pulse count agreed with the delivered values. A linear response (R^2 = 0.999) was established between the delivered beam current and the measured dose at the detector position (orders of nGy). The difference between the average measured and average delivered pulse length was 0.003(30) us. This simple non-invasive method, exhibits no limitations on the delivered DPP within the range used during this investigation. It enhances the precision and real-time monitoring of FLASH treatment plans with nanosecond precision., Comment: 24 pages, 8 figures

We define Hamiltonian Floer homology with differential graded (DG) local coefficients for symplectically aspherical manifolds. The differential of the underlying complex involves chain representatives of the fundamental classes of the moduli spaces of Floer trajectories of arbitrary dimension. This setup allows in particular to define and compute Floer homology with coefficients in chains on fibers of fibrations over the free loop space of the underlying symplectic manifold. We develop the DG Floer toolset, including continuation maps and homotopies, and we also define and study symplectic homology groups with DG local coefficients. We define spectral invariants and establish general criteria for almost existence of contractible periodic orbits on regular energy levels of Hamiltonian systems inside Liouville domains. In the case of cotangent bundles, we prove a Viterbo isomorphism theorem with DG local coefficients. This serves as a stepping stone for applications to the almost existence of contractible closed characteristics on closed smooth hypersurfaces. In this context, our methods allow to access for the first time the dichotomy between closed manifolds that are aspherical and those that are not., Comment: 125 pages, 3 figures. v2: we have partially rewritten the introduction and we have added some references

This contribution presents the recent research developments within the Cosmic Ray Extremely Distributed Observatory (CREDO) in the search for resolution of various scientific puzzles, ranging from fundamental physical questions to applications like the determination of earthquake precursors. The state-of-the art theoretical, numerical and computational aspects of these phenomena are addressed, as well as recent experimental developments for detection., Comment: 9 pages, 7 figures. Based on the contribution to the XVIII Mexican Workshop on Particles and Fields in Puebla, Mexico, November 2022. M\'exico

The modernization of offi cial statistics involves the use of new data sources, such as data collected through remote sensing. The document contains a description of how an urban green index, derived from the SDG 11.7 objective, was obtained for Romania's 41 county seat cities based on free data sets collected by remote sensing from the European and North American space agencies. The main result is represented by an estimate of the areas of surfaces covered with vegetation for the 40 county seat towns and the municipality of Bucharest, relative to the total surface. To estimate the area covered with vegetation, we used two data sets obtained by remote sensing, namely data provided by the MODIS mission, the TERRA satellite, and data provided by the Sentinel 2 mission from the Copernicus space program. Based on the results obtained, namely the surface area covered with vegetation, estimated in square kilometers, and the percentage of the total surface area or urban green index, we have created a national top of the county seat cities

We derive the notions of BV unital infinitesimal bialgebra and BV Frobenius algebra from the topology of suitable compactifications of moduli spaces of decorated genus 0 curves. We construct these structures respectively on reduced symplectic homology and Rabinowitz Floer homology. As an application, we construct these structures in nonequivariant string topology. We also show how the Lie bialgebra structure in equivariant string topology, and more generally on $S^1$-equivariant symplectic homology, is obtained as a formal consequence., Comment: 76 pages, including 1 appendix

This study aims to assess the composition of scattered particles generated in proton therapy for tumours situated proximal to titanium dental implants. The investigation involves decomposing the mixed field and recording Linear Energy Transfer (LET) spectra to quantify the influence of metallic dental inserts located behind the tumour. A conformal proton beam was used to deliver the treatment plan to an anthropomorphic head phantom with two types of implants (Ti and plastic) inserted in the target volume. The stray radiation resulting during the irradiation was detected by a hybrid semiconductor pixel detector MiniPIX Timepix3 that was placed distal to the Spread-out Bragg peak. Visualization and field decomposition of stray radiation were generated using algorithms trained in particle recognition based on artificial intelligence convolution neural networks (AI CNN). Spectral sensitive aspects of the scattered radiation were collected using two angular positions of the detector relative to the beam direction: 0 and 60{\deg}. Using AI CNN, 3 classes of particles were identified: protons, electrons & photons, ions & fast neutrons. Placing a Ti implant in the beam's path resulted in predominantly electrons and photons, contributing 52.2%, whereas for plastic implants, the contribution was 65.4%. Scattered protons comprised 45.5% and 31.9% with and without Ti inserts, respectively. The LET spectra was derived for each group of particles, with values ranging from 0.01 to 7.5 keV{\mu}m-1 for Ti/plastic implants. The low-LET component was primarily composed of electrons and photons, while the high-LET component corresponded to protons and ions. This method, complemented by directional maps, holds potential for evaluating and validating treatment plans involving stray radiation near organs at risk, offering precise discrimination of the mixt field, enhancing in this way the LET calculation., Comment: 26 pages, 6 figures, 1 table

The hybrid architecture of the Timepix (TPX) family of detectors enables the use of different semiconductor sensors, most commonly silicon (Si), as well as high-density materials such as Cadmium Telluride (CdTe) or Gallium Arsenide (GaAs). For this purpose, we explore the potential of a silicon carbide (SiC) sensor bump-bonded on a Timepix3 detector as a radiation imaging and particle tracking detector. SiC stands as a radiation-hard material also with the ability to operate at elevated temperatures up to several hundreds of degrees Celsius. As a result, this sensor material is more suitable for radiation harsh environments compared to conventional e.g., Si sensors. In this work, we evaluate the response for precise radiation spectrometry and high-resolution particle tracking of newly developed SiC Timepix3 detector which is built and operated as a compact radiation camera MiniPIX-Timepix3 with integrated readout electronics. Calibration measurements were conducted with mono-energetic proton beams with energies of 13, 22, and 31 MeV at the U-120M cyclotron at the Nuclear Physics Institute Czech Academy of Science (NPI CAS), Prague, as well as 100 and 226 MeV at the Proton Therapy Center Czech (PTC) in Prague. High-resolution pattern recognition analysis and single-particle spectral tracking are used for detailed inspection and understanding of the sensor response. Results include distributions of deposited energy and linear energy transfer (LET) spectra. The spatial uniformity of the pixelated detector response is examined in terms of homogeneously distributed deposited energy., Comment: 9 pages, proceedings iWoRiD

Hybrid semiconductor pixelated detectors from the Timepix family are advanced detectors for online particle tracking, offering energy measurement and precise time stamping capabilities for particles of various types and energies. This inherent capability makes them highly suitable for various applications, including imaging, medical fields such as radiotherapy and particle therapy, space-based applications aboard satellites and the International Space Station, and industrial applications. The data generated by these detectors is complex, necessitating the development and deployment of various analytical techniques to extract essential information. For this purpose, and to aid the Timepix user community, it was designed and developed the "Data Processing Engine" (DPE) as an advanced tool for data processing designed explicitly for Timepix detectors. The functionality of the DPE is structured into three distinct processing levels: i) Pre-processing: This phase involves clusterization and the application of necessary calibrations and corrections. ii) Processing: This stage includes particle classification, employing machine learning algorithms, and the recognition of radiation fields. iii) Post-processing: Involves various analyses, such as directional analysis, coincidence analysis, frame analysis, Compton directional analysis, and the generation of physics products, are performed. The core of the DPE is supported by an extensive experimental database containing calibrations and referential radiation fields of typical environments, including protons, ions, electrons, gamma rays and X-rays, as well as thermal and fast neutrons. To enhance accessibility, the DPE is implemented into various user interface platforms such as a command-line tool, an application programming interface, and as a graphical user interface in the form of a web portal., Comment: 9 pages, proceedings IWORID

We present and evaluate the Futhark implementation of reverse-mode automatic differentiation (AD) for the basic blocks of parallel programming: reduce, prefix sum (scan), and reduce by index. We first present derivations of general-case algorithms and then discuss several specializations that result in efficient differentiation of most cases of practical interest. We report an experiment that evaluates the performance of the differentiated code in the context of GPU execution and highlights the impact of the proposed specializations as well as the strengths and weaknesses of differentiating at high level vs. low level (i.e., ``differentiating the memory'')., Comment: Presented at IFL'23 (i.e., 35th Symposium on Implementation and Application of Functional Languages, Aug. 29th - 31st, 2023, Braga, Portugal)

In this contribution we study the possibility of the formation of cosmic ray ensembles (CRE) created by the interaction of ultra-high energy (UHE) photons with the magnetic field of the Sun. The lack of observation of those UHE and the difficulties for their identification given the current methodologies motivates this study. We performed simulations using the PRESHOWER program in order to simulate the expected extensive air showers which might be spatially correlated generated upon entering the Earth's atmosphere. We found characteristic features like very thing and extremely elongates cascades of secondary photons with their corresponding energies spanning the entire cosmic range spectrum. Shower footprints are as large as hundreds of kilometres. An application of this study is the scenario of gamma-ray emission from the vicinity of the Sun as a result of ultra-high energy photon cascading in the solar magnetic field in order to understand recent observations made by the HAWC and Fermi-LAT observatories., Comment: 8 pages, 4 figures, 38th International Cosmic Ray Conference (ICRC2023) 26 July - 3 August, 2023 Nagoya, Japan

We develop a theory of Morse homology and cohomology with coefficients in a derived local system, for manifolds and also more generally for colimits of spaces that have the homotopy type of manifolds, with a view towards Floer theory. The model that we adopt for derived, or differential graded (DG) local systems is that of DG modules over chains on the based loop space of a manifold. These encompass both classical (non DG) local systems and chains on fibers of Hurewicz fibrations. We prove that the Morse homology and cohomology groups that we construct are isomorphic to DG Tor and Ext functors. The key ingredient in the definition is a notion of twisting cocycle obtained by evaluating into based loops a coherent system of representatives for the fundamental classes of the moduli spaces of Morse trajectories of arbitrary dimensions. From this perspective, our construction sits midway between classical Morse homology with twisted coefficients and more refined invariants of Floer homotopical flavor. The construction of the twisting cocycle is originally due to Barraud and Cornea with Z/2-coefficients. We show that the twisting cocycle with integer coefficients is equivalent to Brown's universal twisting cocycle. We prove that Morse homology with coefficients in chains on the fiber of a Hurewicz fibration recovers the homology of the total space of the fibration. We study several structural properties of the theory: invariance, functoriality, and Poincar\'e duality, also in the nonorientable case., Comment: 256 pages. v2: Minor modifications and additions to address referee's comments. Change to book format. v3: Minor change

Wave packets propagating in inhomogeneous media experience a coupling between internal and external degrees of freedom and, as a consequence, follow spin-dependent trajectories. These phenomena, well known in optics and condensed matter physics, are referred to as spin Hall effects. Similarly, the gravitational spin Hall effect is expected to affect the propagation of gravitational waves on curved spacetimes. In this general-relativistic setup, the curvature of spacetime acts as impurities in a semiconductor or inhomogeneities in an optical medium, leading to a frequency- and polarization-dependent propagation of wave packets. In this letter, we study this effect for strong-field lensed gravitational waves generated in hierarchical triple black hole systems in which a stellar-mass binary merges near a more massive black hole. We calculate how the gravitational spin Hall effect modifies the gravitational waveforms and show its potential for experimental observation. If detected, these effects will have profound implications for astrophysics and tests of general relativity.

We consider the effects of Weyl geometry on the propagation of electromagnetic waves and on the gravitational spin Hall effect of light. It is usually assumed that in vacuum the electromagnetic waves propagate along null geodesics, a result which follows from the geometrical optics approximation. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, the ray dynamics is affected by the wave polarization. Therefore, the propagation of the electromagnetic waves can deviate from null geodesics, and this phenomenon is known as the gravitational spin Hall effect of light. On the other hand, Maxwell's equations have the remarkable property of conformal invariance. This property is a cornerstone of Weyl geometry and the corresponding gravitational theories. As a first step in our study, we obtain the polarization-dependent ray equations in Weyl geometry, describing the gravitational spin Hall effect of light in the presence of nonmetricity. As a specific example of the spin Hall effect of light in Weyl geometry, we consider the case of the simplest conformally invariant action, constructed from the square of the Weyl scalar, and the strength of the Weyl vector only. The action is linearized in the Weyl scalar by introducing an auxiliary scalar field. In static spherical symmetry, this theory admits an exact black hole solution, which generalizes the standard Schwarzschild solution through the presence of two new terms in the metric, having a linear and a quadratic dependence on the radial coordinate. We numerically study the polarization-dependent propagation of light rays in this exact Weyl geometric metric, and the effects of the presence of the Weyl vector on the magnitude of the spin Hall effect are estimated., Comment: 25 pages, 8 figures

In many areas of physics, the propagation of wave packets carrying intrinsic angular momentum is generally influenced by spin-orbit interactions. This is the main mechanism behind spin Hall effects, which result in wave packets following spin-dependent trajectories. Spin Hall effects have been observed in several experiments for electrons in condensed matter systems and for light propagating in inhomogeneous optical media. Similar effects have also been predicted for wave packets propagating in inhomogeneous gravitational fields. We give a brief introduction to gravitational spin Hall effects, emphasizing the analogies with the spin Hall effect of light in optics. Furthermore, we review the most promising astrophysical avenues that could lead to experimental observations of the gravitational spin Hall effect.

We consider the propagation of light in arbitrarily curved step-index optical fibers. Using a multiple-scales approximation scheme, set-up in Fermi normal coordinates, the full vectorial Maxwell equations are solved in a perturbative manner. At leading order, this provides a rigorous derivation of Rytov's law. At next order, we obtain non-trivial dynamics of the electromagnetic field, characterized by two coupling constants, the phase and the polarization curvature moments, which describe the curvature response of the light's phase and its polarization vector, respectively. The latter can be viewed as an inverse spin Hall effect of light, where the direction of propagation is constrained along the optical fiber and the polarization evolves in a frequency-dependent way., Comment: 13 pages, 5 figures

FLASH is a new treatment modality that requires optimization of dose, dose rate, and LET. Here we validate these three quantities under FLASH conditions, which includes the quantum uncertainty in the time-dependent instantaneous dose rate (IDR) curves and LET spectra that underlie the newly proposed integrated optimization framework. Measurements of dose, IDR, and LET were performed at the Emory Proton Therapy Center using a FLASH proton beam with a nominal energy of 250 MeV and a 3D printed ridge filter. Because 3D printing resin is made from a proprietary chemical formula, we developed a method for realistically characterizing and modeling the material in simulations. Absolute dose in 3D space was measured using a 2D MatriXX PT detector as well as by a novel 4D multi-layer strip ionization chamber (MLSIC), which also simultaneously measures IDR. Further timing data was measured in the secondary beam by detecting prompt gammas using a Minipix Timepix3; a second detector, Advapix Timepix3, was used to measure LET. To account for the quantum mechanical nature of particle transport, we developed a technique for detecting individual protons within a high flux primary beam, which was necessary for properly measuring LET spectra. TOPAS simulations agreed with measurement, with absolute dose typically having a gamma passing rate of at least 95% (3 mm/3% criteria). Likewise, IDR and LET showed good agreement, with averaged IDR values agreeing within 0.3% with fluctuations on the order of 10%, and LET distributions overlapping by at least 85% and showing an increase in high LET components (greater than 4 keV/um) with increasing depth. As LET and FLASH optimization continues to grow in popularity, measuring IDR, LET, and dose will become even more important, and we expect that the methods described here will prove to be useful tools in radiotherapy treatment planning and QA.

We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed at leading and next-to-leading order in the small expansion parameter $\hbar$. Taking into account the spin-orbit coupling between the internal and external degrees of freedom of wave packets, we derive effective ray equations with spin-dependent terms. These equations describe the gravitational spin Hall effect of localized Dirac wave packets. We treat both massive and massless Dirac fields and show how a covariantly defined Berry connection and the associated Berry curvature govern the semiclassical dynamics. The gravitational spin Hall equations are shown to be particular cases of the Mathisson-Papapetrou equations for spinning objects.

The propagation of gravitational waves can be described in terms of null geodesics by using the geometrical optics approximation. However, at large but finite frequencies the propagation is affected by the spin-orbit coupling corrections to geometrical optics, known as the gravitational spin Hall effect. Consequently, gravitational waves follow slightly different frequency- and polarization-dependent trajectories, leading to dispersive and birefringent phenomena. We study the potential for detecting the gravitational spin Hall effect in hierarchical triple black hole systems, consisting of an emitting binary orbiting a more massive body acting as a gravitational lens. We calculate the difference in time of arrival with respect to the geodesic propagation and find that it follows a simple power-law dependence on frequency with a fixed exponent. We calculate the gravitational spin Hall-corrected waveform and its mismatch with respect to the original waveform. The waveform carries a measurable imprint of the strong gravitational field if the source, lens, and observer are sufficiently aligned, or for generic observers if the source is close enough to the lens. We present constraints on dispersive time delays from GWTC-3, translated from limits on Lorentz invariance violation. Finally, we address the sensitivity of current and future ground detectors to dispersive lensing. Our results demonstrate that the gravitational spin Hall effect can be detected, providing a novel probe of general relativity and the environments of compact binary systems.

We define the notions of unital/counital/biunital infinitesimal anti-symmetric bialgebras and coFrobenius bialgebras and discuss their algebraic properties. We also define the notion of a graded 2D open-closed TQFT. These structures arise in Rabinowitz Floer homology, loop space homology, quantum homology, and the homology of finite dimensional manifolds. The underlying vector spaces, which are typically infinite dimensional, belong to a class of topological vector spaces known as Tate vector spaces., Comment: 64 pages, 9 figures. v2: major revision, in which we use in a systematic way the formalism of Tate vector spaces. Title changed

We introduce the notion of a Weinstein domain with strongly R-essential skeleton and study a reduced version of symplectic homology in this context. In the open string case we introduce the notion of a strongly R-essential Lagrangian submanifold and study a reduced version of wrapped Floer homology. These reduced homologies provide a common domain of definition for the pair-of-pants product and for pair-of-pants secondary coproducts, which combine into the structure of a unital infinitesimal anti-symmetric bialgebra. The coproducts on reduced homology depend on choices, and this dependence is controlled by secondary continuation maps. Reduced homology and cohomology provide splittings of Rabinowitz Floer homology which are compatible with the products and the coproducts. These splittings also depend on choices, in the same way as the coproducts. We provide sufficient conditions under which the secondary continuation maps vanish, giving rise to canonical coproducts and splittings., Comment: 55 pages, 10 figures

We aim to investigate the feasibility of online monitoring of irradiation time (IRT) and scan time for FLASH radiotherapy using a pixelated semiconductor detector. Measurements of the time structure of FLASH irradiations were performed using fast, pixelated spectral detectors, AdvaPIX-TPX3 and Minipix-TPX3. The latter has a fraction of its sensor coated with a neutron sensitive material. With little or no dead time and an ability to resolve events that are closely spaced in time (tens of ns), both detectors can accurately determine IRTs as long as pile-ups are avoided. To avoid pile-ups, we placed the detectors beyond the Bragg peak or at a large scattering angle. We acquired prompt gamma rays and secondary neutrons and calculated IRTs based on timestamps of the first (beam-on) and the last (beam-off) charged species. We also measured scan times in x, y, and diagonal directions. We performed these measurements for a single spot, a small animal field, a patient field, and a ridge filter optimized field to demonstrate in vivo online monitoring of IRT. All measurements were compared to vendor log files. Differences between measurements and log files for a single spot, a small animal field, and a patient field were within 1%, 0.3% and 1%, respectively. In vivo monitoring of IRTs was accurate within 0.1% for AdvaPIX-TPX3 and within 6.1% for Minipix-TPX3. The scan times in x, y, and diagonal directions were 4.0, 3.4, and 4.0 ms, respectively. Overall, the AdvaPIX-TPX3 can measure FLASH IRTs within 1% accuracy, indicating that prompt gamma rays are a good surrogate for primary protons. The Minipix-TPX3 showed a higher discrepancy, suggesting a need for further investigation. The scan times (3.4 \pm 0.05 ms) in the 60-mm distance of y-direction were less than (4.0 \pm 0.06 ms) in the 24-mm distance of x-direction, confirming the much faster scanning speed of the Y magnets than that of X., Comment: 11 pages, 5 figures

The spin Hall effects of light represent a diverse class of polarization-dependent physical phenomena involving the dynamics of electromagnetic wave packets. In a medium with an inhomogeneous refractive index, wave packets can be effectively described by massless spinning particles following polarization-dependent trajectories. Similarly, in curved spacetime the gravitational spin Hall effect of light is represented by polarization-dependent deviations from null geodesics. In this paper, we analyze the equations of motion describing the gravitational spin Hall effect of light. We show that these equations are a special case of the Mathisson-Papapetrou equations for spinning objects in general relativity. This allows us to use several known results for the Mathisson-Papapetrou equations, and apply them to the study of electromagnetic wave packets. We derive conservation laws, we discuss the limits of validity of the spin Hall equations, and we study how the energy centroids of wave packets, effectively described as massless spinning particles, depend on the external choice of a timelike vector field, representing a family of observers. In flat spacetime, the relativistic Hall effect and the Wigner(-Souriau) translations are recovered, while our equations also provide a generalization of these effects in arbitrary spacetimes. We construct a large class of wave packets that can be described by the spin Hall equations, but also find its limits by giving examples of wave packets which are more general and are not described by the spin Hall equations. Lastly, we examine the assumption that electromagnetic wave packets are massless. While this is approximately true in many contexts, it is not exact. We show that failing to carefully account for the limitations of the massless approximation results in the appearance of unphysical centroids which are nowhere near the wave packet itself.