Given a decorated planar graph $(G,ω)$, where $G$ is a planar graph and $ω\in H^1(|\mathcal{Q}G|,\mathbb{Z})$ with $\mathcal{Q}G$ the directed medial graph of $G$, we call some angular functions $ω$-compatible and study two distinct but related directed graphs: $\mathcal{L}(G,ω)$, which is the directed graph of such functions, and $BMS(G,ω)$, the directed graph of BMS states which are some pairs of $ω$-compatible functions plus additional data. We give sufficient conditions for $\mathcal{L}(G,ω)$ to be a graded distributive lattice, recovering Kauffman's Clock Theorem when $G$ is a knot diagram. We also define a potential on $\mathcal{Q} G$ and associate a representation of the corresponding quiver with potential to every BMS state. Under suitable assumptions, this construction yields an isomorphism between $\mathcal{L}(G,ω)$ and the lattice of subrepresentations of a maximal representation, generalizing a result of Bazier-Matte--Schiffler.

The \textsc{Co-Path Packing} (resp., \textsc{Co-Path Set}) problem asks whether a given graph can be edited to a collection of induced paths by deleting at most $k$ vertices (resp., $k$ edges). Both are fundamental problems with significant applications in bioinformatics and have been extensively studied within the framework of exact and parameterized algorithms. Currently, the state-of-the-art approach utilizes the randomized ``Cut \& Count'' technique, which solves \textsc{Co-Path Set} in $O^*(4^{\mathbf{tw}})$ time and \textsc{Co-Path Packing} in $O^*(5^{\mathbf{pw}})$ time, where $\mathbf{tw}$ is treewidth and $\mathbf{pw}$ is pathwidth. However, as there is no known method to derandomize the ``Cut \& Count'' technique, the existence of deterministic single exponential time algorithms for these problems parameterized by treewidth has remained an open question. In this paper, we resolve this gap by providing deterministic single exponential time algorithms for both problems when parameterized by treewidth.

Network Intrusion Detection System is a critical means of ensuring cybersecurity. However, existing Genetic Algorithm-based feature selection methods face several limitations when dealing with high-dimensional redundant traffic features. For example, population diversity is difficult to maintain, and evolutionary operators lack guidance. To solve these problems, this study proposes the Multi-Population Diversity-Guided Genetic Algorithm (MPDGGA). First, we build a chained multi-population evolutionary structure. Second, we introduce a diversity-guided operator based on information gain ratio. Experiments on NSL-KDD, UNSW-NB15, and 9 UCI datasets show that the proposed model significantly outperforms four other advanced multi-population feature selection models. Across the 11 datasets, it attains the highest accuracy on 10 datasets and at least 2.26% of the features were selected.

With the increasing precision of asteroseismic observations, it becomes possible to reliably measure oscillation properties of an increasing number of stars. Interpreting these measurements requires a good theoretical understanding of their link to fundamental stellar properties. In this study, we focus on the phase offset in gravity(g)-mode frequencies, which is imprinted in the asymptotic eigenfrequency pattern of mixed dipole modes observed in red--giant branch stars. We aim to unravel its physical origin and thus enable an informed interpretation of observations. Using stellar models, we empirically test the contribution of the g-mode offset $\varepsilon_\mathrm{g}$ (which is related to the wave reflection at cavity boundaries and commonly considered to be the dominant phase term) and glitches to the total observable phase. We find that, additionally to $\varepsilon_\mathrm{g}$, buoyancy glitches play an important role in the correct interpretation of the g--mode frequency phase. We further find that glitches in the evanescent zone also contribute to the phase, and we present a formalism to quantify this contribution. Finally, we propose a modification to the widely used formula for $\varepsilon_\mathrm{g}$. The g--mode frequency phase carries more information than previously considered. It has large analytic potential to study not only the reflection properties of the buoyancy cavity, but also the properties of glitches in the Brunt-Väisälä frequency.

Stationary subspace analysis (SSA) is a blind source separation framework that decomposes linearly mixed multivariate data into stationary and nonstationary components. We extend SSA to spatially indexed data by introducing spatial stationary subspace analysis (spSSA), which explicitly accounts for spatial dependence. We propose three estimation procedures for the unmixing matrix based on first- and second-order spatial statistics. Each procedure targets a different type of nonstationarity and can be formulated as the solution to a generalized eigenvalue problem. To address situations where multiple forms of nonstationarity are present simultaneously, we combine the three procedures using approximate joint diagonalization. Simulation studies demonstrate that this combined approach yields superior separation performance. When the dimension of the nonstationary subspace is known, the proposed methods reliably recover the latent stationary and nonstationary components. However, determining this dimension remains a fundamental challenge in SSA, for which no generally accepted solution currently exists. Building on our estimation procedures, we propose a novel data augmentation approach to estimate the dimension of the nonstationary subspace and demonstrate its effectiveness through simulation studies. The proposed methodology is easily transferable to time series settings, making it of broader methodological interest.

We present an accelerated ``on-the-fly'' coupled-cluster path-integral molecular dynamics (PIMD) method for finite-temperature simulations in which electron correlation and nuclear quantum effects are treated simultaneously. The approach is based on our quantum ring-polymer contraction (qRPC) technique, in which the inexpensive Hartree-Fock potential is evaluated on the full ring-polymer, while the expensive coupled-cluster correction is evaluated on the centroid only. This qRPC decomposition is combined with a second-generation Car-Parrinello-like dynamics of the Hartree-Fock reference and a basis-consistent extrapolation of the coupled-cluster and de-excitation amplitudes. The combination of all three acceleration layers is essential for making correlated PIMD calculations feasible. We apply the method to a proton shared by water and formaldehyde. Relative to classical nuclei, nuclear quantum effects broaden covalent X--H bond-length distributions, reduce the bias of the shared proton toward formaldehyde, and shift the mean proton-transfer coordinate from 0.206 to 0.135A. The probability of finding the proton closer to formaldehyde decreases from 81.7$\%$ to 61.1$\%$. The corresponding nuclear magnetic shielding tensors show that electron correlation and nuclear quantum effects are of comparable magnitude and can act in opposite directions. These results demonstrate that predictive simulations of asymmetric hydrogen bonds require a simultaneous treatment of correlated electronic structure and nuclear quantum fluctuations.

A linear code is said to be $Δ$-divisible if the Hamming weights of all its codewords are divisible by $Δ$. The $p$-adic valuation of a code is defined as the greatest integer $t$ such that the code is $p^t$-divisible. In this paper, we establish a divisibility criterion for trace codes. Specifically, this criterion provides a systematic method to determine the $p$-adic valuation of the associated trace code, thereby extending Ward's classical divisibility criterion from standard generating sets (or matrices) to generalized generator matrices over an extension field. Furthermore, we present two applications of our framework. The first application provides a concise proof of the celebrated divisibility results on abelian codes established by Delsarte and McEliece. The second application establishes several explicit lower bounds on the $p$-adic valuation of the number of solutions over $\mathbb{F}_{q^m}$ (where $q = p^e$) to the Artin-Schreier type equation $ f(x_1,\ldots,x_k)=y^q-y $. In particular, under the condition $\left(d,\frac{q^m-1}{q-1}\right)=1$, we determine the exact minimum $p$-adic valuation of the number of solutions when $f$ is restricted to homogeneous polynomials of degree $d$.

Quantum computers are emerging as a promising new technology due to their ability to solve complex problems that exceed the capabilities of classical systems in terms of time. Among various implementations, superconducting qubits have become the leading technology due to their scalability and compatibility with quantum error correction mechanisms. Although time has traditionally been the primary focus, energetic efficiency is becoming an increasingly important consideration, especially with the possibility of a quantum energetic advantage. In this article, the energy consumption of the Semiclassical Quantum Fourier Transform was analyzed on a superconducting quantum computing platform based on cat qubits. Quantum error correction mechanisms were studied and considered in the energy estimations. The results show how the energy consumption scales with the number of qubits and how the most relevant parameters required for qubit stabilization, gate implementation, and error correction codes contribute to the overall energy usage. An optimization method was developed to tune these parameters with the goal of minimizing energy consumption while maintaining qubit fidelities above a given threshold. Additionally, a comparative study with state-of-the-art classical computers indicates a potential quantum energetic advantage for systems with more than 26 qubits, assuming cryogenic systems operating at Carnot efficiency, with this energetic advantage arising before any computational advantage. This behavior persists even when realistic cryogenic systems and control electronics are taken into account.

The \textsc{$l$-Exact Component Order Connectivity} problem asks whether, given an input graph $G$ and an integer $k$, there exists a vertex subset $S\subseteq V(G)$ of size at most $k$ such that every connected component in $G - S$ has exactly $l$ vertices. In this paper, we present an $O(kl)$-vertex kernel for this problem, computable in $|V(G)|^{O(l)}$ time. This is the first known linear kernel for each fixed $l\geq 3$. For $l=1$, this problem reduces to the classical \textsc{Vertex Cover}, and our result matches the best-known $2k$-vertex kernel. For $l=2$ (known as \textsc{Deletion to Induced Matching}), we can get a $(3k + 1)$-vertex kernel, improving the previously known result of $6k$ vertices. Our kernelization algorithm is built upon on an extended crown decomposition combined with linear programming and other techniques.

Multi-photon dressing and interference in atomic systems is a key to several cutting edge technologies like Rydberg atom radio frequency sensors, clocks and magnetometers because it enables the engineering of atomic properties. Rydberg atom sensors are attracting significant interest because they can be used for applications where it is difficult or impossible to use conventional antennas, opening a number of new opportunities in fields like communications, test and measurement and radar. To date, radio frequency field amplitude detection is well-established in Rydberg electrometry. Phase detection, which is crucial for encoding radio frequency signals, typically requires an external heterodyning field or an atomic closed-loop interferometer. The heterodyne method compromises the intrinsic transparency of the sensor to the radio frequency wave and its inherently broad carrier bandwidth, in addition to increasing its complexity by introducing a local oscillator. In prior theoretical work, aimed at overcoming the disadvantages of the heterodyne method, we theoretically investigated the possibility of using the oscillatory dynamics of an all-optical five-level closed loop to sense the phase and amplitude of the target radio frequency fields. In this work, we experimentally demonstrate the scheme. We determine the coherence time of the loop to be on the order of ms and show that in-phase and quadrature signals can be extracted from a radio frequency signal.

We characterise position-error behaviour of Two-Line Element (TLE) propagation against operator-updated truth on Starlink, sweeping 24,641 next-TLE-truth pairs across 501 satellites stratified by altitude shell (540, 550, 560 km) and platform generation (v1.0, v1.5, v2-mini) over April 2026. Each pair is propagated with SGP4 and GMAT at high fidelity (EGM2008 $70\times70$, NRLMSISE-00 drag, Sun and Moon third-body gravity, conical-shadow SRP), then compared against the operator's next TLE as proxy truth. Three findings: First, position error follows a per-cell power law $\lVertΔ\mathbf{r}(Δt)\rVert \approx A\,Δt^{k}$ with fitted exponents in $(1,2)$ on every v2-mini cell and on the high-fidelity v1.x cells at 540 and 560 km, while SGP4 v1.x and high-fidelity v1.x at 550 km are sub-linear ($k \lesssim 1$); the cohort-specific mix of mean-motion bias and unmodelled in-track acceleration sets the per-cell exponent. Pooled $L_{2}$ medians grow from $\sim 1$ km at 6 h to $\sim 38$ km (SGP4) / $\sim 76$ km (high-fid) at 7 d. Second, high-fidelity propagation from public-TLE inputs does not improve over SGP4 at any of the four staleness horizons; SGP4 wins on $\sim 65$--$75\%$ of pairs, with v2-mini at long $Δt$ the one regime where high-fidelity wins on a majority of pairs at both populated shells. The negative result reflects operator-OD residual dominance at epoch, SGP4-vs-SGP4 truth-construction kernel alignment, and spacecraft-property bias amplification on the high-fidelity arm. Third, the per-satellite SGP4 staleness coefficient regressed against F10.7 returns a positive slope clearing conventional significance at one shell (560 km) on the 30-day, $\sim 17$ sfu window -- direction-consistent with the LEO density-gradient expectation, not a calibrated F10.7-modulation measurement.

Deep learning (DL) has been widely used in future 6G physical layer communications, but task-specific DL models are difficult to generalize across different physical layer tasks. Recently emerging wireless foundation models demonstrate strong generalization capability. However, existing methods mainly adapt pretrained language/vision models or rely on CSI reconstruction objectives for pretraining, with limited use of channel knowledge, and thus have limited performance. To address this limitation, we propose SPA-MAE, a physics-guided wireless foundation model by exploiting the adapted MAE backbone and channel knowledge. A physical prior module is developed to provide two complementary guidance signals in the pretraining stage. Specifically, the parameter-aware guidance branch extracts features from explicit multipath parameters and encourages the encoder output to align them, while the structure-aware guidance branch encourages the encoder to capture the sparse transformed-domain CSI structure obtained after a 2D FFT. After end-to-end learning, the MAE encoder will be retained for downstream tasks. Experiments on four wireless tasks show that SPA-MAE outperforms state-of-the-art CSI foundation models with smaller number of parameters, especially under low-SNR and limited-data conditions.

Percolation of fine particles (fines) in a static bed of larger particles is central to many industrial and natural processes. Non-cohesive fines either pass through the bed or become trapped depending on multiple factors including particle sizes, friction and restitution coefficients, and size-polydispersity. Here we consider the additional factor of cohesion. We use the discrete element method to simulate gravity-driven percolation of cohesive fine particles through a static bed of randomly packed large particles; fines interact with bed particles but not with each other. A large-to-fine particle diameter ratio of 7 geometrically permits non-cohesive fines to pass the narrowest pore throats formed by the large particles so they can freely percolate. However, sufficiently large cohesion and friction lead to non-geometric trapping. Fines are trapped when they fail to rebound after a collision, due to large cohesion, low restitution, and low collision velocity, and any subsequent rolling or sliding is insufficient to cause detachment. This establishes a sequence of local interactions -- collision, adhesion, and post-contact motion -- that governs the ultimate fate of a fine particle. A collisional model that incorporates a trapping probability per collision and a collision frequency predicts the trapping distance in the regime dominated by collision-induced trapping. For non-rebounding collisions, frictional effects are enhanced by cohesion and, when large enough, prevent the fine particle from subsequently detaching. A static equilibrium condition based on force balance predicts whether a fine particle remains stationary after contact. These results show that percolation of cohesive fine particles is not determined by geometric accessibility alone, but also by particle-scale interaction dynamics that can override geometric expectations.

Let $G$ be a group and $N$ its normal subgroup. On the mixed commutator subgroup $[G,N]$, the mixed stable commutator length $\mathrm{scl}_{G,N}$ and the restriction of the ordinary stable commutator length $\mathrm{scl}_{G}$ are defined. We characterize when they are bi-Lipschitz equivalent by the vanishing of a certain $\mathbb{R}$-linear space $\mathrm{W}(G,N)$ related to invariant quasimorphisms. For the proof, we obtain a refined version of the generalized mixed Bavard duality theorem, and perform functional analysis on the completion of a certain space of $1$-chains.

We investigate a dark energy model driven by a planar domain-wall-like structure with a thickness comparable to, or larger than, the current Hubble radius, focusing on its intrinsic anisotropy and observational viability. Near the centre of the domain wall (DW), the spacetime is anisotropic, with distinct expansion rates parallel and perpendicular to the wall. This anisotropic structure induces direction-dependent cosmic expansion and modifies photon geodesics from cosmological sources, leaving characteristic signatures in cosmological observables. We confront the model with recent observational data. We first compute the anisotropic Cosmic Microwave Background (CMB) temperature multipoles generated by the DW and impose constraints from the Planck 2018 measurements. These constraints severely limit the allowed DW abundance, requiring the DW energy density to be less than $\mathcal{O}(10^{-5})$ of the current critical density in order to suppress the quadrupole contributions. We then perform a Markov Chain Monte Carlo (MCMC) analysis using Type Ia supernova (SNe Ia) data, including the Pantheon+ SH0ES and DESY5 samples, to compare the DW scenario with the standard $Λ$CDM model. We find that although the DW naturally realises anisotropic accelerated expansion, the combined constraints from the CMB and SNe Ia favour the $Λ$CDM limit, in which the DW contribution is negligible, and the universe is effectively isotropic. Our results demonstrate that a Hubble-scale domain wall is tightly constrained by current observations and can only play a subdominant role in the late-time cosmic acceleration.

Agentic AI has taken on the role of assistant, collaborator, and decision-support tool. We argue the next role on that list is more personal: you. These are digital twins of each individual -- twin agents -- representing their knowledge, perspective, and communicative style to colleagues when they are unavailable. Drawing on early design work in an ongoing project in which agents represent knowledge workers in a professional setting, we identify a trust calibration problem specific to this approach. When a human colleague doubts a twin agent's output, they face three failure modes (a schema gap, an epistemic gap, and a model artifact) with no reliable attribution path between them. Cognitive forcing functions and related frameworks address overreliance effectively in contexts where there is a clear boundary between the AI and the human decision-maker. However, twin agents dissolve that boundary, raising a class of trust calibration challenge these frameworks were not designed to handle. We introduce the concept, distinguish it from digital twins, and outline the research questions this new class of agent demands.

In this paper, we introduce and study the notion of $n$-ary S-hyperideals in a Krasner $(m,n)$-hyperring

The SIRS process is a continuous-time process for how infections spread on a graph. In this model, each vertex is in one of the following three states: susceptible (to the infection; S), infected (I), or recovered (R) and thus immune to the infection. For each vertex, the transition among these states is exponentially distributed according to the parameters of the process. It was recently shown that recovered vertices effectively stop the infection on stars, that is, the expected survival time of SIRS processes on stars is bounded from above by a polynomial in the number of the vertices, independently of the infection rate of the process. The setting where the process has, so far, been shown to exhibit epidemic behavior, i.e., super-polynomial survival time when the infection rate is above some threshold value, requires the host graph to be an expander. This is in contrast to the shown behavior of the well-studied SIS process, a related model in which vertices never transition to R, and in which even sparsely connected graphs, in particular stars, exhibit epidemic behavior. In this work, we show that expansion of the host graph is not a necessary condition for the SIRS process to result in an epidemic. Our main technical contribution shows that, while the SIRS process does not survive super-polynomially long on a single star, it does so on a network of poly-logarithmic (in the total number of vertices) stars of polynomial size. In addition, we show that such substructures appear in popular complex network models, providing for each a bound on the epidemic threshold. In particular, on hyperbolic random graphs, we compare our threshold for connected stars with the previously known one based on expansion, finding that both of them can be more permissive depending on the graph's power-law exponent and the rate that determines how long immunity lasts.

Human-AI collaboration research has largely positioned the human as a judge of AI output, centering effort on evaluating whether rec- ommendations are reliable enough to accept. This decision-support framing leaves little room for the human as creator. We argue that for creative work, this framing misdirects human effort toward eval- uating correctness rather than exploring and shaping the creative space. Drawing on Schön's theory of reflective practice, we propose an alternative: treating generative AI as an active creative medium. As a potter works with clay, humans Shape, Observe, Stir, and Se- lect (SOSS) their medium through ongoing conversation. Where generative AI actively tends toward convergence and resolution, the human role of disruption and curation becomes essential for sustaining creative quality. We present a creative writing probe, Loom, in which users orchestrate simulated narrative agents. We also introduce the SOSS framework for this mode of engagement, and discuss design implications.

We report the ground-state entropy of a 2-d Ising model on the Shastry-Sutherland lattice. We also study a generalization of this model, where a constraint on the zero temperature allowed configurations is removed continuously.

Motivated by their relevance to the interior of nonrotating black holes, classical and quantum Kantowski-Sachs cosmologies have recently attracted increasing attention. This interest has led to the development of a Hamiltonian formalism for axial and polar perturbations, which can be extended to applications in the exterior region. The formalism provides also a description of the background physical degrees of freedom. Moreover, it allows for the construction of all physical perturbative gauge invariants, which can be arranged into canonical pairs associated with master functions. In this work, we review the basis of this Hamiltonian formalism, putting the emphasis on its foundations and fundamental steps rather than on details of the involved calculations. Our discussion focuses on classical and effective aspects, although we also briefly comment on its natural role in the quantization of perturbed black holes. Adopting this formalism we present a geometric interpretation of Darboux transformations between pairs of master functions, characterizing them as generalized canonical transformations that preserve the Hamiltonian structure of the perturbations as harmonic oscillators subject to certain potentials. This bijective correspondence between such canonical transformations and Darboux transformations, which was recently proved to hold for axial perturbations, is here extended to the case of polar perturbations. In addition, we demonstrate the existence of canonical transformations that, similarly to Darboux transformations, mix axial and polar master functions.

We study projection-free optimization for convex objectives that satisfy abs-smoothness, a structural property that captures many non-smooth yet piecewise smooth functions arising, e.g., in modern machine learning models. We develop a unified framework for Abs-Smooth Frank-Wolfe methods, establishing a clean primal-dual analysis that guarantees convergence without requiring classical smoothness assumptions. Our framework extends the available results in two important directions. First, we introduce a heavy ball momentum variant and show that momentum can be incorporated naturally under abs-smoothness while preserving convergence guarantees. Second, we analyze inexact minimization oracles, demonstrating robustness to approximate inner solutions. Moreover, we relax the full convexity assumption and study the case where convexity holds only for the piecewise linear approximations of the objective, further broadening the applicability of conditional gradient methods to a wider class of non-smooth problems.

Variational quantum algorithms (VQAs) for combinatorial optimization routinely employ entangling gates as a default design choice, yet the role of entanglement, in its amount and structure, remains poorly understood. This gap is particularly consequential for problems governed by diagonal Hamiltonians, whose ground states are classical product states and therefore require no entanglement in principle, raising the fundamental question of whether and how entangling gates help or hinder the variational search. We investigate this question for MaxCut by introducing two complementary control mechanisms that provide smooth, monotonic control over hardware-efficient ansatz (HEA) entanglement as quantified by the Meyer-Wallach measure $Q$, and by benchmarking against QAOA as a problem-structured reference. Tracking the entanglement trajectory $Q(t)$ throughout VQA training reveals that when the ansatz grants the optimizer indirect control over entanglement through its parameters, it consistently drives entanglement down. In line with this tendency, a fully separable ansatz outperforms all entangled hardware-efficient configurations, establishing a monotonic relationship: less problem-agnostic entanglement yields better performance. In contrast, QAOA, whose entanglement is structurally derived from the problem Hamiltonian, maintains high entanglement yet achieves competitive solution quality, demonstrating that entanglement structure, not merely quantity, determines its utility. These findings suggest that HEAs for diagonal Hamiltonians are inappropriate and that variational approaches to combinatorial optimization should prioritize problem-structured circuit designs.

Primordial Black Holes (PBHs) forming prior to Big Bang Nucleosynthesis evolve during the reheating epoch, an environment dominated by an oscillating inflaton field decaying into a relativistic thermal bath. In this work, we track the complete lifecycle of PBHs within this coupled inflaton-radiation background. Utilizing $α$-attractor E-models, we analytically anchor the reheating initial conditions directly to Cosmic Microwave Background observations. By matching exact scalar field solutions in a Schwarzschild spacetime to the cosmological far-zone, we derive the cycle-averaged mass accretion rate and couple it to the growing radiation bath. We find that this combined accretion induces a highly non-linear enhancement of the final PBH mass. Because the Hawking evaporation timescale scales cubically with mass, PBHs forming near their critical runaway limits experience a massive extension of their lifespans. Surviving deeper into the radiation-dominated era triggers a multi-order-of-magnitude amplification in their emitted Stochastic Gravitational Wave Background (SGWB).

Quantum geometry characterizes the variation of wavefunctions in momentum space through their overlaps and relative phases, providing a general framework for understanding many transport and optical properties. It is generally formulated in terms of interband matrix elements, which, entering the response functions, allow obtaining experimental access to the quantum geometric tensor. Recently, it has been emphasized that quantum geometry can also be interpreted in terms of quantum dipole fluctuations in the ground state driven by interband mixing. Here, we extend this picture to include contributions from many-body collective fluctuations, in which propagators and response vertices are dressed dynamically by the interaction with collective modes. Focusing on the Berry curvature, we show that contributions from collective fluctuations can be experimentally distinguished from bare band-geometric contributions, via specific antisymmetric channels in inelastic scattering spectra. We further identify the non-commutative properties of transverse quantum fluctuations as well as non-local-time interactions as the generators of this dynamical curvature in the susceptibility response.

We study the satisfiability problem for a modal logic expressing knowing-how assertions, which captures an agent's ability to achieve a given goal under the standard semantics based on linear plans. Our main result shows that satisfiability of knowing-how formulas is NP-complete, improving previously known complexity bounds. The proof proceeds via a translation into modal logic S5, an instrumental tool for addressing a variety of problems in knowledge representation.

We prove that compact non-flat manifolds with constant sectional curvature admit no conformal product structure. Furthermore, we demonstrate that the methods extend naturally to irreducible, compact locally symmetric spaces of non-positive curvature.

Based on quantum field theory of linearized gravity, we formulate the Wigner function for right- and left-handed gravitons. By applying the Wigner transformation to the second-order metric perturbations in the graviton energy-momentum tensor obtained from the Einstein-Hilbert action, we demonstrate the emergence of the spin Hall effect of gravitons in curved spacetime. This effect originates from the Berry curvature of gravitons, which has opposite signs for right- and left-handed helicities, and leads to a helicity-dependent splitting of the graviton energy Hall current. The magnitude of this splitting is found to be exactly twice that of the corresponding spin Hall current for photons.

Purpose: To investigate psychophysically the ability of low vision individuals with central visual field loss (CFL) to perform a visually-guided pointing task in a virtual reality environment. Methods: Patients with CFL (n=25, ages = 67-90 years) and normally-sighted controls (n=26, ages = 67-85 years) had to select a target (2{\textdegree} diameter dot) with a head-contingent cursor (6{\textdegree} diameter reticle). Target selection occurred when target was validly pointed at for 1.5 seconds. Pointing was valid when target was inside an invisible pointer activation zone (PAZ) centered on reticle. Task difficulty was decreased by increasing PAZ diameter from 0.5{\textdegree} to 8{\textdegree}. Performance was assessed by measuring the time needed to select the target. The task was also performed with an array of three simultaneously-displayed cursors. Results: Selection times decreased (from 14.1 and 8.4 seconds for patients and controls respectively) with increasing PAZ diameter and reached a similar asymptote for both groups (1.4 seconds). The rate of this decrease was smaller for patients so that PAZ diameter needed for their best performance was much larger than PAZ diameter needed for controls' best performance (average: 3.48{\textdegree} vs 1.32{\textdegree}). In the three-reticle condition, both groups tended to use the cursor closer to the target. Conclusions: Patients with CFL are able to point at a 2{\textdegree} target thanks to head-pointing. Their performance can get close to controls' best performance by increasing PAZ size. Translational relevance: This research suggests guidelines to improve the accessibility of visually-guided pointing tools for human-machine interfaces designed for low vision individuals.

The preservation of witness beam polarization in wakefield accelerators will be crucial for future collider applications. While extensive theoretical studies on the injection and initial acceleration of polarized electrons exist, a study concerning higher-energy regimes has been neglected thus far. Besides the spin precession usually considered in wakefield-related research, radiative effects could become increasingly relevant at higher energies as the witness electrons perform betatron oscillations during which they will emit photons. In the present study, we use particle-in-cell simulations extended with Monte-Carlo routines to study the influence of radiative spin-flips on beam polarization. We find that at high energies, the importance of radiative effects on beam polarization mainly comes down to the alignment of the witness beam with respect to the wakefield.