Collateralized prediction markets are contingent-claim markets in which economic uncertainty can disappear before winning claims become redeemable. This paper studies the pricing effect of that delay. When collateral remains locked until oracle settlement, a near-certain dollar is a delayed dollar, so prices embed a maturity-dependent settlement discount in addition to beliefs about outcomes. We recover an implied settlement-discount term structure from persistent near-certain contracts using realized settlement times and summarize it as an annualized settlement wedge (ASW). The recovered wedges are positive, maturity-dependent, and time-varying. Adjusting pricesby these curves reduces the near-certainty horizon gradient by roughly 48-88%, indicating that much of the raw maturity pattern reflects priced settlement frictions rather than forecast error alone. Market architecture changes the wedge: negRisk conversion compresses discounts by recycling part of the position into synthetic collateral, while yield-bearing collateral flattens the term structure by reducing the opportunity cost of lock-up. The results show that pricing quality in prediction markets is endogenous to settlement mechanics, collateral productivity, and capital-recycling design. Prediction-market prices therefore aggregate information through a financial infrastructure whose funding conditions are measurable and economically important.

The spectral density estimation problem asks for an algorithm that, given an $n\times n$ matrix $A$, outputs a probability measure that is a good approximation to the uniform distribution on the eigenvalues of $A$, called the spectral density of $A$. This paper considers the setting where $A$ is a large normal matrix that is accessible only through matrix-vector product queries. We provide an algorithm that makes just $m$ matrix-vector queries to $A$ and returns, with high probability, a measure within earth mover's distance $O(1/m+\log m/{\sqrt n})$ of the true spectral density of $A$. We provide a complementary lower bound that any algorithm producing an $\varepsilon$-approximation to the true spectral density for large matrices must make $Ω(1/\varepsilon)$ matrix-vector queries. The lower bound holds even for the more restricted case of real symmetric input matrices. In combination with our upper bound, it shows that spectral density estimation is essentially no harder for complex normal matrices than for real symmetric matrices.

Extreme ultraviolet (XUV) radiation plays a central role in a wide range of applications. Despite being a cornerstone of attosecond science, efficient XUV generation remains highly challenging. Here, we investigate XUV generation via nonlinear Thomson scattering driven by a toroidal pulse. Unlike conventional laser pulses, toroidal pulses possess intrinsically non-separable spatiotemporal field distributions. This unique field structure produces strongly asymmetric electron acceleration, resulting in substantially enhanced XUV emission that is 2-4 orders of magnitude stronger than that generated by a Gaussian pulse. Our results identify toroidal pulses as a promising route toward compact ultrafast XUV sources and advanced strong-field light-matter interaction studies.

A mixed-precision GPU-oriented optimization framework is developed for computing the minimum enclosing ball of a collection of balls. The approach is built on an equivalent second-order cone programming reformulation and a relative-type inexact proximal augmented Lagrangian method (ripALM), which provides a high-accuracy optimization backbone while solving the inner subproblems only to a progress-dependent relative accuracy. The proximal augmented Lagrangian inherits a constraint-wise separable structure: its objective, gradient, generalized Hessian, and multiplier updates can be efficiently evaluated on GPUs as parallel maps over the input balls followed by reductions. To further improve efficiency, a mixed-precision reduction strategy is introduced. A low-precision ripALM run identifies balls near the approximate boundary, a high-precision ripALM run refines the reduced problem, and a full a posteriori feasibility check detects and reintroduces any violated discarded balls. Thus, low precision is used only for screening and warm starting, while the final feasibility is enforced against the original problem. Numerical experiments show that ripALM and mixed-precision ripALM achieve high accuracy and are substantially faster than the tested CPU-based geometric software and general-purpose conic solvers on large-scale instances.

We present CJ26, the new CTEQ-JLab global QCD analysis that incorporates for the first time the complete suite of JLab 6 GeV DIS measurements and the first published JLab 12 GeV measurements. Focused on the large-$x$ region, the analysis utilizes the increased $Q^2$ leverage of the 12 GeV data to uniquely disentangle higher-twist effects from off-shell nucleon corrections. This leads to a highly accurate determination of the $n/p$ structure function ratio and the $d/u$ valence quark ratio, with uncertainties reduced by 30-50% and 5-10%, respectively. We highlight the critical role of experimental correlated systematic uncertainties in achieving this precision and provide the resulting NLO PDFs and structure functions in LHAPDF format for general use.

We introduce the framework of cotangent buildings to complement and refine that of Weinstein handlebodies. While Weinstein handlebodies are suitable for a ``bottom-up" analysis of the Weinstein structure, cotangent buildings also enable a ``top down" analysis. Further, cotangent buildings include a precise control over the interaction of any subcollection of the various building blocks, each of which is modeled on the cotangent bundle of a manifold with corners. Our main result is that any Weinstein manifold is Weinstein homotopic to one admitting the structure of a cotangent building.

In this third study of the series, we extend our U-Net Variational Autoencoder-based galaxy classification framework to a significantly larger JWST sample spanning the redshift range $0.5 < z < 4$. Focusing on massive systems with stellar masses exceeding $10^{10}\,M_\odot$, we analyze 1,380 galaxies that satisfy these criteria and apply our previously developed denoising and classification pipeline to identify disk-like morphologies across cosmic time. Within this population, our classifier detects 382 disk-like galaxies, with a subset showing uncertain features consistent with the expected performance limits of current deep-learning models. This expanded dataset allows us to examine the distribution of disk-like systems in a statistically meaningful high-redshift regime, including epochs where well-ordered disks are traditionally expected to be rare. The results demonstrate that disk-like structures persist across a broad range of redshifts and stellar masses, suggesting that massive disks may be more common in the early universe than previously assumed. These findings emphasize the value of combining advanced denoising techniques with machine-learning-based morphological analysis for characterizing galaxy populations in large JWST surveys.

In complex media, transport and geometric properties deeply influence the kinetics of random encounters between reactants. Here, we consider the situation where a random walker, moving in a regularly diffusing medium, has to reach and activate a target located inside a compartment characterized by fractal (obstructed) sub-diffusion. We focus on dual-site reactions, which end when two activation events occur within a given time window. Each activation event happens with a finite probability whenever the random walker visits the target. For weakly reactive targets, we demonstrate that the reaction time can be minimized for an optimal compartment size and can even be accelerated when compared to the same system without compartment. Our analytical predictions are validated through simulations of a random walker on a cubic lattice, where some sites inside the compartment are obstructed at the critical percolation threshold. Our theory illustrates the fact that adding a crowded compartment around a target, even if it slows down the motion in its vicinity, can accelerate the kinetics of complex reactions, especially for weakly reactive targets.

We revisit the Binary Closest String problem, which asks, given a set of binary strings $X \subseteq \{0, 1\}^n$, to compute a string minimizing the maximum Hamming distance to $X$. A long line of work has focused on parameterized algorithms with respect to the optimal distance $d$, yielding a sequence of improvements from $O^*(d^d)$ through $O^*(16^d)$, $O^*(9.513^d)$, $O^*(8^d)$, $O^*(6.731^d)$ to the current best-known running time of $O^*(5^d)$ [Chen, Ma, Wang; Algorithmica '16]. We present a faster randomized algorithm running in time $O^*(4^d)$. Our result matches a recent fine-grained lower bound [Abboud, Fischer, Goldenberg, Karthik C.S., Safier; ESA '23], and is therefore conditionally optimal. As an extra benefit, our algorithm is remarkably simple.

We present the evolution of galaxy size and surface brightness in the rest-frame $J$ band (1.22 $μ$m), tracing the stellar mass distribution, over $0.5 \leq z \leq 3$, using a sample of 15,420 galaxies with stellar masses $M_\star=10^{10}$-$10^{11.5}\ M_{\odot}$ from the JWST COSMOS-Web survey. The rest-frame $J$-band effective radius ($R_{e,J}$) is obtained from previous measurements and mapped from the available JWST/NIRCam filters, while the surface brightness ($μ_J$) is corrected for dust extinction and cosmological dimming. At a characteristic mass of $M_\star = 5 \times 10^{10}\ M_{\odot}$, star-forming galaxies exhibit a size evolution of $R_{e,J} \propto (1+z)^β$ with $β= -0.92 \pm 0.04$, falling between previously reported shallower and steeper measurements. Quiescent galaxies evolve more rapidly, with $β= -1.34 \pm 0.05$, consistent with earlier studies. Among star-forming galaxies, lower-mass systems ($10^{10}$ to $10^{10.5}\ M_{\odot}$) show slower ($β=-0.66\pm0.02$) size evolution compared to their higher-mass counterparts. Furthermore, the surface brightness brightens toward higher redshifts, scaling as $μ_J \propto -2.5 \log(1+z)^γ$. We find $γ= 3.07 \pm 0.08$ for star-forming galaxies and $γ= 3.70 \pm 0.08$ for quiescent galaxies. We also find that massive star-forming galaxies ($M_\star > 10^{10.5}\ M_{\odot}$) exhibit similar $μ_J$ values at fixed redshift, independent of mass. Finally, we demonstrate that the observed surface brightness evolution is driven by the combined evolution of galaxy luminosity and size.

Collaborative filtering (CF) is widely used in recommender systems (RecSys) due to its simplicity and efficiency. However, existing CF methods follow an instance-level learning paradigm. During the instance learning stage, a large number of uninteracted user-item instances, of which items are potential interested by the user, are incorrectly treated as true negative samples resulting in a severe limitation to the generalization and scalability of models. Moreover, mainstream graph convolutional networks (GCNs) inherently suffer from high computational cost and over-smoothing issues, which limit the ability in capturing higher-order connectivity and lead to a poor generalization under sparse supervision signals. To address the above limitations, we propose Semantic Factor enhanced Alignment and Uniformity (SaFeAU), a novel framework that augments interacted instances with semantic factors, thereby mitigating false negative labeling and enabling matrix factorization (MF) to capture high-order CF signals without graph neighborhood aggregation. Specifically, SaFeAU consists of three tightly coupled components. First, Semantic Factor Routing (SFR) disentangles item representations into independent and global semantic factors. Building on these factors, Semantic Factor Matching (SFM) identifies uninteracted items, which share the same semantic factors with interacted ones, as potential positive pairs for enriching sparse supervision signals. Finally, Semantic Pairs Alignment (SPA) aligns both observed and potential positive pairs while promoting uniformity of user and item representations. Extensive experiments on four sparse real-world datasets show that SaFeAU consistently outperforms GCN-based and MF-based state-of-the-art CF methods in both recommendation accuracy and computational efficiency, confirming the effectiveness of the proposed semantic enhanced learning paradigm.

Although globally-integrated studies often find that, at fixed stellar mass, high star formation rate (SFR) galaxies are relatively metal-poor while lower-SFR systems are more metal-rich, the corresponding coupling between gas-phase metallicity ($Z_{\rm gas}$) and star formation on sub-galactic scales remains poorly constrained. In this study, we analyse 14 Virgo spirals from the MAUVE-MUSE survey to revisit the resolved mass-metallicity relation (rMZR) and its secondary dependence on SFR surface density ($Σ_\mathrm{SFR}$) at $\sim 100$\,pc scales. We construct co-spatial maps of stellar mass surface density ($Σ_*$), $Σ_\mathrm{SFR}$, and oxygen abundance. MAUVE-MUSE galaxies follow a standard rMZR, but when binned by $Σ_*$, we find a mass-dependent inversion in the $Z_\mathrm{gas}$-$Σ_\mathrm{SFR}$ relation using O3N2 calibrations: the standard anti-correlation is confined to low-$Σ_*$ bins, while high-$Σ_*$ regions show a positive correlation, inverting at $\log_{10}(Σ_*/M_\odot\,\mathrm{kpc}^{-2})\simeq 7.5$-8.0. Correlated and anti-correlated \ion{H}{ii} regions coexist within the same discs; the mass dependence emerges only when grouping spaxels by $Σ_*$. We develop a spatially resolved gas-regulator model showing this $Z_\mathrm{gas}$-$Σ_\mathrm{SFR}$ (anti-)correlation arises from competition between star-formation-driven and gas-supply-driven variability. This framework naturally extrapolates to the integrated scenario, providing a unified explanation for resolved and global relations. However, the presence and strength of the $Z_\mathrm{gas}$-$Σ_\mathrm{SFR}$ (anti-)correlation depend strongly on the metallicity indicator used, highlighting the challenge of disentangling physical secondary trends within metallicity scaling relations.

Magnons, as charge-neutral spin excitations, can transport spin information without Joule heating and therefore offer a promising platform for low-power spintronics. However, in collinear magnets, the effective time-reversal symmetry forbids odd-parity magnon band splitting. Here we propose odd-parity magnons and establish a general mechanism for realizing them in collinear antiferromagnets. We provide a complete spin-point-group classification of odd-parity magnon splitting in two-dimensional collinear antiferromagnets by identifying the leading splitting types and their symmetry-allowed basis functions. This classification serves as a practical guide for searching for odd-parity magnons. We show that breaking effective time-reversal symmetry, for example by circularly polarized light or loop currents, can induce highly tunable $p$- and $f$-wave magnon splitting. In bilayer systems, the dynamical modulation can drive a topological magnon phase transition, accompanied by chiral edge modes and an abrupt jump in the magnon thermal Hall conductivity. Material-specific first-principles calculations further demonstrate the feasibility of this mechanism in real van der Waals antiferromagnets. Our study identifies the odd-parity magnons as a new class of spin excitations and provides a theoretical foundation for odd-parity magnons and ultrafast optically controlled topological magnonic devices.

Excitation of trapped-ion hyperfine qubits with fast optical Raman pulses enables faster-than-trap-period entangling gates with qubits of long coherence time for practical quantum computation. Achieving high-fidelity fast two-qubit gates requires high-quality spin-dependent kicks (SDKs), which form their fundamental building blocks. Here, we characterize the control parameters (including Raman frequency difference, pulse arrival times, Lamb--Dicke parameter, temperature, pulse width, and SDK time) that maximize the performance of single-ion SDKs for protocols compatible with performed experiments involving a small number of fast pulses. We demonstrate through analytical methods and numerical simulations that, within the model commonly used for infidelity optimization, finite pulse duration is the dominant source of error, exceeding the contribution of secular motion by orders of magnitude for nanosecond-scale SDKs. Low infidelities -- below $10^{-3}$ for schemes with $\gtrsim10$ fixed-amplitude, equispaced, picosecond pulses -- are achievable in SDK times on the order of nanoseconds. These results provide quantitative design rules for achieving competitive SDK fidelities with current pulsed-laser technology, laying the foundation for sub-microsecond trapped-ion quantum entangling operations.

We prove a finite-scale comparison between lower Brin-Katok local entropy and Katok covering entropy. Let $(\mathcal{X},d,T)$ be a compact metric topological dynamical system and let $μ$ be ergodic. Then, for every $ε>0$ and every $δ\in(0,1)$, $$ h^K_μ(6ε,δ)\leq \underline h^{BK}_μ(ε). $$ Combining this estimate with the usual Katok-type variational principle for metric mean dimension gives the corresponding variational principle with lower Brin-Katok local entropy.

This paper describes AIM (Automatic Index Manager), a configurable index management system, which identifies impactful secondary indexes for SQL databases to efficiently use available resources such as CPU, I/O and storage. It has been validated on thousands of databases which support production systems. With AIM, the physical design of the database adapts itself to the changes in the workload.We lay out the end to end design of AIM while calling out the guarantees and tradeoffs associated with our design choices. Some of the salient features of AIM include fast convergence even while recommending wide composite indexes, reduced reliance on the query optimizer and a "no regression" guarantee for production workloads. Each index recommendation from AIM is accompanied with a metrics driven explanation, making it easier to verify machine driven changes.AIM is one of the few industrial strength index recommendation engines that is deployed on production databases at a large scale. The experimental results show that AIM is quick in identifying the most effective indexes and the resulting physical design is close to optimal.

We prove a lower bound on the Weil height, the so-called Bogomolov property, for the algebraic extensions of $\mathbb Q$ cut out by the adelic Galois representations attached to certain eigenforms whose local component at a prime $p$ is supercuspidal. To this end, we give a method for constructing metric inequalities over $p$-adic Lie extensions of fields over $\mathbb Q$ that are finitely ramified at $p$.

A randomly perturbed digraph is an $n$-vertex directed graph with all out- and in-degrees linear in $n$, to which a linear number (depending on the degree) of random edges have been randomly added. We show that randomly perturbed digraphs whose edges have been colored uniformly with $n$ colors have a rainbow copy of every orientation of every possible length cycle, simultaneously, with high probability. This is a common generalization of work of Araujo, Balogh, Krueger, Piga, and Treglown in the uncolored setting and Katsamaktsis, Letzter, and Sgueglia for consistently oriented spanning cycles. Our proof uses Montgomery's distributive absorption method.

We study constant horizontal mean curvature surfaces in the sub-Lorentzian Heisenberg group. We derive the first-variation formula for horizontal area under volume-preserving radial variations and show that smooth isoperimetric candidates have constant horizontal mean curvature away from the characteristic set. We then give a complete classification of smooth boost-symmetric constant mean curvature surfaces: their characteristic sets, causal behaviour, and ambient sub-Lorentzian isometry classes. From this classification, we single out a family of smooth, acausal, boost-symmetric surfaces with nonzero constant mean curvature. Written as a two-sheeted graph over the exterior of a future hyperbola, this family is a natural sub-Lorentzian analogue of the Pansu bubbles and leads us to conjecture that it gives the isoperimetric maximisers in the sub-Lorentzian Heisenberg group.

The electrification of on-road fleet logistics promises improved air quality, lower noise emissions, major climate benefits, increased energy flexibility through the use of locally generated electricity and reduced dependence on imported fuels. However, battery electric vehicles can introduce operational planning challenges not present with internal combustion engine vehicles, including heterogeneous charging speeds, exposure to volatile electricity prices, and scarcity in infrastructure. Managing these complexities requires solutions that balance cost efficiency and robustness, supported by sector coupling between transport and electricity systems. This paper reviews the current state of digital systems for operational decision-making in electric fleet management through a grey literature analysis, drawing on practitioner-oriented sources such as industry reports, company documentation, and technical blogs that reflect real-world practices and developments. We identify key trends and gaps, providing insights to guide future research and development.

This study provides experimental evidence of chemical short-range order (CSRO) in the equiatomic CoCrNi alloy, identified through neutron diffraction. The phenomenon manifests as a distinct diffuse peak at Q = 1.85 A-1, the intensity increases under thermodynamically favorable conditions for CSRO development such as prolonged aging (100 h and 240 h) at 748 K or shorter aging (24 h) at slightly higher temperature (798 K). The degree of ordering was measured by integrating the diffuse scattering intensity, revealing that the gas-atomized sample, i.e. the sample with the least amount of CSRO, still displays approximately 70% of the CSRO level observed in the sample subsequently aged for 240 h at 748 K, i.e. the sample with the highest amount of CSRO produced in this study. Predictive atomistic simulations reproduced both the presence and position of the diffuse peak, while two-dimensional fast Fourier transform (FT-2D) analyses indicated that reflections at (1 1/2 0) within the <001> zone axis originate from some structural projections associated with like D022, Pt2Mo and D1a motifs. Complementary small-angle neutron scattering (SANS) measurements identified Ni-rich, disk-shaped domains with radii of approximately 11 A and thicknesses of about 1 A, consistent with nanoscale CSRO characteristic length scale. These findings demonstrate that CSRO is an intrinsic and energetically favorable feature of the CoCrNi system, remaining stable even under rapid solidification and further enhanced by low-temperature aging. Combined use of neutron diffraction and atomistic modeling provides a framework for probing local ordering phenomena in multi-principal element alloys (MPEAs).

Healthcare mobility -- patients seeking treatment outside their territory of residence -- represents a major source of inequality and financial imbalance in decentralised health systems. In Italy, persistent north-south asymmetries in patient flows among Local Health Authorities (ASLs) have reinforced existing disparities within the National Health Service; yet the structural organisation and temporal dynamics of these flows remain poorly understood at the sub-regional level. We propose a Bayesian dynamic latent space model for directed weighted networks with a hurdle negative binomial likelihood, and apply it to administrative discharge records on mobility for hip replacement procedures among 109 Italian ASLs over 2018-2024. The model jointly addresses excess zeros, overdispersion and network dependence, while capturing directional heterogeneity through multiplicative sender and receiver effects and controlling for differences in territorial size via an appropriate exposure term. Applied to Italian mobility data, the model reveals the evolving geometry of the healthcare system, quantifies the disruption induced by the COVID-19 pandemic, and uncovers structural asymmetries in outward propensity and ASLs attractiveness. The framework provides a flexible tool for the statistical analysis of dynamic healthcare mobility networks with direct relevance to the monitoring and evaluation of territorial healthcare provision.

Polyconvex constitutive modeling is attractive as it guarantees stability of numerical simulations and can improve the generalization behavior of material models. However, in certain applications, polyconvex formulations perform poorly in reproducing the underlying ground truth material response, which can effectively preclude their practical use. In this work, we address this issue and investigate the limitations of polyconvex constitutive modeling. The main contributions of this paper are as follows: (1) We analyze the theoretical reasons why polyconvexity may, in some cases, impose overly restrictive constraints that limit the achievable accuracy of constitutive models. Thereby, we provide analytical ellipticity guarantees for two non-polyconvex Mooney-Rivlin type potentials. (2) We investigate the practical limitations of polyconvex physics-augmented neural network constitutive models using two representative formulations: models using structural tensor-based invariants and models using signed singular values. Their performance is evaluated on datasets obtained from homogenized microstructured materials, and their predictive capabilities are assessed in finite element simulations. (3) Overall, we provide an overview of benefits, limitations, and mitigation strategies of polyconvex constitutive modeling.

We study spectral invariants arising in the noncommutative geometry of topological Markov chains and Cuntz--Krieger algebras. Their noncommutative geometry is described by spectral triples built from log-Laplacians, which are known to have non-trivial index theory and exotic quantum symmetries. We prove statistical eigenvalue asymptotics, local heat trace asymptotics, local Weyl laws, and an analogue of Connes' trace theorem. In all cases the local asymptotics are governed by the Kubo--Martin--Schwinger state of the gauge action on the Cuntz--Krieger algebra.

Recent large language models (LLMs) incorporate reasoning capabilities that allow them to perform well in predicting whether a smart contract respects a certain property, suggesting a complementary approach to traditional formal-methods-based techniques for smart contract verification. However, the application of LLMs in such context has two major issues: 1) properties expressed in natural language are intrinsically ambiguous, and 2) answers returned by LLMs have no guarantee of correctness. In this paper, we address both issues simultaneously by: 1) introducing a new formal specification language that extends Solidity with abstract types, and 2) designing a workflow that combines LLMs with type checking and concrete execution to generate and validate violation witnesses (i.e., counterexamples). The key idea is to represent a specification as a Solidity test with (existentially quantified) variables of abstract type; finding an instantiation of these variables to concrete values (of the correct type) concretizes the test into an executable counterexample (PoC) for the target property. We implemented our procedure in the tool Neuroforger, experimentally evaluating it on a smart-contract verification dataset drawn from literature, obtaining promising results that demonstrate its potential applicability in the wild.

Recent computations of weakly unstable equilibria, traveling waves, and periodic orbits in transitional shear flows suggest a spatiotemporal, dynamical-systems approach to low-Reynolds turbulence. Many invariant solutions have been computed precisely using high-dimensional direct numerical simulations, but little is known about how many solutions exist, how they are organized, or which sets of solutions best characterize the flow. In this paper we present a framework for addressing these questions in a low-dimensional context. Using classical approximation methods and exploiting symmetries and kinematic constraints, we derive ordinary differential equation models of plane Couette flow whose equilibria are governed by systems of quadratic algebraic equations. Solutions of these algebraic systems approximate known equilibria of plane Couette flow in as few as 17 dimensions and converge toward the known solutions as dimension increases. Searches over the systems produce sixteen distinct equilibrium solution branches in seven different symmetry groups. These results suggest that the equilibrium and traveling-wave solutions of closed shear flows are organized by the algebraic structure of systems of quadratic equations. Additionally, the differential equations and divergence-free basis provide explicit, closed-form, and convergent dynamical-systems representations of plane Couette flow.

Let $G$ be a discrete group with a finite-dimensional model for the classifying space for proper actions, and let $k$ be a commutative Noetherian ring of finite global dimension. In this setting, we prove that the homotopy category of projective $kG$-modules, the stable module category of $kG$-modules as defined by Mazza-Symonds, and the derived category of permutation $kG$-modules with finite isotropy, admit descent to finite subgroups. As an application, we show that any $kG$-module of type $FP_\infty$ is a retract of a module that admits a finite resolution by finitely generated $\natural$-permutation modules with finite isotropy, generalizing a result of Balmer-Gallauer.

Let $Σ_g^0\subset S^4$, $g\ge 3$, be the standard unknotted closed oriented surface, and let $a\subsetΣ_g^0$ be an oriented nonseparating curve. For a nontrivial knot $J\subset S^3$, let $Σ_{g,a,J}\subset S^4$ be the surface obtained by ordinary untwisted rim surgery along $a$. Assuming a meridian-longitude rigidity condition on the knot group of $J$, we compute the extendable mapping-class subgroup exactly: \[ E(Σ_{g,a,J})= \operatorname{Stab}_{\operatorname{Mod}(Σ_g)}(q_0)\cap \operatorname{Stab}_{\operatorname{Mod}(Σ_g)}([a]), \] where $q_0$ is the Rokhlin quadratic form of the standard embedding and $[a]\in H_1(Σ_g;\mathbb Z)$ is the oriented homology class.

Neutron-induced reactions play a central role in stellar and Big Bang nucleosynthesis models. Yet many of the cross sections remain poorly constrained at astrophysically relevant energies. To address these needs, we are developing a multi-purpose Optical Time Projection Chamber (OTPC) optimized for precision neutron-reaction studies at the Soreq Applied Research Accelerator Facility (SARAF) upcoming high-intensity, time-of-flight neutron beam. The detector combines a drift chamber filled with CF4-based scintillating gas mixtures, fast photodetectors for prompt scintillation detection, and high-speed optical readout of avalanche-induced secondary scintillation to enable full 3D reconstruction of charged-particle tracks. A prototype system has been assembled and tested. This has enabled systematic characterization of electron drift velocity, charge and light amplification, and 2D optical imaging of alpha-particle tracks in an Ar/CF4 gas mixture. These studies guide the design of a larger, fully integrated OTPC system intended for operation at SARAF. In parallel, we are exploring advanced image sensors to further enhance tracking resolution. We report on recent progress with the prototype and outline the next steps toward commissioning the full system.

The trade-off relations between the two types of error probabilities in binary i.i.d. quantum state discrimination can be expressed by single-copy formulas in terms of the Petz-type and the sandwiched Rényi divergences of the two states representing the two hypotheses. In the non-i.i.d. setting, the error exponents can usually be expressed in terms of regularized Rényi divergences, which do not admit explicit formulas in general. Here, we consider a class of states, translation-invariant and gauge-invariant quasifree states on doubly infinite fermionic chains, and give explicit formulas for a wide range of regularized Rényi divergences between such states, including $(α,z)$, log-Euclidean, maximal, measured, and the recently introduced integral Rényi divergences. We show that the case where there is a single mode at each lattice site becomes asymptotically classical, with all the different types of regularized Rényi divergences being equal, while in the case of multiple modes per site, non-commutativity persists under regularization, and for any fixed $α$, the regularized Rényi $(α,z)$-divergences give different regularized values for different $z$ parameters in general. We also generalize a previous construction from [Bunth, Maróti, Mosonyi, Zimborás, Lett.~Math.~Phys.~113:(7), 2023] to the case of multiple modes per lattice site to obtain a large class of states exhibiting super-exponential decay of the discrimination error probabilities.