We show that for any $\varepsilon>0$ if $ϕ:\mathbb{T} \rightarrow \mathbb{T}$ is continuous and $\|\exp(-2πi z ϕ)\|_{A(\mathbb{T})} =O_{|z|\rightarrow \infty}(\log^{\frac{1}{8}-\varepsilon} |z|)$ then $ϕ(x)=wx+t$ for some $w \in\mathbb{Z}$ and $t \in \mathbb{T}$.

Interior-point methods (IPMs) are a cornerstone of Euclidean convex optimization, due to their strong theoretical guarantees and practical performance. Motivated by scaling problems, recent work by Hirai and the last two authors (FOCS'23) extended IPMs to geodesically convex optimization on Hadamard manifolds. Crucially, the complexity of IPMs (both in Euclidean and Hadamard spaces) is governed by the \emph{barrier parameter} of the domain. Here we prove that already in hyperbolic space, several natural domains -- including geodesic balls and triangles -- have a barrier parameter that grows polynomially with the domain's diameter. By extension, the same holds for the positive-definite matrices and other symmetric Hadamard spaces. This growth implies a fundamental limitation: interior-point methods relying on barriers for a ball cannot efficiently solve challenging scaling problems, such as tensor scaling, where the domain's diameter can be exponentially large in the input size. Our results are partially inspired by, and complement, lower bounds on the condition number of geodesically convex functions established by Hamilton and Moitra (NeurIPS'21).

COFFEE series is a HVCMOS pixel sensor using the advanced 55 nm process, currently being developed for the Upstream Pixel (UP) tracker of the LHCb Upgrade II. To ensure that COFFEE will be able to handle the particle hit rates at UP tracker, which reach a maximum of 322.5 MHz/chip, detailed simulation of the digital readout circuitry was performed. Simulation results show that the column-drain readout mechanism achieves nearly 100\% efficiency when the single readout cycle does not exceed 100 ns. Meanwhile, the buffer depth and memory resources required for the peripheral readout adapted to the BXID-sharing data format are also evaluated. These provide guidance for the design of COFFEE. The column-drain readout mechanism was used in COFFEE3 (fabricated in 2025), while the peripheral readout architecture adapted to the BXID-sharing data format is implemented in CHiR (taped out in early 2026).

Multi-dimensional unified model atmospheres with winds of massive stars have so far been studied under the assumption of equal flux, Planck, and energy weighted mean opacities, which effectively means these models have been in local thermodynamic equilibrium (LTE). Although LTE may be a valid approximation in deeper atmospheric layers, it breaks down in the extended outflowing parts. As such, the opacities governing the heating and cooling of the gas are neither the same nor equal to flux-mean opacity in those regions. We present an approximate NLTE procedure that accounts for scattering in the computation of energy and Planck-mean opacity from a multitude of spectral lines in an accelerating medium. The formalism evaluates the opacities using Sobolev escape probabilities and effective thermalization parameters from a line database consisting of ~4 million spectral lines. RHD simulations are calculated as before with a hybrid opacity scheme combining Rosseland means with line opacities in an accelerating medium. Due to their high velocity dispersion, upon interaction, they produce localized shock fronts with the gas temperature exceeding the photon temperature. Due to improved treatment of heating and cooling in outflowing parts, the radiation and gas temperatures in the wind are no longer the same, as was the case in previous multi-dimensional simulations. Instead, gas gets heated at shock fronts, but due to strong radiative cooling remains localized. The net result is a multi-component wind structure not only in density and velocity, but also in temperature. This likely has important consequences for the formation and interpretation of observed O-type star wind spectra.

MnBi$_2$Te$_4$ (MBT) thin films provide a unique material platform in which magnetism, topology, and magneto-optical (MO) response can be tuned through layer-thickness and relative spin alignments. In this work, using a low-energy coupled Dirac cone model together with Wannier-based tight-binding Hamiltonian derived from \textit{ab-initio} calculations, we investigate topological MO switching in even-layered MBT films. We argue that the relative spin alignment of the outermost septuple-layers (SL) mainly controls the total Chern number, optical conductibility, and consequently, the MO response. For a 6-SL MBT thin film, we found that reversing the outermost-SL alignments from antiparallel to parallel switches the system from axion insulating state with $C=0$ and vanishing Faraday rotation to a Chern insulating state with $C=1$ and a quantized MO response, irrespective of $PT$-symmetry and net magnetization. Increasing thickness reveals an additional regime: while 8-SL MBT hosts only $C=0$ and $1$ states, a 12-SL MBT film supports a higher Chern number phase with $C=2$ with a doubled low-frequency Faraday rotation. Our results provide a thickness-dependent route to multilevel MO switching and establish MO spectroscopy as a direct probe of surface magnetism and topological order in MBT thin films.

We construct a model of a three-dimensional helical second-order topological superconductor formed by an array of weakly coupled Rashba nanowires. We identify the parameter regime in which there are energy gaps in both the bulk and surface energy spectra, while a pair of gapless helical $\mathbb{Z}_{2q}$ parafermionic modes (with $q$ being an odd integer) remains gapless along a closed path of one-dimensional hinges. The precise trajectory of these hinge modes is dictated by the hierarchy of interwire couplings and the boundary termination of the sample. In the noninteracting limit $q= 1$, the system hosts gapless Majorana hinge modes.

Online marketplaces increasingly do more than simply match buyers and sellers: they route orders across competing sellers and, in many categories, offer ancillary fulfillment services that make seller inventory a source of platform revenue. We investigate how a platform can use intertemporal demand allocation to influence sellers' inventory choices without directly controlling stock. We develop a model in which the platform observes aggregate demand, allocates orders across sellers over time, and sellers choose between two fulfillment options, fulfill-by-merchant (FBM) and fulfill-by-platform (FBP), while replenishing inventory under state-dependent base-stock policies. The key mechanism we study is informational: by changing the predictability of each seller's sales stream, the platform changes sellers' safety-stock needs even when average demand shares remain unchanged. We focus on nondiscriminatory allocation policies that give sellers the same demand share and forecast risk. Within this class, uniform splitting minimizes forecast uncertainty, whereas any higher level of uncertainty can be implemented using simple low-memory allocation rules. Moreover, increasing uncertainty above the uniform benchmark requires routing rules that prevent sellers from inferring aggregate demand from their own sales histories. These results reduce the platform's problem to choosing a level of forecast uncertainty that trades off adoption of platform fulfillment against the inventory held by adopters. Our analysis identifies demand allocation as a powerful operational and informational design lever in digital marketplaces.

We leverage highly successful prior projects sponsored by multiple NSF grants and gifts from industry: the BLAS-like Library Instantiation Software (BLIS) and the libflame efforts to lay the foundation for a new flexible framework by vertically integrating the dense linear and multi-linear (tensor) software stacks that are important to modern computing. This vertical integration will enable high-performance computations from node-level to massively-parallel, and across both CPU and GPU architectures. The effort builds on decades of experience by the research team turning fundamental research on the systematic derivation of algorithms (the NSF-sponsored FLAME project) into practical software for this domain, targeting single and multi-core (BLIS, TBLIS, and libflame), GPU-accelerated (SuperMatrix), and massively parallel (PLAPACK, Elemental, and ROTE) compute environments. This project will implement key linear algebra and tensor operations which highlight the flexibility and effectiveness of the new framework, and set the stage for further work in broadening functionality and integration into diverse scientific and machine learning software.

This article presents a computational framework for determining the optimal slip velocity of a microswimmer with arbitrary three-dimensional geometry suspended in a viscous fluid. The objective is to minimize the hydrodynamic power dissipation required to maintain unit speed along the net swimming direction. By exploiting the linearity of the Stokes equations and the Lorentz reciprocal theorem, we derive an explicit linear operator that maps the tangential surface slip velocity to the resulting rigid-body translational and rotational velocities, effectively decoupling the hydrodynamic boundary value problem from the optimization loop. The a priori infinite-dimensional search space for the slip optimization is reduced to the finite dimension $r$ of rigid-body motions by finding an appropriate subspace of the operator's domain. This reduces the PDE-constrained optimization to a low-dimensional programming problem that can be solved at negligible computational cost once the system matrices are assembled. The optimization algorithm requires 2$r$ auxiliary flow problems that are solved numerically using a high-order boundary integral method. We validate the accuracy of the proposed method and present optimal slip profiles and swimming trajectories for a variety of microswimmer shapes. We investigate the effect of some common geometrical symmetries of the swimmer shape on the resulting optimal motion, and in particular present a modified version of the slip optimization algorithm for axisymmetric shapes, where tangential rigid-body velocities may occur

Conventional delay-Doppler (DD) communication and sensing systems require transmitting pilot frames at every channel coherence time interval in order to keep track of channel variations at the cost of spectral efficiency. In this paper, we propose an approach to utilize data transmissions modulated using arbitrary waveforms for DD channel estimation without requiring pilot transmissions in every coherence time interval. Numerical evaluation over practical doubly-selective channel models demonstrate $\sim 1.8 \times$ improvement in spectral efficiency with our proposed data-based approach over conventional pilot-based approaches across various 6G modulation schemes.

Approximate full mass matrix methods for the material point method, known as FMPM(k) of order k, can improve the calculation of grid velocities from grid momentum. It can be implemented in any MPM code by inserting a new calculation task whenever grid velocities are needed. The implementation recommended in this paper only needs these calculations once per time step just before when updating particle positions and velocities. FMPM implementation issues arise, however, when its methods are mixed with other MPM feature that rely on lumped mass calculations. Some common lumped-mass MPM features are grid-based, velocity boundary condition, multimaterial contact calculations, crack contact calculations, and imperfect interfaces. This paper first derives a revised FMPM(k) implementation that both simplifies and clarifies the "FMPM Loop" that can be added to MPM codes. Next, that loop is modified to allow FMPM(k) to work well even in simulations that need other MPM features that previously caused conflicts. Two other FMPM(k) issues are apparent loss of stability at very higher order k and inherent computational cost. These issues are discussed in an analysis of temporal stability as a function of order k and in consideration of options to improve efficiency.

Nonadiabatic removal of an external transverse magnetic field provides a phase-selective mechanism for controlling betatron oscillations in laser wakefield accelerators. When the field is switched off on a timescale shorter than the betatron period, the equilibrium orbit shifts abruptly and acts as an impulsive transverse drive. The induced motion interferes coherently with the preexisting betatron oscillation, leading to phase-dependent enhancement or suppression of the oscillation amplitude. A theoretical model shows that the excitation is governed by the dimensionless switching parameter $χ=ω_βL_s/c$, which distinguishes nonadiabatic and adiabatic regimes. Particle-in-cell simulations confirm the predicted scaling and demonstrate controllable modulation of the betatron radiation spectrum while leaving longitudinal acceleration largely unaffected. These results establish magnetic-field switching as a direct mechanism for phase control of relativistic betatron oscillations in plasma-based accelerators.

Optically levitated sensors inside a Fabry-Pérot cavity have been proposed for high-frequency gravitational-wave (GW) detection, though their configuration for gravitational wave sensitivity exhibits counterintuitive features. We provide a new detailed general relativistic derivation of the interaction between a gravitational wave and a levitated object in an optical cavity, demonstrating gauge independence of the observable response. We find a strong asymmetric dependence of the strain signal on trap position, maximized when the sensor is located near the input mirror, in agreement with previous results. A key new result of this work is the consequence of this asymmetry on the noise coupling: the coupling of input-mirror displacements to the strain signal can be highly suppressed relative to that of end-mirror displacements and common-mode mirror motion. These results clarify the physical origin of the gravitational wave interaction with such a sensor and establish crucial design principles for optical levitation based high-frequency GW detectors.

Realizing Weyl semimetals (WSMs) with the minimal number of Weyl points (WPs) fundamentally simplifies extracting intrinsic topological responses. While a minimum of four conventional ($|C|=1$) WPs in nonmagnetic crystals is well-established, the exact symmetry requirements and material realization for the unique configuration of four unconventional double-Weyl points (DWPs, $|C|=2$) remain unresolved. Here, we establish rigorous crystalline symmetry constraints restricting the existence of exactly four symmetry-protected DWPs to merely 28 space groups in both nonmagnetic spinless and spinful systems. Guided by this classification, we identify an $sp$$^2$--$sp$$^3$ hybridized chiral carbon allotrope, THRLN-C$_{32}$, as an ideal candidate hosting precisely this four-DWP configuration near the Fermi level. These $C_4$-protected DWPs project extended or closed-loop Fermi arcs onto the surface Brillouin zone, providing unambiguous spectroscopic signatures. Furthermore, external strain drives profound topological phase transitions encapsulated in a unified evolution landscape: the pristine four-DWP state dissociates into two exotic three-terminal Weyl complexes, degenerates into eight conventional $|C|=1$ WPs, or collapses into a trivial insulator. This work provides a definitive theoretical framework for minimal double-WSMs in nonmagnetic spinful systems and introduces an optimal material platform for investigating strain-tunable topological quantum phenomena.

The LHC is achieving energies never reached before, opening up possibilities for the discovery of exotic particles in the TeV mass range. Such states include magnetic monopoles, which can explain the electric charge quantisation and restore the symmetry in Maxwell's equations with respect to the magnetic and electric fields. Scenarios proposed to shed light to dark matter and neutrino masses introduce high-electric-charge objects (HECOs). The existence of both classes of particles can be probed in precision measurements in a manner complementary to direct searches. We focus on the contributions of such virtual particles to light-by-light scattering in the context of effective field theories and a Born-Infeld scenario. Specifically, measurements of central exclusive production of photon pairs with proton tagging carried out by the CMS-TOTEM Precision Proton Spectrometer with LHC Run 2 proton-proton collision data are used to constrain magnetic monopole and HECOs. Resummation techniques have been employed to deal with the large HECO-photon coupling. Masses of up to a few tens of TeV have been excluded for monopoles and HECOs of various spins and magnetic and electric charges, respectively.

In India, Community Healthcare Workers (CHWs) serve as critical intermediaries between the state and beneficiaries, including pregnant mothers and children. Effective planning and prioritization of care and services necessitate the collection of accurate health data from the community. Crowdsourcing child anthropometric data through CHWs could establish a valuable repository for evidence-based decision-making and service planning. However, existing platforms often fail to maintain CHWs' engagement over time and across different spatial contexts, resulting in spatially misrepresented and outdated data. This study addresses these challenges by conducting a co-design exercise to develop innovative methods for collecting anthropometric data over time and space. The exercise involved analyzing data to create hotspot and density distribution maps. We implemented a trial of the developed game with two groups (n=94 per group) from various states across India, comparing the game-based and non-game-based data collection methods. Our findings reveal that the game-based approach significantly improved measuring efficiency (p<0.05) and demonstrated superior engagement and retention compared to the non-game-based method. This research contributes to the expanding literature on co-design and Research through Design (RtD) methodologies for developing geospatial games, highlighting their potential to enhance data collection practices and improve engagement among CHWs.

The formation of late-type galaxies has traditionally been described via two pathways: one producing pressure-supported classical bulges, the other rotationally supported pseudo-bulges. Early studies relied on photometric decompositions assuming an exponential disk extrapolated inwards. Recent high-resolution observations, however, reveal a far more complex landscape in disk galaxy centres. We investigated the morphology of central stellar components in intermediate-to-massive spiral galaxies, focusing on disentangling cold, warm, and hot orbital contributions, critically reassessing the standard approach of extrapolating the exponential disk profile inwards. We developed GLANCE (Galactic archaeoLogy via chronochemicAl and dyNamiCal modElling), a tool for photometric, chronochemical, and dynamical galaxy analysis, applied to 8 high-resolution MUSE galaxies to derive stellar population properties and decompose orbits into cold, warm, hot, and counter-rotating (CR) components. We uncovered remarkable structural diversity in the dynamically cold central component: one galaxy displays an exponential profile throughout, while the majority exhibit either a pronounced central drop resembling a doughnut-shaped structure or a compact inner disk significantly steeper than the outer disk. Most galaxies hosting nuclear disks are classifiable as classical bulges - hot, old, red, high bulge-to-total ratio - contrasting with galaxies showing a central cold-component deficit. Beyond the bulge, cold plus warm orbit contributions remain below the total, indicating non-negligible hot or CR orbits with Sérsic indexes consistently above unity. These results highlight the composite nature of disk galaxy centres and the need for decomposition methods that avoid extrapolating the outer disk inwards, requiring large IFS samples across a broad mass range, complemented by simulations such as IllustrisTNG50.

Two elliptic curves defined over $\mathbb{Q}$ are called discriminant twins if they have the same minimal discriminant and the same conductor. Deines, in 2014, conjectured that there exist infinitely many semi-stable non-isogenous discriminant twins. In this article we present an explicit infinite family of semi-stable non-isogenous discriminant twins, providing a proof for Deines' conjecture.

We show that the Galois cohomology of negative Tate twists can be organized by a single universal cyclotomic complex over the cyclotomic tower of $\mathbb{Q}$. Using cyclotomic descent and Teichmüller branch decomposition, we prove that a negative twist contributes only on the corresponding branch and is recovered by specializing the Iwasawa variable at a single point; equivalently, it is computed as the fiber of $γ-u^{-m}$, or $T=u^{-m}-1$ in Iwasawa coordinates. In the case $\mathbb{Q}_p/\mathbb{Z}_p$, this gives explicit descriptions of $H^1$ and $H^2$ in terms of the quotient and torsion of the $S$-ramified Iwasawa module.

Distributed Acoustic Sensing (DAS) enables continuous monitoring of dynamic strain along tens of kilometers of optical fiber, generating massive datasets whose interpretation and automated analysis remain challenging. DAS measurements often lack a standardized visual representation, and their physical interpretation depends strongly on acquisition conditions and signal processing choices. This work introduces a systematic framework for visualization and feature extraction of DAS data based on a multispectral signal representation. The approach decomposes strain-rate measurements into predefined frequency bands and computes band-limited energy images that describe the spatial and temporal distribution of acoustic energy across distinct spectral regimes. The framework is evaluated using DAS recordings containing Fin Whale (Balaenoptera physalus) and Blue Whale (Balaenoptera musculus) vocalizations. Three experiments are conducted to assess the approach: enhanced visualization of bioacoustic signals, unsupervised clustering of acoustic patterns, and supervised event detection using a convolutional neural network. Using multispectral composites as input, a ResNet-18 classifier achieves an accuracy of 97.3% in whale vocalization detection, demonstrating that the proposed representation captures biologically meaningful spectral structure and provides an effective feature space for automated analysis of DAS data.

This proceedings contribution provides an overview of Loop Blow-up Inflation and updates its observational predictions and their comparison with the latest CMB and BAO data from combined analyses of SPT, Planck, ACT, and BICEP/Keck, as well as ACT DR6 constraints on extra dark radiation. It is based on work originally published in arXiv:2403.04831, carried out in collaboration with L. Brunelli, M. Cicoli, A. Hebecker, and R. Kuespert, and presented at the 2025 Workshop on Quantum Gravity and Strings. We focus on string loop corrections to the Kähler potential, long regarded as a potential threat to blow-up inflation in the Large Volume Scenario. We argue that these corrections, previously assumed avoidable, are in fact generically present and qualitatively alter the original non-perturbative picture: they invalidate slow-roll near the minimum and instead generate a new slow-roll regime at larger field values, where the scalar potential transitions from an exponential to a power-law plateau. This leads to modified inflationary dynamics and distinct cosmological predictions, including an increased tensor-to-scalar ratio. We confront all three SM-location scenarios with the latest constraints on $n_s$, $r$, and $ΔN_{\rm eff}$. The tighter bound on extra dark radiation requires an updated Giudice-Masiero coefficient in Scenario III, yielding revised predictions presented here for the first time. All scenarios remain consistent with recent observations, with the ACT+DESI combination yielding near-perfect agreement in $n_s$ for vanishing extra dark radiation at $0.03σ$ deviation. We also comment on subleading loop corrections, which improve robustness by reducing the field value required for slow roll. These results highlight that string loop effects, rather than being merely detrimental, can play a constructive role in realising viable inflation in string compactifications.

This work presents a symbolic approach for estimating the energy consumption for nested loop programs when mapped and scheduled on parallel processor array accelerator architectures. Instead of simulation-based evaluation, we derive a methodology for symbolic energy analysis that captures the impact of mapping and scheduling decisions of loop nests on processor arrays. We compare our approach against simulation-based results for selected benchmarks and varying sizes of the iteration spaces. Whereas the latter are not scalable, our symbolic analysis is shown to be independent of the problem size. The presented evaluation methodology can be beneficially used during the design space exploration of mapping and scheduling decisions, for studying the influence of array size variations, and for comparisons with other loop nest accelerator architectures.

We consider the problem of identifying the onset of the conformal window for QCD with $N_f$ massless flavors in the fundamental representation, and propose a new effective method to determine it from lattice simulations. This method is based on the investigation of the so-called Roberge-Weiss transition temperature $T_{RW}$, which is encountered at specific values of the imaginary baryon chemical potential, and can also be interpreted as the inverse of the critical spatial size at which charge conjugation is spontaneously broken in a finite box. Since $T_{RW}$ corresponds to a genuine phase transition for any value of the quark masses, it is a well-defined quantity; we argue that the critical $N_f$ at which $T_{RW}$ vanishes in the chiral limit coincides with the onset of the conformal window. We implement our proposal by investigating QCD with $N_f = 8$ flavors, discretized via stout improved staggered fermions and the tree-level improved Symanzik pure gauge action, at Euclidean temporal extents $N_t = 8, 10, 12, 16, 24$. In this case, we find evidence that $T_{RW}$ already vanishes in the chiral limit, indicating that $N_f = 8$ is already in the conformal window.

In rotary-wing aircraft, rotating blades are exposed to collisions and subsequent damage. The detection and isolation of blade damage constitute the first step in fault mitigation; however, they are particularly challenging when considerable input redundancy is available, as in the case of multirotors. In this article, we propose an active model-based approach that deliberately perturbs the control inputs to isolate blade faults in multirotor vehicles. By exploiting a model that captures the vibrations caused by blade damage, the isolation method relies solely on vibration data from the onboard inertial measurement unit. The strategy is tested in simulation using an octarotor platform, and both time-domain and frequency-domain features are analyzed. Several accuracy-related metrics of the technique are evaluated on a set of 9600 simulations and compared with the most relevant variables.

Rydberg excitons, characterized by large spatial extension and reduced electron-hole overlap, must have a spin-valley dynamics different from that of ground state excitons. Here we report a direct measurement of spin relaxation of Rydberg excitons in high-quality WSe2 monolayer using continuous-wave and time-resolved optical orientation experiments. Excited excitonic states exhibit exceptionally large photoluminescence circular polarization, approaching 90% for the 3s state. Time-resolved measurements reveal a strong increase of the spin relaxation time with the principal quantum number, from ~2 ps for the 1s exciton to ~75 ps for the 3s exciton. A microscopic model based on electron-hole exchange-driven spin relaxation quantitatively reproduces the observed trend, demonstrating that Rydberg excitons enable tunable spin-valley dynamics in two-dimensional semiconductors.

We study computational limitations in \emph{multi-plant} average-case inference problems, in which $t$ disjoint planted structures of size $k$ are embedded in a random background on $n$ elements. A natural parameter in this setting is the total planted size $K := kt$. For several classic planted-subgraph problems, including planted clique, existing algorithmic and lower-bound evidence suggests a characteristic computational threshold near $\sqrt{n}$ in the single-plant setting. Our main result is a Sum-of-Squares (SoS) integrality gap for refuting the presence of multiple planted cliques. Specifically, for $G \sim G(n,1/2)$, we construct a degree-$d$ SoS pseudoexpectation for the natural relaxation that maximizes the total size of up to $t$ disjoint cliques. Throughout the regime $kt \le n^{1/2 - c\sqrt{d/\log n}},$ for a universal constant $c>0$, this relaxation achieves objective value $kt(1-o(1))$, and therefore degree-$d$ SoS cannot certify an upper bound below $kt$. This extends the planted-clique SoS lower bounds of~\cite{BarakHKKMP19} to a multi-plant setting with explicit disjointness constraints. As complementary evidence from a different computational model, we prove a lower bound in the statistical query (SQ) framework, extending the results of~\cite{FeldmanGRVX17}. We show that for detecting $t$ disjoint planted $k \times k$ bicliques (equivalently, a row-mixture distribution), when $kt = O(n^{1/2-δ})$ for any fixed $δ>0$, no polynomial-time SQ algorithm can distinguish the planted and null distributions with constant advantage.

In this paper, we obtain some additional probabilistic properties of the renewal process $\{\hat{N}_α(t)\}_{t\ge0}$, $0<α\le 1$ introduced by Beghin and Orsingher (2010). A time-changed relationship connecting $\{\hat{N}_α(t)\}_{t\ge0}$ with its special case $\{\hat{N}(t)\}_{t\ge0}$ by means of the random time process $\{T_{2α}(t)\}_{t>0}$ whose distribution is related to a fractional diffusion equation is established. We compute its various distributional properties such as the variance, factorial moments, moment generating function, moments, covariance in the Laplace domain, etc. We show that the ratios given by $\{\hat{N}_α(t)\}_{ t \ge 0}$ and its power over their means tend to $1$ in probability. Moreover, we derive an integral form of its bivariate distribution and describe the scaling limits of its marginal distributions. It is also shown that its one-dimensional distributions are not infinitely divisible. Furthermore, we study the compound version of $\{\hat{N}_α(t)\}_{ t \ge 0}$ and discuss an application to ruin theory. Later, we consider two time-changed versions of $\{\hat{N}_α(t)\}_{ t \ge 0}$ which are obtained by time-changing it with an independent Lévy subordinator and its inverse. Some distributional properties and examples are discussed for these time-changed processes.

Resolving the three-dimensional (3D) atomic geometry of free-standing graphene in real time is essential for understanding how intrinsic rippling governs its electronic properties. However, the low electron doses required to mitigate radiation damage impose severe signal-to-noise constraints that limit conventional reconstruction methods. Here, we present a physics-informed computational framework that reconstructs 3D atomic coordinates of single-layer graphene from individual low-dose transmission electron microscopy (TEM) frames (8x10^3 e-/Ang^2, 1 ms temporal resolution). The approach combines simulated annealing optimisation with molecular dynamics regularisation, achieving sub-angstrom out-of-plane accuracy (sigma_z < 0.45 Ang), validated against ground-truth simulations. A Kullback-Leibler divergence-based calibration aligns the forward model with experimental image statistics, reducing systematic bias. Applied to high-speed time-series data, the framework enables simultaneous extraction of real-time ripple dynamics, strain tensors, surface curvature, bond-length distributions, and density functional theory (DFT)-derived electron localisation functions (ELF). We establish quantitative relationships linking local geometry, strain, and bond-length variations to electron localisation, demonstrating that sub-angstrom structural fluctuations drive spatially localised, millisecond-scale electronic modulation. A critical dose threshold is identified below which structural information becomes irrecoverable, providing practical guidance for experimental design. The framework is broadly applicable to beam-sensitive two-dimensional materials.

HATS-75 b is one of the recently discovered Giant Exoplanets orbiting M-dwarf Stars (GEMS) with a transmission spectrum shaped by both its atmosphere and the active stellar surface it transits. As part of a JWST program studying 7 GEMS, we observed three transits of HATS-75 b with the NIRSpec PRISM instrument (0.6-5.3 um). The planet's spectra exhibit a slightly larger transit depth at shorter wavelengths, indicative of hazes or stellar contamination due to stellar heterogeneities outside the transit chord, i.e., the transit light source (TLS) effect. While both a hazy atmospheric model or TLS model can replicate the transmission spectrum, independent evidence (.e.g, stellar rotation, spot-crossing events) favors a model that includes contamination from unocculted starspots and faculae. Within this stellar heterogeneity / TLS-based framework, atmospheric retrievals yield remarkably low atmospheric metallicity (log[M/H]=-1.74^{+0.92}_{-0.76}) and super-solar carbon-to-oxygen (C/O=1.04^{+0.40}_{-0.09}), which paired with a best-fit interior model with bulk metallicity of Z_p=0.20+/-0.04, implies poor vertical mixing within the planet. Retrievals also detect robust absorption signatures of CH4, CO, and CO2. We obtain only an upper limit for H2O, consistent with its atmospheric spectral features being masked by stellar contamination. These results underscore the importance of accounting for stellar heterogeneity when interpreting exoplanet transmission spectra and highlight HATS-75 b as a significant asset to our understanding of giant exoplanets around M-dwarfs with JWST.

Secret key generation (SKG) from wireless channel reciprocity has been demonstrated on WiFi, LTE, and LoRaWAN, but has never been demonstrated on 5G New Radio (NR) Sounding Reference Signal (SRS) and CSI Reference Signal (CSIRS) measurements.