We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral operators. Third, its proof synthesizes a broad range of existing results in operational calculus and highlights their combined effectiveness. As an illustration, we obtain a new and natural extension of the Laguerre polynomials.

We present infant-phase observations of the SN Ic-BL 2020lao, including optical spectroscopy beginning 48 hrs after explosion. The explosion time was constrained by power-law fits to the rising TESS and ZTF light curves, with the first ZTF detection occurring 27 hrs after explosion. The optical light curves show a rapid rise lasting 8.8 days and a peak luminosity typical of SNe Ic-BL (Mr=-18.5 mag). Unlike some engine-driven SN Ic-BL events, the light curve of SN 2020lao shows no evidence of an optical afterglow or excess emission, and the absence of shock-cooling in the TESS and ZTF data constrains the progenitor to a Wolf-Rayet-like star with radius less than a few times the solar radius, ruling out any extended envelope. The spectra resemble those of the X-ray-flash-associated SN 2006aj but with higher expansion velocities. From Arnett-type fits to the bolometric light curve and measured FeII velocities, we infer a Ni mass of 0.2 solar masses, an ejecta mass of 3.2 solar masses, and a kinetic energy of about 23x10^51 erg, corresponding to a specific kinetic energy of 7x10^51 erg per solar mass. Spectral synthesis modeling broadly reproduces the photospheric spectra of SN 2020lao and suggests a specific kinetic energy of 5x10^51 erg per solar mass. SN 2020lao and SN 2006aj synthesized comparable amounts of Ni, yet SN 2020lao exhibits specific kinetic energy values 5-10 times larger. VLA and Swift/XRT non-detections reveal no afterglow emission, allowing limits on relativistic ejecta and dense circumstellar material. Given that SN 2020lao reaches a specific kinetic energy typical of engine-driven SNe Ic-BL, the lack of an optical excess with the non-detections in the radio and X-ray bands suggests that if a relativistic jet was launched, it was either viewed far off axis or choked before breakout. If there was no relativistic jet, SN 2020lao would be an extreme nonrelativistic SN Ic-BL.

Quantum hypergraph states emerged in the literature as a generalization of graph states, and since then, considerable progress has been made toward implementing this class of genuine multipartite entangled states for quantum information and computation. Here, we review the definition of hypergraph states and their main applications so far, both in discrete-variable and continuous-variable quantum information.

We explore, both analytically and numerically, the quantum dynamics of a many-body free-fermion system subjected to local density measurements. We begin by extending the mapping to the nonlinear sigma-model (NLSM) field theory for the case of finite evolution time $T$ and different classes of initial states, which lead to different NLSM boundary conditions. The analytical formalism is then used to study how quantum correlations gradually develop, with increasing $T$, from those determined by the initial state towards their steady-state form. The analytical results are confirmed by numerical simulations for several types of initial states. We further consider the long-time limit, when the system in $d+1$ space-time dimensions becomes quasi-one-dimensional, and analyze the scaling of the ``localization'' time (which is simultaneously the purification time and the charge-sharpening time for this class of problems). The analytical predictions for scaling properties are fully confirmed by numerical simulations in a $d=2$ model around the measurement-induced phase transition. We use this dynamical approach to determine numerically the measurement-induced transition point and the associated correlation-length critical exponent.

High-energy gamma-ray spectroscopy is crucial for studying and advancing the application of high-energy photons in areas like strong-field physics, high-energy-density science, and laboratory astrophysics. However, high-energy gamma-ray spectroscopy in the multi-MeV to GeV range faces significant challenges in precise spectral reconstruction. This study presents a machine learning-based inversion approach that combines a spectrometer design with advanced deconvolution algorithms. We develop a gamma-ray spectrometer optimized through Monte Carlo simulations for maximum positron yield and minimal noise. A two-stage neural network framework is proposed based on the structure of the spectrometer: a denoising autoencoder suppresses statistical noise in measured positron spectra, while a U-Net architecture solves the ill-posed inverse problem to reconstruct incident gamma spectra. This approach establishes a new methodology for gamma-ray diagnostics in strong-field QED experiments and high-energy photon sources.

We propose a pulse and continuous wave (CW) hybrid architecture of continuous-variable measurement-based optical quantum computation utilizing the strengths of both pulsed and CW light. In this architecture, input and ancillary non-Gaussian quantum states necessary for fault-tolerance and universality are generated with pulsed light, whereas quantum processors including continuous-variable cluster states and homodyne measurement systems are operated with CW light. This architecture is expected to enable both generation of quantum states with shorter optical wavepackets for ultrafast computation and low-loss manipulation and measurement of these states. In this study, as a proof-of-principle, an ultrafast homodyne measurement using a CW local oscillator was performed on single-photon states generated with pulsed light. The measured single-photon state's temporal width was around 70 ps and the value of the Wigner function at the origin was $W(0,0) = -0.153\pm0.003$, which is highly non-classical. This will be a core technology for high-speed optical quantum information processing.

For several years, students at an art college, working with NASA astronomers, have produced animations inspired by research on black holes, dark matter and more. They can be whimsical or poetic but still constrained by scientific rigour. The animations are used for scientific outreach and are freely available. Our program received a positive assessment through an evaluation we undertook. We are now planning a mobile STEAM exhibition to engage teenagers from underrepresented communities who may not typically consider STE(A)M for their studies. "Science anxiety" has been reported to be a significant barrier to learning. Mixing animation with astronomy can stimulate interest in STEAM, making science engaging in an unconventional way. One component would be activities where participants create artistic responses to astronomy. We undertook a workshop at a local city-run school, specialising in the arts for ages 14-17, to brainstorm the art/science activities. There we gave short scientific presentations leading to art activities: a giant colouring wall with projected celestial phenomena, a stop-motion station, and colouring images of comet 67P to produce an animation. Surveys before and after the activities showed positive responses. The hand of the artist has long been an important concept in animation (Crafton 1991). In a film entitled "The Movements of the Universe", this concept is adapted to the hands of scientists. Combining animation, filmed interviews at NASA (including a Nobel prize winner), and the scientists' hands, bring unexpected feelings of dream and humour to the audience. In this paper we explore three different viewpoints of these activities from a scientist, an animator, and an animation student.

We examine the sensitivity of the beam normal spin asymmetry in Bhabha scattering to beyond the Standard Model (BSM) mediators, in the context of the JLab polarized positron program. A key property of this observable is that the Standard Model contribution exhibits a zero crossing at a fixed scattering angle, providing a clean, effectively background-free point for these searches. We consider scalar, vector, and axial vector mediators and present projected bounds, finding that scalar and vector scenarios allow a significant extension of the search ranges beyond existing constraints.

Bayesian hypothesis testing via Bayes factors offers a principled alternative to classical p-value methods in meta-analysis, particularly suited to its cumulative and sequential nature. Unlike commonly reported p-values for standard null hypothesis significance testing, Bayes factors allow for quantifying support both for and against the existence of an effect, facilitate ongoing evidence monitoring, and maintain coherent long-run behavior as additional studies are incorporated. Recent theoretical developments further show how Bayes factors can flexibly control Type I error rates through connections to e-value theory. Despite these advantages, their use remains limited in the meta-analytic literature. This paper provides a critical overview of their theoretical properties, methodological considerations, such as prior sensitivity, and practical advantages for evidence synthesis. Two illustrative applications are provided: one on statistical learning in individuals with language impairments, and another on seroma incidence following post-operative exercise in breast cancer patients. New tools supporting these methods are available in the open-source R package BFpack.

We report electrical spin state readout and coherent control of an ensemble ($\sim$540) of silicon vacancies ($\mathrm{V}_{\mathrm{Si}}^{-}$) in a silicon carbide-on-insulator (SiCOI) platform, with excitation wavelengths from 780 to 990 nm, demonstrating for the first time spin state readout well beyond the zero phonon line of the V2 $\mathrm{V}_{\mathrm{Si}}^{-}$. By implementing photoelectrical detection of magnetic resonance in thin-film SiCOI, we merge a scalable spin readout technique requiring no collection optics, together with a promising platform for future scalable and CMOS-compatible integrated photonics. Furthermore, we provide a comparison of optical and electrical readout between bulk silicon carbide (SiC) and thin-film SiCOI, revealing that our thin-film processing has a measured $T_2$ coherence time of $\approx 7 μ$s , similar to that in the bulk SiC. These results extend the capabilities of SiCOI toward electronic and spin-based devices for scalable quantum technologies over a wide range of excitation wavelengths.

The electroproduction of $η'$ mesons from a $\mathrm{^{1}H}$ target at $W=2.13~\text{GeV}$, $Q^{2} = 0.46~\left( \text{GeV}/c\right)^{2}$ and $\cos θ^{\text{CM}}_{γ^{*}η'} \approx -1$ has been experimentally measured. The differential cross section of virtual-photoproduction has been obtained as $4.4 \pm 0.8 ~\left( \text{stat.} \right) \pm 0.4 ~\left( \text{sys.} \right)~ \text{nb/sr}$ in the One-Photon-Exchange Approximation. This value is one-sixth of that of real-photoproduction at backward angles. A comparison with newly-developed isobar model calculations not only shows validity of the theoretical framewark employed, but also imposes new constrains on coupling strength between the $η'p$ final state and nucleon resonances.

There are a number of classical double copies, each providing a prescription for generating solutions to the Maxwell and scalar wave equations from exact solutions of Einstein's equations. Two such prescriptions are the Kerr-Schild and twistorial double copies. We argue that for a broad class of self-dual vacuum solutions of the Kerr-Schild form, which we refer to as twistorial Kerr-Schild spacetimes, these two prescriptions are in fact equivalent. The approach is elementary, utilizing null Lorentz transformations, with homogenous functions on twistor space playing a central role. The equivalence is illustrated explicitly for the example of the self-dual (Kerr)-Taub-NUT spacetime. A detailed proof and several more examples will be presented in a long-form companion to this letter.

Quantum computing holds the promise of solving computational mechanics problems in polylogarithmic time, meaning computational time scales as $\mathscr{O}((\log N)^c)$, where $N$ is the problem size and $c$ a constant. We propose a quantum spectral method with polylogarithmic complexity for solving non-periodic boundary value problems with arbitrary Dirichlet boundary conditions. Our method extends the recently proposed approach by Liu et al. (2025), in which periodic problems are discretised using truncated Fourier series. In such spectral methods, the discretisation of boundary value problems with constant coefficients leads to a set of algebraic equations in the Fourier space. We implement the respective diagonal solution operator by first approximating it with a polynomial and then quantum encoding the polynomial. The mapping between the physical and Fourier spaces is accomplished using the quantum Fourier transform (QFT). To impose zero Dirichlet boundary conditions, we double the domain size and reflect all physical fields antisymmetrically. The respective reflection matrix defines the quantum sine transform (QST) by pre- and post-multiplying with the QFT. For non-zero Dirichlet boundary conditions, the solution is decomposed into a boundary-conforming and a homogeneous part. The homogenous part is determined by solving a problem with a suitably modified forcing vector. We illustrate the basic approach with a Dirichlet-Poisson problem and demonstrate its generality by applying it to a fractional stochastic PDE for modelling spatial random fields. We discuss the circuit implementation of the proposed approach and provide numerical evidence confirming its polylogarithmic complexity.

Quantum reflection occurs when ultra-cold atoms are incident on a material surface with sufficiently low velocity. The reflecting matter wave can interfere with the incident wave to form a detectable pattern, and this pattern contains information about atom-surface interactions at micrometer scales. We discuss how such an interferometer could be used to probe for anomalous short-range forces that are predicted by some beyond-standard model theories. We compare a simple analytical model for the anomalous phase to numerical solution of both the Schroedinger and Gross-Pitaevskii equations, finding good agreement. With interactions, the phase does depend on the atomic density, which can be a source of noise. We nonetheless predict that under realistic conditions, the reflection technique can reach sensitivities approaching those obtained with macroscopic objects, and significantly improve the limits on anomalous coupling to atoms.

In this paper, we study semilinear damped equations $u_{tt}+u_t-Δu=|u|^p$ with the initial data in $({\dot{H}^{-γ}}\cap H^s)\times({\dot{H}^{-γ}}\cap L^2)$. Chen-Reissig (2023) studied the case $0<γ<\frac{n}{2}$ and showed that the exponent $p_{\mathrm{crit}}=1+\frac{4}{n+2γ}$ of $p$ distinguishes the time global existence and the blow-up of solution. In this paper, we discuss the case $γ\ge\frac{n}{2}$.

The Tayler-Spruit dynamo (TSD) is able to generate a small-scale magnetic field in the differentially rotating stably stratified layers of stars and was recently observed in numerical simulations. In parallel, the propagation of internal gravity waves in stars can be modified in the presence of a magnetic field. Here we first want to estimate the interaction between a magnetic field generated by the TSD and internal gravity waves in the radiative core of low-mass stars. This allows us to then characterise the effect of this interplay on the observed standing modes spectrum and on the internal transport of angular momentum by progressive waves. To do this, we use the STAREVOL evolution code to compute the structure of low-mass rotating stars along their evolution. In particular, we implement a formalism to describe the TSD and estimate the regions where the generated magnetic field is strong enough to change the identity of internal gravity waves to magneto-gravity waves. In addition, we evaluate the possible limitation of angular momentum transport by the combined action of rotation and magnetism. We show that along the pre-main sequence and main-sequence evolution, the lowest frequencies of the excited gravity wave spectrum could be converted to magneto-gravity waves by the magnetic field generated by the TSD. During the red-giant branch we find that most of the excited spectrum of progressive internal gravity waves could be converted into magneto-gravity waves in the very central region.

We investigate the local characteristics of the Fulling-Rindler vacuum for a massive Dirac field induced by a planar boundary moving with constant proper acceleration in $(D+1)$-dimensional flat spacetime. On the boundary, the field operator obeys the bag boundary condition. The boundary divides the right Rindler wedge into two separate regions, called RL and RR regions. In both these regions, the fermion condensate and the vacuum expectation value (VEV) of the energy-momentum tensor are decomposed into two contributions. The first one presents the VEVs in the Fulling-Rindler vacuum when the boundary is absent and the second one is the boundary-induced contribution. For points away from the boundary, the renormalization is reduced to the one for the boundary-free geometry. The total VEVs are dominated by the boundary-free parts near the Rindler horizon and by the boundary-induced parts in the region near the boundary. For a massive field the boundary-free contributions in the fermion condensate and the vacuum energy density and effective pressures are negative everywhere. The boundary-induced contributions in the fermion condensate and the energy density are positive in the RL region and negative in the RR region. For a massless field the fermion condensate vanishes in spatial dimensions $D\geq 2$, while the VEV of the energy-momentum tensor is different from zero. This behavior contrasts with that of the VEVs in the Minkowski vacuum for the geometry of a boundary at rest relative to an inertial observer. In the latter case, the fermion condensate for a massless field is nonzero, while the VEV of the energy-momentum tensor becomes zero. The obtained results are used to investigate the VEV of the fermionic energy-momentum tensor in weak gravitational fields and background geometries that are conformally related to Rindler spacetime.

We investigate fluctuations of electric and heat currents, along with their cross-correlations, in a two-channel charge Kondo circuit driven by either a voltage bias or a temperature gradient applied across the weak link. The ratios of voltage-driven electric/heat noise to the applied voltage $V$ exhibit oscillations with the gate voltage $N$, resembling the behavior of the thermoelectric coefficient $G_T$. In contrast, the ratios of temperature-driven electric/heat noise to the temperature difference $ΔT$ vary with $N$ in a manner analogous to the thermal coefficient $G_H$ or the electric conductance $G$. The mixed noise, which is defined as the correlation function between electric and heat currents, displays behavior opposite to that of the above noises. The logarithmic temperature dependence of these noises signals non-Fermi-liquid behavior, while their oscillations with gate voltage reflect the roles of particle-hole and time-reversal symmetries in thermoelectric transport. Our results demonstrate that the fundamental relations linking voltage- and temperature-induced noises to thermoelectric transport across a tunnel junction persist beyond the Fermi-liquid paradigm.

The full extended Gaia mission spans slightly over 10 years, whilst the current data releases represent only a fraction of it, 34 months in Gaia's third data release (DR3). The longer baseline improves the quality of astrometric fits, lowering the noise floor and making consistently bad fits (e.g., due to binarity) more apparent. In this paper, we use simulated binaries from the Gaia Universe Model to examine the long-term astrometric behaviour of single stars and stellar binaries. We calculate nominal upper limits on the spread of goodness of astrometric fits for well-behaved single stars. Specifically, for the RUWE parameter, for upcoming DR4 ($\rm RUWE_{lim}=1.15$) and DR5 ($\rm RUWE_{lim}=1.11$), using the full mission nominal scanning law. These can be used to identify poor astrometric fits and can flag potential binary systems. We show the increase in the number and type of binaries detectable through RUWE. With our updated RUWE thresholds, the number of detectable short-period binaries increases by 5-10% with each subsequent data release, suggesting detections may be possible for orbital periods down to days. The number of detectable long-period systems increases by 10-20%, with periods up to 100 years, causing significant deviations in low and moderate-eccentricity binaries. Very eccentric systems with much longer periods (thousands of years) can still be detected if they pass through periapse during the observing window. Finally, we compare our results to the analytic estimate for the spread in UWE, which we predict from a $χ$-distribution moderated by the number of observations. These agree with our inferred population limits but suggest that we may be biased by a small number of poorly sampled systems. In regions of the sky that are more frequently observed, lower limits could be employed, potentially bringing even more binaries above the threshold for detectability.

As AI becomes more deeply embedded in knowledge work, building assistants that support human creativity and expertise becomes more important. Yet achieving synergy in human-AI collaboration is not easy. Providing AI with detailed information about a user's demographics, psychological attributes, divergent thinking, and domain expertise may improve performance by scaffolding more effective multi-turn interactions. We implemented a personalized LLM-based assistant, informed by users' psychometric profiles and an AI-guided interview about their work style, to help users complete a marketing task for a fictional startup. We randomized 331 participants to work with AI that was either generic (n = 116), partially personalized (n = 114), or fully personalized (n=101). Participants working with personalized AI produce marketing campaigns of significantly higher quality and creativity, beyond what AI alone could have produced. Compared to generic AI, personalized AI leads to higher self-reported levels of assistance and feedback, while also increasing participant trust and confidence. Causal mediation analysis shows that personalization improves performance indirectly by enhancing collective memory, attention, and reasoning in the human-AI interaction. These findings provide a theory-driven framework in which personalization functions as external scaffolding that builds common ground and shared partner models, reducing uncertainty and enhancing joint cognition. This informs the design of future AI assistants that maximize synergy and support human creative potential while limiting negative homogenization.

We show that both temporal and spatial symmetry breaking in canonical K-type transition arise as organized hydrodynamic structures rather than stochastic fluctuations. Before the skin-friction maximum, the flow is fully described by a periodic, spanwise symmetric, harmonic response to the Tollmien-Schlichting wave, forming a spatially compact coherent structure that produces hairpin packets. This fundamental harmonic response may visually resemble turbulence, but remains fully periodic and delimits the exact extent of the deterministic regime. A distinct regime change occurs after this point; a hierarchy of new (quasi-)periodic and aperiodic space-time structures emerges, followed shortly by anti-symmetric structures that develop similarly despite no anti-symmetric inputs, marking the onset of aperiodicity and spanwise asymmetry. We identify these structures as symmetry-decomposed spectral and space-time proper orthogonal modes that resolve the full progression from deterministic to broadband dynamics. The key insight is that laminar-turbulent transition can be viewed as a sequence of symmetry breaking events, each driven by energetically dominant, space-time coherent modes that gradually turn an initially harmonic flow into broadband turbulence.

The unique off-shell fermionic gauge invariance of a vector-spinor field theory is found, and the invariant action is derived. The latter is Weyl invariant in any dimension in the massless limit, and it coincides with the singular point of the one-parameter family of Rarita-Schwinger Lagrangians, in agreement with previous findings in flat space. Pure gauge configurations are represented by gamma-trace vector-spinors, which can be gauged away in a global fashion. Previous claims that this theory is classically inconsistent are shown to be flawed, and the Velo-Zwanziger instability is proved to be absent. The theory propagates a massive spin-3/2 particle together with a spin-1/2 state whose mass is twice that of the j=3/2 mode. The causal construction of the quantum field is consistent with the field equations in that the ratio of the masses is the same, while it shows that the lower-spin component is a negative-norm state. The conformal anomaly is derived using known results for the heat kernel of nonminimal second-order operators, and the resulting $a$ charge is negative consistently with the Hofman-Maldacena bound, which applies only to unitary theories.

We build on the foundational work of Deffner and Zurek [S. Deffner and W. H. Zurek, New J. Phys. 18, 063013 (2016)] to show how central equilibrium structures of statistical mechanics can be understood within standard quantum mechanics using the concept of envariance (environment-assisted invariance). In particular, we show how the Binomial, Poisson, and Gaussian distributions naturally emerge from entangled system-environment states. We revisit the Gibbs paradox from a quantum information perspective, demonstrating that the standard Sackur-Tetrode entropy and its 1/N! factor arise from indistinguishability enforced through entanglement with an environment, without introducing additional thermodynamic corrections. Within the same framework, we analyze ionization equilibrium and show how the classical Saha equation is recovered, while clarifying how indistinguishability enters through an entanglement-induced reduction of permutation redundancy. Assuming the standard exchange symmetries of identical quantum particles, we further show how the Bose-Einstein and Fermi-Dirac distributions follow as the equilibrium weighting of symmetry-allowed occupation configurations. Overall, our results support the view that equilibrium statistical mechanics can be consistently interpreted as an emergent consequence of quantum information-theoretic structure and symmetry, rather than as a collection of independent phenomenological postulates.

Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct numerical simulation (DNS) applied to real-world turbulent applications. Consequently, extensive research has focused on analysing turbulent flows from a data-driven perspective. However, due to the complex and chaotic nature of these systems, traditional models often become unstable as they accumulate errors through autoregression, severely degrading even short-term predictions. To overcome these limitations, we propose a purely stochastic approach that separately addresses the evolution of large-scale coherent structures and the closure of high-fidelity statistical data. To this end, the dynamics of the filtered data (i.e. coherent motion) are learnt using an autoregressive model. This combines a VAE and Transformer architecture. The VAE projection is probabilistic, ensuring consistency between the model's stochasticity and the flow's statistical properties. To recover high-fidelity velocity fields from the filtered latent space, Gaussian Process (GP) regression is employed. This strategy has been tested in the context of a Kolmogorov flow exhibiting chaotic behaviour analogous to real-world turbulence. We compare the performance of our model with state-of-the-art probabilistic baselines, including a VAE and a diffusion model. We demonstrate that our Gaussian process-based closure outperforms these baselines in capturing first and second moment statistics in this particular test bed, providing robust and adaptive confidence intervals.

In multitemporal InSAR, phase linking (PL) refers to the estimation of a single-reference interferometric phase history for distributed scatterers (DS) from the information contained in the sample coherence matrix. Because the phase information in this matrix is typically inconsistent, DS processing needs practical reliability indicators to decide whether a pixel's PL estimate is sufficiently supported by the data for subsequent deformation analysis. For maximum-likelihood estimation, uncertainty can be quantified via Fisher-information-based covariance estimates, but no analogous, generally applicable uncertainty quantification is available for the broad range of non-ML methods. We propose three heuristic quality coefficients within a unified mathematical framework that covers common PL methods: (1) a method-specific goodness-of-fit coefficient that normalizes the achieved PL objective between a method-consistent upper bound and an empirically modeled noise floor level; (2) a closure phase coefficient computed from the sample coherence matrix in advance; and (3) an ambiguity coefficient that compares the obtained PL estimate with the best alternative in its orthogonal complement in the solution space. All coefficients are normalized to the interval $[0,1]$, where 1 indicates maximum reliability and 0 matches the behavior expected under pure noise. Simulations under exponential and seasonal decorrelation models show that the goodness-of-fit coefficient tracks the normalized absolute phase error most consistently, whereas the closure phase coefficient provides an a priori indicator for pre-screening. Experiments on a TerraSAR-X stack over Visp, Switzerland, reveal plausible spatial patterns across urban and vegetated areas and show that the ambiguity coefficient provides complementary information, especially in regions with temporally varying scattering mechanisms.

The increase in computation and storage has led to a significant growth in the scale of systems powering applications and services, raising concerns about sustainability and operational costs. In this paper, we explore power-saving techniques in high-performance computing (HPC) and datacenter networks, and their relation with performance degradation. From this premise, we propose leveraging Energy Efficient Ethernet (EEE) protocol, with the flexibility to extend to conventional Ethernet or upcoming Ethernet-derived interconnect versions of BXI and Omnipath. We analyze the PerfBound power-saving mechanism, identifying possible improvements and modeling it into a simulation framework. Through different experiments, we examine its impact on performance and determine the most appropriate interconnect. We also study traffic patterns generated by selected HPC and machine learning applications to evaluate the behavior of power-saving techniques. From these experiments, we provide an analysis of how applications affect system and network energy consumption. Based on this, we disclose the weakness of dynamic power-down mechanisms and propose an approach that improves energy reduction with minimal or no performance penalty. To the best of our knowledge, this work presents the first thorough analysis of PerfBound and an enhancement to the technique, while also targeting emerging post-exascale networks.

We study an LCM-based analogue of Rowland's GCD-based prime-generating recurrence, introduced by the author in 2008. The multiplicative increments of this sequence are conjectured always to be $1$ or prime, but a complete proof requires a strengthening of Linnik's theorem on the least prime in an arithmetic progression that lies beyond current reach. We develop a Companion--Sieve framework that reduces the conjecture to an equidistribution problem for primes in the progression $-1\bmod p$, and applying the Bombieri--Vinogradov theorem we prove unconditionally that the conjecture holds for a set of integers of asymptotic density $1$. We also give an effective finite reduction showing that any counterexample beyond a computable threshold involves only large prime factors. A closely related recurrence turns out to encode twin prime pairs through its increment pattern, and we prove a conditional density-$1$ result for it under a prime-index detection hypothesis, using an upper-bound Selberg sieve estimate for twin primes in arithmetic progressions. The analysis also leads to three new conjectures on the distribution of primes in arithmetic progressions.

The Wilson formulation of fermions in lattice gauge theory provides a unified description of the chiral anomalies in the standard model. The discrete Dirac operator diagonalizes into a series of two by two blocks. In each block the possible eigenvalues either form a complex pair or separate into two real eigenvalues that have specific chirality. The collision of these pairs of eigenvalues occurs outside the perturbative region and provides a path between topological sectors.

We present an extremely simple polynomial-space exponential-time $(1-\varepsilon)$-approximation algorithm for MAX-k-SAT that is (slightly) faster than the previous known polynomial-space $(1-\varepsilon)$-approximation algorithms by Hirsch (Discrete Applied Mathematics, 2003) and Escoffier, Paschos and Tourniaire (Theoretical Computer Science, 2014). Our algorithm repeatedly samples an assignment uniformly at random until finding an assignment that satisfies a large enough fraction of clauses. Surprisingly, we can show the efficiency of this simpler approach by proving that in any instance of MAX-k-SAT (or more generally any instance of MAXCSP), an exponential number of assignments satisfy a fraction of clauses close to the optimal value.

Stellar flares are intense bursts of radiation caused by magnetic reconnection on active stars. They are especially frequent on M dwarfs, where they can significantly influence the habitability of orbiting planets. Flare frequency distributions (FFDs) are typically modelled as power laws. However, recent studies challenge this assumption and propose alternatives such as lognormal laws that imply different flare generation mechanisms and planetary impacts. This study investigates which statistical distribution best describes flare occurrences on M dwarfs, considering both equivalent duration (ED), directly measured from light-curve photometry, and bolometric energy, relevant for physical interpretation and habitability. We analysed 110 M dwarfs observed with TESS and CHEOPS, detecting 5620 flares. We decomposed complex events, corrected for detection biases in recovery rate and energy estimation, and scaled the FFDs to construct a combined distribution spanning six orders of magnitude in bolometric energy. We find that ED-based FFDs follow a power law, reflecting intrinsic photometric flare occurrence. However, bolometric-energy-based FFDs deviate from a pure power law. They are better described by a lognormal distribution, although the best fit is a truncated power law with a break at $1.8 \times 10^{35}$ erg. Using right-tail-stabilised Kolmogorov-Smirnov and exceedance tests, we attribute this deviation to limited sampling of the most energetic events. Our results show that the low-energy flattening, previously interpreted as lognormal behaviour, arises from observational biases and can be corrected through flare injection-recovery and combining observations with different sensitivities. Current instruments cannot reliably sample flares above $10^{35}$ erg, the most relevant for exoplanetary atmospheres. The upcoming PLATO mission will be able to investigate both regimes.