The soft-output successive cancellation list (SO-SCL) decoder provides a methodology for estimating the a-posteriori probability log-likelihood ratios by only leveraging the conventional SCL decoder of polar codes. However, the sequential decoding nature of SCL introduces high decoding latency to SO-SCL. In this paper, we incorporate node-based fast decoding into the SO-SCL framework. After addressing the challenge of soft output extraction in special node decoding, we proposed the soft-output fast SCL (SO-FSCL) decoding algorithm, along with its log-domain implementation and hardware-friendly version. The proposed SO-FSCL decoder can be regarded as an add-on extension to FSCL decoder, enabling us to autonomously choose whether to output only hard decisions like FSCL or to provide additional soft outputs. Latency and complexity analyses demonstrate that SO-FSCL can significantly reduce, for example, decoding time steps by 81.8\% (with unlimited resources), the number of additions by 41.3\%, and the number of comparisons by 46.4\%. Meanwhile, simulation results indicate that SO-FSCL delivers almost the same soft-output performance as SO-SCL, outperforming other soft-output polar decoders, especially in scenarios involving iterative decoding.

Nontransiting planets can reveal themselves through transit timing variations (TTVs), but inferring the properties of the perturbing planet is a highly degenerate inverse problem. We present a systematic reassessment of all 12 published cases in which a nontransiting planet was claimed to have been uniquely characterized using TTVs. Two systems (KOI-142 and Kepler-419) stand out clearly with compelling evidence for unique solutions. Two other systems (KOI-872 and KOI-884) exhibit complex degeneracies, but the data are just precise enough to single out a best solution. Six systems (Kepler-82, Kepler-411, Kepler-725, KOI-134, Kepler-138, and TOI-4562) admit multiple viable solutions involving very different perturbing planets. In the remaining two systems (WASP-18 and WASP-126), the evidence for any perturbing planet is weak. We find that a necessary (but not sufficient) condition for a unique solution is the detection of short-timescale TTV structure associated with conjunctions, either in the near-resonant "chopping" regime or in eccentric systems with phase-dependent close approaches. In some systems, aliasing of the synodic period leads to ambiguities in associating observed TTV timescales with physical timescales, threatening uniqueness. Our results highlight the difficulty of achieving unique solutions in TTV inversions and underscore the need for long time baselines, accurate timing uncertainties, and complementary constraints from radial velocities or other observations when characterizing nontransiting planets.

We present updated hard X-ray polarization measurements of the Crab pulsar and nebula obtained with the balloon-borne polarimeter XL-Calibur in the ~19-64 keV energy range. During the flight, intermittent GPS-failure resulted in poorly constrained timing for ~38% of the Crab dataset. By implementing a new phase-recovery method that reconstructs timing during extended GPS-off intervals, phase tag data is recovered for ~95% of the GPS-off dataset, increasing the precision of the phase-resolved analysis. Phase-information for the data is recovered by using the Crab pulsar, with its 33 ms period, as an external timing source. Using a Markov-Chain Monte-Carlo framework to jointly fit phase offsets and frequency derivatives, sufficient phase accuracy is achieved, across multiple periods without GPS for a phase-resolved analysis. This enables inclusion of nearly the full dataset in the polarization study. The polarization degree of the nebular emission is found to be (27.7${\pm}$4.9)% at a polarization angle of 127.2°${\pm}$5.1° confirming previous XL-Calibur results and remaining aligned with the Crab's spin axis, consistent with synchrotron emission from the inner nebula. Phase-resolved measurements show that the off-pulse and bridge intervals exhibit a strong polarization, while the pulsar peaks, although weakly constrained, remain in agreement with the softer-energy trends of IXPE. These findings reinforce a scenario in which hard X-ray emission arises primarily in the nebular torus and wind regions. The successful recovery of precise phase tagging from GPS-off data demonstrates the capacity to use the pulsar as an external clock even in the case of sparsely populated data.

In the present paper, we study the diffusion limit of the classical solution to the modified Vlasov-Poisson-Boltzmann (mVPB) System with initial data near a global Maxwellian. Based on the spectral analysis, weprove the convergence and establish the convergence rate of the global strong solution to the mVPB system towards the solution to an incompressible Navier-Stokes-Poisson-Fourier system with the precise estimation on the initial layer.

We present a statistical measurement of the transverse coherence of Mg II $λ\lambda2796,2803$ absorption using a large sample of 9204 absorber-centric quasar sightline pairs from the Sloan Digital Sky Survey. We quantify the probability that an Mg II absorber detected along one sightline is also present along a nearby sightline, and measure how this coincidence probability varies with projected separation from $\sim$50 kpc to $\sim$1 Mpc. The resulting coincidence curve exhibits a clear two-regime structure: the coincidence probability rises steeply to $\sim$5-8% at separations below $\sim$100 kpc, but declines rapidly beyond this scale and settles into a low plateau of $\sim$1--2% out to $\sim$1 Mpc. A simple geometrical single-halo model reproduces the enhanced probability at $\lesssim$100 kpc, while the large-scale plateau is well explained by the expected contribution from galaxy clustering, confirmed using both photometric galaxy counts and the two-point correlation function. A complementary stacking analysis reveals a significant excess in Mg II equivalent width in paired sightlines lacking individual detections, implying a coherence scale of $\sim$100-200 kpc for the cool, metal-enriched CGM. Together, these results identify the transition from a halo-dominated coherence regime at small separations to a clustering-dominated regime at large scales, bridging the gap between small-scale lensing constraints and megaparsec-scale absorber clustering studies.

We present JWST MIRI and NIRCam imaging of the inner ~5 kpc of the M82 superwind at 0.05-0.375'' (~0.9-6.5 pc) resolution. Targeted filters probe emission from polycyclic aromatic hydrocarbons (PAHs; F335M, F360M, F770W, F1130W) and continuum (F250M, F360M). The images reveal a network of cool wind filaments traced by PAHs. PAH surface brightness declines with the inverse square of distance to the midplane, suggesting that the incident radiation field from the starburst drives the observed PAH intensity out to 2.5 kpc. The 3.3/11.3 and 3.3/7.7 band ratios show uniformity with distance from the starburst, though comparisons with mid-IR dust emission models indicate a modest shift toward larger PAHs. Outside the disk, 11.3/7.7 increases moderately, reflecting that PAHs become more neutral with distance from the starburst as they are exposed to a declining radiation field and ionization parameter. Overall, PAHs in the wind are consistent with standard-to-large sizes and standard-to-high ionization states. Including Spitzer and Herschel data, PAH abundance (qPAH) is set at ~1% in the starburst and remains unchanging out to 5 kpc off the disk. This flat qPAH profile suggests that PAHs are shielded from the hot wind, perhaps residing in the surface layers of cool clouds, with possible replenishment from cloud interiors and enrichment of the halo from previous bursts. In this picture, clouds are not dense enough to promote PAH growth, and they likely undergo radiative cooling and mixing with the hot phase to survive the gauntlet for at least ~20 Myr.

Near-term quantum computers must protect fragile coherence against decoherence to deliver useful results. Catalytic quantum error correction (CQEC) addresses this challenge by amplifying residual coherence with a reusable catalyst, achieving threshold-free recovery whenever the target coherent modes survive in the noisy state. However, the original protocol requires complete knowledge of the ideal target -- an assumption that fails for variational and iterative algorithms whose output is unknown to the correction module. Here we show that this requirement can be removed by estimating the target from the noisy output alone, in a two-stage protocol we call \emph{blind CQEC}. We benchmark five estimation strategies across three noise channels, four quantum algorithms ($d = 4$--$64$), Haar-random states up to $d = 256$, and mixed targets, and find that estimation and recovery fidelities are linearly correlated ($r > 0.99$); we prove an analytical Lipschitz bound $F_\mathrm{rec} \geq 1 - 2\|\hatρ_\mathrm{est} - ρ_\mathrm{target}\|_1$ that explains the correlation, derive a crossover dimension $d^* \approx 25$--$40$, and show that a tunable hybrid bridges the two regimes. Unlike error-mitigation methods (zero-noise extrapolation, probabilistic error cancellation, virtual distillation), blind CQEC returns the state itself rather than corrected expectation values, with single-copy overhead. A noisy-VQE demonstration for H$_2$ yields $3.4\times$ energy-error reduction, and a \texttt{qiskit-aer} circuit-level check confirms transfer to small circuits. These results identify the bottleneck of blind error correction as a classical estimation problem, opening a route to autonomous, threshold-free recovery in algorithms where pre-encoding is unavailable.

The ultrafast nonlinear optical response of molecular ensembles is fundamentally altered under strong light-matter coupling. To rigorously isolate the genuine many-body contributions, an exact time-domain field-subtraction protocol is developed within a fully non-perturbative Maxwell-Liouville framework explicitly incorporating the two-exciton manifold in real space and time. This approach reveals that while collective cavity delocalization drives the macroscopic nonlinear signal toward a severe harmonic cancellation (an effect termed "spectral starvation"), intrinsic many-body molecular interactions robustly resurrect genuine polaritonic double-quantum coherences (DQCs). This many-body resurrection is governed by a universal two-photon matching rule, $Δ_B + 4J = Ω_R$, linking molecular anharmonicity ($Δ_B$) to the macroscopic Rabi splitting ($Ω_R$) and excitonic coupling ($J$). Crucially, this resonance exploits the spatial mismatch between macroscopic polaritons and localized two-exciton pairs to break harmonic cancellation. For J-aggregates ($J < 0$), this condition uniquely isolates the resonant many-body state below the dense manifold of localized dark states, protecting the macroscopic coherence from spatial fragmentation. This predictive framework establishes a direct phase diagram to engineer and protect optical nonlinearities across diverse strongly coupled platforms.

Employing the Schwinger-Keldysh formalism, we formulate an effective field theory for s-wave superconducting phase transition, where the dynamical variables consist of electromagnetic gauge field and complex scalar order parameter. Symmetry-constrained effective action allows systematic handling of dissipations and fluctuations. In particular, we explore the physical implications of higher-order terms, including those involving additional dynamical fields as well as higher time derivatives, on the real-time dynamics near the superconducting critical point. When appropriately truncated, the effective field theory reproduces the phenomenological Ginzburg-Landau equations. Upon crossing the critical temperature into the low-temperature phase, the electromagnetic gauge symmetry undergoes spontaneous breaking induced by the condensate of the order parameter. Collective excitation analysis reveals that the Higgs mode behaves as an overdamped diffusive mode near the critical point, while the phase fluctuation is absorbed into the gauge field via the Higgs mechanism. Via the holographic Schwinger-Keldysh technique, rigorous validation in a holographic superconductor confirms the structure of the effective action and quantifies the Wilsonian coefficients. Holographic results revaeal a complex relaxation parameter that indicates oscillatory dynamics characteristic of strongly coupled systems.

We establish the well-posedness of the Helmholtz equation with rough and compactly supported coefficients in Rd under sharp regularity assumptions. Using a paraproduct calculus in rescaled weighted Besov spaces, we rigorously define the product between the solution and the coefficient at the lowest regularity level without renormalization. A rescaled Lippmann-Schwinger formulation is shown to be equivalent to the Helmholtz equation with the Sommerfeld radiation condition. We prove existence, uniqueness, and explicit wavenumber dependent resolvent estimates in a general Lp setting, including an L2 theory relevant to scattering amplitudes. The results provide a sharp analytic foundation for wave propagation and scattering in highly irregular media.

Topological semimetals have emerged as an important class of quantum materials with novel electronic responses and unconventional transport phenomena. Among them, nodal-line semimetals are distinguished by band crossings that extend along one-dimensional lines in momentum space rather than occurring at discrete points, forming closed loops, chains, or extended lines. The stability of these nodal structures is governed by crystalline symmetries such as mirror, spin-rotation, and nonsymmorphic operations, which give rise to characteristic topological invariants and surface states, including drumhead-like bands. In this review, we present a comprehensive overview of the theoretical framework and experimental realization of nodal-line semimetals, with particular emphasis on symmetry protection and the consequences of symmetry breaking. We discuss the classification of nodal-line structures, their evolution into other topological phases, and their signatures in electronic structure measurements and transport phenomena. Special attention is given to insights obtained from angle-resolved photoemission spectroscopy and related probes. By bringing together symmetry analysis, band topology, and experimental observations, this review aims to clarify the relationship between topology, magnetism, and measurable electronic responses in nodal-line semimetals. These considerations highlight their potential as a versatile platform for next-generation topological electronic functionalities and emergent quantum phenomena beyond conventional paradigms.

We establish the global existence of weak solutions to the isentropic compressible Navier-Stokes equations in three-dimensional annular cylinders with Navier-slip boundary conditions, allowing large axisymmetric initial data and vacuum states, provided that the bulk viscosity is sufficiently large. We identify a regime in which compressible and incompressible effects coexist. The compressible component interacts with pressure and density to produce an effective dissipation mechanism, while the divergence-free component enjoys improved regularity. This shows that large bulk viscosity strongly suppresses the compressible effect, thereby relaxing restrictions on the size of the initial data. Moreover, such solutions converge globally in time to weak solutions of the inhomogeneous incompressible Navier-Stokes system as the bulk viscosity tends to infinity. The proof relies on a Desjardins-type logarithmic interpolation inequality and Friedrichs-type commutator estimates. Our results build upon the works of Hoff (Indiana Univ. Math. J. 41 (1992), pp. 1225-1302) and Danchin-Mucha (Comm. Pure Appl. Math. 76 (2023), pp. 3437-3492), and further develop Hoff-type time-weighted estimates uniform in the bulk viscosity in the presence of boundaries.

In the Stable Roommates Problem (SR), a set of $2n$ agents rank one another in a linear order. The goal is to find a matching that is stable: one that has no pair of agents who mutually prefer each other over their assigned partners. We consider the problem of finding an optimal stable matching. Agents associate weights with each of their potential partners, and the goal is to find a stable matching that minimizes the sum of the associated weights. Efficient algorithms exist for finding an optimal stable matching in the Stable Marriage Problem (SM), but the problem is NP-hard for general SR instances. In this paper, we define a notion of structural distance between SR instances and SM instances, which we call the minimum crossing distance. When an SR instance has minimum crossing distance $0$, the instance is structurally equivalent to an SM instance, and this structure can be exploited to find an optimal stable matching efficiently. More generally, we show that when an SR instance has minimum crossing distance $k$, an optimal stable matching can be computed in time $2^{O(k)} n^{O(1)}$. Thus, the optimal stable matching problem is fixed-parameter tractable (FPT) with respect to minimum crossing distance.

Mixed quantum-classical models are widely used to reduce the computational cost of fully quantum simulations. However, their general applicability across different classes of problems remains an open question. Here, we address this issue for systems featuring spin-orbit coupling. In particular, we study the interaction dynamics of quantum spin-1/2 and classical orbital momentum in one-dimensional models of Rashba nanowires. We tackle this problem by resorting to a new quantum-classical Hamiltonian model that, unlike conventional approaches, retains the Heisenberg principle and captures correlation effects beyond the common Ehrenfest approach. Based on Koopman wavefunctions in classical mechanics, the new model was recently implemented numerically via a particle scheme -- the koopmon method -- which is extended here to treat spin-orbit coupling. We apply the koopmon method to study the quantum-classical dynamics of nanowire models, with and without the presence of a harmonic potential and in both Rashba-dominated (strong coupling) and Zeeman-dominated (weak coupling) regimes. Considering realistic semiconductor parameters, the results are contrasted with both fully quantum and quantum-classical Ehrenfest dynamics. In the absence of external potential, the koopmon method qualitatively reproduces the features of the fully quantum evolution for all coupling regimes. While it exhibits a slight loss in spin accuracy compared to Ehrenfest simulations, the latter fail to capture the orbital dynamics. In the presence of a harmonic potential, the koopmon scheme reproduces the full quantum results with accuracy levels that are unachievable by the Ehrenfest model in both quantum and classical sectors. We conclude by presenting a test case that exhibits the formation of cat-like states.

We provide a description of the code implementation and structure of Cosmology Likelihood for Observables in Euclid (CLOE), developed by members of the Euclid Consortium. CLOE is a modular Python code for computing the theoretical predictions of cosmological observables and evaluating them against state-of-the-art data from galaxy surveys such as Euclid in a unified likelihood. This primarily includes the core observables of weak gravitational lensing, photometric galaxy clustering, galaxy-galaxy lensing, and spectroscopic galaxy clustering, but also extended probes such as the clusters of galaxies and cross-correlations of galaxy positions and shapes with the cosmic microwave background. While CLOE has been developed to serve as the unified framework for the parameter inferences in Euclid, it has general capabilities that can serve the broader cosmological community. It is different from other comparable cosmological tools in that it is written entirely in Python, performs the full likelihood calculation, and includes both photometric and spectroscopic observables. We will focus on the primary probes of Euclid and will describe the overall code structure, rigorous code development practices, extensive documentation, unique features, speed optimization, and future development plans. CLOE is publicly available at https://github.com/cloe-org/cloe.

Order dimension theory measures the complexity of partially ordered sets by quantifying how far they are from being linearly ordered. In this paper we study classical bounding results for order dimension within the framework of reverse mathematics. We focus on principles asserting that the dimension of a poset can be bounded in terms of the dimension of subposets obtained by removing chains or points, denoted by $\mathsf{DBi_n}$, $\mathsf{DBc_n}$, and $\mathsf{DB_p}$. We prove that, over $\mathsf{RCA}_0$, both $\mathsf{DBi_n}$ and $\mathsf{DBc_n}$ are equivalent to $\mathsf{WKL}_0$. To analyze $\mathsf{DB_p}$, we introduce a natural strengthening $\mathsf{DB^+_p}$ and show that both $\mathsf{DB_p}$ and $\mathsf{DB^+_p}$ are provable from $\mathsf{WKL}_0$ and from $\mathsf{I}Σ^0_2$, while $\mathsf{B}Σ^0_2$ does not suffice to prove $\mathsf{DB^+_p}$. The latter result is obtained by showing that the statement \lq\lq $\mathsf{DB^+_p}$ is computably true\rq\rq\ is equivalent to $\mathsf{I}Σ^0_2$.

We used a deep learning workflow to enhance earthquake detection during the 2025 seismic unrest between Santorini and Amorgos islands to track the evolution of the crisis in near real-time. We analysed the continuous seismic waveforms daily (1/2 - 3/3/25) as the crisis unfolded. Our analysis enhanced the earthquake catalogue from around 4,000 to 80,000 earthquakes. The enhanced catalogue allowed this international expert group to identify the volcanic-tectonic character, clearly revealing burst-like, spasmodic seismicity swarms, which is a pattern associated with fluid-driven processes from early stages of the crisis. Detailed moment tensor inversions in early events characterised by a significant non-double couple component indicated the involvement of magmatic or high-pressure hydrothermal fluids driving the unrest. Concurrent DL-enhanced tomography efforts identified a third, deep magmatic reservoir beneath Anydros Islet, consistent with pressure-driven processes. To date, volcanic-tectonic swarms in which >200 earthquakes of ML > 4 occurred within only a few weeks, largely within episodic bursts of seismicity, have not been observed elsewhere.

Let $\mathcal B=\mathcal B_{k,n,p}$ be a random collection of $k$-subsets of $[n]$ where each possible set is present independently with probability $p$. Let $\cal E_{\mathcal B}$ be the event that $\mathcal B$ defines the set of bases of a matroid. We prove that If $p= 1-\frac{c_n}{(k(n-k)\binom nk)^{1/2}}$ where $0\leq c_n\leq \infty$, then \[ \lim_{n\to\infty}\Pr[\cal E_{\cal B}\mid |\cal B|\geq2]=\begin{cases}1&c_n\to0.\\e^{-c^2/2}&c_n\to c.\\0&c_n\to \infty.\end{cases}\] In addition, we identify a condition preventing the occurence of $\cal E_{\cal B}$ and prove a hitting time version for the occurence of $\cal B$. We also prove that when $\cal E_{\mathcal B}$ occurs, $\mathcal B$ defines a sparse paving matroid w.h.p. In addition, study a greedy algorithm that produces a random matroid defined by a collection of hyperplanes. We use this to improve the estimates in \cite{HPV} on $\log m(n,k),\log p(n,k), \log s(n,k)$ where $ m(n, k), p(n, k), s(n, k)$ denote the number of matroids, paving matroids, and sparse paving matroids (respectively) of rank $k$ on $[n]$. Our improvement lies in that we can deal with $k$ growing slowly with $n$ as opposed to $k=O(1)$ in \cite{HPV}. More generally, we obtain estimates for the number of matchings in nearly-regular hypergraphs with small codegree, which may be of independent interest.

A knot $K$ is called $n$-adjacent to a knot $K'$ if there is a set of $n$ crossing circles $\mathcal C$ in $K$ so that a generalized crossing change at any nonempty subset of crossings in $\mathcal C$ yields $K'$. In this paper, the authors define a new graph $Γ_n$ to represent $n$-adjacency relationships between knots. We prove several results about this new object.

We consider optical communications with intensity modulation and direct detection affected by laser relative intensity noise (RIN). Starting from a continuous-time waveform model, we derive an equivalent discrete-time channel model. As a result of RIN, the resulting channel model exhibits signal-dependent noise with memory. Unlike the commonly-assumed model in the literature, the conditional variance of this noise term has a polynomial dependence on the symbol of interest. Finally, we study achievable information rates for this channel under practically-relevant system parameters. We take a mismatched decoding approach and compute the generalized mutual information (GMI) using a memoryless decoding metric. Our numerical results show that when the memory in the channel is ignored by the receiver, GMI saturates as the constellation size increases, and thus, dense constellations do not offer gains. We also show that this saturation results from nonsymmetric nonvanishing contributions of the symbols to the GMI.

Magic states are a scarce resource for two-dimensional qubit stabilizer codes. Magic state cultivation was recently proposed to reduce the cost of magic state preparation by measuring the transversal Clifford operator of the color code. Cultivation achieves $\sim 10^{-9}$ logical error rates for the $d=5$ color code, with substantially lower space-time overhead than magic state distillation. However, due to the $\mathcal{O}(d)$ depth of the Clifford measurement circuit, magic state cultivation becomes impractical for $d>5$. Here, we perform logical $XS^\dagger$ measurements on the color code by gauging a transversal Clifford gate, resulting in a constant-depth logical measurement circuit. We employ repeated gauging measurements with post-selection rather than performing error correction on the Clifford stabilizer code that emerges during the gauging protocol, thus gaining simplicity at the cost of scalability. Our protocol requires a regular square grid connectivity and yields logical error rates comparable to magic state cultivation. The $d=7$ version of our protocol gives access to the $10^{-12}$ logical error rate regime at $0.05\%$ physical error rate while retaining more than $1\%$ of the shots after the equivalent of the cultivation stage.

NEXUS is a JWST Multi-Cycle (Cycles 3-5) GO Treasury imaging and spectroscopic survey around the North Ecliptic Pole during 2024-2028. It contains two overlapping tiers in depth and area coverage. The Wide tier ($\sim 400~{\rm arcmin}^2$) performs NIRCam/WFSS 2.4-5 $μ$m grism spectroscopy with three annual epochs over 3 years (final spectral continuum ${\rm S/N/pixel>3}$ at F444W $<22.2$), accompanied by NIRCam multi-band imaging in F090W, F115W, F150W, F200W, F356W and F444W. The Deep tier ($\sim 50~{\rm arcmin}^2$) performs high-multiplexing NIRSpec 0.54-5.5 $μ$m MOS/PRISM spectroscopy for ~10,000 targets in total, over 18 epochs with a 2-month cadence, along with F200W+F444W NIRCam imaging for each epoch. Parallel imaging observations with MIRI and additional NIRCam filters are also performed within the Wide and Deep tiers. The primary data covering the Deep tier (including NIRCam imaging, NIRSpec/MSA spectra, and vetted MSA spectroscopic redshifts) are released in regular Quick Data Releases to facilitate follow-up studies. This evolving document describes the MSA targeting information and observing status for each of the 18 Deep epochs, which started in May 2025 and continue on the regular 2-month cadence. We also describe the content and caveats of the quick release data and report selected cases of diverse scientific interests.

Multimode circuits provide an avenue for flexible control of single and multi-qubit gates. In this work we implement a multimode circuit known as a trimon integrated in a planar geometry. The trimon features three transmon-like modes with strong all-to-all $ZZ$ coupling. We demonstrate high fidelity operations on the trimon, achieving flexible control of its rich state space. This includes qubit rotations conditioned on one or both other qubits, unconditional single-qubit rotations, and both excitation-conserving and double-excitation two-qubit entangling gates. Through multi-tone driving we are able to implement all 16 two-qubit Pauli operators in the two-qubit space. We further demonstrate using the trimon as a qudit with up to 8 states and higher coherence than typical transmon-based implementations. Our results show a compact, highly controllable device that can potentially replace transmons in standard superconducting processor architectures.

Plasma accelerators are rapidly evolving toward user-relevant machines with increasing repetition rates, particle energies and average beam powers. Despite their compact size, the operational characteristics of plasma accelerators are comparable to those of radio-frequency linacs, involving the continuous generation and dumping of electron bunches. However, beam properties and loss patterns can differ substantially from those of conventional accelerators, leading to radiation safety considerations dominated by high peak charges and distributed beam losses relevant for both personnel protection and machine integrity. Using established scaling laws, we show that significant dose rates already occur at electron energies of several MeV, underscoring the relevance of radiation protection even for comparatively low-energy plasma accelerators. Based on a combination of Monte Carlo and particle-in-cell simulations, supported by radiation measurements from plasma accelerator experiments at DESY, we analyze typical radiation fields with a particular focus on radiation generated close to the plasma source. These findings highlight the need for dedicated shielding and beam-dump concepts tailored to plasma accelerators, especially in view of increasing average beam powers and future application-oriented operation.

The problem of sums of independent, identically distributed random variables with stretched-exponential tails exhibits a dynamical phase transition and has recently reemerged in the context of active transport and condensation phenomena. We develop a perturbative expansion for the distribution of the sum that systematically extends the Big Jump Principle beyond its asymptotic regime. The expansion yields explicit higher order corrections that describe moderate deviations, bridging the gap between typical Gaussian fluctuations and the far-tail behavior dominated by single big jump events. In this sense, our approach is complementary to the classical Edgeworth expansion, which provides corrections to the Gaussian core, whereas we construct systematic corrections to the big jump regime. The leading terms reveal the scaling structure governing the crossover between typical and condensed fluctuations, in agreement with large deviation predictions but without relying on its asymptotic limit. We further extend the framework to continuous-time random walks (CTRWs), where stretched-exponential jump statistics combined with stochastic renewal times generate nontrivial propagators through subordination. This setting is particularly relevant for transport processes with non-Gaussian displacement statistics, where super-exponential or Laplace-like tails emerge from the interplay of rare large jumps and temporal fluctuations. All analytical predictions are supported by numerical simulations.

In this paper, we aim to study traces of Frobenius of certain one parameter families of elliptic curves and their relationships with $p$-adic hypergeometric functions. For example, we consider a DIK family of curves and establish the trace of Frobenius as weighted averages of special values of certain families of $p$-adic hypegeometric functions, where the average is taken over the arrays of parameters. Moreover, we consider Jacobi curves and express the trace of Frobenius as a special values of $p$-adic hypergeomtric functions. As a consequence of these results we obtain four summation identities for the $p$-adic hypegeometric functions that arise from the DIK family. Furthermore, we obtain $p$-adic analogous of Euler and Pfaff transformations for certain $p$-adic hypergemetric functions.

We investigate the modifications to inflationary observables that arise when adopting an $α$-vacuum instead of the standard Bunch--Davies vacuum for quantum fluctuations during inflation. Within the Starobinsky inflationary model, we compute and compare the scalar spectral index, its running, and the running of the running arising from different choices of the initial vacuum state. We further examine the energy scales associated with $α$-vacua and argue that, for any number of extra spatial dimensions, the relevant scale can be truncated at the Hubble scale, $\sim$$\mathcal{O}(10^{13})\,\mathrm{GeV}$, without conflict with current Cavendish-type experimental bounds on sub-millimeter gravity ($\sim$$250\,μ\mathrm{m}$). Our analysis demonstrates that the $α$-vacuum is subject to stringent constraints as a viable de~Sitter-invariant alternative to the Euclidean (Bunch--Davies) vacuum, with the corrections that it induces in the inflationary observables being strongly limited by the latest Planck data.

Controlling light-matter interactions is central to photonic technologies ranging from lasers to optical information processing. Suitably designed photonic structures give rise to flat (dispersionless) bands, where the density of states diverges, and group velocity goes to zero, allowing light localization. These properties make flat bands attractive for lasing; however, designing photonic structures supporting flat bands suitable for lasing is challenging. Here, we introduce nanoparticle chain lattices. These chain geometries provide long-range coupled systems that support, at predictable wavelengths, bands that are totally flat and extend over the full angular range. We demonstrate lasing in the transverse-magnetic (TM) mode of single chains of nanoparticles and explain the transition from flat band lasing to the single-mode normal-incidence (Gamma-point) lasing as the number of chains is increased. Moreover, we show partially coherent emission from square and triangular two-dimensional chain lattices. The excited modes depend on the pump power and polarization. Our results establish chain lattices as a versatile platform for exploring flat band lasing and suggest new routes toward narrowband, linearly polarized, and bright light sources with tailored coherence.

We study incentive design when multiple principals simultaneously design mechanisms for their respective teams in environments with strategic spillovers. In this environment, each principal's set of incentive-compatible mechanisms--those that satisfy their own agents' incentive compatibility constraints--depends on the mechanisms offered by the other teams. Following a classic example by Myerson (1982), such games may lack equilibrium due to discontinuities in the correspondence of incentive-compatible mechanisms. We establish general conditions for equilibrium existence by introducing a novel approach that involves tracking both the outcome distributions along the truthful-obedient path and the sets of outcome distributions achievable through unilateral deviations, thereby providing a foundation for analyzing a wide range of multi-principal mechanism design with team production and agency problems.

This note provides a simple derivation of the overdamped approximation for kinetic (or underdamped) equilibrium Langevin dynamics, in cases where certain coefficients depend on the position variable. The equivalent small-mass limit of these dynamics, known as the Kramers--Smoluchowski approximation, in the case of a state-dependent friction coefficient, has been previously studied by a variety of approaches. Our new approach uses hypocoercivity estimates, which may be of interest in their own right, and lead to a very direct derivation, providing in particular a clear explanation of the ``noise-induced drift'' term in the overdamped equation in the case of a state-dependent friction term. Using the same approach, we also treat effective kinetic dynamical models derived from a coarse-graining approximation of a high-dimensional system, as well as a class of kinetic dynamics with position-dependent mass matrices. All of these models are relevant to applications in computational chemistry. We finally identify a mistake in a related work, and suggest a solution.