Cuffless blood pressure (BP) estimation based on Pulse Transit Time (PTT) has emerged as a promising solution for continuous health monitoring. However, conventional models relying on the Moens-Korteweg equation often fail during rapid hemodynamic fluctuations, as they assume arterial walls are purely elastic and neglect inherent viscoelasticity. To address this limitation, we propose a physics-informed framework introducing a viscoelastic compensation mechanism. First, raw photoplethysmogram (PPG) signals undergo high-fidelity reconstruction using Modified Akima (Makima) interpolation. Second, a robust Intersecting Tangent Method is applied for precise pulse foot localization. Crucially, we utilize Ensemble Empirical Mode Decomposition (EEMD) to isolate high-frequency Intrinsic Mode Functions (IMFs), defining a ``Viscoelastic Velocity Metric'' to quantify the vascular damping effect ($η\cdot \dotε$) typically ignored by elastic models. The framework was rigorously validated on a challenging subset of the MIMIC-II database (364 subjects, 28,525 cardiac cycles) characterized by a high prevalence of hypertension (23.4\%). Experimental results demonstrate medical-grade accuracy, yielding a Root Mean Square Error (RMSE) of 5.22 mmHg for Systolic and 3.65 mmHg for Diastolic BP, with Pearson correlation coefficients ($R > 0.97$). These findings confirm that incorporating viscoelastic features significantly enhances robustness against vascular hysteresis.

Though online platforms claim to amplify Indigenous voices, Indigenous communities are worried that these systems are instead eroding their language and culture. We conduct a community-informed algorithmic audit to explore whether online platforms sustain or endanger Indigenous cultural practice. First, we review ethnographic research pertaining to the cultural anxieties of a specific Indigenous community, as Indigenous peoples are not a monolith. We consider concerns from Kyrgyz communities who believe that platforms are expanding Russia's linguistic influence and threatening their language. Next, we construct and conduct an algorithmic audit in conversation with the community. Our audit investigates deep-seated fears among Kyrgyz caregivers that YouTube encourages their children to speak Russian instead of Kyrgyz, their heritage language. We measure how the YouTube recommendation algorithm prioritizes content across Indigenous and non-Indigenous languages for child users. Our results validate caregiver concerns, as we find that YouTube primarily recommends non-Kyrgyz content to Kyrgyz children, even when children signal clear preferences for Kyrgyz content. Thus, platform recommendations reinforce Kyrgyz children's offline uptake of colonial language ideologies. Finally, we evaluate strategies to align platform behavior with Indigenous values. We identify effective end-user practices for reducing the proportion of Russian-language YouTube recommendations, like cross-generational device sharing. Overall, our work uncovers how platforms can amplify colonial influence, rather than revitalizing Indigenous cultural heritage. We encourage researchers to consider how algorithmic systems can reimpose oppressive power structures that decolonial efforts have sought to dismantle.

As web browsers increasingly restrict client-side tracking, the web tracking ecosystem is shifting from client-side to server-side tracking (SST). In SST, the browser sends tracking requests to an intermediate endpoint, which then forwards them to the tracker's endpoint, eliminating direct client-to-tracker requests. As a result, existing tracking protections that block requests to known tracker endpoints are rendered ineffective. In this paper, we investigate server-side implementation of Google Analytics, the most widely deployed third-party tracking service on the web today. We also present SST-Guard, a multi-modal, browser-based system for detecting and blocking server-side Google Analytics (sGA). Our key insight is that even when the tracker's endpoints change, sGA must necessarily still collect and share the same semantic information as client-side Google Analytics (e.g., identifiers, event metadata). Therefore, rather than detecting requests to known Google Analytics endpoints, SST-Guard aims to detect underlying artifacts of collection and sharing of these semantic values to any arbitrary endpoint. Operationalizing this insight is challenging because real-world sGA deployments commonly customize endpoints and obfuscate URLs/payloads. SST-Guard addresses this challenge using a value-template approach that employs regular expressions to match semantic value patterns across multiple modalities: network requests, cookies, and the window object. We validate SST-Guard on Tranco top-10k websites, detecting 4.02\% (403) sGA domains with over 93\% accuracy across three modalities, with network request classifier demonstrating the highest accuracy (99.8\%). By deploying SST-Guard in the wild, we find 4.21\% (6,314) of Tranco top-150k websites using sGA.

We revisit the production of primordial black holes (PBHs) by a U(1) gauge field with a pseudo-scalar coupling to the inflaton. We improve upon the existing literature by working in the homogeneous backreaction regime with numerically computed gauge mode functions, adopting state-of-the-art PBH abundance calculations, and incorporating the uncertainty in the statistics of $δρ$. We find that PBHs can account for all of the dark matter in the asteroidal mass range, even when the inflaton gradient energy density is highly subdominant ($10^{-4}$--$10^{-3}$ of the kinetic energy), supporting the validity of the backreaction scheme. This mechanism also unavoidably generates a stochastic gravitational wave background with an amplitude that will be measured at LISA and that will allow to indirectly discriminate between different statistics of $δρ$.

Understanding the boundary between classical and nonclassical phenomena is important for both fundamental researches in quantum optics and applications in quantum information. One of the most interesting research directions in this field is exploring nonclassical effects with classical light. In this paper, we will show that it is possible to observe antibunching with thermal light in a Hanbury Brown-Twiss interferometer by treating single-photon detectors as photon-number-resolving detectors to perform photon-number projection measurements. Both temporal and spatial antibunching is observed via the correlation of two detectors detecting one and zero photon, respectively. By comparing the measured results of thermal and laser light, it is found that the observed antibunching arises from the combined effect of photon statistics of thermal light and photon-number projection measurement.The classical and nonclassical nature of the observed antibunching is analyzed. The results are helpful to understand the connection between classical and nonclassical correlation and may find applications in multiphoton interference and quantum imaging.

This study examined intermittent discontinuance in AI-mediated informal digital learning of English (AI-IDLE) through the cognition-affect-conation framework. Survey data were collected from 632 Chinese university EFL learners with prior AI-IDLE experience and analysed using structural equation modelling and fuzzy-set qualitative comparative analysis. The SEM results showed that perceived intelligence, perceived interactivity, and perceived personalisation reduced AI-IDLE intermittent discontinuance indirectly through enjoyment, whereas perceived ineffectiveness, perceived uncontrollability, and perceived complexity increased discontinuance indirectly through boredom. The fsQCA results further identified four configurational pathways leading to intermittent discontinuance, indicating that learners' temporary withdrawal from AI-IDLE can result from different combinations of cognitive barriers and affective disengagement. These findings extend AI-IDLE research from adoption and continuance to post-adoption discontinuance and highlight the need to design AI-supported English learning experiences that are enjoyable, personalised, controllable, and cognitively manageable.

We investigate the existence of positive solutions to fractional equations presenting a double criticality: a multi-polar Hardy-type potential and a Sobolev critical nonlinearity. The nonlocal nature of the operator and the absence of explicit ground states for the single-pole equation stand as major difficulties. We overcome these obstacles by passing to an extended formulation of the problem and by establishing sharp asymptotic estimates for the solutions in the case of a single pole. Then, through a concentration-compactness argument, we show that the existence of minimizers is dictated by the magnitude of the masses and the mutual distances between the corresponding poles.

Let $q_1, \ldots , q_t$ be distinct prime numbers. Let $a_1, \ldots , a_t$ be nonnegative integers. We establish effective lower bounds for $|z^d - q_1^{a_1} \ldots q_t^{a_t}|$ and for its greatest prime factor, which tend to infinity with $z^d$, where $z$ is a positive integer coprime with $q_1 \ldots q_t$ and $d \ge 2$ is an integer.

Anomalous tunneling refers to the phenomenon in which the transmission coefficient through a potential barrier approaches unity as the energy of an incident particle or quasiparticle tends to zero. This counterintuitive effect has been reported in systems exhibiting spontaneous symmetry breaking (SSB), such as superfluids, yet the general conditions for its occurrence remain unclear. In this Letter, we establish that anomalous tunneling of Nambu-Goldstone (NG) modes is a universal low-energy theorem dictated solely by symmetry and scaling, using a low-energy effective field theory (EFT) framework. We formulate the scattering of NG modes by external potentials in terms of spatially dependent EFT coefficients and demonstrate that symmetry-preserving localized potentials are irrelevant in the long-wavelength limit, leading to perfect transmission. In contrast, symmetry-breaking perturbations are relevant and suppress transmission, resulting in the absence of anomalous tunneling. We illustrate this universal behavior with explicit examples of superfluid phonons and magnons.

GPU compilers merge all data types into a single unified register file, erasing the type information that binary-analysis tools rely on. We show that type recovery from this untyped register file is the central challenge of GPU binary lifting. We present CuLifter, a SASS-to-LLVM IR lifting framework that recovers register types via constraint propagation with conflict detection, reconstructs explicit control flow, and aggregates multi-instruction patterns. Across eight benchmark suites (24,437 GPU functions in 919 cubins) spanning open-source applications, vendor libraries, and optimized ML runtimes, CuLifter successfully lifts 99.98% of functions to valid LLVM IR. An ablation study confirms that type recovery is the only step required to produce semantically correct IR: disabling it drops the x86 pass rate from 73.8% to 0%, a 73.8 percentage-point drop.

Let $Z=\{Z(t): t\in \mathbb R\}$ be a stochastic process with trajectories in space $\mathbb D (\mathbb R)$. It is assumed that there exists an essentially smooth function $A:\mathbb R\to (-\infty, \infty] $ such that, for all $α\in \mathbb R, $ $ μ\in \mbox{dom}\, A$, one has \begin{equation*} \frac1{T} \ln {\mathbf E} \big( e^{μ(Z(T)-αT)} \big|Z(s), \ s\le 0 \big) = A(μ) +o(1) \end{equation*} uniformly on the event $C(T):=\{|Z(0)/T - α|< η_T \} $, where $ η_T \to 0$ as $T\to\infty.$ Under this condition, a uniform conditional local large deviation principle (l.l.d.p.) is established: for any fixed $α, β\in \mathbb R$ and a positive function $η_T=o(1)$, for $\varepsilon_T \to 0$ sufficiently slowly as $T\to\infty,$ one has \begin{equation*} \lim_{T\to\infty}\frac1T \ln {\mathbf P} \big( {Z(T)}/T-α \in (β-\varepsilon_T, β+\varepsilon_T) \big| Z(s), \ s\le 0\big) = - D(β) \end{equation*} uniformly on $C(T)$, where $D$ is the Legendre transform of the function $A$. This result is used to establish a conditional l.l.d.p. for the finite-dimen\-sional distributions of the process $ \{ z_T(s) = Z(sT)/T: s\in [0,1]\}$. Under additional conditions on the magnitude of oscillations of the trajectories $z_T$, a functional l.l.d.p. is obtained for the asymptotics of $\ln {\mathbf P} (z_T\in (f)_{\varepsilon_T})$ as $T\to\infty$, where $f\in \mathbb D(0,1),$ $(f)_\varepsilon$ is the $\varepsilon$-neighborhood of $f$ in the space $ \mathbb D(0,1)$ with respect to the uniform metric, and $\varepsilon_T \to 0$ sufficiently slowly. The obtained results can be extended to a more general triangular array scheme where the process itself $Z=Z^{(T)}$ also depends on the parameter $T$.

Imaginary-time evolution is a standard primitive for ground-state preparation but is nonunitary, precluding direct quantum implementation. We develop Finite Imaginary-Time Evolution (FinITE), a finite-beta construction for diagonal Pauli-Z cost Hamiltonians arising from polynomial unconstrained binary optimization (PUBO) instances, including QUBO and HUBO cases. FinITE uses the linear-combination-of-unitaries (LCU) framework to implement a scaled imaginary-time propagator. The commuting Pauli-Z structure makes termwise block-encodings compose without product-formula error, and higher-order Pauli-Z terms are handled directly without quadratization. The structure yields an exact finite-beta identity between the LCU success probability and the ground-subspace fidelity. Combined with a gap-based fidelity lower bound, the identity yields a closed-form sufficient imaginary-time threshold beta-star for a chosen target fidelity. The threshold depends on estimates of the spectral gap and the initial ground-subspace overlap. Because the LCU success event is flagged by a known ancilla outcome, we integrate fixed-point amplitude amplification with an explicit query-complexity bound. Statevector simulations verify the identity on a five-vertex MaxCut (QUBO) and an eight-qubit cubic HUBO instance, and shot-based simulations on the MaxCut instance illustrate the predicted finite-beta threshold and amplification procedure.

We extend Atiyah's holomorphic jet bundle formalism to holomorphic vector bundles over noncommutative algebras endowed with a bigraded differential calculus truncated at bidegree $(1,1)$; we refer to such structures as noncommutative complex curves. For a holomorphic vector bundle $(E,\overline{\nabla}_E)$ over such an algebra $\mathcal{A}$, we construct a canonical holomorphic structure $\overline{\nabla}_J$ on the first jet module $J_E^1\,$, making the jet sequence \[ 0\longrightarrow Ω^{1,0}(\mathcal{A})\otimes_{\mathcal A}E\longrightarrow J_E^1\longrightarrow E\longrightarrow 0 \] exact in the holomorphic category. The association $(E,\overline\nabla_E)\rightsquigarrow(J_E^1\,,\overline\nabla_J)$ defines an endofunctor on the category of holomorphic vector bundles over $\mathcal{A}$. We define the notion of holomorphic connection in this setting and prove that a holomorphic vector bundle admits a holomorphic connection if and only if the jet sequence splits in the holomorphic category, or equivalently, if and only if its Atiyah class vanishes. This yields a noncommutative analogue of Atiyah's classical correspondence for Riemann surfaces. Finally, we specialize to the quantum projective line $\mathbb{CP}_q^1\,$ and determine when $\overline{\nabla}_J$ defines a bimodule connection, assuming that $\overline{\nabla}_E$ does.

We report the detection of linear polarization in the radio afterglow of GRB 260310A, representing the first centimeter-wavelength polarization detection of a gamma-ray burst (GRB) afterglow and the first measurement of Faraday rotation in a GRB environment. We detect linearly polarized emission across $11-25$ GHz, with a polarization fraction decreasing monotonically from $(3.18 \pm 0.18)\%$ at 25 GHz to $(0.69 \pm 0.22)\%$ at 11 GHz. Interpreting the radio data as emission from a reverse shock in a structured, relativistic jet, the observed depolarization toward lower frequencies is consistent with suppression by synchrotron self-absorption, while the low observed polarization at high frequencies relative to the theoretical maximum suggests a patchy magnetic field in the jet with a coherence scale, $θ_{\rm B}\approx10^{-2}$ rad. We identify a frequency-dependent rotation of the polarization angle consistent with Faraday rotation, with a rotation measure of ${\rm RM} = -(8300 \pm 90)~\rm{rad/m^2}$ at the GRB redshift. The magnitude of the rotation measure is consistent with propagation through a dense, magnetized environment, such as a progenitor HII region. These findings demonstrate that GRB afterglows exhibit measurable linear polarization at centimeter wavelengths, and that their polarimetric properties probe both intrinsic jet magnetization and the surrounding medium. Future multi-frequency polarimetric monitoring over timescales of days to weeks will enable detailed studies of the evolution of magnetic field structure and provide new constraints on the role of magnetic fields in GRB afterglows.

Recommendation algorithms have become the dominant mechanism for information distribution on digital platforms, profoundly shaping personalized information consumption environments. However, gender bias, as a significant form of algorithmic discrimination, may cause users to experience unequal exposure within different political information environments. Taking YouTube as a case, we conduct a controlled social-bot field experiment, where male-coded and female-coded profiles are constructed. We track the exposure and click patterns of these bots to analyze their recommendation trajectories. We analyze the distribution of recommended content from two dimensions: allocative bias and structural bias. First, we find statistically significant differences in allocative bias across male-coded and female-coded profiles, particularly in terms of issue distribution, ideological orientation, and political entities. Secondly, we observe structural bias in the political information environments, characterized by distinct clustering patterns. Additionally, time-series analysis shows that exposure pathways continue to be shaped over time by both communities detected in the co-occurrence network and individual profile-level dynamics. Finally, we construct a simple collaborative-filtering model that reproduces the observed gender bias. We argue that gender bias in recommendation systems is reflected not only in the allocation of political content, but also in how community structures shape these environments, reinforcing societal inequalities and highlighting the need for algorithmic fairness.

We investigate the physical origin of critical mass, a threshold where many galaxy properties and scaling relations undergo fundamental transitions, using the Horizon Run 5 simulation. Focusing on massive ($M_{\rm tot} \geq 10^{12}{\rm M_\odot}$) central galaxies, we examine the mass-dependent turnover of the stellar-to-total mass ratio (STR) and the physical processes driving it. We decompose STR into the stellar-to-baryon mass ratio ($M_*/M_{\rm bar}$) and baryon retention fraction ($M_{\rm bar}/M_{\rm tot}$) to examine galaxies' ability to retain baryons and convert them into stars. We find that STR evolution is dominated by variation in $M_*/M_{\rm bar}$, which changes by over a factor of three, peaking within a narrow range of $M_{\rm tot} \sim 10^{12.4\text{--}12.7}{\rm M_\odot}$ independent of redshift, while $M_{\rm bar}/M_{\rm tot}$ varies by at most 30%. A redshift-independent critical mass at $M_{\rm tot} \sim 10^{12.5}{\rm M_\odot}$ ($M_* \sim 10^{10.7}{\rm M_\odot}$) arises from the changing nature of gas accretion. At this scale, a dynamically stable hot gas halo develops that suppresses cool gas inflow, reducing in-situ star formation efficiency such that $M_{\rm tot}$ growth exceeds in-situ $M_{*}$ growth. Consequently, the hot gas reservoir grows while $M_{*}$ growth slows, producing upturns in $M_{\rm gas}/M_{\rm tot}$ and $M_{\rm bar}/M_{\rm tot}$ and a downturn in $M_{*}/M_{\rm bar}$ that ultimately drives the STR turnover. We also identify a secondary critical mass at $M_{\rm tot} \approx 10^{11}{\rm M_\odot}$ (or $M_{*} \approx 10^{9\text{--}9.5}{\rm M_\odot}$) where gas retention fraction peaks, above which increasing hot gas fraction gradually suppresses in-situ star formation efficiency.

We study the quantum Gromov-Hausdorff convergence of spectral truncations for compact quantum groups. Using a proper length function, we define a Dirac operator and the associated spectral truncations. This work extends the previous convergence results for tori (Leimbach-van Suijlekom) to a broad class of quantum groups, and provides the first Gromov-Hausdorff convergence result for spectral truncations on quantum groups, encompassing both compact and discrete quantum groups. Our results are applicable to $SU(N)$,$SO(N)$ and discrete quantum groups with strong polynomial growth.

Computing edge-connected components in directed and undirected graphs is a fundamental and well-studied problem in graph algorithms. In a very recent breakthrough, Korhonen [STOC 2025] showed that for any fixed $k$, the $k$-edge connected components of an undirected graph can be computed in linear time. In contrast, the directed case remains significantly more challenging: linear-time algorithms are only known for $k \le 3$, and for any fixed $k > 3$, the best known bound for sparse or moderately dense graphs is still the $O(mn)$-time algorithm of Nagamochi and Watanabe (1993). In this paper, we break the $O(mn)$ barrier for all $k = o(n^{1/4}/\sqrt{\log{n}})$. We present a randomized algorithm that computes the $(k+2)$-edge-connected components of a $k$-edge-connected directed graph in $O(k^2 m \sqrt{n} \log n)$ time, for any~$k$. This constitutes the first improvement over the classic Nagamochi--Watanabe bound for any constant $k > 3$. Our approach introduces new structural insights into directed edge-cuts and combines these with both new and existing techniques. A central contribution of our work is a substantial simplification and generalization of the framework introduced in~\cite{GKPP:3ECC}, which achieved an $\widetilde{O}(m\sqrt{m})$ bound for computing the $3$-edge-connected components of a digraph. In addition, we develop a variant of our algorithm that achieves the same $O(m \sqrt{n} \log n)$ running time for computing the $4$-edge-connected components of a \emph{general} directed graph.

We investigate the phenomenology of the Standard Model extended by a real gauge-singlet scalar field, focusing on exotic Higgs decay channels. For a light scalar mass in the range \(0 < m_ϕ < 40\) GeV, the Higgs boson can decay to both two and three scalar final states. We derive analytical expressions for these decay rates and impose a global constraint on the model parameters by requiring that their sum does not exceed the total Standard Model Higgs boson decay width. This requirement translates into a fourth-order inequality with respect to the singlet vacuum expectation value, \(v_ϕ\). We demonstrate that satisfying this inequality imposes an upper bound of \(\cos θ< 0.12 - 0.13\) across the entire mass range, providing a complementary constraint to existing direct search limits. Utilizing stronger independent constraints on the mixing (e.g., \(\cos θ< 0.1\)), we then predict upper bounds on the individual exotic decay rates as a function of \(m_ϕ\) as \(Γ_{h \rightarrow ϕϕ} < 0.06\) MeV and \(Γ_{h \rightarrow ϕϕϕ} < 5 \times 10^{- 6}\) MeV, respectively.

We obtain estimates of the modulus of continuity for the real part of the Cauchy-type integral in the closure of domain bounded by an Ahlfors-regular integration curve. These estimates are more exact than the well-known Zygmund estimate for the modulus of continuity of the Cauchy-type integral. The accuracy of estimates is proved by constructing an example of a curve and an integral density for which the specified estimates are exact with respect to the order of smallness.

An étale space over a topological space $Y$ is defined as a local homeomorphism from a topological space $X$ into $Y$. They often come up in topos theory because of the equivalence between sheaves and étale spaces over a space. In this note, we define computable étale spaces over a computable topological space $Y$ within the TTE framework of computable topology, and show they are naturally equivalent to computable functions from $Y$ to $\mathsf{ODS}$, the effective quasi-Polish category of overt-discrete quasi-Polish spaces. More generally, if $\cal C$ is a computable category (or groupoid), then there is an equivalence between computable functors from $\cal C$ to $\mathsf{ODS}$, and computable étale spaces equipped with a computable action by $\cal C$.

We present a comprehensive analysis of the 21 cm intensity mapping (IM) data from the Tianlai Cylinder Pathfinder Array (TCPA), focusing on multi-scale foreground mitigation and three-dimensional power spectrum estimation. Utilizing 20 days of drift-scan observations (714.4-781.7 MHz, corresponding to HI emission at redshift $z \approx 0.82-0.99$), we reconstruct high-fidelity sky maps by incorporating a high-precision, drone-measured primary beam model. This in-situ calibration significantly enhances reconstruction accuracy over previous analytical approximations. To address astrophysical foregrounds, which exceed the cosmological signal by approximately five orders of magnitude, we implement a robust multi-scale subtraction strategy--mPCA-UWTS--which combines an isotropic Undecimated Wavelet Transform on the Sphere (UWTS) with independent Principal Component Analysis (PCA) within each wavelet domain. We subsequently estimate the 3D power spectrum via Spherical Fourier-Bessel (SFB) decomposition, providing a mathematically rigorous treatment of wide-angle and line-of-sight curvature effects inherent in wide-field surveys. Our analysis demonstrates that the SFB framework effectively isolates systematic contaminants and recovers the clustering signal without the biases introduced by conventional flat-sky approximations. This work represents the first application of the SFB formalism to observational 21 cm IM data, establishing it as a computationally efficient and scalable diagnostic tool for the next generation of wide-field 21 cm surveys, including the Square Kilometre Array (SKA) and the full Tianlai array.

The primary goal of this paper is to give a precise definition and prove existence and uniqueness of multiphase quadrature domains for subharmonic functions, ensuring that the prescribed measures are supported in the interior of the resulting domains. The approach to prove existence is based on a variational framework, where we minimize an energy functional over so called segregated states. In this respect we refine earlier results in this direction. But we also show that this approach alone is not enough for two reasons. First of all it seems hard to get existence results which ensure that the interior support condition is satisfied. And second it may happen, as we show by an example, that a multiphase quadrature domain exists but is not a minimizer of the energy functional. The main novelty of this work is the study of minimizers, if they exist, of the energy functional over a subset of the segregated states given by a natural constraint with respect to the given measures. From this approach we are able to prove uniqueness, and also give sufficient conditions for existence. We also give an example showing that, unlike the energy minimization and partial balayage approaches which are equivalent in the one-phase case, this equivalence breaks down already in the two-phase setting.

We report the indication of a long-term quasi-periodic oscillation (QPO) in the $γ$-ray emission of the BL Lac object 4FGL J1037.7+5711 (GB6 J1037+5711) using more than 17 years of monthly binned Fermi-LAT observations. Since blazar $γ$-ray variability is typically dominated by stochastic red-noise processes from turbulent jet activity and accretion fluctuations, we applied multiple independent timing techniques to test periodic modulation. These include the Lomb--Scargle periodogram (LSP), weighted wavelet $Z$-transform (WWZ), first-order autoregressive red-noise modeling (REDFIT), and epoch-folding analysis. The LSP reveals a significant periodic signal at $478.74 \pm 17.55$ days, exceeding the $99.99\%$ confidence level from Monte Carlo simulations. The WWZ analysis independently recovers a comparable period of $474.72 \pm 27.24$ days at $99.7\%$ significance, while the REDFIT analysis identifies a similar periodic feature at $481.67 \pm 35.41$ days above the $99\%$ confidence level. The epoch-folding analysis further confirms the same modulation timescale. The small differences in period estimates across methods are expected given the distinct mathematical frameworks and sensitivity functions. The long-term flux distribution of the source is better described by a lognormal profile than a Gaussian, suggesting that the underlying variability arises from multiplicative processes. The indication of a $\sim$478 day QPO, independently confirmed across all four timing techniques, may be associated with the orbital dynamics of a supermassive binary black hole system driving Newtonian jet precession or periodic Doppler-factor modulation, Lense--Thirring precession of the inner accretion disk around a rapidly spinning SMBH, or accretion-driven instabilities at the disk--jet interface amplified through relativistic beaming.

Tracing out a Galilean-invariant Caldeira-Leggett environment breaks Galilean boost covariance of the reduced dynamics, while spatial translations and rotations survive intact. An operator-level analysis of the exact Hu-Paz-Zhang master equation localizes the violation entirely in the dissipative anticommutator term, scaling with the damping coefficient $Γ(t)f(t)$. The fluctuation-dissipation theorem ties this coefficient to the absorptive bath response that drives equilibrium momentum diffusion, so for any non-trivial bath spectral density bilinear-coupled Galilean invariance, the fluctuation-dissipation theorem, and reduced boost covariance cannot hold simultaneously. The stochastic decomposition of the influence functional extends the mechanism beyond the quadratic regime. The dimensionless ratio $\hbarγ/k_\mathrm{B} T$ delineates the crossover: cold atoms in dissipative optical lattices and ultracold molecules sit at its edge. Parametric driving offers a one-directional escape: the squeezing rate that protects nonequilibrium entanglement above the standard quantum limit also suppresses boost-breaking over a driving cycle.

We consider the following two-component coupled nonlinear Schrödinger (CNLS) system: \[ \begin{cases} -Δu +(P(x) + λ) u=μ_1 u^3+βu v^2, & \text{in } \mathbb{R}^N,\\ -Δv +(Q(x) + λ) v =μ_2 v^3+βvu^2, & \text{in } \mathbb{R}^N \end{cases} \] with the mass constraint $\int_{\mathbb{R}^N} (u^2+v^2)\,dx = ρ^2$ for $N=2,3$, where $ρ>0$ is a parameter. By employing the Lyapunov-Schmidt reduction and local Pohozaev identities, we establish the existence and local uniqueness of normalized multi-peak solutions: the result holds for sufficiently small $ρ$ when $N=3$, and for $ρ$ approaching a critical threshold when $N=2$. The main difficulty lies in that the mass constraint involves interactions among all concentration points, while a more refined characterization of such normalized solutions further requires sharp order estimates. In this work, we have discovered some new phenomena that differ from those of solutions without mass constraint and single-peak solutions.

The Nash-Williams conjecture establishes degree sequence conditions ensuring Hamilton cycles in digraphs. An asymptotic version of this conjecture for large digraphs was independently derived by several researchers. We strengthen these results by proving the following results under the same asymptotic degree sequence conditions. For any digraph $H$, a digraph $D$ is $(\mathcal{N}H)$-linked if there exists an integer $l_0$ such that for any vertex set $U$ of cardinality $|V(H)|$ and every integer set $\mathcal{N}=\{l_i\}_{i=1}^{|A(H)|}$ with $l_i\geq l_0$, $D$ contains an $H$-subdivision with $U$ as branch-vertex set and the values in $\mathcal{N}$ specifying the lengths of the subdivided paths. Let $D$ be a sufficiently large digraph of order $n$ with the out-degree sequence $d_1^+\leq\cdots\leq d_n^+$ and the in-degree sequence $d_1^-\leq\cdots\leq d_n^-$. We prove that if for every $γ\in(0, 1)$ and every integer $0\leq i<n/2$, the following conditions hold: (i) $d_i^+\geq i+γn$ or $d_{n-i-γn}^-\geq n-i$, and (ii) $d_i^-\geq i+γn$ or $d_{n-i-γn}^+\geq n-i$, then $D$ is $(\mathcal{N}H)$-linked, and also admits a perfect $H$-subdivision tiling with subdivision orders $\{n_1, \ldots, n_k\}$, where each $n_i\geq C_0$ for some integer $C_0$.

We present an efficient implementation of the second-order two-component relativistic core-valence-separated algebraic diagrammatic construction method (CVS-ADC(2)) for core-excitation calculations. The approach employs state-averaged frozen natural spinors (SA-FNS) to reduce the number of floating-point operations, together with the Cholesky decomposition (CD) technique, which lowers the storage requirements associated with two-electron integrals. These reductions make the method particularly well-suited for systems containing heavy elements. Systematic benchmarking against four-component reference calculations confirms the reliability and robustness of the two-component (X2CMP/X2CAMF)-based framework. The close agreement with canonical results further demonstrates that the SA-FNS-based CVS-ADC(2) approach achieves comparable accuracy at only a fraction of the computational cost. Moreover, benchmark studies of L$_{2,3}$-edge spectra for 3$d$ transition-metal compounds demonstrate that CVS-ADC(2) serves as a computationally efficient and reliable alternative to the non-Hermitian EOM-CC method for reproducing experimental spectra. Finally, calculations on a ruthenium complex illustrate the method's applicability to relativistic studies of medium-sized molecular systems.

We study Carrollian limits of Schwarzschild-AdS black-hole thermodynamics using covariant phase space. Allowing the cosmological constant to vary, we derive the extended Iyer-Wald identity and identify the renormalized bulk term proportional to \(δΛ\) with the generator-normalized thermodynamic volume contribution \(V_ξ\,δP\). We show that the Carroll limit contracts the full thermodynamic phase space together with the metric. For fixed Newton constant, the Lorentzian generator \(\partial_t\) collapses to a zero-norm direction as \(c\to0\), yielding a degenerate sector with vanishing Hamiltonian variation, temperature and volume. Introducing \(ξ_λ=c^{-α}\partial_t\) and \(G=c^γG_C\), we find that the extended first law scales as \(c^{1-α-γ}\), so finite phase-space contractions require \(α+γ=1\). The endpoint \((α,γ)=(1,0)\), obtained by \(τ=ct\), is the ordinary non-degenerate Lorentzian finite-clock normalization. Carrollian finite first laws lie on the segment \(α<1\), hence \(γ=1-α>0\), and give \(T\to0\), \(S\to\infty\), with finite \(T\,δS\) and \(V_ξ\,δP\). We test the scaling principle for fixed-charge and fixed-rotation AdS black holes, and extend it to arbitrary spacetime dimension within the Schwarzschild-AdS family.

The reciprocality means a duality in Kirchberg algebras between K-theory groups and strong extension groups. In the paper, we will find a certain class of unital simple Exel--Laca algebras for which the reciprocal duals are simple Cuntz--Krieger algebras in terms of the underlying infinite matrices. In our procedure to obtain simple Cuntz--Krieger algebras from Exel--Laca algebras, we compute the strong extension groups for Exel--Laca algebras belonging to the class.