We report a comparative high-pressure study of two fluorite-type rare-earth oxides with increasing configurational entropy, (CePr)O$_{2-δ}$ and (CePrLa)O$_{2-δ}$. Synchrotron-based powder X-ray diffraction and Raman spectroscopy were carried out up to 30 GPa and 20 GPa, respectively. Both compounds retain the cubic fluorite structure throughout the pressure range explored, although an anomaly is observed between 9-16 GPa, characterized by a compressibility plateau and changes in vibrational modes. This behavior is attributed to local lattice distortions and a progressive bond angle bending rather than abrupt phase transitions. In (CePrLa)O$_{2-δ}$, the onset of amorphization is observed above 22 GPa, highlighting its reduced structural stability. The bulk modulus of both systems shows a slight decrease after the onset of the anomaly, suggesting subtle lattice softening. Raman spectroscopy reveals suppression of the F$_{2g}$ mode intensity with increasing cationic disorder, and under compression, partial reordering is evidenced by an increase in the RE-O mode intensity. Our results highlight the complex interplay between configurational entropy, cation size, and pressure in determining the structural stability and vibrational properties of rare-earth high-entropy oxides and provide insight into the mechanisms governing their resilience and local disorder under extreme conditions.

Liquid bridges form between particles during wet mixing with binders or by condensation due to ambient humidity. The consequences of capillary bridges can be quite drastic, creating macroscopic cohesion, as seen in sandcastles and in the formation of particulate agglomerates. Bulk effects in cohesive particles arise from forces generated by capillary bridges, so particle-scale measurements are needed to develop predictive models. Most existing studies at the particle scale assume Newtonian liquids. Yet many binders in industry and in the environment can exhibit viscoelastic behavior. In this study, we measure the axial force generated by liquid bridges of viscoelastic polymer solutions between two spherical beads during controlled uniaxial separation. We vary the polymer concentration, separation velocity, and particle size, and track the force as the bridge thins and ruptures. At quasi-static rates, the axial force remains dominated by capillarity and is not significantly affected by polymer rheology. However, increasing the stretching rate increases the peak force through viscous dissipation and promotes the formation of a viscoelastic filament, thereby delaying rupture. The peak axial forces collapse when rescaled by a capillary number and particle size, while the effective rupture distance collapses with a Weissenberg number. These results provide a simple first-order particle-scale force law for polymeric binders.

Two-dimensional (2D) hybrid organic--inorganic perovskites (HOIPs) are promising candidates for next-generation optoelectronic and spintronic applications. This work systematically investigates the relationship between structural distortions and functional responses in three $C_{2v}$-symmetric Ruddlesden--Popper (RP) ferroelectric perovskites, $(4,4\text{-DFPD})_{2}\mathrm{PbI}_{4}$, $(\mathrm{DFCHA})_{2}\mathrm{PbI}_{4}$, and PEPI, using first-principles calculations combined with irreducible representation decomposition and wave-vector point-group symmetry (WPGS) analysis. The results reveal that the lead--iodide framework yields shift-current (SC) magnitudes comparable to, and in specific cases even an order of magnitude larger than, those of traditional ferroelectric oxides, with PEPI reaching a maximum of $69.16\ μ\mathrm{A}/\mathrm{V}^{2}$. The SC magnitude correlates positively with the octahedral distortion index ($D_i$), while a competition mechanism is identified between covalent bond strength and structural asymmetry, where increased average bond lengths can offset the enhancement induced by $D_i$. Regarding spintronics, $C_{2v}$ symmetry-protected persistent spin textures (PST) are identified. A transition to $C_2$-protected quasi-PST occurs in monoclinic $(4,4\text{-DFHHA})_{2}\mathrm{PbI}_{4}$, leading to a persistent spin helix (PSH) with long-distance spin transport. The synergy among ferroelectricity, SC, and PST enables nonvolatile electrical control of both photocurrent direction and spin configurations. This work provides evaluation criteria and practical guidance for designing high-performance integrated spintronic--photovoltaic devices.

This paper presents a Gaze-Guided Audio-Visual Speech Enhancement (GG-AVSE) framework to address the cocktail party problem. A major challenge in conventional AVSE is identifying the listener's intended speaker in multi-talker environments. GG-AVSE addresses this issue by exploiting gaze direction as a supervisory cue for target-speaker selection. Specifically, we propose the GG-VM module, which combines gaze signals with a YOLO5Face detector to extract the target speaker's facial features and integrates them with the pretrained AVSEMamba model through two strategies: zero-shot merging and partial visual fine-tuning. For evaluation, we introduce the AVSEC2-Gaze dataset. Experimental results show that GG-AVSE achieves substantial performance gains over gaze-free baselines: a 10.08% improvement in PESQ (2.370 to 2.609), a 5.18% improvement in STOI (0.8802 to 0.9258), and a 23.69% improvement in SI-SDR (9.16 to 11.33). These results confirm that gaze provides an effective cue for resolving target-speaker ambiguity and highlight the scalability of GG-AVSE for real-world applications.

Systematic investment strategies are exposed to a subtle but pervasive vulnerability: the progressive erosion of their effectiveness as market regimes change. Traditional risk measures, designed to capture volatility or drawdowns, overlook this form of structural fragility. This article introduces a quantitative framework for assessing the durability of systematic strategies through minimum regime performance (MRP), defined as the lowest realized risk-adjusted return across distinct historical regimes. MRP serves as a lower bound on a strategy's robustness, capturing how performance deteriorates when underlying relationships weaken or competitive pressures compress alpha. Applied to a broad universe of established factor strategies, the measure reveals a consistent trade-off between efficiency and resilience -- strategies with higher long-term Sharpe ratios do not always exhibit higher MRPs. By translating the persistence of investment efficacy into a measurable quantity, the framework provides investors with a practical diagnostic for identifying and managing strategy-decay risk, a novel dimension of portfolio fragility that complements traditional measures of market and liquidity risk.

We extend the beat-wave framework for laser harmonic generation - where spectra form regular lattices in Fourier space - to the nonlinear response of isotropic chiral media driven by locally chiral light. We represent the enantio-sensitive response of the medium by a chiral zero-frequency (DC) mode derived from the transverse spin density induced by structured or focused fields. Beating between this DC mode and the driving electromagnetic modes yields alternating chiral and achiral contributions on a regular harmonic lattice. We derive a general criterion for when chiral and achiral pathways overlap at the same harmonic and generate enantio-sensitive interference that survives spatial or angular integration (global chirality), versus when enantio-sensitivity remains confined to spatially varying patterns (local chirality). We apply the criterion to published configurations of synthetic chiral light, including OAM-carrying bicircular fields and crossed multicolour beams, and show that it reproduces and clarifies their reported global-chirality and beam-bending regimes.

This chapter examines the impact of the geopolitical rivalry between the United States and China on the prospects for inclusive innovation in artificial intelligence (AI) development. We explore three critical aspects of the American and Chinese legal infrastructure that significantly impact AI innovation: data privacy, intellectual property (IP rights), and export restrictions. Through this comparative analysis, we argue that, while China's legal environment may offer certain advantage in terms of access to training data and IP protection, the United States maintains superior resources by enforcing strict export controls on semiconductor chips, AI models, as well as outbound investments in these areas. This nuanced examination helps illuminate how each country's legal framework could influence the ultimate trajectory of AI race and how the technological rivalry has led to exclusionary rulemaking on a global scale.

Generative Artificial Intelligence (GenAI) has become a central component of many development tools (e.g., GitHub Copilot) that support software practitioners across multiple programming tasks, including code completion, documentation, and bug detection. However, current research has identified significant limitations and open issues in GenAI, including reliability, non-determinism, bias, and copyright infringement. While prior work has primarily focused on assessing the technical performance of these technologies for code generation, less attention has been paid to emerging concerns of software developers, particularly in the security realm. OBJECTIVE: This work explores security concerns regarding the use of GenAI-based coding assistants by analyzing challenges voiced by developers and software enthusiasts in public online forums. METHOD: We retrieved posts, comments, and discussion threads addressing security issues in GitHub Copilot from three popular platforms, namely Stack Overflow, Reddit, and Hacker News. These discussions were clustered using BERTopic and then synthesized using thematic analysis to identify distinct categories of security concerns. RESULTS: Four major concern areas were identified, including potential data leakage, code licensing, adversarial attacks (e.g., prompt injection), and insecure code suggestions, underscoring critical reflections on the limitations and trade-offs of GenAI in software engineering. IMPLICATIONS: Our findings contribute to a broader understanding of how developers perceive and engage with GenAI-based coding assistants, while highlighting key areas for improving their built-in security features.

We present the first lattice QCD calculation of the next-to-leading order (NLO) hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment with sub-percent precision. We employ the time-momentum representation combined with the spatially summed vector correlator computed on CLS ensembles with $N_{\mathrm{f}}=2+1$ flavors of $\mathrm{O}(a)$-improved Wilson fermions, spanning six lattice spacings ($0.039$-$0.097\,$fm) and a range of pion masses including the physical value. After accounting for finite-size corrections and isospin-breaking effects, we obtain in the continuum limit $a_μ^{\mathrm{hvp,\,nlo}} = (-101.57 \pm 0.26_{\rm stat} \pm 0.54_{\rm syst}) \times 10^{-11}$, corresponding to a total relative error of 0.6$\%$. Our result lies 1.4$σ$ below the estimate of the 2025 White Paper update and is two times more precise. It also shows a tension of $4.6σ$ with data-driven evaluations based on hadronic cross section measurements prior to the CMD-3 result.

We introduce a systematic hierarchy of one-body Green's function methods derived from the $GW$ approximation, constructed by progressively reducing the dynamical content of the self-energy. Starting from the fully dynamical Dyson formulation, we generate a family of approximations that interpolates between the standard $GW$ approximation to purely static effective single-particle Hamiltonians. This framework enables a controlled investigation of the role of dynamical effects and particle-hole coupling in the description of ionization potentials. Within this unified formalism, the hole and particle branches can be selectively decoupled through downfolding strategies into reduced one-particle spaces. By benchmarking the different members of this hierarchy on molecular ionization energies, we assess their accuracy, numerical robustness, and algorithmic complexity. We demonstrate that consistently derived partially static schemes can yield reliable quasiparticle energies while significantly simplifying the underlying eigenvalue problem. We further introduce a novel static Hermitian self-energy obtained as the static limit of this hierarchy. Despite its conceptually distinct origin, it produces results remarkably close to those of qs$GW$, thereby providing an alternative static route toward partial self-consistency.

Understanding the kinematic behaviour of the Small Magellanic Cloud (SMC) remains a challenge addressed by many authors using diverse approaches. Over time, increasing observational evidence has accumulated for tidal perturbations induced by the Large Magellanic Cloud (LMC) on the SMC, especially in its outer regions. In this study, we adopt star clusters as kinematic tracers of the SMC. We analyse 36 clusters distributed across the galaxy's structural regions (Northern Bridge, Southern Bridge, Wing/Bridge, West Halo, Main Body and Counter-Bridge). From each cluster's proper motions, radial velocity and heliocentric distance we estimate Cartesian velocities \((V_x,\,V_y,\,V_z)\) in the SMC reference frame. We also compute the same velocity components under the assumption that the SMC behaves as a rotating disc. We then define the residual velocity \(ΔV\) for each cluster as the difference between the two velocities derived. Additionally, we perform a kinematic anisotropy analysis to characterise the distribution of kinetic energy across the SMC. We find that increasing values of \(ΔV\) correlate with increasing cluster distance from the SMC center, and that \(ΔV \approx 60\ \mathrm{km\,s^{-1}}\) it appears to be a lower limit that separates, in kinematic terms, the areas of tidal origin from those with the best behavior.

In this work, we extend the meshfree generalized multiscale exponential integration framework introduced in Nikiforov et al. (2025) to the simulation of three-dimensional advection--diffusion problems in heterogeneous and high-contrast media. The proposed approach combines meshfree generalized multiscale finite element methods (GMsFEM) for spatial discretization with exponential integration techniques for time advancement, enabling stable and efficient computations in the presence of stiffness induced by multiscale coefficients and transport effects. We introduce new constructions of multiscale basis functions that incorporate advection either at the snapshot level or within the local spectral problems, improving the approximation properties of the coarse space in advection-dominated regimes. The extension to three-dimensional settings poses additional computational and methodological challenges, including increased complexity in basis construction, higher-dimensional coarse representations, and stronger stiffness effects, which we address within the proposed framework. A series of numerical experiments in three-dimensional domains demonstrates the viability of the method, showing that it preserves accuracy while allowing for significantly larger time steps compared to standard time discretizations. The results highlight the robustness and efficiency of the proposed approach for large-scale multiscale simulations in complex heterogeneous media.

\textbf{Background:} Mediation analysis is widely used to investigate how treatments and programs exert their effects, but standard ordinary least squares (OLS) inference can be unreliable when regression errors are non-Gaussian. In medical and public-health studies, this can affect whether indirect and direct effects are judged clinically or scientifically meaningful. \textbf{Methods:} We developed a semiparametric causal mediation framework for linear models allowing possibly non-Gaussian errors, covering both standard models and models with treatment--mediator interaction. The method combines semiparametric efficient regression estimation, a reproducible multi-start fitting algorithm for numerical stability, and stacked estimating equations for confidence-interval construction without requiring Gaussian error assumptions. \textbf{Results:} Across Gaussian, skewed, and mixture-error simulations, the semiparametric estimator reduced root mean squared error and confidence-interval length relative to OLS, with the largest gains under non-Gaussian errors. In a near-boundary power design, the OLS confidence interval achieved 18.3\% empirical power, whereas the semiparametric confidence interval identified significant effects in all replications. In the \textit{uis} drug-treatment data, it yielded sharper treatment-specific effect estimates under clear treatment--mediator interaction. In the \textit{jobs} social-program data, the semiparametric analysis produced shorter confidence intervals for mediated effects and detected nonzero mediation where OLS did not. \textbf{Conclusions:} Semiparametric mediation analysis can improve the precision and reliability of effect decomposition in studies with non-Gaussian outcomes, offering a practical alternative to OLS when indirect and direct effects may inform clinical or policy decision-making.

This paper re-examines the problem of fairly and efficiently allocating indivisible goods among agents with additive bivalued valuations. Garg and Murhekar (2021) proposed a polynomial-time algorithm that purported to find an EFX and fPO allocation. However, we provide a counterexample demonstrating that their algorithm may fail to terminate. To address this issue, we propose a new polynomial-time algorithm that computes a WEFX (Weighted Envy-Free up to any good) and fPO allocation, thereby correcting the prior approach and offering a more general solution. Furthermore, we show that our algorithm can be adapted to compute a WEQX (Weighted Equitable up to any good) and fPO allocation.

We consider two-dimensional periodic gravity water waves with constant nonzero vorticity $γ$, in infinite depth and with periodic boundary conditions. We prove that, if the characteristic wave number $\frac{γ^2}{g}$ is rational, the system admits smooth small-amplitude solutions whose high Sobolev norms grow arbitrarily large while lower-order norms remain arbitrarily small, thereby exhibiting a genuine transfer of energy toward high frequencies. This yields the first rigorous construction of weakly turbulent solutions for a quasilinear hydrodynamic wave system, in a regime where the flow remains smooth. Moreover, the growth occurs simultaneously in the free surface and in the vertical component of the velocity at the interface, showing that the instability involves the full hydrodynamic evolution. The proof relies on a new mechanism for generating energy cascades in quasilinear dispersive PDEs with sublinear dispersion and a nonlinear transport structure. A central ingredient is to exploit quasi-resonances from 2-wave interactions to produce a transport operator that drives energy to high modes and causes Sobolev norm growth. A virial-type argument then shows that the resulting instability affects both the free surface elevation and the velocity field.

Along with some known and less known results, we discuss new insights relating combinatorics of words and the ordering of the rationals from a dynamical systems point of view, somehow continuing along the path started in [BI]. We obtain in particular a set of results that structure and enrich the correspondence between the Stern-Brocot (SB) ordering of rational numbers and the corresponding ordering of Farey-Christoffel (FC) words, a class of words that, since their appearance in literature at the end of the 18th century, have revealed numerous relationships with other fields of mathematics. Among the results obtained here is the construction of substitution rules that act on the FC words in a parallel way to the maps on the positive reals that generate the permuted SB tree both vertically and horizontally. We further show that these rules naturally induce a map of the space of (infinite) Sturmian sequences into itself. Finally, a complete correspondence is obtained between the vertical and horizontal motions on the SB tree and the geodesic motions along scattering geodesics and the horocyclic motion along Ford circles in the upper half-plane, respectively.

We present a stochastic mean-reverting jump-diffusion model to simulate rainfall time series and validate it using long-term half-hourly rain fall data from the North-East region of India. The model captures the intermittent and extreme-event dynamics of rainfall, reproducing superdiffusive behavior with an exponent $\sim 1.8$, along with the observed probability distributions and multifractal features. By systematically varying key parameters, we demonstrate a transition between Log-Normal and Gamma distributions, and show how the occurrence of extreme events and dry-patch durations can be controlled. Spectral and wavelet analyses further confirm that the simulated series reproduces the dominant temporal scales observed in real rainfall data. Our proposed framework provides a robust tool for generating realistic synthetic rainfall series and serves as an effective approach for understanding the influence of underlying stochastic processes that governs the rainfall statistics.

mmid (Multi-Modal Integration and Downstream analyses for healthcare analytics) is a Python package that offers multi-modal fusion and imputation, classification, time-to-event prediction and clustering functionalities under a single interface, filling the gap of sequential data integration and downstream analyses for healthcare applications in a structured and flexible environment. mmid wraps in a unique package several algorithms for multi-modal decomposition, prediction and clustering, which can be combined smoothly with a single command and proper configuration files, thus facilitating reproducibility and transferability of studies involving heterogeneous health data sources. A showcase on personalised cardiovascular risk prediction is used to highlight the relevance of a composite pipeline enabling proper treatment and analysis of complex multi-modal data. We thus employed mmid in an example real application scenario involving cardiac magnetic resonance imaging, electrocardiogram, and polygenic risk scores data from the UK Biobank. We proved that the three modalities captured joint and individual information that was used to (1) early identify cardiovascular disease before clinical manifestations with cardiological relevance, and (2) do it better than single data sources alone. Moreover, mmid allowed to impute partially observable data modalities without considerable performance losses in downstream disease prediction, thus proving its relevance for real-world health analytics applications (which are often characterised by the presence of missing data).

We perform a comprehensive study of a certain class of discrete symmetries of families of Feynman integrals, defined as affine changes of variables that map different sectors of the family into each other. We show that these transformations are always encoded into permutations of the Feynman parameters that relate the Lee-Pomeransky polynomials of the two sectors, irrespective of the integral representation used to define the Feynman integrals. We then construct an affine map in loop-momentum space that encodes such a permutation. We also show that these symmetries can be naturally embedded into the framework of twisted cohomology theories, and the period and intersection parings are invariant under the symmetry transformations. If we focus on symmetries within a fixed sector, we obtain a group acting on the twisted cohomology group, and we study the decomposition of this action into irreducible representations. One of our main mathematical results is that the character of this representation is proportional to the Euler characteristic of the corresponding fixed-point set. We then study the implications for Feynman integrals, in particular for the intersection matrix in a canonical basis. We also present a formula for the number of master integrals in a given sector in the presence of a non-trivial symmetry group in terms of the Euler characteristics of fixed-point sets. As an application, we obtain the numbers of master integrals for banana integrals with up to four loops for arbitrary configurations of non-zero masses. In order to achieve our results, we had to combine tools from various different areas of mathematics, including graph theory, group theory and algebraic topology.

We present a categorical framework for formal systems in which inference rules with $m$ metavariables over a category of syntax $\mathscr{S}$, taken to be a cartesian PROP, are represented by operations of arity $k \to n$ equipped with spans $k \leftarrow m \to n$ in $\mathscr{S}$, encoding the hypotheses and conclusions in a common metavariable context. Composition is by substitution of metavariables, which is the sole primitive operation, as in Metamath. Proofs in this setting form a symmetric monoidal category whose monoidal structure encodes the combination and reuse of hypotheses. This structure admits a proof-checking algorithm; we provide an open-source implementation together with a surface syntax for defining formal systems. As a demonstration, we encode the formulae and inference rules of first-order logic in Metacat, and give axioms and representative derivations as examples.

Let $f:\mathbb{R}^n\to\mathbb{R}$ be an unknown object, and suppose the observations are tomographic projections of randomly rotated copies of $f$ of the form $Y = P(R\cdot f)$, where $R$ is Haar-uniform in $\mathrm{SO}(n)$ and $P$ is the projection onto an $m$-dimensional subspace, so that $Y:\mathbb{R}^m\to\mathbb{R}$. We prove that, whenever $d\le m$, the $d$-th order moment of the projected data determines the full $d$-th order Haar-orbit moment of $f$, independently of the ambient dimension $n$. We further provide an explicit algorithmic procedure for recovering the latter from the former. As a consequence, any identifiability result for the unprojected model based on $d$-th order group-invariant moment extends directly to the tomographic setting at the same moment order. In particular, for $n=3$, $m=2$, and $d=2$, our result recovers a classical result in the cryo-EM literature: the covariance of the 2D projection images determines the second order rotationally invariant moment of the underlying 3D object.

We present a perceptually-driven video compression framework integrating implicit neural representations (INRs) and pre-trained video diffusion models to address the extremely low bitrate regime (<0.05 bpp). Our approach exploits the complementary strengths of INRs, which provide a compact video representation, and diffusion models, which offer rich generative priors learned from large-scale datasets. The INR-based conditioning replaces traditional intra-coded keyframes with bit-efficient neural representations trained to estimate latent features and guide the diffusion process. Our joint optimization of INR weights and parameter-efficient adapters for diffusion models allows the model to learn reliable conditioning signals while encoding video-specific information with minimal parameter overhead. Our experiments on UVG, MCL-JCV, and JVET Class-B benchmarks demonstrate substantial improvements in perceptual metrics (LPIPS, DISTS, and FID) at extremely low bitrates, including improvements on BD-LPIPS up to 0.214 and BD-FID up to 91.14 relative to HEVC, while also outperforming VVC and previous strong state-of-the-art neural and INR-only video codecs. Moreover, our analysis shows that INR-conditioned diffusion-based video compression first composes the scene layout and object identities before refining textural accuracy, exposing the semantic-to-visual hierarchy that enables perceptually faithful compression at extremely low bitrates.

This paper investigates the state estimation problem for linear systems subject to Gaussian noise, where the model parameters are unknown. By formulating and solving an optimization problem that incorporates both offline and online system data, a novel data-driven moving horizon estimator (DDMHE) is designed. We prove that the expected 2-norm of the estimation error of the proposed DDMHE is ultimately bounded. Further, we establish an explicit relationship between the system noise covariances and the estimation error of the proposed DDMHE. Moreover, through a sample complexity analysis, we show how the length of the offline data affects the estimation error of the proposed DDMHE. We also quantify the performance gap between the proposed DDMHE using noisy data and the traditional moving horizon estimator with known system matrices. Finally, the theoretical results are validated through numerical simulations.

This paper presents a technique to drive the state of a constrained nonlinear system to a specified target state in finite time, when the system suffers a partial loss in control authority. Our technique builds on a recent method to control constrained nonlinear systems by building a simple, linear driftless approximation at the initial state. We construct a partition of the finite time horizon into successively smaller intervals, and design controlled inputs based on the approximate dynamics in each partition. Under conditions that bound the length of the time horizon, we prove that these inputs result in bounded error from the target state in the original nonlinear system. As successive partitions of the time horizon become shorter, the error reduces to zero despite the effect of uncontrolled inputs. A simulation example on the model of a fighter jet demonstrates that the designed sequence of controlled inputs achieves the target state despite the system suffering a loss of control authority over one of its inputs.

We develop a comprehensive analysis of the Kirkwood-Dirac distributions in classical optics, revealing their deep connection with optical coherence as fundamental concept in optics. From their very definition, the Kirkwood-Dirac distributions emerge as generalized mutual coherence functions involving two different bases instead of just one. This perspective provides a unified interpretation of the so-called anomalous values, that are complex and negative values, as direct manifestations of coherence. We show that this interpretation consistently applies across all field variables considered in this work, including polarization, interference and wave propagation. Furthermore, we propose diverse methods of experimental determination of these distributions based on interference, in full agreement with their coherence-based interpretation.

We investigate superconductivity in a two-band $t$-$J$ model consisting of an itinerant orbital (orbital-0) and a quasi-localized orbital (orbital-1) using variational Monte Carlo. A robust orbital-selective $d$-wave superconducting state is found to emerge exclusively from the itinerant orbital. An analysis of the superexchange energy hierarchy shows that the quasi-localized orbital-1 competes with superconductivity by favoring local inter-orbital bound states, which act as energy defects and disrupt phase coherence. Consistently, the superconducting order parameter is monotonically suppressed as the occupancy of orbital-1 increases. Motivated by superconductivity in nickelate La$_3$Ni$_2$O$_7$, these results highlight the essential role of multi-orbital physics beyond the single-band $t$-$J$ framework and point to a concrete route to enhance $T_c$: suppressing the involvement of localized $d_{z^2}$-derived orbitals.

The stochastic gravitational wave background (SGWB) is conventionally treated as a passive relic of its astrophysical and cosmological sources, with negligible back-reaction on the matter content of the Universe. Here we show that this assumption needs to be modified once the SGWB and matter are treated as a dynamically coupled non-equilibrium system. Combining linearized general relativity with the fluctuation-dissipation theorem, we derive a generalized Langevin framework that drives the coupled system toward a dynamical equilibrium, which is characterized by a distinctive strain spectrum with a high-frequency cutoff $\mathcal{W}$, and a scale-dependent coupling parameter that screens gravity progressively for the most massive structures. Three findings support this framework. Fitting the equilibrium spectrum to the NANOGrav 15-year dataset yields a Bayes factor of $48\pm 3.8$ over the supermassive black hole binary baseline, achieved entirely within general relativity and the Standard Model. The PTA-calibrated screening mass scale $m_{c}\sim 10^{12}\text{--}10^{14}\,M_{\odot}$ overlaps, with no free cosmological parameter, the $Λ$CDM-derived linear-to-nonlinear transition mass $M_{\rm NL}$ of cosmic structure at $\sim 8\,h^{-1}\,\mathrm{Mpc}$. Most strikingly, promoting this concordance to a structural identification expresses $\mathcal{W}$ entirely in terms of $M_{\rm NL}$, and its inverse acquires a transparent physical reading as a coherence threshold for SGWB-matter coupling. $\mathcal{W}$ is thereby a derived quantity linking nanohertz gravitational-wave observables to the late-time cosmological sector. The framework makes distinctive scale-dependent predictions testable by forthcoming large-scale structure surveys and space-borne gravitational-wave observatories.

Cells control the size and organization of biomolecular condensates formed by liquid-liquid phase separation (LLPS), but multiple mechanisms likely contribute to this control and remain to be fully elucidated. Here we propose a transport-driven mechanism in which stochastic binding of phase-separating proteins to cytoskeletal motor proteins, followed by active redistribution along filament networks, generates an effective long-range repulsion that arrests coarsening and selects a finite condensate size. A minimal diffusion-transport model, analyzed by linear stability theory and three-dimensional simulations, reveals a transition from macroscopic to microphase separation at remarkably low binding/release fractions, corresponding to minute motor-bound populations. Tuning motor binding rates $b$ or transport velocities enables sublinear control of condensate sizes ($L \sim b^{-1/4}$) from nanometers to micrometers. In anisotropic cytoskeletal environments, transport asymmetry drives morphological transitions from spherical to cylindrical condensates. Operating independently of thermodynamic parameters, this mechanism provides a versatile, spatiotemporally programmable route to condensate organization and informs the design of synthetic active emulsions with tunable architectures.

Black hole thermodynamics has recently witnessed three distinct classification schemes: based on local geometric properties of the temperature function, global topological invariants, and Riemann surface foliations in the complex plane. We show that these schemes are equivalent in the real domain via two dictionaries: one linking thermal stability to the monotonicity of the temperature curve, and the other connecting the number of black hole states to the foliation number of a Riemann surface. The number of extremal points of the temperature curve determines the classification in all three frameworks, tracing this unification to the critical point structure of the black hole solution space. As an illustration, several black holes demonstrate how counting extrema yields topological invariants and phase transition information. This unified framework simplifies black hole thermodynamic analysis and provides a foundation for exploring more complex black holes.

We present an analysis of the parallel peculiar velocity correlation function using data from the Cosmicflows-4 (CF4) survey. CF4 significantly extends the depth of the peculiar velocity measurements, mitigating the impact of observers on the cosmic variance. We examine the distribution of cosmic variance using different velocity correlation estimators. The combination of the large peculiar velocity uncertainties and the anisotropy distribution of the CF4 data across the northern and southern hemispheres results in substantial statistical uncertainties in the velocity correlation function. To address this, we test different weighing schemes in the velocity correlation function and implement a more accurate peculiar velocity estimator that reduces velocity uncertainties, consequently decreasing the statistical uncertainty. Using the CF4 group dataset, we derive a growth rate of $fσ_8=0.384^{+0.116}_{-0.194}$ and a local growth rate of $fσ_8=0.569^{+0.054}_{-0.06}$ through a Markov Chain Monte Carlo method.