We study harmonic map sequences from surfaces to compact homogeneous spaces. For sequences developing a single bubble, we derive refined asymptotic expansions in the neck region and prove new obstruction relations among the leading coefficients. These strengthen earlier results by converting an inequality into an equality. For weakly conformal maps, this yields geometric constraints: in low dimensions the tangent planes of the limit map and bubble must coincide, while in higher dimensions they are isoclinic.

We classify extended Abelian Chern-Simons theories with gauge group $U(1)^n$ as extended $(2+1)$-dimensional topological quantum field theories. For an even integral nondegenerate lattice $(Λ,K)$, let $(G_K,q_K)$ denote its discriminant quadratic module. We prove that the associated theory is determined, up to symmetric monoidal natural isomorphism, by this finite quadratic module, and that every finite quadratic module is realized as the discriminant quadratic module of an even integral nondegenerate lattice. It follows that finite quadratic modules classify extended Abelian Chern-Simons theories, pointed Abelian Reshetikhin-Turaev TQFTs, and pointed modular tensor categories.

The Dynamic Mode Decomposition (DMD) and the more general Extended DMD (EDMD) are powerful tools for computational analysis of dynamical systems in data-driven scenarios. They are built on the theoretical foundation of the Koopman composition operator and can be considered as numerical methods for data snapshot-based extraction of spectral information of the composition operator associated with the dynamics, spectral analysis of the structure of the dynamics, and for forecasting. In high fidelity numerical simulations, the state space is high dimensional and efficient numerical methods leverage the fact that the actual dynamics evolves on manifolds of much smaller dimension. This motivates computing low rank approximations in a streaming fashion and the DMD matrix is adaptively updated with newly received data. In this way, large number of high dimensional snapshots can be processed very efficiently. Low dimensional representation also requires fast updating for online applications. This paper revisits the pioneering works of Hemati, Williams and Rowley (Physics of Fluids, 2014), and Zhang, Rowley, Deem and Cattafesta (SIAM Journal on Applied Dynamical Systems, 2019) on the streaming DMD and proposes improvements in functionality (using residual bounds, Exact DMD vectors), computational efficiency (more efficient algorithm with smaller memory footprint) and numerical robustness (smaller condition numbers and better forecasting skill).

We consider the problem of wrapping three-dimensional solid bodies with a given planar sheet of paper, where the paper may be folded or wrinkled but not stretched or torn. We propose a conjecture characterising the maximumvolume solid wrappable by any given sheet: the maximum is always achieved (or approached) by a non-convex body. In other words, for any convex solid wrappable by a given sheet, there exists a non-convex solid of strictly greater volume that the same sheet can wrap. We discuss related work, a key subquestion involving the sphere, and several further directions.

Unlike canonical Kondo lattices in f-electron systems, where localized f orbitalsnaturally provide local moments, d-electron Kondo lattices require a distinct mechanism for local-moment formation. However, the study of d-electron Kondo lattices in bulk materials remains far from settled, particularly with regard to the microscopic origin of the local moments. Here, we report a microscopic mechanism for this process in the bilayer kagome metal CsCr6Sb6, where strong correlations drive a Mott splitting of the kagome flat band to supply the requisite local moments. By combining STM/STS and ARPES, we resolve a spectroscopic hierarchy between high-energy correlation effects and low temperature hybridization. Low-temperature STS reveals a robust asymmetric suppression of the density of states near EF that is well captured phenomenologically by a Fano-type lineshape, while ARPES detects a sharp quasiparticlepeak near EF. These low-energy signatures evolveon the same temperature scale and disappear upon warming, consistent with the onset of Kondo hybridization. At the same time, STS resolves symmetric humps at approximately +-50 mV and ARPES identifies a weakly dispersive feature around 50 meV below EF; unlike the near-EF hybridization signatures, these features persist to substantially higher temperatures. This separation of energy and temperature scales supports a two-stage picture in which a kagome flat band first undergoes correlation-driven splitting into lower and upper Hubbard bands, and the occupied lower Hubbard band supplies the local moments that later hybridize with itinerant electrons at lower temperature. Our results therefore move beyond the phenomenology of a kagome Kondo lattice candidate and instead provide a microscopic spectroscopic picture linking Mottness to Kondo hybridization in a frustrated d-electron system.

We conducted a homogeneous chemical analysis of pre-main sequence stars with effective temperatures ranging from $\sim$ 3000 K to $\sim$ 5500 K in eight nearby star-forming regions (SFRs): Chamaeleon I, $η$ Chamaeleonis, Lupus, Orion OB1a, Orion OB1b, $σ$Orionis, Taurus, and Corona-Australis. Our study aims to: 1) derive the lithium abundance (A(Li)) and highlight the impact of veiling correction on both A(Li) and age determination; 2) perform the iron (Fe) and barium (Ba) abundance analysis in regions with scarce previous measurements; 3) investigate the possible Ba enhancement. The analyzed data were obtained as part of the PENELLOPE Large Program using the ESPRESSO, UVES, and X-Shooter instruments. We measured the equivalent width of the lithium line (EWLi) at $λ$ = 6707.8 Angstrom, from which A(Li) is derived using the curves of growth method. The Fe and Ba abundances have been measured through spectral synthesis analysis. Using the EAGLES code, we derived an upper limit on the age of the eight SFRs. Our findings underscore the necessity of veiling corrections on EWLi, which can shift A(Li) and age estimates by up to $\sim$ 0.7 dex and $\sim$ 20 Myr, respectively. Accounting for veiling, the A(Li) distributions peak in a range between 3.3 and 3.8 dex for most clusters, and the upper age limit is approximately 5 Myr for all SFRs. We successfully measured the mean iron and barium abundances in Lupus, Taurus, Cha I, and $η$ Cha, showing slightly sub-solar iron abundance, and a clear Ba overabundance, with [Ba/H] values reaching up to 0.75 dex.

This paper studies the memory-type null controllability of a class of one-dimensional non-autonomous degenerate parabolic equations with Volterra-type memory terms. The diffusion operator is considered in both divergence and non-divergence forms and may exhibit weak or strong degeneracy at the boundary, while the diffusion coefficient depends explicitly on time. Due to the presence of memory effects, classical null controllability is insufficient, and a stronger notion requiring the vanishing of both the state and the accumulated memory is introduced. To address this problem, we establish new Carleman estimates adapted to non-autonomous degenerate operators in weighted spaces. The memory term is handled as a lower-order perturbation within the Carleman framework. These estimates yield suitable observability inequalities, which allow us to prove memory-type null controllability under appropriate structural conditions. Extensions to cases with double boundary degeneracy and moving control regions are also discussed.

The fluctuation-dissipation theorem is a hallmark of equilibrium system that stem from their time-reversal symmetry. In many non-equilibrium systems, in particular active ones, extensions and explicit violations of this theorem are used to assess their ''distance'' to equilibrium. In Hamiltonian flocks, conservative yet non-Galilean models of polar liquids, previous work reported collective motion without the activity that usually underlies it. In this paper, we show that this model obeys a generalized time-reversal symmetry that yields a fluctuation-dissipation theorem that mixes position and polarity degrees of freedom. Due to the oddness of spin under time reversal, the system also obeys Onsager-Casimir reciprocity rather than standard Onsager relations. The coupling also induces rich spin orientation dynamics, including a non-trivial diffusion constant at long times. Finally, we show that considering the naïve time-reversal operation rather than the generalized one that leaves the system invariant leads to a spurious entropy production rate, that could be wrongly interpreted as a distance to equilibrium. Our findings suggest looking for possible extensions of time-reversal symmetry in active-looking systems, which may lead to yet unknown generalizations of the fluctuation-dissipation theorem.

We extend AMM trade functions to negative inputs via the \textit{concave continuation}, derived from the invariance of the local conservation law under allocation direction flips. This unifies routing and arbitrage into a single problem. We extend the one-hop transfer algorithm proposed in \cite{jiang} to this setting.

Describing the proton structure function $F_2$ in the non-perturbative and transition regimes of quantum chromodynamics (QCD) remains a significant theoretical challenge. In this work, we introduce a Physics-Guided Neural Network (PGNN) that integrates Holographic QCD with deep learning. By embedding the five-dimensional $\text{AdS}_5$ Dirac equation and the string diffusion kernel directly into the computational graph, the network is strictly constrained to the physical proton mass ($M_p \equiv 0.938 \text{ GeV}$). Applying this framework to high-precision SLAC deep inelastic scattering data yields a global fit of $χ^2/\text{d.o.f.} \simeq 0.91$. Rather than relying on predetermined empirical forms, the network dynamically extracts the transition between the $s$-channel bulk fermion mechanism (hadronic resonance excitations) and the $t$-channel holographic Pomeron exchange (diffractive background), identifying a kinematic crossover near $x \approx 0.19$. Furthermore, the optimization naturally recovers a Pomeron intercept of $α_0 \approx 1.0786$ and generates higher-twist scale-breaking effects through the evolution of resonance mass spectra. This demonstrates that embedding analytical differential equations into neural networks provides an interpretable, data-driven approach for phenomenological studies of strongly coupled systems.

The supernova remnant (SNR) G25.1-2.3 was identified in the radio band during the Sino-German $λ$6 cm survey of the Galactic plane. We present a detailed investigation of the optical, HI, and CO emission towards the G25.1-2.3 to better understand its characteristics and environment. In this study, optical spectroscopic data of the remnant and its environment have been analysed for the first time, providing new insights into their emission properties. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) and 1.5-m Russian-Turkish Telescope (RTT150) data show variations across the observed regions, with [SII]/H$α$ ranging from 0.16 to 0.83. We identified shock-heated gas in the northern and southern regions and several photoionized regions around the SNR based on their [SII]/H$α$ ratios derived from spectra. The [SII]$λ$6716/$λ$6731 ratio observed in the northern region suggests electron densities ($n_{\rm e}$) ranging from 120 to 1030 cm$^{-3}$, whereas the southern regions show higher values, between 490 and 4500 cm$^{-3}$. The variations in the observed H$α$/H$β$ ratios indicate significant differences in extinction across the regions. H$α$ images obtained using the 1-m Turkish Telescope (T100) reveal optical emission in the northern and southern, characterized by filamentary and diffuse structures. We newly found a hole-like distribution of HI, whose spatial extent is roughly consistent with the diameter of the SNR. Based on radio data, we examine the evolutionary stage of G25.1-2.3 using the surface brightness-diameter ($Σ-D$) relation and the equipartition method.

New recursive estimators for computing higher-order derivatives of mean queueing time from a single sample path of a first-come, first-served single-server queue are presented, derived using the well-known Lindley equation and applying the Leibniz integral rule of differential calculus. Illustrative examples are provided.

We present a comprehensive $^{31}$P and $^{65}$Cu nuclear magnetic resonance (NMR) study of the layered van der Waals magnet CuCrP$_2$S$_6$. The compound exhibits a sequence of structural and magnetic phase transitions: a high-temperature paraelectric state, followed by a quasi-antiferroelectric (QAFE) state near 185 K, a long-range antiferroelectric (AFE) phase below 150 K, and finally, antiferromagnetic (AFM) order below $T_\mathrm{N}$ = 30 K. The evolution of the NMR spectra, NMR shift, and spin-lattice ($T_1^{-1}$) and spin-spin ($T_2^{-1}$) relaxation rates provide direct microscopic fingerprints of these transitions. The splitting of both the NMR line and $T_1^{-1}$ below the AFE transition demonstrates the emergence of two inequivalent P sites. From $K - χ$ analysis, we extract nearly isotropic transferred hyperfine couplings and show that the NMR shift anisotropy originates primarily from the dipolar contribution, in contrast to Mn$_2$P$_2$S$_6$ and Ni$_2$P$_2$S$_6$. We determine the ferromagnetic intralayer exchange $J_{intra}\approx$ -4.9 K from the Curie Weiss temperature, consistent with ferromagnetic layers antiferromagnetically stacked along the $c$ axis, and evaluate the Moriya high temperature relaxation rate including cross correlation effects of the P P dimer. Critical divergence of $T_1^{-1}$ near $T_\mathrm{N}$ yields a critical exponent $γ\simeq$ 0.45(4), placing CuCrP$_2$S$_6$ in a three dimensional Heisenberg universality regime.

We show that the notion of a black hole mass could be superceded by that of a topological charge in a spacetime without matter and curvature singularity. This feature emerges through a set new spacetime solutions of first order gravity in vacuum, named as bubble spacetimes, constructed here by weaving together the degenerate and nondegenerate metric phases. For a static bubble, the boundary surface connecting the two phases is characterized by a universal topological number. Notably, this surface coincides with the photon sphere of the conventional black hole irrespective of the presence of the cosmological constant. In contrast, a phase boundary located at the event horizon is shown to be topologically trivial. Thus, along with the black hole mass, the photon sphere also acquires a topological interpretation.

Answering a question of Leo Versteegen, we prove that for $n\ge 3$ every sum-free set $A\subseteq\mathbb{F}_5^n$ with $|A|\ge 28\cdot 5^{n-3}$ is either contained in the union of two parallel hyperplanes, or isomorphic to $Λ\times \mathbb{F}_5^{n-3}$, where $Λ\subseteq \mathbb{F}_5^3$ denotes a certain sum-free set of size $28$ discovered by Vsevolod Lev and Leo Versteegen.

We analyse a posteriori error estimates for the discretization with mixed finite elements on simplicial or Cartesian meshes of the multigroup neutron simplified transport (SPN ) equations, in the case where a Robin (or Fourier type) boundary condition is imposed on the boundary. This boundary condition is of particular importance in neutronics, since it corresponds to the well-known vacuum boundary condition. We provide guaranteed and locally efficient estimators. In particular, a specific estimator is designed to handle the Robin boundary condition. We also develop the theory in the case of mixed imposed boundary conditions, of Dirichlet, Neumann or Fourier type. The approach is further extended to a Domain Decomposition Method, the so-called DD+L 2 jumps method. In this framework, the adaptive mesh refinement strategy is implemented for a discretization using Cartesian meshes on each subdomain. Numerical experiments illustrate the theory.

Bilevel optimization is a field of significant theoretical and practical interest, yet solving such optimization problems remains challenging. Evolutionary methods have been employed to address these problems in the black-box setting; however, they incur high computational cost due to the nested nature of bilevel optimization. Although previous methods have attempted to reduce this cost through various heuristic techniques, such approaches limit versatility on challenging optimization landscapes, such as those with multimodality and significant interaction between upper- and lower-level decision variables. In this study, we propose an efficient framework that exploits the invariance of rank-based evolutionary algorithms to monotonic transformations, thereby reducing the computational burden of the lower-level optimization loop. Specifically, our method directly approximates the rankings of the upper-level value function, bypassing the need to run the lower-level optimizer until convergence for each upper-level iteration. We apply this framework to the setting where both levels are continuous, adopting CMA-ES as the optimizer. We demonstrate that our method achieves competitive performance on standard bilevel optimization benchmarks and can solve problems that are intractable with previously proposed methods, particularly those with multimodality and strong inter-variable interactions.

We study high-dimensional mediation analysis in which exposures, mediators, and outcomes are all multivariate, and both exposures and mediators may be high-dimensional. We formalize this as a many (exposures)-to-many (mediators)-to-many (outcomes) (MMM) mediation analysis problem. Methodologically, MMM mediation analysis simultaneously performs variable selection for high-dimensional exposures and mediators, estimates the indirect effect matrix (i.e., the coefficient matrices linking exposure-to-mediator and mediator-to-outcome pathways), and enables prediction of multivariate outcomes. Theoretically, we show that the estimated indirect effect matrices are consistent and element-wise asymptotically normal, and we derive error bounds for the estimators. To evaluate the efficacy of the MMM mediation framework, we first investigate its finite-sample performance, including convergence properties, the behavior of the asymptotic approximations, and robustness to noise, via simulation studies. We then apply MMM mediation analysis to data from the Alzheimer's Disease Neuroimaging Initiative to study how cortical thickness of 202 brain regions may mediate the effects of 688 genome-wide significant single nucleotide polymorphisms (SNPs) (selected from approximately 1.5 million SNPs) on eleven cognitive-behavioral and diagnostic outcomes. The MMM mediation framework identifies biologically interpretable, many-to-many-to-many genetic-neural-cognitive pathways and improves downstream out-of-sample classification and prediction performance. Taken together, our results demonstrate the potential of MMM mediation analysis and highlight the value of statistical methodology for investigating complex, high-dimensional multi-layer pathways in science. The MMM package is available at https://github.com/THELabTop/MMM-Mediation.

Let $L$ be one of the finite simple classical groups $L_8(q)$, $U_8(q)$, $O_{10}^+(q)$, $O_{10}^-(q)$ or $O_{12}^+(q)$, with $q$ odd. We prove that every finite group having the same set of element orders as $L$ is an almost simple group with socle isomorphic to $L$. This completes the study of the recognition-by-spectrum problem for simple classical groups whose prime graph independence number is equal to $4$.

Optically pumped magnetometers (OPMs) have demonstrated significant potential in weak magnetic field detection due to their high sensitivity. In this study, we developed an Mz-type optically pumped rubidium magnetometer using a paraffin-coated anti-relaxation vapor cell. The system optimization and performance characterization were conducted inside a magnetic shield. Specifically, the pump light intensity and radio-frequency (RF) magnetic field were jointly optimized by using the linewidth-amplitude ratio as the core metric. Based on the frequency-domain noise spectrum, the sensitivity in open-loop mode was measured to be approximately 30.8 pT/Hz^{1/2}. Furthermore, a closed-loop feedback locking technique was applied, reducing the measured noise floor under the tested conditions and improving the sensitivity to 22.9 pT/Hz^{1/2}, with a measured -3 dB bandwidth of 123 Hz. The dynamic characteristics were evaluated via magnetic-field step response, showing that the system could track magnetic-field changes stably under closed-loop operation. Finally, by using tri-axial modulation and frequency-domain demodulation, we overcame the scalar measurement limitation of traditional Mz magnetometers. This work realizes vector magnetic field detection and provides a technical basis for applications such as geomagnetic navigation and magnetic anomaly detection.

Grid search and random search are widely used techniques for hyperparameter tuning in machine learning, especially when gradient information is unavailable. In these methods, a finite set of candidate configurations is evaluated, and the best-performing one is selected. We propose a simple and computationally inexpensive refinement of this paradigm: instead of selecting a single best point, we form a weighted average of the evaluated configurations, where the weights are chosen using an importance sampling scheme inspired by the Laplace principle. This scheme can be implemented as a post-processing step on top of a random search, with no additional function evaluations. We also propose an iterative variant, where the sampling distributions are chosen adaptively to generate new candidate points around the previous estimate, in the spirit of Evolution Strategy (ES) methods. In a general non-convex setting, we show that, after n evaluations, the error of the proposed methods is of smaller order than n -2/(d+2) . This compares favorably to random search or grid search rates of n -1/d as soon as d > 2. We illustrate the practical benefits of this averaging strategy on several examples.

We study how to implement and transform frame perspectives for quantum processes in the process-matrix formalism. We argue that, for pure processes, the causal reference frames (CRF)and time-delocalized subsystems (TDS) formalisms should be understood as coordinate parametrizations of a single perspective-neutral higher-order object. A genuine perspective arises when one endows the process with additional frame data by choosing an operational foliation into circuit fragments (events). With this distinction, existing no-go results acquire a clear scope: they rule out unitary transformations that preserve time foliation, attempting to switch perspectives while keeping the fragment boundaries -- hence the global past/future partition -- fixed. Focusing on the quantum switch, we construct explicit maps that transform perspectives unitarily at the price of reshuffling the notions of past and future. We then show that unitary transformations between perspectives can also be achieved in a different way, namely by extending the process with subsystems that define quantum reference frames and provide a shared spatiotemporal scaffold. In this extended setting, complementary CRF/TDS perspectives become unitarily related while preserving global past and future. We discuss how this frame-perspectival approach informs the broader question of empirical realizability of abstract process matrices.

In nonequilibrium suspensions, static number fluctuations $N$ in virtual observation boxes reveal remarkable structural properties, but the dynamic potential of $N(t)$ signals remains unexplored. Here, we develop a theory to learn the dynamical parameters of self-propelled particle models from $N(t)$ statistics. Unlike traditional trajectory analysis, $N(t)$ statistics distinguish between models, by sensing subtle differences in reorientation dynamics that govern re-entrance events in boxes. This paves the way for quantifying advanced dynamic features in dense nonequilibrium suspensions.

The Bell-Bloom-type optically pumped atomic magnetometers are well suited for weak geomagnetic field detection. However, conventional single-beam pumping introduces an atomic spin polarization gradient, which limits the measurement accuracy and sensitivity. To address this issue, this paper proposes and experimentally demonstrates a Bell-Bloom-type rubidium FID magnetometer scheme integrating orthogonally polarized counter-propagating pumping and multi-pass probe detection. This design homogenizes the atomic spin polarization distribution and suppresses light shifts and power broadening effects induced by the pump beam. Meanwhile, the five-pass probe configuration significantly enhances the signal amplitude. Experimental results reveal that, compared with the traditional single-beam pumping and single-pass detection scheme, the proposed magnetometer achieves a remarkable improvement in magnetic field measurement accuracy, and the magnetic field sensitivity is improved from 18.9 pT/\sqrt{Hz} to 3.1 pT/\sqrt{Hz}. This work provides an effective technical approach and reference for optimizing the performance of atomic magnetometers and extending their applications in integrated arrays.

Within a general semimartingale framework, we study the relationship between collective market efficiency and individual rationality. We derive a necessary and sufficient condition for the existence of (possibly zero-sum) exchanges among agents that strictly increase their indirect utilities and characterize this condition in terms of the compatibility between agents' preferences and collective pricing measures. The framework applies to both continuous- and discrete-time models and clarifies when cooperation leads to a strict improvement in each participating agent's indirect utility.

Individual multi-loop diagrams for the massive Sudakov form factor contain an infinite tower of ultra-collinear momentum regions. We show that, for the on-shell form factor in QCD, these contributions cancel to all orders as a consequence of gauge invariance, so the leading-power SCET$_{\rm II}$ factorization formula is unchanged. Using the $η$ rapidity regulator, we compute the soft function and the massive jet function of the quark and gluon Sudakov form factors through two loops and resum logarithms at NNLL accuracy, including hierarchies of fermion masses. We also show that with a gauge-boson mass regulator, the infinite tower of modes is truncated and ultra-collinear and ultra-soft modes become manifest and factorize explicitly, providing a direct EFT derivation of the regulated infrared dependence.

This paper studies random reshuffling (RR)-based distributed Nash equilibrium seeking for noncooperative games. The game is motivated as a sample-average approximation of an underlying expected-value stochastic game, while the algorithmic focus is placed on the resulting finite-sum equilibrium problem. Unlike existing distributed stochastic Nash equilibrium methods that mainly rely on with-replacement sampling, the proposed approach incorporates without-replacement component updates into equilibrium computation over networks. We first consider a full-information benchmark, for which an intermediate reference trajectory and a shuffling variance are introduced to characterize the epoch-wise dynamics induced by RR. The method is then extended to the more practical partial-decision-information setting, where each player updates its action using local estimates of the joint action profile. For the full-information case, a descent-type bound is established for the RR iterates. For the distributed partial-decision-information case, it is shown that, under constant parameters, the proposed algorithm converges linearly to a neighborhood of the Nash equilibrium, while under diminishing parameters, it converges exactly to the Nash equilibrium almost surely and in mean square. Numerical experiments on an EV charging game and a nonquadratic edge resource admission game demonstrate that RR consistently outperforms the conventional with-replacement SGD baseline in both steady-state accuracy and long-horizon performance.

't Hooft anomalies impose fundamental constraints on quantum matter and often lead to emergent symmetry structures upon gauging. We analyze a lattice model with four global symmetries realizing a mixed anomaly described by $\sim a_1\wedge a_2\wedge a_3\wedge a_4$, where the $a_i$ denote background gauge fields for the global symmetries. Through explicit lattice gauging, we demonstrate the emergence of higher symmetry structures, including 2-group, non-invertible, and higher fusion categorical symmetries. We also provide a field-theoretical understanding of these results. Applying this framework to systems with Lieb-Schultz-Mattis anomalies, obtained by promoting part of the internal symmetries to translational symmetries, we demonstrate that modulated (dipole) symmetries arise as direct counterparts of those in systems with purely internal typeIV anomalies. Importantly, we uncover a qualitatively new feature absent in previously studied modulated symmetries: their realization can become intrinsically defect-dependent. In particular, the emergent symmetry structure changes depending on whether symmetry defects are present. This work establishes a concrete lattice realization of mixed anomalies and reveals a rich structure of emergent symmetries, thereby clarifying their role in constraining quantum phases of matter.

In studies of turbulence, there has been extensive use of physical quantities such as {\it energy transfers} and {\it structure functions}. We examine whether these quantities can be useful in understanding problems of domain growth or coarsening, as modeled by the {\it time-dependent Ginzburg-Landau} (TDGL) equation and the {\it Cahn-Hilliard} (CH) equation. This paper has two major themes. First, we review our recent papers on energy transfers in domain growth. Second, we study structure functions and intermittency for coarsening systems. As a consequence of sharp interfaces, the structure functions scale as $S_q \sim r^{ζ_q}$, where $r$ is the distance between two points. For the TDGL and CH models, $ζ_q = 1$, indicating {\it anomalous scaling}

We explore the applicability of a stochastic time-evolution algorithm based on probabilistic angle interpolation. To simplify the pre-processing of the algorithm, we take the continuous-time limit, thereby explicitly eliminating Trotter errors and streamlining the resource analysis. We also introduce a noise-mitigation method tailored to it. As demonstrations, we apply the algorithm to two representative problems: estimating the ground-state energy of the $H_3^+$ molecular Hamiltonian and computing out-of-time-ordered correlators in the sparse Sachdev--Ye--Kitaev model. We evaluate the protocol's performance through numerical simulations and experiments on a trapped-ion quantum computer, Quantinuum Reimei.