We present a rigorous construction and uniqueness proof of the matrix Green's function for coupled radial Schrödinger equations with symmetric coupling potentials. The Green's matrix $g_{γγ'}(R,R')$ is built from two fundamental sets of $N$ linearly independent solutions, regular and outgoing, of the coupled radial equations. We prove that the associated Wronskian matrix is diagonal with elements $W_n = -k_n$ and independent of the radial coordinate, and demonstrate through the symplectic structure of the $2N$-dimensional phase space that the resulting construction is the unique Green's matrix satisfying the defining equation with correct boundary conditions, continuity at the source point, and the prescribed derivative discontinuity. The construction applies to any system of coupled radial Schrödinger equations with symmetric coupling potentials and open channels, including coupled-channels problems arising in nuclear, atomic, and molecular scattering. As an illustrative application, we show how the Green's matrix enters the nonlocal dynamical polarization potential (DPP) within the continuum-discretized coupled-channels (CDCC) framework, where retaining the off-diagonal elements captures multistep excitation pathways beyond the weak-coupling approximation.

The topological magnet MnBi$_2$Te$_4$ (MBT), with gapped topological surface state, is an attractive platform for realizing quantum anomalous Hall and Axion insulator states. However, the experimentally observed surface state gaps fail to meet theoretical predictions, although the exact mechanism behind the gap suppression has been debated. Recent theoretical studies suggest that intrinsic antisite defects push the topological surface state away from the MBT surface, closing its gap and making it less accessible to scanning probe experiments. Here, we report on the local effect of defects on the MBT surface states and demonstrate that high defect concentrations lead to a displacement of the surface states well into the MBT crystal, validating the theorized mechanism. The local and global influence of antisite defects on the topological surface states are studied with samples of varying defect densities by combining scanning tunneling microscopy (STM), angle-resolved photoemission (ARPES), and density functional theory (DFT). Our findings identify a combination of increased defect density and reduced defect spacing as the primary factors underlying the displacement of the surface states and suppression of surface gap, guiding further development of topological quantum materials.

Recent advances have linked various statements involving sumsets and cardinalities with corresponding statements involving sums of random variables and entropies. In this vein, this paper shows that the quantity $2{\bf H}\{X, Y\} - {\bf H}\{X+Y\}$ is a natural entropic analogue of the additive energy $E(A,B)$ between two sets. We develop some basic theory surrounding this quantity, and demonstrate its role in the proof of Tao's entropy variant of the Balog--Szemerédi--Gowers theorem. We examine the regime where entropic additive energy is small, and discuss a family of random variables related to Sidon sets. In finite fields, one can define an entropic multiplicative energy as well, and we formulate sum-product-type conjectures relating these two entropic energies.

The core of time series analysis lies in effectively modeling the physical laws within complex signals. Existing Transformer and Convolution Neural Network (CNN) architectures are often constrained by insufficient temporal inductive bias, restricted frequency extraction capabilities, or weak local phase alignment. To this end, this paper proposes Adaptive Network Based on Cascaded Harmonic Offset Routing (ANCHOR), an Adaptive Network based on Cascaded Harmonic Offset Routing. The model utilizes the Real Fast Fourier Transform (RFFT) to extract explicit dominant periods, injecting them as physical anchors into the dilation operators of multi-branch deformable convolutions. This guides the adaptive optimization of sampling locations in the time domain, achieving synergistic modeling of macroscopic periodic priors and microscopic geometric deformations. Furthermore, to address the quantization errors and picket-fence effects introduced by the discrete RFFT, this paper imports a continuously differentiable 1D Gaussian Radial Basis Function interpolation operator to replace traditional linear interpolation. This maintains the differentiability of the interpolation process and enhances the accuracy of sub-pixel phase compensation. Additionally, ANCHOR introduces an asymmetric routing mechanism and orthogonal channel partitioning to dynamically balance the extraction weights between high-energy strong signals and low-energy weak features. Multi-task benchmark experiments demonstrate that ANCHOR achieves the best or solid performance in short-term forecasting, anomaly detection, and time series classification tasks. Code is available at https://github.com/Jwy-EE/Anchor_pub

F, G, K and M type stars are the most abundant stellar population in the Milky Way and are expected to contribute to its diffuse X-ray emission. Yet their intrinsic average X-ray spectrum remains poorly constrained due to their faint X-ray luminosities, leaving their collective role in the X-ray background of the Milky Way uncertain. We analysed the volume-complete sample of M- (M0--M6) and FGK-type stars within 10 pc of the Sun using data from eROSITA all-sky survey aboard the Spectrum-Roentgen-Gamma (SRG) mission (eRASS:4). Individual spectra were normalized by exposure and distance and stacked to produce representative averages. The distance-normalized emission measures yield an average X-ray luminosity of $(2.6 \pm0.1)\times 10^{27}$ erg/s for M-type stars, and $(15\pm3)\times 10^{27}$ erg/s for F, G and K-type stars in 0.2--2.0 keV. The average spectra could be well described by a sum of three and two thermal models. Fitted temperatures and abundances remain consistent across M-star subgroups, while early-M stars are surprisingly on average less luminous than mid/late-M types. These results offer new insights into the collective X-ray properties of nearby stars, and provide motivation to explore the link with the unresolved soft X-ray background of the Galaxy.

Additives of sparingly soluble components are known to slow down or completely inhibit Ostwald ripening in dispersed systems. In this paper series, our earlier model of the stabilization against Ostwald ripening is revisited and extended over the whole range of compositions, molar volumes of components, and their activity coefficients. In the first paper, a simpler problem, the dissolution of a two-component drop under the action of excess Laplace pressure inside is analyzed. Three stages of dissolution are identified. In the first stage, called pre-lock-in, the concentration of the poorly soluble component undergoes a quick increase, and the system enters the lock-in state, in which the Laplace pressure effect on the chemical potential of the more soluble component is nearly completely counterbalanced by the Raoult effect. After this, the dissolution kinetics slows down and enters a steady state. In the process, the concentration of the sparingly soluble component continues to increase, first slowly and then more rapidly in the very end of the particle lifetime; this latter stage is called the 'late lock-in'. Despite all those variations, if the initial concentration of the poorly soluble component is above a certain threshold, the dissolution kinetics nearly follows the classical cubic law. An improved equation for the rate of dissolution is proposed that covers the whole formulation range and represents an extension over our previous formula.

We investigate the superconducting Anderson impurity model for interacting quantum dot Josephson junctions with spin-orbit coupling and a term accounting for tunnelling through higher-energy orbitals. These elements establish the conditions required for spin polarization in the absence of external magnetic field at finite superconducting phase bias. This Hamiltonian has been previously used to model the Andreev spin qubit, where quantum information is encoded in spinful odd-parity subgap states. Here we instead analyse the even-parity sector, i.e., the Andreev pair qubit based on Andreev bound states (ABS). The model is solved using the zero-bandwidth approximation and the numerical renormalization group, with further insight from variational calculations. Electron-electron interaction admixes single-occupancy Yu-Shiba-Rusinov (YSR) components into the ABS states, thereby strongly enhancing spin transitions in the presence of spin-orbit coupling. The ABS states can thus become sensitive to local magnetic field fluctuations, which has implications for decoherence in Andreev pair qubits. For strong interaction $U$, especially in the cross-over region between the ABS and YSR regimes for $U \sim 2Δ$, charge, spin, and inductive transitions can all become strong, offering avenues for spin control and quantum transduction.

This work is concerned with categorical methods for studying singularities. Our focus is on birational derived splinters, which is a notion that extends the definition of rational singularities beyond varieties over fields of characteristic zero. Particularly, we show that an invariant called `level' in the associated derived category measures the failure of these singularities.

We demonstrate imaging $^{171}$Yb single atoms in clock-magic tweezers of 759.4 nm wavelength, with above 99.9% fidelity and survival. We use alternating dual-tone narrowline imaging for more efficient three-dimensional cooling in tweezers, allowing several-millisecond imaging in 200 $μ$K trap depth, which is half of typical depth used for imaging in clock-magic tweezers. Accordingly, even without repumping, imaging survival is still close to 99.9% with the high fidelity, which can enable high performance nondestructive qubit measurements based on metastable shelving. Moreover, our simulation predicts that more optimal configuration could further reduce the trap depth, as improving the imaging performance. This imaging capability in shallow traps opens high performance imaging for more general trap wavelength, and lays the foundation for large scale systems over 1,000 qubits, and highly repeatable tweezer clocks.

Quantum Key Distribution (QKD) systems require rigorous verification of device properties to ensure implementation security. A critical requirement is the indistinguishability of transmitted pulses encoded by different modulation patterns, as distinguishability through non-encoded degrees of freedom could enable undetected eavesdropping. We present a practical method for testing pulse indistinguishability in QKD transmitters based on Hong-Ou-Mandel (HOM) interference. We establish the theoretical equivalence between the SWAP test and HOM measurement for characterizing quantum state fidelity, demonstrating that HOM visibility directly relates to the trace of density matrix products for phase-randomized weak coherent pulses. We experimentally validated this approach using a high-speed QKD transmitter implementing the decoy BB84 protocol with time-bin encoding at 1.25 GHz. HOM interference was measured between adjacent pulses prepared in different Bennett-Brassard 1984 states (X0, X1, Y0, Y1) using superconducting nanowire single-photon detectors. The observed HOM visibility was approximately 0.3 across all state combinations, with no statistically significant differences detected. These results confirm that modulation does not compromise pulse indistinguishability in our transmitter. The HOM test provides a practical, quantum-optical method for security certification of QKD systems without requiring assumptions about specific degrees of freedom, using only standard fiber-optic components and single-photon detectors.

The atmospheric characterisation of temperate exoplanets is becoming accessible with JWST, providing a critical connection between Solar System planets and the more commonly observed hot-Jupiters. K2-18 b, a temperate sub-Neptune orbiting an M dwarf, has emerged as a benchmark case following extensive JWST observations and ongoing debate regarding its atmospheric composition. We investigate K2-18 b using a self-consistent forward model to constrain its metallicity, composition, and thermal structure, with particular emphasis on the role of disequilibrium chemistry, photochemical hazes and clouds. For the first time in this context, we also assess the impact of photoelectrons on the atmospheric chemistry of an exoplanet. We explore a wide range of metallicities and intrinsic temperatures, evaluate haze and cloud formation, and compare the resulting transmission spectra with available JWST observations from multiple independent pipelines. We find that a high metallicity (200-400xsolar) H2-rich atmosphere consistently reproduces the observed transit spectra, independent of the data reduction pipeline used. The atmospheric composition is strongly shaped by disequilibrium chemistry, with CH4 dominating the spectrum alongside contributions from CO2 and OCS, and a potential contribution from C2H4 at mid-infrared wavelengths. Photoelectrons enhance the production of several disequilibrium species, particularly nitrogen-bearing molecules. Photochemical hazes play a key role in shaping the thermal structure, producing a temperature minimum near the 10-100 mbar range that enables efficient H2O condensation, suppressing its gaseous abundance. Under sufficiently strong haze cooling, NH4SH condensation provides a natural explanation for the apparent absence of NH3 in the observed spectra. No additional molecular species beyond those considered here are required to reproduce the observed spectra.

Let $\mathfrak g$ be a complex semisimple Lie algebra. We define what it means for a finite dimensional representation of $\mathfrak g$ to be rectangular and completely classify faithful rectangular representations. As an application, we obtain new $λ$-independence results on the algebraic monodromy groups of compatible systems of $λ$-adic Galois representations of number fields.

Photon echo (PE) spectroscopy is a powerful technique for probing decoherence mechanisms and charge carrier dynamics in semiconductor systems. Beyond traditional coherence measurements, characterizing the photon statistics of the echo signal is important for assessing its potential in quantum information applications and understanding the underlying quantum mechanical processes. Here, we study the photon statistics of PE signals generated by excitons in ensembles of lead halide perovskite CsPbI$_3$ nanocrystals at cryogenic temperature of 2 K using continuous-variable quantum state optical tomography based on homodyne detection. Pronounced Rabi oscillations of the PE amplitude allow us to evaluate the statistics for various pulse areas in the excitation sequence. The damping of the oscillations with increasing pulse area is attributed to spatial excitation inhomogeneity and excitation-induced dephasing. Despite the large ensemble of optically addressed excitons, the efficiency of generated PE signals is low which is attributed to the complex energy level structure of excitons and non-radiative recombination channels in CsPbI$_3$ nanocrystals. We analyze the statistical characteristics of PE via the second-order correlation function $g^{(2)}(0)$ and the characteristic function for different combinations of the areas of the excitation pulses. Our results show that $g^{(2)}(0) = 1$, and the characteristic function of the PE signal corresponds to classical behavior. The formation of photon echoes as well as $g^{(2)}(0) = 1$ at the echo time is reproduced by a quantized free-space multimode model. Despite the relatively low efficiency, the photon echo exhibits a high degree of coherence and minimal classical noise, consistent with Poissonian statistics.

Dark energy is one of the deepest puzzles in modern cosmology, and mounting evidence suggests that it is not just a cosmological constant but a genuinely dynamical component. Although cosmology and dynamical systems theory emerged from different disciplines, dynamical systems methods have become essential tools to uncover the qualitative evolution of the universe. The equations governing homogeneous and isotropic cosmologies can be naturally written as systems of ordinary differential equations, making them an ideal arena for dynamical system analysis. This review begins with a sharp, streamlined introduction to the standard dynamical systems toolkit widely used in cosmology. We then move on to alternative formulations based on polar and hyperbolic variable transformations. These approaches unlock powerful new ways to probe a broad spectrum of scalar field dark energy models, to set and constrain initial conditions, and to analyze tracking behavior across wide classes of potentials. The review is self-contained, but consistently directs the reader to more specialized and in-depth treatments where needed.

The Fermi-Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi-Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi-Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi-Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Finally, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.

Standard phase-field fracture methods are rooted in brittle fracture theory and therefore do not inherently prescribe a material strength for crack nucleation, while also struggling to capture cohesive fracture behaviour. Recent eigenstrain-based formulations overcome both limitations by introducing fracture eigenstrains that decouple the strength surface from the fracture energy, but their implementation has so far relied on direct energy-minimization frameworks rather than standard finite-element procedures. In this work, we exploit the fact that the eigenstrains require no spatial gradients and reformulate the eigenstrain evolution as a local constitutive model, analogous to those used in plasticity, that is resolved at each integration point. As a result, the cohesive phase-field requires no additional global degrees of freedom beyond those of a standard phase-field formulation and can be readily integrated into existing finite-element codes. Two strength criteria are considered: a non-smooth criterion with independent tensile and shear strengths, and a smooth Drucker-Prager-like criterion that captures pressure-dependent strengthening under compression. Consistent tangent operators are derived for both criteria, ensuring robust convergence of the global Newton-Raphson solver. The framework is validated against three benchmark problems: a plate with a hole under tension and compression, a single-edge notched plate under shear, and a notched plate under dynamic loading. The results demonstrate mesh-independent and phase-field length-scale-independent behaviour, confirm that the fracture energy governs the transition between brittle and cohesive regimes, and show that complex phenomena such as crack branching under dynamic loading are naturally captured. All source codes are openly available.

Local-operator entanglement (LOE) quantifies the nonlocal structure of Heisenberg operators and serves as a diagnostic of many-body chaos. We provide rigorous bounds showing when an operator can be well-approximated by a matrix-product operator (MPO), given asymptotic scaling of its LOE $α$-Rényi entropies. Specifically, we prove that a volume law scaling for $α\geq 1$ implies that the operator cannot be approximated efficiently as an MPO while faithfully reproducing all expectation values. On the other hand, if we restrict to correlations over a relevant sub-class of (ensembles of) states, then logarithmic scaling of the $α< 1$ entropies implies MPO simulability. This result covers a range of relevant quantities, including infinite temperature autocorrelation functions, out-of-time-ordered correlators, and average-case expectation values over ensembles of computational basis states. Beyond this regime, we provide numerical evidence together with a random matrix model to argue that this simulability result also typically holds for arbitrary states. Our results put on firm footing the heuristic expectation that a low operator entanglement implies efficient tensor network representability, extending celebrated foundational results from the theory of matrix-product states and providing a formal link between quantum chaos and classical simulability.

The prototypical Mott-Hubbard insulator LaVO3 undergoes a structural phase transition accompanied by the onset of spin and orbital ordering below 140 K. By combining ultrafast optical pump-probe spectroscopy and two-dimensional electronic spectroscopy, we investigate the interplay between fluctuations of the local spin and orbital order parameter and the lifetime of high-energy electron-hole excitations. Specifically, we demonstrate that the pump-induced perturbation of the order parameter leads to a change of the Hubbard exciton decoherence time and, consequently, of its homogeneous linewidth. Dynamical mean-field theory calculations confirm that the exciton scattering rate is crucially affected by the degree of order of the spin and orbital lattices in LaVO3. Our results demonstrate that multi-dimensional ultrafast optical spectroscopy can be used to track the dynamics of the order parameter, thus opening new routes in the study of correlated quantum materials characterized by intertwined orders.

Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of ergodic behavior, we perform a systematic study of three-state cellular automata (with a stable `vacuum' state and `particles' with $\pm$ charges). The classification is aided by the automata's different transformation properties under discrete symmetries: charge conjugation, spatial parity and time reversal. In particular, we propose a simple classification that distinguishes between types and levels of ergodic behavior in such system as quantified by the following observables: the mean return time, the number of conserved quantities, and the scaling of correlation functions. In each of the physically distinct classes, we present examples and discuss some of their phenomenology. This includes chaotic or ergodic dynamics, phase-space fragmentation, Ruelle-Pollicott resonances, existence of quasilocal charges, and anomalous transport with a variety of dynamical exponents.

Quantum noise has long served as a powerful probe of quantum transport in mesoscopic junctions. Recently, temperature-driven noise, or $Δ_T$ noise, has attracted growing interest due to its presence even in the absence of average charge current. In this work, we investigate a normal metal-insulator-iron-pnictide junction and demonstrate how thermovoltage, Seebeck coefficient, zero temperature quantum shot noise, finite temperature quantum noise and $Δ_T$ noise can discriminate between $S_{++}$ and $S_{+-}$ pairing symmetries, which are relevant to iron-based superconductors. We introduce $Δ_T$ noise as a novel probe for distinguishing between the two pairing symmetries. In contrast to conductance, which exhibits a single peak for both $S_{++}$ and $S_{+-}$ states with only a difference in magnitude, the $Δ_T$ noise reveals qualitatively distinct features: a twin-peak structure for the $S_{++}$ pairing symmetry and a single-peak profile for the $S_{+-}$ state. A similar symmetry-dependent contrast is observed in both zero temperature quantum shot noise and finite temperature quantum noise, where the $S_{++}$ state consistently exhibits a twin-peak structure, while the $S_{+-}$ state shows a single-peak response. Furthermore, both the thermovoltage and the Seebeck coefficient display sign reversals for the two pairing symmetries, with opposite trends in the $S_{++}$ and $S_{+-}$ cases. Our results demonstrate that noise-based measurements, together with Seebeck coefficient and thermovoltage, form a mutually reinforcing set of probes that enables reliable identification of superconducting gap symmetry in Iron Pnictide superconductors.

It has been an unsolved question what leads a supernova remnant (SNR) to a thermal composite rather than a typical shell-like morphology, and what causes recombining plasma inside it. With the 13-ks observation of the Following-up X-ray Telescope onboard the Einstein Probe, we give an overall X-ray picture of W28, one of the prototypical thermal composite SNRs. The observation revealed a shell-like structure west of W28 in radio, optical, and X-ray images, which may revise the known extent of the SNR to $72'\times45'$. Spectral analysis explicitly maps that the special relationship where the plasma experiences recombination in the interior of the remnant, spatially coincident with H$α$ emissions, while in the other regions, the plasma is ionization-dominated. We found that W28 is generally isobaric from its center to the newly discovered shell, and it is even isothermal with a temperature of $\sim0.6$-0.7 keV in the center before the cooling of the plasma. Saturated thermal conduction and cloud evaporation may cool down the plasma within $\sim3$ kyr, the estimated recombination timescale. We revised the SNR dynamical age to $\sim8$ kyr, much younger than previous estimates. The complex structure and complex ionization state distribution may suggest that centrally filled and shell-like morphologies coexist in W28. This state may depend on the environment in which the SNR evolves.

Material strength effects have been recently shown to be significant in giant impacts even at scales of planetary collisions. Despite this, their effects are often neglected in numerical giant impact simulations. We present an implementation of a basic strength model (pressure dependent shear strength) in the massively parallel smoothed particle hydrodynamics code pkdgrav3. The model includes elastic deviatoric stresses, plasticity with pressure-dependent yield strength, and thermal softening, and is fully integrated into the GPU-accelerated framework introduced in Paper I, preserving its scalability and performance characteristics. We validate the implementation against laboratory experiments of granular cliff collapse and our simulation results are in excellent agreement. We then determine the catastrophic disruption threshold, $Q_{RD}^*$, over a wide mass range of the colliding bodies using simulations performed both with and without material strength. Consistent with prior work, we find that strength substantially increases $Q_{RD}^*$ in the low-mass regime, while convergence toward the fluid limit occurs only near $R_{C1} \sim 10^7$ m ($\sim 0.7,M_\oplus$), well above the often assumed $\sim 100$ km size limit. Entropy production and remnant morphology likewise remain sensitive to rheology at intermediate masses. Performance measurements show that including strength introduces only modest computational overhead while maintaining favorable scaling, thereby enabling realistic solid mechanics in large-scale impact simulations.

We provide the community with a homogeneous catalogue of small, significant substructures (henceforth NESTs) extracted from the spatial distribution of Young Stellar Objects (YSOs) in a large, consistent sample of star-forming regions. The catalog allows us to explore the relevance of small scale spatial substructure and discuss the interpretation of NESTs as tracers of star formation activity and remnants of the star formation process. We apply our procedure to consistent catalogues of YSOs to obtain NESTs in a sample of star-forming regions. We apply a photometric classification scheme to obtain the evolutionary stage of YSOs and statistically explore the distribution of class 0/I objects as a proxy of recent star formation activity. The region sample is diverse (in distance, size, structure, and global evolutionary stage), and we consequently find different structural properties and star formation histories. Most NESTs in regions with high recent star formation activity show even higher levels of activity. Moreover, the proportion of NESTs with higher activity than the region average increases with the global level of activity of the region. In approximately half of the regions we also find significant spans in the evolutionary stages of the NESTs, consistent with gradients and episodes of star formation. The combination of NESTs with a statistical exploration of the star formation history within each region provides robust and powerful insights into the star formation process. Our results support the role of NESTs as pristine remnants of star formation in highly active regions,stressing the role of fragmentation. The combination of small structures with large scale spatio-evolutionary patterns suggests hyerarchical, prolonged, dynamic, and complex star formation scenarios.

We consider the red-blue-yellow matching problem: given two natural numbers $k_R$, $k_B$ and a graph $G$ whose edges are colored red, blue or yellow, the goal is to find a matching of $G$ that contains exactly $k_R$ red edges and exactly $k_B$ blue edges, and is of maximum cardinality subject to these constraints. This is a natural generalization of the well known red-blue matching problem, whose complexity status is unknown: although a randomized polynomial-time algorithm exists, a deterministic algorithm has remained elusive for nearly four decades. The best known deterministic approach to the red-blue matching problem, due to Yuster (2012), gives an additive approximation. In this paper, we show a similar result for the red-blue-yellow matching problem, giving a polynomial-time deterministic algorithm that, under natural assumptions, finds a matching satisfying the color requirements almost exactly and has cardinality within 3 of the optimal solution. Our algorithm is a mix of classic linear programming techniques and ad hoc existence results on restricted classes of graphs such as paths and cycles. As a key ingredient, we prove a curious topological property of plane curves, which is a strengthened version of a result by Grandoni and Zenklusen (2010) in the related context of budgeted matchings.

We study how the vector-field structure of nonlinear port-Hamiltonian systems is reflected in the infinitesimal Koopman generator. The generator admits a natural bracket decomposition into a conservative interconnection-bracket derivation, a dissipative metric-bracket derivation, and an input-port derivation. The conservative component is formally skew-adjoint on a test space whenever the conservative flow preserves the reference measure and the relevant boundary terms vanish. The dissipative component is not claimed to be a positive operator on arbitrary observables; rather, the positive semidefinite object is the metric bracket $[f,f]_R=\nabla f^\intercal\mathbf{R}\nabla f\ge 0$, which yields the exact port-Hamiltonian energy balance for the Hamiltonian observable: \[ \mathcal{K}_{\mathbf{u}}\mathcal{H} =-[\mathcal{H},\mathcal{H}]_R +\mathbf{y}^\intercal\mathbf{u} \le \mathbf{y}^\intercal\mathbf{u}. \] We use these bracket identities to motivate finite-dimensional weak Galerkin and data-driven lifted models: when the Galerkin measure is conservative for the Hamiltonian interconnection flow and boundary terms vanish, the conservative contribution is skew in the Galerkin mass metric, while the dissipative bracket induces a positive semidefinite Dirichlet matrix. These identities motivate structure-preserving lifted port-Hamiltonian surrogates that are passive and support damping injection in the lifted coordinates, while distinguishing exact bracket identities, projection residuals, finite-data estimation error, and the residual and injectivity assumptions needed to transfer lifted conclusions back to the original nonlinear state.

We consider the Gauss-Bonnet term coupled to the inflaton in the Palatini formulation of gravity. Unlike in the metric formulation, the Gauss-Bonnet term is not always a total derivative. We solve for the connection and insert it into the action, exactly for the spatially flat FLRW spacetime, and using the gradient approximation and order reduction for a general spacetime. We consider three cases: when the connection is unconstrained, and when non-metricity or torsion is put to zero. In all cases, the leading order change to the inflaton kinetic has the same form as that generated by the Chern-Simons term, but a negative sign. The modification of the gravitational wave sector also has the same form as in the Chern-Simons case but with a negative sign, except possibly for zero torsion, depending on the coupling and the potential. Within the range of validity of our approximations, differences from the metric formulation are small unless the kinetic term flips sign or is close to doing so.

We consider continuous-time heterogeneous agent models with recursive utility (Epstein-Zin utility) cast as mean field games, in which agents prefer late resolution of uncertainty. The model leads to a system coupling a pair of Hamilton-Jacobi-Bellman equations with state constraints and Fokker-Planck-Kolmogorov equations. We investigate the existence of solutions to the mean field game system and discuss some important qualitative features of the model.

Upcoming weak-lensing surveys will probe the matter distribution at a few percent level on nonlinear scales ($k>1\,{\rm h\,Mpc}^{-1}$) where baryonic feedback from galaxy formation modifies the clustering of matter. Using the IllustrisTNG hydrodynamical simulations, we quantify the mass and radial dependence of baryonic suppression of the matter power spectrum by selectively replacing matter around the center of halos out to a specified radius in the collisionless run with that around their full-physics counterparts. We find that group-scale halos with $\log M_{\rm 200m}/h^{-1}M_\odot \in[13, 14]$ dominate the suppression, contributing a large fraction of the total reduction in power at $k\sim2-30\,h\,{\rm Mpc}^{-1}$, with smaller suppression on either sides of this mass bin. Correctly reproducing the full suppression of the power spectrum requires accounting for matter redistribution (while enforcing mass conservation) beyond the virial radius of each halo. We show that the same group-scale regime produces the most detectable deviations in the weak gravitational lensing of background galaxies measured around foreground galaxy groups binned by mass or richness. Such a lensing signal could be a powerful observational test of feedback models together with SZ measurements. Our results motivate emulators that jointly predict the matter power spectrum and halo-matter cross-power spectrum including baryonic effects, enabling unbiased cosmological inference from small scales.

AI-assisted protein design has emerged as a critical tool for advancing biotechnology, as deep generative models have demonstrated their reliability in this domain. However, most existing models primarily utilize protein sequence or structural data for training, neglecting the physicochemical properties of proteins.Moreover, they are deficient to control the generation of proteins in intuitive conditions. To address these limitations,we propose CMADiff here, a novel framework that enables controllable protein generation by aligning the physicochemical properties of protein sequences with text-based descriptions through a latent diffusion process. Specifically, CMADiff employs a Conditional Variational Autoencoder (CVAE) to integrate physicochemical features as conditional input, forming a robust latent space that captures biological traits. In this latent space, we apply a conditional diffusion process, which is guided by BioAligner, a contrastive learning-based module that aligns text descriptions with protein features, enabling text-driven control over protein sequence generation. Validated by a series of evaluations including AlphaFold3, the experimental results indicate that CMADiff outperforms protein sequence generation benchmarks and holds strong potential for future applications. The implementation and code are available at https://github.com/HPC-NEAU/PhysChemDiff.

We consider nonlinear model predictive control (MPC) schemes without stabilizing terminal conditions, where the model used in the optimization step is generated based on input-output data only. We establish exponential stability for sufficiently long prediction horizons assuming exponential stabilizability and a proportional error bound. Moreover, we verify the imposed condition on the approximation using kernel interpolation and demonstrate the practical applicability to nonlinear systems by numerical simulations.