AI for Science

The Kolmogorov-Zakharov stationary states for weak wave turbulence involve solving a leading-order kinetic equation. Recent calculations of higher-order corrections to this kinetic equation using the Martin-Siggia-Rose path integral are reconsidered in terms of stationary states of a Fokker-Planck Hamiltonian. A non-perturbative relation closely related to the quantum mechanical Ehrenfest theorem is introduced and used to express the kinetic equation in terms of divergences of two-point expectation values in the limit of zero dissipation. Similar equations are associated to divergences in higher-order cumulants. It is additionally shown that the ordinary thermal equilibrium state is not actually a stationary state of the Fokker-Planck Hamiltonian, and a non-linear modification of dissipation is considered to remedy this.

Recent studies have shown that a soliton can be {\it fractionally} transported by slowly varying a system parameter over one period in a nonlinear system. This phenomenon is attributed to the nontrivial topology of the corresponding energy bands of a linear Hamiltonian. Here we find the occurrence of fractional Thouless pumping of solitons in a nonlinear off-diagonal Aubry-André-Harper model. Surprisingly, this happens despite the fact that all the energy bands of the linear Hamiltonian are topologically trivial, indicating that nonlinearity can induce fractional Thouless pumping of solitons. Specifically, our results show that a soliton can be pumped across one unit cell over one, two, three or four pump periods, implying an average displacement of $1$, $1/2$, $1/3$ or $1/4$ unit cells per cycle, respectively. We attribute these behaviors to changes in on-site potentials induced by a soliton solution, leading to the nontrivial topology for the modified linear Hamiltonian. Given that our model relies solely on varying nearest-neighbor hoppings, it is readily implementable on existing state-of-the-art photonic platforms.

We present a systematic study of von Neumann entropy estimation in multi-qutrit quantum systems using two complementary approaches: variational quantum algorithms (VQAs) and classical convolutional neural networks (CNNs), evaluated using an ideal (noise-free) quantum simulator. For systems up to three qutrits, we construct and evaluate 11 hardware-efficient SU(3)-inspired ansatzes. A parameter sweep shows that estimation accuracy is primarily determined by the number of trainable parameters, provided sufficient entanglement is present. Based on this study, we fix the parameter count to approximately 120 for subsequent experiments, observing that increasing entangling-gate counts beyond a threshold yields only marginal improvements. For larger systems (two to five qutrits), we use a CNN trained on measurement outcomes from tensor-product mutually unbiased bases. The model achieves accurate and stable predictions and exhibits a systematic improvement in performance with system size, with the highest errors for two-qutrit systems and the lowest for five-qutrit systems. Notably, using only 12.5% of the measurements required for full state tomography is sufficient to reach 90th-percentile absolute errors of approximately 0.13-0.16 nats for both four- and five-qutrit systems. The CNN model is also robust to shot noise and generalizes well to out-of-distribution states. Overall, within the simulated settings studied here, our results indicate a transition in practical methods: VQAs are effective for small systems, while CNN-based estimators offer improved scalability and robustness for larger qutrit systems.

Estimating nonlinear properties of quantum states is a central task in quantum information science. Multivariate traces, $\mathrm{tr}(ρ_1 \cdots ρ_K)$, and nonlinear observables such as $\mathrm{tr}(ρ^K)$, for integer $K$, can be accessed through collective measurements on multiple state copies, but standard protocols based on swap tests require coherent operations on the full Hilbert space and become experimentally unfeasible for large systems. In this work, we introduce a framework for multi-copy measurements based on random projections onto lower-dimensional subspaces prior to the collective measurement, which is then performed only on the reduced Hilbert space. This procedure yields a tunable tradeoff between coherent quantum resources and statistical sampling overhead, allowing the amount of coherent processing to be matched to the capabilities of the underlying hardware. We derive explicit formulas relating the Haar-averaged projected moments to multivariate traces of the original states and analyze the sampling overhead induced by the projection procedure. Specifically, after compressing an $n$-qubit state to a reduced $q$-qubit subspace, estimating $\mathrm{tr}(ρ^K)$ requires approximately $O(2^{(n-q)(K-1)})$ copies of $ρ$, with each qubit projected out increasing the sampling cost by a factor of $2^{K-1}$. Our results establish how coherent multi-copy operations can be traded for additional state copies, enabling multi-copy quantum protocols to be optimized for the available hardware resources.

Electric field noise produced by the surface of ion trap electrodes reduces the fidelity of quantum computing operations. Despite decades of investigation its microscopic origins remain unclear. Here, we measure electric field noise at trapping locations along the symmetry axis of a linear surface Paul trap. We find that noise levels vary by three orders-of-magnitude in one 600$\,μ$m section of the trap. Optical and scanning electron microscope images show micron-sized particles close to the trapping locations with the highest noise levels. We find that modeling the particles as a lossy dielectric with a effective loss tangent $\tanθ=0.33(0.06)$ describes the magnitude of the noise, as well as its spatial and frequency dependence. Our observations may explain the large variation of reported noise levels in literature.

High-harmonic generation (HHG) is governed by interference between electron trajectories. We propose that the dominant short and long trajectories define an experimentally addressable two-level subsystem: an attosecond path qubit (APQ). We formulate a trajectory-resolved density matrix to identify two distinct coherence-loss mechanisms: classical dephasing from ensemble averaging and quantum decoherence arising from the trace-out of unobserved degrees of freedom. By investigating shot-to-shot fluctuations and unresolved transverse momentum, we demonstrate that while dephasing suppresses coherence through averaging, the ``trace-out'' channel produces mixed states even for fixed driving parameters. We explore how these mechanisms modify APQ purity and show that mode selection and conditioning provide operational routes to isolate them. These results establish a reduced-state framework for diagnosing coherence loss in HHG and for engineering trajectory-based quantum states in attosecond interferometry.

Recent evidence on the sustainment of wall-normal-velocity bursts in wall-bounded turbulence challenges the classical streak-dependent picture, suggesting that the problem should be approached relying on no a priori knowledge regarding other flow structures. This paper discusses the restarts of bursts in a log-minimal channel within the framework of a linearised Navier-Stokes system with forcing terms encapsulating the nonlinear effects of all other structures. Two generic issues are addressed. The first concerns the conditions for burst-restart-like solutions for the forced linearised system itself. We formulate optimisation problems to understand the 'minimal requirements' for burst restarting. The solutions illustrate three conceptual periods in a typical restarting process, distinguished by the behaviour of spanwise vorticity structures: breakup, counter-rotating catch-up, and co-rotating catch-up. External forces promote this process by breaking up forward-inclined vortices and merging co-rotating, catching-up vortices. A quantity termed linearly available energy (LAE) is accordingly proposed to parameterise the restarting process. The second issue concerns the contributory features to the observed burst restarts in real turbulence. We show that an essential role of nonlinearity in restarting a burst is to increase a decaying state's LAE to a level sufficient for the onset of the subsequent burst. Flow patterns extracted during the restarting stage exhibit breakup and merging effects, both facilitated by nonlinearity. This suggests that the two effects observed in both the linearised models and real turbulence are manifestations of real flow structures that cause burst restarts.

This study investigates the predictive capability of a threshold inception-based multiphysics modeling approach for ionic wind fans by direct comparison with experimental measurements. A wire-to-cylinder electroaerodynamic (EAD) fan with variable electrode spacing is used as a reference system to assess the model's ability to reproduce airflow characteristics, discharge current, and performance trends under atmospheric conditions. Numerical simulations show good qualitative agreement with experimental results across all tested configurations; however, systematic deviations emerge at higher voltages and larger electrode gaps. Analysis of these discrepancies indicates that the commonly adopted assumption of perfectly smooth emitter surfaces can limit model accuracy. Experimental characterization of the emitter wire reveals micro-scale surface protrusions, which locally enhance the electric field and alter corona inception behavior. Incorporating representative surface roughness into the numerical model improves quantitative agreement with measured airflow velocities. The results demonstrate that while the threshold inception model provides a robust foundation for EAD fan simulations, electrode surface morphology is a critical factor for reliable prediction. This work advances the validation and refinement of ionic wind fan modeling methodologies and identifies key considerations for the development of more accurate engineering-oriented simulation tools.

We present a theoretical study of Cherenkov and transition radiation for swift electron beams penetrating dielectric nanospheres using material models of different sophistication. Specifically, we perform a combined time-domain (numerically, via the discontinuous Galerkin time-domain method) and frequency-domain (numerically and analytically, via Mie-based theory) study, including the induced-field distribution, cathodoluminescence (CL) multipole/directional decomposition, as well as the time-dependent angular power flow. For low velocities below the Cherenkov threshold, we show that transition radiation is dominant in the far-field CL, and the near-fields at the transition points are primarily responsible for the main features observed in the far-field. For higher velocities far beyond the Cherenkov threshold, we identify the fingerprints of the observable Cherenkov front. Specifically, a constant-permittivity model allows us to isolate the respective contributions of CR and TR to the far-field radiation, thereby facilitating the interpretation of the results for a more realistic material model that includes material resonances. Our combined time- and frequency-domain framework provides a direct view of radiative excitation channels for swift electron beams penetrating dielectric nanoparticles, thereby revealing their interplay beyond the conventional frequency-domain analyses.

Planar 3D models of hydraulic fracturing provide a practical balance between models with restrictive geometric assumptions and fully 3D simulators, capturing fractures with arbitrary planar footprints at moderate computational cost. Nevertheless, applications such as treatment design optimization and mini-frac test interpretation require large ensembles of simulations, for which the cost of planar 3D models remains a significant bottleneck. This work presents acceleration strategies for the planar 3D Implicit Level Set Algorithm (ILSA) to reduce simulation runtime while preserving numerical accuracy. A unified planar 3D ILSA scheme that consolidates the nested loops of the elastohydrodynamic solver and the front tracking algorithm into a single iterative process is introduced. A matrix splitting approach is applied to the linearized elastohydrodynamic system, moving the dense part of the elasticity operator to the right-hand side and yielding a sparse system matrix that can be solved more efficiently. Anderson acceleration is incorporated into the solution of the elastohydrodynamic system to improve convergence under varying fracture geometry. Additionally, a predictor--corrector scheme is examined with the proposed methods to assess their combined effect. Each technique is evaluated individually and in combination on both the reference and unified planar 3D ILSA schemes across five benchmark cases. Numerical experiments demonstrate that the unified scheme alone delivers an average 2.5x speedup, reaching 5.7x for the sandglass geometry. The combined application of all techniques achieves an average 4x speedup and up to 11x for the sandglass case, with the relative discrepancy in fracture aperture below 5% compared with the reference scheme.

Understanding the time evolution of physical observables in open quantum many-body systems coupled to external environments is a natural and difficult problem, and exact results are still rare. In this work, we study this problem for Wess-Zumino-Witten (WZW) conformal field theories with Lindblad jump operators linear in Kac-Moody current modes. We investigate the exact operator dynamics generated by these Lindbladians, identifying classes of current operators whose Heisenberg equations close and can therefore be solved analytically using the underlying current algebra. In Abelian $U(1)_k$ WZW theories, this closure of operator dynamics holds for arbitrary settings of jump rates and includes exactly tractable cooling dynamics. In contrast, for non-Abelian WZW theories, exact closure occurs only for symmetric current-mode dissipation, where upward and downward current-mode transitions occur with equal rates, and even then it leads to a simple closed evolution only for a single current operator. Generic imbalances, including those needed for cooling, produce additional non-Abelian terms and prevent closure of the opeartor dynamics. Consequently, the current algebra gives rise to a broad family of exactly solvable dissipative dynamics in the Abelian setting, whereas in the non-Abelian case it singles out only a special exactly solvable dynamics corresponding to an infinite-temperature bath.

Cellular automata are discrete dynamical systems defined on a lattice, in which each site carries a finite set of states that evolve in time according to local deterministic rules. An important application of cellular automata is in lattice gas models of fluids, where the cellular automaton framework provides a particle-based microscopic description of hydrodynamic behavior. The macroscopic fluid equations emerge after coarse-graining over many lattice sites and time steps, offering a bottom-up route to hydrodynamics. A celebrated example is the Frisch-Hasslacher-Pomeau (FHP) model, an automaton defined on a two-dimensional triangular lattice that yields the two-dimensional Navier-Stokes equations upon coarse-graining. In this work, we construct a parity-breaking generalization of the FHP model through two modifications: introducing chiral two-body collision rules and systematically rotating particle velocities to mimic the effect of a background magnetic field. We show that this automaton yields a hydrodynamic model with odd viscosity, a transverse transport coefficient that is a hallmark of odd fluids. We verify the analytical transport coefficients using Poiseuille-flow simulations of the chiral FHP automaton. Our results demonstrate that the chiral automaton introduced here provides a bridge between microscopic parity-breaking scattering processes and macroscopic odd-fluid hydrodynamics.

We theoretically investigate the role of higher-order Lifshitz invariants in nonreciprocal charge transport in two-dimensional noncentrosymmetric superconductors with Rashba spin-orbit coupling. In the superconducting state, these symmetry-allowed terms give rise to critical-current nonreciprocity, while in the normal state near the superconducting transition they generate a pronounced magnetochiral anisotropy. Using symmetry-constrained group-theoretical methods, we systematically construct the allowed Lifshitz invariants and derive the corresponding vector structure of the nonreciprocal current. To describe nonlinear transport in the fluctuation regime, we apply a generalized time-dependent Ginzburg-Landau theory that incorporates both the Aslamazov-Larkin contribution from fluctuation-induced Cooper pairs and the Maki-Thompson contribution associated with quantum interference in the Cooper channel. We further analyze the effects of disorder scattering and dephasing on the resulting nonreciprocal response.

We investigate the evolution of cosmic structures in the power-law modified gravity model $f(R)=R+R^{1+δ}/R_c^δ$, where the dimensionless parameter $δ$ characterizes deviations from General Relativity. The background cosmological dynamics and the evolution of linear matter density perturbations are studied within the framework of metric $f(R)$ gravity. The modified perturbation equation is derived by introducing an effective gravitational coupling associated with the additional scalar degree of freedom, and the evolution of the growth factor, logarithmic growth rate, growth index, and the observable quantity $fσ_8(z)$ are investigated. The results show that the curvature correction enhances the growth of matter perturbations while remaining compatible with the observed late-time accelerated expansion for suitable values of the model parameter. The theoretical viability of the model is established through the ghost-free condition, Dolgov--Kawasaki stability criterion, positive scalaron mass, stable de Sitter solution, and chameleon screening mechanism. Comparison with representative viable $f(R)$ gravity models shows that the present theory achieves a consistent cosmological evolution with a single deviation parameter. The predicted modifications in the growth of structures and the effective gravitational coupling provide observable signatures that can be tested by forthcoming large-scale structure and weak-lensing surveys, providing a means to test curvature-induced modifications of gravity.

Phenomenological model building has traditionally relied on human reasoning: equations are proposed from theoretical intuition, analogy, or empirical convenience, and only then tested against data. Here we show that this cycle can be recast as an iterative AI reasoning process for dynamical dark energy. Our framework uses a large language model to propose equations of state together with cosmological rationales, grounded by retrieval from the dark-energy literature and refined through autonomous evaluation. Each candidate is embedded in a cosmological model, optimized against observations, and assessed using likelihood performance and theoretical consistency. An independent language-model critic scores the physical motivation, novelty, clarity, stability and implementation validity of both the equation and its rationale, allowing subsequent proposals to evolve jointly in mathematical structure and physical reasoning. Applied to cosmological data combinations including supernovae, baryon acoustic oscillations and Planck likelihoods, the framework identifies two parameterizations that, to the best of our knowledge, have not previously been explored and that are competitive with established forms. For Pantheon+ supernovae, DESI DR2 baryon acoustic oscillations and the full Planck 2018 temperature, polarization, and lensing likelihoods, the best AI-selected model attains larger Bayesian evidence than the traditional parameterizations considered here by more than one unit. These results show that AI-guided reasoning can complement physical model building by proposing and evaluating interpretable phenomenological parameterizations for dynamical dark energy.

We study the initial-value problem for the Schrödinger map flow from flat torus $\mathbb{T}^d$ into compact Kähler manifold $\mathcal{N}$. When $d \geq 3$ and $\mathcal{N} = \mathbb{S}^2$, we establish local well-posedness in $H^σ_x$ with $σ> d/2 + 1/2$. In this case, the evolution equation for the gradient of the solution reduces to a certain semilinear nonlinear Schrödinger equation (also known as modified Schrödinger map flow) when formulated in orthonormal frames. For general compact Kähler targets, we only obtain local well-posedness in $H^σ_x$ with $ σ> d/2 + 5/6$ due to the quasilinear nature of the flow, but in all dimensions $d \geq 2$. To the best of our knowledge, this is the first low-regularity local well-posedness result for Schrödinger map flow in the periodic setting, which yields a gain of $1/2$ derivatives for $\mathbb{S}^2$ targets and $1/6$ derivatives for general Kähler targets compared to the classical results \cite{DW,M}. The key ingredients of our method are an $L_{t, x}^2$ bilinear estimate for the first case and an \emph{a priori} $L_t^6L_x^{\infty}$ estimate for the second case, which are both achieved by combining the mass/energy and momentum balance laws of the equation with a new type of div-curl lemma introduced by the second author.

Standard dot-product self-attention computes, in a single layer, only pairwise (order-2) interactions between tokens; representing a generic order-$k$ interaction is known to require either super-quadratic resources in one layer or composition across depth. We introduce \textbf{Quantum Higher-Order Attention (QHA)}, a shallow, hardware-realizable quantum attention head that, via data re-uploading and an all-to-all non-Clifford entangler, synthesizes order-$k$ token interactions inside the circuit and exposes them through a local single-qubit read-out. We prove (i) an expressivity separation: any single standard self-attention layer with embedding dimension $m$, $H$ heads and $p$-bit precision satisfying $mHp=o(N/\log\log N)$ cannot represent the order-$k$ correlation family that one QHA head represents with circuit depth $O(\log k)$ ($O(k)$ two-qubit gates); and (ii) a trainability guarantee for its local-design instantiation: with a local read-out and $O(\log n)$ depth the gradient variance is $Ω(1/\mathrm{poly}(n))$ (no barren plateau), which we confirm empirically -- while being explicit that the more expressive all-to-all instantiation we benchmark is trained empirically and shows exponentially decaying gradients. Empirically, at a $6.5\times$ smaller parameter budget, QHA generalizes hidden-subset parity of every order $k\le6$ from disjoint inputs, whereas the larger classical attention head collapses past order~2; consistent with theory, the size of the advantage tracks the target's Fourier degree - largest for parity and shrinking when low-order structure is present. As an application, QHA serves as a compact high-order interaction detector across three domains - genetic epistasis, learning-parity-with-noise, and graph triangle detection - reaching the noise ceiling at the smallest parameter budget where field-standard linear methods fail.

Could two worlds localised on neighbouring branes communicate through gravity alone? We investigate this question in a minimal higher-dimensional framework in which Standard Model fields are confined to our brane while gravity propagates through the bulk. From the brane-to-brane graviton propagator we derive the retarded transfer kernel of the inter-brane link and identify the transition from evanescent to propagating Kaluza-Klein modes. The central idea is to give the Kaluza-Klein tower a new role: not only as a spectrum of massive gravitational states, but as a set of communication carriers. Below the first KK threshold the channel is effectively four-dimensional and is mediated only by the massless graviton. Above threshold, massive KK modes open as additional propagating subchannels, and information may be encoded in their occupation pattern, relative phases, and arrival-time structure as well as in ordinary signal variables. The compactification determines the KK masses, wavefunctions, brane overlap factors, and propagation phases, which together define a multi-input multi-output (MIMO) channel matrix. In the resolved-mode limit, the tower yields approximate parallel subchannels, to which standard information-theoretic notions such as capacity bounds, water-filling, effective rank, and sparse occupancy codes apply. The production and detection of such signals are highly model-dependent and not assumed to be feasible with known technology. Nevertheless, the channel structure is well defined: a neighbouring brane-world could be separated from us by a microscopic distance in the compact space while remaining hidden because the only shared interaction is gravity. The first observable signature may not be a deliberate message, but the spectral and modal structure of the Kaluza-Klein tower itself, revealing partial information about the geometry of a nearby hidden world.

In this work, we prove the equivalence between the zero distributions of the Riemann zeta function ζ(s) and a two-dimensional (2D) Ising model with a mixture of ferromagnetic and randomly distributed competing interactions. At first, we review briefly the characteristics of the Riemann hypothesis and its connections to physics, in particular, to statistical physics. Second, we build a 2D Ising model, M_(FI+SGI)^2D, in which interactions between the nearest neighboring spins are ferromagnetic along one crystallographic direction while competing ferromagnetic/antiferromagnetic interactions are randomly distributed along another direction. Third, we prove that all energy eigenvalues of this 2D Ising model M_(FI+SGI)^2D are real and randomly distributed as the Möbius function μ(n), the Dirichlet L(s,\c{hi}_k ) function as well as the Riemann zeta function ζ(s). Fourth, we prove that the eigenvectors of the 2D Ising model M_(FI+SGI)^2D are constructed by the eigenvectors of the 1D Ising model with phases related to the Riemann zeta function ζ(s), via the relation ω(γ_2j) between the angle ω and the energy eigenvalues γ_2j, which form the Hilbert-Pólya space. Fifth, we prove that all the zeros of the partition function of the 2D Ising model M_(FI+SGI)^2D lie on an unit circle in a complex temperature plane (i.e. Fisher zeros), which can be mapped to the zero distribution of the Dirichlet L(s,\c{hi}_k ) function and also the Riemann zeta function ζ(s) in the critical line. In a conclusion, we have proven the closure of the nontrivial zero distribution of the L(s,\c{hi}_k ) function (including the Riemann zeta function ζ(s)).

We study the thermodynamics of the (2+1) dimensional Gross-Neveu model inspired from graphene. We focus on the entropy density of the Gaussian fluctuation beyond the mean field. The full in-medium, momentum-dependent evaluation reveals that the fluctuations give a substantial contribution, even comparable to that of the mean field. We argue that the back-reaction from the fluctuations to the mean field should be included, which reduces the contribution mainly coming from the Landau-damping region. To treat this self-consistently, we use the generalized version of the Beth-Uhlenbeck approach for the entropy density. Compared with the standard Beth-Uhlenbeck formulation, the generalized version suppresses the low-energy contributions while preserving the bound-state effects. The fractional entropy carried by bound excitons and free fermions reveals a sharper crossover of the degrees of freedom in the generalized version, which is consistent with Mott-transition physics in two-dimensional materials.

To address the challenges of interoperability in computational science, we present the latest updates to the software package MaRDI Open Interfaces. This software package aims to decrease the time and coding/testing efforts spent by computational scientists on tasks such as writing bindings to numerical solvers and adapting experiment codes to the varying interfaces of solvers for the same problem type (e.g., for benchmarking, which solver is better). By streamlining these tasks, this software package helps researchers focus on the actual essence of their computational projects. Here, we demonstrate a recently developed interface for nonlinear optimization and illustrate how it can be applied for computational experiments with optimization problems. As an example of such problem, we consider training of physics-informed neural networks to predict the solutions of viscous Burgers' equation.

The geometry of an object plays a vital role in modulating its interactions with the physical world. It nevertheless remains difficult to describe geometric information numerically for the purposes of statistical inference or classification tasks. Here, we introduce a new topological transform which leverages directional piecewise-linear Morse theory to quantify the geometry of an embedded object by cataloguing critical points across multiple height-functions. The output of this Morse transform records both the heights and the local topological type (peak, trough or saddle) of the critical points that characterise the underlying shape, retaining finer information than the Euler characteristic transform whilst naturally prioritising a shape's outermost regions. Crucially, this output can be further compressed into a rich but compact feature vector. We benchmark the Morse feature vector as a descriptor for ligand-based virtual screening (LBVS), which intrinsically depends on the shape of molecules. Under a common gradient-boosted tree classification pipeline, Morse descriptors achieve the highest mean AUROC when compared to other topological transform descriptors and to standard shape-based LBVS descriptors.

Data encountered in practice are frequently contaminated by additive noise, and wavelet shrinkage remains a fundamental tool for recovering underlying signals in nonparametric estimation. Classical procedures such as hard and soft thresholding decide whether to retain a wavelet coefficient almost entirely from its magnitude. Although effective in many settings, these rules can be too rigid for coefficients whose magnitudes fall in an intermediate region where the distinction between signal and noise is uncertain. We propose MLShrink, a two-threshold wavelet denoising procedure that combines wavelet shrinkage with machine learning. Coefficients below a lower threshold are discarded, coefficients above an upper threshold are retained, and coefficients in the intermediate band are classified using local wavelet-domain features. In this way, MLShrink preserves the simplicity of classical thresholding away from the decision boundary while allowing data-adaptive decisions for ambiguous coefficients. The paper also develops a theoretical framework tailored to this architecture. We show that MLShrink is a nonexpansive support-selection rule, derive an oracle-based risk decomposition showing that excess denoising risk is determined by classification errors on the undecided band, and establish an oracle-consistency result under suitable assumptions on classifier performance. Simulation experiments on standard benchmark signals indicate that MLShrink is competitive with several established wavelet shrinkage methods and is especially effective for signals with irregular, edge-rich, or non-smooth structure. These findings suggest that learned decisions on the intermediate threshold band provide a useful and interpretable connection between classical wavelet denoising and modern statistical learning.

Haematocrit influences blood viscosity and may affect coronary computational fluid dynamics (CFD). However, previous studies examined broad or pathological haematocrit ranges, and it remains unclear whether female-specific haematocrit variations within the physiological range produce meaningful changes in coronary haemodynamics. 15 female coronaries were analysed, including healthy arteries and diseased models with mild, moderate and severe stenosis. A haematocrit-dependent Carreau-Yasuda model was developed. CFD simulations were performed using the standard rheology model and a female-specific haematocrit-based model (40%). Time-averaged endothelial shear stress (TAESS), ESS gradient (ESSG), temporal shear variation index (TSVI), helicity, and low/high TAESS exposure were compared across coronary trees, arterial segments, bifurcations, stenosed vessels and corresponding narrowed regions. The female-specific model produced statistically significant differences from the standard model across all metrics and coronary regions (p < 0.05). However, the absolute differences were small, indicating a limited haemodynamic impact. Bland-Altman analysis showed narrow biases and limits of agreement. Linear regression demonstrated significant associations between inter-model differences and haemodynamic magnitude for TAESS, ESSG, helicity intensity, and adverse TAESS exposure, but the slopes were small. Similar findings were observed in stenosed arteries, where both models captured comparable flow disturbances across stenosis severities. Female-specific haematocrit variation within the physiological range is computationally detectable but haemodynamically negligible in coronary CFD. A standard rheology model is therefore likely sufficient for most coronary CFD studies, while personalised haematocrit modelling is more relevant for patients with abnormal haematocrit or rheology-focused studies.

The geochemical evolution of long-lived magma oceans is strongly regulated by volatile exchange between the molten mantle and the atmosphere. For planets inside the runaway-greenhouse limit, this coupled evolution can persist for billions of years. However, most existing studies assume Earth-like (oxidized) conditions and neglect the influence of redox state on melt thermodynamics and volatile release. We quantified how experimentally derived, oxygen-fugacity-dependent melting curves implemented within the coupled interior-atmosphere framework PROTEUS propagate into the thermal structure, melt fraction, and rheological evolution of rocky exoplanet interiors, applying this to the short-period super-Earth GJ 1132 b. We found strongly non-linear thermal responses to variations in melting curves. In volatile-poor systems, reduced melting curves promote earlier deep-mantle crystallisation relative to oxidised and Earth-like cases, favouring late-stage surface magma oceans sustained by greenhouse warming, while oxidized melting curves maintain higher melt fractions and a vertically extended magma ocean. Reduced mantles produce massive H$_2$-CO-rich atmospheres; oxidized mantles favour thinner H$_2$O-CO$_2$ envelopes. In volatile-rich systems, the interior reaches radiative equilibrium at high melt fractions, sustaining a steady-state global magma ocean in which melting curve variations do not significantly influence solidification timing. This indicates a hierarchical control: volatile inventory and surface oxygen fugacity act as the primary regulators of thermal state, while oxygen-fugacity-dependent melting relations provide a secondary modulation. These contrasting regimes produce distinct atmospheric compositions and formation timescales, offering testable spectral predictions for close-in rocky exoplanets evaluable with forthcoming JWST observations.

Tree-like structures appear in many areas of science, and their shapes can help understand the underlying processes they drive or that give rise to them. By thinking of these structures as geometric graphs in $\mathbb{R}^3$, we gain access to tools from computational geometry and topology to study them. In this paper, we adopt the theory of quadratic forms to measure the directional spread of geometric graphs, and we introduce the hexplot model -- equipped with a metric derived from the Fisher metric on the standard triangle -- to visualize, measure, and collect statistics.

Tsetlin Machine (TM) is a logic-based machine learning approach that relies on simple bitwise operations and finite-state automata, which makes it attractive for edge AI deployments. Recent work has focused on co-processor and accelerator designs based on Tsetlin Machines (TMs). Although these designs achieve high performance, they typically depend on tightly coupled interfaces, microcode-style programming, and external host processors, limiting flexibility and ease of programming. In this work, we present a domain-specific RISC-V microprocessor architecture and design flow tailored for TM inference. Leveraging the modular structure of RISC-V, we design a reduced instruction subset processor that retains programmability while targeting improved performance and lower energy consumption for TM workloads. Instruction profiling is employed to guide instruction reduction, followed by datapath and control path simplifications tailored to TM inference. Both the baseline RV32IM core and the proposed reduced core are evaluated across multiple datasets and compared with Binarized Neural Networks (BNNs), which serve as a hardware-efficient baseline due to their reliance on bitwise operations during inference. Results show that TM achieves comparable or higher accuracy (e.g., up to 88.18% on CIFAR-2 compared to 60.0% for BNN) while reducing execution time by up to 98% across multiple datasets. Furthermore, the proposed design achieves an average $29.7\times$ reduction in energy consumption, demonstrating its effectiveness for programmable and efficient edge AI systems.

Graph neural networks (GNNs) provide a flexible framework for learning from scientific data linked through physical, biological, or functional relationships. One promising domain is plant physiology, where measured responses often arise from multiple interacting processes whose exact separation remains difficult even with manual intervention. In plant physiology, a key example is the A-Ci curve, which relates net CO2 assimilation rate (Anet) to leaf intercellular CO2 concentration (Ci) and is used to estimate photosynthetic parameters in leaf and crop-canopy models. However, reliable estimation requires identifying the active biochemical limitation state at each curve point, which remains a major source of uncertainty. Here, we formulate limitation-state identification along A-Ci curves as a graph-based node classification problem, with curve points as nodes. Domain-specific graph representations are created using distance-based k-nearest-neighbor (kNN) and auxiliary-signal-guided (ASG) connectivity, with edge attributes encoding pairwise relations. The framework was evaluated against conventional learning baselines, graph-based architectures, and an automated fitting-based benchmark. Results on a large synthetic dataset with known ground-truth limitation states show that graph-based models improve classification, particularly near biochemical transition regions. The best-performing configuration, SEAGAN (domain-Specific and Edge-Aware Graph Attention Network for Dynamic Plant Processes), integrates process-aware node features, edge attributes, kNN connectivity, and graph attention with weighted cross-entropy loss, achieving an F1-score of 0.857 and an accuracy of 0.882. The results show that representing A-Ci curves as graphs improves biochemical limitation-state analysis, with edge-aware attention over local kNN neighborhoods providing the most effective strategy.

Recent work on Kan-Do-Calculus (KDC) has established that the boundary between passive observation and active intervention in causal inference is a category-theoretic bi-adjunction, with interventions modeled by left Kan extensions and conditioning by right Kan extensions. This paper introduces two causal discovery algorithms under latent confounding, building on the information-geometric and categorical consequences of KDC. In smooth statistical settings, Radon-Nikodym derivatives between observational and interventional measures induce local causal vector fields; failures of these fields to close under Lie brackets become computable Frobenius residuals, which we interpret as witnesses of failed visible integrability and possible latent or unmodeled structure. Our first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines an interventional density or Radon-Nikodym-ratio engine with a geometric screen that proposes a high-recall family of admissible arrows, identifies non-closing visible pairs as latent-obstruction candidates, and passes the reduced family to downstream score-based or differentiable discovery routines. The second algorithmic contribution, Spectral Kan-Do Flow Matching (SKFM), learns amortized intervention fields and factors latent curvature spectrally, exposing the direct Lie-space endpoint toward which BRIDGE points. A detailed set of experiments show that both algorithms are capable of discovering causal models with latent confounders while collapsing the super-exponential space of possible DAGs by many orders of magnitude. This paper introduces a new paradigm in causal discovery, where latent structure is inferred directly from the geometry of intervention-induced flows.

Phosphatidylcholine liposomes fill a special niche in alleviating osteoarthritis via intra-articular (IA) administration, attributed to their superlubricity at the articular cartilage surface, but their co-utilization as drug delivery vesicles in such therapy remains challenging as they may rupture under mechanical stress. Here, we describe cytoskeleton-inspired, supramolecular, self-assembled nanolipogels (NLGs), encompassing liposome-encased nanogels with a dynamic network formed by hydrogen bonding and cation-pi interactions, as a platform for simultaneous robust drug-delivery and massive reduction of interfacial frictional dissipation. We use a surface force balance to assess such dissipation at the sub-nanometer level, elucidating the mechanism involved, and atomic force microscopy to probe the NLGs structural stability. A useful proxy for the interfacial dissipation is the coefficient of friction, which remains as low as 10-4 at contact pressures at least up to 2 MPa, while under higher pressures exceeding the H-bonding energy density it increases abruptly and irreversibly to the still-low value 10-2. Under sustained sliding above this threshold, however, friction gradually decreases again, indicating recovery of the lubricating interface. Molecular dynamics simulations identify the compressive stress decrease due to hydrogen-bond rupture/rearrangement within the nanogel as a buried supramolecular transition associated with lubrication breakdown and recovery, while cargo release during sliding emphasizes the drug-delivery potential of such NLGs. These findings reveal how supramolecular core-shell reinforcement regulates load-bearing hydration lubrication, and provides a framework for designing adaptive biomimetic lubricants which are at the same time load-bearing intra-articular cargo-delivery vehicles.