We report the observation of quantized conductance in high-mobility three-dimensional Dirac semimetal Cd$_3$As$_2$ nanowire and nanoribbon p-n junctions. By employing suspended device geometries with dual local gates, we form tunable p-n junctions and realize ballistic transport across sub-micron channel lengths. In a wide nanoribbon device with a channel width of $\sim 330$ nm, conductance plateaus appear at integer multiples of $2e^2/h$ in the n-n regime under high magnetic fields. Numerical simulations suggest that these features represent unresolved spin-split subbands due to the smaller subband spacing in wider channels, and support the interpretation that the observed quantization may originate from surface-state-dominated conduction. In contrast, narrower nanoribbons and nanowires exhibit conductance steps of $1e^2/h$, demonstrating spin-resolved subbands likely due to enhanced confinement effects. From spin-resolved subband spectroscopy, we extract an effective Landé $g$-factor of $\sim 43$ for the first subband in the bulk gap, establishing these nanostructures as a prospective platform for fault-tolerant quantum electronics.

When it comes to estimating an unknown spectral density as simply and reliably as possible, parametric spectral density estimation using AR models and order selection via AIC is the method of choice. In contrast, no standard method has yet emerged for automatic nonparametric spectral density estimation, and there seems to be little willingness to weigh the advantages and disadvantages of different risk functions and the various methods for estimating them on a case-by-case basis, particularly because it is unclear whether the effort is even worthwhile without concrete prior information about the unknown spectral density. As a result, subjective visual methods are still widely used in practice to determine the appropriate smoothing parameter for a nonparametric estimation. This article aims to encourage the increased use of objective automatic methods by presenting evidence that using what is arguably the simplest and most straightforward frequency-domain version of the AIC for the automatic determination of an appropriate bandwidth enables results that are comparable to those obtained using the standard parametric approach. This evidence is based on both real-world time series and synthetic time series with spectral densities of varying complexity.

We investigate localization in two models: a single particle in a two-dimensional square lattice described by the tight binding Hamiltonian, and a two-dimensional square qubit lattice. It is well-known that Anderson localization occurs under suitable conditions in which the system parameters are chosen randomly from some statistical distribution. We propose a situation in which the parameters, specifically the on-site energies, are carefully chosen in such a way that a localization-quantifying parameter is maximized. We demonstrate the optimization procedure with numerical calculations in which the engineered localization significantly exceeds the average localization caused by a random distribution of the on-site energies. We explore the relation between spatial patterns and localization efficiency. Furthermore, we use perturbation theory to gain insight into the localization mechanism and obtain an improved cost function for optimization calculations, leading to enhanced localization in both the single-particle and full Hilbert spaces. Although large-scale simulations for qubit lattices are computationally infeasible, we use small-system simulations to demonstrate that results obtained using the single-particle tight binding model can be adapted to identify optimal settings for qubit lattice systems to achieve maximum decoupling between the qubits, which can be valuable for optimizing the idle-state settings on a quantum processor.

We investigate a three-dimensional ghostly Hamiltonian realisation of the fully degenerate resonant sixth-order Pais-Uhlenbeck oscillator. On the classical level, the phase-space flow is non-diagonalisable and decomposes into two complex-conjugate Jordan chains of length three, explaining the appearance of oscillatory solutions with secular terms. Upon quantisation, we construct intertwining operators whose quadratic combinations generate a hidden spectrum-generating $\mathfrak{u}(2,1)$-algebra. The associated descendant spaces are finite-dimensional invariant subspaces carrying non-trivial Jordan structure. Although these spaces admit a natural decomposition into irreducible modules of a distinguished $\mathfrak{sl}_2$-subalgebra, this decomposition does not in general coincide with the Jordan decomposition of the Hamiltonian. We further derive a tri-Hamiltonian formulation from Lie point symmetries of the classical flow and show that the corresponding Hamiltonians are naturally encoded by the same hidden algebra. Nevertheless, unlike in the non-resonant case, no positive-definite linear combination of them generates the same dynamics. Finally, we analyse the common centraliser of the tri-Hamiltonian family in $U(\mathfrak u(2,1))$, showing that the natural higher-order candidate $Q$ is reducible and yields no independent classical or quantum integral. The model thus provides a resonant higher-derivative system in which hidden $\mathfrak{u}(2,1)$ symmetry, classical and quantum Jordan structures, and multi-Hamiltonian geometry coexist.

The deterministic incompressible Navier-Stokes equations are physically incomplete: any viscous fluid at finite temperature must exhibit thermal fluctuations whose form is dictated by the fluctuation-dissipation relation. We formulate the stochastic Navier-Stokes equations with the kinematically selected deformation Laplacian on compact Riemannian manifolds with strictly negative Ricci curvature. The fluctuation-dissipation relation, derived from a topological (Poincaré lemma) argument, uniquely determines the noise from the viscous operator. For the spectrally truncated system, we prove that the unique stationary distribution is the Gibbs measure (Gaussian in the mode amplitudes, because the nonlinear convective terms preserve energy), and that convergence to equilibrium is exponentially fast with rate at least $2νλ_\Def$, where $ν$ is the kinematic viscosity and $λ_\Def$ is the spectral gap of the deformation Laplacian. The spectral gap satisfies $λ_\Def \geq κ^2$ when $\Ric \leq -κ^2 g$, and is independent of the volume of the domain. On flat space, the analogous thermalisation rate vanishes in the infinite-volume limit. The equilibrium velocity-velocity correlation function decays exponentially in geodesic distance, in contrast to the algebraic decay on flat space. These results provide a rigorous statistical-mechanical foundation for viscous fluids on negatively curved manifolds and illustrate how the geometry of the domain controls not only the deterministic dynamics but also the approach to thermal equilibrium.

We report the first measurement of charged-hadron pseudorapidity ($η$) distributions in oxygen-oxygen (OO) collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_\mathrm{NN}}$ = 5.36 TeV. The data were recorded by the CMS experiment at the LHC in 2025. Primary charged-hadron yields are measured in the range $|η|$ $\lt$ 2.4 as a function of centrality (the overlap of the two nuclei). The results are compared with previous measurements in lead-lead (PbPb) and xenon-xenon collisions at similar energies, as well as predictions from several Monte Carlo event generators and a hydrodynamic model. The charged-hadron pseudorapidity density in the midrapidity region ($|η|$ $\lt$ 0.5) is $\langle$dN$_{\text{ch}}$/d$η\rangle$ = 41.8 $\pm$ 1.1 (syst) integrated over centrality and 135.0 $\pm$ 4.0 (syst) for the most central (i.e., largest nuclear overlap) events. The hydrodynamic model TRAJECTUM provides the best overall description of the data, particularly in central collisions. The particle density at midrapidity divided by the number of nucleons participating in the interaction in central OO collisions is consistent with that observed in central PbPb collisions at similar collision energy. While the overall energy-scaling behavior observed in other nucleus-nucleus collisions is preserved, the data exhibit deviations from simple participant and system-size scaling, highlighting the role of collision geometry and finite-size effects in light ion collisions.

We show that virtually nilpotent groups are coarse median if and only if they are virtually abelian. The main idea is that the sub-Riemannian geometry of the asymptotic cone obstructs the existence of a locally convex Lipschitz median of finite rank. As an application, we deduce that non-compact lattices in the isometry group of a rank 1 symmetric space of non-compact type other than real hyperbolic space are not coarse median. This establishes the remaining case in the classification of lattices with the coarse median property initiated by Haettel. The same approach applies more generally to complete finite-volume non-compact Riemannian manifolds $M$ of pinched negative sectional curvature: if at least one cusp cross-section does not admit a flat metric, then $π_1(M)$ is not coarse median.

Cell-free Massive multiple input and multiple output (MIMO) is recognized as a key technology for beyond-5G networks, where distributed access points (APs) jointly serve user equipments (UEs) to address the inherent inter-cell interference issue inherent in cellular systems. While conventional distributed signal detection methods offer a practical balance between performance and fronthaul load, they are fundamentally limited by linear processing constraints. In this paper, we propose a novel deep learning based uplink detection framework by introducing the distributed mixture of experts detection network (DMoE-DetNet). In this architecture, each AP acts as a local expert employing convolutional neural networks (CNNs) for non-linear feature extraction, and transmits the local minimum mean square error (MMSE) detection results and statistical channel information to the central processing unit (CPU). In the CPU, an attention-based encoder module captures complex spatio-temporal dependencies among users for global feature fusion, with a gating network at the central processor dynamically weighting the contributions from different APs. At last, a linear detector outputs the symbol probability. Simulation results demonstrate that the proposed DMoE-DetNet significantly outperforms conventional linear processing based cell-free signal detection methods in terms of symbol error rate, showcasing the potential of artificial intelligence-enabled communication systems.

For graphs $G$ and $F$, we say that $G$ is $F$-free if $F$ does not occur as an induced subgraph of $G$. This paper is concerned with the following question: Given an $F$-free graph $G$ having two vertices between which there exists at least one Hamiltonian path, how many Hamiltonian paths between these endpoints must exist (in terms of the order of $G$)? Our main result shows that there exists a sharp dichotomy. More precisely, we show that if $F$ is not an induced subgraph of $P_3+sP_1$ for any integer $s \geq 0$, then there exists an infinite family of $F$-free graphs having two vertices between which there exists a unique Hamiltonian path. On the other hand, we prove that if $F$ is an induced subgraph of $P_3+sP_1$ for some integer $s \geq 0$, then any $F$-free graph having two vertices between which there exists a Hamiltonian path contains exponentially many such paths between these two vertices. Our proofs use Ramsey-theoretic methods, a result on the existence of two vertices with low degree in graphs containing a unique Hamiltonian cycle, a path variant of Thomassen's red-independent weakly green-dominating sets, and a structural analysis of Hamiltonian paths in $P_3+sP_1$-free graphs. As an algorithmic consequence we obtain that for every fixed $s \geq 1$, given a Hamiltonian $sP_1$-free graph together with a Hamiltonian cycle, one can decide in linear time whether a second Hamiltonian cycle exists and construct one if it does.

Biomolecular condensates must assemble at specific locations and times inside living cells to perform their biological functions. However, it remains unclear how condensate formation achieves high spatiotemporal precision, responding sensitively to local chemical modifications while remaining robust to fluctuations in protein concentration. Here we study chromatin-associated BRD4 condensates to identify a physical mechanism that enables this combination of sensitivity and robustness. Using an ultra-coarse-grained molecular-dynamics model, we show that co-condensation of BRD4 with chromatin enables rapid assembly below the bulk coexistence concentration, thereby suppressing off-chromatin condensation and enhancing spatial selectivity. Multivalent binding between BRD4 and acetylated histone tails sharpens the dependence of co-condensation on acetylation density through combinatorial effects, increasing contrast between highly acetylated regions and weakly acetylated background chromatin. This mechanism explains how co-condensation and multivalent binding jointly enable sensitive yet robust spatiotemporal targeting by chromatin-associated condensates.

Clock asynchronism between base stations (BSs) and users significantly degrades scatterer localization accuracy. To address this issue, this paper proposes a multi-BS joint channel estimation and localization scheme that exploits shared scatterer information among multiple BSs. First, channel modeling in the location domain is performed by leveraging the joint sparsity of multi-BS channels. Subsequently, a multi-BS scatterer association algorithm is developed based solely on Angle of Arrival (AoA) estimates. By utilizing the shared scatterers and the geometric relationships among the scatterers, BSs, and the user equipment (UE), coarse estimates of the UE location and timing offsets are obtained. Based on these coarse estimates of scatterer locations, UE location, and timing offsets, an expectation-maximization (EM) framework is employed. Specifically, the UE location and timing offsets are iteratively refined while jointly enabling high-precision estimation of scatterer locations and channel coefficients. Simulation results demonstrate that the proposed scheme achieves significant improvements in both channel estimation and localization accuracy compared with baseline methods.

Exact \(k\)-leaf powers are graphs whose edges are exactly the pairs of leaves at distance \(k\) in a tree. We prove explicit structure theorems for exact leaf powers on several representative graph families that test different exact-distance phenomena. Our most detailed root-classification theorem concerns chordless cycles: all exact \(5\)-leaf roots of \(C_\ell\), \(\ell\ge 8\), are described by a complete terminal block language. We also prove that the \(t\)-square ladder \(L_t\) is an exact \(5\)-leaf power if and only if \(t\le 2\). In contrast, dense bipartite square structures are often representable: among block-complete multipartite graphs, the exact \(5\)-leaf powers are precisely the bipartite members, and every bipartite co-cluster graph, including every crown \(K_{n,n}-M\), is an exact \(k\)-leaf power for every \(k\ge 5\). Finally, we give parity classifications for complete multipartite graphs and multipartite block graphs at larger exact distances, and isolate a sharp fan boundary at exact distance six.

Background: The experimental study of the $^{6}$Li-transfer reaction and alpha-scattering resulted in a rich spectrum of $^{18}$O, including some strong indication for band structure. Different configurations are proposed for the structural interpretation of different energy domains. Purpose: We intend to investigate whether a uniform description is possible for the complete spectrum, including the high-lying states from scattering measurement. Methods: We apply the multiconfigurational dynamical symmetry for the determination of the shape isomers and for the calculation of the spectrum obtained from different reactions. Results: The shape isomers of $^{18}$O is obtained from the study of the stability and self-consistency of the SU(3) symmetry, which is in the intersection of the shell and different cluster configurations. The $^{14}$C+$^{4}$He spectrum is calculated, and its connection to other configurations is revealed. A very simple Hamiltonian is applied, including only a harmonic oscillator term, a quadrupole interaction and an $L^2$ term. Conclusions: The spectrum (from the ground state up to the high-lying states) can be reasonably well described by a $^{14}$C+$^{4}$He cluster configuration. All the state allows the $^{12}$C+$2n$+$^{4}$He clusterization as well, and has definite shell model content. For the lowest-lying three bands the shell configuration is unique, and the overlap of the shell and the different cluster configurations is 100%.

Nucleosynthesis reaction networks leading to $p$-nuclei involve a combination of different types of photodisintegration and capture reactions, as well as $β^+$ decays or electron captures. Photodisintegration reactions involving $α$ particles present a particular interest as they serve as branching points of the reaction networks. The cross sections of these reactions depend crucially on the $α$-nucleus interaction. The $α$ optical model potential (AOMP) is determined mostly by means of experimental differential elastic scattering distributions. Several previous studies have focused on the case of $\rm ^{144}Sm$, an intriguing $p$-nucleus that is semi-magic with 82 neutrons. This work presents new experimental data on $α$ elastic and inelastic scattering on $\rm ^{148}Sm$, its closest stable isotope. Isotopic effects on the description of the AOMP are studied, as well as their consequences on the prediction of $α$-induced reaction cross sections at astrophysical energies. It is shown that the isotopic ratio for $(α,γ)$ cross sections can be multiplied up to a factor of two when these effects are included.

Topological textures of light offer powerful routes for structuring optical fields, controlling wave transport, and manipulating matter. Skyrmions, long studied as topological solitons in vector fields, have recently been extended to scalar wave systems, including acoustics, hydrodynamics, and plasmonics. However, their realization in two-dimensional scalar wave propagation with nonlinearities and in quantum fluids remains uncharted. Here, we establish such a Skyrmion framework for scalar fields in optical microcavities. With focus on exciton-polaritons, we show that nonresonant excitation without imposed phase can spontaneously generate isolated Skyrmions and self-organized Skyrmion lattices in a polariton condensate. We trace this mechanism to gain- and loss-induced phase curvature together with outward polariton flow. We further demonstrate that polariton nonlinearities provide all-optical control of these textures, enabling switching of the Skyrmion number and reconfiguration of Skyrmion moiré lattices through resonant and nonresonant excitation schemes. These results establish nonlinear non-Hermitian resonators as a versatile platform for the spontaneous generation and active control of scalar topological light fields.

String theory is a minefield for philosophers in terms of conceptual difficulty and mathematical technicality. Presentations aimed at philosophers generally focus on providing precise and technical mathematical descriptions of toy models and inter-theoretical toy derivations to give an idea of what is at play in the field. This presentation takes the opposite approach, filtering out most mathematical considerations to provide an overview of the field, eyes on the ontology. The aim is to provide a compass for metaphysicians to find their way around string theory and the philosophy of string theory. The development of metaphysical arguments based on string theory against the fundamentality of spacetime is deferred to the next chapter.

We study exact uniform sampling of permutations of length $n$ whose longest increasing subsequence (LIS) has prescribed length $k$. For $k \in Θ(n)$, we give a direct rejection sampler whose expected running time is $O(n\log\log n)$ in the word-RAM model. The sampler uses an expanded proposal space consisting of permutations together with a specified increasing subsequence, and accepts exactly those proposals whose specified subsequence is the leftmost LIS. For arbitrary $1\le k\le n$, we give an exact sampler based on the Robinson--Schensted correspondence. The algorithm samples the corresponding Plancherel-conditioned shape by computing exact completion counts via determinant identities, and then samples two uniform tableaux of that shape. The direct implementation runs in $\tilde O(n^4k^5)$ expected time. We then show that the same sampler can be implemented in expected $\tilde O(n^3k^4)$ time by evaluating a determinant oracle through Hankel moment matrices.

In spite of the intensive study of cyclic codes and the recent construction of an infinite family of self-dual binary cyclic codes whose minimum distances have the square-root bound in IEEE Trans. IT, vol. 71, no. 4, 2025, it is still a 70-year-old open problem whether there is an infinite family of self-dual binary cyclic codes whose minimum distances have a lower bound better than the square-root bound. This paper settles this long-standing open problem in coding theory by presenting infinite families of such self-dual binary cyclic codes. As by-products, several families of cyclic codes with better parameters than those in some references are also constructed in this paper.

Electronic absorption spectra of multichromophoric systems are often governed by complex excited-state structures arising from excitonic and charge-transfer (CT) interactions between chromophores, while direct identification of the underlying electronic transitions is frequently hindered by strong vibronic and solvent-induced broadening. In this paper, we develop a theoretical framework for the analysis and decomposition of absorption spectra of molecular dimers with coupled Frenkel exciton (FE) and charge-transfer states, including solvent-induced stabilization of zwitterionic configurations within a unified adiabatic-state formalism. The analysis reveals that exciton-CT mixing strongly reorganizes the electronic absorption profile and produces pronounced spectral broadening, while leaving the first spectral moment essentially unaffected. Numerical calculations show that the dominant mechanism of CT-induced broadening originates primarily from additional energetic splitting between spectral components rather than from broadening of the individual bands themselves. The electronic model is further extended to include coupling to high-frequency intramolecular vibrations and low-frequency environmental degrees of freedom, providing a practical framework for interpretation of realistic experimental spectra. The developed formalism is applied to the absorption spectrum of a covalently linked 9,10-bis(phenylethynyl)anthracene dimer in dichloromethane, where spectral decomposition reveals a predominantly excitonic low-energy doublet and higher-energy states with substantial CT character. The proposed approach offers a physically transparent framework for the analysis of complex absorption spectra in molecular aggregates and organic electronic materials with coupled excitonic and CT states.

Generative AI systems are aggressively reshaping how students engage with information and perform cognitive work; convenience-oriented use has the potential to displace effortful reasoning, reflection, and learning, especially for those who lack domain expertise and effective human-AI interaction strategies. Current AI tools are heavily focused on chat-style interfaces geared towards answer generation and efficiency in a linear and fragmented stream of text, offering limited support for structured reflection, argument construction, and sensemaking in collaborative contexts. We introduce Guided Sensemaking, an AI-augmented multiagent discourse platform that facilitates composition of well-thought-out ideas around a central question, provides scaffolding for critical thinking, and enables visualization of argumentative structure to support critical thinking and collaborative deliberation. The system uses several interactive agents to provide context-sensitive questioning prompts and a scaffolding for thought that exposes thematic clusters, agreements, and points of contention without collapsing diverse perspectives. This paper proposes a conceptual design and interaction paradigm that positions generative AI not as a shortcut to answers but as a research partner that externalizes reasoning, preserves user agency, and fosters structured, traceable sensemaking in educational and civic contexts.

The edge-cloud paradigm improves service delivery by orchestrating resources across edge nodes and cloud data centres. These environments consist of heterogeneous, interconnected computing nodes that cooperate to deliver continuous services. However, their scale and complexity increase vulnerability to failures from hardware malfunctions, software defects, and dynamic operating conditions. These failures can disrupt system configurations and service execution, leading to reduced reliability, performance degradation, and violations of service-level objectives. Ensuring service execution requires adaptive service placement strategies across edge-cloud resources. This study introduces a fault-tolerant service placement approach (Enhanced Evolution Strategy for Collaborative Neural Decision-making, EES-CND) for edge-cloud environments. The method employs collaborative decision-making, wherein multiple lightweight neural networks jointly infer redeployment strategies during failure events. To address the system dynamics and mitigate performance drift, adaptive models are updated online using an enhanced evolution strategy. Extensive simulations show that EES-CND effectively handles performance drift and significantly outperforms existing methods in service recovery time, response time, and reliability, achieving a 44.8\% reduction in fault-tolerance cost compared to standalone models.

AI co-scientists are increasingly used for scientific discovery, but current evaluations still do not test them on a key task: moving from a concrete scientific or technological problem to a plausible, mechanism-grounded solution hypothesis. This gap is especially important in materials science and, in particular, battery research, where a useful proposal must identify the relevant failure mode, propose a credible intervention, and explain why that intervention should improve the target property. We introduce Matter to Mechanism, a benchmark for evaluating AI co-scientists on problem-to-hypothesis reasoning in materials science, with a focus on battery materials research. The benchmark contains 2,645 instances derived from scientific publications. Each instance includes a structured problem statement, a candidate solution hypothesis, an explicit reasoning trace, and domain-grounded annotations such as material system, component, failure mode, intervention, mechanism, target property, and claimed outcome. We also introduce a metric suite that measures reasoning fidelity, problem alignment, mechanistic specificity, novelty, plausibility, and problem decomposition quality, and combine them into a composite score. Using this framework, we evaluate several AI co-scientist systems and show that Matter to Mechanism reveals interpretable system differences that are only partially recovered by standard text-similarity metrics. We further show through adversarial stress tests that the aggregate score is more stable than individual metric dimensions under superficial gaming attacks.

Ross and Yong conjectured a $K$-theoretic Kohnert rule for Grothendieck polynomials. Robichaux exhibited a counterexample to the Ross--Yong rule and proposed a revised ghost $K$-Kohnert rule, proving both rules hold for 321-avoiding permutations. We provide counterexamples to Robichaux's rule and give an explicit bijection showing that both the Ross--Yong and Robichaux rules hold for 1432-avoiding permutations. As an application, we provide a Kohnert-theoretic characterization of 1432-avoidance.

This paper investigates a single species reaction-diffusion system incorporating a spatiotemporal delay memory kernel, which models the cognitive map of animals, under Neumann boundary conditions. The model can be used to describe the process in which individuals are influenced by historical information during spatial diffusion. An equivalent system construction method with auxiliary variables is introduced to transform the original system into a delay-free coupled reaction-diffusion equation. By employing Fourier modal decomposition and eigenvalue analysis, we conduct stability and bifurcation analyses for both the exponentially decaying weak kernel and the peak type strong kernel, obtaining explicit expressions for the steady state and Hopf bifurcation points. Compared with the model in which the memory term of the continuous-time integral kernel using its own population density, our model exhibits Hopf bifurcations and steady state bifurcations even under a weak kernel because of the introduce of a dynamic cognitive map. This implies that a dynamic cognitive map introduces sufficient flexibility to generate both steady state bifurcations and Hopf bifurcations across a broader range of temporal kernels. Numerical simulations are presented to demonstrate the influence of stable, steady state and Hopf bifurcation regions on the spatiotemporal distribution of solutions.

We give generators and relations for the monoidal categories of crystals generated by the fundamental crystals of a simple complex Lie algebra. We also spell out several small-rank examples.

We consider the matrix element of the axial-vector current between two nucleon states in a finite box. Starting from the chiral Lagrangian density with nucleon and $Δ$-isobar degrees of freedom, we study the finite-volume effects at the one-loop level. We show that the standard decomposition into the axial-vector and pseudoscalar form factor is incomplete in a finite box. We derive expressions for the complete set of form factors at one loop. We verify that the axial Ward identity holds in the chiral limit. Selected numerical results are shown for two flavor-SU(2) lattice ensembles. Sizable finite-volume effects are observed, with an important role for the $Δ$-isobar. We discuss the implications of our results for lattice studies of the axial-vector current. We conclude that full finite-box results are crucial for a precise determination of the form factors.

How does a persistent random walker perceive a complex energy landscape? We address this question by studying the persistent Langevin dynamics of the p=3 spherical spin glass, a paradigmatic mean-field model with a scale-free hierarchical landscape. By tuning the persistence time tau_p, which controls the walker's inertia and effectively sets its energy resolution delta E proportional to 1/tau_p, we measure the energy correlation time tau_corr. At temperature T=1.0, we find tau_corr scales as tau_p to the power alpha with alpha = 0.337 plus or minus 0.035 for tau_p in the range [2,32] (for N=64), in excellent agreement with the Kardar-Parisi-Zhang (KPZ) universality class prediction alpha = 1/3. Finite-size scaling using N = 16,32,48,64,128 yields the thermodynamic limit alpha(infinity) = 0.3333 plus or minus 0.0134, fully consistent with 1/3. Thus, tau_p acts as a tunable probe that reveals the predicted scale-free hierarchy of the landscape. Moreover, the temperature dependence alpha(T) for T = 0.5,1.0,1.5,2.0 exhibits a clear U-shaped curve, identifying three dynamical regimes: ballistic/inertial, KPZ, and noise-dominated. Our results establish persistent Langevin dynamics as a powerful tool for uncovering hidden landscape topology and demonstrate that the p=3 spherical spin glass belongs to the KPZ universality class.

In quantum mechanics, a wavepacket acquires a geometric phase, known as the Berry phase, as it evolves along a closed trajectory in parameter space. In condensed matter systems, the Berry phase underlies a broad range of phenomena, including the anomalous Hall effect, orbital magnetism, and electric polarization. However, in centrosymmetric materials possessing time-reversal (TR) symmetry, its manifestation is suppressed and effectively vanishes. When a system is driven by a strong terahertz (THz) field, it can be coherently driven far from equilibrium, transiently reshaping its symmetry on sub-picosecond timescales. This capability opens new avenues for quantum control with potential applications in information processing and sensing. Here, we experimentally demonstrate that a strong THz field can transiently break inversion symmetry in MgO, inducing a dynamical complex Berry phase, thereby manipulating the topological properties of the material. Applying high-harmonic generation (HHG) spectroscopy, we directly resolve the Berry phase, accessing both its real and imaginary components. The first is associated with coherent intraband dynamics while the second with quantum tunneling through a potential barrier. This observation enables the reconstruction of the time-dependent evolution of the Berry phase within the cycle of the THz field. The coherent manipulation of solids with strong fields, combined with attosecond-resolved HHG spectroscopy, represents a fundamental step toward unveiling and controlling geometric quantum phenomena in condensed matter systems.

Genetic programming (GP) approaches are among the state-of-the-art for symbolic regression, the task of constructing symbolic expressions that fit well with data. To find highly accurate symbolic expressions, both the expression structure and any contained real-valued constants, are important. GP-GOMEA, a modern model-based evolutionary algorithm, is one of the leading algorithms for finding accurate, yet compact expressions. Yet, GP-GOMEA does not perform dedicated constant optimization, but rather uses ephemeral random constants. Hence, the accuracy of GP-GOMEA may well still be improved upon by the incorporation of a constant optimization mechanism. Existing research into mixed discrete-continuous optimization with EAs has shown that a simultaneous and well-integrated approach to optimizing both discrete and continuous parts, leads to the best results on a variety of problems, especially when there are interactions between these parts. In this paper, we therefore propose a novel approach where constants in expressions are optimized at the same time as the expression structure by merging the real-valued variant of GOMEA with GP-GOMEA. The proposed approach is compared to other forms of handling constants in GP-GOMEA, and in the context of other commonly used techniques such as linear scaling, restarts, and constant tuning after GP optimization. Our results indicate that our novel approach generally performs best and confirms the importance of simultaneous constant optimization during evolution.

Shor's algorithm represents the main threat of quantum computers to cryptography. In order to precisely understand its feasibility, many authors have worked towards reducing its costs, either at the logical level (assuming a fault-tolerant architecture), or at the physical level (taking into account the constraints of envisioned hardware). In particular, recent works by Chevignard et al. (CRYPTO 2024) and Gidney (arXiv 2025) used improved arithmetic to significantly reduce the qubit cost of factoring RSA public keys. Even more recently, Babbush et al. (arXiv 2026) improved the cost of computing elliptic curve discrete logarithms, with a reduction of a factor 2 to 3 in gate count and qubit count compared to a previous work by Litinski (arXiv 2023). Their result relies on optimized point addition circuits on elliptic curves over prime fields. However they did not reveal their logical quantum circuits, relying instead on a zero-knowledge proof. In this paper, we detail a quantum logical circuit architecture which gives similar results as Babbush et al., with a slightly higher number of qubits (around 1.5% increase) and a slightly smaller Toffoli gate count (between 6.5% and 10% reduction) for the curve secp256k1. We also give gate counts for a generic variant of the circuit, which is valid for any prime field.