The last decade has witnessed a rapid advancement in laser technology, enabling the direct monitoring and control of electronic motion on its natural attosecond to sub-femtosecond timescales. Ultrafast processes are conventionally studied using pump-probe spectroscopic techniques, where a pump pulse drives the molecule out of equilibrium and a time-delayed probe pulse records the response of the coherent non-stationary state. Since, these processes are non-linear and non-perturbative in nature, real-time formalisms provide a suitable theoretical framework for studying ultrafast light-induced dynamics. In addition, relativistic effects can play an important role in such simulations, either because the external field lies in the XUV to soft-X-ray region targeting core-level excitations, or because the molecular system contains heavy elements. In this chapter, we provide an overview of recent developments in real-time time-dependent density functional theory for simulating pump-probe spectroscopies (namely, transient absorption and transient electronic circular dichroism) at both non-relativistic and relativistic Hamiltonian levels. In order to further interpret these spectroscopic signals, we analyze several spectroscopically relevant time-dependent sub-observables, such as induced electronic densities and induced dipole moments as well as analytical formulations of generalized non-equilibrium response functions. We provide examples to show that the framework can be used to investigate and design new light-induced phenomena that emerge only in the attosecond regime.

Capillarity-driven self-assembly at fluidic interfaces offers a scalable route to large, reconfigurable materials. Microscale particles with high horizontal-to-vertical aspect ratios become attractive building blocks for shape-directed organization, but the capillary rules governing their assembly remain incompletely understood. Here, we combine experiments and theory to explain the transition between two capillary regimes: monopolar interactions arising from millimeter-scale curved interfaces, and quadrupolar interactions arising from local contact-line distortions. We show that the conventional Bond number is insufficient to predict this transition because it omits key material and surface-topography effects. Instead, we identify a new dimensionless parameter that captures the coupled roles of particle size, density, surface roughness, contact angle, and quadrupolar strength. This criterion correctly predicts when gravitationally induced monopolar attraction or surface-pinning-induced quadrupolar attraction dominates, providing a general design rule for interfacial particle assembly. The resulting model explains how particles self-organize across length scales and offers guiding principles for engineering next-generation interfacial materials from miniaturized particulate building blocks.

The ability to build atomically precise structures on surfaces with complete control over both atomic placement and chemical bonding remains a central challenge in nanoscale fabrication. Here, we demonstrate simultaneous spatial and chemical control over the mechanosynthetic fabrication of carbon structures. Using inverted-mode STM, C$_2$ units are donated from surface-deposited molecules to pre-patterned reactive sites on a hydrogen-passivated Si(100) surface. We demonstrate single-site C$_2$ donation, spatially patterned multi-site C$_2$ donation, and the stepwise assembly of polyyne structures through successive C-C bond formation. Together, these results establish controlled mechanosynthetic donation as a foundational capability for programmable atomically precise fabrication.

Order-of-addition experiments arise when the response depends on the order in which a set of components is added. Since the number of possible orders increases factorially with the number of components, full permutation designs are rarely feasible except for small problems. This paper studies space-filling fractional designs for order-of-addition experiments based on the Kendall tau distance, a natural metric for comparing permutations through pairwise ordering disagreements. We consider the maximin Kendall tau distance criterion and related dispersion criteria, and establish their connections with statistical optimality under the pairwise ordering model and a Gaussian process model with the Mallows kernel. To construct such designs, we propose an efficient foldover simulated annealing algorithm, denoted by FSA-KD, based on swap moves in the permutation space, together with foldover and incremental updating strategies. Numerical studies show that the resulting FSA-KD designs have large minimum pairwise Kendall tau distances, denoted by k_min(D), and stable pairwise distance distributions, and perform well in surrogate modeling and permutation-based optimization tasks.

We investigate a new notion of regularity for tensor triangulated categories, called residual regularity. We show that residual regularity descends and ascends via finite separable extensions and we classify all finite groups whose derived category of permutation modules is residually regular.

In this paper, we explore the strong gravitational lensing properties of black holes embedded in self-interacting scalar field dark matter halos, together with NFW-type configurations for comparison. The corresponding spacetime geometry is reconstructed numerically through the Einstein cluster formalism, allowing us to study how the surrounding dark matter distribution affects the propagation of photons near the black hole. We first analyze the effective function governing photon trajectories and calculate the corresponding photon sphere radius and critical impact parameter. We then investigate different strong-lensing observables, including relativistic Einstein rings, finite-order image positions, image separations, magnifications, and time delays, with particular attention to the supermassive black holes M87* and Sgr A*. Our results show that the considered halo configurations produce only small deviations with respect to the Schwarzschild case, typically at the level of $\mathcal{O}(10^{-3})$ or smaller, leading to a strong observational degeneracy among the models. Nevertheless, small but systematic differences remain present, especially in the time delay between relativistic images, which provides the clearest amplification of the halo-induced corrections for very massive black holes. These results suggest that, although standard strong-lensing observables remain highly robust against the considered halo environments, time-domain signatures may offer a more promising way to probe the effect of dark matter surrounding black holes.

We prove the finite abelian two-generator conjecture of Darijani--Miraftab--Witte Morris: every directed Cayley digraph on a finite abelian group with two distinct nonzero generators has two arc-disjoint Hamiltonian paths. The proof uses a cut-reflection theorem for Hamiltonian cut values in the family Cay(Z_k; a, a+1): if Z is the set of such values and N=k-1, then, with N-Z={N-z : z in Z}, dist(Z,N-Z)<=1. The proof uses sector-filling inequalities for primitive-ray multiplicities and an extremal graph recording pairs at minimal reflected distance. The estimate is sharp modulo parity: exact reflection occurs for odd k, while distance one occurs for even k. The second remaining cyclic family, Cay(Z_k; -a, a+1), is treated by an explicit quotient--fiber construction. We also prove the remaining three-factor case for Cartesian products of directed cycles. Together with the two-factor and at-least-four-factor theorems of Darijani--Miraftab--Witte Morris, this resolves their directed-cycle product conjecture for all numbers of factors.

LLM-based agents have moved automated program repair (APR) from fixed-context patch generation to interactive repository-level repair. However, existing agentic APR systems still struggle to use execution evidence to guide localization, patch generation, and validation. We propose EviACT (Evidence-to-Action), an agentic APR framework that coordinates three evidence-driven guardrails across repair stages. The retrieval scaffold grounds repair context, the compile gate filters invalid edits, and the test-driven gate checks target-test recovery before full regression. Across four benchmarks, EviACT improves resolve rate over the strongest reported comparable baselines by 1.6-6.0 percentage points and shows 70.1-88.6% lower reported per-bug API cost where baseline costs are available. Ablations and diagnostics suggest that these gains are associated with the coordinated evidence-to-action chain, making agentic APR more effective and efficient.

Complete isotopic fission yields distributions of $^{240}$Pu have been measured as a function of the initial excitation energy. The $^{240}$Pu fissioning system was produced through a two-proton transfer reaction between a $^{238}$U beam and a $^{12}$C target. The reaction was measured in inverse kinematics at Coulomb barrier energies, allowing for the full distribution of fission fragments to be isotopically identified with the VAMOS++ Spectrometer. The excitation energy of the system was measured on an event-by-event basis by detecting the target-like recoil $^{10}$Be in a segmented silicon telescope. This manuscript reports on the evolution of the fission yields as a function of the excitation energy of the system between 8.2 to 11.9 MeV. The influence of the excitation energy is manifested in the damping of shell effects that feed the yields in the symmetry valley, as well as in a reduction of the neutron content of the fragments. This reduction, however, is observed only in the heavy fragment, while the neutron content of the light fragment remains unaffected. The comparison with previous measurements, models, and evaluations highlights the importance of correlated observables for improving fission models.

Let $d\geq 2$ and $k\geq 1$ be fixed. We prove that, for every $ε>0$ and every real $β$, there exist integers $1\leq b_1,\ldots,b_k\leq N$ such that \[ \left\|\sum_{j=1}^k b_j^{1/d}-β\right\| \ll_{d,k,ε} N^{-k/d+ε}. \] The proof combines Schmidt's Subspace Theorem with an explicit inhomogeneous transference argument. This improves Iyer's (2025) higher-root exponent $(k-d+1)/d^2$, and also the analogous $d$-ary full-basis exponent away from the cases where $k+1$ is a power of $d$, at the cost of ineffectivity. We also record a conjectural uniform exponent $k-1/d$. In the square-root case $d=2$, we give explicit integer-target constructions for $k=2,3,4$ attaining this conjectural value.

Scalar Induced Gravitational Waves (SIGW) are generated at second order in perturbation theory and to achieve observational relevance, inflationary dynamics must evade the standard slow-roll scenario at small scales, generating large curvature perturbations following strongly non-Gaussian statistics. We propose a method to efficiently compute the SIGW spectrum including arbitrary non-Gaussianities. First, we solve the wave equation adopting semi-analytic methods; this results in an expression involving integrals in Fourier space which are impossible to solve directly on a lattice. We overcome this bottleneck by recasting these integrals as a sum of about 50 convolutions, each of which can be computed efficiently with FFT methods. Finally, the power spectrum is measured directly from the lattice realization. We implement this in FLAN-SIGW, a GPU-accelerated code capable of computing fully non-perturbative, non-Gaussian SIGW spectra in seconds with an error within 10% with modest computational resources. The code is made public at https://github.com/giovannipiccoli99/FLAN-SIGW. In this first implementation, in order to assess the performance of the method, we adopt a standard radiation-dominated background with $w = 1/3$.

Recent DESI data suggest that dark energy may be evolving and motivate the use of model-independent diagnostics such as $Om(z)$ and probes of the equation of state (EoS) of dark energy, $w(z)$. Traditional reconstructions of $w(z)$ rely on differentiating the expansion history, $h(z)=H(z)/H_0$, which amplifies noise and systematic uncertainties. In this work, we introduce a new diagnostic, the $w_0$-probe, which is constructed from $Om(z)$, and which enables a direct determination of the current EoS from $h(z)$ without any additional differentiation. While retaining the null-test capability of $Om(z)$ for $Λ$CDM, the $w_0$-probe also provides a direct estimate of $w_0$ -- the current EoS of dark energy. We demonstrate that this reconstruction of $w_0$ is robust for any smooth underlying $w(z)$. We apply this method to Gaussian-process (GP) reconstructions of $h(z)$ using current SNe Ia+BAO+CMB data. Both $Om(z)$ and the $w_0$-probe exclude $Λ$CDM at the $95\%$ confidence level (C.L.), with the latter favouring $w_0\simeq-0.62 \pm 0.03$ at $95\%$ C.L. To mitigate potential over-constraining from GP priors, we additionally analyze $χ^2$-limited reconstructions with likelihoods exceeding the $95\%$ CPL threshold. The $w_0$-probe obtained from these high-likelihood samples again predominantly excludes $Λ$CDM and yields $w_0\in(-0.8,-0.5)$ at $z\to 0$, demonstrating the robustness of our results. The $w_0$-probe therefore provides a simple, model-independent, and robust diagnostic of the current EoS of dark energy.

Sodium-ion batteries (SIBs) share similar electrochemistry with Li but offer several advantages, including high abundance in nature and low cost, as well as suitability for fast charging due to a Na-ion mobility higher than that of Li. The development of high-voltage SIBs heavily relies on the discovery of novel, robust cathode-active materials (CAMs). All-inorganic materials represent the most mature and practical choice as CAMs for next-generation SIBs; however, their family spans a vast and chemically diverse space. In this work, we present a large-scale, chemically validated database of stable materials for SIB cathode discovery, curated from four major databases: Materials Project, AFLOW, OQMD, and GNoME. Generalizable and transferable descriptor-based machine learning (ML) models are developed based on a dataset of charged-only structures rather than charged/discharged pairs. Using a committee of the top four trained ML models, average voltage and specific capacity are predicted as target properties. Finally, a subset of top-ranked candidate CAMs is validated through explicit, high-throughput first-principles calculations of voltage profiles, phase stability, structural robustness upon sodiation/desodiation, and electronic properties. Together, this integrated data curation, ML ranking and predictions, and first-principles validation strategy establishes a scalable and transferable framework for accelerating the discovery of stable, high-voltage CAMs for SIBs and beyond.

We establish that semidefinite programs (SDPs) over the unbounded positive semidefinite cone are mathematically equivalent to thermodynamic systems of independent bosonic modes: the eigenvalues of the optimization variable play the role of expected occupation numbers, the linear objective plays the role of total expected energy, and the linear equality constraints play the role of conserved non-commuting charges. Building on this perspective, we recast general SDPs as bosonic free-energy minimization problems at strictly positive temperature, regularized by the Bose-Einstein entropy; the original SDP is recovered in the zero-temperature limit. The optimal primal variable takes the form of a Bose-Einstein thermal operator parametrized by the dual variables. We prove an approximation-error bound that depends on the ground-space degeneracy and the spectral gap of the dual slack operator, improving on the linear-in-dimension worst-case duality gap of interior-point methods. We also introduce the Bose-Einstein quantum relative entropy as a Bregman divergence on the unbounded positive semidefinite cone, generated by the negative Bose-Einstein entropy. We propose it as a natural divergence for unnormalized positive operators, for which the standard Umegaki relative entropy can become negative, and we show that it satisfies a restricted monotonicity property under affine maps modeling bosonic Gaussian channels. Finally, we develop hybrid quantum-classical algorithms for the regularized SDP using only Hamiltonian simulation, Hadamard tests, and classical sampling, and bound their runtime in closed form. Unlike existing quantum SDP solvers, whose runtimes scale polynomially with an a priori upper bound on the primal trace, our framework operates directly on the unbounded cone, replacing this bound with a dependence on the spectral structure of the dual slack operator.

We employ 236 gravitational-wave (GW) sources in the fifth LIGO--Virgo--KAGRA Collaboration (LVK) Gravitational-Wave Transient Catalog (GWTC-5.0) to estimate the Hubble constant $H_0$. We compare the luminosity distance measured from GWs to the redshift inferred i) using features in the mass spectrum, and ii) using statistical host galaxy association. Probing the relationship between source luminosity distances and redshifts obtained in this way yields constraints on cosmological parameters. We estimate $H_0 = {71.0}_{-7.1}^{+9.0}\,{\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}}$ (median with $68\%$ symmetric credible interval). This combines information from the source-frame mass distribution with the $H_0$ measurement from GW170817 and its electromagnetic counterpart as well as galaxy catalog information from Dark Energy Survey Year 6 (DES-Y6). We improve over the GWTC-4.0 measurement by using more GW sources, some with significantly smaller sky localization volumes, which leads to a reduction by $25.7\%$ of the $H_0$ uncertainty and a reconstructed mass distribution with lower uncertainties. We also constrain deviations from general relativity (GR) which affect GW propagation, specifically that modify the luminosity distance inferred from the GW signal. We find no departures from GR in parameterized tests of GW propagation.

We present the population properties of merging compact binaries inferred using 267 mergers from the cumulative Gravitational-Wave Transient Catalog 5.0. As this data set contains no new sources with a neutron star, we primarily focus on the properties of the binary black hole mergers. We infer the merger rate of binary black holes with component masses between $2.5\,\mathrm{M}_\odot $ and $200\,\mathrm{M}_\odot $ to be $27.5\text{--} 49.4 \, \mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ (all intervals at $90\%$ credible levels) at redshift $z = 0.2$. We find evidence for a subpopulation of binary black hole mergers that host a rapidly spinning black hole (dimensionless spins $χ\sim 0.7$), consistent with signatures of hierarchical mergers. We find that these occur at two mass scales, the first at primary masses $\sim 10$--$20\,\mathrm{M}_\odot $ and the second above $\sim 45\,\mathrm{M}_\odot $, and we estimate their total rate at $z=0.2$ to be $0.2\text{--} 3.11 \, {\rm Gpc}^{-3} {\rm yr}^{-1}$. We infer that, above $40\,\mathrm{M}_\odot $, the mass distribution of the less massive (secondary) black hole declines more steeply than that of the more massive (primary) one. This is consistent with a flatter mass-ratio distribution and indicates the prevalence of unequal-mass binaries with large primary masses. We find evidence for two features in the black hole mass spectrum: a peak around $10\,\mathrm{M}_\odot $ and a change of slope at around $35\,\mathrm{M}_\odot $. Black holes of $\sim 35\,\mathrm{M}_\odot $ pair preferentially with companions of similar mass. Additionally, we find that the effective inspiral spin distribution of binary black holes is asymmetric about zero, based on which we infer that at least $9 \%$ of mergers occur in channels with some preference for spin-orbit alignment. We find evidence that...

The Gravitational-Wave Transient Catalog (GWTC) is a collection of candidate gravitational-wave transient signals identified and characterized by the LIGO-Virgo-KAGRA Collaboration. Producing the contents of the GWTC from detector data requires complex analysis methods. These comprise techniques to model the signal; identify the transients in the data; evaluate the quality of the data and mitigate possible instrumental issues; infer the parameters of each transient; compare the data with the waveform models for compact binary coalescences, and handle the large amount of results associated with all these different analyses. In this paper, we describe the methods employed to produce the catalog's fifth release, GWTC-5.0, focusing on the analysis of the second part of the fourth observing run of LIGO, Virgo and KAGRA.

The Gravitational-Wave Transient Catalog (GWTC) is a collection of short-duration (transient) gravitational-wave signals identified by the LIGO-Virgo-KAGRA Collaboration in gravitational-wave data produced by the eponymous detectors. The catalog provides information about the identified candidates, such as the arrival time and amplitude of the signal and properties of the signal's source as inferred from the observational data. GWTC is the release of this dataset and version 5.0 extends the catalog to include observations made during the second part of the fourth LIGO-Virgo-KAGRA observing run up until 2025 January 28. This paper marks an introduction to a collection of articles related to this version of the catalog, GWTC-5.0. This update significantly increases the number of detected merging binary systems of black holes and neutron stars to over 300, enabling many follow-up studies toward understanding the gravitational-wave universe. The collection of articles accompanying the catalog provides documentation of the methods used to analyze the data, summaries of the catalog of events, observational measurements drawn from the population, and detailed discussions of selected candidates.

Amorphous grain-boundary (GB) complexions in thermally stable nanocrystalline alloys are commonly assumed to be structurally homogeneous, yet their disordered nature makes them susceptible to local short-range ordering (SRO). The influence of local SRO on GB-mediated plasticity mechanisms in such complexions remains poorly understood. This article employs large-scale Monte Carlo and molecular dynamics simulation to address this gap through simulations of nanocrystalline Al-Ni alloys at two Ni concentrations, 2 at.% and 4 at.%. Annealing at 913 K produces thick uniform amorphous intergranular film complexions, while annealing at 378 K produces semi-amorphous complexions containing FCC-type and BCC-type SRO. These two complexion states produce fundamentally different mechanical responses. Amorphous complexions act as dislocation sinks, suppressing shear localization and promoting homogeneous plasticity through shear transformation zones, but at the cost of lower strength. SRO complexions generate higher strength but also promote heterogeneous stress concentrations across the GB network, leading to intense shear localization regardless of Ni concentration. This contrast reflects a fundamental shift in governing mechanism, from shear-transformation-zone-controlled behavior in amorphous complexion alloys to GB-stress-heterogeneity-controlled behavior in SRO complexion alloys. These findings highlight the potential of complexion engineering to tailor the mechanical properties of nanocrystalline materials.

Dwarf galaxies have long been recognised as important testing grounds for models of dark matter. For instance, it is here where the cusp-core problem is most apparent. In this work we select two dwarf galaxy samples: LITTLE THINGS and dwarf galaxies in SPARC. We use these to examine whether there are preferences for MOND or dark matter halos in these objects. Notably, our analysis employs the latest developments in Hamiltonian Monte Carlo sampling methodology and robust model comparison via ELPD differences. Our findings suggest a $>4σ$ preference for cored halo models over MOND. However, this relies on significant preferences from 7 out of 19 SPARC galaxies and 11 of 18 from LITTLE THINGS (few of which are overwhelming). It is notable that only a single galaxy prefers MOND over a cored halo. Thus, this evidence is suggestive, but does not conclusively decide against MOND. We also test for evidence of a MOND external field effect, and find weak evidence against its presence. Despite these statistical preferences, most SPARC galaxies remain compatible with a universal MOND scale. In LITTLE THINGS, a free MOND model is preferred to a universal value at $\sim 8σ$, but this is of doubtful physical significance. For MOG, the story is different, here we find $\gtrsim 8σ$ preferences for all halos (or MOND) against universal MOG models with significant exclusions in individual galaxies across both samples. Thus, a proposed universal rotation curve model derived from MOG is quite strongly disfavoured.

Efficient electrical manipulation of domain walls is key to developing magnetic devices with fast switching capabilities and low energy consumption. Here we demonstrate Bloch-type domain wall velocities exceeding 1 km s$^{-1}$ in the single-layer ferrimagnetic spinel oxide NiCo$_2$O$_4$ induced by spin-transfer torque at a current density of $2 \times 10^{11}$ A m$^{-2}$. This exceptional domain wall mobility is attributed to the combination of giant nonadiabatic spin-transfer torque, low magnetization, and high spin polarization. Additionally, we report a pronounced domain wall inertia effect in this ferrimagnet due to the large nonadiabaticity of the torque. The characteristic time for domain wall acceleration and deceleration is $\sim 1$ ns, shorter than that reported for typical ferromagnets. Our findings highlight the potential of spinel oxides as a promising platform for engineering high-performance domain wall devices that take advantage of ultrafast ferrimagnetic dynamics.

Spin-orbit torque (SOT) enables ultra-fast, energy-efficient magnetization switching, making it a promising mechanism for introducing MRAMs for cache memory applications. However, current SOT-MRAM devices face write efficiency limitations, with charge-to-spin conversion ($ξ_{DL}$) reaching $\sim$ 45\%, far below the projected $\sim$ 80\% needed to comply with the current delivery of advanced transistor nodes. Recent advances in orbital current physics, evidenced in a wide class of materials, offer a path to enhance $ξ_{DL}$. Here, we study the Ta(3-30 nm)\slash W(1-4 nm) system, revealing a large additional spin-orbit torque contribution arising from Ta, a four-fold increase compared to the spin Hall effect in Ta alone, attributed to the orbital Hall contribution. This system exhibits larger $ξ_{DL}$ than W-based SOT systems with more robust perpendicular magnetic anisotropy and compatibility with 400$^\circ$C annealing. Leveraging these advantages, we integrate the Ta/W system into 3-terminal SOT-MTJ devices, showing a level of performance similar to that of W-based systems. Our results show that orbital physics can be easily integrated into SOT-MTJ systems, offering a viable strategy to enhance SOT-MRAM efficiency. In addition, we propose and demonstrate a proof-of-concept for vertical non-local switching of SOT-MTJ using orbital torques, simplifying bottom-pinned SOT-MRAM fabrication.

Problem 8.1 in Astaiza et. al. asks about the relationship between the cycle decomposition of a permutation $σ$ and that of its symmetric tensor power $σ^{\odot k}$. In this paper, we investigate this question and give formulas for computing the number of fixed points and, in the case of a permutation containing at most one cycle of length greater than one, the number of $s$-cycles.

We define metrics in space that are natural counterparts of the hyperbolic metric in plane domains, using the characterization of the hyperbolic metric due to Beardon and Pommerenke. We obtain inequalities for these metrics under quasiconformal homeomorphisms between domains in space that have at least two boundary points. We discuss the failure of the existence of such estimates for non-homeomorphic quasiregular mappings.

In Diaconis and Saloff-Coste (1996), the authors introduced the simple ``transvection" walk on $\mathrm{GL}_n(\mathbb F_2)$: at each step, choose two distinct rows and add one to the other. In Ben-Hamou (2025), the author recently proved that this walk has mixing time $O(n^2\log n)$. Inspired by applications in cryptography (see Sotiraki (2016)), Ben-Hamou and Peres (2018) conjectured that the first $k$ columns of this walk mixed in $O(nk \log(n))$ steps. Our main result is a proof of this conjecture uniformly in $n$ and $k.$ Our proof is based on a local-to-global entropy estimate, in the spirit of block factorization results such as Caputo et al (2015), Caputo et al (2021). In our setting, the kernels that correspond roughly to the block kernels of Caputo et al (2021) do not have uniformly large log-Sobolev constants, and so naively applying these techniques does not improve over Ben-Hamou (2025). We avoid these bad blocks by combining our entropy estimates with a burn-in argument similar to classical drift-and-minorization arguments of Rosenthal (1995). This method may be of broader interest, and so we illustrate it by proving an analogous result for a family of product-replacement algorithms on the Heisenberg group.

Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external driving or environment. While related phenomena have long been studied in classical nonlinear systems, their realization in entangled quantum matter represents a distinct frontier. The theoretical understanding of discrete time crystals has substantially advanced, yet recent experiments using modern quantum devices and quantum processors reveal regimes beyond established paradigms. These developments call for an extended classification of time-crystalline phases according to both their stabilization mechanisms and their physical character, including discrete and continuous, closed and open, critical, topological, quasiperiodic, and controlled realizations. We review recent implementations of time crystals on quantum platforms and propose such a classification framework, identifying promising directions for the discovery of novel time-crystalline phases of matter.

In this paper, we study the behavior of Ekedahl-Oort strata under natural embeddings between the good reductions modulo $p$ of GSpin Shimura varieties and Rapoport-Smithling-Zhang unitary Shimura varieties, a prototypical setting for the construction of special cycles in the Kudla program. In each case, we determine the EO stratum containing the image of a given EO stratum under the embedding. We also compute discrete invariants of these Shimura varieties, including their $p$-ranks and $a$-numbers; in the GSpin case, these are obtained via the Kuga-Satake embedding.

Quantifying the workplace productivity effects of Generative Artificial Intelligence is now central to economics, management, and public policy. The deployment of AI tools in customer service, writing, software development, and consulting operations has been reported to generate large per-task productivity gains, typically measured as tasks completed per worker-hour or reductions in mean handle time. We argue that such mean-based metrics can misrepresent AI's effects in workflows where tasks accumulate and compete for scarce human attention. AI assistance can generate a deceptive productivity signature: average completion times fall because AI tools typically supply a fast first draft, yet workflow-level performance deteriorates when a subset of AI errors escapes review and returns as costly downstream rework. We call this divergence between mean task speed and system-level delay the variance wedge. Depending on the operational parameters, the most time-efficient way to complete a workflow may undergo a transition between two task-processing regimes, a fully AI-assisted and a fully manual one. We formalize the mechanism as a queueing model and derive two main implications analytically. First, under congestion, reviewers rationally raise the risk threshold for checking AI outputs, reducing scrutiny precisely when it would matter the most. Second, AI assistance can stabilize an overloaded workflow only when (i) the fraction of tasks handled by AI exceeds a critical threshold, and (ii) the human attention required for review and expected rework is lower than the attention for manual completion, a requirement substantially more stringent than faster draft generation. These results suggest that AI deployment should be evaluated not only by average task speed, but by its overall effects on congestion, rework, and the robustness of human oversight under load.

We apply persistent homology to the ORBIS Geospatial Network Model of the Roman World in order to quantify the structural resilience of the Eastern Mediterranean trade network between 0 and 400 ce. The network is represented as a weighted transport system whose edges correspond to road, maritime, and riverine routes, each carrying a base cost derived from the ORBIS cost model. To introduce historical dynamics into this static spatial infrastructure, we construct a differential friction model in which edge weights vary by decade and by transport mode according to documented historical perturbations, including epidemic mortality, civil war, military pressure, administrative reorganisation, and imperial reunification. For each decadal snapshot, we compute all-pairs shortest-path distances on the active sub-network and construct a Vietoris--Rips filtration using an adaptive threshold defined by the 90th percentile of finite pairwise distances. The resulting betti number ($β_1$) persistent entropy time series identifies three structurally distinct phases in the Eastern Mediterranean network. Phase~I, from 0 to 200 ce, is a stationary high-redundancy regime consistent with the commercial integration of the early imperial and Antonine periods. Phase~II, from 210 to 280ce, corresponds to recoverable stress during the Crisis of the Third Century: betti number ($β_1$) entropy declines during the crisis but returns to the Phase~I baseline following Aurelianic reunification. Phase~III, from 290 to 400 ce, is qualitatively different: cycle redundancy declines monotonically and does not recover. The main contribution of this study is to show that persistent homology detects a dimension of imperial stress that is not reducible to single economic, military, or political indicators.

We investigate beyond-mean-field dynamics in a fully connected $\mathrm{SU}(3)$ spin-exchange model, focusing on the interplay between chaotic dynamics and quantum fluctuations. Using the two-particle irreducible (2PI) effective action formalism, we derive equations of motion that systematically account for higher-order correlations generated by interactions, and demonstrate how quantum fluctuations can regularize chaotic dynamics displayed by macroscopic observables. Our results show that an accurate treatment of fluctuations is essential for describing macroscopic dynamics in quantum many-body systems and promote 2PI as a robust framework for connecting microscopic correlations to macroscopic nonequilibrium phenomena.