Large-scale spectroscopic surveys have collectively observed millions of stars across the Milky Way, but each derives stellar labels using independent pipelines with distinct modelling assumptions, introducing systematic offsets that obscure signals in chemical space and hinder large-scale Galactic archaeology. We present a unified deep-learning framework that delivers atmospheric parameters, chemical abundances for 20 elements, distances, and ages -- all on a single, self-consistent scale -- for an arbitrary number of spectroscopic surveys simultaneously. Our approach uses a Transformer model that ingests spectra of arbitrary wavelength range and resolution, trained end-to-end as a single model across all surveys, eliminating the need for post-hoc recalibration. We apply this framework to spectra from APOGEE DR17, GALAH DR3, DESI DR1, and $\textit{Gaia}$ RVS DR3, spanning resolutions from R ~ 2,000 to 28,000 and wavelengths from the optical to the near-infrared. On high-resolution APOGEE spectra the model achieves precisions of $18~$K in $\textrm{T}_{\rm eff}$, $0.04~$dex in $\textrm{log}\,\textit{g}$, $0.015~$dex in [Fe/H], and ${<}\,0.03~$dex across all abundances; on lower-resolution DESI spectra, typical precisions are $51~$K, $0.09~$dex, $0.04~$dex, and ${\sim}\,0.06~$dex, respectively. Cross-survey comparisons demonstrate that labels for the same stars observed by different surveys are consistent within model uncertainties; we further validate against external distance catalogs and open cluster metallicities and ages. The resulting homogeneous catalog enables Galactic archaeology at unprecedented scale and consistency, and the framework is readily extensible to forthcoming spectroscopic surveys such as SDSS-V, WEAVE, and 4MOST. The catalog is publicly available at https://doi.org/10.5281/zenodo.19830515.

We study the asymptotic distribution of level crossings for random matrix pencils A_n+λB_n in several ensembles, including complex and real i.i.d. matrices and Gaussian/Hermitian settings. We derive a representation of the normalized log-discriminant in terms of pairwise eigenvalue interactions and formulate conditions under which its limit is governed by a deterministic potential. Under assumptions combining a uniform circular law, logarithmic tail control, and small-spacing (repulsion) estimates, we prove convergence of the empirical measure of level crossings to an explicit deterministic limit. In the complex Gaussian case these assumptions are verified (modulo a uniformity step), while in the general i.i.d. setting the results are conditional and motivated by universality theory. We further analyze the real case, showing that any limiting measure does not concentrate on the real projective line under suitable hypotheses, and discuss analogous phenomena for elliptic/Hermitian ensembles. Our results highlight the role of logarithmic energy and universality in governing spectral degeneracies of random matrix pencils.

Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form. However, it is not defined for extensive-form games in which a player can choose among a continuum of actions. We define a class of infinite extensive form games in which information behaves continuously as a function of past actions and define a natural notion of sequential equilibrium for this class. Sequential equilibria exist in this class and refine Nash equilibria. In standard finite extensive-form games, our definition selects the same strategy profiles as the traditional notion of sequential equilibrium.

In this paper, we investigate arithmetical completeness with respect to finite Kripke models of quantified modal logic. We adapt the finite-model embedding techniques of Artemov and Japaridze to two settings involving finite Kripke models. First, for conversely well-founded finite Kripke models of quantified modal logic, we construct a $Σ_2$ Fefermanian provability predicate together with an arithmetical interpretation that embeds the model into arithmetic. Second, for finite constant domain Kripke models of quantified modal logic, we construct a $Σ_1$ provability predicate satisfying $\mathbf{D2^G}$ and an arithmetical interpretation yielding such an embedding.

Federated inference enhances LLM performance in edge computing through weighted averaging of distributed model predictions. However, autoregressive LLM inference requires frequent full-model forward passes across workers, severely limiting decoding throughput. Distributed deployment further aggravates this due to a communication bottleneck: each worker must transmit full token probability distributions per draft token, dominating end-to-end latency. To address these challenges, we introduce speculative decoding to enable parallel LLM processing and propose a top-K compressed transmission scheme with two server-side reconstruction strategies. We theoretically analyze the robustness of our method in terms of local reconstruction error, aggregation bias, and acceptance-rate bias, and derive corresponding bounds. Experiments demonstrate that our scheme achieves high generation fidelity while significantly reducing communication overhead.

Neural Quantum States (NQS) are now among the most accurate methods for studying strongly correlated many-fermion systems, outperforming existing many-body approaches for large systems. However, NQS calculations remain extremely resource-intensive. Here, we introduce a new Pareto frontier of efficiency and accuracy for NQS in simulating strongly correlated lattice fermions, defined by two complementary backflow-related architectures: the Sparse Convolutional Ansatz for Lattice Electrons (SCALE) (state-of-the-art efficiency) and the Accurate Convolutional ansatz for lattice Electrons (ACE) (state-of-the-art accuracy), benchmarked on the iconic Hubbard and $t-J$ models for large lattices. SCALE uses a tailored convolutional design enabling efficient local updates via low-rank determinant updates, reducing computational scaling from $O(N^4)$ to $O(N^3)$ in backflow methods and yielding a >40$\times$ practical speed-up in tests while maintaining high variational accuracy. As an application, we study the previously inaccessible 1/8-doped pure Hubbard model up to $32 \times 32$, finding no significant energy difference between horizontal and vertical filled stripe states - contrasting with half-filled stripe states when next-nearest-neighbor hoppings are included. ACE employs a deep convolutional stack to maximize expressive power, achieving unprecedented accuracy on large systems. Extensive benchmarks on Hubbard and $t-J$ models show SCALE delivers variational energies competitive with leading methods at a fraction of the cost, while ACE sets a new accuracy benchmark, surpassing recent results with only 1/6 the runtime for $16 \times 4$ systems. These new NQS approaches provide scalable, affordable, and accurate tools for exploring strongly correlated fermionic physics, such as the microscopic mechanism of unconventional superconductivity.

We analyze a three-dimensional discontinuous piecewise linear system \(Z=(X,Y)\) whose switching manifold \(Σ\) contains visible-visible two-fold intersection lines. Assuming that the matrices \(DX\) and \(DY\) each have one nonzero real eigenvalue and one pair of complex conjugate eigenvalues, we reduce the system to a canonical form. Under a resonant condition, we use Darboux integrability theory to obtain a first integral common to \(X\) and \(Y\). Its restriction to \(Σ\) defines a hyperbola \(Γ\), which parametrizes the crossing points of symmetric periodic orbits. On this curve we construct the half-return maps, derive analytic expansions for the corresponding return times near infinity, and introduce a time-matching function given by their difference. By means of the Weierstrass Preparation Theorem, we prove the existence of a large-amplitude symmetric limit cycle for a suitable subfamily of systems. We then study stability through a saltation-corrected monodromy matrix and reduce the problem to Schur--Cohn inequalities for the two transverse Floquet multipliers.

We present the SCenario Specification Language (SCSL) for automated generation and execution of system-level tests. SCSL targets complex distributed systems (e.g., collaborating autonomous robots) where classical model-based testing becomes impractical because (1) the overall system complexity is too high for a single monolithic model, (2) test behaviour cannot be fully precomputed due to substantial nondeterminism in the distributed system under test (SUT), and (3) the SUT configuration may change dynamically at runtime. Challenge (1) is addressed by scenarios: each scenario specifies test-specific expected SUT behaviour and/or stimuli to be applied during execution. Complex system tests are composed from elementary scenarios using sequential and parallel composition. To address (2), the SCSL tool platform supports online (on-the-fly) testing, selecting and executing test steps during runtime. For (3), SCSL provides a collaboration construct that supports dynamic reconfiguration: removing unavailable components, registering newly joining components, and rewiring interfaces during test execution. We illustrate the syntax and semantics of SCSL using a system-test example in which robots perform a salvage mission, and we use an automatically generated test execution to demonstrate the concepts supported by our prototype tool platform.

We present a systematic technique for constructing the Lorentz-covariant structures of hadronic matrix elements of local operators. The spinor Young tableaux of the Lorentz group is employed to construct all possible structures for the matrix elements of arbitrary operators, using the relativistic wave functions and momenta of the initial and final state particles of arbitrary spin as building blocks. We obtain the form factor bases for the scalar, vector, and rank-2 tensor operators for particles with spin-$\frac{1}{2}$, $1$, $\frac{3}{2}$, and $2$, among which the general $P$ and $T$ form factors for spin-$\frac{3}{2}$ and spin-$2$ particles are presented for the first time. The independent form factor structures are also cross-checked by the non-relativistic counting and Hilbert Series method and we find there is redundant $P$ and $T$ conserved structure for spin-$2$ particles in literature. As an application, the matrix elements of general nonlocal operators can be expanded by towers of the matrix elements of local operators, and thus can be decomposed by the constructed form factor bases above.

We statistically quantified the prevalence and properties of substructure in optical galaxy clusters and directly investigated its impact on X-ray morphology and scaling relations, leveraging new data from the DECaLS Legacy Survey and the SRG/eROSITA all-sky survey. We applied the hierarchical density-based clustering algorithm HDBSCAN to the redMaPPer galaxy cluster catalog to identify and characterize substructure from the probabilistic membership assignments. We then cross-matched this sample with the eROSITA X-ray morphology catalog to correlate optical substructure with a comprehensive set of X-ray morphological parameters. Finally, we analyzed the scaling relation between X-ray luminosity and optical richness for clusters with and without substructure. Substructure is a common feature, present in approximately 40% of clusters; a quarter of the full sample exhibits a fractional contribution to richness in excess of 35%. We find a highly significant correlation between optical substructure and disturbed X-ray morphologies, a trend that is strongest for high-mass clusters. The clusters with substructure also drive a stronger redshift evolution in the scatter of the Lx-lambda relation. At low redshifts (z<0.2), they display a systematically higher X-ray luminosity at fixed richness compared to relaxed systems. We attribute the enhanced effect of mergers on X-ray properties at low redshifts to the increased density contrast of low-redshift cool cores and longer substructure survival times, which are possibly due to the suppression of disruptive mixing by effects such as magnetic draping. At lower cluster richness, a discordance between X-ray morphology and the merging state indicates a growing relative importance of active galactic nucleus feedback in governing X-ray morphology.

The Brownian tree, also known as the continuum random tree, is a canonical random compact, geodesic $\mathbf R$-tree that arises as the universal scaling limit for numerous models of discrete random trees. A key quasisymmetric invariant of a metric space is its conformal dimension, defined as the infimum of the Hausdorff dimensions over all quasisymmetrically equivalent spaces. This value is always bounded below by the space's topological dimension and above by its Hausdorff dimension. In the present paper, we prove that the conformal dimension of the Brownian tree is $1$, matching its topological dimension.

Quantum optimal control methods are widely used to design experimental control pulses such as laser amplitudes, phases, or detunings, that implement a target unitary evolution. In practice, what makes a pulse "good" depends not only on its fidelity, but also on the experimental setting and the relevant hardware constraints. Here, we introduce geometric quantum control with kernel optimisation (GECKO), a model-agnostic method for improving control pulses after a high-fidelity solution has been found. GECKO uses the Riemannian geometry of the special unitary group to identify directions in pulse space that leave the implemented unitary unchanged to first order, allowing one to traverse level sets of the control landscape while optimising a chosen differentiable pulse-quality function. We demonstrate GECKO on a transverse-field Ising Hamiltonian implementing CZ and CNOT gates, optimising pulse properties including spectral filtering, smoothness, robustness to parameter deviations, and pulse duration. In all cases, GECKO finds substantially improved pulse solutions.

Between 1949 and 1980, every U.S. state mandated public schools to provide educational services for disabled students. This is one of the largest education reforms in U.S. history, but little is known about its impacts. Given scarce data in this period, I compile survey and administrative datasets and set up a difference-in-difference design using variation in the mandates' timing. I show that the mandates increased both services for disabled students and preschool enrollments. In adulthood, disabled individuals below school age at a mandate's implementation became about 20% less likely to have no education, attained up to 0.23 more years of education, and were more likely to have worked. Although this policy could have taken away resources from non-disabled students, in fact, education and employment also increased for non-disabled individuals. These effects align with evidence that the mandates increased spending per student by up to 15%. Families were also impacted: the mandates increased employment among mothers of disabled children and the probability that disabled individuals became household heads. Over the long term, the mandates paid for themselves by generating government revenues in excess of their cost. These results provide new evidence on the large, broad impacts of expanding access to education for disabled students.

Many large-scale optimization problems decompose into a master problem and scenario subproblems, a structure that can be exploited by Benders decomposition. In Benders decomposition, each iteration may generate many cuts from scenario subproblems, and adding all of them as constraints then causes the master problem to grow rapidly. These are constraints that may need to be added to the master problem to guarantee optimality and feasibility of solutions, but we can avoid adding those constraints that are never violated. Adding fewer cuts per iteration can reduce the number of cuts added in total, but increase the number of iterations. In contrast, the cuts filtered for regular cut selection in mixed-integer programming solvers are optional and added exclusively to improve runtime behavior. We study Benders cut filtering: given the Benders cuts produced in an iteration, which subset should be added to the master problem? To our knowledge, few prior works have studied this question. We propose violation-based filtering (retaining the most-violated cuts), diversity-based filtering via k-medoids clustering on pairwise cosine distances (adding an original cut closest to the cluster centroid), and a hybrid that selects a most-violated cut per cluster. Each strategy can be augmented with an aggregated cut that retains discarded information. Computational experiments on 149 instances of an affine potential-based flow problem with topology switching and robustness scenarios -- solved via Benders decomposition -- show that all informed filtering strategies solve at least 125 instances (vs. 91 for the unfiltered baseline), reducing shifted geometric mean solve time by 55-57%. The hybrid strategy attains the best geometric mean (271.89 s vs. 629.34 s, a 57% reduction, p < 0.001).

We describe various ways of obtaining the Hadamard coefficients associated to a normally hyperbolic operator from the corresponding Green's operators. As the Hadamard expansion on its own is not enough for this, we include additional information either by considering something like a resolvent or powers of Green's operators or by looking at a product of the original manifold with the real line.

The \textit{Euclid} satellite will deliver a catalogue of optically-selected galaxy clusters spanning from around $2000$ deg$^2$ in Data Release (DR) 1 to around $14\,000$ deg$^2$ in DR3. We assess the validity of cluster clustering (CC) models for template-fitting, which complements the full-shape methodology in providing cosmological information from the anisotropy of the redshift-space two-point correlation function (2PCF). Both will be used to analyse the cluster 2PCF multipoles in \textit{Euclid}. We analyse the multipoles of the two-point redshift-space clustering of galaxy clusters simulated with the semi-analytic \code{PINOCCHIO} code using third-order Lagrangian perturbation theory, assuming a \textit{Euclid} DR1-like footprint of 500 deg$^2$ in the Northern Hemisphere and 1400 deg$^2$ in the Southern Hemisphere. We estimate the first three even multipoles of the 2PCF and associated covariance matrix from 1000 DR1-like synthetic catalogues. We study the impact of the modelling of nonlinearities, halo bias, and photometric redshift uncertainties on the 2PCF. We apply three clustering models to the mock catalogues at $0<z<2$ and virial mass $M_{\rm vir}>10^{14}\;h^{-1}\,M_\odot$ under realistic and optimistic photometric redshift uncertainty scenarios. We formulate a set of permissive and conservative criteria that should be fulfilled by the multipole cut-off scales and validate against 100 mock catalogues via inference of the growth rate times the matter power spectrum normalisation parameter, $fσ_8$. We test the dispersion, Scoccimarro, and Taruya--Nishimichi--Saito models. We find that the simplest of the three -- the dispersion model -- yields unbiased inferences on $fσ_8$ from CC down to $10$ $h^{-1}$ Mpc in a DR1-like setting. All clustering models provide very similar goodness-of-fit metrics in the presence of DR1-like cluster redshift uncertainties.

An economy, large or small, has traditionally been defined in terms of an explicit set of agents and an assignment of characteristics to each agent. But when individual agents are negligible, most economically relevant properties of an economy can be defined in terms of the distribution of characteristics alone. Agents need not be specified. It has been frequently asserted that the distributional description of an economy is too sparse for core analysis. Notions of coalitions and blocking require the individualistic description of agents. This paper shows that this is not so. The presence of blocking coalitions can be directly identified in terms of distributions alone. Indeed, we give a purely distributional proof of the classical core-equivalence theorem that delivers the core-equivalence theorem for individualistic economies as a corollary. Our methods have applications outside of general equilibrium theory. They apply to large matching markets and to analogs of the Shapley-value for atomless economies.

The Quantum Approximate Optimization Algorithm (QAOA) follows a single, fixed evolution path, overlooking the potential computational advantage of coherently superposing multiple trajectories. Here we overcome this limitation with a hybrid quantum walk (HQW) ansatz that super poses multiple Hamiltonian-driven paths coherently within each circuit layer via a dynamical coin operator. QAOA emerges as a special case of this framework with a static Pauli-X coin. Using Pontryagin's minimum principle, we derive the optimal form of the coin operator, demonstrating that it generally differs from a constant gate. A dynamical Lie algebra analysis reveals that HQW generates a strictly larger Jordan-Lie algebra, providing an algebraic foundation for its enhanced expressivity. Especially, we reveal the connection between the unique Jordan product negativity in HQW's DLA and its performance advantages. Numerical experiments on Max-Cut and Maximum Independent Set problems show that HQW systematically outperforms QAOA in convergence speed, solution accuracy, and robustness. Our work establishes a path-superposition paradigm for quantum optimization, combining optimal control theory with algebraic structure to guide the design of advanced quantum algorithms.

We investigate the transport signatures of pseudo-Landau levels (PLLs) in two-dimensional anisotropic Dirac systems with tilted cones, whose effective bandstructure results from strain-induced pseudogauge fields. In contrast to conventional Landau quantisation, the PLLs exhibit explicit momentum-dependence by being dispersive, leading to finite longitudinal group-velocities. We analyse the transport properties within the semiclassical Boltzmann framework by computing the electrical, thermoelectric, and thermal response in the linear regime, which acquire nonzero longitudinal components. We also check the validity of the Mott relation and Wiedemann-Franz law in our system. Our results provide a unified framework for understanding the interplay between tilted spectrum and structural deformation in affecting quantum transport, and suggest unambiguous experimental signatures in strain-engineered systems.

Materials underpin modern technologies, from energy harvesting, storage, and conversion to information and communication technologies. Their functionality is often governed by the interplay between competing phases, as thermodynamic behavior shapes microscopic properties and ultimately determines technological performance; for instance, the light absorption of inorganic metal-halide perovskites in solar cells. Accurately predicting crystal thermodynamics, however, remains a major challenge for computational approaches because strong anharmonic effects require extensive sampling of the potential energy surface. Here, we present an on-the-fly Bayesian framework, combined with the stochastic self-consistent harmonic approximation, for learning first-principles interatomic potentials. This approach enables the prediction of thermodynamic properties over a broad temperature range with first-principles accuracy while requiring training on only a few tens to a few hundreds of atomic configurations. To demonstrate its power, we investigate the thermodynamic and dynamical properties of Li$_2$O, $α$-CsPbI$_3$, and $δ$-CsPbI$_3$, requiring only 44, 256, and 50 total-energy calculations, respectively. Notably, we show that this framework accurately captures the phase diagram of CsPbI$_3$, which explains its spontaneous degradation into the non-absorbing yellow phase, predicting the transition temperature with remarkable accuracy and efficiency. More broadly, the method presented opens a novel route toward accelerated materials engineering under realistic conditions for a wide range of technologically relevant applications, including solid-state batteries, optoelectronic devices, and memristors.

The availability of data from multiple heterogeneous environments has motivated methods that remain reliable under distributional shifts. When the joint distribution of response and predictors varies across environments, the response may still depend on a subset of predictors through an invariant mechanism. Existing methods typically assess candidate invariant sets through pooled stability criteria, treating environmental variation as nuisance. In this paper, we propose a Bayesian framework that explicitly separates a shared response mechanism from environment-specific or response-dependent associations, exploiting heterogeneity as evidence for structure learning. A competitive spike-and-slab prior is designed to force each predictor to compete between invariant and non-invariant spurious effects. Under a tractable working model, we establish invariant model selection consistency and posterior contraction for invariant coefficients. We further study the presence of irrelevant predictors, characterize posterior concentration on an equivalent invariant class, and introduce a post-selection refinement that consistently recovers the minimal invariant model. Simulations and a real application illustrate the robustness and finite-sample efficiency of the proposed method.

Two-dimensional spectroscopy (2DS) is a powerful ultrafast technique for probing electronic and vibrational dynamics in complex microscopic systems. Extracting detailed information on system dynamics and system-bath interactions from 2DS experiments requires precise theoretical simulations for comparison, which motivates the development of numerically-exact and computationally-efficient simulation approaches. Here, we propose a quantum-simulation approach for 2DS based on the bath-engineering technique (BET), which has been successfully employed in quantum simulations of open quantum dynamics. To demonstrate our approach, we first simulate the 2DS of a driven four-level system in chiral enantiodetection, where we also assess the applicability of the center-line slope (CLS) method for extracting time correlation functions (TCFs) from the 2DS. We further apply our approach to the 2DS of ${\rm Rh(CO)_2C_5H_7O_2}$ (RDC) dissolved in chloroform, where the results reproduce the main spectral patterns observed in experiments. Our work provides a numerically-exact and efficient framework for simulating 2DS, and can offer additional insight into the dynamics of open quantum systems.

Nuclear magnetic resonance (NMR) spectroscopy provides unparalleled access to molecular structure and dynamics but is traditionally limited by weak signal strength, requiring large sample volumes and high magnetic fields. Here, we demonstrate nanoscale deuterium (2H) NMR spectroscopy using nitrogen vacancy (NV) centers in diamond, reproducing the characteristic quadrupolar powder line shapes that are present in the conventional bulk NMR spectra. By detecting statistical spin fluctuations from nanometer scale detection volumes, our approach delivers a sensitivity enhancement of six to eight orders of magnitude over inductive detection while operating at magnetic fields two orders of magnitude lower than those used in conventional NMR. Temperature dependent measurements of a deuterated polymer and molecular solid reveal distinct motional averaging and phase transitions with nanoscale sensitivity. Powder-like NV detected 2H NMR establishes a powerful tool for probing molecular dynamics on the nanoscale and, in the ultimate limit, at the single molecule level - capabilities beyond those of most existing spectroscopic techniques.

In this paper, we analyze the solutions of the following non-linear differential-difference equations f^n(z) +ωf^(n-1)f'(z) +p(z)f(z+c) = p_1e^α_1z +p_2e^α_2z and f^n(z)f'(z) +q(z)e^Q(z)f(z+c) = p_1e^α_1z +p_2e^α_2z, where n is a positive integer,ω, p1, p2,α1 & α2 are non-zero constants satisfying α1 not equal to α2, α1/α2 not equal to (n)^+-1, q(z) is a non-vanishing polynomial and Q(z) is a non-constant polynomial.

Dengue virus transmission models commonly assume an exponential distribution for the mosquito extrinsic incubation period (EIP), potentially oversimplifying biological variability. We developed a stochastic mechanistic dengue transmission model comparing epidemic dynamics under commonly assumed exponential (EXP) versus experimentally derived (ED) EIP distributions. Our results show that using an experimentally derived EIP distribution delays and flattens epidemic peaks, resulting in lower but more prolonged peaks, slightly prolongs crisis durations, and reduces peak intensity compared to the exponential assumption, while outbreak probability remains largely unaffected. These differences are modulated by mosquito mortality and human recovery principally. Incorporating experimentally informed EIP distributions enhances the biological realism of models and may improve predictions of dengue epidemic dynamics, informing more effective vector control strategies and public health responses.

The CONUS+ experiment has recently reported the first detection of coherent elastic neutrino-nucleus scattering (CEvNS) of reactor antineutrinos on germanium nuclei and is now entering a precision phase. The dominant uncertainty in the first measurement was the energy scale, which contributed 14% to the uncertainty of the prediction of the combined signal. We present a dedicated neutron activation campaign in which one of the new 2.4 kg CONUS+ germanium detectors was irradiated with a strong 241AmBe source, demonstrating that a contribution below 4% to the uncertainty of signal prediction is achievable. For the first time, the 71Ge M-shell X-ray line was clearly resolved at (158.7+-1.4) eVee, validating the CONUS+ energy reconstruction down to the detection threshold. This validation includes the understanding of the energy scale, the energy resolution, the trigger efficiency, and the correct separation of physical from noise events. These results establish the foundation for a future activation campaign at the Kernkraftwerk Leibstadt reactor site, strengthening the CONUS+ energy calibration and extending its sensitivity to precision CEvNS and beyond Standard Model physics measurements.

We prove that for $C^{1+β}$ flows whose generating vector fields may have singularities, every weakly mixing hyperbolic SRB measure is Bernoullian.

We experimentally, numerically and analytically explore the diffusive transport of active colloidal particles with sensory delay, navigating motility landscapes in which the self-propulsion speed depends on space. We show how the transport properties can be obtained by replacing the space dependence of the self-propulsion speed by a dynamical stochastic switching process in the absence of delay, and extend the theory for systems with finite delayed responses. We obtain analytical results for the mean square displacement and the effective diffusion coefficient which accurately predict experimental measurements and numerical simulations across multiple scales. We show how, within the regime of validity of the delay-extended theory, density patterns and effective diffusion obey universal scaling forms. Our work provides minimal framework describing the transport properties of active swimmers with internal adaptation dynamics in motility landscapes.

We test the hypothesis that simulataneous linear contrasts of multiple variance components equal zero in a Gaussian variance components model via a parametric bootstrap. Applications include but are not limited to nested and crossed designs. The main technical contributions are a computationally efficient decomposition of the normalized residual log-likelihood that does not require the variance components to be non-negative or variance design matrices to be positive semi-definite, a modified Newton method for its minimization, and a method for efficient optimization and sampling under the null hypothesis that certain linear combinations of variance components equal zero. A special case of the proposed procedure is a test for multiple variance components simulataneously equalling zero, for which a likelihood ratio test was not previously available. However, the proposed procedure is significantly more general.

Temporal coherence of driven-dissipative condensates is limited by phase noise. We show that mirror-mediated time-delayed self-feedback enables control of coherence in a trapped exciton-polariton condensate. Reinjecting a small fraction of the emitted light with a tunable delay reveals two regimes set by the ratio of delay time to intrinsic coherence time. Long delays result in pronounced coherence revivals at integer multiples of the feedback delay, while short delays suppress phase diffusion and nearly double the coherence time. A minimal stochastic delayed model reproduces both regimes and supports an interpretation in terms of phase stabilization and delay-induced spectral filtering.