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A non-conserving zero-range process with extensive creation, annihilation and hopping rates is subjected to local resetting. The model is formulated on a large, fully-connected network of states. The states are equipped with a (bounded) fitness level: particles are added to each state at a rate proportional to the fitness level of the state. Moreover, particles are annihilated at a constant rate, and hop at a fixed rate to a uniformly-drawn state in the network. This model has been interpreted in terms of population dynamics: the fitness is the reproductive fitness in a haploid population, and the hopping process models mutation. It has also been interpreted as a model of network growth with a fixed set of nodes (in which particles occupying a state are interpreted as links pointing to this state). In the absence of resetting, the model is known to reach a steady state, which in a certain limit may exhibit a condensate at maximum fitness. If the model is subjected to global resetting by annihilating all particles at Poisson-distributed times, there is no condensation in the steady state. If the system is subjected to local resetting, the occupation numbers of each state are reset to zero at independent random times. These times are distributed according to a Poisson process whose rate (the resetting rate) depends on the fitness. We derive the evolution equation satisfied by the probability law of the occupation numbers. We calculate the average occupation numbers in the steady state. The existence of a condensate is found to depend on the local behavior of the resetting rate at maximum fitness: if the resetting rate vanishes at least linearly at high fitness, a condensate appears at maximum fitness in the limit where the sum of the annihilation and hopping rates is equal to the maximum fitness., Comment: 26 pages, 1 figure; v2: 27 pages, some clarifications, typos corrected, references added; v3: 28 pages, some more clarifications and corrections, references added

The distributed filtering problem sequentially estimates a global state variable using observations from a network of local sensors with different measurement models. In this work, we introduce a novel methodology for distributed nonlinear filtering by combining techniques from transportation of measures, dimensionality reduction, and consensus algorithms. We illustrate our methodology on a satellite pose estimation problem from a network of direct and indirect observers. The numerical results serve as a proof of concept, offering new venues for theoretical and applied research in the domain of distributed filtering., Comment: 7 pages, 2 figures

Neural networks find widespread use in scientific and technological applications, yet their implementations in conventional computers have encountered bottlenecks due to ever-expanding computational needs. Photonic neuromorphic hardware, which manipulates information and represents data continuously in the optical domain, is one of the promising platforms with potential advantages of massive parallelism, ultralow latency, and reduced energy consumption. While linear photonic neural networks are within reach, photonic computing with large-scale optical nonlinear nodes remains largely unexplored. Here, we demonstrate a large-scale, high-performance nonlinear photonic neural system based on a disordered polycrystalline slab composed of lithium niobate nanocrystals. Mediated by random quasi-phase-matching and multiple scattering, linear and nonlinear optical speckle features are generated as the interplay between the simultaneous linear random scattering and the second-harmonic generation, defining a complex neural network in which the second-order nonlinearity acts as internal nonlinear activation functions. Benchmarked against linear random projection, such nonlinear mapping embedded with rich physical computational operations shows improved performance across a large collection of machine learning tasks in image classification, regression, and graph classification with varying complexity. Demonstrating up to 27,648 input and 3,500 nonlinear output nodes, the combination of optical nonlinearity and random scattering serves as a scalable computing engine for diverse applications.

Nonlinear optical effects are used to generate coherent light at wavelengths difficult to reach with lasers. Materials periodically poled or nanostructured in the nonlinear susceptibility in three spatial directions are called 3D nonlinear photonic crystals (NPhCs). They enable enhanced nonlinear optical conversion efficiencies, emission control, and simultaneous generation of nonlinear wavelengths. The chemical inertness of efficient second-order nonlinear materials ($\chi^{(2)}$) prohibited their nanofabrication until 2018. The current method is restricted to top-down laser-based techniques limiting the periodicity along z-axis to 10 um. We demonstrate the first bottom-up fabricated 3D NPhC in sol-gel derived barium titanate by soft-nanoimprint lithography: a woodpile with eight layers and periodicities of 1 um (xy-plane) and 300 nm (z-plane). The surface areas exceed $5.3\cdot 10^4$ um^2, which is two orders of magnitude larger than the state-of-the-art. This study is expected to initiate bottom-up fabrication of 3D NPhCs with a supremely strong and versatile nonlinear response., Comment: 11 pages, 4 figures

In this paper we extend recent developments in computational optimal transport to the setting of Riemannian manifolds. In particular, we show how to learn optimal transport maps from samples that relate probability distributions defined on manifolds. Specializing these maps for sampling conditional probability distributions provides an ensemble approach for solving nonlinear filtering problems defined on such geometries. The proposed computational methodology is illustrated with examples of transport and nonlinear filtering on Lie groups, including the circle $S^1$, the special Euclidean group $SE(2)$, and the special orthogonal group $SO(3)$., Comment: 6 pages, 7 figures

We present a new measurement of the positive muon magnetic anomaly, $a_\mu \equiv (g_\mu - 2)/2$, from the Fermilab Muon $g\!-\!2$ Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, $\tilde{\omega}'^{}_p$, and of the anomalous precession frequency corrected for beam dynamics effects, $\omega_a$. From the ratio $\omega_a / \tilde{\omega}'^{}_p$, together with precisely determined external parameters, we determine $a_\mu = 116\,592\,057(25) \times 10^{-11}$ (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain $a_\mu\text{(FNAL)} = 116\,592\,055(24) \times 10^{-11}$ (0.20 ppm). The new experimental world average is $a_\mu (\text{Exp}) = 116\,592\,059(22)\times 10^{-11}$ (0.19 ppm), which represents a factor of 2 improvement in precision., Comment: 8 pages, 3 figures

The quest of a nonlinear optical material that can be easily nanostructured over a large surface area is still ongoing. Here, we demonstrate a nanoimprinted nonlinear barium titanate 2D nanohole array that shows optical properties of a 2D photonic crystal and metasurface, depending on the direction of the optical axis. The challenge of nanostructuring the inert metal-oxide is resolved by direct soft nanoimprint lithography with sol-gel derived barium titanate enabling critical dimensions of 120 nm with aspect ratios of 5. The nanohole array exhibits a photonic bandgap in the infrared range when probed along the slab axis while lattice resonant states are observed in out-of-plane transmission configuration. The enhanced light-matter interaction from the resonant structure enables to increase the second-harmonic generation in the near-UV by a factor of 18 illustrating the potential in the flexible fabrication technique for barium titanate photonic devices.

We carry on the study of the synthesis problem on data words for fragments of first order logic, and delineate precisely the border between decidability and undecidability.

We present a graph-based model for multiple scattering of light in integrated lithium niobate on insulator (LNOI) networks, which describes an open network of single-mode integrated waveguides with tunable scattering at the network nodes. We first validate the model at small scale with experimental LNOI resonator devices and show consistent agreement between simulated and measured spectral data. Then, the model is used to demonstrate a novel platform for on-chip multiple scattering in large-scale optical networks up to few hundred nodes, with tunable scattering behaviour and tailored disorder. Combining our simple graph-based model with material properties of LNOI, this platform creates new opportunities to control randomness in large optical networks.

Quantum computers comprise elementary logic gates that initialize, control and measure delicate quantum states. One of the most important gates is the controlled-NOT, which is widely used to prepare two-qubit entangled states. The controlled-NOT gate for single photon qubits is normally realized as a six-mode network of individual beamsplitters. This architecture however, utilizes only a small fraction of the circuit for the quantum operation with the majority of the footprint dedicated to routing waveguides. Quantum walks are an alternative photonics platform that use arrays of coupled waveguides with a continuous interaction region instead of discrete gates. While quantum walks have been successful for investigating condensed matter physics, applying the multi-mode interference for logical quantum operations is yet to be shown. Here, we experimentally demonstrate a two-qubit controlled-NOT gate in an array of lithium niobate-on-insulator waveguides. We engineer the tight-binding Hamiltonian of the six evanescently-coupled single-mode waveguides such that the multi-mode interference corresponds to the linear optical controlled-NOT unitary. We measure the two-qubit transfer matrix with $0.938\pm0.003$ fidelity, and we use the gate to generate entangled qubits with $0.945\pm0.002$ fidelity by preparing the control photon in a superposition state. Our results highlight a new application for quantum walks that use a compact multi-mode interaction region to realize large multi-component quantum circuits.