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We consider traveling waves on a surface of an ideal fluid of finite depth. The equation describing Stokes waves in conformal variables formulation are referred to as the Babenko equation. We use a Newton-Conjugate-Gradient method to compute Stokes waves for a range of conformal depths from deep to shallow water. In deep water, we compute eigenvalues of the linearized Babenko equation with Fourier-Floquet-Hill method. The secondary bifurcation points that correspond to double period bifurcations of the Stokes waves are identified on the family of waves. In shallow water, we find solutions that have broad troughs and sharp crests, and which resemble cnoidal or soliton-like solution profiles of the Korteweg-de Vries equation. Regardless of depth, we find that these solutions form a $2\pi/3$ angle at the crest in the limit of large steepness.

Fiber-based long-haul quantum communication would greatly benefit from a robust and deterministically integrated source of quantum state. Here, we report the design, fabrication, and optical characterization of InAs/InP quantum dots in the InP H1 point defect 2D photonic crystal cavity, integrated with the standard single-mode fiber using a micro-transfer printing technique. The device was placed in a compact cryocooler maintaining a cryogenic temperature of 15 K with single-photon emission characterized by $g^{(2)}(0)=0.14(14)$ and reliable and stable emission (intensity fluctuations given by a standard deviation $\sigma = 0.13$), so that an all-fiber based connection between two laboratory nodes through an open area was established and utilized for testing the quantum channel. In this way, we demonstrate a plug-and-play all-fiber single-photon source operating in the third telecom window, where standard telecommunication fiber networks can be used as a low-loss medium.

Stochastic processes model various natural phenomena from disease transmission to stock prices, but simulating and quantifying their uncertainty can be computationally challenging. For example, modeling a Gaussian Process with standard statistical methods incurs an $\mathcal{O}(n^3)$ penalty, and even using state-of-the-art Neural Processes (NPs) incurs an $\mathcal{O}(n^2)$ penalty due to the attention mechanism. We introduce the Transformer Neural Process - Kernel Regression (TNP-KR), a new architecture that incorporates a novel transformer block we call a Kernel Regression Block (KRBlock), which reduces the computational complexity of attention in transformer-based Neural Processes (TNPs) from $\mathcal{O}((n_C+n_T)^2)$ to $O(n_C^2+n_Cn_T)$ by eliminating masked computations, where $n_C$ is the number of context, and $n_T$ is the number of test points, respectively, and a fast attention variant that further reduces all attention calculations to $\mathcal{O}(n_C)$ in space and time complexity. In benchmarks spanning such tasks as meta-regression, Bayesian optimization, and image completion, we demonstrate that the full variant matches the performance of state-of-the-art methods while training faster and scaling two orders of magnitude higher in number of test points, and the fast variant nearly matches that performance while scaling to millions of both test and context points on consumer hardware.

We study two-crested traveling Stokes waves on the surface of an ideal fluid with infinite depth. Following Chen and Saffman (1980), we refer to these waves as class $\mathrm{II}$ Stokes waves. The class $\mathrm{II}$ waves are found from bifurcations from the primary branch of Stokes waves away from the flat surface. These waves are strongly nonlinear, and are disconnected from small-amplitude solutions. Distinct class $\mathrm{II}$ bifurcations are found to occur in the first two oscillations of the velocity versus steepness diagram. The bifurcations in distinct oscillations are not connected via a continuous family of class $\mathrm{II}$ waves. We follow the first two families of class $\mathrm{II}$ waves, which we refer to as the secondary branch (that is primary class $\mathrm{II}$ branch), and the tertiary branch (that is secondary class $\mathrm{II}$ branch). Similar to Stokes waves, the class $\mathrm{II}$ waves follow through a sequence of oscillations in velocity as their steepness rises, and indicate the existence of limiting class $\mathrm{II}$ Stokes waves characterized by a $120$ degree angle at every other wave crest.

In recent years, the hardware implementation of neural networks, leveraging physical coupling and analog neurons has substantially increased in relevance. Such nonlinear and complex physical networks provide significant advantages in speed and energy efficiency, but are potentially susceptible to internal noise when compared to digital emulations of such networks. In this work, we consider how additive and multiplicative Gaussian white noise on the neuronal level can affect the accuracy of the network when applied for specific tasks and including a softmax function in the readout layer. We adapt several noise reduction techniques to the essential setting of classification tasks, which represent a large fraction of neural network computing. We find that these adjusted concepts are highly effective in mitigating the detrimental impact of noise.

We present a study of the multiwavelength (MW) variability of the blazar AO 0235+164 based on the radio-to-$\gamma$-ray data covering a long time period from 1997 to 2023. The radio data are represented by the 1-22 GHz measurements from the RATAN-600 radio telescope, the 5 and 8 GHz data from the RT-32 telescopes, and the 37 GHz data from the RT-22 telescope. The optical measurements in the $R$-band were collected with the 1-m Zeiss-1000 and 0.5-m AS-500/2 telescopes. Additionally we used the archive data at 230~GHz from the SMA and the $\gamma$-ray data in the 0.1-100 GeV band from the Fermi-LAT point source 4FGL-DR2 catalogue. The variability properties during four epochs containing major flares and one epoch of relatively low activity were analysed. A significant correlation ($\geq\!2\sigma$) between the radio, optical, and $\gamma$-ray bands is found for all these periods with time delays from 0 to 1.7 yrs. The relation between time delay and frequency is described by a linear law with a negative slope of -10 day/GHz. The discovered properties of MW variability for the low activity period and for flaring states suggest that the mechanisms dominating the radio-$\gamma$-ray variations are not substantially different. The detected quasi-periodic oscillations of about 6 and 2 years are tentative, as the time span of the observations includes fewer than 4 full cycles for the radio and optical data and only about 3 cycles for the Fermi-LAT data. The physical parameters of the radio jet were obtained using the Hedgehog model applied to the average radio spectrum of AO 0235+164 in the range 0.1-300 GHz. The effectiveness of replacing electrons with protons in the synchrotron radio emission of relativistic jets is shown for describing the nature of blazars and the generation of high energy neutrinos., Comment: Accepted 2024 October 30 for publication in MNRAS

This article addresses the question of reporting a lower confidence band (LCB) for optimal welfare in a policy learning problem. A straightforward procedure inverts a one-sided t-test based on an efficient estimator of the optimal welfare. We show that under empirically relevant data-generating processes, this procedure can be dominated by an LCB corresponding to suboptimal welfare, with the average difference of the order N-1/2. We relate the first-order dominance result to a lack of uniformity in the margin assumption, a standard sufficient condition for debiased inference on the optimal welfare ensuring that the first-best policy is well-separated from the suboptimal ones. Finally, we show that inverting the existing tests from the moment inequality literature produces LCBs that are robust to the non-uniqueness of the optimal policy and easy to compute. We find that this approach performs well empirically in the context of the National JTPA study.

The demand for advanced photonics technology is increasing rapidly, fueled by the necessity for high-performance and cost-effective optical information processing systems extending into the quantum domain. Silicon, benefiting from its mature fabrication processes, stands as an ideal platform. However, its inherent indirect bandgap leads to inefficient light emission. The integration of III-V materials has been proven essential to overcome this drawback. These materials are recognized for their efficient light emission and superior bandgap engineering capabilities, making them indispensable in photonics and beyond. Here, we present the monolithic integration of small-volume III-V nano-heterostructures with silicon via selective area epitaxy in the pyramidal openings etched in (100)-oriented silicon substrate. The precise positioning of the nano-heterostructures is achieved using electron beam lithography. Our atomic resolution imaging and chemical analysis confirms the epitaxial nature of InP growth, revealing well-defined heterointerfaces. Each structure incorporates an InAsP quantum dot-like active medium, and the correlation of the growth parameters with the nanoscale structure was analyzed using advanced electron microscopy. The eight-band k.p calculations demonstrate energy level quantization in three spatial dimensions. Optical characterization shows that heterostructure emission can be engineered to cover the entire telecom wavelength range. Consequently, these InAsP/InP nano-heterostructures could serve as a gain medium for silicon-based hybrid nano-lasers and nano-LEDs and quantum light sources in the telecom wavelength range., Comment: 4 figures, Supplementary Information included

The Rashomon Effect, coined by Leo Breiman, describes the phenomenon that there exist many equally good predictive models for the same dataset. This phenomenon happens for many real datasets and when it does, it sparks both magic and consternation, but mostly magic. In light of the Rashomon Effect, this perspective piece proposes reshaping the way we think about machine learning, particularly for tabular data problems in the nondeterministic (noisy) setting. We address how the Rashomon Effect impacts (1) the existence of simple-yet-accurate models, (2) flexibility to address user preferences, such as fairness and monotonicity, without losing performance, (3) uncertainty in predictions, fairness, and explanations, (4) reliable variable importance, (5) algorithm choice, specifically, providing advanced knowledge of which algorithms might be suitable for a given problem, and (6) public policy. We also discuss a theory of when the Rashomon Effect occurs and why. Our goal is to illustrate how the Rashomon Effect can have a massive impact on the use of machine learning for complex problems in society.

Foundation models are increasingly ubiquitous in our daily lives, used in everyday tasks such as text-image searches, interactions with chatbots, and content generation. As use increases, so does concern over the disparities in performance and fairness of these models for different people in different parts of the world. To assess these growing regional disparities, we present World Wide Dishes, a mixed text and image dataset consisting of 765 dishes, with dish names collected in 131 local languages. World Wide Dishes has been collected purely through human contribution and decentralised means, by creating a website widely distributed through social networks. Using the dataset, we demonstrate a novel means of operationalising capability and representational biases in foundation models such as language models and text-to-image generative models. We enrich these studies with a pilot community review to understand, from a first-person perspective, how these models generate images for people in five African countries and the United States. We find that these models generally do not produce quality text and image outputs of dishes specific to different regions. This is true even for the US, which is typically considered to be more well-resourced in training data - though the generation of US dishes does outperform that of the investigated African countries. The models demonstrate a propensity to produce outputs that are inaccurate as well as culturally misrepresentative, flattening, and insensitive. These failures in capability and representational bias have the potential to further reinforce stereotypes and disproportionately contribute to erasure based on region. The dataset and code are available at https://github.com/oxai/world-wide-dishes/.

Electron beam lithography is a standard method for fabricating photonic nanostructures around semiconductor quantum dots (QDs), which are crucial for efficient single and indistinguishable photon sources in quantum information processing. However, this technique lacks direct 3D control over the nanostructure shape, complicating the design and enlarging the 2D footprint to suppress in-plane photon leakage while directing photons into the collecting lens aperture. Here, we present an alternative approach to employ Xenon plasma-focused ion beam (Xe-PFIB) technology as a reliable method for the 3D shaping of photonic nanostructures containing low-density self-assembled InAs/InP quantum dots emitting in the C-band range of the 3rd telecommunication window. We explore both deterministic and non-deterministic fabrication approaches, resulting in mesas naturally shaped as truncated cones. As a demonstration, we fabricate mesas using a heterogeneously integrated structure with a QDs membrane atop an aluminum mirror and silicon substrate. Finite-difference time-domain (FDTD) simulations show that the angled sidewalls significantly increase photon extraction efficiency, achieving {\eta} = 0.89 for NA = 0.65. We demonstrate experimentally a high purity of pulsed single-photon emission (~99%) and a high extraction efficiency of {\eta} = 0.24, with the latter surpassing the highest reported values obtained using electron beam lithography in the C-band.

We present a study of the radio variability of bright, $S_{1.4}\geq100$ mJy, high-redshift quasars at $z\geq3$ on timescales up to 30-40 years. The study involved simultaneous RATAN-600 measurements at frequencies of 2.3, 4.7, 8.2, 11.2, and 22.3 GHz in 2017-2020. In addition, data from the literature were used. We have found that the variability index, $V_S$, which quantifies the normalized difference between the maximum and minimum flux density while accounting for measurement uncertainties, ranges from 0.02 to 0.96 for the quasars. Approximately half of the objects in the sample exhibit a variability index within the range of 0.25 to 0.50, comparable to that observed in blazars at lower redshifts. The distribution of $V_S$ at 22.3 GHz is significantly different from that at 2.3-11.2 GHz, which may be attributed to the fact that a compact AGN core dominates at the source's rest frame frequencies greater than 45 GHz, leading to higher variability indices obtained at 22.3 GHz (the $V_S$ distribution peaks around 0.4) compared to the lower frequencies (the $V_S$ distribution at 2.3 and 4.7 GHz peaks around 0.1-0.2). Several source groups with distinctive variability characteristics were found using cluster analysis of quasars. We propose 7 new candidates for gigahertz peaked-spectrum (GPS) sources and 5 new megahertz peaked-spectrum (MPS) sources based on their spectrum shape and variability features. Only 6 out of 23 sources previously reported as GPS demonstrate a low variability level typical of classical GPS sources ($V_{S} < 0.25$) at 4.7-22.3 GHz. When excluding the highly variable peaked-spectrum blazars, we expect no more than 20% of the sources in the sample to be GPS candidates and no more than 10% to be MPS candidates., Comment: 56 pages, 20 Figures. Published in MDPI Galaxies

In this paper, we study optimization problems of numerical differentiation and summation methods on classes of univariate functions. Sharp estimates (in order) of the optimal recovery error and information complexity are calculated for these classes. Algorithms are constructed based on the truncation method and Chebyshev polynomials to implement these estimates. Moreover, we establish under what conditions the summation problem is well-posed., Comment: arXiv admin note: text overlap with arXiv:2309.05425, arXiv:2309.09710

Federated learning (FL) allows for collaborative model training across decentralized clients while preserving privacy by avoiding data sharing. However, current FL methods assume conditional independence between client models, limiting the use of priors that capture dependence, such as Gaussian processes (GPs). We introduce the Structured Independence via deep Generative Model Approximation (SIGMA) prior which enables FL for non-factorizable models across clients, expanding the applicability of FL to fields such as spatial statistics, epidemiology, environmental science, and other domains where modeling dependencies is crucial. The SIGMA prior is a pre-trained deep generative model that approximates the desired prior and induces a specified conditional independence structure in the latent variables, creating an approximate model suitable for FL settings. We demonstrate the SIGMA prior's effectiveness on synthetic data and showcase its utility in a real-world example of FL for spatial data, using a conditional autoregressive prior to model spatial dependence across Australia. Our work enables new FL applications in domains where modeling dependent data is essential for accurate predictions and decision-making., Comment: 25 pages, 7 figures, 2 tables

In recent years, more and more works have appeared devoted to the analog (hardware) implementation of artificial neural networks, in which neurons and the connection between them are based not on computer calculations, but on physical principles. Such networks offer improved energy efficiency and, in some cases, scalability, but may be susceptible to internal noise. This paper studies the influence of noise on the functioning of recurrent networks using the example of trained echo state networks (ESNs). The most common reservoir connection matrices were chosen as various topologies of ESNs: random uniform and band matrices with different connectivity. White Gaussian noise was chosen as the influence, and according to the way of its introducing it was additive or multiplicative, as well as correlated or uncorrelated. In the paper, we show that the propagation of noise in reservoir is mainly controlled by the statistical properties of the output connection matrix, namely the mean and the mean square. Depending on these values, more correlated or uncorrelated noise accumulates in the network. We also show that there are conditions under which even noise with an intensity of $10^{-20}$ is already enough to completely lose the useful signal. In the article we show which types of noise are most critical for networks with different activation functions (hyperbolic tangent, sigmoid and linear) and if the network is self-closed., Comment: 10 pages 8 figures

In this article we consider the influence of a periodic sequence of Gaussian pulses on a chimera state in a ring of coupled FitzHugh-Nagumo systems. We found that on the way to complete spatial synchronization one can observe a number of variations of chimera states that are not typical for the parameter range under consideration. For example, the following modes were found: breathing chimera, chimera with intermittency in the incoherent part, traveling chimera with strong intermittency, and others. For comparison, here we also consider the impact of a harmonic influence on the same chimera, and to preserve the generality of the conclusions, we compare the regimes caused by both a purely positive harmonic influence and a positive-negative one., Comment: 7 pages, 5 figures

The problem of optimal recovering high-order mixed derivatives of bivariate functions with finite smoothness is studied. Based on the truncation method, an algorithm for numerical differentiation is constructed, which is order-optimal both in the sense of accuracy and in terms of the amount of involved Galerkin information. Numerical examples are provided to illustrate the fact that our approach can be implemented successfully., Comment: arXiv admin note: substantial text overlap with arXiv:2309.05425, arXiv:2309.09710, arXiv:2405.20020

Context : Understanding the mechanisms that launch and shape powerful relativistic jets from supermassive black holes (SMBHs) in high-redshift active galactic nuclei (AGN) is crucial for probing the co-evolution of SMBHs and galaxies over cosmic time. Aims :We study the high-redshift ($z=3.396$) blazar OH~471 to explore the jet launching mechanism in the early Universe. Methods : Using multi-frequency radio monitoring observations and high-resolution Very Long Baseline Interferometry imaging over three decades, we study the milliarcsecond structure and long-term variability of OH~471. Results : Spectral modelling of the radio flux densities reveals a synchrotron self-absorbed spectrum indicating strong magnetic fields within the compact core. By applying the flux freezing approximation, we estimate the magnetic flux carried by the jet and find that it reaches or exceeds theoretical predictions for jets powered by black hole spin energy via the Blandford-Znajek mechanism. This implies that OH~471 was in a magnetically arrested disk (MAD) state where the magnetic flux accumulated near the horizon regulates the accretion flow, allowing efficient extraction of black hole rotational energy. Conclusions : Our study demonstrates the dominance of MAD accretion in powering the prominent radio flares and relativistic jets observed in the radio-loud AGN OH~471 and statistical studies of large samples of high-redshift AGN will shed light on the role of MAD accretion in launching and accelerating the earliest relativistic jets., Comment: 16 pages, 7 figures, 3 tables

We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with respect to coperiodic and subharmonic perturbations is studied, using new matrix-free numerical methods. We provide evidence for a plethora of conjectures on the nature of the instabilities as the steepest wave is approached, especially with regards to the self-similar recurrence of the stability spectrum near the origin of the spectral plane.

In the rapidly evolving domain of Recommender Systems (RecSys), new algorithms frequently claim state-of-the-art performance based on evaluations over a limited set of arbitrarily selected datasets. However, this approach may fail to holistically reflect their effectiveness due to the significant impact of dataset characteristics on algorithm performance. Addressing this deficiency, this paper introduces a novel benchmarking methodology to facilitate a fair and robust comparison of RecSys algorithms, thereby advancing evaluation practices. By utilizing a diverse set of $30$ open datasets, including two introduced in this work, and evaluating $11$ collaborative filtering algorithms across $9$ metrics, we critically examine the influence of dataset characteristics on algorithm performance. We further investigate the feasibility of aggregating outcomes from multiple datasets into a unified ranking. Through rigorous experimental analysis, we validate the reliability of our methodology under the variability of datasets, offering a benchmarking strategy that balances quality and computational demands. This methodology enables a fair yet effective means of evaluating RecSys algorithms, providing valuable guidance for future research endeavors., Comment: 8 pages with 11 figures

We present an optical-to-radio study of the BL Lac object S4 0954+658 observations during 1998-2023. The measurements were obtained with the SAO RAS Zeiss-1000 1-m and AS-500/2 0.5-m telescopes in 2003-2023, with the RATAN-600 radio telescope at 1.25 (0.96, 1.1), 2.3, 4.7 (3.7, 3.9), 8.2 (7.7), 11.2, 22.3 (21.7) GHz in 1998-2023, with the IAA RAS RT-32 Zelenchukskaya and Badary telescopes at 5.05 and 8.63 GHz in 2020--2023, and with the RT-22 single-dish telescope of CrAO RAS at 36.8 GHz in 2009-2023. In this period the blazar had been showing extremely high broadband activity with the variability amplitude of flux densities up to 70-100% both in the optical and radio domains. In the period of 2014-2023 the blazar had been showing the historically highest activity in the radio wavelengths, and we detected multiple radio flares of varying amplitude and duration. The large flares last on average from 0.3 to 1 year at 22-36.8 GHz and slightly longer at 5-11.2 GHz. The optical flares are shorter and last 7-50 days. In the most active epoch of 2018-2023 the characteristic time scale $\tau$ of variation at 5-22 GHz is about 100 days and about 1000 days for the state with lower activity in 2009-2014. We found a general correlation between the optical, radio, and $\gamma$-ray flux variations, which suggests that we observe the same photon population from different emission regions. We estimated linear size of this region as 0.5-2 pc for different epochs. A broadband two components radio spectrum of S4 0954+658 jet was modelled by using both electrons and protons as emitting particles. It is shown that the synchrotron radio waves in this AGN may be generated by relativistic protons., Comment: Published in Astrophysical Bulletin Vol.78, N4 (2023)