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We present a long-term strong correlation between millimeter (mm) radio and $\gamma$-ray emission in the flat-spectrum radio quasar (FSRQ) PKS 1424-418. The mm$-\gamma$-ray connection in blazars is generally thought to originate from the relativistic jet close to the central engine. We confirm a unique long-lasting mm$-\gamma$-ray correlation of PKS 1424-418 by using detailed correlation analyses and statistical tests, and we find its physical meaning in the source. We employed ~8.5 yr of (sub)mm and $\gamma$-ray light curves observed by ALMA and Fermi-LAT, respectively. From linear and cross-correlation analyses between the light curves, we found a significant, strong mm$-\gamma$-ray correlation over the whole period. We did not find any notable time delay within the uncertainties for the mm$-\gamma$-ray correlation, which means zero lag. The mm wave spectral index values (S$_{\nu}$ $\propto$ $\nu_{\alpha}$) between the band 3 and 7 flux densities indicate a time-variable opacity of the source at (sub)mm wavelengths. Interestingly, the mm wave spectral index becomes temporarily flatter (i.e., $\alpha$ > $-$0.5) when the source flares in the $\gamma$-rays. We relate our results with the jet of PKS 1424-418, and we discuss the origin of the $\gamma$-rays and opacity of the inner (sub)parsec-scale jet regions., Comment: 11 pages, 11 figures, accepted for publication in A&A, in press

Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function's internal mechanisms. One promising approach to address this is the Stochastic Order Oracle Concept. This concept, similar to other Order Oracle Concepts, relies solely on relative comparisons of function values without requiring access to the exact values. This paper presents a novel, improved estimation of the covariance matrix for the asymptotic convergence of the Stochastic Order Oracle Concept. Our work surpasses existing research in this domain by offering a more accurate estimation of asymptotic convergence rate. Finally, numerical experiments validate our theoretical findings, providing strong empirical support for our proposed approach.

Frequently, when dealing with many machine learning models, optimization problems appear to be challenging due to a limited understanding of the constructions and characterizations of the objective functions in these problems. Therefore, major complications arise when dealing with first-order algorithms, in which gradient computations are challenging or even impossible in various scenarios. For this reason, we resort to derivative-free methods (zeroth-order methods). This paper is devoted to an approach to minimizing quasi-convex functions using a recently proposed comparison oracle only. This oracle compares function values at two points and tells which is larger, thus by the proposed approach, the comparisons are all we need to solve the optimization problem under consideration. The proposed algorithm to solve the considered problem is based on the technique of comparison-based gradient direction estimation and the comparison-based approximation normalized gradient descent. The normalized gradient descent algorithm is an adaptation of gradient descent, which updates according to the direction of the gradients, rather than the gradients themselves. We proved the convergence rate of the proposed algorithm when the objective function is smooth and strictly quasi-convex in $\mathbb{R}^n$, this algorithm needs $\mathcal{O}\left( \left(n D^2/\varepsilon^2 \right) \log\left(n D / \varepsilon\right)\right)$ comparison queries to find an $\varepsilon$-approximate of the optimal solution, where $D$ is an upper bound of the distance between all generated iteration points and an optimal solution.

We present a novel gradient-free algorithm to solve a convex stochastic optimization problem, such as those encountered in medicine, physics, and machine learning (e.g., adversarial multi-armed bandit problem), where the objective function can only be computed through numerical simulation, either as the result of a real experiment or as feedback given by the function evaluations from an adversary. Thus we suppose that only a black-box access to the function values of the objective is available, possibly corrupted by adversarial noise: deterministic or stochastic. The noisy setup can arise naturally from modeling randomness within a simulation or by computer discretization, or when exact values of function are forbidden due to privacy issues, or when solving non-convex problems as convex ones with an inexact function oracle. By exploiting higher-order smoothness, fulfilled, e.g., in logistic regression, we improve the performance of zero-order methods developed under the assumption of classical smoothness (or having a Lipschitz gradient). The proposed algorithm enjoys optimal oracle complexity and is designed under an overparameterization setup, i.e., when the number of model parameters is much larger than the size of the training dataset. Overparametrized models fit to the training data perfectly while also having good generalization and outperforming underparameterized models on unseen data. We provide convergence guarantees for the proposed algorithm under both types of noise. Moreover, we estimate the maximum permissible adversarial noise level that maintains the desired accuracy in the Euclidean setup, and then we extend our results to a non-Euclidean setup. Our theoretical results are verified on the logistic regression problem., Comment: 10 pages, 1 figure

The first very long baseline interferometry (VLBI) detections at 870$\mu$m wavelength (345$\,$GHz frequency) are reported, achieving the highest diffraction-limited angular resolution yet obtained from the surface of the Earth, and the highest-frequency example of the VLBI technique to date. These include strong detections for multiple sources observed on inter-continental baselines between telescopes in Chile, Hawaii, and Spain, obtained during observations in October 2018. The longest-baseline detections approach 11$\,$G$\lambda$ corresponding to an angular resolution, or fringe spacing, of 19$\mu$as. The Allan deviation of the visibility phase at 870$\mu$m is comparable to that at 1.3$\,$mm on the relevant integration time scales between 2 and 100$\,$s. The detections confirm that the sensitivity and signal chain stability of stations in the Event Horizon Telescope (EHT) array are suitable for VLBI observations at 870$\mu$m. Operation at this short wavelength, combined with anticipated enhancements of the EHT, will lead to a unique high angular resolution instrument for black hole studies, capable of resolving the event horizons of supermassive black holes in both space and time., Comment: Corresponding author: S. Doeleman

The challenges of black box optimization arise due to imprecise responses and limited output information. This article describes new results on optimizing multivariable functions using an Order Oracle, which provides access only to the order between function values and with some small errors. We obtained convergence rate estimates for the one-dimensional search method (golden ratio method) under the condition of oracle inaccuracy, as well as convergence results for the algorithm on a "square" (also with noise), which outperforms its alternatives. The results obtained are similar to those in problems with oracles providing significantly more information about the optimized function. Additionally, the practical application of the algorithm has been demonstrated in maximizing a preference function, where the parameters are the acidity and sweetness of the drink. This function is expected to be convex or at least quasi-convex.

The galaxy M87 is one of the prime targets for high resolution radio imaging pursuing the ringlike shadow of its supermassive black hole, the innermost regions of accretion flow, and the formation of the relativistic jet. However, it remains challenging to observe both jointly. Only recently, global mm-VLBI array (GMVA)+ALMA observations at 86 GHz in 2018 were able to reconstruct the M87 black hole shadow and the extended jet emission simultaneously. In order to analyze the ring and jet of M87, conventional CLEAN algorithms were mainly employed alongside the RML method SMILI in the previous work. To test the robustness of the reconstructed structures of M87 GMVA+ALMA observations at 86GHz, we estimate the ring diameter, width, and the extended jet emission with the possible central spine by two different novel imaging algorithms: resolve and DoG-HiT. Overall reconstructions are consistent with the results reported in the previous paper. The ring structure of the M87 is resolved at higher resolution and the posterior distribution of M87 ring features is explored. The resolve images show that the ring diameter is 60.9 +- 2.2 muas and width is 16.0 +- 0.9 muas. The ring diameter is 61.0 muas and width is 20.6 muas by DoG-HiT. The ring diameter is therefore in agreement with the estimation (64+4-8 muas) by SMILI and the geometrical modeling. Two bright spots in the ring are reconstructed by four independent imaging methods, the substructure in the ring is therefore most likely originated from the data. A consistent limb-brightened jet structure is reconstructed by resolve and DoG-HiT, albeit with a less pronounced central spine. Modern data-driven imaging methods confirm the ring and jet structure in M87, complementing traditional VLBI methods with novel perspectives on the significance of recovered features. They confirm the result of the previous report., Comment: submitted to A&A

Self-calibration methods with the CLEAN algorithm have been widely employed in Very Long Baseline Interferometry (VLBI) data processing in order to correct antenna-based amplitude and phase corruptions present in the data. However, human interaction during the conventional CLEAN self-calibration process can impose a strong effective prior, which in turn may produce artifacts within the final image and hinder the reproducibility of final results. In this work, we aim to demonstrate a combined self-calibration and imaging method for VLBI data in a Bayesian inference framework. The method corrects for amplitude and phase gains for each antenna and polarization mode by inferring the temporal correlation of the gain solutions. We use Stokes I data of M87 taken with the Very Long Baseline Array (VLBA) at 43GHz, pre-calibrated using the rPICARD CASA-based pipeline. For antenna-based gain calibration and imaging, we use the Bayesian imaging software resolve. To estimate gain and image uncertainties, we use a Variational Inference method. We obtain a high-resolution M87 Stokes I image at 43GHz in conjunction with antenna-based gain solutions using our Bayesian self-calibration and imaging method. The core with counter-jet structure is better resolved, and extended jet emission is better described compared to the CLEAN reconstruction. Furthermore, uncertainty estimation of the image and antenna-based gains allows us to quantify the reliability of the result. Our Bayesian self-calibration and imaging method is able to reconstruct robust and reproducible Stokes I images and gain solutions with uncertainty estimation by taking into account the uncertainty information in the data., Comment: accepted for publication in A&A

In traditional neural network architectures, a multilayer perceptron (MLP) is typically employed as a classification block following the feature extraction stage. However, the Kolmogorov-Arnold Network (KAN) presents a promising alternative to MLP, offering the potential to enhance prediction accuracy. In this paper, we propose the replacement of linear and convolutional layers of traditional networks with KAN-based counterparts. These modifications allowed us to significantly increase the per-pixel classification accuracy for hyperspectral remote-sensing images. We modified seven different neural network architectures for hyperspectral image classification and observed a substantial improvement in the classification accuracy across all the networks. The architectures considered in the paper include baseline MLP, state-of-the-art 1D (1DCNN) and 3D convolutional (two different 3DCNN, NM3DCNN), and transformer (SSFTT) architectures, as well as newly proposed M1DCNN. The greatest effect was achieved for convolutional networks working exclusively on spectral data, and the best classification quality was achieved using a KAN-based transformer architecture. All the experiments were conducted using seven openly available hyperspectral datasets. Our code is available at https://github.com/f-neumann77/HyperKAN.

This paper is devoted to the study (common in many applications) of the black-box optimization problem, where the black-box represents a gradient-free oracle $\tilde{f} = f(x) + \xi$ providing the objective function value with some stochastic noise. Assuming that the objective function is $\mu$-strongly convex, and also not just $L$-smooth, but has a higher order of smoothness ($\beta \geq 2$) we provide a novel optimization method: Zero-Order Accelerated Batched Stochastic Gradient Descent, whose theoretical analysis closes the question regarding the iteration complexity, achieving optimal estimates. Moreover, we provide a thorough analysis of the maximum noise level, and show under which condition the maximum noise level will take into account information about batch size $B$ as well as information about the smoothness order of the function $\beta$.

A novel method to reconstruct the energy of hadronic showers in the CMS High Granularity Calorimeter (HGCAL) is presented. The HGCAL is a sampling calorimeter with very fine transverse and longitudinal granularity. The active media are silicon sensors and scintillator tiles readout by SiPMs and the absorbers are a combination of lead and Cu/CuW in the electromagnetic section, and steel in the hadronic section. The shower reconstruction method is based on graph neural networks and it makes use of a dynamic reduction network architecture. It is shown that the algorithm is able to capture and mitigate the main effects that normally hinder the reconstruction of hadronic showers using classical reconstruction methods, by compensating for fluctuations in the multiplicity, energy, and spatial distributions of the shower's constituents. The performance of the algorithm is evaluated using test beam data collected in 2018 prototype of the CMS HGCAL accompanied by a section of the CALICE AHCAL prototype. The capability of the method to mitigate the impact of energy leakage from the calorimeter is also demonstrated., Comment: Prepared for submission to JINST

An optimal protocol for the current-induced switching of a perpendicularly magnetized nanoelement placed on the surface of a topological insulator is presented. The time dependence of both in-plane components of the surface current that induces the magnetization reversal via Dirac spin-orbit torque with minimal Joule heating is derived analytically as a function of the required switching time and material properties. It is demonstrated that a particularly energy-efficient switching is realized for vanishing dampinglike torque. The optimal reversal time providing a tradeoff between the switching speed and energy efficiency is derived. The obtained switching protocol is contrasted with the one realized in heavy-metal systems. Topological insulators provide a highly tunable platform for the realization of energy-efficient magnetization switching.

This paper focuses on solving a stochastic saddle point problem (SPP) under an overparameterized regime for the case, when the gradient computation is impractical. As an intermediate step, we generalize Same-sample Stochastic Extra-gradient algorithm (Gorbunov et al., 2022) to a biased oracle and estimate novel convergence rates. As the result of the paper we introduce an algorithm, which uses gradient approximation instead of a gradient oracle. We also conduct an analysis to find the maximum admissible level of adversarial noise and the optimal number of iterations at which our algorithm can guarantee achieving the desired accuracy.

In very long baseline interferometry (VLBI) the combination of multiple antennas permits the synthesis of a virtual telescope with a larger diameter and consequently higher resolution than the individual antennae. Yet, due to the sparse nature of the array, recovering an image from the observed data is a challenging ill-posed inverse problem. The VLBI community is interested in not only recovering an image in total intensity from interferometric data, but also to obtain results in the polarimetric and the temporal domain. Only a few algorithms are able to work in all these domains simultaneously. In particular, the algorithms based on optimization that consider various penalty terms specific to static total intensity imaging, time-variability and polarimetry are restricted to grids the domain of the objective function. In this work we present a novel algorithm, multiobjective particle swarm optimization, that is able to recover the optimal weights without any space-gridding, and to obtain the marginal contribution of each the playing terms. To this end, we utilize multiobjective optimization together with particle swarm metaheuristics. We let the swarm of weights to converge together to the best position. We evaluate our algorithm with representative synthetic data sets focused on the instrumental configuration of the Event Horizon Telescope Collaboration and its planned successors. We successfully recover the polarimetric, static and time-dynamic signature of the ground truth movie, even with relative sparsity, and a set of realistic data corruptions. This is a novel, fast, weighting space gridding-free algorithm that successfully recovers static and dynamic polarimetric reconstructions. Compared to Regularized Maximum Likelihood methods, it avoids the need for parameter surveys, and it is not limited to the number of pixels such as recently proposed multiobjective imaging algorithms., Comment: Accepted in A&A

The Spin Physics Detector collaboration proposes to install a universal detector in the second interaction point of the NICA collider under construction (JINR, Dubna) to study the spin structure of the proton and deuteron and other spin-related phenomena using a unique possibility to operate with polarized proton and deuteron beams at a collision energy up to 27 GeV and a luminosity up to $10^{32}$ cm$^{-2}$ s$^{-1}$. As the main goal, the experiment aims to provide access to the gluon TMD PDFs in the proton and deuteron, as well as the gluon transversity distribution and tensor PDFs in the deuteron, via the measurement of specific single and double spin asymmetries using different complementary probes such as charmonia, open charm, and prompt photon production processes. Other polarized and unpolarized physics is possible, especially at the first stage of NICA operation with reduced luminosity and collision energy of the proton and ion beams. This document is dedicated exclusively to technical issues of the SPD setup construction.

The flat-spectrum radio quasar 3C 345 has been showing gamma-ray activity since the mid-2000s along with activity across the electromagnetic spectrum. A gamma-ray burst in 2009 was successfully linked to relativistic outflow in 43 GHz VLBI observations and has since been analyzed also using single dish measurements. A multi-wavelength follow-up VLBI observation to the 2009 flare in conjunction with 43 GHz catalogue data from the VLBA-BU-BLAZAR and BEAM-ME programs are analyzed in this study in the context of the long-term evolution of the source. We aim to probe the innermost few milli-arcseconds of the ultracompact 3C 345 jet. In the process, we analyze the long-term kinematics of the inner jet and discuss the magnetic field morphology at different scales, as well as the origin of the gamma-ray emission. New observations at 23, 43, and 86 GHz took place on ten epochs between 2017 and 2019. We calibrate the 30 data sets using the rPicard pipeline, image them in Difmap and carry out polarization calibration using the GPCAL pipeline. We complement our VLBI data with ancillay VLBI maps at multiple frequencies, as well as 43 GHz observations carried out in the framework of the BEAM-ME and VLBA-BU-BLAZAR monitoring programs. We find multiple distinct component paths in the inner jet, forming a helical geometry. The helix is anchored at a stationary feature some 0.16 mas from the 43 GHz VLBI core and has a timescale of about 8 years. The characteristic bends in the jet morphology are caused by variations in the component ejection angle. We confirm the result of previous studies that the gamma-ray emission is produced (or caused) by relativistic outflow and violent interactions within the jet.

Stability domains (i.e. pump frequency detuning range) of a single dark soliton (or platicon) and dark breather in high-Q Kerr optical microresonators with normal group velocity dispersion is studied for a wide range of pump amplitudes within the framework of the Lugiato-Lefever model. The effect of the significant fragmentation of the stability domains at high pump intensities is revealed. The existence of stable drifting dark solitons (platicons) is demonstrated above the threshold pump amplitude value. Properties of drifting solitons are investigated., Comment: 28 pages, 13 figures; to appear in PRA

Frequently, the burgeoning field of black-box optimization encounters challenges due to a limited understanding of the mechanisms of the objective function. To address such problems, in this work we focus on the deterministic concept of Order Oracle, which only utilizes order access between function values (possibly with some bounded noise), but without assuming access to their values. As theoretical results, we propose a new approach to create non-accelerated optimization algorithms (obtained by integrating Order Oracle into existing optimization "tools") in non-convex, convex, and strongly convex settings that are as good as both SOTA coordinate algorithms with first-order oracle and SOTA algorithms with Order Oracle up to logarithm factor. Moreover, using the proposed approach, we provide the first accelerated optimization algorithm using the Order Oracle. And also, using an already different approach we provide the asymptotic convergence of the first algorithm with the stochastic Order Oracle concept. Finally, our theoretical results demonstrate effectiveness of proposed algorithms through numerical experiments.

We present here Multem 3, an updated and revised version of Multem 2, which syntax has been upgraded to Fortran 2018, with the source code being divided into modules. Multem 3 is equipped with LAPACK, the state-of-the art Faddeeva complex error function routine, and the Bessel function package AMOS. The amendments significantly improve both the speed, convergence, and precision of Multem 2. Increased stability allows to freely increase the cut-off value LMAX on the number of spherical vector wave functions and the cut-off value RMAX controlling the maximal length of reciprocal vectors taken into consideration. An immediate bonus is that Multem 3 can be reliably used to describe bound states in the continuum (BICs). To ensure convergence of the layer coupling scheme, it appears that appreciably larger values of convergence paramaters LMAX and RMAX are required than those reported in numerous published work in the past using Multem 2. We hope that Multem 3 will become a reliable and fast alternative to generic commercial software, such as COMSOL Multiphysics, CST Microwave Studio, or Ansys HFSS, and that it will become the code of choice for various optimization tasks for a large number of research groups. The improvements concern the core part of Multem 2, which is common to the extensions of Multem 2 for acoustic and elastic multiple scattering and to the original layer-Kohn-Korringa-Rostocker (LKKR) code. Therefore, the enhancements presented here can be readily applied to the above codes as well.

In this paper, we consider non-smooth convex optimization with a zeroth-order oracle corrupted by symmetric stochastic noise. Unlike the existing high-probability results requiring the noise to have bounded $\kappa$-th moment with $\kappa \in (1,2]$, our results allow even heavier noise with any $\kappa > 0$, e.g., the noise distribution can have unbounded expectation. Our convergence rates match the best-known ones for the case of the bounded variance. To achieve this, we build the median gradient estimate with bounded second moment as the mini-batched median of the sampled gradient differences. We apply this technique to the stochastic multi-armed bandit problem with heavy-tailed distribution of rewards and achieve $\tilde{O}(\sqrt{dT})$ regret. We demonstrate the performance of our zeroth-order and MAB algorithms for different $\kappa$ on synthetic and real-world data. Our methods do not lose to SOTA approaches, moreover, they dramatically outperform SOTA for $\kappa \leq 1$.

Three machine learning models are used to perform jet origin classification. These models are optimized for deployment on a field-programmable gate array device. In this context, we demonstrate how latency and resource consumption scale with the input size and choice of algorithm. Moreover, the models proposed here are designed to work on the type of data and under the foreseen conditions at the CERN LHC during its high-luminosity phase. Through quantization-aware training and efficient synthetization for a specific field programmable gate array, we show that $O(100)$ ns inference of complex architectures such as Deep Sets and Interaction Networks is feasible at a relatively low computational resource cost., Comment: 13 pages, 3 figures, 3 tables. Mach. Learn.: Sci. Technol (2024)

3C84 is a nearby radio source with a complex total intensity structure, showing linear polarisation and spectral patterns. A detailed investigation of the central engine region necessitates the use of VLBI above the hitherto available maximum frequency of 86GHz. Using ultrahigh resolution VLBI observations at the highest available frequency of 228GHz, we aim to directly detect compact structures and understand the physical conditions in the compact region of 3C84. We used EHT 228GHz observations and, given the limited (u,v)-coverage, applied geometric model fitting to the data. We also employed quasi-simultaneously observed, multi-frequency VLBI data for the source in order to carry out a comprehensive analysis of the core structure. We report the detection of a highly ordered, strong magnetic field around the central, SMBH of 3C84. The brightness temperature analysis suggests that the system is in equipartition. We determined a turnover frequency of $\nu_m=(113\pm4)$GHz, a corresponding synchrotron self-absorbed magnetic field of $B_{SSA}=(2.9\pm1.6)$G, and an equipartition magnetic field of $B_{eq}=(5.2\pm0.6)$G. Three components are resolved with the highest fractional polarisation detected for this object ($m_\textrm{net}=(17.0\pm3.9)$%). The positions of the components are compatible with those seen in low-frequency VLBI observations since 2017-2018. We report a steeply negative slope of the spectrum at 228GHz. We used these findings to test models of jet formation, propagation, and Faraday rotation in 3C84. The findings of our investigation into different flow geometries and black hole spins support an advection-dominated accretion flow in a magnetically arrested state around a rapidly rotating supermassive black hole as a model of the jet-launching system in the core of 3C84. However, systematic uncertainties due to the limited (u,v)-coverage, however, cannot be ignored., Comment: 15 pages, 6 figures, published in A&A

In Very Long Baseline Interferometry (VLBI), signals from multiple antennas combine to create a sparsely sampled virtual aperture, its effective diameter determined by the largest antenna separation. The inherent sparsity makes VLBI imaging an ill-posed inverse problem, prompting the use of algorithms like the Multiobjective Evolutionary Algorithm by Decomposition (MOEA/D), as proposed in the first paper of this series. This study focuses on extending MOEA/D to polarimetric and time dynamic reconstructions, particularly relevant for the VLBI community and the Event Horizon Telescope Collaboration (EHTC). MOEA/D's success in providing a unique, fast, and largely unsupervised representation of image structure serves as the basis for exploring these extensions. The extension involves incorporating penalty terms specific to total intensity imaging, time-variable, and polarimetric variants within MOEA/D's multiobjective, evolutionary framework. The Pareto front, representing non-dominated solutions, is computed, revealing clusters of proximities. Testing MOEA/D with synthetic datasets representative of EHTC's main targets demonstrates successful recovery of polarimetric and time-dynamic signatures despite sparsity and realistic data corruptions. MOEA/D's extension proves effective in the anticipated EHTC setting, offering an alternative and independent claim to existing methods. It not only explores the problem globally but also eliminates the need for parameter surveys, distinguishing it from Regularized Maximum Likelihood (RML) methods. MOEA/D emerges as a novel and useful tool for robustly characterizing polarimetric and dynamic signatures in VLBI datasets with minimal user-based choices. Future work aims to address the last remaining limitation of MOEA/D, specifically regarding the number of pixels and numerical performance, to establish it within the VLBI data reduction pipeline., Comment: Both first authors have contributed equally to this work. To appear in A&A

One of the most well-known extragalactic sources in the sky, quasar 3C 454.3, shows a curved parsec-scale jet that has been exhaustively monitored with very-long-baseline interferometry (VLBI) over the recent years. In this work, we present a comprehensive analysis of four years of high-frequency VLBI observations at 43 GHz and 86 GHz, between 2013-2017, in total intensity and linear polarization. The images obtained from these observations enabled us to study the jet structure and the magnetic field topology of the source on spatial scales down to 4.6 parsec in projected distance. The kinematic analysis reveals the abrupt vanishing of at least four new superluminal jet features in a characteristic jet region (i.e., region C), which is located at an approximate distance of 0.6 milliarcseconds from the VLBI core. Our results support a model in which the jet bends, directing the relativistic plasma flow almost perfectly toward our line of sight, co-spatially with the region where components appear to stop., Comment: 15 pages, 7 figures

We present total intensity and linear polarization images of OJ287 at 1.68GHz, obtained through space-based VLBI observations with RadioAstron on April 16, 2016. The observations were conducted using a ground array consisting of the VLBA and the EVN. Ground-space fringes were detected with a maximum projected baseline length of 5.6 Earth's diameter, resulting in an angular resolution of 530 uas. With this unprecedented resolution at such a low frequency, the progressively bending jet structure of OJ287 has been resolved up to 10 pc of the projected distance from the radio core. In comparison with close-in-time VLBI observations at 15, 43, 86 GHz from MOJAVE and VLBA-BU-BLAZAR monitoring projects, we obtain the spectral index map showing the opaque core and optically thin jet components. The optically thick core has a brightness temperature of 10$^{13}$ K, and is further resolved into two sub-components at higher frequencies labeled C1 and C2. These sub-components exhibit a transition from optically thick to thin, with a SSA turnover frequency estimated to be 33 and 11.5 GHz, and a turnover flux density 4 and 0.7 Jy, respectively. Assuming a Doppler boosting factor of 10, the SSA values provide the estimate of the magnetic field strengths from SSA of 3.4 G for C1 and 1.0 G for C2. The magnetic field strengths assuming equipartition arguments are also estimated as 2.6 G and 1.6 G, respectively. The integrated degree of linear polarization is found to be approximately 2.5 %, with the electric vector position angle being well aligned with the local jet direction at the core region. This alignment suggests a predominant toroidal magnetic field, which is in agreement with the jet formation model that requires a helical magnetic field anchored to either the black hole ergosphere or the accretion disk. Further downstream, the jet seems to be predominantly threaded by a poloidal magnetic field., Comment: 15 pages, 11 figures, 3 tables

We analyze a single-epoch Global mm-VLBI Array (GMVA) observation of the blazar BL Lacertae (BL Lac) at 86 GHz from April 2021. The participation of the upgraded, phased Northern Extended Millimetre Array (NOEMA) adds additional sensitivity to the GMVA, which has facilitated the imaging of BL Lac during an unprecedentedly strong $\gamma$-ray flare. We aim to explore the nature of the inner subparsec jet of BL Lac and the impact of the NOEMA participation in the observation. For the data reduction, we employed two advanced automatic pipelines: rPICARD for the flux density calibration as well as the model-agnostic signal stabilization and GPCAL for the antenna leakage calibration. The conventional hybrid imaging (CLEAN + amplitude and phase self-calibration) was applied to the calibrated visibilities to generate final VLBI images. We performed a ridge-line analysis and Gaussian model-fits on the final jet image to derive the jet parameters. In our data, the presence of NOEMA improves the image sensitivity by a factor of 2.5. The jet shows a clear wiggling structure within 0.4 mas from the core. Our ridge-line analysis suggests the presence of a helical jet structure (i.e., a sinusoidal pattern). Six circular Gaussian components were fitted to the inner jet region. We estimated an apparent brightness temperature of $\sim$3 $\times$ 10$^{12}$ K in the two innermost components. They are likely to be highly boosted by relativistic beaming effect. We find four significant polarized knots in the jet. Interestingly, two of them are located in the core region. Finally, we suggest a number of physical scenarios to interpret our results., Comment: 11 pages, 12 figures, 3 tables, accepted for publication in A&A, in press

The paper presents a review of the state-of-the-art of subgradient and accelerated methods of convex optimization, including in the presence of disturbances and access to various information about the objective function (function value, gradient, stochastic gradient, higher derivatives). For nonconvex problems, the Polak-Lojasiewicz condition is considered and a review of the main results is given. The behavior of numerical methods in the presence of sharp minima is considered. The purpose of this survey is to show the influence of the works of B.T. Polyak (1935 -- 2023) on gradient optimization methods and their neighborhoods on the modern development of numerical optimization methods., Comment: in Russian language

The Next Generation Very Large Array (ngVLA) is a planned radio interferometer providing unprecedented sensitivity at wavelengths between 21 cm and 3 mm. Its 263 antenna element array will be spatially distributed across North America to enable both superb low surface brightness recovery and sub-milliarcsecond angular resolution imaging. The project was developed by the international astronomy community under the lead of the National Radio Astronomy Observatory (NRAO), and is anticipated to be built between 2027 and 2037. Two workshops have been held in 2022 and 2023 with the goal to discuss and consolidate the scientific interests in the ngVLA within the German astronomical community. This community paper constitutes a collection of 48 science ideas which the German community aims to pursue with the ngVLA in the 2030s. This is not a complete list and the ideas are not developed at the level of a "Science Book", such that the present document is mainly meant provide a basis for further discussion within the community. As such, additional contributions are welcome, and will be considered for inclusion in future revisions., Comment: Version 2.0 (status June 18, 2024): 169 pages, comments and future contributions welcome [v2.0: 7 new science cases added, some minor revisions to other chapters]

Supermassive black holes at the centre of active galactic nuclei power some of the most luminous objects in the Universe. Typically, very long baseline interferometric (VLBI) observations of blazars have revealed only funnel-like morphologies with little information of the ejected plasma internal structure, or lacked the sufficient dynamic range to reconstruct the extended jet emission. Here we show microarcsecond-scale angular resolution images of the blazar 3C 279 obtained at 22 GHz with the space VLBI mission RadioAstron, which allowed us to resolve the jet transversely and reveal several filaments produced by plasma instabilities in a kinetically dominated flow. Our high angular resolution and dynamic range image suggests that emission features traveling down the jet may manifest as a result of differential Doppler-boosting within the filaments, as opposed to the standard shock-in-jet model invoked to explain blazar jet radio variability. Moreover, we infer that the filaments in 3C 279 are possibly threaded by a helical magnetic field rotating clockwise, as seen in the direction of the flow motion, with an intrinsic helix pitch angle of ~45 degrees in a jet with a Lorentz factor of ~13 at the time of observation., Comment: 15 pages, 7 figures. Initial version of an article published in Nature Astronomy

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the batched accelerated gradient method, was proposed in (Gasnikov et. al., 2022). This optimality is defined in terms of iteration and oracle complexity, as well as the maximal admissible level of adversarial noise. However, the assumption of finite variance is burdensome and it might not hold in many practical scenarios. To address this, we demonstrate how to adapt a refined clipped version of the accelerated gradient (Stochastic Similar Triangles) method from (Sadiev et al., 2023) for a two-point zero-order oracle. This adaptation entails extending the batching technique to accommodate infinite variance -- a non-trivial task that stands as a distinct contribution of this paper.

In this paper, we study the standard formulation of an optimization problem when the computation of gradient is not available. Such a problem can be classified as a "black box" optimization problem, since the oracle returns only the value of the objective function at the requested point, possibly with some stochastic noise. Assuming convex, and higher-order of smoothness of the objective function, this paper provides a zero-order accelerated stochastic gradient descent (ZO-AccSGD) method for solving this problem, which exploits the higher-order of smoothness information via kernel approximation. As theoretical results, we show that the ZO-AccSGD algorithm proposed in this paper improves the convergence results of state-of-the-art (SOTA) algorithms, namely the estimate of iteration complexity. In addition, our theoretical analysis provides an estimate of the maximum allowable noise level at which the desired accuracy can be achieved. Validation of our theoretical results is demonstrated both on the model function and on functions of interest in the field of machine learning. We also provide a discussion in which we explain the results obtained and the superiority of the proposed algorithm over SOTA algorithms for solving the original problem.