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We use the theory of $x-y$ duality to propose a new definition / construction for the correlation differentials of topological recursion; we call it "generalized topological recursion". This new definition coincides with the original topological recursion of Chekhov-Eynard-Orantin in the regular case and allows, in particular, to get meaningful answers in a variety of irregular and degenerate situations., Comment: v2: 29 pages, a section on KP integrability is added

In the field of Image Quality Assessment (IQA), the adversarial robustness of the metrics poses a critical concern. This paper presents a comprehensive benchmarking study of various defense mechanisms in response to the rise in adversarial attacks on IQA. We systematically evaluate 25 defense strategies, including adversarial purification, adversarial training, and certified robustness methods. We applied 14 adversarial attack algorithms of various types in both non-adaptive and adaptive settings and tested these defenses against them. We analyze the differences between defenses and their applicability to IQA tasks, considering that they should preserve IQA scores and image quality. The proposed benchmark aims to guide future developments and accepts submissions of new methods, with the latest results available online: https://videoprocessing.ai/benchmarks/iqa-defenses.html.

Future generations of cellular systems presume to use an extremely high number of antennas to enable mm waves. Increasing the number of antennas requires a growth in connections between a remote radio head (RRH) and a baseband unit (BBU). Therefore, the traffic load between RRH and BBU has to grow, and the compression of interconnection between them becomes a serious problem. In this paper, we propose a compression scheme to reduce the bitrate of the fronthaul interface that connects BBU and RRU. Then we justify compression block size and mantissa length to guarantee the required error vector magnitude (EVM). The knowledge of propagation channel sparsity and the condition number of the channel matrix helps to achieve higher compression ratios without performance loss. Simulation results with a realistic propagation channel are provided to confirm theoretical derivations.

We prove that for any initial data on a genus zero spectral curve the corresponding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the $r$-th roots of the twisted powers of the log canonical bundles., Comment: 13 pages

In this paper we relate a well-known in symplectic geometry compactification of the space of symmetric bilinear forms considered as a chart of the Lagrangian Grassmannian to the specific compactifications of the space of electrical networks in the disc obtained in \cite{L}, \cite{CGS} and \cite{BGKT}. In particular, we state an explicit connection between these works and describe some of the combinatorics developed there in the language of symplectic geometry. We also show that the combinatorics of the concordance vectors forces the uniqueness of the symplectic form, such that corresponding points of the Grassmannian are isotropic. We define a notion of Lagrangian concordance which provides a construction of the compactification of the space of electrical networks in the positive part of the Lagrangian Grassmannian bypassing the construction from \cite{L}., Comment: Minor corrections, journal version

We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log topological recursion. As a corollary, we establish nice properties of symplectic duality: various convenient explicit formulas, invertibility, group property, compatibility with topological recursion and KP integrability. As an application of these properties, we get a new and uniform proof of topological recursion for large families of weighted double Hurwitz numbers; this encompasses and significantly extends all previously known results on this matter., Comment: 28 pages

Spectral proper orthogonal decomposition (SPOD) is proposed for identification of the multipole structure of aeroacoustic noise sources from far-field measurements. The method is verified via tests with point multipoles and validated using experimental data on flow-induced cylinder noise and turbulent jet noise., Comment: 22 pages, 9 figures

In this paper, we propose a new approach to justify a round-off error impact on the accuracy of the linear least squares (LS) solution using Cholesky decomposition. This decomposition is widely employed to inverse a matrix in the linear detector of the Multi-User multi-antenna receiver. The proposed stochastic bound is much closer to actual errors than other numerical bounds. It was tested with a half-precision format and validated in realistic scenarios. Experimental results demonstrate our approach predicts errors very close to those achieved by simulations. The proposed approach can be employed to analyze the resulting round-off error in many other applications.

Hybrid beamforming (HBF) is a key technology to enable mm-wave Massive multiple-input multiple-output (mMIMO) receivers for future-generation wireless communications. It combines beamforming in both analog (via phase shifters) and digital domains, resulting in low power consumption and high spectral efficiency. In practice, the problem of joint beamforming in multi-user scenarios is still open because an analog beam can't cover all users simultaneously. In this paper, we propose a hierarchical approach to divide users into clusters. Each cluster consists of users inside a virtual sector produced by the analog beamforming of an HBF-based mMIMO receiver. Thus, inside each sector, a lower-cost digital beamforming serves a limited number of users within the same cluster. Simulations with realistic non-line-of-sight scenarios generated by the QuaDRiGa 2.0 demonstrate that our methods outperform standard FFT-based alternatives and almost achieve SVD-based beamspace performance bound.

In this paper, we propose a trainable least squares (LS) approach for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals in a hybrid beamforming (HBF) system. Compared to digital beamforming (DBF), in HBF technology the number of antennas exceeds the number of digital ports. Therefore, PAPR reduction capabilities are restricted by both a limited bandwidth and the reduced size of digital space. The problem is to meet both conditions. Moreover, the major HBF advantage is a reduced system complexity, thus the complexity of the PAPR reduction algorithm is expected to be low. To justify the performance of the proposed trainable LS, we provide a performance bound achieved by convex optimization using the CVX Matlab package. Moreover, the complexity of the proposed algorithm can be comparable to the minimal complexity of the digital ``twin'' calculation in HBF. The abovementioned features prove the feasibility of the trained LS for PAPR reduction in fully-connected HBF.

It is shown that the velocity fluctuation spectra measured using a hot-wire in the potential flow region of a turbulent jet near field in the presence of a co-flow can be converted into the spectra of pressure fluctuations. The proposed conversion method is based on the fact that the structure of instability waves, which make a decisive contribution to the jet near-field fluctuations, resembles homogeneous one-dimensional waves, which makes it possible to locally link the pressure fluctuations and the fluctuations of the streamwise velocity component measured by a hot-wire., Comment: 25 pages, 13 figures

We introduce a new concept of logarithmic topological recursion that provides a patch to topological recursion in the presence of logarithmic singularities and prove that this new definition satisfies the universal $x-y$ swap relation. This result provides a vast generalization and a proof of a very recent conjecture of Hock. It also uniformly explains (and conceptually rectifies) an approach to the formulas for the $n$-point functions proposed by Hock., Comment: 30 pages; minor corrections and modifications; Section 3.11 on the new Family III of generalized double Hurwitz numbers added

The $K^{+} \to \pi^{+}\pi^{0}\pi^{0}\gamma$ decay is observed by the OKA collaboration. The branching ratio is measured to be $(4.1 \pm 0.9(stat) \pm 0.4(syst))\times 10^{-6}$. The branching ratio and $\gamma$ energy spectrum are consistent with ChPT prediction., Comment: arXiv admin note: text overlap with arXiv:2310.16429

A high statistics data sample of the $K^{+}$ decays is recorded by the OKA collaboration. A missing mass analysis is performed to search for a light invisible pseudoscalar axion-like particle (ALP) $a$ in the decay $K^{+} \to \pi^{+} \pi^{0} a$. No signal is observed, the upper limits for the branching ratio of the decay are calculated. The $90\%$ confidence level upper limit is changing from $2.5\cdot10^{-6}$ to $2\cdot10^{-7}$ for the ALP mass from 0 to 200 MeV/$c^{2}$, except for the region of $\pi^{0}$ mass, where the upper limit is $4.4\cdot10^{-6}$., Comment: 6 pages, 6 figures

We discuss a universal relation that we call the $x-y$ swap relation, which plays a prominent role in the theory of topological recursion, Hurwitz theory, and free probability theory. We describe in a very precise and detailed way the interaction of the $x-y$ swap relation and KP integrability. As an application, we prove a recent conjecture that relates some particular instances of topological recursion to the Mironov-Morozov-Semenoff matrix integrals., Comment: 27 pages; minor corrections

For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions on the original curve. As a corollary, we prove topological recursion for the generalized fully simple maps generating functions., Comment: 16 pages

Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chemical reaction modeling and mathematical analysis. A quadratization reveals new variables and structures of a model, which may be easier to analyze, simulate, control, and provides a convenient parametrization for learning. This paper presents novel theory, algorithms and software capabilities for quadratization of non-autonomous ODEs. We provide existence results, depending on the regularity of the input function, for cases when a quadratic-bilinear system can be obtained through quadratization. We further develop existence results and an algorithm that generalizes the process of quadratization for systems with arbitrary dimension that retain the nonlinear structure when the dimension grows. For such systems, we provide dimension-agnostic quadratization. An example is semi-discretized PDEs, where the nonlinear terms remain symbolically identical when the discretization size increases. As an important aspect for practical adoption of this research, we extended the capabilities of the QBee software towards both non-autonomous systems of ODEs and ODEs with arbitrary dimension. We present several examples of ODEs that were previously reported in the literature, and where our new algorithms find quadratized ODE systems with lower dimension than the previously reported lifting transformations. We further highlight an important area of quadratization: reduced-order model learning. This area can benefit significantly from working in the optimal lifting variables, where quadratic models provide a direct parametrization of the model that also avoids additional hyperreduction for the nonlinear terms. A solar wind example highlights these advantages.

We prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of $x$ and $y$ in the input data. We also show that this universal formula can be drastically simplified (as it was already done by Hock). As an application of this general $x-y$ swap result, we prove an explicit closed formula for the topological recursion differentials for the case of any spectral curve with unramified $y$ and arbitrary rational $x$., Comment: 51 pages; various corrections and clarifications