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This paper presents neural networks for network intrusion detection systems (NIDS), that operate on flow data preprocessed with a time window. It requires only eleven features which do not rely on deep packet inspection and can be found in most NIDS datasets and easily obtained from conventional flow collectors. The time window aggregates information with respect to hosts facilitating the identification of flow signatures that are missed by other aggregation methods. Several network architectures are studied and the use of Kolmogorov-Arnold Network (KAN)-inspired trainable activation functions that help to achieve higher accuracy with simpler network structure is proposed. The reported training accuracy exceeds 99% for the proposed method with as little as twenty neural network input features. This work also studies the generalization capability of NIDS, a crucial aspect that has not been adequately addressed in the previous studies. The generalization experiments are conducted using CICIDS2017 dataset and a custom dataset collected as part of this study. It is shown that the performance metrics decline significantly when changing datasets, and the reduction in performance metrics can be attributed to the difference in signatures of the same type flows in different datasets, which in turn can be attributed to the differences between the underlying networks. It is shown that the generalization accuracy of some neural networks can be very unstable and sensitive to random initialization parameters, and neural networks with fewer parameters and well-tuned activations are more stable and achieve higher accuracy., Comment: 18 pages, 3 figures, 9 tables

Let $\delta(p)$ tend to zero arbitrarily slowly as $p\to\infty$. We exhibit an explicit set $\mathcal{S}$ of primes $p$, defined in terms of simple functions of the prime factors of $p-1$, for which the least primitive root of $p$ is $\le p^{1/4-\delta(p)}$ for all $p\in \mathcal{S}$, where $\#\{p\leq x: p\in \mathcal{S}\} \sim \pi(x)$ as $x\to\infty$.

Despite recent success in discriminative approaches in monocular depth estimation its quality remains limited by training datasets. Generative approaches mitigate this issue by leveraging strong priors derived from training on internet-scale datasets. Recent studies have demonstrated that large text-to-image diffusion models achieve state-of-the-art results in depth estimation when fine-tuned on small depth datasets. Concurrently, autoregressive generative approaches, such as the Visual AutoRegressive modeling~(VAR), have shown promising results in conditioned image synthesis. Following the visual autoregressive modeling paradigm, we introduce the first autoregressive depth estimation model based on the visual autoregressive transformer. Our primary contribution is DepthART -- a novel training method formulated as Depth Autoregressive Refinement Task. Unlike the original VAR training procedure, which employs static targets, our method utilizes a dynamic target formulation that enables model self-refinement and incorporates multi-modal guidance during training. Specifically, we use model predictions as inputs instead of ground truth token maps during training, framing the objective as residual minimization. Our experiments demonstrate that the proposed training approach significantly outperforms visual autoregressive modeling via next-scale prediction in the depth estimation task. The Visual Autoregressive Transformer trained with our approach on Hypersim achieves superior results on a set of unseen benchmarks compared to other generative and discriminative baselines.

Leveraging 3D semantics for direct 3D reconstruction has a great potential yet unleashed. For instance, by assuming that walls are vertical, and a floor is planar and horizontal, we can correct distorted room shapes and eliminate local artifacts such as holes, pits, and hills. In this paper, we propose FAWN, a modification of truncated signed distance function (TSDF) reconstruction methods, which considers scene structure by detecting walls and floor in a scene, and penalizing the corresponding surface normals for deviating from the horizontal and vertical directions. Implemented as a 3D sparse convolutional module, FAWN can be incorporated into any trainable pipeline that predicts TSDF. Since FAWN requires 3D semantics only for training, no additional limitations on further use are imposed. We demonstrate, that FAWN-modified methods use semantics more effectively, than existing semantic-based approaches. Besides, we apply our modification to state-of-the-art TSDF reconstruction methods, and demonstrate a quality gain in SCANNET, ICL-NUIM, TUM RGB-D, and 7SCENES benchmarks.

Autoencoders (AE) are simple yet powerful class of neural networks that compress data by projecting input into low-dimensional latent space (LS). Whereas LS is formed according to the loss function minimization during training, its properties and topology are not controlled directly. In this paper we focus on AE LS properties and propose two methods for obtaining LS with desired topology, called LS configuration. The proposed methods include loss configuration using a geometric loss term that acts directly in LS, and encoder configuration. We show that the former allows to reliably obtain LS with desired configuration by defining the positions and shapes of LS clusters for supervised AE (SAE). Knowing LS configuration allows to define similarity measure in LS to predict labels or estimate similarity for multiple inputs without using decoders or classifiers. We also show that this leads to more stable and interpretable training. We show that SAE trained for clothes texture classification using the proposed method generalizes well to unseen data from LIP, Market1501, and WildTrack datasets without fine-tuning, and even allows to evaluate similarity for unseen classes. We further illustrate the advantages of pre-configured LS similarity estimation with cross-dataset searches and text-based search using a text query without language models., Comment: 19 pages,18 figures, 2 tables, 15 equations

We prove that for any $\epsilon>0$ and any trigonometric polynomial $f$ with frequencies in the set $\{n^3: N \leq n\leq N+N^{2/3-\epsilon}\}$, one has $$ \|f\|_4 \ll \epsilon^{-1/4}\|f\|_2 $$ with implied constant being absolute. We also show that the set $\{n^3: N\leq n\leq N+(0.5N)^{1/2}\}$ is a Sidon set., Comment: 6 pages; inaccuracy in the proof of the main theorem is corrected

We show that for any polynomial $f$ from the integers to the integers, with positive leading coefficient and irreducible over the rationals, if $x$ is large enough then there is a string of $(\log x)(\log\log x)^{1/835}$ consecutive integers $n \in [1,x]$ for which $f(n)$ is composite. This improves a result of the first author, Konyagin, Maynard, Pomerance and Tao, which states that there are such strings of length $(\log x)(\log\log x)^{c_f}$, where $c_f$ depends on $f$ and $c_f$ is exponentially small in the degree of $f$ for some polynomials., Comment: 22 pages

For a function $f\colon \mathbb{N}\to\mathbb{N}$, let $$ N^+_f(x)=\{n\leq x: n=k+f(k) \mbox{ for some } k\}. $$ Let $\tau(n)=\sum_{d|n}1$ be the divisor function, $\omega(n)=\sum_{p|n}1$ be the prime divisor function, and $\varphi(n)=\#\{1\leq k\leq n: \gcd(k,n)=1 \}$ be Euler's totient function. We show that \begin{align*} &(1) \quad x \ll N^+_{\omega}(x), \\ &(2) \quad x\ll N^+_{\tau}(x) \leq 0.94x, \\ &(3) \quad x \ll N^+_{\varphi}(x) \leq 0.93x. \end{align*}

We prove that $$ \sum_{p \leq x} \frac{1}{\tau(p-1)} \asymp \frac{x}{(\log x)^{3/2}}, \quad \quad \sum_{n \leq x} \frac{1}{\tau(n^2+1)} \asymp \frac{x}{(\log x)^{1/2}}, $$ where $\tau(n)=\sum_{d|n}1$ is the number of divisors of $n$, and the summation in the first sum is over primes.

Network Intrusion and Detection Systems (NIDS) are essential for malicious traffic and cyberattack detection in modern networks. Artificial intelligence-based NIDS are powerful tools that can learn complex data correlations for accurate attack prediction. Graph Neural Networks (GNNs) provide an opportunity to analyze network topology along with flow features which makes them particularly suitable for NIDS applications. However, successful application of such tool requires large amounts of carefully collected and labeled data for training and testing. In this paper we inspect different versions of ToN-IoT dataset and point out inconsistencies in some versions. We filter the full version of ToN-IoT and present a new version labeled ToN-IoT-R. To ensure generalization we propose a new standardized and compact set of flow features which are derived solely from NetFlowv5-compatible data. We separate numeric data and flags into different categories and propose a new dataset-agnostic normalization approach for numeric features. This allows us to preserve meaning of flow flags and we propose to conduct targeted analysis based on, for instance, network protocols. For flow classification we use E-GraphSage algorithm with modified node initialization technique that allows us to add node degree to node features. We achieve high classification accuracy on ToN-IoT-R and compare it with previously published results for ToN-IoT, NF-ToN-IoT, and NF-ToN-IoT-v2. We highlight the importance of careful data collection and labeling and appropriate data preprocessing choice and conclude that the proposed set of features is more applicable for real NIDS due to being less demanding to traffic monitoring equipment while preserving high flow classification accuracy., Comment: 8 pages, 2 equations, 3 tables

The impact of convective flow due to the temperature gradient between discharge cell electrodes and ambient air was studied for parallel-plate electrode arrangement. It was shown that an increase in temperature during the discharge operation leads to an increase in MD number in the discharge gap. The convective gas flow velocity also increased at a higher thermal gradient, and MD channels follow the gas flow direction. The velocity of convective flow was estimated by the CFD simulation and compared with the mean velocity of MD channels obtained by the particle image velocimetry method.

Person reidentification (re-ID) is becoming one of the most significant application areas of computer vision due to its importance for science and social security. Due to enormous size and scale of camera systems it is beneficial to develop edge computing re-ID applications where at least part of the analysis could be performed by the cameras. However, conventional re-ID relies heavily on deep learning (DL) computationally demanding models which are not readily applicable for edge computing. In this paper we adapt a recently proposed re-ID method that combines DL human parsing with analytical feature extraction and ranking schemes to be more suitable for edge computing re-ID. First, we compare parsers that use ResNet101, ResNet18, MobileNetV2, and OSNet backbones and show that parsing can be performed using compact backbones with sufficient accuracy. Second, we transfer parsers to tensor processing unit (TPU) of Google Coral Dev Board and show that it can act as a portable edge computing re-ID station. We also implement the analytical part of re-ID method on Coral CPU to ensure that it can perform a complete re-ID cycle. For quantitative analysis we compare inference speed, parsing masks, and re-ID accuracy on GPU and Coral TPU depending on parser backbone. We also discuss possible application scenarios of edge computing in re-ID taking into account known limitations mainly related to memory and storage space of portable devices., Comment: 11 pages, 3 figures, 3 tables

For a positive integer $n$, we denote by $F(n)$ the distance from $n$ to the nearest prime number. We prove that every sufficiently large positive integer $N$ can be represented as the sum $N=n_1+n_2$, where $$ F(n_i) \geqslant (\log N)(\log\log N)^{1/325565}, $$ for $i=1,2$. This improves the corresponding "trivial" statement where only $F(n_i)\gg \log N$ is required.

Person reidentification (re-ID) has been receiving increasing attention in recent years due to its importance for both science and society. Machine learning and particularly Deep Learning (DL) has become the main re-id tool that allowed researches to achieve unprecedented accuracy levels on benchmark datasets. However, there is a known problem of poor generalization of DL models. That is, models trained to achieve high accuracy on one dataset perform poorly on other ones and require re-training. To address this issue, we present a model without trainable parameters which shows great potential for high generalization. It combines a fully analytical feature extraction and similarity ranking scheme with DL-based human parsing used to obtain the initial subregion classification. We show that such combination to a high extent eliminates the drawbacks of existing analytical methods. We use interpretable color and texture features which have human-readable similarity measures associated with them. To verify the proposed method we conduct experiments on Market1501 and CUHK03 datasets achieving competitive rank-1 accuracy comparable with that of DL-models. Most importantly we show that our method achieves 63.9% and 93.5% rank-1 cross-domain accuracy when applied to transfer learning tasks. It is significantly higher than previously reported 30-50% transfer accuracy. We discuss the potential ways of adding new features to further improve the model. We also show the advantage of interpretable features for constructing human-generated queries from verbal description to conduct search without a query image., Comment: 20 pages, 7 figures, 6 tables, 15 equations

Let $\gamma_0=\frac{\sqrt5-1}{2}=0.618\ldots$ . We prove that, for any $\varepsilon>0$ and any trigonometric polynomial $f$ with frequencies in the set $\{n^2: N \leqslant n\leqslant N+N^{\gamma_0-\varepsilon}\}$, the inequality $$ \|f\|_4 \ll \varepsilon^{-1/4}\|f\|_2 $$ holds, which makes a progress on a conjecture of Cilleruelo and Cordoba. We also present a connection between this conjecture and the conjecture of Ruzsa which asserts that, for any $\varepsilon>0$, there is $C(\varepsilon)>0$ such that each positive integer $N$ has at most $C(\varepsilon)$ divisors in the interval $[N^{1/2}, N^{1/2}+N^{1/2-\varepsilon}]$

For a function $f\colon \mathbb{N}\to\mathbb{N}$, define $N^{\times}_{f}(x)=\#\{n\leq x: n=kf(k) \mbox{ for some $k$} \}$. Let $\tau(n)=\sum_{d|n}1$ be the divisor function, $\omega(n)=\sum_{p|n}1$ be the prime divisor function, and $\varphi(n)=\#\{1\leq k\leq n: (k,n)=1 \}$ be Euler's totient function. We prove that \begin{gather*} \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! 1) \quad N^{\times}_{\tau}(x) \asymp \frac{x}{(\log x)^{1/2}}; \\ 2) \quad N^{\times}_{\omega}(x) = (1+o(1))\frac{x}{\log\log x}; \\ \!\!\!\!\!\!\!\!\! 3) \quad N^{\times}_{\varphi}(x) = (c_0+o(1))x^{1/2}, \end{gather*} where $c_0=1.365...$\,., Comment: The error term in Theorem 1.2 is improved in this version of the paper

Let $\{c_k\}$ be a nonincreasing sequence of positive numbers (more general classes of sequences are also considered), and $\alpha>0$ be not an integer. We find necessary and sufficient conditions for the uniform convergence of the series $\sum_k c_k\sin k^{\alpha}x$ and $\sum_k c_k\cos k^{\alpha}x$ on the real line and its bounded subsets.

Following (Shevtsova, 2010) we introduce detailed classification of the asymptotically exact constants in natural estimates of the rate of convergence in the Lindeberg central limit theorem, namely in Esseen's, Rozovskii's, and Wang-Ahmad's inequalities and their structural improvements obtained in our previous works. The above inequalities involve algebraic truncated third-order moments and the classical Lindeberg fraction and assume finiteness only the second-order moments of random summands. We present lower bounds for the introduced asymptotically exact constants as well as for the universal and for the most optimistic constants which turn to be not far from the upper ones., Comment: 29 pages