Ing. Ivo Petr, Ph.D.

Článek

10.1016/j.comnet.2026.112188

Katedra číslicového návrhu
Katedra aplikované matematiky

Machine learning techniques provide powerful tools for analysis of encrypted network traffic. We present a novel set of features and a distance measure suitable for a wide variety of distance-based machine learning techniques useful in classification, clustering, and novelty detection in encrypted traffic flow data. The proposed features are given by distances between probability distributions of such characteristics as packet sizes or inter-arrival times. The proposed distance measure incorporates those features in a fractional lp-metric with p close to 0.1. The effectiveness of the distance measure is evaluated using an extensive labeled dataset containing 154 web services. The dataset was captured on the ISP backbone, and we present it as supplementary material. Application of k-nearest neighbors (kNN) algorithm in combination with the proposed distance measure and feature selection gives the classification accuracy of 91.0%. Comparison with a deep learning model shows that the kNN is competitive with state-of-the-art models. On a different publicly available dataset with a low number of classes, our approach reaches accuracy 99.6%, outperforming models presented in the literature. The benefits of novel features are further demonstrated using the LightGBM model, i.e. without relying on distance-based techniques. Besides direct classification, we have used the local outlier factor and rank-based detection algorithms to detect novel traffic flows. We show that their performance improves when using the proposed distance measure. Finally, to speed up traffic classification we compared the performance of kNN and Approximate Nearest Neighbors (ANN) algorithm, and applied the Affinity propagation clustering algorithm to select a suitable subset of kNN/ANN training points.

Článek

10.1093/ptep/ptaf154

Katedra aplikované matematiky

Four- and six-dimensional Drinfeld doubles were classified in the past in terms of Manin triples. We provide an important step toward the classification of eight-dimensional Drinfeld doubles by presenting an extensive list of Manin triples formed by pairs of four–dimensional Lie algebras. Due to the high complexity of the classification we focus on Manin triples formed by algebras in a certain standard form. The list contains 188 nonisomorphic Manin triples plus their duals. To apply the results, we construct several four-dimensional Wess–Zumino–Witten (WZW) models on non-semisimple Lie groups. Some of the WZW models are known from the literature, but new cases are presented as well. As a consequence of the construction method, the WZW models are Poisson–Lie dualizable.

Článek

10.1093/ptep/ptaf057

Katedra aplikované matematiky

The recently introduced Jacobi-Lie T-plurality has turned out to be a solution-generating technique in string theory. Being based on Leibniz algebras instead of Drinfel'd doubles, it can be understood as a generalization of Poisson-Lie T-plurality. In this paper we investigate the Jacobi-Lie T-plurality with spectators, and focus particularly on modification of the spectator fields by an arbitrary function f. Using this modification, new sigma model backgrounds can be constructed as Jacobi-Lie models. For low-dimensional Leibniz algebras classified a few years ago and warping factor f(omega )=gamma e^omega, we find sigma model backgrounds satisfying the supergravity equations and check that their plurals again satisfy the supergravity equations.

Článek

10.1088/1361-6382/adaabb

Katedra aplikované matematiky

T-duality and its generalizations are widely recognized either as symmetries or solution-generating techniques in string theory. Recently introduced Jacobi-Lie T-plurality is based on Leibniz algebras whose structure constants f_{ab}^c, f_c^{ab}, Z_a, Z^a satisfy further conditions. Low dimensional Jacobi-Lie bialgebras were classified a few years ago. We study four- and six-dimensional algebras with structure constants f_b^{ba} = Z^a = 0 and show that there are several classes consisting of mutually isomorphic algebras. Using isomorphisms between Jacobi-Lie bialgebras we investigate three- and four-dimensional sigma models related by Jacobi-Lie T-plurality with and without spectators. In the Double Field Theory formulation constant generalized fluxes F_A are used in the literature to transform dilaton field. We extend the procedure to non-constant fluxes and verify that obtained backgrounds and dilatons solve Supergravity Equations. Most of the resulting backgrounds have vanishing curvature scalars and, as can be seen by finding Brinkmann coordinates, represent plane-parallel waves.

Článek

10.1093/ptep/ptae054

Katedra aplikované matematiky

Poisson-Lie T-duality/plurality was recently generalized to Jacobi-Lie T-plurality formulated in terms of Double Field Theory and based on Leibniz algebras given by structure coefficients $f_{ab}{}^{c}, f_{c}{}^{ab},$ and $Z_a, Z^a$. We investigate three- and four-dimensional sigma models corresponding to six-dimensional Leibniz algebras with $f_b{}^{ba} \neq 0$, $Z^a=0$. We show that these algebras are plural one to another and, moreover, to an algebra with $f_b{}^{ba}= 0$, $Z^a=0$. These pluralities are used for construction of Jacobi--Lie models. It was conjectured that plural models should satisfy generalized supergravity equations. We have found examples of models satisfying ``true'' generalized supergravity equations where no trivialization to usual supergravity equations s is possible. On the other hand, we show that there are also models corresponding to algebras with $f_b{}^{ba}\neq 0$, $Z^a=0$ where the Killing vector appearing in generalized supergravity equations either vanishes or can be removed by suitable gauge transformation. Such models then satisfy usual supergravity equations, i.e. vanishing beta-function equations.

Článek

10.1140/epjc/s10052-021-09254-x

Katedra aplikované matematiky

In this paper we investigate Poisson–Lie transformation of dilaton and vector field J appearing in generalized supergravity equations. While the formulas appearing in literature work well for isometric sigma models, we present examples for which generalized supergravity equations are not preserved. Therefore, we suggest modification of these formulas.

Článek

10.1007/JHEP04(2020)068

Katedra aplikované matematiky

Poisson--Lie T-duality and plurality are important solution generating techniques in string theory and (generalized) supergravity. Since duality/plurality does not preserve conformal invariance, the usual beta function equations are replaced by Generalized Supergravity Equations containing vector $\mathcal{J}$. In this paper we apply Poisson--Lie T-plurality on Bianchi cosmologies. We present a formula for the vector $\mathcal{J}$ as well as transformation rule for dilaton, and show that plural backgrounds together with this dilaton and $\mathcal{J}$ satisfy the Generalized Supergravity Equations. The procedure is valid also for non-local dilaton and non-constant $\mathcal{J}$. We also show that $Div\,\Theta$ of the non-commutative structure $\Theta$ used for non-Abelian T-duality or integrable deformations does not give correct $\mathcal{J}$ for Poisson--Lie T-plurality.

Článek

10.1140/epjc/s10052-020-08446-1

Katedra aplikované matematiky

In previous papers we have presented many purely bosonic solutions of Generalized Supergravity Equations obtained by Poisson-Lie T-duality and plurality of flat and Bianchi cosmologies. In this paper we focus on their compactifications and identify solutions that can be interpreted as T-folds. To recognize T-folds we adopt the language of Double Field Theory and discuss how Poisson-Lie T-duality/plurality fits into this framework. As a special case we confirm that all non-Abelian T-duals can be compactified as T-folds.

Článek

10.1007/JHEP04(2019)157

Katedra aplikované matematiky

We investigate (non-)Abelian T-duality from the perspective of Poisson-Lie T-plurality. We show that sigma models related by duality/plurality are given not only by Manin triples obtained from decompositions of Drinfel’d double, but also by their particular embeddings, i.e. maps that relate bases of these decompositions. This allows us to get richer set of dual or plural sigma models than previously thought. That’s why we ask how T-duality is defined and what should be the “canonical” duality or plurality transformation.

Článek

10.1140/epjc/s10052-019-7356-5

Katedra aplikované matematiky

We investigate a special class of Poisson--Lie T-plurality transformations of Bianchi cosmologies invariant with respect to non-semisimple Bianchi groups. For six-dimensional semi-Abelian Manin triples $\mathfrak{b}\bowtie\mathfrak{a}$ containing Bianchi algebras $\mathfrak{b}$ we identify general forms of Poisson--Lie identities and dualities. We show that these can be decomposed into simple factors, namely automorphisms of Manin triples, B-shifts, $\beta$-shifts, and ``full'' or ``factorized'' dualities. Further, we study effects of these transformations and utilize the decompositions to obtain new backgrounds which, supported by corresponding dilatons, satisfy Generalized Supergravity Equations.

Článek

10.1088/1361-6382/aaaeed

Katedra aplikované matematiky

By addition of non-zero, but torsionless B -field, we expand the classification of (non-)Abelian T-duals of the flat background in four dimensions with respect to 1, 2, 3 and 4D subgroups of the Poincaré group. We discuss the influence of the additional B -field on the process of dualization, and identify essential parts of the torsionless B -field that cannot in general be eliminated by coordinate or gauge transformation of the dual background. These effects are demonstrated using particular examples. Due to their physical importance, we focus on duals whose metrics represent plane-parallel (pp-)waves. Besides the previously found metrics, we find new pp-waves depending on parameters originating from the torsionless B -field. These pp-waves are brought into their standard forms in Brinkmann and Rosen coordinates.

Článek

10.1088/1361-6382/aa7908

Katedra aplikované matematiky

We give the classification of T-duals of the flat background in four dimensions with respect to one-, two-, and three-dimensional subgroups of the Poincaré group using non-Abelian T-duality with spectators. As duals we find backgrounds for sigma models in the form of plane-parallel waves or diagonalizable curved metrics often with torsion. Among others, we find exactly solvable time-dependent isotropic pp-wave, singular pp-waves, or generalized plane wave (K-model).

Článek

10.1088/0264-9381/32/3/035005

Katedra aplikované matematiky

We give a classification of non-Abelian T-duals ('T' standing for topological or toroidal) of the flat metric in D = 4 dimensions with respect to the four-dimensional continuous subgroups of the Poincaré group. After dualizing the flat background, we identify the majority of dual models as conformal sigma models in plane-parallel wave backgrounds, most of them having torsion. We give their form in Brinkmann coordinates. We find, besides the plane-parallel waves, several diagonalizable curved metrics with nontrivial scalar curvature and torsion. Using the non-Abelian T-duality, we find general solutions of the classical field equations for all the sigma models in terms of dʼAlembert solutions of the wave equation.