Search Results (16)

As 5G and beyond networks grow in heterogeneity, complexity, and scale, traditional Intrusion Detection Systems (IDS) struggle to maintain accurate and precise detection mechanisms. A promising alternative approach to this problem has involved the use of Deep Learning (DL) techniques; however, DL-based IDS suffer from issues relating to interpretation, performance variability, and high computational overheads. These issues limit their practical deployment in real-world applications. In this study, CiNeT is introduced as a novel DL-based IDS employing Convolutional Neural Networks (CNN) within a bijective encoding–decoding framework between network traffic features (such as IPv6, IPv4, Timestamp, MAC addresses, and network data) and their RGB representations. This transformation facilitates our DL IDS in detecting spatial patterns without sacrificing fidelity. The bijective pipeline enables complete traceability from detection decisions to their corresponding network traffic features, enabling a significant initiative towards solving the ‘black-box’ problem inherent in Deep Learning models, thus facilitating digital forensics. Finally, the DL IDS has been evaluated on three datasets, UNSW NB-15, InSDN, and ToN_IoT, with analysis conducted on accuracy, GPU usage, memory utilisation, training, testing, and validation time. To summarise, this study presents a new CNN-based IDS with an end-to-end pipeline between network traffic data and their RGB representation, which offers high performance and enhanced interpretability through revisable transformation. Full article

This paper investigates the use of Riordan arrays in the enumeration and transformation of lattice paths through a combinatorial framework of promotion. We demonstrate how Dyck paths can be promoted to generalised Motzkin and Schröder paths via two key transformations: the Binomial and Chebyshev transforms, each associated with specific Riordan arrays. These promotions yield classical integer sequences and continued fraction representations that enumerate weighted lattice paths. The framework is further extended to analyse grand paths, which are permitted to cross below the x-axis. We develop constructive bijections establishing explicit correspondences between promoted path families. The promotion framework offers new insights into known integer sequences and enables a unified approach to the generalisation and classification of lattice paths. Full article

The S-box is a key component of modern ciphers, determining the quality and performance of the cryptographic algorithms in which it is applied. Many constructions for synthesizing high-quality S-boxes have been established, and those based on Galois fields theory—for example, the Nyberg construction applied in the AES cryptographic algorithm—are particularly important. An integral component of the Nyberg construction is the affine transformation, which is used to improve the avalanche and correlation properties of the S-box. In this paper, a new approach is adopted for synthesizing affine transformations for S-boxes based on the quaternary matrices over the Galois field GF(4). We describe four basic structures that serve as the foundation for synthesizing a complete class of 648 affine transformation matrices of order n = 3 and a class of 7776 matrices of order n = 4 and introduce a recurrent structure to facilitate the synthesis of matrices for higher orders. Using these matrices in combination with the Nyberg construction, it is possible to construct bijective S-boxes that outperform the original Nyberg construction and many other known S-boxes in terms of strict avalanche criterion (SAC) and bit independence criterion strict avalanche criterion (BIC SAC) values, while maintaining a maximal level of nonlinearity and good cryptographic properties. We also propose modified GF(4) affine transformations that can be applied to specialized S-boxes which already satisfy the SAC for both component Boolean and 4-functions, as well as the criterion of minimal correlation between input and output, allowing us to enhance their nonlinearity to the value of N_f = 96. We integrate the synthesized S-boxes into the AES algorithm and evaluate their practical performance. The encryption outputs successfully pass the NIST statistical test suite in 96 out of 100 cases, outperforming both the original AES S-box and other reference constructions, confirming the practical strength of the proposed method. Full article

The Burrows–Wheeler Transform (BWT) is a widely used reversible data compression method, forming the foundation of various compression algorithms and indexing structures. Prior research has analyzed the sensitivity of compression methods and repetitiveness measures to single-character edits, particularly in binary alphabets. However, the impact of such modifications on the compression efficiency of the bijective variant of BWT (BBWT) remains largely unexplored. This study extends previous work by examining the compression sensitivity of both BWT and BBWT when applied to larger alphabets, including alphabet reordering. We establish theoretical bounds on the increase in compression size due to character modifications in structured sequences such as Fibonacci words. Our devised lower bounds put the sensitivity of BBWT on the same scale as of BWT, with compression size changes exhibiting logarithmic multiplicative growth and square-root additive growth patterns depending on the edit type and the input data. These findings contribute to a deeper understanding of repetitiveness measures. Full article

A graph, $G=(V,E)$, is edge odd graceful if it possesses edge odd graceful labeling. This labeling is defined as a bijection $g:E\left(G\right)\to \{1,3,\dots ,2m-1\}$, from which an injective transformation is derived, $g^{*}:V\left(G\right)\to \{1,2,3,\dots ,2m-1\}$, from the rule that the image of $u\in V\left(G\right)$ under $g^{*}$ is ${\sum }_{uv\in E\left(G\right)}g\left(uv\right)\mathrm{mod}\left(2m\right)$. The main objective of this manuscript is to introduce new classes of planar graphs, namely water wheel graphs, $W{W}_n$; triangulated water wheel graphs, $T{W}_n$; closed water wheel graphs, $C{W}_n$; and closed triangulated water wheel graphs, $C{T}_n$. Furthermore, we specify conditions for these graphs to allow for edge odd graceful labelings. Full article

Atom-to-atom maps (AAMs) are bijections that establish the correspondence of reactant and product atoms across chemical reactions. They capture crucial features of the reaction mechanism and thus play a central role in modeling chemistry at the level of graph transformations. AAMs are equivalent to so-called “imaginary transition state” (ITS) graphs, making it possible to reduce tasks such as the computational comparison of AAMs to testing graph isomorphisms. In many application scenarios, nonetheless, only partial information is available, i.e., only partial maps or, equivalently, only subgraphs of the ITS graphs, are known. Here, we investigate whether and how, and to what extent, such partial chemical data can be completed and compared. The focus of this contribution is entirely on the development of a solid mathematical foundation for the analysis of partial AAMs and their associated partial ITS graphs. Full article

With the exponential growth of the Internet of Things (IoT), ensuring robust end-to-end encryption is paramount. Current cryptographic accelerators often struggle with balancing security, area efficiency, and power consumption, which are critical for compact IoT devices and system-on-chips (SoCs). This work presents a novel approach to designing substitution boxes (S-boxes) for Advanced Encryption Standard (AES) encryption, leveraging dual quad-bit structures to enhance cryptographic security and hardware efficiency. By utilizing Algebraic Normal Forms (ANFs) and Walsh–Hadamard Transforms, the proposed Register Transfer Level (RTL) circuitry ensures optimal non-linearity, low differential uniformity, and bijectiveness, making it a robust and efficient solution for ASIC implementations. Implemented on 65 nm CMOS technology, our design undergoes rigorous statistical analysis to validate its security strength, followed by hardware implementation and functional verification on a ZedBoard. Leveraging Cadence EDA tools, the ASIC implementation achieves a central circuit area of approximately 199 μm². The design incurs a hardware cost of roughly 80 gate equivalents and exhibits a maximum path delay of 0.38 ns. Power dissipation is measured at approximately 28.622 μW with a supply voltage of 0.72 V. According to the ASIC implementation on the TSMC 65 nm process, the proposed design achieves the best area efficiency, approximately 66.46% better than state-of-the-art designs. Full article

A graph’s edge labeling involves the allocation of symbols (colors or numbers) to the edges of a graph governed by specific criteria. Such labeling of a graph G with order n and size m is named edge odd graceful if there is a bijective map $\phi$ from the set of edges $E\left(G\right)=\{e_1,\dots ,e_m\}$ to the set $\{1,3,\dots ,2m-1\}$ in a way that the derived transformation ${\phi }^{\ast }$ from the vertex-set $V\left(G\right)=\{v_1,\dots ,v_n\}$ to the set $\{0,1,2,\dots ,2m-1\}$ given by ${\phi }^{\ast }\left(u\right)={\sum }_{uv\in E\left(G\right)}\phi \left(uv\right)mod\left(2m\right)$ is injective. Any graph is named edge odd graceful if it permits an edge odd graceful allocation (Solairaju and Chithra). The primary aim of this study is to define and explore the edge odd graceful labeling of five new families of wheel-related graphs. Consequently, necessary and sufficient conditions for these families to be edge odd graceful are provided. Full article

The variety of catastrophe bond issuances can be used for portfolio diversification. However, the structure of catastrophe bonds differs from traditional bonds in that the face value and coupons depend on triggering events. This study aims to build a diversification strategy model framework using probabilistic–possibilistic bijective transformation (PPBT) and credibility measures in fuzzy environments based on the payoff function. The stages of modeling include identifying the trigger distribution; determining the membership degrees for the face value and coupons using PPBT; calculating the average face value and coupons using the fuzzy quantification theory; formulating the fuzzy variables for the yield; defining the function of triangular fuzzy membership for the yield; defining the credibility distribution for the triangular fuzzy variables for the yield; determining the expectation and total variance for the yield; developing a model of the catastrophe bond diversification strategy; the numerical simulation of the catastrophe bond strategy model; and formulating a solution to the simulation model of the diversification strategy using the sequential method, quadratic programming, transformation, and linearization techniques. The simulation results show that the proposed model can overcome the self-duality characteristic not possessed by the possibilistic measures in the fuzzy variables. The results obtained are expected to contribute to describing the yield uncertainty of investing in catastrophe bond assets so that investors can make wise decisions. Full article

We propose a new polymerization scheme for scalar fields coupled to gravity. It has the advantage of being a (non-bijective) canonical transformation of the fields, and therefore ensures the covariance of the theory. We study it in detail in spherically symmetric situations and compare to other approaches. Full article

Snake graphs are connected planar graphs consisting of a finite sequence of adjacent tiles (squares) $T_1,T_2,\dots ,T_n$. In this case, for $1\le j\le n-1$, two consecutive tiles $T_j$ and $T_{j+1}$ share exactly one edge, either the edge at the east (west) of $T_j$ ($T_{j+1}$) or the edge at the north (south) of $T_j$ ($T_{j+1}$). Finding the number of perfect matchings associated with a given snake graph is one of the most remarkable problems regarding these graphs. It is worth noting that such a number of perfect matchings allows a bijection between the set of snake graphs and the positive continued fractions. Furthermore, perfect matchings of snake graphs have also been used to find closed formulas for cluster variables of some cluster algebras and solutions of the Markov equation, which is a well-known Diophantine equation. Recent results prove that snake graphs give rise to some string modules over some path algebras, connecting snake graph research with the theory of representation of algebras. This paper uses this interaction to define Brauer configuration algebras induced by schemes associated with some multisets called polygons. Such schemes are named Brauer configurations. In this work, polygons are given by some admissible words, which, after appropriate transformations, permit us to define sets of binary trees called groves. Admissible words generate codes whose energy values are given by snake graphs. Such energy values can be estimated by using Catalan numbers. We include in this paper Python routines to compute admissible words (i.e., codewords), energy values of the generated codes, Catalan numbers and dimensions of the obtained Brauer configuration algebras. Full article

The aim of this paper is to define and study the composition vector spaces as a type of tri-operational algebras. In this regard, by presenting nontrivial examples, it is emphasized that they are a proper generalization of vector spaces and their structure can be characterized by using linear operators. Additionally, some related properties about foundations, composition subspaces and residual elements are investigated. Moreover, it is shown how to endow a vector space with a composition structure by using bijective linear operators. Finally, more properties of the composition vector spaces are presented in connection with linear transformations. Full article

We provide a general method for identifying real quadratic polynomial dynamical systems that can be transformed to symmetric ones by a bijective polynomial map of degree one, the so-called affine map. We mainly focus on symmetry groups generated by rotations, in other words, we treat equivariant and reversible equivariant systems. The description is given in terms of affine varieties in the space of parameters of the system. A general algebraic approach to find subfamilies of systems having certain symmetries in polynomial differential families depending on many parameters is proposed and computer algebra computations for the planar case are presented. Full article

In this paper, we introduce reflection-like maps in n-dimensional Euclidean spaces, which are affinely conjugated to $\theta :(x_1,x_2,\dots ,x_n)\to \left({\displaystyle \frac{1}{x_1}},{\displaystyle \frac{x_2}{x_1}},\dots ,{\displaystyle \frac{x_n}{x_1}}\right).$ We shall prove that reflection-like maps are line-to-line, cross ratios preserving on lines and quadrics preserving. The goal of this article was to consider the rigidity of line-to-line maps on the local domain of ${\mathbb{R}}^n$ by using reflection-like maps. We mainly prove that a line-to-line map $\eta$ on any convex domain satisfying ${\eta }^{\circ 2}=id$ and fixing any points in a super-plane is a reflection or a reflection-like map. By considering the hyperbolic isometry in the Klein Model, we also prove that any line-to-line bijection $f:{\mathbb{D}}^n\mapsto {\mathbb{D}}^n$ is either an orthogonal transformation, or a composition of an orthogonal transformation and a reflection-like map, from which we can find that reflection-like maps are important elements and instruments to consider the rigidity of line-to-line maps. Full article

Background: Codon directional asymmetry (CDA) classifies the 64 codons into palindromes (XYX, CDA = 0), and 5′- and 3′-dominant (YXX and XXY, CDA < 0 and CDA > 0, respectively). Previously, CDA was defined by the purine/pyrimidine divide (A,G/C,T), where X is either a purine or a pyrimidine. For the remaining codons with undefined CDA, CDA was defined by the 5′ or 3′ nucleotide complementary to Y. This CDA correlates with cognate amino acid tRNA synthetase classes, antiparallel beta sheet conformation index and the evolutionary order defined by the self-referential genetic code evolution model (CDA < 0: class I, high beta sheet index, late genetic code inclusion). Methods: We explore associations of CDAs defined by nucleotide classifications according to complementarity strengths (A:T, weak; C:G, strong) and keto-enol/amino-imino groupings (G,T/A,C), also after swapping 1st and 2nd codon positions with amino acid physicochemical and structural properties. Results: Here, analyses show that for the eight codons whose purine/pyrimidine-based CDA requires using the rule of complementarity with the midposition, using weak interactions to define CDA instead of complementarity increases associations with tRNA synthetase classes, antiparallel beta sheet index and genetic code evolutionary order. CDA defined by keto-enol/amino-imino groups, 1st and 2nd codon positions swapped, correlates with amino acid parallel beta sheet formation indices and Doolittle’s hydropathicities. Conclusions: Results suggest (a) prebiotic swaps from N2N1N3 to N1N2N3 codon structures, (b) that tRNA-mediated translation replaced direct codon-amino acid interactions, and (c) links between codon structures and cognate amino acid properties. Full article