Article
Mathematics
Emina Milovanovic, Serife Burcu Bozkurt Altindag, Marjan Matejic, Igor Milovanovic
Summary: This paper investigates the bounds of a certain type of nonincreasing sequence of positive real numbers, and uses the obtained results to generalize some results regarding Laplacian and normalized Laplacian eigenvalues of graphs.
CZECHOSLOVAK MATHEMATICAL JOURNAL
(2022)
Article
Statistics & Probability
Vishesh Jain, Ashwin Sah, Mehtaab Sawhney
Summary: Every matrix A in R-n(xn) is shown to be at least delta parallel to a real matrix A + E in R-nxn, with eigenvectors having condition number at most (O tilde (n))(delta(-1)). It is proved that taking E to be a sufficiently small multiple of an i.i.d. real sub-Gaussian matrix of bounded density is enough with high probability. Non-asymptotic estimates on the minimum distance between any two eigenvalues of a random matrix with arbitrary means are also provided in this study.
ANNALS OF PROBABILITY
(2021)
Article
Mathematics, Applied
Ali Mohammadian
Summary: The article discusses the finiteness of the number of symmetric matrices M with a specified number of eigenvalues and distinct entry values. This result generalizes known conclusions about adjacency matrices of graphs and proposes a conjecture regarding twinfree graphs.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2022)
Article
Physics, Mathematical
Marco Aldi, Niel de Beaudrap, Sevag Gharibian, Seyran Saeedi
Summary: In this study, the problem of computing satisfying assignments to k-QSAT instances with a dimer covering or matching is investigated. The results fall into three directions related to the dimer covering setting: (1) A polynomial-time classical algorithm for k-QSAT when all qubits occur in at most two interaction terms or clauses is provided. (2) A parameterized algorithm for k-QSAT instances from a certain non-trivial class is presented, leading to exponential speedups in some cases by solving for a single root of a single univariate polynomial. (3) A structural graph theoretic study of 3-QSAT interaction graphs with a dimer covering is conducted, introducing new tools to the study of Quantum SAT such as transfer filtrations and blow-ups from algebraic geometry.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Computer Science, Theory & Methods
Laszlo Merai, Arne Winterhof
Summary: Automatic sequences like the Thue-Morse sequence or the Rudin-Shapiro sequence possess desirable features of pseudorandomness, but also have certain undesirable properties. Research shows that certain subsequences may retain the good properties of the original sequence while avoiding the bad ones.
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
(2022)
Article
Biochemical Research Methods
Chirag Jain, Arang Rhie, Nancy F. Hansen, Sergey Koren, Adam M. Phillippy
Summary: Approximately 5-10% of the human genome is inaccessible due to the presence of repetitive sequences. Existing long-read mappers often yield incorrect alignments and variant calls within repetitive sequences. To address this issue, a new long-read mapping method called Winnowmap2 was developed, which is more tolerant of structural variation and more sensitive to paralog-specific variants within repeats.
Article
Physics, Mathematical
Naoki Sasakura
Summary: We derived exact analytic expressions for the eigenvalue/vector distributions of real symmetric order-three tensors with Gaussian distributions for N≤8. The distributions were expressed as combinations of polynomial, exponential, and error functions, obtained from complex integrals. By extrapolating the expressions and comparing with Monte Carlo simulations, we provided a large-N expression. The results showed precise agreement with the exact expression and good agreement with the large-N expression.
JOURNAL OF MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
Chaoran Zhang, Xiaoyan Jing, Zhefeng Xu
Summary: This study focuses on quaternary sequences with high linear complexity and N-adic complexity in cryptography. By using the Gray mapping, researchers constructed a new class of generalized cyclotomic quaternary sequences over Z(4) with period pq. The linear complexity over F-4 and 4-adic complexity of these sequences were determined. The results show that these sequences possess high linear complexity and 4-adic complexity.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Computer Science, Information Systems
Zhimin Sun, Xiangyong Zeng, Chunlei Li, Yi Zhang, Lin Yi
Summary: The paper introduces the expansion complexity as a new figure of merit for cryptographic sequences. It presents an explicit formula for determining the (irreducible) expansion complexity of ultimately periodic sequences over finite fields, as well as improved upper and lower bounds on the Nth irreducible expansion complexity when not explicitly determined. Additionally, it provides a tighter upper bound of the Nth expansion complexity for some infinite sequences with given nonlinear complexity.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Biochemical Research Methods
Shengji Jia, Lei Shi
Summary: In this study, two new change-points detection procedures were developed within the framework of cumulative segmented regression. Simulations and application to genetic data showed that these methods not only improved efficiency of each estimator but also provided similar variations for all change points.
Article
Physics, Fluids & Plasmas
Alessandro Pacco, Valentina Ros
Summary: This paper investigates the correlation between pairs of Gaussian orthogonal ensemble matrices and their rank-one perturbations. It focuses on the regime of parameters in which the perturbations generate outliers in the matrices' spectrum. The results have implications for the signal recovery problem for spiked matrices and high-dimensional random landscapes.
Article
Mathematics, Applied
Yan Wang, Ying Cao, Ziling Heng, Weiqiong Wang
Summary: This paper investigates a construction method for binary sequences with period 4N and optimal autocorrelation magnitude based on sampling and interleaving technique. The exact value of the linear complexity of the constructed sequences is determined by studying the deep relationship among the characteristic polynomials, which is found to be 2N + 2. Furthermore, the 2-adic complexity of these sequences is determined by the autocorrelation function, and it is shown to achieve the maximum value. The results indicate that such sequences can resist both the Berlekamp-Massey attack and the Rational Approximation Algorithm, and are good for communication purposes.
Article
Mathematics
Jiemeng Zhang
Summary: This paper proposes a nuanced variation in the kernel words of the tribonacci sequence and investigates the intrinsic properties of the kernel words and associated gap sequences when expanded over an infinite alphabet.
Article
Materials Science, Multidisciplinary
Nishan C. Jayarama, Viktor Svensson
Summary: Circuit complexity is a useful tool for studying properties in condensed matter systems, particularly for probing the phase diagram. However, compared to measures based on entanglement, it is found to be lacking. By imposing penalty factors to punish nonlocality, we demonstrate that complexity becomes a stronger probe of the phase diagram, capable of identifying more subtle features. We provide analytical solutions for the complexity in the XY chain with transverse field.
Article
Mathematics
Jie Ma, Tianchi Yang
Summary: The research proves that the maximum number of edges in a 2-connected graph without repeated cycle lengths can be conceptually reduced to the classic problem of finding the maximum Sidon sequences in number theory, as shown by the proof and the lower bound construction.
ISRAEL JOURNAL OF MATHEMATICS
(2021)
