On the influence of a constant force on the appearance of period-doubling bifurcations and chaos in a harmonically excited pure cubic oscillator

A pure cubic oscillator with a constant and a harmonic force acting on it, which represents a nonlinear asymmetric system, is considered. Building on previous studies on the matter, analytical and numerical approaches are used to examine and illustrate its dynamics related to the phenomenon of period-doubling bifurcations and their development into chaos for different values of the constant force. The region of control parameters in which this scenario is possible is determined and discussed with a view to revisiting literature results and to giving novel and deeper insights into the phenomenon related to the influence of the magnitude of the constant force and certain resonances.     

Generic cryptographic weakness of k-normal Boolean functions in certain stream ciphers and cryptanalysis of grain-128

This paper considers security implications of k-normal Boolean functions when they are employed in certain stream ciphers. A generic algorithm is proposed for cryptanalysis of the considered class of stream ciphers based on a security weakness of k-normal Boolean functions. The proposed algorithm yields a framework for mounting cryptanalysis against particular stream ciphers within the considered class. Also, the proposed algorithm for cryptanalysis implies certain design guidelines for avoiding certain weak stream cipher constructions. A particular objective of this paper is security evaluation of stream cipher Grain-128 employing the developed generic algorithm. Contrary to the best known attacks against Grain-128 which provide complexity of a secret key recovery lower than exhaustive search only over a subset of secret keys which is just a fraction (up to 5%) of all possible secret keys, the cryptanalysis proposed in this paper provides significantly lower complexity than exhaustive search for any secret key. The proposed approach for cryptanalysis primarily depends on the order of normality of the employed Boolean function in Grain-128. Accordingly, in addition to the security evaluation insights of Grain-128, the results of this paper are also an evidence of the cryptographic significance of the normality criteria of Boolean functions.     

Correlated atomic force microscopy and fluorescence lifetime imaging of live bacterial cells

We report on imaging living bacterial cells by using a correlated tapping-mode atomic force microscopy (AFM) and confocal fluorescence lifetime imaging microscopy (FLIM). For optimal imaging of Gram-negative Shewanella oneidensis MR-1 cells, we explored different methods of bacterial sample preparation, such as spreading the cells on poly-L-lysine coated surfaces or agarose gel coated surfaces. We have found that the agarose gel containing 99% ammonium acetate buffer can provide sufficient local aqueous environment for single bacterial cells. Furthermore, the cell surface topography can be characterized by tapping-mode in-air AFM imaging for the single bacterial cells that are partially embedded. Using in-air rather than under-water AFM imaging of the living cells significantly enhanced the contrast and signal-to-noise ratio of the AFM images. Near-field AFM-tip-enhanced fluorescence lifetime imaging (AFM-FLIM) holds high promise on obtaining fluorescence images beyond optical diffraction limited spatial resolution. We have previously demonstrated near-field AFM-FLIM imaging of polymer beads beyond diffraction limited spatial resolution. Here, as the first step of applying AFM-FLIM on imaging bacterial living cells, we demonstrated a correlated and consecutive AFM topographic imaging, fluorescence intensity imaging, and FLIM imaging of living bacterial cells to characterize cell polarity.     

On the convergence order of accelerated root iterations

Summary A Gauss-Seidel procedure for accelerating the convergence of the generalized method of the root iterations type of the (k+2)-th order (kN) for finding polynomial complex zeros, given in [7], is considered in this paper. It is shown that theR-order of convergence of the accelerated method is at leastk+1+ _n (k), where _n (k)>1 is the unique positive root of the equation ⁿ --k-1 = 0 andn is the degree of the polynomial. The examples of algebraic equations in ordinary and circular arithmetic are given.     

Note on the Coulson integral formula

Let P be a polynomial of degree n, whose zeros λ₁, λ₂, ..., λ _n are real-valued. The Coulson integral formula (first reported in 1940) is an expression for the sum of the positive–valued zeros of P, in terms of P. We show that the Coulson formula holds if and only if the condition λ₁+λ₂+...+λ _n =0 is obeyed. We also show how the formula has to be modified, so that it be applicable in the case when λ₁+λ₂+...+λ _n ≠ 0. Ams Classification (2000): primary: 92E10, secondary: 32A27, 81Q99     

On some iteration functions for the simultaneous computation of multiple complex polynomial zeros

Second order methods for simultaneous approximation of multiple complex zeros of a polynomial are presented. Convergence analysis of new iteration formulas and an efficient criterion for the choice of the appropriate value of a root are discussed. A numerical example is given which demonstrates the effectiveness of the presented methods.     

Information Dynamics of Electric Field Intensity before and during the COVID-19 Pandemic

This work investigates the temporal statistical structure of time series of electric field (EF) intensity recorded with the aim of exploring the dynamical patterns associated with periods with different human activity in urban areas. The analyzed time series were obtained from a sensor of the EMF RATEL monitoring system installed in the campus area of the University of Novi Sad, Serbia. The sensor performs wideband cumulative EF intensity monitoring of all active commercial EF sources, thus including those linked to human utilization of wireless communication systems. Monitoring was performed continuously during the years 2019 and 2020, allowing us to investigate the effects on the patterns of EF intensity of varying conditions of human mobility, including regular teaching and exam activity within the campus, as well as limitations to mobility related to the COVID-19 pandemic. Time series analysis was performed using both simple statistics (mean and variance) and combining the information-theoretic measure of information storage (IS) with the method of surrogate data to quantify the regularity of EF dynamic patterns and detect the presence of nonlinear dynamics. Moreover, to assess the possible coexistence of dynamic behaviors across multiple temporal scales, IS analysis was performed over consecutive observation windows lasting one day, week, month, and year, respectively coarse grained at time scales of 6 min, 30 min, 2 h, and 1 day. Our results document that the EF intensity patterns of variability are modulated by the movement of people at daily, weekly, and monthly scales, and are blunted during periods of restricted mobility related to the COVID-19 pandemic. Mobility restrictions also affected significantly the regularity of the EF intensity time series, resulting in lower values of IS observed simultaneously with a loss of nonlinear dynamics. Thus, our analysis can be useful to investigate changes in the global patterns of human mobility both during pandemics or other types of events, and from this perspective may serve to implement strategies for safety assessment and for optimizing the design of networks of EF sensors.     

An Approach for Security Enhancement of Certain Encryption Schemes Employing Error Correction Coding and Simulated Synchronization Errors

An approach for the cryptographic security enhancement of encryption is proposed and analyzed. The enhancement is based on the employment of a coding scheme and degradation of the ciphertext. From the perspective of the legitimate parties that share a secret key, the degradation appears as a transmission of the ciphertext through a binary erasure channel. On the other hand, from the perspective of an attacker the degradation appears as a transmission of the ciphertext over a binary deletion channel. Cryptographic security enhancement is analyzed based on the capacity of the related binary deletion channel. An illustrative implemementation framework is pointed out.     

An efficient higher order family of root finders

A one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial, based on a cubically convergent Hansen–Patrick's family, is studied. We show that the convergence of the basic family of the fourth order can be increased to five and six using Newton's and Halley's corrections, respectively. Since these corrections use the already calculated values, the computational efficiency of the accelerated methods is significantly increased. Further acceleration is achieved by applying the Gauss–Seidel approach (single-step mode). One of the most important problems in solving nonlinear equations, the construction of initial conditions which provide both the guaranteed and fast convergence, is considered for the proposed accelerated family. These conditions are computationally verifiable; they depend only on the polynomial coefficients, its degree and initial approximations, which is of practical importance. Some modifications of the considered family, providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions, are also studied. Numerical examples demonstrate the convergence properties of the presented family of root-finding methods.