Discrete Moments Research Articles

On the problem of controlling a second-order nonlinear system by means of discrete control under disturbance

The problem of bringing a trajectory to a neighborhood of zero under disturbance is considered in terms of a differential pursuit game. The dynamics are described by a nonlinear autonomous system of second-order differential equations. The set of values of the pursuer's controls is finite, and that of the evader (disturbance) is compact. The goal of the control, that is, the goal of the pursuer, is to bring, within a finite time, the trajectory to any predetermined neighborhood of zero, regardless of the actions of the disturbance. To construct the control, the pursuer knows only the phase coordinates and the value of the velocity at some discrete moments of time and the choice of the disturbance control is unknown. Conditions are obtained for the existence of a set of initial positions, from each point of which a capture occurs in the specified sense. Moreover, this set contains a certain neighborhood of zero. The winning control is constructed constructively and has an additional property specified in the theorem. In addition, an estimate of the time required to bring the speed from one given point to the neighborhood of another given point under disturbance conditions was obtained.

Statistical inference on the exponentiated moment exponential distribution and its discretization

Hasnain and Ahmad (2013) propose a two-parameter Exponentiated Moment Exponential (EME) Distribution and investigate its some characteristics. In this paper we study its additional properties in the context of its applications. The study classifies the EME distribution to homogeneous subfamilies with respect to hazard rate. A simulation study is conducted for EME distribution to observe the parameters for maximum likelihood and quartile estimates based on bias and mean square error. Based on EME distribution, we develop a discretized model that gives its importance in the industry. However, some important structural properties are studied for discrete Exponentiated moment exponential distribution with useful characterizations. Shapes of density and failure rate function of new discrete model are studied. Moreover, we provide justifications for the usefulness of the model and its enhanced scope as compared to the existing discretized model with the help of real-life data sets.

Negative discrete moments of the derivative of the Riemann zeta‐function

AbstractWe obtain conditional upper bounds for negative discrete moments of the derivative of the Riemann zeta‐function averaged over a subfamily of zeros of the zeta function that is expected to be arbitrarily close to full density inside the set of all zeros. For , our bounds for the ‐th moments are expected to be almost optimal. Assuming a conjecture about the maximum size of the argument of the zeta function on the critical line, we obtain upper bounds for these negative moments of the same strength while summing over a larger subfamily of zeta zeros.

Discrete moments models for Vlasov equations with non constant strong magnetic limit

Discrete moments models for Vlasov equations with non constant strong magnetic limit

Ecologies of co-production in the Anthropocene

The urgency, uncertainty and unevenness of the Anthropocene has foregrounded the spatial and temporal multiplicity of co-production between science and society. In this article, we draw together work in geography, science and technology studies and cognate disciplines concerned with ‘co-producing’ knowledge for environmental governance, and with the ‘co-production’ of science and politics. Yet these existing studies and approaches have tended to focus on discrete moments of co-production within bounded time-spaces. Building on work associated with ecologies of participation and geographies of science, we introduce the notion of ‘ecologies of co-production’ as a way to more faithfully attend to multiple co-existing co-productions and the interrelations between them. We define this as diverse interrelating practices and spaces of co-production which intermingle and are co-produced with(in) wider systems and political cultures in which they are situated. We set out how this opens up new ways of thinking about and attending to the spaces and interrelations, diversities and exclusions, histories and constitutions, and responsibilities and affects of co-productions between science and society in the Anthropocene. We suggest that this approach can make a difference in how we do co-production, how we analyse co-production and how we live, act and figure in an Anthropocene world.

NICU Language, Everyday Ethics, and Giving Better News: Optimizing Discussions about Disability with Families.

The Neonatal Intensive Care Unit (NICU) has a language and culture that is its own. For professionals, it is a place of intense and constant attention to microdetails and cautious optimism. For parents, it is a foreign place with a new and unique language and culture. It is also the setting in which they are introduced to their child and parenthood for this child. This combination has been referred to as an emotional cauldron. The neonatal ethics literature mainly examines complex ethical dilemmas about withholding/drawing life sustaining interventions for fragile children. Rarely are everyday ethics or mundane ethics discussed. Microethics describe the mundane, discrete moments that occur between patients/families and clinicians. A key piece of these microethics is the language used to discuss patient care. Perception of prognoses, particularly around long-term neurodevelopmental outcome, is shaped with the language used. Despite this, clinicians in the NICU often have no specific training in the long-term neurodevelopment outcomes that they discuss. This paper focuses on the microethics of language used to discuss long-term neurodevelopmental outcomes, the developmental neuroscience behind language processing, and offers recommendations for more accurate and improved communication around long-term outcomes with families with critically ill neonates.

Efficient color image steganography based on new adapted chaotic dynamical system with discrete orthogonal moment transforms

In today's rapidly evolving digital landscape, safeguarding the secure transmission of sensitive information is paramount. Traditional steganography methods, while effective at data concealment, have grown vulnerable to brute force attacks in our age of powerful computing. This paper addresses the pressing need to bolster data transmission security. To address the challenges posed by limited key space and security concerns associated with 1-D chaotic maps in data transmission, we introduce a novel 1-D chaotic map, the Multi-Parameter Chebyshev Map (MCM). The MCM boasts four control parameters, each with a broad chaotic range and high chaos level, significantly enhancing security. Furthermore, we present an innovative steganography technique for color images that leverages the MCM in conjunction with discrete moment transforms. This method chaotically embeds the secret message within the moment coefficients of a cover color image using MCM and quantization rules. The expansive chaotic range and high chaos level of the MCM substantially reinforce the security of this approach. The considered moment transforms include Tchebichef, Krawtchouk, Hahn, Charlier, Meixner, Shmaliy, Racah, and Dual-Hahn. The performance of the proposed steganography method is thoroughly evaluated and compared with other state-of-the-art methods in terms of hiding capacity and image quality in both spatial and transform domains. The quantization of moment coefficients demonstrates its superior performance. This method holds crucial implications for practical applications requiring secure communication of color images, such as military and medical contexts. The combination of MCM and moment transforms in this method presents a promising avenue for future research in the field of information hiding.

Optimal algorithm for color medical encryption and compression images based on DNA coding and a hyperchaotic system in the moments

Currently, visual data security plays a significant role in various fields, especially in medical imaging. Addressing the challenges associated with limited key space and vulnerability to different types of attacks within current encryption schemes, this work proposes an optimal compression-encryption scheme for large medical images that incorporates elements of Archimedes' optimization algorithm, discrete orthogonal Hahn moments, chaotic systems, and DNA coding. The primary aim of this study is to develop an optimal and exceptionally resilient compression-encryption scheme capable of countering various attack types effectively. This approach is structured into three principal phases: a compression phase harnessing the efficiencies of Hahn's discrete orthogonal moments (HMs) in signal and image representation, coupled with the Archimedes optimization algorithm (AO) to ensure optimal tuning of polynomial parameters (a, b) for superior image reconstruction quality. The encryption phase is performed on the compressed image, using hyperchaotic memristive 4-D (HCM-4D), adapted logistics map (ALM) and DNA coding. Initially, the adapted logistics map is responsible for generating random sequences linked to the compressed image. Subsequently, chaotic sequences originating from the hyperchaotic 4-D memristive system govern both random sequences and DNA processes. The optimization phase, facilitated by the AO algorithm, focuses on minimizing the value of the objective function (correlation) on the compressed and encrypted images. Ultimately, the image with the lowest correlation value is designated as the optimal compressed-encrypted representation.The simulation results clearly illustrate the resilience of the AO algorithm when juxtaposed with other optimization algorithms, especially with respect to convergence speed and computational efficiency. On the other hand, the proposed compression approach demonstrated exceptional efficiency in compressing medical images, offering us the possibility to achieve impressive compression ratio (CR) as well as exceptional quality in decompressed images, evident thanks to high PSNR values. In addition, security analyze demonstrate that the proposed compression-encryption benefits from a larger key space and superior resistance against different types of attacks. Furthermore, our approach was subjected to a comparative analysis alongside various encryption method. These comparisons demonstrate that our encryption algorithm surpasses others in terms of both security and effectiveness.

Note on control for hybrid stochastic systems by intermittent feedback rooted in discrete observations of state and mode with delays

<abstract> <p>For a hybrid stochastic system, most existing feedback controllers need to observe modes at continuous times, which is feasible when the system's mode is observable and does not incur any cost. However, in most cases, the mode is not readily apparent, and identifying it always incurs a certain expense. Therefore, in order to reduce control costs, when designing a feedback controller, both the state and the mode should be observed at discrete moments. This paper introduces an intermittent feedback controller for stabilizing an unstable hybrid stochastic system through discrete delayed observations of state and mode. By utilizing M-matrix theory, intermittent control approach, and the comparison principle, we propose sufficient conditions for the stabilization theory of hybrid stochastic systems. An illustrative example is taken to validate the proposed theory.</p> </abstract>

Numerical modeling of surface subsidence due to compaction of soil with fine inclusions

A mathematical model of filtration consolidation of an inhomogeneous soil mass was formed taking into account the change in the size of the area during the compaction process. The inhomogeneity is considered as the presence of fine inclusions (geobarriers) the physical and mechanical characteristics of which differ from those of the main soil. From a mathematical viewpoint, the model is described by a one-phase Stefan problem that has a kinematic boundary condition on the upper moving boundary as its component. The purpose of the research is to find out the effect of fine inclusion on the dynamics of subsidence of the soil surface in the process of compaction. The change in the dimensions of the solution area is physically determined by the change in the volume of the pores of the porous medium in the process of dissipating excess pressure. If the permeability of the geobarrier is low, it affects the dynamics of consolidation processes and, accordingly, the magnitude of subsidence. Finite element solutions of the initial-boundary value problem for the nonlinear parabolic equation in the heterogeneous region with the conjugation condition of non-ideal contact were found. Numerical time discretization methods, a method for determining the change in the position of the upper boundary at discrete moments of time, and an algorithm for determining the physical and mechanical characteristics of a porous medium depending on the degree of consolidation are given. A number of test examples were considered, and the effect of a thin inclusion on the dynamics of the change in the position of the upper boundary of the problem solution area was investigated.

On some discrete mean values of higher derivatives of Hardy’s Z-function

Yıldırım obtained an asymptotic formula of the discrete moment of [Formula: see text] over the zero of the higher derivatives of Hardy’s [Formula: see text]-function. We give a generalization of his result on Hardy’s [Formula: see text]-function.

Event-triggered affine formation maneuver control for second-order multi-agent systems with sampled data

This paper addresses the affine formation maneuver problem for second-order multi-agent systems with distributed event-triggered controllers. For multiple leaders moving with constant accelerations, a sampled-data-based event-triggered proportional–integral controller is proposed to reduce the frequencies of controller update, where triggering moments are determined by the relative states between agent and its neighbors. Moreover, based on the proposed event-triggered control scheme, a self-triggered mechanism is designed to avoid continuous measurements for relative states and continuous calculating of local events at each discrete moment. Some sufficient conditions for achieving affine formation maneuver control are obtained and the Zeno behavior is naturally eliminated due to periodic sampling setting. Finally, the theoretical results are illustrated through numerical simulations.

A Generalized Stacked Reinforcement Learning Method for Sampled Systems

A common setting of reinforcement learning (RL) is a Markov decision process (MDP) in which the environment is astochastic discrete-time dynamical system. Whereas MDPs are suitable in such applications as video-games or puzzles, physical systems are time-continuous. A general variant of RL is of digital format, where updates of the value (or cost) and policy are performed at discrete moments in time. The agent-environment loop then amounts to a sampled system, whereby sample-and-hold is a specific case. In this paper, we propose and benchmark two RL methods suitable for sampled systems. Specifically, we hybridize model-predictive control (MPC) with critics learning the optimal Q- and value (or cost-to-go) function. Optimality is analyzed and performance comparison is done in an experimental case study with a mobile robot.

High-Order Finite Element Second Moment Methods for Linear Transport

We present high-order, finite element–based Second Moment Methods (SMMs) for solving radiation transport problems in two spatial dimensions. We leverage the close connection between the Variable Eddington Factor (VEF) method and SMM to convert existing discretizations of the VEF moment system to discretizations of the SMM moment system. The moment discretizations are coupled to a high-order Discontinuous Galerkin discretization of the SN transport equations. We show that the resulting methods achieve high-order accuracy on high-order (curved) meshes, preserve the thick diffusion limit, and are effective on a challenging multimaterial problem both in outer fixed-point iterations and in inner preconditioned iterative solver iterations for the discrete moment systems. We also present parallel scaling results and provide direct comparisons to the VEF algorithms from which the SMM algorithms were derived.

Artificial Magnetic Tripod Ice.

We study the collective behavior of interacting arrays of nanomagnetic tripods. These objects have six discrete moment states, in contrast to the usual two states of an Ising-like moment. Our experimental data demonstrate that triangular lattice arrays form a "tripod ice" that exhibits charge ordering among the effective vertex magnetic charges, in direct analogy to artificial kagome spin ice. The results indicate that the interacting tripods have effective moments that act as emergent local variables, with strong connections to the well-studied Potts and clock models. In addition, the tripod moments display a tendency toward a nearest neighbor alignment in our thermalized samples that separates this system from kagome spin ice. Our results open a path toward the study of the collective behavior of nonbinary moments that is unavailable in other physical systems.

“The less said the soonest mended”

Jody Griffith, “‘The less said the soonest mended’: Time and Etiquette in The Way We Live Now” (pp. 142–163) Anthony Trollope’s novels were usually popular, but his 1875 novel The Way We Live Now was an exception. Contemporary readers and critics alike considered the novel unpleasant, or even rude. This article argues that reception was not only a response to the novel’s unlikable characters, but also to its uncomfortable temporal disruptions. The novel’s frequently repeated maxim “the less said the soonest mended” connects saying too much with incivility; to say less means to move quickly back to the status quo. The novel says “too much” by slowing down the present moment into its fragmented parts. The “now” in the title The Way We Live Now emphasizes the temporality of its narrative form, especially the tension of stabilizing a discrete present moment within the forward momentum of a novel. The instability of the “now” is a thematic focus of the novel, with characters unsettled by changing etiquette expectations. Similarly, as timelines slow down and speed up, skip ahead and reverse, the novel leaves us as temporally disoriented as the characters.

Integrated approach to analyzing the stress-strain state of the tubbing erector manipulator mechanism based on the SolidWorks program

Purpose. The research purpose is todevelop and substantiate a method for computer analysis of the stress-strain state that occurs in the tubbing erector manipulator mechanism with several degrees of freedom, using modern computing complexes based on the finite-element method. Methods. The research uses software complexes, with the help of which a calculation-theoretical apparatus has been created, which is intended for calculating dynamic and static loads that occur in the elements of the tubbing erector manipulator mechanism. The results of modeling the stress-strain state in the parts and nodes of this mechanism, obtained using the SolidWorks Motion and SolidWorks Simulation programs, have been compared. The errors in these results have been estimated. Findings. The effectiveness of the proposed analysis method, based on the combination of SolidWorks applications, in particular, SolidWorks Motion and SolidWorks Simulation, has been proven on the example of modeling the most complex design of the UT62 tubbing erector mechanism.The essence of the method is that initially, using the SolidWorks Motion application, the laws of motion of the motors are set. The tubbing erecting process itself is divided into discrete moments of time with the selection of parts in which the stress fields are calculated and with the determination of the maximum equivalent stress, using the Simulation Setup tool. The change in these stresses during the erecting cycle is analyzed, and if it is necessary to refine the data, the discrete time step of the mechanism motion is reduced. Specific information about the stress-strain state of the part is obtained in the SolidWorks Simulation application, using data imported from the SolidWorks Motion program about gravitational and inertial forces that occur in the tubbing erector mechanism. Originality. The scientific novelty of the developed method of computer analysis for the mechanism of the manipulator of the UT62 type tubing stacker is manifested in a comprehensive approach to modeling the stress-strain state, which includes the integration of data from SolidWorks Motion and SolidWorks Simulation programs for accurate determination of stresses, taking into account both gravitational forces and dynamic loads, which ensures high accuracy and complexity of calculations in real operating conditions of the mechanism. Practical implications. The proposed method can be used for modeling the motion of mechanisms of different complexity, in particular, in the design of domestic tubbing erectors.

Algorithm for Calculating Noise Immunity of Cognitive Dynamic Systems in the State Space

The research method consists in applying the state space method, widely used in the study of automatic dynamical systems, to describe the behavior of cognitive systems. It is assumed, that at the input of the cognitive system, there is a signal and interference described by Poisson point processes, modeling the amount of information, the amount of emotional stress, etc., corresponding to each event. The cognitive properties of the system in the paper are taken into account by two circumstances. Firstly, events localized in time are characterized in the paper not only by the Poisson distribution of the times of their occurrence, but also by some random variables that characterize the importance (significance) events for the system. A typical example is the attribution of a certain amount of information to each event, if an information processing system is modeled. Another example is the emotional reaction of a person to the appearance of stress, described in a classic work on psychology. In this case, the point is the event that causes stress, and the effects of stress on the system are modeled by the relative magnitude of stress in accordance with the Holmes and Rahe scale. Secondly, the cognitive system processes, assimilates, adapts to the impact that each event has on it with its inherent speed. In this paper, this phenomenon is modeled as the passage of a point process through a dynamic system described by differential equations. Such processes are called filtered point processes. Examples of impacts are given and, for simplicity, an assumption is made about the magnitude of the impact as the amount of information received by the system when an event occurs. Thus, the model of a cognitive system is a dynamic system described by a differential equation in the state space, at the input of which messages with a certain information load appear at random discrete moments of time.As for any technical system, the cognitive system faces the task of evaluating the quality of its work. In this regard, the paper substantiates the use of a convenient quality index from an engineering point of view and an appropriate criterion in the form of a signal – interference ratio. The new results are differential equations in the state space for the mathematical expectations of the signal and interference, as well as an algorithm for calculating the noise immunity of the cognitive system. As an example, a graph of the noise immunity of a particular cognitive system is calculated and presented, confirming an intuitive idea of its behavior.In conclusion, it is noted that the main result of the paper is an algorithm for calculating the noise immunity of cognitive systems using differential equations that allow calculating the behavior of non-stationary cognitive systems under any point impacts described by a non-stationary function of the intensities of the appearance of points. The equations of behavior of the mathematical expectation of the processed information are reduced to a canonical form, which allows them to be applied to a variety of practical tasks, for example, to the description of hierarchical cognitive structures when the output of one level is the input of another.

Secure and optimized satellite image sharing based on chaotic eπ map and Racah moments

The objective of this paper is to contribute to the sharing, transfer, and secured indexing of large color images. Watermarking and digital encryption have emerged as alternative and complementary solutions to ensure authorized access, facilitate authentication of content, or prevent illegal reproduction. For this reason, we suggest a new system based on four techniques derived from various transformation and decomposition methods, such as the discrete orthogonal Racah moment transformations (DORMT), which allows the information capacity to be reduced to a number of coefficients, as well as the discrete wavelet transform (DWT), which makes it possible to decompose into a certain number of multilevel sub-bands, to have the sub-band that represents most of the image information. In addition, Schur decomposition (SD) and singular value decomposition (SVD) have been used to increase security. The proposed system consists of two main phases. The first phase is the integration of a color watermark, first applying DORMT-SD-SVD to a color host image and then applying DWT-SD-SVD to achieve a compromise between capacity, invisibility and robustness in terms of quality and privacy. The second phase is the encryption of the watermarked image with an eπ map to increase security for sharing, transfer and indexing. This system uses an Aquila Optimization Algorithm (AOA) as an optimization procedure to find the best set of DORMT parameters and provide a dynamic and adaptive scale factor. The experimental results, in which the proposed system's properties are tested and compared to those of other systems, make it clear that the proposed system is useful in terms of its level of security, capacity, invisibility, and resistance to attacks that use signal processing.

Novel Integer Shmaliy Transform and New Multiparametric Piecewise Linear Chaotic Map for Joint Lossless Compression and Encryption of Medical Images in IoMTs

The discrete Shmaliy moment transform (DST) is a type of discrete orthogonal moment transform that is widely used in signal and image processing. However, DST is not suitable for lossless image applications due to its non-integer reversible nature. To overcome this limitation, we introduce the integer discrete Shmaliy transform (IDST) that performs integer-to-integer encoding, leading to a perfect and unique reconstruction of the input image. Next, a new 1D chaotic system model, the 1D multiparametric piecewise linear chaotic map (M-PWLCM), is presented as an extension of the existing 1D PWLCM. The M-PWLCM includes eight control parameters defined over an unlimited interval. To demonstrate the relevance of IDST and M-PWLCM in reversible image processing applications, they are used in a new scheme for lossless compression and encryption of medical images in the internet of medical things (IoMTs). On the one hand, the simulation results show that our scheme offers a good compression ratio and a higher level of security to resist differential attacks, brute force attacks and statistical attacks. On the other hand, the comparative analysis carried out shows the overall superiority of our scheme over similar state-of-the-art ones, both in achieving a higher compression ratio and better security when communicating medical images over unsecured IoMTs.