Offset boosting in a discrete system.

Offset boosting plays an important role in chaos application in electronic engineering. A direct variable substitution typically will destroy the dynamics of a discrete map even though the initial condition is well considered. The internal fundamental reason is that the left-hand side of a discrete system does not have the dimension of variable differentiation (DVD) like the one of a continuous system. When the key property of DVD is completely preserved, the offset boosting based on a parameter or the initial condition can be reasonably achieved like in a differential system. Consequently, by the initial condition-oriented offset boosting, flexible multistability like attractor self-reproducing or attractor doubling can be further realized. A circuit experiment is completed for the verification of reliable offset boosting. The systematic exploration of offset boosting in a map will cast a new light on chaos regulation and attractor transportation in a discrete map. As a simple case, a two-dimensional Hénon map is taken as the example demonstrating the achievement of offset boosting via the parameter or initial condition.

Memristor-type chaotic mapping.

In this letter, a compact memristor structure unit is applied for constructing the discrete chaotic system and, consequently, a memristor-type chaotic mapping is designed. Two independent system parameters are proven to be partial and total amplitude controllers. Meanwhile, the internal memristor parameter returns the map a typical bifurcation. Finally, a hardware experiment based on STM32 is carried out by verifying the theoretical finding. To the best of our knowledge, the memristor-type chaotic mapping has not been previously reported.

Offset parameter cancellation produces countless coexisting attractors.

The average value of a system variable determines the position of its attractor. When the offset parameters come together and get disappeared after an algebraic operation, the location of the attractor is then governed by an initial condition only. In this case, parameter-dominated offset control turns out to be the initial condition-defined coexisting attractors. In this Letter, a special mechanism for generating countless coexisting attractors is disclosed. Furthermore, a new regime of multistability is revealed, which explains where and how countless coexisting attractors are born and arranged.

Periodic offset boosting for attractor self-reproducing.

The special regime of multistability of attractor self-reproducing is deeply decoded based on the conception of offset boosting in this letter. Attractor self-reproducing is essentially originated from periodic initial condition-triggered offset boosting. Typically, a trigonometric function is applied for attractor self-reproducing. The position, size, and clone frequency determine the selected periodic function. Specifically, in-depth investigation on three elements of sinusoidal quantity is taken into account and then a universal law of attractor self-reproducing is built: the original position of an attractor determines the initial phase and the size of attractor sets the amplitude, while the reproducing interval between two attractors determines the frequency of the trigonometric function. It is found that the product of amplitude and frequency is a constant determined by the reproducing periodic function. The positive and negative switching of the slope in sinusoidal function also leads to the waste of phase space since in general there is no attractor reproduced at the region with negative slope except that new polarity balance is reconstructed paying back the attractor with conditional symmetry. Three-element-oriented offset boosting makes attractor self-reproducing more designable, achievable, and adjustable, which brings great convenience to engineering applications.

A 2D hyperchaotic map with conditional symmetry and attractor growth.

By introducing trigonometric functions, a 2D hyperchaotic map with conditional symmetric attractors is constructed, where a symmetric pair of hyperchaotic attractors and asymmetric hyperchaotic attractors is found. For the existence of periodic feedback, the newly proposed map also exhibits attractor growth under specific circumstances. The polarity balance of the discrete map can be restored from the applied sinusoidal functions, combined with an extra inversion of the constant term. To the best of our knowledge, the above properties are not found in other chaotic maps. Finally, the hardware implementation based on STM32 is conducted, and the corresponding results agree with the numerical simulation and the theoretical analysis.

Dynamics editing based on offset boosting.

Multistability in a dynamical system has attracted great attention recently for its complex and unexpected states. Since in most chaotic systems coexisting attractors reside in their own individual basin of attraction with a fractal structure, it becomes a challenge to choose correct initial conditions to obtain desired dynamics. Selecting typical dynamics as the basic components in a dynamical sequence and then arranging them in the phase space in a desired order make the multistability transparent and controllable in the domain of initial conditions; thereafter, one can identify an attractor according to its initial sequence. Dynamics editing provides an effective technique to select typical attractors under different system parameters to form a flexible sequence in the phase space, which shows great potential for chaos-based secure communications.

Polarity balance for attractor self-reproducing.

There are complex chaotic manifolds in practical nonlinear dynamical systems, especially in nonlinear circuits and chemical engineering. Any system attractor has its own geometric and physical properties, such as granularity, orientation, and spatiotemporal distribution. Polarity balance plays an important role in the solution of a dynamical system including symmetrization, attractor merging, and attractor self-reproducing. The absolute value function and the signum function manage and control the polarity balance, strictly regulating the attractor distribution by switching the polarity balances. Attractor self-reproducing is an attractive regime for constructing the desired multistability, where the coexisting attractors at different positions can be extracted by a selected initial value. Polarity balance is the key factor for attractor self-reproducing, where the offset boosting of an attractor needs an available polarity controller to restore the imbalanced polarity.

Gene Expression Changes Accompanying the Duodenal Adenoma-Carcinoma Sequence in Familial Adenomatous Polyposis.

OBJECTIVES: Duodenal cancer in familial adenomatous polyposis (FAP) arises from adenomas. Differentially expressed genes (DEGs) in the duodenal adenoma-carcinoma pathway have been identified in murine FAP models, but similar data in patients with FAP are limited. Identifying such changes may have significance in understanding duodenal polyposis therapies and identifying cancer biomarkers. We performed a genome-wide transcriptional analysis to describe the duodenal adenoma-carcinoma sequence and determine changes distinguishing patients with FAP with and without duodenal cancer. METHODS: Transcriptional profiling was performed with the Affymetrix Human Transcriptome Array 2.0 on duodenal biopsies from 12 FAP patients with duodenal cancer (FAP cases) and 12 FAP patients without cancer (FAP controls). DEGs were compared between cancer-normal, adenoma-normal, and cancer-adenoma in FAP cases and between adenomas from FAP cases and FAP controls. Significant results at P < 0.05 were filtered using fold change > 2. RESULTS: Two hundred twenty-four DEGs were identified at an absolute fold change > 2. In adenoma-normal, downregulation of DEGs involved in metabolism of brush border proteins (LCT), lipids (APOB/A4), reactive oxygen species (GSTA2), and retinol (RBP2) was observed. In the cancer-adenoma comparison, upregulation of DEGs involved in cell invasion/migration (POSTN, SPP1) and downregulation of DEGs involved in Paneth differentiation (DEFA5/6) were observed. In the adenoma-adenoma comparison, downregulation of several DEGs (CLCA1, ADH1C, ANXA10) in FAP case adenomas was observed. DEGs with therapeutic potential include SPP1, which is involved in both cyclooxygenase and epidermal growth factor receptor pathways targeted by the sulindac/erlotinib combination for duodenal polyposis. DISCUSSION: We describe DEGs in the human duodenal adenoma-carcinoma sequence in FAP, which may have prognostic and therapeutic significance. Validation studies are needed to confirm these findings.

Doubling the coexisting attractors.

When the offset boosting technique is introduced into a chaotic system for attractor shifting, the number of coexisting attractors in the system can be doubled under the application of the employed absolute-value function. Consequently, the offset booster becomes a doubling parameter determining the distance between the two coexisting attractors, and therefore can polymerize these attractors to become a pseudo-multi-scroll attractor. This paper demonstrates that the attractor doubling operation can be applied to any dimension of the system and can also be nested at any time leading to the geometric growth of the coexisting attractors. Furthermore, various regimes of coexistence can be merged and composed together to reproduce an integrated attractor in the system.

A New Chaotic System with a Self-Excited Attractor: Entropy Measurement, Signal Encryption, and Parameter Estimation.

In this paper, we introduce a new chaotic system that is used for an engineering application of the signal encryption. It has some interesting features, and its successful implementation and manufacturing were performed via a real circuit as a random number generator. In addition, we provide a parameter estimation method to extract chaotic model parameters from the real data of the chaotic circuit. The parameter estimation method is based on the attractor distribution modeling in the state space, which is compatible with the chaotic system characteristics. Here, a Gaussian mixture model (GMM) is used as a main part of cost function computations in the parameter estimation method. To optimize the cost function, we also apply two recent efficient optimization methods: WOA (Whale Optimization Algorithm), and MVO (Multi-Verse Optimizer) algorithms. The results show the success of the parameter estimation procedure.

Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems.

Designing a chaotic system with infinitely many attractors is a hot topic. In this paper, multiscale multivariate permutation entropy (MMPE) and multiscale multivariate Lempel-Ziv complexity (MMLZC) are employed to analyze the complexity of those self-reproducing chaotic systems with one-directional and two-directional infinitely many chaotic attractors. The analysis results show that complexity of this class of chaotic systems is determined by the initial conditions. Meanwhile, the values of MMPE are independent of the scale factor, which is different from the algorithm of MMLZC. The analysis proposed here is helpful as a reference for the application of the self-reproducing systems.

A new chaotic oscillator with free control.

A novel chaotic system is explored in which all terms are quadratic except for a linear function. The slope of the linear function rescales the amplitude and frequency of the variables linearly while its zero intercept allows offset boosting for one of the variables. Therefore, a free-controlled chaotic oscillation can be obtained with any desired amplitude, frequency, and offset by an easy modification of the linear function. When implemented as an electronic circuit, the corresponding chaotic signal can be controlled by two independent potentiometers, which is convenient for constructing a chaos-based application system. To the best of our knowledge, this class of chaotic oscillators has never been reported.

A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design.

This paper reports about a novel three-dimensional chaotic system with three nonlinearities. The system has one stable equilibrium, two stable equilibria and one saddle node, two saddle foci and one saddle node for different parameters. One salient feature of this novel system is its multiple attractors caused by different initial values. With the change of parameters, the system experiences mono-stability, bi-stability, mono-periodicity, bi-periodicity, one strange attractor, and two coexisting strange attractors. The complex dynamic behaviors of the system are revealed by analyzing the corresponding equilibria and using the numerical simulation method. In addition, an electronic circuit is given for implementing the chaotic attractors of the system. Using the new chaotic system, an S-Box is developed for cryptographic operations. Moreover, we test the performance of this produced S-Box and compare it to the existing S-Box studies.

Research on the treatment of oily wastewater by coalescence technology.

Recently, oily wastewater treatment has become a hot research topic across the world. Among the common methods for oily wastewater treatment, coalescence is one of the most promising technologies because of its high efficiency, easy operation, smaller land coverage, and lower investment and operational costs. In this research, a new type of ceramic filter material was chosen to investigate the effects of some key factors including particle size of coarse-grained materials, temperature, inflow direction and inflow velocity of the reactor. The aim was to explore the optimum operating conditions for coarse-graining. Results of a series of tests showed that the optimum operating conditions were a combination of grain size 1-3 mm, water temperature 35 °C and up-flow velocity 8 m/h, which promised a maximum oil removal efficiency of 93%.

Comment on "how to obtain extreme multistability in coupled dynamical systems".

We note that extreme multistability of the type described in the referenced paper can be achieved in virtually any dynamical system by adding extraneous variables and using their initial conditions in place of the existing parameters or as additional parameters. We show several simple examples of this and show how the referenced examples are similar.

Elevated AF1q expression is a poor prognostic marker for adult acute myeloid leukemia patients with normal cytogenetics.

Nearly half of the patients with newly diagnosed acute myeloid leukemia have normal cytogenetics (NC-AML) and are classified as intermediate risk, but their 5-year overall survival (OS) ranges from 24 to 42%. Therefore, molecular biomarkers to identify poor-risk patients are needed. Elevated AF1q expression in the absence of specific poor cytogenetics is associated with poor outcomes in pediatric patients with AML and adult patients with myelodysplastic syndrome. We examined AF1q expression in 290 patients with NC-AML. We found that patients with low AF1q (n = 73) expression (AF1q(low)) have better OS (P = 0.026), disease-free survival (P = 0.1), and complete remission rate (P = 0.06) when compared with patients with high AF1q expression (AF1q(high) n = 217). The patients with AF1q(high) had significantly greater incidence of concurrent tyrosine kinase3 internal tandem duplication. A subgroup of the patients with AF1q(high) who received allogeneic stem cell transplantation (SCT) had a significant better relapse-free survival when compared with patients who received chemotherapy/autologous SCT (P = 0.04). This study suggests that high AF1q expression is a poor prognostic marker for adult patients with NC-AML.