Nonlinear Chain Research Articles

Variational Inference for Large Bayesian Vector Autoregressions

We propose a novel variational Bayes approach to estimate high-dimensional Vector Autoregressive (VAR) models with hierarchical shrinkage priors. Our approach does not rely on a conventional structural representation of the parameter space for posterior inference. Instead, we elicit hierarchical shrinkage priors directly on the matrix of regression coefficients so that (a) the prior structure maps into posterior inference on the reduced-form transition matrix and (b) posterior estimates are more robust to variables permutation. An extensive simulation study provides evidence that our approach compares favorably against existing linear and nonlinear Markov chain Monte Carlo and variational Bayes methods. We investigate the statistical and economic value of the forecasts from our variational inference approach for a mean-variance investor allocating her wealth to different industry portfolios. The results show that more accurate estimates translate into substantial out-of-sample gains across hierarchical shrinkage priors and model dimensions.

An Autocatalytic Platform Combining a Nonlinear Hybridization Chain Reaction and DNAzyme to Detect microRNA

An Autocatalytic Platform Combining a Nonlinear Hybridization Chain Reaction and DNAzyme to Detect microRNA

Smart Tumor Cell-Derived DNA Nano-Tree Assembly for On-Demand Macrophages Reprogramming.

Without coordinated strategies to balance the population and activity of tumor cells and polarized macrophages, antitumor immunotherapy generally offers limited clinical benefits. Inspired by the "eat me" signal, a smart tumor cell-derived proximity anchored non-linear hybridization chain reaction (Panel-HCR) strategy is established for on-demand regulation of tumor-associated macrophages (TAMs). The Panel-HCR is composed of a recognition-then-assembly module and a release-then-regulation module. Upon recognizing tumor cells, a DNA nano-tree is assembled on the tumor cell surface and byproduct strands loaded with CpG oligodeoxynucleotides (CpG-ODNs) are released depending on the tumor cell concentration. The on-demand release of CpG-ODNs can achieve efficient regulation of M2 TAMs into the M1 phenotype. Throughout the recognition-then-assembly process, tumor cell-targeted bioimaging is implemented in single cells, fixed tissues, and living mice. Afterward, the on-demand release of CpG-ODNs regulate the transformation of M2 TAMs into the M1 phenotype by stimulating toll-like receptor 9 to activate the NF-κB pathway and increasing inflammatory cytokines. This release-then-regulation process is verified to induce strong antitumor immune responses both in vitro and in vivo. Altogether, this proposed strategy holds tremendous promise for on-demand antitumor immunotherapy.

On linear stabilization of a class of nonlinear systems in a critical case

In this paper, we address the stabilization problem for nonlinear systems in a critical case. Namely, we study the class of canonical nonlinear systems. Canonical nonlinear systems or chain of power integrators is an important subject of research. Studying such systems is complicated by the fact that they cannot be mapped onto linear systems. Moreover, they have the uncontrollable first approximation. Previous results on smooth stabilization of such systems were obtained under the assumption that the powers in the right-hand side are strictly decreasing. In this work, we consider a case of non-increasing powers in the right-hand side for a three-dimensional system. A popular approach for studying such systems is the backstepping method, which is a method of step-wise stabilization. This method requires a sequential investigation of lower-dimensional subsystems. Backstepping enables the study of a wide range of nonlinear triangular systems but requires technically complex and cumbersome computations. Therefore, a natural question arises about constructing stabilizing controls of a simple form. Polynomial controls can serve as an example of such controls. In the paper, we demonstrate that linear controls can be considered as stabilizing controls. We derive sufficient conditions for the coefficients of the linear control that ensure the asymptotic stability of the zero equilibrium point of the corresponding closed-loop system. The asymptotic stability is proven using the Lyapunov function method, which is found as the sum of squares. The negative definiteness of the Lyapunov function derivative in a neighborhood of the origin guarantees asymptotic stability. In contrast to the case of strictly decreasing powers, additional conditions on the control coefficients, apart from their negativity, emerge. The obtained result extends to a broader class of nonlinear systems through stabilization by nonlinear approximation. This allows the consideration of systems with higher-order terms in the right-hand side. The effectiveness of the applied approach is illustrated by several model examples. The method used in this work to investigate the case of non-increasing powers can be applied to systems of higher dimensions.

Developing a resilient and sustainable non-linear closed-loop supply chain management framework for the automotive sector industry using a gaussian fuzzy optimization based non-linear model predictive control approach

ABSTRACT Efforts to merge sustainability and resilience within the automotive industry’s supply chain models have proven challenging. This paper proposes a novel non-linear closed-loop supply chain management framework tailored to the tire industry supply chain from the automotive sector to address the issue of exploring interrelationships. Framework employs trapezoidal linguistic cubic fuzzy Z-score technique for order of preference by similarity to the ideal solution ranking approach to prioritize resilience strategies to maintain sustainability performance during sudden disturbances. Furthermore, Gaussian fuzzy optimization-based non-linear model predictive control acts as a feedback controller to integrate sustainability and resilience by providing a stable output based on the objective function related to sustainability dimensions. An experimental study assesses the impact of resilience strategies on total supply chain costs, highlighting significant cost savings. Adopting strategies like multiple sourcing, information sharing, and improved design quality of the supply chain keeps total expected costs optimal for various sustainability levels.

An artificial intelligence approach to design periodic nonlinear oscillator chains under external excitation with stable damped solitons

In this paper, an artificial intelligence approach is developed to create a metamodel of damped solitons in periodic nonlinear oscillator chains under external excitation. Unlike resonators subjected to parametric excitation, chains subjected exclusively to external excitation do not have known analytical solutions for Intrinsic Localized Modes (ILMs) when damping is pondered. The proposed metamodel is a quick design tool of nonlinear damped periodic structures describing effectively the behavior of solitonic solutions, demonstrating a computational cost considerably lower than that of the Newton method. The results of this work highlight the potential of ANN regression models in the description of physical phenomena represented by the Nonlinear Schrödinger Equation when damping is considered.

Incorporating fractional operators into interaction dynamics of a chaotic biological model

In the exploration of mathematical models in biology, the traditional use of integer-order calculus may fall short in adequately capturing elements such as randomness and memory. As a viable alternative, fractional calculus has been embraced by mathematicians, extending derivatives and integrals to non-integer orders to provide more appropriate tools for managing complexity. In this research, we investigate the effectiveness of two well-known fractional operators, namely the Caputo–Fabrizio and Atangana–Baleanu derivatives, in studying the dynamics of a nonlinear food chain model consisting of three populations. This specific biological system exhibits highly chaotic behavior driven by its sensitivity to various parameters. To approximate solutions, we employ two implicit numerical approaches based on Lagrange interpolation and product integration rules. Furthermore, we analyze the equilibrium points of the system and evaluate their stability characteristics, offering insights into the long-term behavior of the model. To verify the presence of chaotic patterns across different parameter values, we employ two chaos detection techniques—the smaller alignment index and the 0-1 test. By incorporating fractional calculus operators into the dynamic equations, we are able to obtain a more precise representation of such biological systems. Future research endeavors should focus on leveraging additional fractional operators to further enhance the accuracy of modeling nonlinear systems in the field of biology.

Exploring lump soliton solutions and wave interactions using new Inverse $$(G'/G)$$-expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

Exploring lump soliton solutions and wave interactions using new Inverse $$(G'/G)$$-expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

On the classification of nonlinear integrable three-dimensional chains via characteristic Lie algebras

Продолжена работа по описанию интегрируемых нелинейных цепочек с тремя независимыми переменными вида $u^j_{n+1,x}=u^j_{n,x}+f(u^{j+1}_{n},u^{j}_n,u^j_{n+1 },u^{j-1}_{n+1})$ по признаку наличия иерархии редукций, интегрируемых в смысле Дарбу. В основе классификационного алгоритма лежит хорошо известный факт, что характеристические алгебры интегрируемых по Дарбу систем имеют конечную размерность. В работе использована характеристическая алгебра по направлению $x$, структура которой для данного класса моделей определяется некоторым полиномом $P(\lambda)$, степень которого для известных примеров не превосходит 3. Предполагается, что $P(\lambda)=\lambda^2$, в этом случае классификационная задача сводится к отысканию восьми неизвестных функций одной переменной. Получен достаточно узкий класс претендентов на интегрируемость.

Non-reciprocal selective frequency transmission with nonlinear bi-layer cylinder chains

Recent advancements in wave physics have led to the development of systems that break the principle of wave transmission reciprocity. In this study, we present selective frequency transmission with asymmetry in bi-layer phononic crystals, which are composed of two layers of cylinder contact chains. We demonstrate significant non-reciprocal harmonic transmission effects, as well as self-demodulated displacement amplification under excitation from different sides. These effects are achieved through a combination of contact nonlinearity and cascaded bandgaps formed by adjusting the chain lengths in both layers. We find that the evanescent waves generated through nonlinear frequency conversion in the stopband are converted into propagating waves at the interface, subsequently leading to the transmission. Our findings have implications for programmable asymmetric acoustic devices, providing a novel framework for energy mitigation, conversion, and harvesting.

On the classification of nonlinear integrable three-dimensional chains via characteristic Lie algebras

On the classification of nonlinear integrable three-dimensional chains via characteristic Lie algebras

Nanofluidic sensing platform for PNK assay using nonlinear hybridization chain reaction and its application in DNA logic circuit

In this study, a polyethyleneimine (PEI)/Zr4+-functionalized nanofluidic sensing platform based on nonlinear hybridization chain reaction (NHCR) was developed for PNK activity assay. With the existence of PNK, the hairpin HPNK was cleaved by λ exonuclease, liberating the initiator T-DNA. Then T-DNA triggered the nonlinear HCR in solution and the reaction products were absorbed onto the nanopore, which changed the surface charge of nanofluidic device and could be detected by current-voltage characteristic curves. Compared to traditional linear HCR, the nonlinear HCR exhibits a higher sensitivity and order of growth kinetics, making it a powerful signal amplifier in bioanalysis. Due to the powerful amplification efficiency of nonlinear HCR, high sensitivity of the nanopore and specific recognition site of PNK/λ-Exo, an ultrasensitive and selective PNK sensing approach had been developed and applied to precisely quantitate the PNK activity with a LOD of 0.0001 U/mL. Moreover, utilizing this nanofluidic system as a foundation, we constructed a logic circuit that utilized PNK, adenosine diphosphate (ADP), and (NH4)2SO4 as input elements. ADP and (NH4)2SO4 had a crucial function in facilitating the PNK to regulate the DNA logic gate. By modifying the target and inhibitors, the nanofluidic device could detect a variety of stimuli and execute more advanced logical operations.

Perturbation observer design based on extremum seeking control: An analytical insight

In this paper, an optimal extended state observer (ESO) is designed for nonlinear integral chain system. For the first time, in this paper, proportional–integral (PI) extremum seeking control (ESC; PIESC) approach is applied to design a perturbation observer by minimizing the estimation error. The PI type structure of the ESC provides fast transient response for the closed-loop system to attain optimum equilibrium point. A mathematical proof is presented to show that the average error dynamic asymptotically converges to zero while the estimation error is minimized. The simulation results verify that the estimation error achieved by the proposed PIESC-based ESO (PIESC-ESO) is found significantly less than that achieved by the classic ESO and PSO-based ESO. Moreover, if slow changes occur within the system or external to it, the PIESC-ESO is still able to modify the observer gains such that the estimation error is minimized again. Therefore, this may help PIESC-ESO to be used in practical applications.

Construction of abundant solitons in a coupled nonlinear pendulum lattice through two discrete distinct techniques

In this paper, we deal with two distinct discrete techniques named the discrete Tanh method and the differential-difference Jacobi elliptic functions sub-ODE method to extract abundant soliton solutions for a coupled nonlinear pendulum chains. According to the two straightforward schemes’, we construct various solutions likewise, kink, anti-kink, bright, dark, singular-bright solitary wave, traveling compacton, traveling gray soliton-like, periodic soliton-like have not reported on the most recently studied mechanical model. We extract the sought solutions with less approximation (introduction of a discrete wave transformation) and display some graphical representations showing well known, novel shapes discovered in a coupled nonlinear pendulum lattice. More often, the tediousness computations of discrete techniques lead some researchers to changing a nonlinear differential-difference equation into a nonlinear ordinary differential equation throughout the semi-discrete approximation before introducing a wave transformation. Nonetheless, the semi-discrete approximation involve a Taylor bounded expansion’s such as the threshold order depends on the ability and skills of researchers to get solutions through available methods and those that they can perform. Hence, while an algorithm can be lead us to avoiding approximation (eventual source of errors), tediousness analytical computations, we perform by using it, in addition of software availability. And therefore, we establish as is the case in the present work various soliton-like solutions by means of two direct discrete techniques. The effect of some physical parameters are displayed on the shaped through 2D and 3D graphical simulations. The used methods (tanh, sn, cn, dn Jacobi elliptic functions approaches) previously applied on other physical models (discrete electrical transmission lattices) are presented here in manner to be replicable for exploring more soliton solutions in different nonlinear discrete physical models.

Multi-degenerate hill-top bifurcation of Fermi–Pasta–Ulam softening chains: Exact and asymptotic solutions

A one-dimensional nonlinear elastic chain, known as Fermi–Pasta–Ulam system, is analyzed in the static field. The chain is made of elements admitting a quartic potential, with softening nonlinear behavior. When the chain is subject to pure tension, it exhibits a multi-degenerate hill-top bifurcation, from which several softening branches bifurcate. On each path, the springs either behave softening or hardening, in all the possible combinations, making the response non-unique. Both exact and asymptotic solutions are pursued, and the multitude of the bifurcated paths is illustrated by bifurcation diagrams. A proof of their instability is given. The role of the imperfections is commented, either in modifying the equilibrium paths and in unfolding the degenerate bifurcation.

A photoelectrochemical biosensor based on Ti3C2Tx MXene/Ag2S as a novel photoelectric material for ultrasensitive detection of microRNA-141

In this work, a novel photoelectric active material Ti3C2Tx MXene/Ag2S with strong photocurrent signal was prepared to construct the photoelectrochemical (PEC) biosensor for ultrasensitive detection of target miRNA-141. Impressively, Ti3C2Tx MXene with excellent metal conductivity could shorten the electron transmission path to prominently improve the separation of electron-hole pairs and significantly enhance the photocurrent signal of Ti3C2Tx MXene/Ag2S nanocomposite. Meanwhile, streptavidin (SA) was used as a scaffold to assemble a DNA tetrad for constructing a spatial DNA structure by a nonlinear hybrid chain reaction (HCR) triggered via target miRNA-141, which embedded amount of thionine as a sensitizer for significantly increasing the photocurrent response. The biosensor could achieve the sensitive detection of miRNA-141 with detection limit of 34 aM. This strategy demonstrated a novel photoactive material to construct the PEC biosensor for sensitive detection of biomarkers with potential application value in disease diagnosis.

Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms

Nonlinear chains of atoms (NCA) are complex systems with rich dynamics, that influence various scientific disciplines. The lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. We have converted assumed PDE into nonlinear ODE by using the optimal system. The new auxiliary scheme is used to find the Travelling wave solutions, while graphical behaviour visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, and fundamental principles in physics that assert certain quantities remain constant over time.

Nonlinear inviscid damping and shear‐buoyancy instability in the two‐dimensional Boussinesq equations

AbstractWe investigate the long‐time properties of the two‐dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size ε. Under the classical Miles‐Howard stability condition on the Richardson number, we prove that the system experiences a shear‐buoyancy instability: the density variation and velocity undergo an inviscid damping while the vorticity and density gradient grow as . The result holds at least until the natural, nonlinear timescale . Notice that the density behaves very differently from a passive scalar, as can be seen from the inviscid damping and slower gradient growth. The proof relies on several ingredients: (A) a suitable symmetrization that makes the linear terms amenable to energy methods and takes into account the classical Miles‐Howard spectral stability condition; (B) a variation of the Fourier time‐dependent energy method introduced for the inviscid, homogeneous Couette flow problem developed on a toy model adapted to the Boussinesq equations, that is, tracking the potential nonlinear echo chains in the symmetrized variables despite the vorticity growth.

Diode behaviors of curved elastic wave metamaterials with a nonlinear granular chain

Diode behaviors of curved elastic wave metamaterials with a nonlinear granular chain

Moving Modulating Pulse and Front Solutions of Permanent Form in a FPU Model with Nearest and Next-to-Nearest Neighbor Interaction

We consider a nonlinear chain of coupled oscillators, which is a direct generalization of the classical Fermi–Pasta–Ulam (FPU) lattice and exhibits, besides the usual nearest neighbor interaction, also next-to-nearest neighbor interaction. For the case of nearest neighbor attraction and next-to-nearest neighbor repulsion we prove that such a lattice admits, in contrast to the classical FPU model, moving modulating front solutions of permanent form, which have small converging tails at infinity and can be approximated by solitary wave solutions of the nonlinear Schrödinger equation. When the associated potentials are even, then the proof yields moving modulating pulse solutions of permanent form, whose profiles are spatially localized. Our analysis employs the spatial dynamics approach as developed by Iooss and Kirchgässner. The relevant solutions are constructed on a five-dimensional center manifold, and their persistence is guaranteed by reversibility arguments.