Bifurcations and chaos of a discrete mathematical model for respiratory process in bacterial culture

The discrete mathematical model for the respiratory process in bacterial culture obtained by Euler method is investigated. The conditions of existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, condition of existence of chaos in the sense of Marotto＇s definition of chaos is proved. The bifurcation diagrams, Lyapunov exponents and phase portraits are given for different parameters of the model, and the fractal dimension of chaotic attractor was also calculated. The numerical simulation results confirm the theoretical analysis and also display the new and complex dynamical behaviors compared with the continuous model. In particular~ we found that the new chaotic attractor, and new types of two or four coexisting chaotic attractors, and two coexisting invariant torus.     

On a piecewise-smooth map arising in ecology

In this paper, we study a two-dimensional piecewise smooth map arising in ecology. Such map, containing two parameters d and β, is derived from a model describing how masting of a mature forest happens and synchronizes. Here d is the energy depletion quantity and β   is the coupling strength. Our main results are the following. First, we obtain a “weak” Sharkovskii ordering for the map on its nondiagonal invariant region for a certain set of parameters. In particular, we show that its Sharkovskii ordering is the natural number (resp., the positive even number) for β>1$\beta >1$ (resp., 0<β<1$0<\beta <1$). Second, we obtain a region of parameter space for which its corresponding global dynamics can be completely characterized.     

Neural Networks Predict Protein Folding and Structure: Artificial Intelligence Faces Biomolecular Complexity

Abstract

In the genomic era DNA sequencing is increasing our knowledge of the molecular structure of genetic codes from bacteria to man at a hyperbolic rate. Billions of nucleotides and millions of aminoacids are already filling the electronic files of the data bases presently available, which contain a tremendous amount of information on the most biologically relevant macromolecules, such as DNA. RNA and proteins. The most urgent problem originates from the need to single out the relevant information amidst a wealth of general features. Intelligent tools are therefore needed to optimise the search. Data mining for sequence analysis in biotechnology has been substantially aided by the development of new powerful methods borrowed from the machine learning approach. In this paper we discuss the application of artificial feedforward neural networks to deal with some fundamental problems tied with the folding process and the structure-function relationship in proteins.     

SSThread: Template‐free protein structure prediction by threading pairs of contacting secondary structures followed by assembly of overlapping pairs

Acquiring the three‐dimensional structure of a protein from its amino acid sequence alone, despite a great deal of work and significant progress on the subject, is still an unsolved problem. SSThread, a new template‐free algorithm is described here that consists of making several predictions of contacting pairs of α‐helices and β‐strands derived from a database of experimental structures using a knowledge‐based potential, secondary structure prediction, and contact map prediction followed by assembly of overlapping pair predictions to create an ensemble of core structure predictions whose loops are then predicted. In a set of seven CASP10 targets SSThread outperformed the two leading methods for two targets each. The targets were all β‐strand containing structures and most of them have a high relative contact order which demonstrates the advantages of SSThread. The primary bottlenecks based on sets of 74 and 21 test cases are the pair prediction and loop prediction stages. © 2014 Wiley Periodicals, Inc.     

Dynamical combinatorics and torsion classes

For finite semidistributive lattices the map κ gives a bijection between the sets of completely join-irreducible elements and completely meet-irreducible elements.Here we study the κ-map in the context of torsion classes. It is well-known that the lattice of torsion classes for an artin algebra is semidistributive, but in general it is far from finite. We show the κ-map is well-defined on the set of completely join-irreducible elements, even when the lattice of torsion classes is infinite. We then extend κ to a map on torsion classes which have canonical join representations given by the special torsion classes associated to the minimal extending modules introduced by the first and third authors and A. Carroll in 2019.For hereditary algebras, we show that the extended κ-map on torsion classes is essentially the same as Ringel's ?-map on wide subcategories. Also in the hereditary case, we relate the square of κ to the Auslander-Reiten translation.     

The geometry of the secant caustic of a planar curve

The secant caustic of a planar curve M is the image of the singular set of the secant map of M. We analyze the geometrical properties of the secant caustic of a planar curve, i.e. the number of branches of the secant caustic, the parity of the number of cusps and the number of inflexion points in each branch of this set. In particular, we investigate in detail some of the geometrical properties of the secant caustic of a rosette, i.e. a smooth regular oriented closed curve with non-vanishing curvature.     

Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices

In this paper, we propose a new method to study intermittent behaviors of coupled piecewise-expanding map lattices. We show that the successive transition between ordered and disordered phases occurs for almost every orbit when the coupling is small. That is,where $x_i(n)$ correspond to the coordinates of $m$ nodes at the iterative step $n$. Moreover, when the uncoupled system is generated by the tent map and the lattice consists of two nodes, we prove a phase transition occurs between synchronization and intermittent behaviors. That is, $$\lim_{n\rightarrow \infty}| x_1(n)-x_2(n)|=0\quad\text{for }\ \ \Big|c-\frac12\Big|<\frac14$$ and intermittent behaviors occur for $|c-\frac12|>\frac14$, where $0\le c\le 1$ is the coupling.     

FABEMD和改进局部能量窗口的红外中波和长波图像融合

针对探测波段为3.7～4.8 μm的中波红外图像和探测波段为8～14 μm长波红外图像融合过程中存在场景对比度低,显著性目标不够凸出,伪影引入严重的问题,采用快速自适应二维经验模态分解（FABEMD)对红外中波和长波图像进行多尺度分解以得到二维内蕴模函数(BIMFs)和残余分量(Residual)。对于每一层内蕴模函数选用改进的局部能量窗口融合规则,首先配置好加权算子以增加区域窗口中心像素的能量占比;选用不同的加权算子,经实验验证能有效突出红外中波和长波图像的能量特征信息;其次充分利用内蕴模函数的相位信息,当相位相反时,采用能量加权平均的方式,以解决融合系数的正负符号极性难以确定的问题;当相位相同时,判断二者的能量差距并依据差距大小选择设定的融合规则,融合规则基于红外中波和长波图像的灰度差异特性设定。对于残余分量则利用红外中波图像和改进区域能量窗口的最大对称环绕显著性权重图指导基础层系数的融合,自适应的局部环绕窗口充分利用了低频显著性信息,对无用背景的抑制效果也相当出色,能够在复杂背景图像中突出显著性对象,最终得到细节信息丰富,对比度明显的指导图像。最后通过FABEMD的逆变化重构过程得到融合图像,对4组不同背景、不同大小的红外中长波图像进行主观和客观性能评价,4组图像均来自多波段红外采集系统且都经过严格配准并和7种相关算法进行对比实验,在主观性能上显著性对象突出、清晰度度高;客观性能上在平均梯度和空间频率这两个评价指标上性能优异,验证了该算法的有效性。     

广义凸空间上重合点定理和极大极小不等式

利用已知的KKM型定理,在广义空间上得到若干个新的重合点定理和推广的Fan-Browder型不动点定理,并且讨论了Von Newmann-Sion型极大极小不等式.主要结果改进和推广了文献中的相应结论.