On Sufficient Conditions for Chaotic Behavior of Multidimensional Discrete Time Dynamical System

In this work, we look at the extension of classical discrete dynamical system to multidimensional discrete-time dynamical system by characterizing chaos notions on $${\mathbb {Z}}^d$$ Z d -action. The $${\mathbb {Z}}^d$$ Z d -action on a space X has been defined in a very general manner, and therefore we introduce a $${\mathbb {Z}}^d$$ Z d -action on X which is induced by a continuous map, $$f:{\mathbb {Z}}\times X \rightarrow X$$ f : Z × X → X and denotes it as $$T_f:{\mathbb {Z}}^d \times X \rightarrow X$$ T f : Z d × X → X . Basically, we wish to relate the behavior of origin discrete dynamical systems (X, f) and its induced multidimensional discrete-time $$(X,T_f)$$ ( X , T f ) . The chaotic behaviors that we emphasized are the transitivity and dense periodicity property. Analogues to these chaos notions, we consider k-type transitivity and k-type dense periodicity property in the multidimensional discrete-time dynamical system. In the process, we obtain some conditions on $$(X,T_f)$$ ( X , T f ) under which the chaotic behavior of $$(X,T_f)$$ ( X , T f ) is inherited from the original dynamical system (X, f). The conditions varies whenever f is open, totally transitive or mixing. Some examples are given to illustrate these conditions.

A Spectral Rotation Method with Triplet Periodicity Property for Planted Motif Finding Problems

Background: Genes are known as functional patterns in the genome and are presumed to have biological significance. They can indicate binding sites for transcription factors and they encode certain proteins. Finding genes from biological sequences is a major task in computational biology for unraveling the mechanisms of gene expression. Objective: Planted motif finding problems are a class of mathematical models abstracted from the process of detecting genes from genome, in which a specific gene with a number of mutations is planted into a randomly generated background sequence, and then gene finding algorithms can be tested to check if the planted gene can be found in feasible time. Method: In this work, a spectral rotation method based on triplet periodicity property is proposed to solve planted motif finding problems. Results: The proposed method gives significant tolerance of base mutations in genes. Specifically, genes having a number of substitutions can be detected from randomly generated background sequences. Experimental results on genomic data set from Saccharomyces cerevisiae reveal that genes can be visually distinguished. It is proposed that genes with about 50% mutations can be detected from randomly generated background sequences. Conclusion: It is found that with about 5 insertions or deletions, this method fails in finding the planted genes. For a particular case, if the deletion of bases is located at the beginning of the gene, that is, bases are not randomly deleted, then the tolerance of the method for base deletion is increased.

Superpixel-Based Temporally Aligned Representation for Video-Based Person Re-Identification

Most existing person re-identification methods focus on matching still person images across non-overlapping camera views. Despite their excellent performance in some circumstances, these methods still suffer from occlusion and the changes of pose, viewpoint or lighting. Video-based re-id is a natural way to overcome these problems, by exploiting space–time information from videos. One of the most challenging problems in video-based person re-identification is temporal alignment, in addition to spatial alignment. To address the problem, we propose an effective superpixel-based temporally aligned representation for video-based person re-identification, which represents a video sequence only using one walking cycle. Particularly, we first build a candidate set of walking cycles by extracting motion information at superpixel level, which is more robust than that at the pixel level. Then, from the candidate set, we propose an effective criterion to select the walking cycle most matching the intrinsic periodicity property of walking persons. Finally, we propose a temporally aligned pooling scheme to describe the video data in the selected walking cycle. In addition, to characterize the individual still images in the cycle, we propose a superpixel-based representation to improve spatial alignment. Extensive experimental results on three public datasets demonstrate the effectiveness of the proposed method compared with the state-of-the-art approaches.

Numerical modeling of induction heating systems with load of azimuthal periodicity

The paper presents developed numerical modelling methodology of induction heating problems of disks with a simple and complex profile in 3D for calculating the coupled electromagnetic and thermal tasks in the parametric design language (ANSYS APDL). We demonstrate that the developed tools can be used for products of various sizes, as well as for other metal engineering components using the example of local electromagnetic processing of a metal disk and a diaphragm spring. The authors used development for parametric research and design of induction heaters. The described methodology has particular specificity, due to which it is possible to expand the scope for a number of engineering units with azimuthal periodicity property.

Properties of Bessel Function Solution to Kepler’s Equation with Application to Opposition and Conjunction of Earth–Mars

In this article, a simple approach is suggested to calculate the approximate dates of opposition and conjunction of Earth and Mars since their opposition on August 28, 2003 (at perihelion of Mars). The goal of this article has been achieved via using accurate analytical solution to Kepler’s equation in terms of Bessel function. The periodicity property of this solution and its particular values at specified times are discussed through some lemmas. The mathematical conditions of opposition and conjunction of the two planets are formulated. Moreover, the intervals of opposition and conjunction have been determined using the graphs of some defined functions. The calculations reveal that there are nine possible oppositions and conjunctions for Earth and Mars during 20 years started on August 28, 2003. The dates of such oppositions and conjunctions were approximately determined and listed in Tables. It is found that our calculations differ few days from the published real dates of Earth–Mars oppositions due to the neglected effects of the gravitational attraction of other planets in the Solar system on the motion of two planets. The period of 20 years can be extended for any number of years by following the suggested analysis. Furthermore, the current approach may be extended to study the opposition and conjunction of the Earth and any outer planet.

T-systems with Boundaries from Network Solutions

In this paper, we use the network solution of the $A_r$ $T$-system to derive that of the unrestricted $A_\infty$ $T$-system, equivalent to the octahedron relation. We then present a method for implementing various boundary conditions on this system, which consists of picking initial data with suitable symmetries. The corresponding restricted $T$-systems are solved exactly in terms of networks. This gives a simple explanation for phenomena such as the Zamolodchikov periodicity property for $T$-systems (corresponding to the case $A_\ell\times A_r$) and a combinatorial interpretation for the positive Laurent property for the variables of the associated cluster algebra. We also explain the relation between the $T$-system wrapped on a torus and the higher pentagram maps of Gekhtman et al.