Numerical differentiation for two-dimensional scattered data on arbitrary domain base on Hermite extension with an implicit iteration process

<abstract><p>In this paper, we develop a method for numerical differentiation of two-dimensional scattered input data on arbitrary domain. A Hermite extension approach is used to realize the approximation and a modified implicit iteration method is proposed to stabilize the approximation process. For functions with various smooth conditions, the numerical solution process of the method is uniform. The error estimates are obtained and numerical results show that the new method is effective. The advantage of the method is that it can solve the problem in any domain.</p></abstract>

Biological factors in the synthetic construction of overlapping genes

Background Overlapping genes (OLGs) with long protein-coding overlapping sequences are disallowed by standard genome annotation programs, outside of viruses. Recently however they have been discovered in Archaea, diverse Bacteria, and Mammals. The biological factors underlying life’s ability to create overlapping genes require more study, and may have important applications in understanding evolution and in biotechnology. A previous study claimed that protein domains from viruses were much better suited to forming overlaps than those from other cellular organisms - in this study we assessed this claim, in order to discover what might underlie taxonomic differences in the creation of gene overlaps. Results After overlapping arbitrary Pfam domain pairs and evaluating them with Hidden Markov Models we find OLG construction to be much less constrained than expected. For instance, close to 10% of the constructed sequences cannot be distinguished from typical sequences in their protein family. Most are also indistinguishable from natural protein sequences regarding identity and secondary structure. Surprisingly, contrary to a previous study, virus domains were much less suitable for designing OLGs than bacterial or eukaryotic domains were. In general, the amount of amino acid change required to force a domain to overlap is approximately equal to the variation observed within a typical domain family. The resulting high similarity between natural sequences and those altered so as to overlap is mostly due to the combination of high redundancy in the genetic code and the evolutionary exchangeability of many amino acids. Conclusions Synthetic overlapping genes which closely resemble natural gene sequences, as measured by HMM profiles, are remarkably easy to construct, and most arbitrary domain pairs can be altered so as to overlap while retaining high similarity to the original sequences. Future work however will need to assess important factors not considered such as intragenic interactions which affect protein folding. While the analysis here is not sufficient to guarantee functional folding proteins, further analysis of constructed OLGs will improve our understanding of the origin of these remarkable genetic elements across life and opens up exciting possibilities for synthetic biology.

Existence results for coupled nonlinear fractional differential equations of different orders with nonlocal coupled boundary conditions

This paper is concerned with the solvability of coupled nonlinear fractional differential equations of different orders supplemented with nonlocal coupled boundary conditions on an arbitrary domain. The tools of the fixed point theory are applied to obtain the criteria ensuring the existence and uniqueness of solutions of the problem at hand. Examples illustrating the main results are presented.

A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.

Fatou and Julia like sets II

This paper is a continuation of authors work: Fatou and Julia like sets, Ukranian Math. J., to appear/arXiv:2006.08308[math.CV](see [5]). Here, we introduce escaping like set and generalized escaping like set for a family of holomorphic functions on an arbitrary domain, and establish some distinctive properties of these sets. The connectedness of the Julia like set is also proved.

Creating explorable extended reality environments with semantic annotations

The main element of extended reality (XR) environments is behavior-rich 3D content consisting of objects that act and interact with one another as well as with users. Such actions and interactions constitute the evolution of the content over time. Multiple application domains of XR, e.g., education, training, marketing, merchandising, and design, could benefit from the analysis of 3D content changes based on general or domain knowledge comprehensible to average users or domain experts. Such analysis can be intended, in particular, to monitor, comprehend, examine, and control XR environments as well as users’ skills, experience, interests and preferences, and XR objects’ features. However, it is difficult to achieve as long as XR environments are developed with methods and tools that focus on programming and 3D modeling rather than expressing domain knowledge accompanying content users and objects, and their behavior. The main contribution of this paper is an approach to creating explorable knowledge-based XR environments with semantic annotations. The approach combines description logics with aspect-oriented programming, which enables knowledge representation in an arbitrary domain as well as transformation of available environments with minimal users’ effort. We have implemented the approach using well-established development tools and exemplify it with an explorable immersive car showroom. The approach enables efficient creation of explorable XR environments and knowledge acquisition from XR.

The Existence and Uniqueness of an Entropy Solution to Unilateral Orlicz Anisotropic Equations in an Unbounded Domain

The purpose of this work is to prove the existence and uniqueness of a class of nonlinear unilateral elliptic problem (P) in an arbitrary domain, managed by a low-order term and non-polynomial growth described by an N-uplet of N-function satisfying the Δ2-condition. The source term is merely integrable.

WingMesh: A Matlab-Based Application for Finite Element Modeling of Insect Wings

The finite element (FE) method is one of the most widely used numerical techniques for the simulation of the mechanical behavior of engineering and biological objects. Although very efficient, the use of the FE method relies on the development of accurate models of the objects under consideration. The development of detailed FE models of often complex-shaped objects, however, can be a time-consuming and error-prone procedure in practice. Hence, many researchers aim to reach a compromise between the simplicity and accuracy of their developed models. In this study, we adapted Distmesh2D, a popular meshing tool, to develop a powerful application for the modeling of geometrically complex objects, such as insect wings. The use of the burning algorithm (BA) in digital image processing (DIP) enabled our method to automatically detect an arbitrary domain and its subdomains in a given image. This algorithm, in combination with the mesh generator Distmesh2D, was used to develop detailed FE models of both planar and out-of-plane (i.e., three-dimensionally corrugated) domains containing discontinuities and consisting of numerous subdomains. To easily implement the method, we developed an application using the Matlab App Designer. This application, called WingMesh, was particularly designed and applied for rapid numerical modeling of complicated insect wings but is also applicable for modeling purposes in the earth, engineering, mathematical, and physical sciences.