Arbitrary Level Research Articles

Blow-Up Phenomena for a Class of Parabolic or Pseudo-parabolic Equation with Nonlocal Source

In this paper, we consider a class of parabolic or pseudo-parabolic equation with nonlocal source term: $$\begin{aligned} u_t-\nu \triangle u_t-\hbox {div}(\rho (|\nabla u|)^2\nabla u)=u^p(x,t)\int _{\Omega }k(x,y)u^{p+1}(y,t)dy, \end{aligned}$$ where $$\nu \ge 0$$ and $$p>0$$ . Using some differential inequality techniques, we prove that blow-up cannot occur provided that $$q>p$$ , also, we obtain some finite-time blow-up results and the lifespan of the blow-up solution under some different suitable assumptions on the initial energy. In particular, we prove finite-time blow-up of the solution for the initial data at arbitrary energy level. Furthermore, the lower bound for the blow-up time is determined if blow-up does occur.

Optimal spinor selectivity for quaternion Bass orders

Let A be a quaternion algebra over a number field F, and O be an OF-order of full rank in A. Let K be a quadratic field extension of F that embeds into A, and B be an OF-order in K. Suppose that O is a Bass order that is well-behaved at all the dyadic primes of F. We provide a necessary and sufficient condition for B to be optimally spinor selective for the genus of O. This partially generalizes previous results on optimal (spinor) selectivity by C. Maclachlan (2008) [21] for Eichler orders of square-free levels, and independently by M. Arenas et al. (2018) [1] and by J. Voight (2021) [27, Chapter 31] for Eichler orders of arbitrary levels.

Computing the Rooted Triplet Distance Between Phylogenetic Networks

The rooted triplet distance measures the structural dissimilarity of two phylogenetic trees or phylogenetic networks by counting the number of rooted phylogenetic trees with exactly three leaf labels (called rooted triplets, or triplets for short) that occur as embedded subtrees in one, but not both, of them. Suppose that N_1 = (V_1, E_1) and N_2 = (V_2, E_2) are phylogenetic networks over a common leaf label set of size n, that N_i has level k_i and maximum in-degree d_i for i in {1,2}, and that the networks’ out-degrees are unbounded. Write N = max (|V_1|, |V_2|), M = max (|E_1|, |E_2|), k = max (k_1, k_2), and d = max (d_1, d_2). Previous work has shown how to compute the rooted triplet distance between N_1 and N_2 in mathrm {O}(n log n) time in the special case k le 1. For k > 1, no efficient algorithms are known; applying a classic method from 1980 by Fortune et al. in a direct way leads to a running time of {Omega }(N^{6} n^{3}) and the only existing non-trivial algorithm imposes restrictions on the networks’ in- and out-degrees (in particular, it does not work when non-binary vertices are allowed). In this article, we develop two new algorithms with no such restrictions. Their running times are mathrm {O}(N^{2} M + n^{3}) and mathrm {O}(M + N k^{2} d^{2} + n^{3}), respectively. We also provide implementations of our algorithms, evaluate their performance on simulated and real datasets, and make some observations on the limitations of the current definition of the rooted triplet distance in practice. Our prototype implementations have been packaged into the first publicly available software for computing the rooted triplet distance between unrestricted networks of arbitrary levels.

Fast scene labeling via structural inference

Scene labeling or parsing aims to assign pixelwise semantic labels for an input image. Existing CNN-based models cannot leverage the label dependencies, while RNN-based models predict labels within the local context. In this paper, we propose a fast LSTM scene labeling network via structural inference. A minimum spanning tree is used to build the image structure for constructing semantic relationships. This structure allows efficient generation of direct parent–child dependencies for arbitrary levels of superpixels, and thus structural relationships can be learned with LSTM. In particular, we propose a bi-directional recurrent network to model the information flow along the parent–child path. In this way, the recurrent units in both coarse and fine levels can mutually transfer the global and local context information in the entire image structure. The proposed network is extremely fast, and it is 2.5× faster than the state-of-the-art RNN-based models. Extensive expseriments demonstrate that the proposed method provides a significant improvement in learning the label dependencies, and it outperforms state-of-the-art methods on different benchmarks.

TreeSummarizedExperiment: a S4 class for data with hierarchical structure.

Data organized into hierarchical structures (e.g., phylogenies or cell types) arises in several biological fields. It is therefore of interest to have data containers that store the hierarchical structure together with the biological profile data, and provide functions to easily access or manipulate data at different resolutions. Here, we present TreeSummarizedExperiment, a R/S4 class that extends the commonly used SingleCellExperiment class by incorporating tree representations of rows and/or columns (represented by objects of the phylo class). It follows the convention of the SummarizedExperiment class, while providing links between the assays and the nodes of a tree to allow data manipulation at arbitrary levels of the tree. The package is designed to be extensible, allowing new functions on the tree (phylo) to be contributed. As the work is based on the SingleCellExperiment class and the phylo class, both of which are popular classes used in many R packages, it is expected to be able to interact seamlessly with many other tools.

TreeSummarizedExperiment: a S4 class for data with hierarchical structure

Data organized into hierarchical structures (e.g., phylogenies or cell types) arises in several biological fields. It is therefore of interest to have data containers that store the hierarchical structure together with the biological profile data, and provide functions to easily access or manipulate data at different resolutions. Here, we present TreeSummarizedExperiment, a R/S4 class that extends the commonly used SingleCellExperiment class by incorporating tree representations of rows and/or columns (represented by objects of the phylo class). It follows the convention of the SummarizedExperiment class, while providing links between the assays and the nodes of a tree to allow data manipulation at arbitrary levels of the tree. The package is designed to be extensible, allowing new functions on the tree (phylo) to be contributed. As the work is based on the SingleCellExperiment class and the phylo class, both of which are popular classes used in many R packages, it is expected to be able to interact seamlessly with many other tools.

DNA repair gene polymorphisms and chromosomal aberrations in healthy, nonsmoking population

Nonspecific structural chromosomal aberrations (CAs) can be found at around 1% of circulating lymphocytes from healthy individuals but the frequency may be higher after exposure to carcinogenic chemicals or radiation. The frequency of CAs has been measured in occupational monitoring and an increased frequency of CAs has also been associated with cancer risk. Alterations in DNA damage repair and telomere maintenance are thought to contribute to the formation of CAs, which include chromosome type of aberrations and chromatid type of aberrations. In the present study, we used the result of our published genome-wide association studies to extract data on 153 DNA repair genes from 866 nonsmoking persons who had no known occupational exposure to genotoxic substances. Considering an arbitrary cut-off level of P< 5 × 10−3, single nucleotide polymorphisms (SNPs) tagging 22 DNA repair genes were significantly associated with CAs and they remained significant at P < 0.05 when adjustment for multiple comparisons was done by the Binomial Sequential Goodness of Fit test. Nucleotide excision repair pathway genes showed most associations with 6 genes. Among the associated genes were several in which mutations manifest CA phenotype, including Fanconi anemia, WRN, BLM and genes that are important in maintaining genome stability, as well as PARP2 and mismatch repair genes. RPA2 and RPA3 may participate in telomere maintenance through the synthesis of the C strand of telomeres. Errors in NHEJ1 function may lead to translocations. The present results show associations with some genes with known CA phenotype and suggest other pathways with mechanistic rationale for the formation of CAs in healthy nonsmoking population.

A kinetics-based model of fatigue crack growth rate in bituminous material

This study aims to propose a kinetics-based model of fatigue crack growth rate coupling with temperature, strain level and damage degree for bituminous materials. The fatigue crack length is calculated by an energy-based mechanistic (EBM) approach, and kinetic parameters characterizing the fatigue crack growth rate are determined based on an Arrhenius equation. Results show that the logarithm of the fatigue crack growth rate is linear to the inverse of absolute temperature, and cracking activation energy is independent of strain level and damage degree. Besides, the proposed kinetics-based model can predict fatigue crack growth rate at arbitrary temperature, strain level and damage degree of bituminous materials.

Webs of integrable theories

We present an intuitive diagrammatic representation of a new class of integrable σ-models. It is shown that to any given diagram corresponds an integrable theory that couples N WZW models with a certain number of each of the following four fundamental integrable models, the PCM, the YB model, both based on a group G, the isotropic σ-model on the symmetric space G/H and the YB model on the symmetric space G/H. To each vertex of a diagram we assign the matrix of one of the aforementioned fundamental integrable theories. Any two vertices may be connected with a number of lines having an orientation and carrying an integer level ki. Each of these lines is associated with an asymmetrically gauged WZW model at an arbitrary level ki. Gauge invariance of the full action is translated to level conservation at the vertices. We also show how to immediately read from the diagrams the corresponding σ-model actions. The most generic of these models depends on at least n2+1 parameters, where n is the total number of vertices/fundamental integrable models. Finally, we discuss the case where the level conservation at the vertices is relaxed and the case where the deformation matrix is not diagonal in the space of integrable models.

Enhancing Bandwidth and Back-Off Range of Doherty Power Amplifier With Modified Load Modulation Network

This article presents a novel methodology for designing a broadband Doherty power amplifier (DPA) with extended output power back-off (OBO) range. A modified load modulation network (LMN) is proposed to enhance the OBO range and the bandwidth of the DPA simultaneously. Analysis is conducted to explore the relationship between the proposed LMN parameters and the broadband performance under various OBO levels. Generalized design formulas of the LMN parameters are then introduced to offer the broadband solution for arbitrary current ratios and OBO levels. An asymmetric DPA is demonstrated and implemented with gallium nitride (GaN) transistors using the proposed approach. The fabricated DPA operates from 1.4 to 2.5 GHz with 9-dB OBO range. The measured drain efficiency reaches 61%-75.5% at saturation and 44.6%-54.6% at 9-dB OBO within the operating bandwidth. When driven by a 60-MHz modulated signal with 9-dB peak-to-average power ratio (PAPR), the fabricated DPA attains 47.4%-53.5% average drain efficiency and better than -45.5-dBc adjacent channel leakage ratio (ACLR) after digital predistortion.

Shimura lifts of certain classes of modular forms of half-integral weight

Shimura defined a family of maps from the space of modular forms of half-integral weight to the space of modular forms of integral weight. Selberg in his unpublished work found explicitly this correspondence (the first Shimura map [Formula: see text]) for the class of forms which are products of a Hecke eigenform of level one and a Jacobi theta function. Later, Cipra generalized the work of Selberg to the case where Jacobi theta functions are replaced by the theta functions associated to Dirichlet character of prime power moduli, and the level one Hecke eigenforms are replaced by newforms of arbitrary level. Hansen and Naqvi generalized Cipra’s work (on the image of a class of modular forms under the first Shimura map [Formula: see text]) to cover theta functions associated to Dirichlet characters of arbitrary moduli. In this paper, we show that the earlier results can be modified to get similar results for the [Formula: see text]th Shimura lifts [Formula: see text], for any positive square-free integer [Formula: see text].

Evading resistance to gene drives.

Gene drives offer the possibility of altering and even suppressing wild populations of countless plant and animal species, and CRISPR technology now provides the technical feasibility of engineering them. However, population-suppression gene drives are prone to select resistance, should it arise. Here, we develop mathematical and computational models to identify conditions under which suppression drives will evade resistance, even if resistance is present initially. Previous models assumed resistance is allelic to the drive. We relax this assumption and show that linkage between the resistance and drive loci is critical to the evolution of resistance and that evolution of resistance requires (negative) linkage disequilibrium between the two loci. When the two loci are unlinked or only partially so, a suppression drive that causes limited inviability can evolve to fixation while causing only a minor increase in resistance frequency. Once fixed, the drive allele no longer selects resistance. Our analyses suggest that among gene drives that cause moderate suppression, toxin-antidote systems are less apt to select for resistance than homing drives. Single drives of moderate effect might cause only moderate population suppression, but multiple drives (perhaps delivered sequentially) would allow arbitrary levels of suppression. The most favorable case for evolution of resistance appears to be with suppression homing drives in which resistance is dominant and fully suppresses transmission distortion; partial suppression by resistance heterozygotes or recessive resistance are less prone to resistance evolution. Given that it is now possible to engineer CRISPR-based gene drives capable of circumventing allelic resistance, this design may allow for the engineering of suppression gene drives that are effectively resistance-proof.

ADAPTIVE RESOURCES OF SUBJECTS WITH DIFFERENT STRATEGIES FOR CHOOSING A WAY OF LIFE IN A STRESS SITUATION OF ORGANIZATIONAL CHANGES

Background. The modern world is characterized by instability, uncertainty, complexity and ambiguity. Therefore, a successful development of an organization requires organizational changes, which provoke the necessity of adaptation for people working in this organization. The study of specific adaptive resources revealed the benefits of a differentiated approach to personnel undergoing organizational changes. The differentiation of the sample depending on the strategies for choosing a way of life is justified. Aim. The paper aims to study the specifics of adaptive resources in the context of organizational changes and the features of experiencing stress, tolerance to uncertainty and resilience. Materials and methods. The study involved 208 employees of a large industrial enterprise in Chelyabinsk (of which 135 females and 73 males). The following methods were used during the study: typology for a personal choice of a way of life by V. Gryazeva-Dobshinskaya, A.S. Maltseva; the Psychological Stress Measure (PSM) by L. Lemyrr, R. Tessier, L. Fillion (adapted by N.E. Vodopyanova); the Hardiness test by S. Maddi (adapted by D. A. Leontiev, E. V. Rasskazova); the tolerance to uncertainty scale adapted by E.G. Lukovitskaya. For statistical processing, discriminant and factor analysis were used. Results. General (nonspecific) adaptive resources were revealed: in all subjects regardless of their strategies for choosing a way of life, an inverse correlation was found between stress exposure and resilience as stress resistance resources. Specific adaptive resources were identified: subjects of a hedonistic type had a positive attitude towards new, diverse situations in life and were characterized by a preference for uncertainty; subjects of a value-oriented type were characterized by an arbitrary level of attitude to uncertain and complex situations; creative subjects demonstrated a set of properties, including “challenge” and all the components of “uncertainty tolerance”.

Compact Dual Band Ring Coupler Using Miniaturized Metamaterial Left-Handed Impedance Inverters

A compact 3-dB dual band ring coupler is designed, fabricated and tested. The coupler consists of three identical miniaturized Left-Handed (LH) impedance inverter transmission lines (TLs) and a dual one. The general principle of using LH TLs' duality to reduce the size of a dual band ring coupler is explained in detail, showing the equivalent lumped element circuits and the designing relations. A numerical example is considered for the duality analysis and the results are used to obtain a size reduction for both the coupler's dimensions and the number of utilized components. Other arbitrary coupling levels (1 dB and 5 dB) and frequency ratios are investigated and the results of simulations show very good results, proving the validity of the general principle of using LH transmission line's duality. The 3-dB coupler is implemented in microstrip technology and using high-quality lumped components. It works at two arbitrary frequencies, 1.1 GHz and 2.5 GHz, respectively with similar performances. The overall dimension of the proposed coupler is 0.07λ×0.07λ for a wavelength, λ computed at 1.1 GHz. The measured results are in good agreement with the predicted ones for both frequencies, having the return loss and isolation loss better than 33 dB, whereas keeping the insertion and coupling losses at around 3.5 dB in both frequency bands. The phase imbalance at the output ports is less than 1.5°, when the difference and sum ports are excited.

An Error Analysis Toolkit for Binned Counting Experiments

We introduce the MINERvA Analysis Toolkit (MAT), a utility for centralizing the handling of systematic uncertainties in HEP analyses. The fundamental utilities of the toolkit are the MnvHnD, a powerful histogram container class, and the systematic Universe classes, which provide a modular implementation of the many universe error analysis approach. These products can be used stand-alone or as part of a complete error analysis prescription. They support the propagation of systematic uncertainty through all stages of analysis, and provide flexibility for an arbitrary level of user customization. This extensible solution to error analysis enables the standardization of systematic uncertainty definitions across an experiment and a transparent user interface to lower the barrier to entry for new analyzers.

IND-CCA1 Secure FHE on Non-Associative Ring

A fully homomorphic encryption (FHE) would be the important cryptosystem as the basic scheme for the cloud computing. Since Gentry discovered in 2009 the first fully homomorphic encryption scheme, some fully homomorphic encryption schemes were proposed. In the systems proposed until now the bootstrapping process is the main bottleneck and the large complexity for computing the ciphertext is required. In 2011 Zvika Brakerski et al. proposed a leveled FHE without bootstrapping. But circuit of arbitrary level cannot be evaluated in their scheme while in our scheme circuit of any level can be evaluated. The existence of an efficient fully homomorphic cryptosystem would have great practical implications in the outsourcing of private computations, for instance, in the field of the cloud computing. In this paper, IND-CCA1secure FHE based on the difficulty of prime factorization is proposed which does not need the bootstrapping and it is thought that our scheme is more efficient than the previous schemes. In particular the computational overhead for homomorphic evaluation is O(1).

Optimal pricing and greening decision in a manufacturer retailer dual-channel supply chain

Abstract In the current situation of globalization, the management of a dual-channel supply chain is a significant phenomenon to mark up a conflict between an online channel and traditional retail channels. Decisions of the green level of the product towards the dual-channel supply chain are beneficial for the growing tendency of a company. In this paper, we have generalized a single manufacturer and single retailer two-echelon dual-channel green supply chain. The manufacturer produces the product considering an arbitrary level of the greenness and then sells it through 1) a traditional retail channel and 2) an online channel. Demand in both the retail channel and online-channel is sensitive to price and level of the greenness of the product. The profit maximization SC model has been generalized under two decision-making structures. At first, a centralized decision-making structure is analyzed and the optimal decisions of SC members are exhausted. Secondly, we propose a decentralized decision-making structure to find the optimal selling price and level of greenness. The Stackelberg-game approach has been used to solve the decentralized scenario. This study provides the supply chain literature by coordinating environmental decisions on the dual-channel supply chain system. According to the numerical findings and sensitivity analyses, the centralized scenario is more profitable compared to the decentralized scenario. Finally, some managerial applications are derived based on the sensitivity of some key parameters.

Encoding and Decoding of Recursive Structures in Neural-Symbolic Systems

One of the ways to join the connectionist approach and the symbolic paradigm is Tensor Product Variable Binding. It was initially devoted to building distributed representation of recursive structures for neural networks to use it as the input. Structures are an essential part of both formal and natural languages and appear in syntactic trees, grammar, semantic interpretation. A human mind smoothly operates with the appearing problems on the neural level, and it is naturally scalable and robust. The question arises of whether it is possible to translate traditional symbolic algorithms to the sub-symbolic level to reuse performance and computational gain of the neural networks for general tasks. However, several aspects of Tensor Product Variable Binding lack attention in public research, especially in building such a neural architecture that performs computations according to the mathematical model without preliminary training. In this paper, those implementation aspects are addressed. A proposed novel design for the decoding network translates a tensor to a corresponding recursive structure with the arbitrary level of nesting. Also, several complex topics about encoding such structures in the distributed representation or tensor are addressed. Both encoding and decoding neural networks are built with the Keras framework’s help and are analyzed from the perspective of applied value. The proposed design continues the series of papers dedicated to building a robust bridge between two computational paradigms: connectionist and symbolic.

Уровневая периодизация онтогенеза. Становление системы ведущих функций для произвольного уровня организации. Часть 1

Based on the idea of organisation level hierarchy, the proposed periodisation scheme of ontogenesis is multi-level. The main advantage of such an approach is that it offers a real opportunity to describe the development of any living creature starting with the minimal level, i. e., maturation of an egg, and finishing at a threshold level of organisation for a given biological species. S. Vygotsky constantly highlighted the need for a constructive approach to general psychology. To him, it should have been replaced by psychology of development a long time before. As for developmental psychology, it could still deal with the psychology of age periods in all the richness of their specific empirical content. Unfortunately, Vygotsky did not manage to bring the results of his fruitful work to the multi-level implementation. The first article in our series (“Topology, metrics and chronology of the multi-level periodization of ontogenesis”) presents an absolute chronological scale of ontogeny. It also provides empirical substantiation of the periodisation of multi-level ontogenesis. The second article in the series (“Multi-level periodisation of ontogenesis: Empirical characteristics of organisation levels”) describes initial basic empirical characteristics of all levels of organisation of ontogenesis. The article below examines the becoming of a system of leading functions for an arbitrary level of organisation. As for the becoming, in addition to the threshold level, the four previous ones are taken as a basis. Finally, the very content of the becoming is derived from the configuration of the interaction cycles of the intra-level layers. The configuration is viewed as a system of leading functions. The given framework of analysis is seen as the basis for describing each particular organisation level.

Уровневая периодизация онтогенеза. Становление системы ведущих функций для произвольного уровня организации.

The article discusses the multi-level periodisation of ontogeny, namely the becoming of a system of leading functions for an arbitrary level of organisation. The adjective arbitrary is understood as a level in which everything that is repeated in other levels is detailed, but any of their specifics is quite omitted. As for the concept of becoming, its content is enhanced by several intra-level layers added to the upper one. And finally, becoming itself is derived from the configuration of cycles, which organizes the interaction of intra-level layers and determines the level system of leading functions. The proposed analysis scheme is declared as a basis for describing each level of ontogeny organisation. The previously published part of the article includes two sections. In the first one, “Arbitrary scheme of level periodization”, definitions and descriptions of its basic concepts are given: a) the level of organisation, the formation of level and the initial function, b) layers of level and the system of leading functions, c) the hierarchy of layers and cycles of interaction, d) leading functions and developmental periods. The second section, “Configuration of interaction cycles”, expands the cycles’ configuration graphs and considers the layers of organisation that constitute them. This second part of the article completes the work presented in the first one. This is indicated by the title of its only section “Becoming of a system of leading functions”, declared as key expression in the title of both parts of the article. Therefore, the second of them begins with the classical (L. Vygotsky) introduction “Structure and dynamics of development”, which is further turned into an analysis of the interaction cycles of intra-level layers with a description of the corresponding leading function.