Expansion Of Base Research Articles

Optimal expansions of Kakeya sequences

AbstractWe investigate optimal expansions of Kakeya sequences for the representation of real numbers. Expansions of Kakeya sequences generalize the expansions in non-integer bases and they display analogous redundancy phenomena. In this paper, we characterize optimal expansions of Kakeya sequences, and we provide conditions for the existence of unique expansions with respect to Kakeya sequences.

Geopolitics of the Red Sea: Implications of foreign military bases expansion to the Horn of Africa security

ABSTRACT The Red Sea region has rapidly changed during the last decades due to growing foreign countries’ rivalry and military base expansion. This study examines foreign countries’ military base expansion and its implications for the Horn of Africa’s security. ⁠The study uses a qualitative research approach, collecting data from secondary sources. The study argues that foreign countries’ military base expansion in the Red Sea region has both advantages and disadvantages to the Horn of Africa region. Foreign military presence in the Red Sea region enables the region’s states to combat terrorism and piracy and has economic benefits and military experience sharing with host states. However, foreign military presence will exacerbate patronage, open avenues for interference in the internal affairs of states, and foreign countries competition complicates the security of the volatile Horn of Africa region. Hence, the Red Sea littoral states shall strengthen their cooperation to reduce the adverse effect of foreign countries’ military base expansion and enhance their political, economic, and diplomatic bargaining power.

Renormalized-Residue-Based Multireference Configuration Interaction Method for Strongly Correlated Systems.

The implementation of multireference configuration interaction (MRCI) methods in quantum systems with large active spaces is hindered by the expansion of configuration bases or the intricate handling of reduced density matrices (RDMs). In this work, we present a spin-adapted renormalized-residue-based MRCI (RR-MRCI) approach that leverages renormalized residues to effectively capture the entanglement between active and inactive orbitals. This approach is reinforced by a novel efficient algorithm, which also facilitates an efficient deployment of spin-adapted matrix product state MRCI (MPS-MRCI). The RR-MRCI framework possesses several advantages: (1) It considers the orbital entanglement and utilizes highly compressed MPS structure, improving computational accuracy and efficiency compared with internally contracted (ic) MRCI. (2) Utilizing small-sized buffer environments of a few external orbitals as probes based on quantum information theory, it enhances computational efficiency over MPS-MRCI and offers potential application to large molecular systems. (3) The RR framework can be implemented in conjunction with ic-MRCI, eliminating the need for high-rank RDMs, by using distinct renormalized residues. We evaluated this method across nine diverse molecular systems, including Cu2O22+ with an active space of (24e,24o) and two complexes of lanthanide and actinide with active space (38e,36o), demonstrating the method's versatility and efficacy.

All-order celestial OPE from on-shell recursion

We determine tree level, all-order celestial operator product expansions (OPEs) of gluons and gravitons in the maximally helicity violating (MHV) sector. We start by obtaining the all-order collinear expansions of MHV amplitudes using the inverse soft recursion relations that they satisfy. These collinear expansions are recast as celestial OPE expansions in bases of momentum as well as boost eigenstates. This shows that inverse soft recursion for MHV amplitudes is dual to OPE recursion in celestial conformal field theory.

The anthropogenic effects on organic matter in sediment core based on Bayesian mixing model: a case study of Daya Bay.

Sediment is an important carrier of evidence about environmental evolution which receives huge volumes of organic material originated from both anthropogenic and natural sources. In this study, based on sedimentary chronology, the vertical trends of particle size distribution, total organic carbon (TOC), total nitrogen (TN), and their stable isotopes (δ13C, δ15N) in the sediment core of the nuclear power sea in southwest Daya Bay were analyzed, and the distribution characteristics and contribution ratios of different sources of organic matter in the sedimentary environment over the past 70years were resolved using a Bayesian mixing model (MixSIAR). TOC, TN, δ13C, and δ15N ranged from 0.89 to 1.56%, 0.09 to 0.2%, - 22.3 to - 20.6‰, and 4.38 to 6.51‰, respectively. The organic matter in the sediment is controlled by a mixture of terrestrial input and marine autochthonous, the proportion of organic matter from terrestrial sources increases, while that from marine sources decreases in the sediment core, which persists from 1960 to 2000, yet organic matter from marine sources still dominates. The first signs of increased primary productivity occurred in 1960, and it was primarily due to agricultural activity. After the 1980s, the rapid increase in population around Daya Bay, the construction of nuclear power plants, the rise of aquaculture, and the quick expansion of industrial bases were all major factors that changed the ecological environment of Daya Bay.

Arithmetics in Generalised Cantor Base Systems

For alternate Cantor real base numeration systems we generalise the result of Frougny and Solomyak on arithmetics on the set of numbers with finite expansions. We generalise the notion of finiteness property, denoted ( F ). We also provide several necessary conditions, and comment on a sufficient condition of this property. The sufficient condition allows us to find a set of generalised Cantor bases with Property ( F ). The used construction also provides a method for performing addition of finite expansions in Cantor real bases.

Learning-Assisted Inversion for Solving Nonlinear Inverse Scattering Problem

Solving inverse scattering problems (ISPs) is challenging because of its intrinsic ill-posedness and the nonlinearity. When dealing with highly nonlinear ISPs, i.e., those scatterers with high contrast and/or electrically large size, the traditional iterative nonlinear inversion methods converge slowly and take lots of computation time, even maybe trapped into local wrong solution. To alleviate the above challenges, a learning-assisted (LA) inversion approach termed as the LA inversion method (LAIM) with advanced generative adversarial network (GAN) in virtue of a new recently established contraction integral equation for inversion (CIE-I) is proposed to achieve a good balance between the computational efficiency and the accuracy of solving highly nonlinear ISPs. The preliminary profiles composed of only small amount of low-frequency components can be got efficiently by the Fourier bases expansion of CIE-I inversion (FBE-CIE-I). The physically exacted information can be taken as the input of the neural network to recover super-resolution image with more high-frequency components. A weighted loss function composed of the adversarial loss, mean absolute percentage error (MAPE), and structural similarity (SSIM) is used under the pix2pix GAN framework. In addition, the self-attention module is used at the end of the generator network to capture the physical distance information between two pixels and enhance the inversion accuracy of the feature scatterers. To further improve the inversion efficiency, the data-driven method (DDM) is used to achieve real-time imaging by cascading U-net and pix2pix GAN, where U-net is used to replace FBE-CIE-I in the LAIM. Compared with other LA inversion, both the synthetic and experimental examples have validated the merits of the proposed LAIM and DDM.

Application of hierarchical grouping and machine learning models for classification of genotypes of Nicotiana tabacum L. with based on morphological characteristics

The maintenance of the variability of plant genetic resources is important both for conservation purposes and for the expansion of the genetic bases of the species. Machine learning is an additional tool with great potential that has been used in the search for solving various agricultural challenges. In this article we study the genetic divergence between tobacco genotypes by multivariate methods and verify the efficiency of computational algorithms, aiming at the identification of promising genotypes. Through multivariate analyses, three divergent groups were formed. Both approaches had high accuracy in classification. An artificial neural network with a hidden layer containing three neurons obtained an accuracy of 0.98, while the Random Forest accuracy was 0.98 and the decision tree 0.96. These values demonstrate how powerful these tools are and reinforce their use in studies aimed at maintaining the germplasm bank and also in tobacco conservation and genetic improvement programs in the Recôncavo region of Bahia.

U.S. Strategic Energy Interests and Tactics for Their Implementation Amid the COVID-19 Pandemic and Russia's Special Military Operation in Ukraine

Relevance. Relations between states, due to either energy cooperation or confrontation, have entered the most acute phase since the beginning of the XXI century, since competition in this industry has become a leading element of the foreign policy of world powers. The purpose is to consider the stages of formation and development of the US energy strategy in the current conditions of world politics.Objectives: to study the activities of us presidents in the context of the implementation of the country's energy interests; to study the legal framework of the US energy dominance in different countries and continents: highlight the significant tactical steps of the US government in the field of realizing the country's energy interests.Methodology. The application of the method of document analysis made it possible to identify the strategic priorities of the policy of the US governments in their dynamics. The retrospective method of analyzing US policy made it possible to prove the idea of the purposeful participation of the US military departments in ensuring the national security of the country in the economic sector.Relevance. The dynamics of the US energy strategy is analyzed on the example of the activities of its presidents from the end of the twentieth century to the present, which showed the transformation of the country's energy strategy from regional dominance, from the position of a net importer of energy resources to global dominance and transformation into a net exporter of energy resources through economic (development of shale deposits), military (expansion of NATO bases in the regions of oil and gas production) and diplomatic (summits, sanctions), etc.Conclusions. Thus, the energy boom leads to a change in the geopolitical alignment of forces in the world, a decrease in the influence of OPEC countries on the formation of oil prices. The shale revolution is at the heart of a fundamental shift in the balance of power. All this makes it possible for the United States to reduce dependence on energy imports and expand freedom of action in Europe, the Middle East, and Central Asia.

BIOTECHNOLOGICAL TERMINOLOGY IN THE RESEARCH OF UKRAINIAN LINGUISTS

The purpose of this review article is to systematize the results of scientific research by Ukrainian linguists devoted to the study of English biotechnological terminology. Biotechnology, as an important field of scientific research and technological development, is developing extremely fast, which requires constant updating and expansion of lexical and terminological bases. Ukrainian linguists analyze the origin and structure of biotechnological terms, classification and evolution of terminology in this field. Aspects of neologization and innovation in the terminology of biotechnology are also considered. The article notes the achieved results of Ukrainian linguists in the study of the origin, semantic and morphological analyzes of terms. It is emphasized that Ukrainian researchers are actively working on the systematization and classification of terminology, as well as researching the specifics of the formation and structure of biotechnological terms. The author identifies problems that require further research. First, the biotech industry continues to grow and evolve, resulting in new terms and concepts. This dynamic requires constant updating and expansion of terminological bases. Some aspects of the semantic nuances of the terms may also require further clarification and analysis. Secondly, an important task is to study the translation of biotechnological terminology and its adaptation to the Ukrainian language. Translation of terms and expressions sometimes requires the creation of new analogues that would reflect the essence of biotechnological processes and concepts. This can be a difficult task due to the specifics of the industry and the ambiguity of some terms. In general, the study of biotechnological terminology is an important element in the development of scientific research and education in Ukraine. The integration of Ukrainian science and education into the global scientific space requires the understanding and use of current terminology, which promotes effective communication and knowledge exchange in this important field. It was emphasized that the further development of biotechnology and the study of its terminology is an important task for scientific research and education in Ukraine, which contributes to the integration of Ukrainian science and education into the global scientific space.

Линейно-пороговые эффекты гамма-облучения наземного моллюска F. fruticum M. третьей возрастной группы

The ecocentric strategy of radiation protection involves the expansion of experimental bases of radiation-induced effects in representatives of biota. In this article we studied the change in the relevant indicator (mortality) of the terrestrial mollusk F. fruticum M. after gamma-irradiation with doses from 10 to 300 Gy. The terrestrial mollusk is not yet included in the list of reference species, but it meets the requirements of the ICRP for reference organisms. The aim of the work is to establish dose-effect relationships in the study of mortality of the terrestrial mollusk F. fruticum M. The third age group after acute -irradiation is used to expand databases on radio-induced effects of biota. The results of a study for mollusks of only the third age group are presented. This research is part of an experiment to identify age-related features of radiosensitivity of a representative of terrestrial malacofauna. The age of the mollusks was determined by the number of revolutions of the shell. The conditions for keeping animals in laboratory were selected in such a way that mortality in the control group remained at zero during the entire experiment. The duration of the experiment is 210 days. The LD50/60 index for the mollusk was estimated by the calculated probit analysis method using the least squares method. The LD50/60 is 141.4+/-26.3 Gy. The change in the indicator was estimated every 30 days after irradiation. A linear threshold dependence was established for each time range, starting from 60 days after irradiation. It contains two threshold transitions to a new level of mortality and, accordingly, three dose ranges: a dose-independent range at low doses of radiation, a dose-dependent range with an increase in the dose of radiation and a dose-independent plateau when switching to the level of absolute lethality. Four dose ranges of mortality of terrestrial mollusks were established for 210 days after irradiation: 10-130 Gy (100% survival rate), 140-160 Gy (absolute mortality after 180 days), 170-190 Gy (absolute mortality after 150 days), 200-300 Gy (100% mortality after 90 days). At the same time, the greatest dynamics of the increase in mortality is observed in the first 60 days after irradiation.

Computing equilibrium measures with power law kernels

We introduce a method to numerically compute equilibrium measures for problems with attractive-repulsive power law kernels of the form K ( x − y ) = | x − y | α α − | x − y | β β K(x-y) = \frac {|x-y|^\alpha }{\alpha }-\frac {|x-y|^\beta }{\beta } using recursively generated banded and approximately banded operators acting on expansions in ultraspherical polynomial bases. The proposed method reduces what is naïvely a difficult to approach optimization problem over a measure space to a straightforward optimization problem over one or two variables fixing the support of the equilibrium measure. The structure and rapid convergence properties of the obtained operators result in high computational efficiency in the individual optimization steps. We discuss stability and convergence of the method under a Tikhonov regularization and use an implementation to showcase comparisons with analytically known solutions as well as discrete particle simulations. Finally, we numerically explore open questions with respect to existence and uniqueness of equilibrium measures as well as gap forming behaviour in parameter ranges of interest for power law kernels, where the support of the equilibrium measure splits into two intervals.

Expansions in multiple bases over general alphabets

Expansions in multiple bases over general alphabets

On the seminormal bases and dual seminormal bases of the cyclotomic Hecke algebras of type G(ℓ,1,n)

This paper studies the seminormal bases {fst},{fst}, and the dual seminormal bases {gst},{gst} of the non-degenerate and the degenerate cyclotomic Hecke algebras Hℓ,n of type G(ℓ,1,n). We present some explicit formulae for the constants αst:=gst/fst∈K×, ast:=gst/fst∈K× in terms of the γ-coefficients {γu,γu′} and the r-coefficients {ru,ru′} of Hℓ,n. In particular, we answer a question [20, Remark 3.6] of Mathas on the rationality of square roots of some quotients of products of γ-coefficients. We obtain some explicit formulae for the expansion of each seminormal bases of Hℓ,n−1 as a linear combination of the seminormal bases of Hℓ,n under the natural inclusion Hℓ,n−1↪Hℓ,n.

Wavelet-based robust estimation and variable selection in nonparametric additive models

This article studies M-type estimators for fitting robust additive models in the presence of anomalous data. The components in the additive model are allowed to have different degrees of smoothness. We introduce a new class of wavelet-based robust M-type estimators for performing simultaneous additive component estimation and variable selection in such inhomogeneous additive models. Each additive component is approximated by a truncated series expansion of wavelet bases, making it feasible to apply the method to nonequispaced data and sample sizes that are not necessarily a power of 2. Sparsity of the additive components together with sparsity of the wavelet coefficients within each component (group), results into a bi-level group variable selection problem. In this framework, we discuss robust estimation and variable selection. A two-stage computational algorithm, consisting of a fast accelerated proximal gradient algorithm of coordinate descend type, and thresholding, is proposed. When using nonconvex redescending loss functions, and appropriate nonconvex penalty functions at the group level, we establish optimal convergence rates of the estimates. We prove variable selection consistency under a weak compatibility condition for sparse additive models. The theoretical results are complemented with some simulations and real data analysis, as well as a comparison to other existing methods.

Expansions in Cantor real bases

We introduce and study series expansions of real numbers with an arbitrary Cantor real base $$\varvec{\beta }=(\beta _n)_{n\in {\mathbb {N}}}$$ , which we call $$\varvec{\beta }$$ -representations. In doing so, we generalize both representations of real numbers in real bases and through Cantor series. We show fundamental properties of $$\varvec{\beta }$$ -representations, each of which extends existing results on representations in a real base. In particular, we prove a generalization of Parry’s theorem characterizing sequences of nonnegative integers that are the greedy $$\varvec{\beta }$$ -representations of some real number in the interval [0, 1). We pay special attention to periodic Cantor real bases, which we call alternate bases. In this case, we show that the $$\varvec{\beta }$$ -shift is sofic if and only if all quasi-greedy $$\varvec{\beta }^{(i)}$$ -expansions of 1 are ultimately periodic, where $$\varvec{\beta }^{(i)}$$ is the i-th shift of the Cantor real base $$\varvec{\beta }$$ .

Sememe knowledge computation: a review of recent advances in application and expansion of sememe knowledge bases

A sememe is defined as the minimum semantic unit of languages in linguistics. Sememe knowledge bases are built by manually annotating sememes for words and phrases. HowNet is the most well-known sememe knowledge base. It has been extensively utilized in many natural language processing tasks in the era of statistical natural language processing and proven to be effective and helpful to understanding and using languages. In the era of deep learning, although data are thought to be of vital importance, there are some studies working on incorporating sememe knowledge bases like HowNet into neural network models to enhance system performance. Some successful attempts have been made in the tasks including word representation learning, language modeling, semantic composition, etc. In addition, considering the high cost of manual annotation and update for sememe knowledge bases, some work has tried to use machine learning methods to automatically predict sememes for words and phrases to expand sememe knowledge bases. Besides, some studies try to extend HowNet to other languages by automatically predicting sememes for words and phrases in a new language. In this paper, we summarize recent studies on application and expansion of sememe knowledge bases and point out some future directions of research on sememes.

Univoque graphs for non-integer base expansions

Unique expansions in non-integer bases have been investigated in many papers during the last thirty years. They are often conveniently generated by labeled directed graphs. We give a precise description of the set of sequences generated by these graphs. This provides a geometric explanation of many former abstract results in this domain. Our results are illustrated by many examples.

Polyhedral approximations of the semidefinite cone and their application

We develop techniques to construct a series of sparse polyhedral approximations of the semidefinite cone. Motivated by the semidefinite (SD) bases proposed by Tanaka and Yoshise (Ann Oper Res 265:155–182, 2018), we propose a simple expansion of SD bases so as to keep the sparsity of the matrices composing it. We prove that the polyhedral approximation using our expanded SD bases contains the set of all diagonally dominant matrices and is contained in the set of all scaled diagonally dominant matrices. We also prove that the set of all scaled diagonally dominant matrices can be expressed using an infinite number of expanded SD bases. We use our approximations as the initial approximation in cutting plane methods for solving a semidefinite relaxation of the maximum stable set problem. It is found that the proposed methods with expanded SD bases are significantly more efficient than methods using other existing approximations or solving semidefinite relaxation problems directly.

Difference of Cantor sets and frequencies in Thue--Morse type sequences

In a recent paper, Baker and Kong have studied the Hausdorff dimension of the intersection of Cantor sets with their translations. We extend their results to more general Cantor sets. The proofs rely on the frequencies of digits in unique expansions in non-integer bases. In relation with this, we introduce a practical method to determine the frequency of any given finite block in Thue--Morse type sequences.