Main Term Research Articles

Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems

In models with insufficient initial information, parameter estimation can be subject to statistical uncertainty, potentially resulting in suboptimal decision-making; however, delaying implementation to gather more information can also incur costs. This paper examines an extension of information-theoretic approaches designed to address this classical dilemma, focusing on balancing the expected profits and the information needed to be obtained about all of the possible outcomes. Initially utilized in binary outcome scenarios, these methods leverage information measures to harmonize competing objectives efficiently. Building upon the foundations laid by existing research, this methodology is expanded to encompass experiments with multiple outcome categories using Dirichlet processes. The core of our approach is centered around weighted entropy measures, particularly in scenarios dictated by Dirichlet distributions, which have not been extensively explored previously. We innovatively adapt the technique initially applied to binary case to Dirichlet distributions/processes. The primary contribution of our work is the formulation of a sequential minimization strategy for the main term of an asymptotic expansion of differential entropy, which scales with sample size, for non-binary outcomes. This paper provides a theoretical grounding, extended empirical applications, and comprehensive proofs, setting a robust framework for further interdisciplinary applications of information-theoretic paradigms in sequential decision-making.

Retinal Organoids from Induced Pluripotent Stem Cells of Patients with Inherited Retinal Diseases: A Systematic Review.

Currently, most inherited retinal diseases lack curative interventions, and available treatment modalities are constrained to symptomatic approaches. Retinal organoid technology has emerged as a method for treating inherited retinal diseases, with growing academic interest in recent years. The purpose of this review was to systematically organize the current protocols for generating retinal organoids using induced pluripotent stem cells from patients with inherited retinal disease and to investigate the application of retinal organoids in inherited retinal disease research. Data were collected from the PubMed, Scopus, and Web of Science databases using a keyword search. The main search term used was "retinal organoid," accompanied by secondary keywords such as "optic cup," "three-dimensional," and "self-organizing." The final search was conducted on October 2, 2024. Of the 2,129 studies retrieved, 130 were included in the qualitative synthesis. The protocols for the generation of retinal organoids in inherited retinal disease research use five major approaches, categorized into 3D and a combination of 2D/3D approaches, implemented with modifications. Disease phenotypes have been successfully reproduced via the generation of retinal organoids from the induced pluripotent stem cells of individuals with inherited retinal diseases, facilitating the progression of research into novel therapeutic developments. Cells have been obtained from retinal organoids for cell therapy, and progress toward their potential integration into clinical practice is underway. Considering their potential applications, retinal organoid technology has shown promise across various domains. In this systematic review, we organized protocols for generating retinal organoids using induced pluripotent stem cells from patients with inherited retinal diseases. Retinal organoid technology has various applications including disease modeling, screening for novel therapies, and cell replacement therapy. Further advancements would make this technology a clinically significant tool for patients with inherited retinal diseases.

The daughter–parent plot: a tool for analyzing thermochronological data

Abstract. Data plots of daughter against parent concentration (D–P plots) are a potential tool for analyzing low-temperature thermochronology, similar to isochron plots in radioisotopic geochronology. Their purposes are to visualize the main term of the radiometric age equation – the daughter–parent ratio – and to inspect the daughter–parent relationship for anomalies indicating influences of geological processes or analytical bias. The main advantages of the D–P plot over other data analysis tools are (1) its ability to detect systematic offsets in D and P concentrations, (2) its unambiguous representation of radiation-damage-dependent daughter retention, and (3) the possibility to analyze potential age outliers. Despite these benefits, the D–P plot is currently not used for analyzing low-temperature thermochronology data, e.g., from fission-track, (U–Th) / He, or zircon Raman dating. We present a simple, decision-tree-based classification for daughter–parent relationships based on the D–P plot that places a dataset into one of seven classes: linear relationship with zero intercept, cluster, linear relationship with systematic offset, nonlinear relationship, several age populations, scattered data, and inverse relationship. Assigning a class to a dataset enables choosing further data analysis steps and how to report a sample age, e.g., as a pooled, central, or isochron age or a range of ages. This classification scheme aims at facilitating thermochronological data analysis and making decisions more transparent. We demonstrate the proposed procedure by analyzing published datasets from a variety of geological settings and thermochronometers and introduce Incaplot, which is graphical user interface software that we developed to facilitate D–P plotting of thermochronology data.

Explicit bounds on the coefficients of modular polynomials for the elliptic 𝑗-invariant

We obtain an explicit upper bound on the size of the coefficients of the elliptic modular polynomials Φ N \Phi _N for any N ≥ 1 N\geq 1 . These polynomials vanish at pairs of j j -invariants of elliptic curves linked by cyclic isogenies of degree N N . The main term in the bound is asymptotically optimal as N N tends to infinity.

Nonlocal Changing-Sign Perturbation Tempered Fractional Sub-Diffusion Model with Weak Singularity

In this paper, we study the existence of positive solutions for a changing-sign perturbation tempered fractional model with weak singularity which arises from the sub-diffusion study of anomalous diffusion in Brownian motion. By two-step substitution, we first transform the higher-order sub-diffusion model to a lower-order mixed integro-differential sub-diffusion model, and then introduce a power factor to the non-negative Green function such that the linear integral operator has a positive infimum. This innovative technique is introduced for the first time in the literature and it is critical for controlling the influence of changing-sign perturbation. Finally, an a priori estimate and Schauder’s fixed point theorem are applied to show that the sub-diffusion model has at least one positive solution whether the perturbation is positive, negative or changing-sign, and also the main nonlinear term is allowed to have singularity for some space variables.

Periodic Solutions of Generalized Lagrangian Systems with Small Perturbations

In this paper we study the generalized Lagrangian system with a small perturbation. We assume the main term in the system to have a maximum, but do not suppose any condition for perturbation term. Then we prove the existence of a periodic solution via Ekeland’s principle. Moreover, we prove a convergence theorem for periodic solutions of perturbed systems.

Conceptual frameworks of integration processes in education

The relevance of the topic is connected with the urgent need in modern socio-political realities to use integrative technological tools in solving educational problems. According to the message of the President of the Russian Federation to the Federal Assembly on February 21, 2023, “a synthesis of all the best that was in the Soviet education system and the experience of recent decades is necessary”. Higher education teachers have been given serious goals to develop effective practices for integrating new regions of the Russian Federation into the cultural and educational space of Russia. Integration is the process and result of the formation of integrity, which plays a priority role in relation to its parts. The emergence of integration is closely related to the need to satisfy the fundamental human need to inherit the experience of previous generations, and subsequently transfer it, which is the mechanism of pedagogical activity: the integration of the experience of generations and the integration of pedagogical and production activities. In the article, the author examines the definition of the main research term; relies on the classification of sources for studying integration processes in pedagogy proposed by Professor N.K. Chapaev; the analysis of modern integrative pedagogical concepts is carried out. In these rapidly developing times, we need specialists who are open to interaction and ready to integrate professionals from seemingly completely different areas into their specific activities: integration becomes the basis for the development of the educational sphere.

A new crack-tip element for the logarithmic stress-singularity of Mode-III cracks in spring interfaces

A new crack-tip finite element able to improve the accuracy of Finite Element Method (FEM) solutions for cracks growing along the Winkler-type spring interfaces between linear elastic adherents is proposed. The spring model for interface fracture, sometimes called Linear-Elastic (perfectly) Brittle Interface Model (LEBIM), can be used, e.g., to analyse fracture of adhesive joints with a thin adhesive layer. Recently an analytical expression for the asymptotic elastic solution with logarithmic stress-singularity at the interface crack tip considering spring-like interface behaviour under fracture Mode III was deduced by some of the authors. Based on this asymptotic solution, a special 5-node triangular crack-tip finite element is developed. The generated special singular shape functions reproduce the radial behaviour of the first main term and shadow terms of the asymptotic solution. This special element implemented in a FEM code written in Matlab has successfully passed various patch tests with spring boundary conditions. The new element allows to model cracks in spring interfaces without the need of using excessively refined FEM meshes, which is one of the current disadvantages in the use of LEBIM when stiff spring interfaces are considered. Numerical tests carried out by h-refinement of uniform meshes show that the new singular element consistently provides significantly more accurate results than the standard finite elements, especially for stiff interfaces, which could be relevant for practical applications minimizing computational costs. The new element can also be used to solve other problems with logarithmic stress-singularities.

A 7-year record of vertical profiles of radar measurements and precipitation estimates at Dumont d'Urville, Adélie Land, East Antarctica

Abstract. Studying precipitation falling over Antarctica is crucial as snowfall represents the main water input term for the polar cap. However, precipitation observations still remain scarce – and, more particularly, in the atmospheric column – due to numerous experimental issues related to the white continent. This paper aims at helping to close this observation gap by presenting 7 years of Micro Rain Radar (Metek MRR-2) data at the Dumont d'Urville station in coastal Adélie Land, East Antarctica. Statistics are calculated on three radar variables (equivalent reflectivity, mean Doppler velocity and signal-to-noise ratio (SNR)) to outline the main characteristics of the radar dataset. Seasonal and interannual variabilities are also investigated, but no significant temporal trends are detected, except for the seasonal mean Doppler velocity, which is higher in summer and lower in winter. We then use the snowfall rate (S) data from a collocated snow gauge to estimate the MRR precipitation profile from the radar equivalent reflectivity (Ze) through a locally derived Ze–S relation. We find the relation Ze=43.3S0.88. The processing method used to obtain this relation, data quality and uncertainty considerations are discussed in the paper. In order to give an example of application of the dataset, a brief statistical comparison of the MRR precipitation rate along the vertical with model data from the ERA5 reanalysis and the LMDZ climate model is performed, which notably shows that models underestimate heavy precipitation events. All datasets are available on the PANGAEA database with the associated DOI: https://doi.org/10.1594/PANGAEA.962727 (Wiener et al., 2023).

Research Advancements on the Correlation Between Spontaneous Intracerebral Hemorrhage of Different Etiologies and Imaging Markers of Cerebral Small Vessel Disease.

The purpose of this review is to identify the correlation between ICH and CSVD imaging markers under SMASH-U classification by searching and analyzing a large number of literatures in recent years, laying a theoretical foundation for future clinical research. At the same time, by collecting clinical data to evaluate patient prognosis, analyzing whether there are differences or supplements between clinical trial conclusions and previous theories, and ultimately guiding clinical diagnosis and treatment through the analysis of imaging biomarkers. In this review, by searching CNKI, Web of Science, PubMed, FMRS and other databases, the use of "spontaneous intracerebral hemorrhage", "hypertensive hemorrhagic cerebral small vessel disease", "cerebral small vessel disease imaging", "Based cerebral small vessel diseases", "SMASH the -u classification" and their Chinese equivalents for the main search term. We focused on reading and analyzing hundreds of relevant literatures in the last decade from August 2011 to April 2020, and also included some earlier literatures with conceptual data sources. After screening and ranking the degree of relevance to this study, sixty of them were cited for analysis and elaboration. In patients with ICH, the number of cerebral microbleeds in lobes, basal ganglia, and the deep brain is positively correlated with ICH volume and independently correlated with neurological functional outcomes; white matter hyperintensity severity is positively correlated with ICH recurrence risk; multiple lacunar infarction independently predict the risk of ICH; severe brain atrophy is an independent risk factor for a poor prognosis in the long term in patients diagnosed with ICH; and the number of enlarged perivascular spaces is correlated with ICH recurrence. However, small subcortical infarct and ICH are the subject of few studies. Higher CSVD scores are independently associated with functional outcomes at 90 days in patients diagnosed with ICH.

General theory of radiative transfer in a magnetized atmosphere with scattering by electrons

ABSTRACT Here, we consider the general radiative transfer theory in a magnetized atmosphere for any value of parameter $x=\omega _B/\omega \simeq 0.933\times 10^{-8}\lambda (\mu \mathrm{m}) B(\text{G})$, where ωB is the cyclotron frequency of electron rotation and ω is the angular frequency of considered monochromatic radiation. The main term of the radiative transfer equations $\textbf {J}_{\alpha \beta }$ for the Stokes parameters I, V, U, and Q describes the scattering of radiation coming from all directions and distances. All Stokes parameters of the incident radiation mutually transform into each other along their path due to interference and different cross-sections for them. To find this transformation of the Stokes parameters one has to solve the complex system of transfer equations without the sources and term $\textbf {J}_{\alpha \beta }$. This is done in our paper. First, we present the general solution and then give the solution for the case of a homogeneous magnetic field, where the formulas have clear algebraic form. We note that for small parameter x our formulas describe the known Faraday rotation. Our formulas allow us to derive an integral equation for the density of polarized radiation, multiple scattered in a magnetized atmosphere for any values of the parameter x. The obtained correct radiation transfer equation allows us to calculate the Stokes parameters of radiation emerging from an atmosphere, in particular, for the Milne problem.

One-level density of zeros of Dirichlet L-functions over function fields

TextWe compute the one-level density of zeros of order ℓ Dirichlet L-functions over function fields Fq[t] for ℓ=3,4 in the Kummer setting (q≡1(modℓ)) and for ℓ=3,4,6 in the non-Kummer setting (q≢1(modℓ)). In each case, we obtain a main term predicted by Random Matrix Theory (RMT) and lower order terms not predicted by RMT. We also confirm the symmetry type of the families is unitary, supporting Katz and Sarnak's philosophy. VideoFor a video summary of this paper, please visit https://youtu.be/0tGmXHvVKF0.

Ancient Israelite Scribal Apprenticeships

This article applies the anthropological model of apprenticeship learning as articulated by Jean Lave and Etienne Wegner to the study of ancient Israelite scribalism. Apprenticeship learning created scribal “communities of practice,” and this can be identified in the ancient Hebrew inscriptional record as well as biblical texts. The main Hebrew term for an “apprentice” is naʿar, and this term appears on Hebrew seals and seal impressions. Scribal skills were learned in a variety of professions such as administrators, soldiers, merchants, prophets, and priests, and each of these professions would have had their own “community of practice.” The close-knit relationships forged by apprenticeship learning is reflected in the use of familial language such as “son of” to express different professional scribal communities.

Asymptotic expansion of the error of the numerical method for solving wave equation with functional delay

A wave equation with functional delay is considered. The problem is discretized. Constructions of the difference method with weights with piecewise linear interpolation are given. A basic method with weights with piecewise cubic interpolation is constructed. The order of the residual is studied without interpolation of the basic method, and the expansion coefficients of the residual with respect to time-steps and space-steps are written out. It is proved that the weighted method with piecewise cubic interpolation converges with order 2 in the energy norm. An equation is written for the main term of the asymptotic expansion of the global error of the basic method. Under certain assumptions, the validity of the application of the Richardson extrapolation procedure is substantiated, and the corresponding numerical method is constructed, that has the fourth order of convergence with respect to time-steps and space-steps. The validity of Runge's formulas for practical estimation of the error is proved. The results of numerical experiments on a test example are presented.

Series Acceleration via Negative Binomial Probabilities

Many special functions and analytic constants allow for a probabilistic representation in terms of inverse moments of [0, 1]-valued random variables. Under this assumption, we give fast computations of them with an explicit upper bound for the remainder term. One of the main features of the method is that the coefficients of the main term of the approximation always contain negative binomial probabilities which, in turn, can be precomputed and stored. Applications to the arctangent function, Dirichlet functions and their nth derivatives, and the Catalan, Gompertz, and Stieltjes constants are provided.

Censorship in teacher training: the case of the lending library of the Pedagogical Academy of Heraklion, Crete, Greece

This paper examines censorship forms implemented in the pedagogical training received by the students (teacher candidates) of the Pedagogical Academy of Heraklion (Crete, Greece) during the period of the April dictatorship (1967-1974). First, a bibliographical overview of the main term of the paper, namely the censorship, is attempted, and then the historical context of the censorship actions undertaken by the dictators is analysed. The research was based on the archival material of the Academy, specifically the documents relating to its lending library. The historical interpretive methodology of 'history from below' was followed. The aim of the research was to highlight the correlation between the examined documents, which seemingly did not relate to the concept of censorship, and the conceptual and historical context set. The results of the research revealed many acts of censorship, overt or latent, concerning the formation of the institution's lending library. The above results constituted important findings, as they contributed to the scientific methodology of ‘history from below’, as the research object was not associated with a person or a group of people, as is common practice. Instead, the focus of the research was placed on an institution of pedagogical training that has been in the margins in terms of research, and there were no papers in the relevant scientific discourse that base their research on such a research unit. Finally, this research attempted to highlight important findings that sometimes confirm and sometimes contradict the hitherto known literature on the implementation of censorship in the period under review. More specifically, the findings were consistent with the general idea of the intense censorship activity of the dictators in the period 1967-1972, but it also highlights similar results for the period 1972-1974, for which relevant research had shown that the phenomenon of censorship was clearly less visible.

An approximation formula for the shifted cubic moment of automorphic L-functions in the weight aspect

Abstract Consider the family of automorphic L-functions associated with primitive cusp forms of level one, ordered by weight k. Assuming that k tends to infinity, we prove a new approximation formula for the cubic moment of shifted L-values over this family which relates it to the fourth moment of the Riemann zeta function. More precisely, the formula includes a conjectural main term, the fourth moment of the Riemann zeta function and error terms of size smaller than that predicted by the recipe conjectures.

Gradient-based multi-label feature selection considering three-way variable interaction

Nowadays, Multi-Label Feature Selection (MLFS) attracts more and more attention to tackle the high-dimensional problem in multi-label data. A key characteristic of existing gradient-based MLFS methods is that they typically consider two-way variable correlations between features and labels, including feature-feature and label-label correlations. However, two-way correlations are not sufficient to steer feature selection since such correlations vary given different additional variables in practical scenarios, which leads to the selected features with relatively-poor classification performance. Motivated by this, we capture three-way variable interactions including feature-feature-label and feature-label-label interactions to further characterize the fluctuating correlations in the context of another variable, and propose a new gradient-based MLFS approach incorporating the above three-way variable interactions into a global optimization objective. Specifically, based on information theory, we develop second-order regularization penalty terms to regard three-way interactions while jointly combining with the main loss term in regard to feature relevance. Then the objective function can be efficiently optimized via a block-coordinate gradient descent schema. Meanwhile, we provide a theoretical analysis demonstrating the effectiveness of the regularization terms in exploiting three-way interaction. In addition, experiments conducted on a series of benchmark data sets also verify the validity of the proposed method on multiple evaluation metrics.

A Singularly Perturbed Dirichlet Problem for a Ring With Singular Boundaries

Uniform asymptotic expansions of small-parameter solutions of bisingular Dirichlet problems for a ring with any degree of accuracy are constructed by a generalized method of boundary functions and a small-parameter method. The investigated problems have two features: equations with a small parameter in the first derivatives and external solutions simultaneously have increasing features on the boundaries of the domain, i. e. limit equations have singularities at the same time on both boundaries of the ring. Formal asymptotic expansions are based on the maxima principle and the method of differential inequalities. The resulting asymptotic series are represented by the Puiseux series. The main term of the asymptotic expansions of the solutions has a negative fractional power with respect to the small parameter.

Implications of Public Interest in Colonoscopy: Analysis of Google Trends Data From 12 European Countries.

Colorectal cancer (CRC) is one of the deadliest diseases in the European Union. Colonoscopy remains the gold standard of CRC screening. Analysis of colonoscopy-related Google Trends (GT; Google LLC, Mountain View, California, United States) data could provide useful information regarding interest in colonoscopy and potential barriers making patients unwilling to attend screening programs. Data were collected using GT for the main search term "colonoscopy" and the two most related queries. Colonoscopy volumes were extracted from the Eurostat database. Due to limited Eurostat data availability, analysis was performed from January 2004 to December 2015 for each of the 12 included countries. Univariate linear regression analysis demonstrated statistically significant correlations between annual search volumes of "colonoscopy" and the annual number of colonoscopies performed in included countries (R2 = 0.923, P<.001). Trend analysis showed that the cumulative search volumes for "colonoscopy" gradually increased through the analyzed period. The spectrum of the most related queries encompassed "preparation for colonoscopy", "endoscopy", "after endoscopy", "colon", "colonoscopy diet", "virtual colonoscopy", "colonoscopy under anesthesia", "waiting times for colonoscopy" and "colonoscopy price". For eight out of nine queries, statistically significant correlations with procedure volumes were revealed. GT could be a useful tool in assessing public interest in colonoscopy. Potential barriers that prevent people from attending CRC screening programs were identified. The study demonstrated that the internet has become an important field for CRC screening promotion. GT utility for colonoscopy and CRC screening providers was highlighted. This was the first analysis of GT data in colonoscopy focused on European countries.