Angular asymptotics for multi-dimensional non-homogeneous random walks with asymptotically zero drift

We study the first exit time $\tau$ from an arbitrary cone with apex at the origin by a non-homogeneous random walk (Markov chain) on $\Z^d$ ($d \geq 2$) with mean drift that is asymptotically zero. Specifically, if the mean drift at \bx \in \Z^d is of magnitude O(\| \bx\|^{-1}), we show that $\tau<\infty$ a.s. for any cone. On the other hand, for an appropriate drift field with mean drifts of magnitude \| \bx\|^{-\beta}, $\beta \in (0,1)$, we prove that our random walk has a limiting (random) direction and so eventually remains in an arbitrarily narrow cone. The conditions imposed on the random walk are minimal: we assume only a uniform bound on $2$nd moments for the increments and a form of weak isotropy. We give several illustrative examples, including a random walk in random environment model

Improved temperature measurement and modeling for 3D USCT II

Medical visualization plays a key role in the early diagnosis and detection of symptoms related to breast cancer. However, currently doctors must struggle to extract accurate and relevant information from the 2D models on which the medical field still relies. The problem is that 2D models lack the spatial definition necessary to extract all of the information a doctor might want. In order to address this gap, we are developing a machine capable of performing ultrasound computer tomography and reconstructing 3D images of the breasts - the KIT 3D USCT II. In order to accurately reconstruct the 3D image using ultrasound, we must first have an accurate temperature model. This is because the speed of sound varies significantly based on the temperature of the medium (in our case, water). We address this issue in three steps: so-called super-sampling, calibration, and modeling. Using these three steps, we were able to improve the accuracy of the hardware from ±1°C to just under 0.1°C

Strong transience for one-dimensional Markov chains with asymptotically zero drifts

For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at $x$ decays as $1/x$ as $x \to \infty$, we quantify degree of transience via existence of moments for conditional return times and for last exit times, assuming increments are uniformly bounded. Our proof uses a Doob $h$-transform, for the transient process conditioned to return, and we show that the conditioned process is also of Lamperti type with appropriately transformed parameters. To do so, we obtain an asymptotic expansion for the ratio of two return probabilities, evaluated at two nearby starting points; a consequence of this is that the return probability for the transient Lamperti process is a regularly-varying function of the starting point.Comment: 26 pages; v2: minor revisions, expanded discussio

Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips

We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non existence of moments for first-passage and last-exit times. In our proofs we also make use of estimates for hitting probabilities and large deviations bounds. Our results are more general than existing results in the literature, which consider only the case of sums of independent (typically, identically distributed) random variables. We do not assume the Markov property. Existing results that we generalize include a circle of ideas related to the Marcinkiewicz-Zygmund strong law of large numbers, as well as more recent work of Kesten and Maller. Our proofs are robust and use martingale methods. We demonstrate the benefit of the generality of our results by applications to some non-classical models, including random walks with heavy-tailed increments on two-dimensional strips, which include, for instance, certain generalized risk processes

КОМПЛЕКС ХАРАКТЕРИСТИК УЧЕБНОГО ВЗАИМОДЕЙСТВИЯ В ПСИХОЛОГИЧЕСКОМ ИССЛЕДОВАНИИ

The article is dedicated to the analysis of educational communication. The author considers such characteristics of educational interaction as content-related, structural and organizational, reflexive, temporal and topological, interactive, individual and psychological. The content-related part of educational interaction assumes didactic content that mediates communication between a teacher and a student. The structural and organizational part specifies concrete forms of educational interaction. The article focuses on the reflexive component that reveals teacher’s and student’s self-perception of educational interaction that influences the process of their didactic communication. Temporal and topological characteristic considers the conditions of time and space when educational interaction is carried out. Interactive feature deals with the procedural aspect of educational interaction. Individual and psychological features outline the impact on educational interaction caused by personal values of the participants. The author suggests considering educational interaction as a process that takes into account Variable “the way of educational impact”.Статья посвящена психологическому рассмотрению процесса учебного взаимодействия. Рассмотрены следующие характеристики учебного взаимодействия: содержательная, структурно-организационная, рефлексивная, темпорально-топологическая, интерактивная, индивидуально-психологическая. Содержательная характеристика учебного взаимодействия подразумевает то дидактическое содержание, которое опосредует коммуникацию обучающего и обучаемого. Структурно-организационная характеристика определяет те конкретные формы, в рамках которых развертывается процесс учебного взаимодействия. Рефлексивная характеристика, которой в статье уделено особое значение, отражает субъективное восприятие процесса учебного взаимодействия обучающим и обучаемым, что оказывает существенное влияние на процесс их дидактической коммуникации. Темпорально-топологическая характеристика учитывает условия времени и пространства, в которых осуществляется учебное взаимодействие. Интерактивная характеристика касается процессуальных аспектов учебного взаимодействия. Индивидуально-психологические характеристики указывают меру воздействия на процесс учебного взаимодействия личностных особенностей его участников. Предложена схема рассмотрения процесса учебного взаимодействия, учитывающая переменную «образ обучающего воздействия»

Современные модификации конструктивистского подхода в контексте исследований дидактической коммуникации

The article is dedicated to the study of educational communication between the teacher and the trainee on the basis of the constructivist approach. The aim of the work was the approbation of the P. Taylor-B. Fraser-D. Fisher’s method with reference to the sample of Russian-speaking trainees. The comparative characteristics of the traditional and constructivist models of didactic communication, as well as the data relating to the approbation of the P. Taylor»s constructivist test, are presented.В статье рассмотрена проблема исследования дидактической коммуникации обучаемого и обучающего в аспекте конструктивистского подхода. Целью работы выступила апробация методики П. Тейлора – Б. Фрейзера – Д. Фишера применительно к выборке русскоязычных обучаемых. Приведены сравнительные характеристики традиционной и конструктивисткой моделей дидактической коммуникации, а также данные, касающиеся апробации конструктивистского теста П. ­Тейлора