Analysis of the barotropic model of the subtropical gyre in the ocean for finite Reynolds numbers. Part I

A barotropic time-dependent model of the wind-driven currents in the subtropical region of the ocean was considered taking both nonlinearity and lateral friction into account. The boundary conditions are the impermeability at all boundaries, no-slip at the coasts and slip at the fluid boundaries. It is shown that the solution of the problem is characterized by two nondimensional parameters ε (the ratio of width of the inertial boundary layer to a basin dimension) and R (Reynolds number for the boundary layer). A series of numerical experiments is discussed with fixed ε = 0.01 and varying R to analyze the joint effect of nonlinearity and lateral friction for a wide range of the coefficient of the horizontal friction. The spin-up and quasistationary regimes in the evolution are identified. The most striking feature of the solution for finite R is the formation of a permanent intensive recirculation gyre. The periodic formation of the northward moving eddies in the boundary current is also observed during the quasistationary regime. A Fourier analysis of the energy oscillations as well as the time records of the stream function at certain points during the quasistationary regime is presented and the time-averaged solution of the problem is introduced. The basic result of the analysis is the proof of the existence of two critical values RC and RL of the Reynolds number R. For R \u3e RC the time-dependent solution of the problem does not stabilize as time proceeds (RC = 0.38). For R \u3e RL the structure of the solution is changed drastically: the motion becomes substantially more chaotic both in the interior and in the boundary layer (RL = 1.6). It will be shown in Sheremet et al. (1996, hereafter will be called SIK) that for R \u3e RC the steady solution still exists but it appears to be unstable, while for R \u3e RL the steady boundary-layer-type solution of the problem ceases to exist. The main feature of the time-averaged solutions for R \u3e RL is a rapid increase of a recirculation gyre in the northwest corner of the basin

Кластеризація даних з пропусками методом k-середніх

Приведен обзор существующих подходов к кластеризации данных с пропусками. Проведены вычислительные эксперименты для их сравнения в случае применения метода k-средних. Для сравнения выбраны методы заполнения пропусков средним, медианой и на основе метода главных компонент, а также методы кластеризации данных с пропусками KSC и k-POD. Полученные результаты показали преимущества метода KSC и заполнения пропусков на основе метода главных компонент.The clustering task is a very important data mining task arising in many applications. However, well known and widely used clustering methods cannot work with datasets that have missing values. The paper provides an overview of the existing approaches to data with missing values clustering and a comparative analysis of chosen approaches when applying the k-means clustering method. Commonly used approaches are: 1) deletion entities or features with missing values with further complete data clustering, 2) imputation (filling in the missing values) with further complete data clustering, 3) using clustering methods that work with missing data. The following methods within these approaches were chosen for comparison: mean substitution, median substitution, imputation based on principal component analysis and two k-means extensions – KSC and k-POD. In order to conduct the comparative analysis the software «ClustDMV» was developed on the C# using the .NET Core framework. The software is a desktop application with a graphical interface.The following computational experiments were carried out using the created software. One hundred two-dimensional datasets were simulated in each experiment.  All the datasets in one experiment were modeled with the same clusters parameters. Each dataset consists of 800 entities from four clusters. Then a certain percentage of omissions were randomly entered into the data. After that, either the missing values were filled in and k-means method was used with the complete data, or the KSC and k-POD methods were applied to the data with missing values. In order to evaluate the clustering quality Rand index was used. Indexes obtained on all 100 datasets were averaged.The paper presents the results of three typical experiments. According to the results the KSC method and imputation based on principal component analysis showed the best performance.Наведено огляд існуючих підходів до кластеризації даних з пропусками. Проведено обчислювальні експерименти для їх порівняння у разі застосування методу k-середніх. Для порівняння обрано методи заповнення пропусків середнім, медіаною і на основі методу головних компонент, а також методи кластеризації даних з пропусками KSC і k-POD. Одержані результати показали перевагу методу кластеризації KSC та заповнення пропусків на основі методу головних компонент

Functional Characterization of Lamina X Neurons in ex-Vivo Spinal Cord Preparation

Functional properties of lamina X neurons in the spinal cord remain unknown despite the established role of this area for somatosensory integration, visceral nociception, autonomic regulation and motoneuron output modulation. Investigations of neuronal functioning in the lamina X have been hampered by technical challenges. Here we introduce an ex-vivo spinal cord preparation with both dorsal and ventral roots still attached for functional studies of the lamina X neurons and their connectivity using an oblique LED illumination for resolved visualization of lamina X neurons in a thick tissue. With the elaborated approach, we demonstrate electrophysiological characteristics of lamina X neurons by their membrane properties, firing pattern discharge and fiber innervation (either afferent or efferent). The tissue preparation has been also probed using Ca2+ imaging with fluorescent Ca2+ dyes (membrane-impermeable or -permeable) to demonstrate the depolarization-induced changes in intracellular calcium concentration in lamina X neurons. Finally, we performed visualization of subpopulations of lamina X neurons stained by retrograde labeling with aminostilbamidine dye to identify sympathetic preganglionic and projection neurons in the lamina X. Thus, the elaborated approach provides a reliable tool for investigation of functional properties and connectivity in specific neuronal subpopulations, boosting research of lamina X of the spinal cord

Electromagnetically induced transparency in inhomogeneously broadened Lambda-transition with multiple excited levels

Electromagnetically induced transparency (EIT) has mainly been modelled for three-level systems. In particular, a considerable interest has been dedicated to the Lambda-configuration, with two ground states and one excited state. However, in the alkali-metal atoms, which are commonly used, hyperfine interaction in the excited state introduces several levels which simultaneously participate in the scattering process. When the Doppler broadening is comparable with the hyperfine splitting in the upper state, the three-level Lambda model does not reproduce the experimental results. Here we theoretically investigate the EIT in a hot vapor of alkali-metal atoms and demonstrate that it can be strongly reduced due to the presence of multiple excited levels. Given this model, we also show that a well-designed optical pumping enables to significantly recover the transparency

Quantum memory for light via stimulated off-resonant Raman process: beyond the three-level Lambda-scheme approximation

We consider a quantum memory scheme based on the conversion of a signal pulse into a long-lived spin coherence via stimulated off-resonant Raman process. For a storing medium consisting of alkali atoms, we have calculated the Autler-Townes resonance structure created by a strong control field. By taking into account the upper hyperfine states of the D1 optical transition, we show important deviations from the predictions of the usual three-level Lambda-scheme approximation and we demonstrate an enhancement of the process for particular detunings of the control. We estimate the memory efficiency one can obtain using this configuration.Comment: 8 pages, 6 figure