Russian Rivers Streamflow Forecasting Using Hydrograph Extrapolation Method

This paper presents a method of hydrograph extrapolation, intended for simple and efficient streamflow forecasting with up to 10 days lead time. The forecast of discharges or water levels is expressed by a linear formula depending on their values on the date of the forecast release and the five previous days. Such forecast techniques were developed for more than 2700 stream gauging stations across Russia. Forecast verification has shown that this method can be successfully applied to large rivers with a smooth shape of hydrographs, while for small mountain catchments, the accuracy of the method tends to be lower. The method has been implemented into real-time continuous operations in the Hydrometcentre of Russia. In the territory of Russia, 18 regions have been identified with a single dependency of the maximum lead time of good forecasts on the area and average slope of the catchment surface for different catchments of each region; the possibilities of forecasting river streamflow by the method of hydrograph extrapolation are approximately estimated. The proposed method can be considered as a first approximation while solving the problem of forecasting river flow in conditions of a lack of meteorological information or when it is necessary to quickly develop a forecasting system for a large number of catchments.

Power-like potentials: From the Bohr–Sommerfeld energies to exact ones

For one-dimensional power-like potentials [Formula: see text], [Formula: see text], the Bohr–Sommerfeld energies (BSE) extracted explicitly from the Bohr–Sommerfeld quantization condition are compared with the exact energies. It is shown that for the ground state as well as for all positive parity states the BSE are always above the exact ones as opposed to the negative parity states where the BSE remain above the exact ones for [Formula: see text] but below them for [Formula: see text]. The ground state BSE as function of [Formula: see text] are of the same order of magnitude as the exact energies for linear [Formula: see text], quartic [Formula: see text] and sextic [Formula: see text] oscillators but their relative deviation grows with [Formula: see text], reaching the value 4 at [Formula: see text]. For physically important cases [Formula: see text], for the 100th excited state BSE coincide with exact ones in 5–6 figures. It is demonstrated that by modifying the right-hand side of the Bohr–Sommerfeld quantization condition by introducing the so-called WKB correction [Formula: see text] (coming from the sum of higher-order WKB terms taken at the exact energies or from the accurate boundary condition at turning points) to the so-called exact WKB condition one can reproduce the exact energies. It is shown that the WKB correction is a small, bounded function [Formula: see text] for all [Formula: see text]. It grows slowly with increasing [Formula: see text] for fixed quantum number [Formula: see text], while it decays with quantum number growth at fixed [Formula: see text]. It is the first time when for quartic and sextic oscillators the WKB correction and energy spectra (and eigenfunctions) are found in explicit analytic form with a relative accuracy of [Formula: see text] (and [Formula: see text]).

Use of GPS at research of roads & a vehicle

The purpose of this work are consideration of use of GPS for a research of roads and modeling of the vehicle/wheel machines (WM).Implementation for this problem of the measuring registering complex on a basis the Raspberry Pi 3/4 minicomputer, the GN-803G sensor and creation of the software in the language C/C ++ is considered.The obtained information about GPS and approaches of selection of necessary data from the messages on the basis of the NMEA 0183 standard submitted in the text ASCII form with the fields divided by a comma is analyzed. An assessment of opportunities of use of the obtained information is given.The scheme of connection of the GN-803N module to Raspberry 3/4 through the GPIO protocol is developed and proved.Reduction of the obtained data to a constant step with use of a polynom of Lagrange of the 2-nd order on three points of a variable step is considered.It is recommended at further use of this corrected data array in process modeling of the car application of a method of interpolation CatMull-Rom on the 4-th points at the fixed step. Program fragments are given in C/C ++.It is offered in the territory of RB during the determining of relative distances and a binding to cards at conversion it is possible to use the simplified linear formula lat_m= 112297,6196∙ Ddec lat , lon_m= 63215,444 ∙ Ddec lon .The offered technique of application of GPS, software, received data are planned to be used for a research of influence of the driver and road conditions on the movement of the vehicle and the subsequent their application when modeling in Matlab/ Simulink, and also in problems of preliminary debugging of management systems by self-driving vehicles.

http://method.meteorf.ru/publ/tr/tr380/htm/02.htm

Forecasting the flow of Russian rivers by hydrograph extrapolation / Borsch S.V., Koliy V.M., Semenova N.K., Simonov Yu.A., Khristoforov A.V. // Hydrometeorological Research and Forecasting, 2021, no. 2 (380), pp. 77-94. An automated system has been developed based on the hydrograph extrapolation method, which allows the year-round daily forecasting of water level and streamflow for the Russian rivers with up to 10-day lead time. The forecast of discharges or water levels is expressed by a linear formula depending on their values on the date of the forecast issue and five previous days. The forecasting scheme limits the possible minimum and maximum values of the discharge or water level based on historical data. Forecast schemes were obtained for 2776 river gauges. The time period from 2010 to 2019 with daily observations of discharge and water level was used. The forecast verification shows that this method can be successfully applied to large rivers with smooth hydrographs. Keywords: daily discharge and water levels, short- and medium-term forecasts, hydrograph extrapolation method, forecast verification, maximum lead time of satisfactory forecasts, self-learning of an automated system for preparing and issuing forecasts

Modeling and Exact Reliability for a Consecutive Linear (k1,k2,…,kn−r+1)-Out-of-r-from-n: F System and Consecutive Circular (k1,k2,…,kn)-Out-of-r-from-n: F System

The consecutive linear [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]:F system consists of [Formula: see text] linear ordered components and the consecutive circular [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]:F system consists of [Formula: see text] circular ordered components. In this paper, we suggest, for the first time, modeling and exact reliability for these models. The linear system fails if and only if there exists a [Formula: see text]-order statistic of [Formula: see text]-consecutive [Formula: see text] [Formula: see text] of components in the failed state, [Formula: see text], [Formula: see text]; and the circular system fails if and only if there exists a [Formula: see text]-order statistic of [Formula: see text]-consecutive [Formula: see text] [Formula: see text] of components in the failed state, [Formula: see text], [Formula: see text]. In this paper, we designed an innovative algorithm to obtain the exact reliability for an extensive class of consecutive linear and circular systems. In continuation, there are the MATLAB Programs of exact reliability for consecutive linear and circular systems. In the following, we applied comparative and numerical results and calculated the exact reliability of this strategic systems. Finally, we calculated the exact reliability for two real-world practical examples.

Differential Galois cohomology and parameterized Picard–Vessiot extensions

Assuming that the differential field [Formula: see text] is differentially large, in the sense of [León Sánchez and Tressl, Differentially large fields, preprint (2020); arXiv:2005.00888 ], and “bounded” as a field, we prove that for any linear differential algebraic group [Formula: see text] over [Formula: see text], the differential Galois (or constrained) cohomology set [Formula: see text] is finite. This applies, among other things, to closed ordered differential fields in the sense of [Singer, The model theory of ordered differential fields, J. Symb. Logic 43(1) (1978) 82–91], and to closed[Formula: see text]-adic differential fields in the sense of [Tressl, The uniform companion for large differential fields of characteristic [Formula: see text], Trans. Amer. Math. Soc. 357(10) (2005) 3933–3951]. As an application, we prove a general existence result for parameterized Picard–Vessiot (PPV) extensions within certain families of fields; if [Formula: see text] is a field with two commuting derivations, and [Formula: see text] is a parameterized linear differential equation over [Formula: see text], and [Formula: see text] is “differentially large” and [Formula: see text] is bounded, and [Formula: see text] is existentially closed in [Formula: see text], then there is a PPV extension [Formula: see text] of [Formula: see text] for the equation such that [Formula: see text] is existentially closed in [Formula: see text]. For instance, it follows that if the [Formula: see text]-constants of a formally real differential field [Formula: see text] is a closed ordered[Formula: see text]-field, then for any homogeneous linear [Formula: see text]-equation over [Formula: see text] there exists a PPV extension that is formally real. Similar observations apply to [Formula: see text]-adic fields.

Countable approximation of topological G-manifolds, II: linear Lie groups G

Let [Formula: see text] be a matrix group. Topological [Formula: see text]-manifolds with Palais-proper action have the [Formula: see text]-homotopy type of countable [Formula: see text]-CW complexes (3.2). This generalizes Elfving’s dissertation theorem for locally linear [Formula: see text]-manifolds (1996). Also, we improve the Bredon–Floyd theorem from compact Lie groups [Formula: see text] to arbitrary Lie groups [Formula: see text].

Hot subdwarf B stars with neutron star components

Context. Subdwarf B stars (sdBs) play a crucial role in stellar evolution, asteroseismology, and far-UV radiation of early-type galaxies, and have been intensively studied with observation and theory. It has theoretically been predicted that sdBs with neutron star (NS) companions exist in the Galaxy, but none have been discovered yet. This remains a puzzle in this field. In a previous study (hereafter Paper I), we have studied the formation channels of sdB+NS binaries from main-sequence (MS) stars plus NS binaries by establishing a model grid, but it is still unclear how these binaries consisting of MS stars and NS binaries came to be in the first place. Aims. We systematically study the formation of sdB+NS binaries from their original zero-age main-sequence progenitors. We bridge the gap left by our previous study in this way. We obtain the statistical population properties of sdB+NS binaries and provide some guidance for observational efforts. Methods. We first used Hurley’s rapid binary evolution code BSE to evolve 107 primordial binaries to the point where the companions of NS+MS, NS+Hertzsprung gap star, and NS+Giant Branch star binaries have just filled their Roche lobes. Next, we injected these binaries into the model grid we developed in Paper I to obtain the properties of the sdB+NS populations. We adopted two prescriptions of NS natal kicks: the classical Maxwellian distribution with a dispersion of σ = 265 km s−1, and a linear formula that assumes that the kick velocity is associated with the ratio of ejected to remnant mass. Different values of αCE, where αCE is the common-envelope ejection efficiency, were chosen to examine the effect of common-envelope evolution on the results. Results. In the Galaxy, the birthrate of sdB+NS binaries is about 10−4 yr−1 and there are ∼7000 − 21 000 such binaries. This contributes 0.3−0.5% of all sdB binaries in the most favorable case. Most Galactic sdB+NS binaries (≳60%) arise from the channel of stable mass transfer. The value of αCE has little effect on the results, but when we use the linear formula prescription of NS natal kick, the number and birthrate doubles in comparison to the results we obtained with the Maxwellian distribution. The orbital periods of sdB+NS binaries from different formation channels differ significantly, as expected. This results in two peaks in the radial velocity (RV) semi-amplitude distribution: 100 − 150 km s−1 for stable mass transfer, and 400 − 600 km s−1 for common-envelope ejection. However, the two sdB+NS binary populations exhibit similar delay-time distributions, which both peak at about 0.2 Gyr. This indicates that Galactic sdB+NS binaries are born in very young populations, probably in the Galactic disk. The sdB+NS binaries produced from the common-envelope ejection channel are potential sources of strong gravitational wave radiation (GWR), and about ∼100 − 300 could be detected by the Laser Interferometer Space Antenna (LISA) with a signal-to-noise ratio of 1. Conclusions. Most sdB+NS binaries are located in the Galactic disk with small RV semi-amplitudes. SdB+NS binaries with large RV semi-amplitudes are expected to be strong GWR sources, some of which could be detected by LISA in the future.

Network structure and naive sequential learning

We study a sequential‐learning model featuring a network of naive agents with Gaussian information structures. Agents apply a heuristic rule to aggregate predecessors' actions. They weigh these actions according the strengths of their social connections to different predecessors. We show this rule arises endogenously when agents wrongly believe others act solely on private information and thus neglect redundancies among observations. We provide a simple linear formula expressing agents' actions in terms of network paths and use this formula to characterize the set of networks where naive agents eventually learn correctly. This characterization implies that, on all networks where later agents observe more than one neighbor, there exist disproportionately influential early agents who can cause herding on incorrect actions. Going beyond existing social‐learning results, we compute the probability of such mislearning exactly. This allows us to compare likelihoods of incorrect herding, and hence expected welfare losses, across network structures. The probability of mislearning increases when link densities are higher and when networks are more integrated. In partially segregated networks, divergent early signals can lead to persistent disagreement between groups.