Input Array Research Articles

EVALUATION OF THE ECONOMIC EFFICIENCY OF RESTORATION OF DRAINAGE SYSTEMS IN THE HUMID ZONE OF UKRAINE: MAKING INVESTMENT DECISIONS

Approaches to assessment of the economic effectiveness of restoring drainage systems in the humid zone of Ukraine are substantiated. A conceptual scheme has been developed that determines the stages of evaluation, sources of the input array of information, strategic orientation, and invariance of restoration projects, provides for considering a number of risks and limitations of a systemic and non-systemic nature when evaluating the project effectiveness of strategic alternatives. The basis of the evaluation is the results of the analysis of materials regarding the technical condition of drainage systems, the restoration of which in the drainage area is carried out according to two options: modernization of working (on an area of 1311,2 thousand ha) and restoration of non-working (on an area of 1962,9 thousand ha) drainage systems. In the calculations of restoration (modernization) costs, the results of a preliminary assessment of the cost of restoration work for various types of drainage systems (drainage, drainage-humidification, polder, and water circulation systems) were used based on the reduced costs for restoration of the intra-farm and inter-farm network, which were adopted in the "Strategy of Irrigation and Drainage ..." [27]. The economic indicators of the production of agricultural crops economically attractive to farming producers (grain corn, sunflower, rapeseed, soybean) were calculated under the conditions of their production before and after the implementation of the project of restoration (modernization) of drainage systems. The application of the traditional scheme for projected indicators calculating, at which the discount rate was defined as the weighted average cost of capital (WACC), is substantiated. Taking into account the specifics of drainage system restoration (modernization) projects and their duration, the weighted average rates for long-term loans and deposits (risk-free) for legal entities, taking into account the inflation component and the value of equity capital of agro-industrial complex enterprises, were chosen as the discount rate for the preliminary pre-investment analysis. Based on the calculation of the project effectiveness of the restoration (modernization) of drainage systems using the scenario approach according to the consolidated option for determining the payback of investment costs, it is proved that the options at the discount rates r1 (for 2021) and r2 (for the beginning of 2022), as well as the discount rate for the equity scheme, they give positive indicators of the investment project, which indicates the expediency of its implementation and economic efficiency. The internal rate of return for the three options shows a sufficient margin of safety (24–26%). The most economically expedient is the option with a source of financing from the equity capital of agro-industrial complex enterprises, for which the non-discounted (RR) and discounted (DPP) payback terms are 3,4 and 4,7 years, respectively.

Sorting Real Numbers in Constant Time Using n^2/log^cn Processors

We study the sorting of real numbers into a linked list on the PRAM (Parallel Random-Access Machine) model. We show that n real numbers can be sorted into a linked list in constant time using n2 processors. Previously n numbers can be sorted into a linked list using n2 processors in O(loglogn) time. We also study the time processor trade-off for sorting real numbers into a linked list on the PRAM (Parallel Random Access Machine) model. We show that n real numbers can be sorted into a linked list with n2/t processors in O(logt) time. Previously n real numbers can be sorted into a linked list using n3 processors in constant time and n2 processors in O(loglogn). And then we show that input array of n real numbers can be sorted into linked list in constant time using n2/logcn processors for any positive constant c. We believe that further reduction on the number of processors for sorting real numbers in constant time will be very difficult if not impossible.

DenseNet-II: an improved deep convolutional neural network for melanoma cancer detection.

Research in the field of medicine and relevant studies evince that melanoma is one of the deadliest cancers. It defines precisely that the condition develops due to uncontrolled growth of melanocytic cells. The current trends in any disease detection revolve around the usage of two main categories of models; these are general machine learning models and deep learning models. Further, the experimental analysis of melanoma has an additional requirement of visual records like dermatological scans or normal camera lens images. This further accentuates the need for a more accurate model for melanoma detection. In this work, we aim to achieve the same, primarily by the extensive usage of neural networks. Our objective is to propose a deep learning CNN framework-based model to improve the accuracy of melanoma detection by customizing the number of layers in the network architecture, activation functions applied, and the dimension of the input array. Models like Resnet, DenseNet, Inception, and VGG have proved to yield appreciable accuracy in melanoma detection. However, in most cases, the dataset was classified into malignant or benign classes only. The dataset used in our research provides seven lesions; these are melanocytic nevi, melanoma, benign keratosis, basal cell carcinoma, actinic keratoses, vascular lesions, and dermatofibroma. Thus, through the HAM10000 dataset and various deep learning models, we diversified the precision factors as well as input qualities. The obtained results are highly propitious and establish its credibility.

A Preform Design Approach for Uniform Strain Distribution in Forging Processes Based on Convolutional Neural Network

Abstract This study provides a preform design approach for uniform strain distribution in forging products based on a convolutional neural network (CNN). The appropriate preform design prevents underfill problems by improving the material flow inside forging dies and achieving a uniform strain distribution in forging products. The forging deformation process and mechanical properties are improved with a uniform strain distribution. The forging and strain distribution results are analyzed through rigid–plastic finite element forging simulations with different initial geometries. The simulation data are fed into the CNN model as an input array, from which the geometric characteristics are extracted by convolution operations with filters (weight array). The extracted features are linked to the considered initial shapes, which are input into the CNN model as an output array. The presented model derives the preform shape for a target forging with uniform strain distributions using the training weights. According to the training database, the proposed design method can be applied to different forging geometries without any iterations. By creating a number of low-level CNN (LC) models based on the training data, the efficiency of the preform design can be improved. The best preform among the derived preform candidates is chosen by comparing the forging results. Compared with previous studies using the same design criteria, the proposed model predicted the preform with a strain distribution improved by 16.3–38.4%.

Дослідження можливості використання збурень, сформованих за записами нерівностей колії, для розрахунків динаміки швидкісного рейкового екіпажу

An urgent task for Ukraine during the post-war reconstruction of the country will be the upgrade of the entire railway transportation system, in particular the development of high-speed passenger traffic. The prediction of the dynamic performance of high-speed rail vehicles calls for the formation of new input arrays (track-induced disturbances) that would account for more stringent track geometry requirements. The aim of this work is to study the possibility of using track irregularities recorded in real sections of the Ukrainian railways to construct the components of track-induced disturbances acting on a rail vehicle moving at a high speed. This paper considers in detail standard specifications for the geometric parameters of a track suitable for high-speed traffic. The data are contained in the Standard DSTU EN 13848-5:2018, which is a European standard adopted in Ukraine as a national one by confirmation. Using the track subsidence and alignment irregularities recorded by a track measurement car in a number of sections of the Pryndiprovska railway during a scheduled track inspection, processes of actual vertical and horizontal irregularities were formed. The quality of those sections had not require any speed limitation. Irregularity parameters for those sections were calculated. A comparison between the calculated parameters and those specified by the DSTU EN 13848-5:2018 showed that among the sections considered there exist ones that meet the track geometry requirements and allow speeds at least up to 230 km/h. The use of the irregularities in the selected track sections as disturbance components in calculations was tested by the example of determining the ride performance of a standard passenger car with KVZ-TsNII-M trucks. The calculated results showed the possibility of using the generated disturbances in numerical calculations of the dynamic performance of rail vehicles at increased speeds and at the same time confirmed the need for new engineering solutions on the design of rail vehicles capable of operating at such speeds.

Broadband circularly polarized 2 × 2 MIMO array for midband 5G wireless applications

Abstract The novel compact size orthogonally fed 2 x 2 Multiple Input and Multiple Output (MIMO) array antenna for mid-band Fifth Generation (5G) wireless application is presented. The antenna configuration consists of diamond-shaped patches employed at the top of substrate. The V-shaped common ground slot structure is employed at the bottom of substrate. A broadband circular polarization is achieved by simply combining two circular polarization modes obtained from ground V slot and top patch feed structure. Mainly, the impedance bandwidth (IBW) and gain are enhanced by protruding slots on ground and cutting edges of patches. The measured result shows that 1.70 – 8.00 GHz (6.30 GHz) of IBW, 8.8 dBic of peak gain, and 3 dB axial ratio bandwidth from 1.81 – 3.87 GHz (2.06 GHz) are obtained. The proposed antenna performances are experimentally validated by fabricating and testing it for measured result analysis without using power divider.

Asthma and the Missing Heritability Problem: Necessity for Multiomics Approaches in Determining Accurate Risk Profiles.

Asthma is ranked among the most common chronic conditions and has become a significant public health issue due to the recent and rapid increase in its prevalence. Investigations into the underlying genetic factors predict a heritable component for its incidence, estimated between 35% and 90% of causation. Despite the application of large-scale genome-wide association studies (GWAS) and admixture mapping approaches, the proportion of variants identified accounts for less than 15% of the observed heritability of the disease. The discrepancy between the predicted heritable component of disease and the proportion of heritability mapped to the currently identified susceptibility loci has been termed the ‘missing heritability problem.’ Here, we examine recent studies involving both the analysis of genetically encoded features that contribute to asthma and also the role of non-encoded heritable characteristics, including epigenetic, environmental, and developmental aspects of disease. The importance of vertical maternal microbiome transfer and the influence of maternal immune factors on fetal conditioning in the inheritance of disease are also discussed. In order to highlight the broad array of biological inputs that contribute to the sum of heritable risk factors associated with allergic disease incidence that, together, contribute to the induction of a pro-atopic state. Currently, there is a need to develop in-depth models of asthma risk factors to overcome the limitations encountered in the interpretation of GWAS results in isolation, which have resulted in the missing heritability problem. Hence, multiomics analyses need to be established considering genetic, epigenetic, and functional data to create a true systems biology-based approach for analyzing the regulatory pathways that underlie the inheritance of asthma and to develop accurate risk profiles for disease.

Sorting Short Keys in Circuits of Size ${o(n \log n)}$

We consider the classical problem of sorting an input array containing $n$ elements, where each element is described with a $k$-bit comparison-key and a $w$-bit payload. A long-standing open problem is whether there exist $(k + w) \cdot o(n \log n)$-sized boolean circuits for sorting. We show that one can overcome the $n\log n$ barrier when the keys to be sorted are short. Specifically, we prove that there is a circuit with $(k + w) \cdot O(n k) \cdot \poly(\log^*n - \log^* (w + k))$ boolean gates capable of sorting any input array containing $n$ elements, each described with a $k$-bit key and a $w$-bit payload. Therefore, if the keys to be sorted are short, say, $k < o(\log n)$, our result is asymptotically better than the classical AKS sorting network (ignoring $\poly\log^*$ terms); and we also overcome the $n \log n$ barrier in such cases. Such a result might be surprising initially because it is long known that comparator-based techniques must incur $\Omega(n \log n)$ comparator gates even when the keys to be sorted are only $1$-bit long (e.g., see Knuth's Art of Programming textbook). To the best of our knowledge, we are the first to achieve non-trivial results for sorting circuits using non-comparison-based techniques. We also show that if the Li-Li network coding conjecture is true, our upper bound is optimal, barring $\poly\log^*$ terms, for every $k$ as long as $k = O(\log n)$.

More than meets the islet: aligning nutrient and paracrine inputs with hormone secretion in health and disease.

The pancreatic islet is responsive to an array of endocrine, paracrine, and nutritional inputs that adjust hormone secretion to ensure accurate control of glucose homeostasis. Although the mechanisms governing glucose-coupled insulin secretion have received the most attention, there is emerging evidence for a multitude of physiological signaling pathways and paracrine networks that collectively regulate insulin, glucagon, and somatostatin release. Moreover, the modulation of these pathways in conditions of glucotoxicity or lipotoxicity are areas of both growing interest and controversy. In this review, the contributions of external, intrinsic, and paracrine factors in pancreatic β-, α-, and δ-cell secretion across the full spectrum of physiological (i.e., fasting and fed) and pathophysiological (gluco- and lipotoxicity; diabetes) environments will be critically discussed.

Research on COVID-19 and air pollution: A path towards advancing exposure science

The COVID-19 pandemic has resulted in an extraordinary incidence of morbidity and mortality, with almost 6 million deaths worldwide at the time of this writing (https://covid19.who.int/). There has been a pressing need for research that would shed light on factors – especially modifiable factors – that could reduce risks to human health. At least several hundred studies addressing the complex relationships among transmission of SARS-CoV-2, air pollution, and human health have been published. However, these investigations are limited by available and consistent data. The project goal was to seek input into opportunities to improve and fund exposure research on the confluence of air pollution and infectious agents such as SARS-CoV-2. Thirty-two scientists with expertise in exposure science, epidemiology, risk assessment, infectious diseases, and/or air pollution responded to the outreach for information. Most of the respondents expressed value in developing a set of common definitions regarding the extent and type of public health lockdown. Traffic and smoking ranked high as important sources of air pollution warranting source-specific research (in contrast with assessing overall ambient level exposures). Numerous important socioeconomic factors were also identified. Participants offered a wide array of inputs on what they considered to be essential studies to improve our understanding of exposures. These ranged from detailed mechanistic studies to improved air quality monitoring studies and prospective cohort studies. Overall, many respondents indicated that these issues require more research and better study design. As an exercise to solicit opinions, important concepts were brought forth that provide opportunities for scientific collaboration and for consideration for funding prioritization. Further conversations on these concepts are needed to advance our thinking on how to design research that moves us past the documented limitations in the current body of research and prepares us for the next pandemic.

Multiscale Decomposition of Astronomical Maps: A Constrained Diffusion Method

Abstract We propose a new, efficient multiscale method to decompose a map (or signal in general) into component maps that contain structures of different sizes. In the widely used wave transform, artifacts containing negative values arise around regions with sharp transitions due to the application of band-limited filters. In our approach, the decomposition is achieved by solving a modified, nonlinear version of the diffusion equation. This is inspired by the anisotropic diffusion methods, which establish the link between image filtering and partial differential equations. In our case, the artifact issue is addressed where the positivity of the decomposed images is guaranteed. Our new method is particularly suitable for signals which contain localized, nonlinear features, as typical of astronomical observations. It can be used to study the multiscale structures of astronomical maps quantitatively and should be useful in observation-related tasks such as background removal. We thus propose a new measure called the “scale spectrum,” which describes how the image values distribute among different components in the scale space, to describe maps. The method allows for input arrays of an arbitrary number of dimensions, and a python3 implementation of the algorithms is included in the Appendix and available at https://github.com/gxli/constrained_diffusion_decomposition.

Engineering In-place (Shared-memory) Sorting Algorithms

We present new sequential and parallel sorting algorithms that now represent the fastest known techniques for a wide range of input sizes, input distributions, data types, and machines. Somewhat surprisingly, part of the speed advantage is due to the additional feature of the algorithms to work in-place, i.e., they do not need a significant amount of space beyond the input array. Previously, the in-place feature often implied performance penalties. Our main algorithmic contribution is a blockwise approach to in-place data distribution that is provably cache-efficient. We also parallelize this approach taking dynamic load balancing and memory locality into account. Our new comparison-based algorithm In-place Parallel Super Scalar Samplesort ( IPS 4 o ) , combines this technique with branchless decision trees. By taking cases with many equal elements into account and by adapting the distribution degree dynamically, we obtain a highly robust algorithm that outperforms the best previous in-place parallel comparison-based sorting algorithms by almost a factor of three. That algorithm also outperforms the best comparison-based competitors regardless of whether we consider in-place or not in-place, parallel or sequential settings. Another surprising result is that IPS 4 o even outperforms the best (in-place or not in-place) integer sorting algorithms in a wide range of situations. In many of the remaining cases (often involving near-uniform input distributions, small keys, or a sequential setting), our new In-place Parallel Super Scalar Radix Sort ( IPS 2 Ra ) turns out to be the best algorithm. Claims to have the – in some sense – “best” sorting algorithm can be found in many papers which cannot all be true. Therefore, we base our conclusions on an extensive experimental study involving a large part of the cross product of 21 state-of-the-art sorting codes, 6 data types, 10 input distributions, 4 machines, 4 memory allocation strategies, and input sizes varying over 7 orders of magnitude. This confirms the claims made about the robust performance of our algorithms while revealing major performance problems in many competitors outside the concrete set of measurements reported in the associated publications. This is particularly true for integer sorting algorithms giving one reason to prefer comparison-based algorithms for robust general-purpose sorting.

MODELING THE INFLUENCE SHADOW ECONOMY ON THE MACROECONOMIC INDICATORS UKRAINE

The presented work summarizes the arguments and counter-arguments within the scientific discussion on the construction of models of the impact of the shadow economy on the macroeconomic indicators of the country. The level of the shadow economy has a negative impact on Ukraine's macroeconomic indicators. The shadow economy is a covert and / or non-covert economic activity whose purpose is to intentionally or forcibly generate excess profits due to uncontrolled socio-economic relations. The main purpose of the study is to identify the impact of the shadow economy on the macroeconomic indicators of the country. The systematization of literature sources and approaches to solving the problem of finding a connection between the level of the shadow economy and macroeconomic indicators has shown that this problem is quite relevant among scientists around the world. The research was carried out in the following logical sequence: 1) acquaintance with the basic concepts of research and analysis of literature sources; 2) formation of the input data set for further research; 3) verification of data for anomalies; 4) calculation of the integrated indicator; 5) verification of data on stationarity; 6) check for multicollinearity; 7) correlation-regression analysis. The methodological tools of the conducted research were the methods of correlation-regression analysis, the application of the Irwin criterion to detect abnormal levels, the Foster-Student method to investigate the stationarity of time series, and the Ferrar-Glober algorithm to detect multicollinearity in the input array. The study period is 2010-2021. Ukraine was chosen as the object of research. The scientific work presents the results of an empirical analysis of models of the impact of macroeconomic indicators on the level of the shadow economy of Ukraine, which showed that this impact exists and is quite strong. Based on the results of the research, conclusions were formulated about the strong influence of macroeconomic indicators on the level of the shadow economy of Ukraine, it was theoretically proven that the level of the shadow economy of Ukraine is more than 90% described by the selected set of macroeconomic indicators.

Cortical Pathways During Postural Control: New Insights From Functional EEG Source Connectivity.

Postural control is a complex feedback system that relies on vast array of sensory inputs in order to maintain a stable upright stance. The brain cortex plays a crucial role in the processing of this information and in the elaboration of a successful adaptive strategy to external stimulation preventing loss of balance and falls. In the present work, the participants postural control system was challenged by disrupting the upright stance via a mechanical skeletal muscle vibration applied to the calves. The EEG source connectivity method was used to investigate the cortical response to the external stimulation and highlight the brain network primarily involved in high-level coordination of the postural control system. The cortical network reconfiguration was assessed during two experimental conditions of eyes open and eyes closed and the network flexibility (i.e. its dynamic reconfiguration over time) was correlated with the sample entropy of the stabilogram sway. The results highlight two different cortical strategies in the alpha band: the predominance of frontal lobe connections during open eyes and the strengthening of temporal-parietal network connections in the absence of visual cues. Furthermore, a high correlation emerges between the flexibility in the regions surrounding the right temporo-parietal junction and the sample entropy of the CoP sway, suggesting their centrality in the postural control system. These results open the possibility to employ network-based flexibility metrics as markers of a healthy postural control system, with implications in the diagnosis and treatment of postural impairing diseases.

Structural modelling for assessing the effectiveness of system for countering legalization of illicit money

The article suggests a scientific and methodological approach to the evaluation of the infrastructural component’s effectiveness in the anti-money laundering system due to digitalization. Structural modelling is the basis for the mentioned approach implementation, which consists of several steps. First, the input data is selected in terms of the effective regulation of the financial services market, law enforcement and judicial activities, and digitalization. Next, the moving average method is used to identify the growth rate of missing values in the available data series. Then, the selection of relevant factors for financial services market regulation, law enforcement activity, judicial activity and digitalization is based on the principal component analysis. After reducing the input array of data to a comparable form, a structural equations system can be constructed to reflect the impact of the digitalization level on the latent integral characteristics of the directions of anti-money laundering work done by regulatory authorities. Finally, the model is checked for adequacy. The result of this research can serve as an information base for further strengthening the digital vector in the development of regulation institutions and law enforcement agencies overseeing the financial services market, as well as for the radical transformation of courts in Ukraine since digitalization currently negatively affects them.

Robust Blind Equalization Algorithm Using Convolutional Neural Network

In this paper, we introduce a novel blind equalization algorithm based on the convolutional neural network (CNN), to improve the bit error rate (BER) performance of equalizers against the multipath fading effect and nonlinear distortion. In contrast to existing neural network (NN)-based blind equalization algorithms, the proposed algorithm performs equalization and soft demapping jointly, which allows it to obtain soft bits directly from received data. In addition, the input preprocessing module is used to reorganize the received data to fully exploit the feature information of the received signals. Afterwards, the two-dimensional (2D) convolutions can be operated on a three-dimensional (3D) input array obtained by input preprocessing to recover the transmitted bits. Simulation results show that the proposed algorithm outperforms other CNN-based blind equalization algorithms, in terms of BER performance, under a wide range of channel models, signal-to-noise (SNR) levels and modulation schemes. Strikingly, the BER obtained by the proposed algorithm approaches the theoretical BER of multiple quadrature amplitude modulation (M-QAM) in linear channels.

ASSESSMENT OF THE QUALITY OF THE STATISTICAL FORECAST FOR THE SHARE PRICE

The stock market is an important part of the world's economy, but the values of stocks change at a significant speed and finding an effective method of forecasting the price of stocks will be a significant victory for investors. The article is devoted to the use of statistical methods in the stock market, evaluating their effectiveness on the example of determining the forecast share price and comparing it with the real share price. In addition, work was carried out to determine the relevance of the research topic by means of bibliographic analysis based on the results of searching a selection of publications in the Scopus database with the subsequent use of the VOSviewer software toolkit. A time series covering the period of daily values of stock prices of Apple Inc. was chosen as the input test sample for developing the forecast. from December 12, 2016 to December 12, 2021. At the same time, the median values of the prices of the monthly financial shares of the Apple com corporation were used to build forecast models, since there is no information that fell on weekends for the studied time period. Forecasts are published using Statgraphics 19 software, which generates 17 forecast models: random walk, random walk with drift, constant mean, linear trend, quadratic trend, exponential trend, S-shaped trend, simple moving average, simple exponential smoothing with a smoothing coefficient α = 0.9999, linear exponential Brownian smoothing with smoothing factor α= 0.5705, linear exponential Holt smoothing with smoothing coefficients α = 0.9999 and β = 0.0359, quadratic exponential Brownian smoothing with smoothing coefficients α = 0.3046, ARIMA model. Akaike's information criterion was used to assess the quality of the models. As a result of the analysis, the ARIMA(1,0,0) model has the lowest value according to Akaike's criteria. On the basis of ARIMA(1,0,0), a forecast of stock market exchange rates was built 6 months ahead of the age of the final value of the input array. In the process of comparison with real data, a significant discrepancy between the forecasting results and the real share price in the forecasted period was found, however, the obtained models were tested for statistical significance. The conducted research showed that it is possible to use classical statistical methods to develop a forecast on the stock market only for a short-term period, while it is necessary to take into account the risk factors inherent in the stock market (the frequency of share price changes during the day, liquidity risks, operational risks, political situation in the world).

Activity and Coupling to Hippocampal Oscillations of Median Raphe GABAergic Cells in Awake Mice.

Ascending serotonergic/glutamatergic projection from the median raphe region (MRR) to the hippocampal formation regulates both encoding and consolidation of memory and the oscillations associated with them. The firing of various types of MRR neurons exhibits rhythmic modulation coupled to hippocampal oscillatory activity. A possible intermediary between rhythm-generating forebrain regions and entrained ascending modulation may be the GABAergic circuit in the MRR, known to be targeted by a diverse array of top-down inputs. However, the activity of inhibitory MRR neurons in an awake animal is still largely unexplored. In this study, we utilized whole cell patch-clamp, single cell, and multichannel extracellular recordings of GABAergic and non-GABAergic MRR neurons in awake, head-fixed mice. First, we have demonstrated that glutamatergic and serotonergic neurons receive both transient, phasic, and sustained tonic inhibition. Then, we observed substantial heterogeneity of GABAergic firing patterns but a marked modulation of activity by brain states and fine timescale coupling of spiking to theta and ripple oscillations. We also uncovered a correlation between the preferred theta phase and the direction of activity change during ripples, suggesting the segregation of inhibitory neurons into functional groups. Finally, we could detect complementary alteration of non-GABAergic neurons’ ripple-coupled activity. Our findings support the assumption that the local inhibitory circuit in the MRR may synchronize ascending serotonergic/glutamatergic modulation with hippocampal activity on a subsecond timescale.

Адаптація масивів газодинамічних характеристик до автоматизованого балістичного супроводу руху космічних апаратів

The current level of the design and use of new-generation spacecraft calls for a maximally automated ballistics support of engineering developments. An integral part of the solution of this problem is the development of an effective tool to adapt discrete functions of gas-dynamic characteristics to the solution of various problems that arise in the development and use of space complexes. Simplifying the use of bulky information arrays together with improving the accuracy of approximation of key coefficients will significantly improve the ballistics support quality. The aim of this work is to choose an optimum method for the approximation of a discrete function of two variable spacecraft aerodynamic characteristics. Based on the analysis of the advantages and drawbacks of basic methods of approximation by two fitting criteria: the maximum error and the root-mean-square deviation, recommendations on this choice were made. The methods were assessed by the example of the aerodynamic coefficients of the Sich-2M spacecraft’s simplified geometrical model tabulated as a function of the spacecraft orientation angles relative to the incident flow velocity. Multiparameter numerical studies were conducted for different approximation methods with varying the parameters of the approximation types under consideration and the approximation grid density. It was found that increasing the number of nodes of an input array does not always improve the accuracy of approximation. The node arrangement exerts a greater effect on the approximation quality. It was established that the most easily implementable method among those considered is a step interpolation, whose advantages are simplicity, quickness, and limitless possibilities in accuracy improvement, while its significant drawbacks are the lack of an analytical description and the dependence of the accuracy on the grid density. It was shown that spline functions feature the best approximating properties in comparison with other mathematical models. A polynomial approximation or any approximation by a general form function provide an analytical description with a single approximating function, but their accuracy of approximation is not so high as that provided by splines. It was found that there exists no approximation method that would be best by all criteria taken together: each method has some advantages, but at the same time, it has significant drawbacks too. An optimum approximation method is chosen according to the features of the problem, the priorities in approximation requirements, the required degree of approximation, and the initial data organization method.

The geometric Burge correspondence and the partition function of polymer replicas

We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation to the geometric Robinson-Schensted-Knuth correspondence and to the geometric Schützenberger involution. We also show a number of properties of the geometric Burge correspondence, specializing them to the case of symmetric input arrays. In particular, our construction shows that such a mapping is volume preserving in log-log variables. As an application, we consider a model of two polymer paths of given length constrained to have the same endpoint, known as polymer replica. We prove that the distribution of the polymer replica partition function in a log-gamma random environment is a Whittaker measure, and deduce the corresponding Whittaker integral identity. For a certain choice of the parameters, we notice a distributional identity between our model and the symmetric log-gamma polymer studied by O’Connell, Seppäläinen, and Zygouras (2014).