Symmetric Tables Research Articles

Surveying the Types of Tables in Ancient Greek Texts

Abstract We may take tables for granted. However, due to a variety of factors, tables were a rarity in the history of ancient Greek culture, used only limitedly in very special contexts and generally in a non-systematic way, except in astronomy. In this paper I present the main types of tables that can be found in ancient Greek texts: non-ruled columnar lists (accounts and other types of informal tables), ruled columnar lists (mostly astronomical tables), and symmetric tables (mainly Pythagorean displays of numbers).

Total Costs Coefficients in the Basic Input-Output Tables

The article presents the results of the author's research devoted to the improvements in domestic developments of Input-Output Tables (IO Tables), significantly increasing their analytical potential. According to the author, the level of development of Russian statistics in the field of Input-Output Tables is quite high – the basic accounts contain not only the symmetrical IO Tables, but also symmetrical tables of domestic products and imports that they are derived from. This is the main condition for implementing the methodology and methodological solutions described and elaborated in the article for compiling the tables with the coefficients of total costs of domestic products and the total need for import of intermediate imports estimates.In the first part of the article, the author characterizes conceptually different versions of the intersectoral model with the features of the technological matrix corresponding to these versions – the basis for estimating the values of total costs coefficients in the national economy. Three «extreme» variants of the economy model representation of indicative country are studied. They define the economy as a part of a global economy within the framework of an inter-country model; in the form of a national model without the allocation of the import matrix in a symmetrical IO Tables (traditional method) and in the form of a national model with the possibility of such allocation (alternative method). The substantial differences in the values of total costs coefficients for the options are described and their preference for study of the country's economy is emphasizedThe second part of the article presents the results of a quantitative analysis based on the basic IO Tables for 2016 data. It contains the estimates of the measure of discrepancy in total costs coefficients values according to traditional and alternative methods; the differences in the associated indicators of intermediate products total costs distribution by specific dimensions of final demand. The analytical possibilities of the alternative method are described, the estimates for the decomposition of final products cost into domestic and imported value added are provided.The author explains the analytical relevance of total costs coefficients using an alternative method in forecasting practice and in the macroeconomic effects of management decisions assessment and proposes to supply the basic IO Tables for 2021 with tables with these coefficients and with the necessary methodological explanations

On the Crossing Numbers of the Join Products of Six Graphs of Order Six with Paths and Cycles

The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main purpose of this paper is to determine the crossing numbers of the join products of six symmetric graphs on six vertices with paths and cycles on n vertices. The idea of configurations is generalized for the first time onto the family of subgraphs whose edges cross the edges of the considered graph at most once, and their lower bounds of necessary numbers of crossings are presented in the common symmetric table. Some proofs of the join products with cycles are done with the help of several well-known auxiliary statements, the idea of which is extended by a suitable classification of subgraphs that do not cross the edges of the examined graphs.

On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete Graph

In the paper, we extend known results concerning crossing numbers of join products of small graphs of order six with discrete graphs. The crossing number of the join product G ∗ + D n for the graph G ∗ on six vertices consists of one vertex which is adjacent with three non-consecutive vertices of the 5-cycle. The proofs were based on the idea of establishing minimum values of crossings between two different subgraphs that cross the edges of the graph G ∗ exactly once. These minimum symmetrical values are described in the individual symmetric tables.

Measurement of the Dynamics of Intersectoral Relations Based on the Econometric Method

Methodological and instrumental problems of working-out a system of econometric calculations that provide the construction of retrospective time series of indicators of inter-industry relations of the domestic economy are considered. The calculation system is based on the joint use of reporting data on inter-industry relations of the domestic economy for any particular year (or years) and data on the dynamics of gross output of activities included in the inter-industry table available in state statistics. This problem can be represented in the form of a system of linear equations in which the number of sought variables to be determined (in this case, the sets of weather values of the inter-industry cost coefficients) exceeds the number of equations (i.e., balance identities for each year of the retrospective period). A special modification of the linear regression model - a model with time-varying structural parameters was applied to generate time series of indicators of inter-industry ties. The econometric method described in the work provides for the disaggregation of the well-known dynamic series of intermediate consumption (at constant prices) in the economy as a whole on the indicators of intermediate consumption (also at constant prices) for certain types of economic activity (economic value). The specified information is not available in state statistics. The developed econometric method provides, further, the disaggregation of time series of the total indicators of intermediate consumption of certain types of economic activity calculated by separate flows of costs (at constant prices) within each given economic value presented in the symmetric table ≪Input-output≫. The numerical results of using the developed calculation system are presented as applied to the construction of time series of intermediate consumption of the real sector and the services sector of the domestic economy for 2004-2016.

Methodological Problems of Using the Structural Decomposition Analysis in the Input-Output Model at the Present Stage

The Input-Output Structural Decomposition Analysis approach enables a fairly comprehensive and detailed analysis of the economic growth sources using the input-output model. The active use of this approach is currently hampered by the lack of a reliable instrumental method for constructing symmetrical input-output tables and deflators that permit the output and import indicators to be recalculated by types of products for different years into constant prices, as well as by ambiguity of interpretations of the content of growth sources. The paper discusses the ways to overcome these methodological problems and gives an example of the experimental use of the structural decomposition analysis approach based on the data of the input-output tables of the Russian Federation for 2011–2015.

Cross-subsidizing in power industry: approaches to development of stage-by-stage decrease in volumes

The paper is devoted to economic effects of decrease in volumes of cross subsidizing for participants of the market of electric energy are considered, and also methodological approaches to modeling of a stage-by-stage decrease of volumes of cross subsidizing in economy are developed. The methodology of the system of national accounts (SNA) – symmetric tables “expenses – release” and intersectoral balance “a product – a product” calculated on release of the final product of 22 industries – was used to model the influence of economic and social effects due to cross subsidies elimination. The comparative analysis of one-stage and gradual options to cross subsidies elimination was carried out. One-stage elimination of cross subsidizing showed more the worst results on economic indicators of participants of a power market, than at its stage-by-stage decrease.Modeling of stage-by-stage decrease in cross subsidizing is aimed at determination of the greatest possible growth rate of tariffs for the electric power for the population. The indicator of the minimum value of economic damage to branches of the economy, calculated as a difference of a balanced gain (departure) of a gross value added in the range of a threshold interval of increase in expenses of house farms on the purchased electric power in the general structure of expenses is used as criterion of an optimality of growth rate of tariffs for the electric power. The macroeconomic model of formation, use and reproduction of a branch value added is used for creation of model. The analysis of impact of change of tariffs for the electric power for the population is carried out with a step to 1% to the level providing full reduction of cross subsidizing. Optimum speed of a gain of tariffs for regions with the maximum rate of a tariff for the electric power (Moscow region) and the minimum rate (Orenburg region) is calculated.

The Perception of Electorate in Kosovo on Structure of the Report between Political Ideology and Political Parties

This paper attempts to explain the perception of Kosovo’s electorate about the relationship of political parties in Kosovo with ideology. For the purpose of empirical testing of the Ideology report with political parties in Kosovo as part of the study, it was judged to undertake a survey to investigate how the Kosovo electorate perceived the policy report with ideology. On primary resources, the data provided by the survey conducted with 310 respondents in Kosovo were used. Through this survey we will present the results of the interpretation of the data provided by the frequency tables and the cross tablets. In this presentation, generally, data from one-variable and two-variable crosstab data and statistical values of Cramer’s V compilation values and Approx. Sig. to the Symmetric Measures table. After the data presentations, the interpretation of these values will be made with their possible significant statistical associations and the empirical test report on the implications under consideration.

Hierarchical Multipartite Function Evaluation

Function evaluation is an important arithmetic computation in many signal processing applications, such as special function units in modern graphics processing units (GPUs). Hardware implementations of function evaluation usually consists of lookup tables (LUT) and some simple arithmetic units of multipliers and/or adders. LUT usually takes a significant portion of total area cost, especially when function evaluators are allowed to compute several different arithmetic functions with shared arithmetic units where evaluation of each function needs separate LUT. In this paper, we focus on the category of table-addition (TA) function evaluators that are composed of two types of LUT, table of initial values ( TI ) and table of offset values ( TO ), followed by a multi-operand adder. It has been shown that multipartite table method (MP) has significant improvement over prior similar designs such as symmetric bipartite table methods (SBTM) and symmetric table addition methods (STAM) for applications with low-to-medium precision requirements. This paper presents an extension of MP, called hierarchical multipartite (HMP), which further reduces total table size by applying several levels of table decompositions. Furthermore, we perform the bit-width optimization by jointly considering the impacts of all error sources during the search of best table decompositions, leading to more efficient hardware design. Besides, a new lossless decomposition of TI is presented, resulting in additional saving of table size without incurring any extra errors. Experimental results show that the proposed design can efficiently reduce the total area cost in ASIC and FPGA implementations.

An Input-Output Table for Germany in 1936: A Documentation of Results, Sources and Research Strategy

Abstract In the following, we present the earliest input-output table for Germany: It covers 40 economic branches, five final demand categories and five primary inputs. The symmetric table for 1936 is completely based on original statistical data and does not rely on separate supply and use tables. The core of our endeavour is based on the German industrial census of 1936. Originally, this census and its forerunner of 1933 had especially been designed by the German Statistical Office (StRA) to compile an input-output-table for Germany as a basis for managing the business cycle. In connection with rearmament, however, this endeavour was given up and instead, these data were used for constructing detailed material balance sheets, which served as a statistical basis for preparing the war. Based on these hitherto secret records and additional statistical information, we fulfilled the original plan of the StRA of constructing the desired input-output table. Government is treated as an intermediate sector and placed into quadrant I of the table. In quadrant II it appears with only one figure (government gross production minus fees for specific government services). Government is delimitated into three sub-sectors: public administration and other government services, military spending and social security. In addition, public investment for civilian purposes is assigned to gross fixed capital formation in quadrant II. Military expenditure, however, is treated as government consumption and not as investment. The input-output table offers a new benchmark for gross domestic product (GDP) and thus production, income and expenditure of Germany in 1936. We found a comparably high level of GDP and a significantly higher mixed income/operating surplus which hints at exceptionally high incomes and hidden profits of the armament industry. Due to our unique production approach of calculating GDP these hidden profits were revealed.

Output, national income, and expenditure: an input–output table of Germany in 1936

We here present the earliest input–output table of Germany: It covers forty economic branches, five final demand categories, and five primary inputs. The symmetric table for 1936 is completely based on original statistical data and does not rely on separate supply and use tables. The core of our endeavor is based on the German industrial census of 1936. The input–output table offers a new benchmark for gross domestic product (GDP) and thus production, income, and expenditure of Germany in 1936. We found a comparably high level of GDP and a significantly higher mixed income/operating surplus, which hints at exceptionally high incomes and hidden profits of armament industry. We illustrate the use of the new input–output table for German historical national accounts and apply our findings to reassess the impact of military spending on employment and production.

Feed Forward Neural Network for Sine Function With Symmetric Table Addition Method Using Labview and Matlab Code

This work is proposed thefeed forward neural network with symmetric table addition methodto design the neuron synapses algorithm of the sine function approximations, and according to theTaylor series expansion. Matlab code and LabVIEW are used to build and create the neural network , which has been designed and traineddatabase set to improve its performance, and gets the besta global convergence with small value of MSE errors and 97.22% accuracy.

A Memory-Efficient Tables-and-Additions Method for Accurate Computation of Elementary Functions

The tables-and-additions methods for accurate computation of elementary functions are fast in computation speed but require large memory. A memory-efficient method named as the integrated Add-Table Lookup-Add (iATA) is proposed in this paper. In iATA, the mathematical formulation for computing the elementary functions is derived without using the central difference formulation to save memory. Three additional techniques, specifically the carry select technique, symmetry property exploitation and unequal partitioning of input with the aid of error analysis, are integrated in iATA to further reduce the memory size. The experimental results show that the proposed method is able to achieve higher memory efficiency than the best existing tables-and-additions methods. For the reciprocal and the natural logarithm function, iATA saves 23.63 and 61.39 percent of memory when compared to the best existing results obtained, respectively, by the unified Multipartite Table Method [39] and the Symmetric Table Addition Method [37].

Input-output modelling based on total-use rectangular tables: is this a better way?

Input-output tables can be presented in different formats, according to three main criteria: 1) symmetric or rectangular format; 2) total or domestic-use flows and 3) valuation prices (basic prices – bp or purchasers’ prices – pp). Official National Accounts (at least in EU) produce in a regular base a total use rectangular table at pp – also known as the Make and Use (M&U) format – that is different from the lay-out upon which traditional input-output models were developed (domestic use, symmetric, bp). The problem with this latter one is of course that it is only available at times in many countries. The objective of this paper is to prove (under common hypotheses) the equivalence between two alternative procedures, from the point of view of the results of an input-output model: 1) to convert the M&U input-output table into the traditional format – a domestic-use symmetric table at bp – and then implement the model; 2) to perform the direct modelling of the original table (the total-use rectangular table at pp). That equivalence is illustrated with Portuguese data for the year 2002.

Regional differentiation of coefficients of direct expenditures in input-output symmetric tables

The necessity to develop input-output regional tables on the basis of analysis of available regional technological coefficients and unit costs in physical and monetary terms is argued in this article.

A SYMMETRIC INPUT–OUTPUT TABLE FOR EU27: LATEST PROGRESS

The European Commission is currently establishing an Environmentally Extended Input–Output (EE-IO) Database for the EU27 developed by the Joint Research Centre at the Institute for Prospective Technological Studies (IPTS). This project attempts to generate an analytical dataset comprising all EU countries and yearly time series for the period 1995–2005. Since, for the time being, IO and environmental accounts data are only available with significant gaps part of the dataset will require estimates based on best available proxy data and reasonable assumptions. This paper is focused on the IO database shaped around Eurostat supply and use tables and symmetric IO tables consistent with the NACE classification. The paper describes the procedure by which the latest preliminary results have been obtained for an aggregate EU27 symmetric input–output table for the year 2000.

The Symmetric Table Addition Method for Accurate Function Approximation

This paper presents a high-speed method for computing elementary functions using parallel table lookups and multi-operand addition. Increasing the number of tables and inputs to the multi-operand adder significantly reduces the amount of memory required. Symmetry and leading zeros in the table coefficients are used to reduce the amount of memory even further. This method has a closed-form solution for the table entries and can be applied to any differentiable function. For 24-bit operands, it requires two to three orders of magnitude less memory than conventional table lookups.

Conversion Problems concerning Automated Mapping from lCD-10 to lCD-9

The increasing parallel use of ICD-9 and ICD-10 complicates the comparability of coded diagnoses. This is the reason why we developed a symmetric table for interactive conversion between ICD-9 and ICD-10, based on a vector space text-retrieval method that resulted in unambiguous mapping from ICD-9 to ICD-10 in 64%, from ICD-10 to ICD-9 in 87% of all three- and four-character classes of the tabular list. Out of the remaining 13% of multi-valued relations, a table for automated mapping from ICD-10 to ICD-9 was created. In 9% of cases, the selection offered no problems. A compromise between preserving information content and maintaining the logical integrity had to be found in 2.4%; in 1.6% automated mapping was impossible because of newly defined concepts and structural differences between ICD-9 and ICD-10 that are not counterbalanced by a consistent system of residual categories. We recommend that in a future revision of the ICD, compatibility with the then existing classification system should be considered.

Exact tests for two-way symmetriccontingency tables

A two-way contingency table in which both variables have the same categories is termed a symmetric table. In many applications, because of the social processes involved, most of the observations lie on the main diagonal and the off-diagonal counts are small. For these tables, the model of independence is implausible and interest is then focussed on the off-diagonal cells and the models of quasi-independence and quasi-symmetry. For ordinal variables, a linear-by-linear association model can be used to model the interaction structure. For sparse tables, large-sample goodness-of-fit tests are often unreliable and one should use an exact test. In this paper, we review exact tests and the computing problems involved. We propose new recursive algorithms for exact goodness-of-fit tests of quasi-independence, quasi-symmetry, linear-by-linear association and some related models. We propose that all computations be carried out using symbolic computation and rational arithmetic in order to calculate the exact p-values accurately and describe how we implemented our proposals. Two examples are presented.

Monte Carlo Exact Methods Used for Analysing Interethnic Unions in Great Britain

The value of using exact rather than asymptotic tests to measure intermarriage in the United Kingdom is examined. "We develop Markov chain Monte Carlo methods for estimating the exact conditional p-value and the exact distribution of the residuals, for quasi-independence and quasi-symmetry. These methods are used to analyse a sparse 10 x 10 symmetric table of interethnic unions, extracted from the 1% household sample of anonymized records from the 1991 U.K. census. With the exception of Pakistani/White and Other Asian/White unions, there is no evidence against quasi-symmetry. We conclude that, with these exceptions, there are no gender differences in the affinities between ethnic groups."