The model of cohesion development of metropolitan areas

Artykuł analizuje doświadczenia jednostek samorządu terytorialnego aglomeracji poznańskiej w rozwijaniu różnych form kooperacji. Szczególna uwaga została poświęcona rozpoznaniu i zaprezentowaniu instytucjonalnych form współdziałania na tworzących się metropolitalnych obszarach funkcjonalnych.Badania dotyczące rozwoju form spójności w aglomeracji poznańskiej przedstawiono na tle aktualnej europejskiej polityki ukierunkowanej terytorialnie, kładącej nacisk na wspieranie rozwoju obszarów funkcjonalnych. Specjalna wagę przykłada się w tej polityce do rozwiązywania wyzwań wynikających z narastania powiązań funkcjonalnych na obszarach metropolitalnych. Aktualne działania podejmowane w kształtujących się funkcjonalnych polskich obszarach metropolitalnych są omawiane także w świetle powstającej obecnie polskiej polityki ukierunkowanej terytorialnie. Szczególną uwagę poświęca ona wzmacnianiu współpracy międzysamorządowej oraz kooperacji z innymi sektorami na obszarach funkcjonalnych, ze szczególnym uwzględnieniem obszarów o charakterze metropolitalnym.Efektem badań prezentowanych w artykule jest propozycja modelu budowania spójności w obszarach metropolitalnych. Model uwzględnia zalecenia polityki europejskiej, polskiej i zmieniające się krajowe ramy legislacyjne oraz uwarunkowania i doświadczenia lokalne.he development of various forms of cooperation. Particular attention has been devoted to the recognition and presentation of institutional forms of cooperation in emerging metropolitan functional areas.The results of a research in the development of forms of cohesion in the Poznań agglomeration are shown in the context of the current European territorially oriented development policy that emphasizes supporting the development of functional areas. Special attention is paid to the policyto deal with the challenges arising from increasing functional connections in metropolitan areas. Current activities in the Polish emerging functional metropolitan areas are discussed in light of the currently emerging Polish territorial based policy. The paper draws special attention to the strengthening of cooperation between local authorities and cooperation with other sectors of the functional areas with special emphasis on metropolitan areas.The result of the research presented in the paper is the proposal to build a model of cohesion in metropolitan areas. The model takes into account the recommendations of European and Polish policy, the changing national legislative framework and local conditions and experience

A homological characterization of topological amenability

Generalizing Block and Weinberger’s characterization of amenability we introduce the notion of uniformly finite homology for a group action on a compact space and use it to give a homological characterization of topological amenability for actions. By considering the case of the natural action of G on its Stone-Cech compactification we obtain a homological characterisation of exactness of the group

Changes in the physiological activity of soybean (Glycine max L. Merr.) under the influence of exogenous growth regulators

In a two-year pot experiment (2008–2009) conducted at the Vegetation Hall, West Pomeranian University of Technology in Szczecin, we investigated the influence of exogenous growth regulators, i.e. indole-3-butyric acid (IBA) and 6-benzylaminopurine (BAP) and their mixture, on the activity of gas exchange and selected physiological features of soybeans (Glycine max L. Merr.). The experimental factors included the following Polish soybean cultivars: ‘Aldana’, ‘Progres’ and ‘Jutro’. During plant growth, CO2 assimilation (A), transpiration rate (E), stomatal conductance (gs), and substomatal CO2 concentration (ci) were determined. Two soybean cultivars, i.e. ‘Jutro’ and ‘Progres’, showed a significant increase in the intensity of assimilation and transpiration after using all kinds of growth regulators as compared with the control plants. It was found that the ‘Jutro’ cultivar, after using a mixture of growth regulators (IBA + BAP), was characterized by the significantly highest CO2 assimilation (A) and transpiration (E) as well as the highest stomatal conductance (gs). The ‘Aldana’ cultivar, on the other hand, responded by a significant reduction in the transpiration rate, stomatal conductance and subsomatal CO2 concentration. The spraying of the plants with exogenous growth regulators had a significant influence on the increase in the number of stomata and stomatal pore length, mostly on the lower epidermis of the lamina. It was also found that plants from the ‘Jutro’ and ‘Aldana’ cultivars sprayed with IBA and IBA + BAP were characterized by the highest yield, as compared with the control plants. In the case of the ‘Jutro’ cultivar, after using the growth regulators, a positive correlation was observed between the assimilation and transpiration rates and the length of stomata, which in consequence produced increased yields

Diffusion in the space of complex Hermitian matrices - microscopic properties of the averaged characteristic polynomial and the averaged inverse characteristic polynomial

We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial differential, diffusion-like, equations. These equations are valid for matrices of arbitrary size. Their solutions can be given an integral representation that allows for a simple study of their asymptotic behaviors for a broad range of initial conditions.Comment: 26 pages, 4 figure

Suggested Framework for Big Data Analysis of Enterprise Websites. A Case Study for Web Intelligence Network

[EN] Big Data gives an opportunity for the researchers and scholars to make surveys in various domains. In this paper we will concentrate on websites as a data source which can be used to provide lots of valuable information for enterprise statistics. In this field, Big Data allows to get various information, including the type of the enterprise (e-commerce etc.), whether the enterprise is present in social media, the frequency of updating the website etc. The main goal of the paper is to present what Big Data methods are the most efficient in acquiring and processing the information from websites. The discussion shows different variants of conducting the work, based on the case studies conducted as experimental statistics at European Union level over the last 6 years. This paper is based on the experience in processing the data from websites in ESSnet grants on Big Data I (2016-2018), Big Data II (2018-2020) and Web Intelligence Network (2021-2025). The process of getting enterprise data from websites can be divided into the following steps: (1) Defining the population of enterprise websites; (2) Web scraping; (3) Data processing (extracting); (4) Data validation (de-duplication, quality indicators); (5) Data analysis; (6) Data dissemination. Each of the steps needs additional validation, especially the first step in this process have an impact on the final results that may not be comparable to the official statistical data. The essential part is also the way the data will be extracted to find the interesting data. In this sense, we need to choose between text mining methods, e.g. machine learning and regular expressions, that gives different results according to the information which should be provided. The paper shows how the use of appropriate methods can increase the overall value of the analysis.Maślankowski, J.; Nowak, D. (2022). Suggested Framework for Big Data Analysis of Enterprise Websites. A Case Study for Web Intelligence Network. En 4th International Conference on Advanced Research Methods and Analytics (CARMA 2022). Editorial Universitat Politècnica de València. 270-270. http://hdl.handle.net/10251/18971027027

Unveiling the significance of eigenvectors in diffusing non-hermitian matrices by identifying the underlying Burgers dynamics

Following our recent letter, we study in detail an entry-wise diffusion of non-hermitian complex matrices. We obtain an exact partial differential equation (valid for any matrix size $N$ and arbitrary initial conditions) for evolution of the averaged extended characteristic polynomial. The logarithm of this polynomial has an interpretation of a potential which generates a Burgers dynamics in quaternionic space. The dynamics of the ensemble in the large $N$ is completely determined by the coevolution of the spectral density and a certain eigenvector correlation function. This coevolution is best visible in an electrostatic potential of a quaternionic argument built of two complex variables, the first of which governs standard spectral properties while the second unravels the hidden dynamics of eigenvector correlation function. We obtain general large $N$ formulas for both spectral density and 1-point eigenvector correlation function valid for any initial conditions. We exemplify our studies by solving three examples, and we verify the analytic form of our solutions with numerical simulations.Comment: 24 pages, 11 figure

Dynamical Isometry is Achieved in Residual Networks in a Universal Way for any Activation Function

We demonstrate that in residual neural networks (ResNets) dynamical isometry is achievable irrespectively of the activation function used. We do that by deriving, with the help of Free Probability and Random Matrix Theories, a universal formula for the spectral density of the input-output Jacobian at initialization, in the large network width and depth limit. The resulting singular value spectrum depends on a single parameter, which we calculate for a variety of popular activation functions, by analyzing the signal propagation in the artificial neural network. We corroborate our results with numerical simulations of both random matrices and ResNets applied to the CIFAR-10 classification problem. Moreover, we study the consequence of this universal behavior for the initial and late phases of the learning processes. We conclude by drawing attention to the simple fact, that initialization acts as a confounding factor between the choice of activation function and the rate of learning. We propose that in ResNets this can be resolved based on our results, by ensuring the same level of dynamical isometry at initialization

Dysonian dynamics of the Ginibre ensemble

We study the time evolution of Ginibre matrices whose elements undergo Brownian motion. The non-Hermitian character of the Ginibre ensemble binds the dynamics of eigenvalues to the evolution of eigenvectors in a non-trivial way, leading to a system of coupled nonlinear equations resembling those for turbulent systems. We formulate a mathematical framework allowing simultaneous description of the flow of eigenvalues and eigenvectors, and we unravel a hidden dynamics as a function of new complex variable, which in the standard description is treated as a regulator only. We solve the evolution equations for large matrices and demonstrate that the non-analytic behavior of the Green's functions is associated with a shock wave stemming from a Burgers-like equation describing correlations of eigenvectors. We conjecture that the hidden dynamics, that we observe for the Ginibre ensemble, is a general feature of non-Hermitian random matrix models and is relevant to related physical applications.Comment: 5 pages, 2 figure

Set Aggregation Network as a Trainable Pooling Layer

Global pooling, such as max- or sum-pooling, is one of the key ingredients in deep neural networks used for processing images, texts, graphs and other types of structured data. Based on the recent DeepSets architecture proposed by Zaheer et al. (NIPS 2017), we introduce a Set Aggregation Network (SAN) as an alternative global pooling layer. In contrast to typical pooling operators, SAN allows to embed a given set of features to a vector representation of arbitrary size. We show that by adjusting the size of embedding, SAN is capable of preserving the whole information from the input. In experiments, we demonstrate that replacing global pooling layer by SAN leads to the improvement of classification accuracy. Moreover, it is less prone to overfitting and can be used as a regularizer.Comment: ICONIP 201