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1

Greener, greater and… safer? How COVID-19 pandemic verified New York’s planning strategies

Jasiński Artur, Oktawiec Wojciech

Teka Komisji Urbanistyki i Architektury Oddział PAN w Krakowie

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2022

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T. 50

109--129

EN

The COVID-19 pandemic has exposed a specific paradox of contemporary urban planning. Cities that since the dawn of civilization have been considered the safest and most attractive human habitats turn into traps in a pandemic. For example New York, the most densely populated city in the United States, became the world’s epicentre of the pandemic in April 2020. Since 1992, successive teams governing the city stimulated proecological planning strategies. From a neglected city, threatened with crime and plagued by terrorism, they turned it into a green metropolis, a symbol of a city of the 21st century. One of the most important planning and urban achievements was the successful revitalization of the post-industrial waterfront piers of Brooklyn and Queens. The rapid growth of bicycle transport stimulated by the planning authorities and supported by the construction of a network of bicycle routes along the main streets and coastal promenades should be noted as well. The aim of this study is to investigate the effects of the planning transformations in New York on the course of the COVID-19 pandemic, and to answer the question whether they made the city more resilient and safer.

PL

Pandemia COVID-19 obnażyła swoisty paradoks współczesnej urbanistyki. Miasta, które od zarania cywilizacji były uważane za najbardziej bezpieczne i atrakcyjne siedliska ludzkie, podczas pandemii zmieniły się w pułapki. Nowy Jork, najgęściej zaludnione miasto USA, w kwietniu 2020 roku stał się światowym epicentrum pandemii. Specyfika Nowego Jorku wynika m.in. z faktu, że począwszy od 1992 roku władze prowadziły w miarę spójną politykę przestrzenną, co przyczyniło się do całkowitej zmiany wizerunku tej metropolii. Z miasta zaniedbanego, zagrożonego przestępczością działania te uczyniły zieloną metropolię, symbol miasta XXI wieku. Jednym z najważniejszych osiągnięć planistycznych i urbanistycznych była udana rewitalizacja poprzemysłowych nadbrzeży Manhattanu i sąsiadujących z nim nadbrzeży dzielnic Brooklyn i Queens. Odnotować należy także stymulowany przez planistów szybki rozwój komunikacji rowerowej. Celem niniejszej pracy jest zbadanie, jakie skutki dla przebiegu pandemii COVID-19 miały rezultaty tych przekształceń planistycznych dokonanych w Nowym Jorku w ciągu ostatniego trzydziestolecia, a także odpowiedź na pytanie, czy dzięki nim miasto stało się bezpieczniejsze i bardziej odporne.

2

Rola łączności sieci dolinnej, rzecznej i drogowej w transporcie materiału zawieszonego w zlewni rolniczej i zalesionej (Pogórze Wiśnickie, Polska)

Święchowicz Jolanta, Natanek Adrianna

Landform Analysis

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2022

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Vol. 41

33--51

PL

Poznanie źródeł osadów, szlaków i dynamiki transportu oraz czynników, które leżą u podstaw przestrzennej i czasowej zmienności w transporcie zawiesiny w rzekach jest nadal kluczowym zagadnieniem poznawczym w geomorfologii. W zlewni nakładają się na siebie trzy sieci umożliwiające transport wody i osadów. Są to naturalne sieci dolinna i rzeczna oraz związana z gospodarczą działalnością człowieka sieć drogowa. Sieć dolinna, rzeczna i drogowa są ze sobą połączone, a w miejscach tych połączeń może następować dostawa materiału do transportu rzecznego. Celem pracy jest poznanie roli sieci dolinnej, rzecznej i drogowej w transporcie zawiesiny w zlewni rolniczej i zalesionej. Podstawą opracowania są badania przeprowadzone w zlewniach Dworskiego Potoku i Leśnego Potoku położonych na Pogórzu Wiśnickim. W rolniczej zlewni Dworskiego Potoku wyróżniono 10 węzłów: ciek–ciek, ciek–dolina, dolina–dolina i droga–droga. Najwięcej skrzyżowań występuje pomiędzy dolinami (połączenie dolina–dolina) oraz pomiędzy dolinami i ciekami (połączenie ciek–dolina). W zalesionej zlewni Leśnego Potoku wyróżniono 497 węzłów: ciek–ciek, ciek–dolina, ciek–droga, dolina–dolina i droga– droga. Najwięcej węzłów występuje pomiędzy dolinami (połączenie dolina–dolina), następnie między drogami (połączenie droga–droga) oraz między dolinami i ciekami wodnymi (połączenie ciek–dolina). Mniej powszechne są połączenia dróg i dolin oraz dróg i cieków wodnych. Najmniej połączeń występuje pomiędzy ciekami wodnymi.

EN

Understanding sediment sources, routes and transport dynamics, and the factors that underlie spatial and temporal variability in suspended sediment transport in rivers is still a key cognitive issue in geomorphology. In the catchment area, three networks allow the transport of water and sediment. These are valley and river natural networks as well as a road network related to anthropogenic activity. The valley, river and road networks are interconnected, and sediment influx to fluvial transport pathways may be entered in sites of these connectivity. The aim of this work is to describe role of valley network, river network and road network in the transport of the suspended sediment in agricultural and forested catchments. The study is based on research performed in the Dworski Potok and Leśny Potok catchments located in Wiśnicz Foothills, Poland. In agricultural Dworski Potok catchment following 10 nodes has been distinguished: watercourse–watercourse, watercourse–valley, valley–valley, and road–road. The most of junction appear between valleys (valley–valley node) and between valleys and watercourses (watercourse–valley node). In Leśny Potok catchment 497 nodes has been distinguished: watercourse–watercourse, watercourse–valley, watercourse–road, valley– valley, and road–road. The most of nodes appear between valleys (valley–valley node), next between roads (road–road node), and between valleys and watercourses (watercourse–valley node). Less common are the connections between roads and valleys and between roads and watercourses. The least of connections appear between watercourses.

3

New filtration parameters from X-ray computed tomography for tight rock images

Krakowska-Madejska Paulina

Geology, Geophysics and Environment

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2022

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Vol. 48, no. 4

381--392

EN

New parameters are proposed to evaluate the filtration properties of rocks obtained on the basis of 3D interpretation of images from X-ray computed tomography. The analyzed parameters are: global average pore connectivity, average blind pore connectivity, blind pore coefficient per object and blind pore coefficient per branch. The 3D pore space from computed X-ray tomography must be subjected to a process of pore space transformation into a skeleton. Then, the presented parameters can be evaluated, taking into consideration the pore channels (branches), pore channel connection points (junctions) and blind pores (pore without connection to the other pore). The calculations were made for low porosity sandstones, mudstones, limestones, and dolomites which differ in terms of age and depth of present deposition. The global average pore connectivity reflects the degree of development of the pore space in which the formation fluid can flow. The higher the global average pore connectivity, the most complex the pore structure can be expected. The higher the parameter of the average blind pore connectivity, the worse are the filtration properties of the rock. The higher the concentration of blind pore coefficient per object or branch, the worse the filtration properties of the rock. Moreover, new parameters were compared with the Euler characteristic and coordination number, revealing a high consistency.

4

Network connectivity dynamic modelling

Eid Mohamed

Safety and Reliability of Systems and Processes

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2021

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Summer Safety and Reliability Seminar 2021

117--127

EN

The chapter presents an approach based on basic notions issued from the graph theory and from the system reliability theory. The approach seeks to describe the transitions in the connectivity state of non-directional graphs induced by systemic losses of nodes and edges. Each component loss (node or edge) represents a transition and results in a connectivity degradation. Some of the transitions are classified as non-critical while others are critical. Degradations are measured using the notion of topological graph diameter issued from the graph theory. The critical transition notion is issued from the system reliability theory. The approach determines the degraded graph diameter corresponding to each possible transition and subsequently the criticality of the transition. The criticality threshold is determined by the highest acceptable connectivity order which is a function of the degraded graph diameter. A network with 9 nodes and 15 edges is used as an academic study case to illustrate the applicability of the approach. Nodes are supposed to be identical, as well as the edges. All network components (nodes and edges) are mutually independent. These precedent hypotheses are intended to evacuate all sources of numerical useless complexity. As our main objective is to highlight the original characteristic of the proposed approach.

5

Connectivity maintenance in IoT-based mobile networks: approaches and challenges

Akram Vahid Khalilpour, Challenger Moharram

Annals of Computer Science and Information Systems

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2021

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Vol. 26

145--149

EN

Connectivity is an important requirement in almost all IoT-based wireless networks. The multi-hop networks use intermediate nodes to create a communication path between other nodes. Hence losing some nodes may cut off all communication paths between other active nodes. Generally, the connectivity of a partitioned network can be restored by adding new or activating redundant nodes, moving available nodes to the new location, and increasing the wireless communication range of nodes. The restoration problem may have many constraints and sub-problems. The network may initially be disconnected, the nodes may be heterogeneous, reliable connections may be required between the nodes, we may have unreachable locations in the network area to put the new nodes or move exciting nodes, more than one node may fail at the same time and the expected coverage area may complicate the connectivity restoration problem. In this paper, we study the main challenges and methods of connectivity restoration in IoT-based wireless networks.

6

Debris-flow functioning and their contribution to sedimentary budgets : the Peynin subcatchment of the Guil River (Upper Queyras, Southern French Alps)

Viel V., Fort M., Lissak C., Graff K., Carlier B., Arnaud-Fassetta G., Cossart E., Madelin M.

Landform Analysis

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2018

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Vol. 36

71--84

EN

The Peynin catchment (15 km2) is prone to catastrophic floods (June 1957 – Recurrence Interval R.I.>100 yr), June 2000 (R.I.-30 yr) with serious damages to infrastructure and buildings located at the outlet. In this paper, PIT tags tracers and Vensim modelling software are used to better assess the sediment delivery unsteadiness, and more specifically to evaluate the respective role of geomorphological processes on sediment supply during flood event. For the last 20 years, our results highlight a significant variability in sediment delivery from a tributary to another one. According to our studies, we suppose that two torrential tributaries of the Peynin river, the Peyronnelle and Three Arbres subcatchments (<2 km2, representing <15% of the Peynin catchment area) are responsible of 80% of the sediments observed at the outlet of the catchment. Several processes take a part of these sediment transfers, but the efficiency of the sediment cascade in this catchment can be explained by a strong connectivity between sediment erosion area and the main channel of the catchment. Debris and torrential flows triggered during high intensity meteorological event are actually effectively coupled in space and time and guarantee an important sediment supply able to reload the downstream part of the sediment cascade. Recent climate trends, marked by extremes, suggest consequently more damaging events to come, in a context of increasing vulnerable assets.

7

Konstrukcje urbanistyczne miast przyszłości. Uwagi do dyskusji nad wizją rozwoju Rzeszowa

Zuziak Z. K.

Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture

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2017

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z. 64, nr 3/II

467--485

PL

Artykuł dotyczy roli modelowania w planowaniu przestrzennym miast, które rozwijają swój potencjał metropolitalny i aspirują do miana miasta przyszłości. Zakładając, że budowa miasta przyszłości wymaga zmian o charakterze modelowym – zwłaszcza w relacjach: transport i użytkowanie terenu – zarysowano koncepcję modelu, który byłby narzędziem planistycznym odpowiadającym takiemu celowi. W tej części publikacji wykorzystano rezultaty projektu badawczego opracowanego, w latach 2016-17, przez zespół architektów, urbanistów i inżynierów transportu z Politechniki Krakowskiej. Projekt dotyczył modelowej interpretacji konstrukcyjnych, morfologicznych i funkcjonalnych atrybutów przestrzennej struktury Krakowa. W artykule akcent położono na konstrukcyjne aspekty tej interpretacji. Stąd kluczowa rola takich pojęć jak: zintegrowanie (connectivity), „konstrukcja urbanistyczna”, sieć przestrzeni publicznych i „strategiczne wiązania” (strategic connectors). To ostatnie pojęcie oznacza miejskie korytarze wiążące główne klastry miejsc węzłowych a zarazem kierunki wzdłuż których należałoby skupiać strategiczne projekty miejskie celem uzyskania efektu synergii. Aczkolwiek model opracowano dla Krakowa, wskazano też na możliwości jego zastosowania w przypadku Rzeszowa. Zwrócono tu uwagę na potrzebę wzmocnienia „strategicznych wiązań” integrujących śródmiejskie węzły miejskości z innymi, kluczowymi elementami przestrzennej struktury metropolitalnej. Podkreślono strukturotwórczą rolę węzłów i korytarzy miejskości o różnych cechach morfologicznych i funkcjonalnych. Mowa tu również o konstrukcyjnych powiązaniach takich obszarów strategicznych jak: historyczne centrum, rejon głównego dworca kolejowego, rejon portu lotniczego, a także potencjalne obszary rewitalizacji terenów poprzemysłowych. W tym sensie kreowanie nowej wizji rozwoju Rzeszowa jako miasta przyszłości wiązałoby się z tworzeniem synergicznych relacji między konstrukcyjnymi, funkcjonalnymi i morfologicznymi warstwami modelu planistycznego. Zakłada się, że prezentowy model mógłby być podstawą badań porównawczych nad zmianami struktury przestrzennej takich miast jak: Kraków, Lublin, Rzeszów.

EN

In the paper, the role of modeling urban spatial structure is discussed in the context of spatial planning process for the cities which are having potentials for the development of metropolitan functions and are revealing aspirations to be recognized as “the city of the future”. The main focus is put on structural aspect of modeling metropolitan space. Assuming that building the city of the future implies the change of the model – particularly in relations between transport systems and land use, the author outlines a new proposal for modelling metropolitan spatial structure based on the research project carried out for the city of Kracow by the team of architects, urbanists and civil engineers from the Cracow University of Technology. The key phrases of this model are: connectivity, urban construction and strategic connectors. This applies to such major components of spatial structure of the city as: the nodes and the corridors of urbanity and the network of public spaces. The model allows for the identification of new structural elements of urbanistic space as well as potential synergic relations between them. In the interpretation of urban connectivity significant role is played by strategic connectors – urban corridors linking major clusters of the nodal places and thus having potentials for concentrating strategic urban projects. It is assumed that this type of concentration helps to achieve the effect of urban synergy. Although the model was developed for the city of Krakow, references to the city Rzeszow are also made. In this case attention was drawn to potential strategic connectors linking the historic center – and other main nodes of urbanity within the inner city – with new potential metropolitan clusters of urban nodes such as close-to-station areas as well as potential areas of urban revitalization. It is emphasized that nodal places, corridors of urbanity, and strategic areas should be diversified in terms of morphological and functional attributes. It is assumed that the model presented in this paper could be used as a starting point for further comparative analyses within the framework of a collaborative project carried out by the joined university research team from the cities of Krakow, Lublin and Rzeszow.

8

Multifunctional and Multiscale Aspects of Green Infrastructure in Contemporary Research

Zaręba A.

Problemy Ekorozwoju

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2014

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Vol. 9, nr 2

149--156

EN

This paper provides information on the definition and benefits of green infrastructure, outlines the green infrastructure solutions and technics and their influence on multifunctionalty and multiscale of current research. Examples of green infrastructure practices include green, blue, and white roofs; hard and soft permeable surfaces; green alleys and streets; urban forestry; green open spaces such as parks and wetlands. Green infrastructure approaches help to achieve sustainability and resilience through practices such as among many others: urban forestry, and water conservation. This paper evaluates benefits of selection of particular green infrastructure solutions on the background of broader ecological context.

PL

Idea zielonej infrastruktury jest jednym z najważniejszych kierunków tworzących nową jakość w zarządzaniu środowiskiem przyrodniczym. Zielona infrastruktura oprócz funkcji ekologicznej ma wpływać na poprawę: warunków zdrowotnych, poprawę poszczególnych komponentów środowiska, a nawet kontrolować rozwój przestrzenny miasta. Niektórzy badacze przyjmują założenie że zielona infrastruktura powinna być traktowana równorzędnie z techniczną. Celem artykułu jest określenie rodzajów zielonej infrastruktury w strefie zurbanizowanej ze szczególnym uwzględnieniem obszarów wielofunkcyjnych, które dzięki swojej atrakcyjności przyrodniczej i krajobrazowej, wynikającej z różnorodnych form użytkowania, mogą zapewnić optymalną ilość i jakość terenów rekreacyjnych. We współczesnych badaniach zauważa się, że strefy wielofunkcyjne w obrębie których preferowane są metody użytkowania gruntów, chroniące różnorodne biologicznie ekosystemy, zatrzymując czysta wodę, zabezpieczając przed erozją, powodziami służyć mogą różnorodnym potrzebom mieszkańców miast. W artykule prezentowane są zasady rządzące funkcjonowaniem zielonej infrastruktury, szczególnie najważniejsza z nich dotycząca poprawy łączności między istniejącymi obszarami przyrodniczymi, w celu przeciwdziałania ich fragmentacji i zwiększenia ich ekologicznej spójności.

9

Temporal fluctuations of the phytoplankton community in an isolated floodplain lake (North Mollaköy Lake) of the Sakarya River (Northern Turkey)

Sevindik T. O., Tunca H., Önem B., Tamer S. A.

Oceanological and Hydrobiological Studies

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2014

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Vol. 43, No. 4

381--392

EN

The aim of this study was to determine the spatial and temporal variation of phytoplankton and water quality in response to the hydrological regime in an isolated floodplain lake (North Mollaköy Lake) of the Sakarya River. Variations in the composition, biomass and functional groups of phytoplankton and environmental parameters were monthly analyzed in sub-surface samples collected from the pelagic zone at four stations from July 2012 to June 2013. A total of 109 taxa were identified, and the species which contributed the most to the phytoplankton biomass were grouped into 14 functional groups (FGs). The distribution of FGs was linked to the transition (T1 and T2), high (HW) and low (LW) water periods in North Mollaköy Lake. FGs J, MP, N, G, X1, X2, Y, W1, W2, S1, H1, B and C were the contributors to the phytoplankton biomass during the low-water period (LW) and the transition periods (T1 and T2), while Lo contributed the most during the high-water period (HW). RDA revealed that the most important factor affecting the temporal distribution of FGs was the water discharge and that there are some differences between stations in terms of Si, pH values and the distribution of FGs.

10

Selected Issues of QoS Provision in Heterogenous Military Networks

Hauge M., Landmark L., Łubkowski P., Amanowicz M., Maślanka K.

International Journal of Electronics and Telecommunications

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2014

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Vol. 60, No. 1

7-13

EN

Tactical ad-hoc networks are evolving today towards complex heterogeneous networks in terms of architecture, protocols and security. Due to the difference in network resources and reliability, end-to-end quality of service provisioning becomes very challenging. If we also take into account communication issues such as unpredictable connectivity, preferential forwarding for special traffic classes, intermittency due to node or communication link failure, the problem is further aggravated. In this article, we examine the major challenges that must be solved in order to provide efficient QoS provisioning in the heterogeneous network. Finally we describe QoS-aware mechanisms for inter-domain and intra-domain heterogeneous networks, also including real-time services provision in highly mobilr environments.

11

A topological model to assess networks connectivity and reliability

Eid M., Hami-EL A., Souza de Cursi E.

Journal of Polish Safety and Reliability Association

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2013

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Vol. 4, No. 2

167--178

EN

The acceleration of the interconnectivity of networks of all sorts brings to the front scene the issue of networks performance measure. Recently, one observed an accelerating course towards quantitative probabilistic models to describe and assess networks’ Connectivity, as being the main vector of performance. However, modelling realistic networks is still far from being satisfactorily achieved using quantitative probabilistic models. On the other hand, little room had been lift to exploring the potential of topological models to develop qualitative and semi- quantitative models in order to assess networks connectivity. In this paper, we are exploring the potential of the topological modelling. The proposed model is based on describing the nodepair connectivity using binary scalars of different orders (tensors). Preliminary results of our explorations sounded very promoting.

12

Towards the development of a topological model to assess networks performance : connectivity, robustness and reliability

Eid M., Cursi-Eduardo-de S., EL Hami A.

Journal of Polish Safety and Reliability Association

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2012

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Vol. 3, No. 1

21--38

EN

Networks are the widest spreading system which Mankind has ever developed, today. New needs, services, and use are created each day where network systems represent the most critical aspect. Additionally, the interconnection between networks of different types is growing as never. This acceleration of interconnection of all sorts brings to the front scene the issue of performance measure in networks design and operation. For that purpose, engineers are orienting their major efforts towards the development of methods, models and codes to assess and measure networks performance in terms of probability of being connected. From this stand point of view, the engineers’ attention is mainly focused on defining the network “Connectivity” and measuring it, in different manner, using probabilities. Subsequently, we are observing an accelerating course towards quantitative probabilistic models to describe and assess networks’ Connectivity, since the sixties. Modelling realistic networks is still far from being satisfactorily achieved using quantitative probabilistic models. On the other hand, little room has been lift to exploring the potential of graphical and topological models to develop qualitative and semi- quantitative models in order to assess networks performance. In this paper, we have tried to explore the potential of the topological modelling and are proposing an original one. The proposed model is still in its earliest phase of development. But, it sounds very promoting at that stage of maturation. According to this model, the term “performance” may be extended, beyond the “connectivity probabilistic concept”, to “robustness” and to a “deepest insight” of the “connectivity concept” itself. The impact is immediate on the way the “reliability concept” would be extended to cover network systems.

13

Vistula River Valley as the ecological corridor for mammals

Romanowski J.

Polish Journal of Ecology

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2007

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Vol. 55, nr 4

805-819

EN

River Vistula, one of the large (1047 km in length) European rivers preserved in semi-natural, dynamic condition, is recognized as important corridor that enables birds and fishes to migrate for long distances. To test whether the Vistula valley provides corridor function also for mammals, field surveys and habitat modelling for six target species: Bank vole Myodes glareolus, Yellow-necked mouse Apodemus flavicollis, Pine marten Martes martes, Beaver Castor fiber, Wild boar Sus scrofa, and Elk Alces alces, were under-taken in the 135 km long fragment of the valley from 529 (Warsaw) to 685 km (Włocławek). The data collected documented the occurrence of at least 51 mammals (5 Insectivora, 14 Chiroptera, 1 Lagomorpha, 16 Rodentia, 11 Carnivora, 4 Artiodactyla), and the higest species richness was noted in the fragment of river valley covered with mixed forests which makes up the protected area called Kampinos National Park. This protected area (385 km[^2]) contains coniferous and mixed forests, inland dunes, wetlands, and mosaic of extensively used meadows, pastures, alder forests and fields. The LARCH (Landscape Ecological Analysis and Rules for the Configuration of Habitat) (Van der Sluis and Romanowski 2005) model outputs indicated the potential for large viable populations of species analysed in the river valley. The LARCH SCAN analysis showed that habitats of modelled species were well connected and their local populations formed highly sustainable network. The spatial cohesion of habitats was generally highest in Kampinos NP and along the fragment of River Vistula from 580 to 618 km. It is concluded that high cohesion of habitats facilitates dispersion of animals and provides potential for gene flow among the populations in the valley. Riparian forests and islands are important for connecting the local populations of mammals of two river banks and are the key elements to provide functional continuity of the corridor along the river in places, where it is discontinued on one bank. The scenario analysis demonstrates potentially negative effects of river regulation and construction of two dams on viability of mammalian populations and spatial cohesion of their habitats. The future corridor function of the River Vistula valley depends mostly on preservation of it.s dynamic, semi-natural condition.

14

Geodesy and connectivity in lattices

Ronse Ch., Serra J.

Fundamenta Informaticae

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2001

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Vol. 46, nr 4

349-395

EN

This paper generalizes the notion of symmetrical neighbourhoods, which have been used to define connectivity in the case of sets, to the wider framework of complete lattices having a sup-generating family. Two versions (weak and strong) of the notion of a symmetrical dilation are introduced, and they are applied to the generation of ``connected components'' from the so-called ``geodesic dilations''. It turns out that any ``climbing'' ``weakly symmetrical'' extensive dilation induces a ``geodesic'' connectivity. When the lattice is the one of subsets of a metric space, the connectivities which are obtained in this way may coincide with the usual ones under some conditions, which are clarified. The abstract theory can be applied to grey-level and colour images, without any assumption of translation-invariance of operators.

15

Logistyczne aspekty integracji sił zbrojnych RP z wymogami NATO

Ficoń K.

Systemy Logistyczne Wojsk

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2000

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Nr 25

85--98

16

Fundamenta morphologicae mathematicae

Goutsias J., Heijmans H.J.A.M.

Fundamenta Informaticae

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2000

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Vol. 41, Nr 1,2

1-31

EN

Mathematical morphology is a geometric approach in image processing and analysis with a strong mathematical flavor. Originally, it was developed as a powerful tool for shape analysis in binary and, later, grey-scale images. But it was soon recognized that the underlying ideas could be extended naturally to a much wider class of mathematical objects, namely complete lattices. This paper presents, in a bird's eye view, the foundations of mathematical morphology, or more precisely, the theory of morphological operators on complete lattices.

17

Connections for sets and functions

Serra J.

Fundamenta Informaticae

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2000

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Vol. 41, Nr 1,2

147-186

EN

Classically, connectivity is a topological notion for sets, often introduced by means of arcs. An algebraic definition, called connection, has been proposed by Serra to extend the notion of connectivity to complete sup-generated lattices. A connection turns out to be characterized by a family of openings parameterized by the sup-generators, which partition each element of the lattice into maximal components. Starting from a first connection, several others may be constructed; e.g., by applying dilations. The present paper applies this theory to numerical functions. Every connection leads to segmenting the support of the function under study into regions. Inside each region, the function is r-continuous, for a modulus of continuity r given a priori, and characteristic of the connection. However, the segmentation is not unique, and may be particularized by other considerations (self-duality, large or low number of point components, etc.). These variants are introduced by means of examples for three different connections: flat zone connections, jump connections, and smooth path connections. They turn out to provide remarkable segmentations, depending only on a few parameters. In the last section, some morphological filters are described, based on flat zone connections, namely openings by reconstruction, flattenings and levelings.