Spatial indexing for scalability in FCA

The paper provides evidence that spatial indexing structures offer faster resolution of Formal Concept Analysis queries than B-Tree/Hash methods. We show that many Formal Concept Analysis operations, computing the contingent and extent sizes as well as listing the matching objects, enjoy improved performance with the use of spatial indexing structures such as the RD-Tree. Speed improvements can vary up to eighty times faster depending on the data and query. The motivation for our study is the application of Formal Concept Analysis to Semantic File Systems. In such applications millions of formal objects must be dealt with. It has been found that spatial indexing also provides an effective indexing technique for more general purpose applications requiring scalability in Formal Concept Analysis systems. The coverage and benchmarking are presented with general applications in mind.

Monitoring the condition of savanna riparian zones in Northern Australia using high spatial resolution imagery and a field based rapid assessment method

Government agencies responsible for riparian environments are assessing the combined utility of field survey and remote sensing for mapping and monitoring indicators of riparian zone condition. The objective of this work was to compare the Tropical Rapid Appraisal of Riparian Condition (TRARC) method to a satellite image based approach. TRARC was developed for rapid assessment of the environmental condition of savanna riparian zones. The comparison assessed mapping accuracy, representativeness of TRARC assessment, cost-effectiveness, and suitability for multi-temporal analysis. Two multi-spectral QuickBird images captured in 2004 and 2005 and coincident field data covering sections of the Daly River in the Northern Territory, Australia were used in this work. Both field and image data were processed to map riparian health indicators (RHIs) including percentage canopy cover, organic litter, canopy continuity, stream bank stability, and extent of tree clearing. Spectral vegetation indices, image segmentation and supervised classification were used to produce RHI maps. QuickBird image data were used to examine if the spatial distribution of TRARC transects provided a representative sample of ground based RHI measurements. Results showed that TRARC transects were required to cover at least 3% of the study area to obtain a representative sample. The mapping accuracy and costs of the image based approach were compared to those of the ground based TRARC approach. Results proved that TRARC was more cost-effective at smaller scales (1-100km), while image based assessment becomes more feasible at regional scales (100-1000km). Finally, the ability to use both the image and field based approaches for multi-temporal analysis of RHIs was assessed. Change detection analysis demonstrated that image data can provide detailed information on gradual change, while the TRARC method was only able to identify more gross scale changes. In conclusion, results from both methods were considered to complement each other if used at appropriate spatial scales.

Efficiently computing weighted proximity relationships in spatial databases

Spatial data mining recently emerges from a number of real applications, such as real-estate marketing, urban planning, weather forecasting, medical image analysis, road traffic accident analysis, etc. It demands for efficient solutions for many new, expensive, and complicated problems. In this paper, we investigate the problem of evaluating the top k distinguished “features” for a “cluster” based on weighted proximity relationships between the cluster and features. We measure proximity in an average fashion to address possible nonuniform data distribution in a cluster. Combining a standard multi-step paradigm with new lower and upper proximity bounds, we presented an efficient algorithm to solve the problem. The algorithm is implemented in several different modes. Our experiment results not only give a comparison among them but also illustrate the efficiency of the algorithm.

On aggregation issues in spatial data management

Large amounts of information can be overwhelming and costly to process, especially when transmitting data over a network. A typical modern Geographical Information System (GIS) brings all types of data together based on the geographic component of the data and provides simple point-and-click query capabilities as well as complex analysis tools. Querying a Geographical Information System, however, can be prohibitively expensive due to the large amounts of data which may need to be processed. Since the use of GIS technology has grown dramatically in the past few years, there is now a need more than ever, to provide users with the fastest and least expensive query capabilities, especially since an approximated 80 % of data stored in corporate databases has a geographical component. However, not every application requires the same, high quality data for its processing. In this paper we address the issues of reducing the cost and response time of GIS queries by preaggregating data by compromising the data accuracy and precision. We present computational issues in generation of multi-level resolutions of spatial data and show that the problem of finding the best approximation for the given region and a real value function on this region, under a predictable error, in general is "NP-complete.

Multiscale histograms: Summarizing topological relations in large spatial datasets

Summarizing topological relations is fundamental to many spatial applications including spatial query optimization. In this paper, we present several novel techniques to eectively construct cell density based spatial histograms for range (window) summarizations restricted to the four most important topological relations: contains, contained, overlap, and disjoint. We rst present a novel framework to construct a multiscale histogram composed of multiple Euler histograms with the guarantee of the exact summarization results for aligned windows in constant time. Then we present an approximate algorithm, with the approximate ratio 19/12, to minimize the storage spaces of such multiscale Euler histograms, although the problem is generally NP-hard. To conform to a limited storage space where only k Euler histograms are allowed, an effective algorithm is presented to construct multiscale histograms to achieve high accuracy. Finally, we present a new approximate algorithm to query an Euler histogram that cannot guarantee the exact answers; it runs in constant time. Our extensive experiments against both synthetic and real world datasets demonstrated that the approximate mul- tiscale histogram techniques may improve the accuracy of the existing techniques by several orders of magnitude while retaining the cost effciency, and the exact multiscale histogram technique requires only a storage space linearly proportional to the number of cells for the real datasets.

Assembly processes of invertebrate communities in springs across different spatial scales

Il presente lavoro ha lo scopo di comprendere i processi sottesi ai pattern di coesistenza tra le specie di invertebrati sorgentizi, distinguendo tra dinamiche stocastiche e deterministiche. Le sorgenti sono ecosistemi complessi e alcune loro caratteristiche (ad esempio l’insularità, la stabilità termica, la struttura ecotonale “a mosaico”, la frequente presenza di specie rare ed endemiche, o l’elevata diversità in taxa) le rendono laboratori naturali utili allo studio dei processi ecologici, tra cui i processi di assembly. Al fine di studiare queste dinamiche è necessario un approccio multi-scala, per questo motivi sono state prese in considerazione tre scale spaziali. A scala locale è stato compiuto un campionamento stagionale su sette sorgenti (quattro temporanee e tre permanenti) del Monte Prinzera, un affioramento ofiolitico vicino alla città di Parma. In questa area sono stati valutati l’efficacia e l’impatto ambientale di diversi metodi di campionamento e sono stati analizzati i drivers ecologici che influenzano le comunità. A scala più ampia sono state campionate per due volte 15 sorgenti della regione Emilia Romagna, al fine di identificare il ruolo della dispersione e la possibile presenza di un effetto di niche-filtering. A scala continentale sono state raccolte informazioni di letteratura riguardanti sorgenti dell’area Paleartica occidentale, e sono stati studiati i pattern biogeografici e l’influenza dei fattori climatici sulle comunità. Sono stati presi in considerazione differenti taxa di invertebrati (macroinvertebrati, ostracodi, acari acquatici e copepodi), scegliendo tra quelli che si prestavano meglio allo studio dei diversi processi in base alle loro caratteristiche biologiche e all’approfondimento tassonomico raggiungibile. I campionamenti biologici in sorgente sono caratterizzati da diversi problemi metodologici e possono causare impatti sugli ambienti. In questo lavoro sono stati paragonati due diversi metodi: l’utilizzo del retino con un approccio multi-habitat proporzionale e l’uso combinato di trappole e lavaggio di campioni di vegetazione. Il retino fornisce dati più accurati e completi, ma anche significativi disturbi sulle componenti biotiche e abiotiche delle sorgenti. Questo metodo è quindi raccomandato solo se il campionamento ha come scopo un’approfondita analisi della biodiversità. D’altra parte l’uso delle trappole e il lavaggio della vegetazione sono metodi affidabili che presentano minori impatti sull’ecosistema, quindi sono adatti a studi ecologici finalizzati all’analisi della struttura delle comunità. Questo lavoro ha confermato che i processi niche-based sono determinanti nello strutturare le comunità di ambienti sorgentizi, e che i driver ambientali spiegano una rilevante percentuale della variabilità delle comunità. Infatti le comunità di invertebrati del Monte Prinzera sono influenzate da fattori legati al chimismo delle acque, alla composizione e all’eterogeneità dell’habitat, all’idroperiodo e alle fluttuazioni della portata. Le sorgenti permanenti mostrano variazioni stagionali per quanto riguarda le concentrazioni dei principali ioni, mentre la conduttività, il pH e la temperatura dell’acqua sono più stabili. È probabile che sia la stabilità termica di questi ambienti a spiegare l’assenza di variazioni stagionali nella struttura delle comunità di macroinvertebrati. L’azione di niche-filtering delle sorgenti è stata analizzata tramite lo studio della diversità funzionale delle comunità di ostracodi dell’Emilia-Romagna. Le sorgenti ospitano più del 50% del pool di specie regionale, e numerose specie sono state rinvenute esclusivamente in questi habitat. Questo è il primo studio che analizza la diversità funzionale degli ostracodi, è stato quindi necessario stilare una lista di tratti funzionali. Analizzando il pool di specie regionale, la diversità funzionale nelle sorgenti non è significativamente diversa da quella misurata in comunità assemblate in maniera casuale. Le sorgenti non limitano quindi la diversità funzionale tra specie coesistenti, ma si può concludere che, data la soddisfazione delle esigenze ecologiche delle diverse specie, i processi di assembly in sorgente potrebbero essere influenzati da fattori stocastici come la dispersione, la speciazione e le estinzioni locali. In aggiunta, tutte le comunità studiate presentano pattern spaziali riconoscibili, rivelando una limitazione della dispersione tra le sorgenti, almeno per alcuni taxa. Il caratteristico isolamento delle sorgenti potrebbe essere la causa di questa limitazione, influenzando maggiormente i taxa a dispersione passiva rispetto a quelli a dispersione attiva. In ogni caso nelle comunità emiliano-romagnole i fattori spaziali spiegano solo una ridotta percentuale della variabilità biologica totale, mentre tutte le comunità risultano influenzate maggiormente dalle variabili ambientali. Il controllo ambientale è quindi prevalente rispetto a quello attuato dai fattori spaziali. Questo risultato dimostra che, nonostante le dinamiche stocastiche siano importanti in tutte le comunità studiate, a questa scala spaziale i fattori deterministici ricoprono un ruolo prevalente. I processi stocastici diventano più influenti invece nei climi aridi, dove il disturbo collegato ai frequenti eventi di disseccamento delle sorgenti provoca una dinamica source-sink tra le diverse comunità. Si è infatti notato che la variabilità spiegata dai fattori ambientali diminuisce all’aumentare dell’aridità del clima. Disturbi frequenti potrebbero provocare estinzioni locali seguite da ricolonizzazioni di specie provenienti dai siti vicini, riducendo la corrispondenza tra gli organismi e le loro richieste ambientali e quindi diminuendo la quantità di variabilità spiegata dai fattori ambientali. Si può quindi concludere che processi deterministici e stocastici non si escludono mutualmente, ma contribuiscono contemporaneamente a strutturare le comunità di invertebrati sorgentizi. Infine, a scala continentale, le comunità di ostracodi sorgentizi mostrano chiari pattern biogeografici e sono organizzate lungo gradienti ambientali principalmente collegati altitudine, latitudine, temperatura dell’acqua e conducibilità. Anche la tipologia di sorgente (elocrena, reocrena o limnocrena) è influente sulla composizione delle comunità. La presenza di specie rare ed endemiche inoltre caratterizza specifiche regioni geografiche.

Stimuli of varying spatial scale induce gamma activity with distinct temporal characteristics in human visual cortex

Gamma activity to stationary grating stimuli was studied non-invasively using MEG recordings in humans. Using a spatial filtering technique, we localized gamma activity to primary visual cortex. We tested the hypothesis that spatial frequency properties of visual stimuli may be related to the temporal frequency characteristics of the associated cortical responses. We devised a method to assess temporal frequency differences between stimulus-related responses that typically exhibit complex spectral shapes. We applied this methodology to either single-trial (induced) or time-averaged (evoked) responses in four frequency ranges (0-40, 20-60, 40-80 and 60-100 Hz) and two time windows (either the entire duration of stimulus presentation or the first second following stimulus onset). Our results suggest that stimuli of varying spatial frequency induce responses that exhibit significantly different temporal frequency characteristics. These effects were particularly accentuated for induced responses in the classical gamma frequency band (20-60 Hz) analyzed over the entire duration of stimulus presentation. Strikingly, examining the first second of the responses following stimulus onset resulted in significant loss in stimulus specificity, suggesting that late signal components contain functionally relevant information. These findings advocate a functional role of gamma activity in sensory representation. We suggest that stimulus specific frequency characteristics of MEG signals can be mapped to processes of neuronal synchronization within the framework of coupled dynamical systems.

Measuring the spatial arrangement patterns of pathological lesions in histological sections of brain tissue

The development of abnormal protein aggregates in the form of extracellular plaques and intracellular inclusions is a characteristic feature of many neurodegenerative diseases such as Alzheimer's disease (AD), Creutzfeldt-Jakob disease (CJD) and the fronto-temporal dementias (FTD). An important aspect of a pathological protein aggregate is its spatial topography in the tissue. Lesions may not be randomly distributed within a histological section but exhibit spatial pattern, a departure from randomness either towards regularity or clustering. Information on the spatial pattern of a lesion may be useful in elucidating its pathogenesis and in studying the relationships between different lesions. This article reviews the methods that have been used to study the spatial topography of lesions. These include simple tests of whether the distribution of a lesion departs significantly from random using randomized points or sample fields, and more complex methods that employ grids or transects of contiguous fields and which can detect the intensity of aggregation and the sizes, distribution and spacing of the clusters. The usefulness of these methods in elucidating the pathogenesis of protein aggregates in neurodegenerative disease is discussed.

Measuring the degree of spatial correlation between histological features in thin sections of brain tissue

Histological features visible in thin sections of brain tissue, such as neuronal perikarya, blood vessels, or pathological lesions may exhibit a degree of spatial association or correlation. In neurodegenerative disorders such as AD, Pick's disease, and CJD, information on whether different types of pathological lesion are spatially correlated may be useful in elucidating disease pathogenesis. In the present article the statistical methods available for studying spatial association in histological sections are reviewed. These include tests of interspecific association between two or more histological features using χ2 contingency tables, measurement of 'complete' and 'absolute' association, and more complex methods that use grids of contiguous samples. In addition, the use of correlation matrices and stepwise multiple regression methods are described. The advantages and limitations of each method are reviewed and possible future developments discussed.

Mach edges: local features predicted by 3rd derivative spatial filtering

Edges are key points of information in visual scenes. One important class of models supposes that edges correspond to the steepest parts of the luminance profile, implying that they can be found as peaks and troughs in the response of a gradient (1st derivative) filter, or as zero-crossings in the 2nd derivative (ZCs). We tested those ideas using a stimulus that has no local peaks of gradient and no ZCs, at any scale. The stimulus profile is analogous to the Mach ramp, but it is the luminance gradient (not the absolute luminance) that increases as a linear ramp between two plateaux; the luminance profile is a blurred triangle-wave. For all image-blurs tested, observers marked edges at or close to the corner points in the gradient profile, even though these were not gradient maxima. These Mach edges correspond to peaks and troughs in the 3rd derivative. Thus Mach edges are inconsistent with many standard edge-detection schemes, but are nicely predicted by a recent model that finds edge points with a 2-stage sequence of 1st then 2nd derivative operators, each followed by a half-wave rectifier.