Does Time Smoothen Space? Implications for Space-Time Representation

The continuous nature of space and time is a fundamental tenet of many scientific endeavors. That digital representation imposes granularity is well recognized, but whether it is possible to address space completely remains unanswered. This paper argues Hales' proof of Kepler's conjecture on the packing of hard spheres suggests the answer to be "no", providing examples of why this matters in GIS generally and considering implications for spatio-temporal GIS in particular. It seeks to resolve the dichotomy between continuous and granular space by showing how a continuous space may be emergent over a random graph. However, the projection of this latent space into 3D/4D imposes granularity. Perhaps surprisingly, representing space and time as locally conjugate may be key to addressing a "smooth" spatial continuum. This insight leads to the suggestion of Face Centered Cubic Packing as a space-time topology but also raises further questions for spatio-temporal representation

A Theory of Granular Partitions

We have a variety of different ways of dividing up, classifying, mapping, sorting and listing the objects in reality. The theory of granular partitions presented here seeks to provide a general and unified basis for understanding such phenomena in formal terms that is more realistic than existing alternatives. Our theory has two orthogonal parts: the first is a theory of classification; it provides an account of partitions as cells and subcells; the second is a theory of reference or intentionality; it provides an account of how cells and subcells relate to objects in reality. We define a notion of well-formedness for partitions, and we give an account of what it means for a partition to project onto objects in reality. We continue by classifying partitions along three axes: (a) in terms of the degree of correspondence between partition cells and objects in reality; (b) in terms of the degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) in terms of the degree of completeness with which a partition represents this domain

Constraints and Explanation

For the past 40 years, causal-mechanical approaches to explanation in science have been the received view. In this paper, I will argue that causal-mechanical approaches to explanation are not the whole story; there is a notable class of explanations that I call constraining explanation. Constraining explanation do not work by describing some causal structure; rather they work by highlighting mathematical constraints on what kinds of structure there can be. Constraining explanations are different that causal explanations because they give a kind of modal knowledge that causal-mechanical explanation alone cannot give

Flows of healthy and hardened RBC suspensions through a micropillar array

Red blood cell (RBC) deformability is an important haemorheological factor; it is impaired in many pathologies leading to microvascular complications. Several microfluidic platforms have been utilized to examine the role of deformability in RBC flows but their geometries tend to be simplified. In the present study, we extend our previous work on healthy RBC flows in micropillar arrays [1] to probe the effect of impaired RBC deformability on the velocity and haematocrit distributions in microscale RBC flows. Healthy and artificially hardened RBC suspensions at 25% haematocrit were perfused through the micropillar array at various flow rates and imaged. RBC velocities were determined by Particle Image Velocimetry (PIV) and haematocrit distributions were inferred from the image intensity distributions. The pillars divide the flow into two distinct RBC streams separated by a cell-depleted region along the centreline and in the rear/front stagnation points. RBC deformability was not found to significantly affect the velocity distributions; the shape of the velocity profiles in the interstitial space remained the same for healthy and hardened RBCs. Time-averaged and spatiotemporal intensity distributions, however, reveal differences in the dynamics and local distributions of healthy and hardened cells; hardened cells appear to enter the cell-depleted regions more frequently and their interstitial distributions are more uniform. The study highlights the importance of local RBC distributions and the impact of RBC deformability on cell transport in complex microscale flows

Recognition of Activities of Daily Living with Egocentric Vision: A Review.

Video-based recognition of activities of daily living (ADLs) is being used in ambient assisted living systems in order to support the independent living of older people. However, current systems based on cameras located in the environment present a number of problems, such as occlusions and a limited field of view. Recently, wearable cameras have begun to be exploited. This paper presents a review of the state of the art of egocentric vision systems for the recognition of ADLs following a hierarchical structure: motion, action and activity levels, where each level provides higher semantic information and involves a longer time frame. The current egocentric vision literature suggests that ADLs recognition is mainly driven by the objects present in the scene, especially those associated with specific tasks. However, although object-based approaches have proven popular, object recognition remains a challenge due to the intra-class variations found in unconstrained scenarios. As a consequence, the performance of current systems is far from satisfactory

Non-Gaussian diffusive fluctuations in Dirac fluids

Dirac fluids - interacting systems obeying particle-hole symmetry and Lorentz invariance - are among the simplest hydrodynamic systems; they have also been studied as effective descriptions of transport in strongly interacting Dirac semimetals. Direct experimental signatures of the Dirac fluid are elusive, as its charge transport is diffusive as in conventional metals. In this paper we point out a striking consequence of fluctuating relativistic hydrodynamics: the full counting statistics (FCS) of charge transport is highly non-gaussian. We predict the exact asymptotic form of the FCS, which generalizes a result previously derived for certain interacting integrable systems. A consequence is that, starting from quasi-one dimensional nonequilibrium initial conditions, charge noise in the hydrodynamic regime is parametrically enhanced relative to that in conventional diffusive metals.Comment: 5 pages, 2 figure

Manhattan Cutset Sampling and Sensor Networks.

Cutset sampling is a new approach to acquiring two-dimensional data, i.e., images, where values are recorded densely along straight lines. This type of sampling is motivated by physical scenarios where data must be taken along straight paths, such as a boat taking water samples. Additionally, it may be possible to better reconstruct image edges using the dense amount of data collected on lines. Finally, an advantage of cutset sampling is in the design of wireless sensor networks. If battery-powered sensors are placed densely along straight lines, then the transmission energy required for communication between sensors can be reduced, thereby extending the network lifetime. A special case of cutset sampling is Manhattan sampling, where data is recorded along evenly-spaced rows and columns. This thesis examines Manhattan sampling in three contexts. First, we prove a sampling theorem demonstrating an image can be perfectly reconstructed from Manhattan samples when its spectrum is bandlimited to the union of two Nyquist regions corresponding to the two lattices forming the Manhattan grid. An efficient ``onion peeling'' reconstruction method is provided, and we show that the Landau bound is achieved. This theorem is generalized to dimensions higher than two, where again signals are reconstructable from a Manhattan set if they are bandlimited to a union of Nyquist regions. Second, for non-bandlimited images, we present several algorithms for reconstructing natural images from Manhattan samples. The Locally Orthogonal Orientation Penalization (LOOP) algorithm is the best of the proposed algorithms in both subjective quality and mean-squared error. The LOOP algorithm reconstructs images well in general, and outperforms competing algorithms for reconstruction from non-lattice samples. Finally, we study cutset networks, which are new placement topologies for wireless sensor networks. Assuming a power-law model for communication energy, we show that cutset networks offer reduced communication energy costs over lattice and random topologies. Additionally, when solving centralized and decentralized source localization problems, cutset networks offer reduced energy costs over other topologies for fixed sensor densities and localization accuracies. Finally, with the eventual goal of analyzing different cutset topologies, we analyze the energy per distance required for efficient long-distance communication in lattice networks.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120876/1/mprelee_1.pd

Modeling and querying spatio-temporal clinical databases with multiple granularities

In molti campi di ricerca, i ricercatori hanno la necessit\ue0 di memorizzare, gestire e interrogare dati spazio-temporali. Tali dati sono classici dati alfanumerici arricchiti per\uf2 con una o pi\uf9 componenti temporali, spaziali e spazio-temporali che, con diversi possibili significati, li localizzano nel tempo e/o nello spazio. Ambiti in cui tali dati spazio-temporali devono essere raccolti e gestiti sono, per esempio, la gestione del territorio o delle risorse naturali, l'epidemiologia, l'archeologia e la geografia. Pi\uf9 in dettaglio, per esempio nelle ricerche epidemiologiche, i dati spazio-temporali possono servire a rappresentare diversi aspetti delle malattie e delle loro caratteristiche, quali per esempio la loro origine, espansione ed evoluzione e i fattori di rischio potenzialmente connessi alle malattie e al loro sviluppo. Le componenti spazio-temporali dei dati possono essere considerate come dei "meta-dati" che possono essere sfruttati per introdurre nuovi tipi di analisi sui dati stessi. La gestione di questi "meta-dati" pu\uf2 avvenire all'interno di diversi framework proposti in letteratura. Uno dei concetti proposti a tal fine \ue8 quello delle granularit\ue0. In letteratura c'\ue8 ampio consenso sul concetto di granularit\ue0 temporale, di cui esistono framework basati su diversi approcci. D'altro canto, non esiste invece un consenso generale sulla definizione di un framework completo, come quello delle granularit\ue0 temporali, per le granularit\ue0 spaziali e spazio-temporali. Questa tesi ha lo scopo di riempire questo vuoto proponendo un framework per le granularit\ue0 spaziali e, basandosi su questo e su quello gi\ue0 presente in letteratura per le granularit\ue0 temporali, un framework per le granularit\ue0 spazio-temporali. I framework proposti vogliono essere completi, per questo, oltre alle definizioni dei concetti di granularit\ue0 spaziale e spazio-temporale, includono anche la definizione di diversi concetti legati alle granularit\ue0, quali per esempio le relazioni e le operazioni tra granularit\ue0. Le relazioni permettono di conoscere come granularit\ue0 diverse sono legate tra loro, costruendone anche una gerarchia. Tali informazioni sono poi utili al fine di conoscere se e come \ue8 possibile confrontare dati associati e rappresentati con granularit\ue0 diverse. Le operazioni permettono invece di creare nuove granularit\ue0 a partire da altre granularit\ue0 gi\ue0 definite nel sistema, manipolando o selezionando alcune loro componenti. Basandosi su questi framework, l'obiettivo della tesi si sposta poi sul mostrare come le granularit\ue0 possano essere utilizzate per arricchire basi di dati spazio-temporali gi\ue0 esistenti al fine di una loro migliore e pi\uf9 ricca gestione e interrogazione. A tal fine, proponiamo qui una base di dati per la gestione dei dati riguardanti le granularit\ue0 temporali, spaziali e spazio-temporali. Nella base di dati proposta possono essere rappresentate tutte le componenti di una granularit\ue0 come definito nei framework proposti. La base di dati pu\uf2 poi essere utilizzata per estendere una base di dati spazio-temporale esistente aggiungendo alle tuple di quest'ultima delle referenze alle granularit\ue0 dove quei dati possono essere localizzati nel tempo e/o nel spazio. Per dimostrare come ci\uf2 possa essere fatto, nella tesi introduciamo la base di dati sviluppata ed utilizzata dal Servizio Psichiatrico Territoriale (SPT) di Verona. Tale base di dati memorizza le informazioni su tutti i pazienti venuti in contatto con l'SPT negli ultimi 30 anni e tutte le informazioni sui loro contatti con il servizio stesso (per esempio: chiamate telefoniche, visite a domicilio, ricoveri). Parte di tali informazioni hanno una componente spazio-temporale e possono essere quindi analizzate studiandone trend e pattern nel tempo e nello spazio. Nella tesi quindi estendiamo questa base di dati psichiatrica collegandola a quella proposta per la gestione delle granularit\ue0. A questo punto i dati psichiatrici possono essere interrogati anche sulla base di vincoli spazio-temporali basati su granularit\ue0. L'interrogazione di dati spazio-temporali associati a granularit\ue0 richiede l'utilizzo di un linguaggio d'interrogazione che includa, oltre a strutture, operatori e funzioni spazio-temporali per la gestione delle componenti spazio-temporali dei dati, anche costrutti per l'utilizzo delle granularit\ue0 nelle interrogazioni. Quindi, partendo da un linguaggio d'interrogazione spazio-temporale gi\ue0 presente in letteratura, in questa tesi proponiamo anche un linguaggio d'interrogazione che permetta ad un utente di recuperare dati da una base di dati spazio-temporale anche sulla base di vincoli basati su granularit\ue0. Il linguaggio viene introdotto fornendone la sintassi e la semantica. Inoltre per mostrare l'effettivo ruolo delle granularit\ue0 nell'interrogazione di una base di dati clinica, mostreremo diversi esempi di interrogazioni, scritte con il linguaggio d'interrogazione proposto, sulla base di dati psichiatrica dell'SPT di Verona. Tali interrogazioni spazio-temporali basate su granularit\ue0 possono essere utili ai ricercatori ai fini di analisi epidemiologiche dei dati psichiatrici.In several research fields, temporal, spatial, and spatio-temporal data have to be managed and queried with several purposes. These data are usually composed by classical data enriched with a temporal and/or a spatial qualification. For instance, in epidemiology spatio-temporal data may represent surveillance data, origins of disease and outbreaks, and risk factors. In order to better exploit the time and spatial dimensions, spatio-temporal data could be managed considering their spatio-temporal dimensions as meta-data useful to retrieve information. One way to manage spatio-temporal dimensions is by using spatio-temporal granularities. This dissertation aims to show how this is possible, in particular for epidemiological spatio-temporal data. For this purpose, in this thesis we propose a framework for the definition of spatio-temporal granularities (i.e., partitions of a spatio-temporal dimension) with the aim to improve the management and querying of spatio-temporal data. The framework includes the theoretical definitions of spatial and spatio-temporal granularities (while for temporal granularities we refer to the framework proposed by Bettini et al.) and all related notions useful for their management, e.g., relationships and operations over granularities. Relationships are useful for relating granularities and then knowing how data associated with different granularities can be compared. Operations allow one to create new granularities from already defined ones, manipulating or selecting their components. We show how granularities can be represented in a database and can be used to enrich an existing spatio-temporal database. For this purpose, we conceptually and logically design a relational database for temporal, spatial, and spatio-temporal granularities. The database stores all data about granularities and their related information we defined in the theoretical framework. This database can be used for enriching other spatio-temporal databases with spatio-temporal granularities. We introduce the spatio-temporal psychiatric case register, developed by the Verona Community-based Psychiatric Service (CPS), for storing and managing information about psychiatric patient, their personal information, and their contacts with the CPS occurred in last 30 years. The case register includes both clinical and statistical information about contacts, that are also temporally and spatially qualified. We show how the case register database can be enriched with spatio-temporal granularities both extending its structure and introducing a spatio-temporal query language dealing with spatio-temporal data and spatio-temporal granularities. Thus, we propose a new spatio-temporal query language, by defining its syntax and semantics, that includes ad-hoc features and constructs for dealing with spatio-temporal granularities. Finally, using the proposed query language, we report several examples of spatio-temporal queries on the psychiatric case register showing the ``usage'' of granularities and their role in spatio-temporal queries useful for epidemiological studies