The growth of a Super Stable Heap : an experimental and numerical study

We report experimental and numerical results on the growth of a super stable heap (SSH). Such a regime appears for flows in a thin channel and for high flow rate : the flow occurs atop a nearly static heap whose angle is stabilized by the flowing layer at its top and the side wall friction. The growth of the static heap is investigated in this paper. A theoretical analysis inspired by the BRCE formalism predicts the evolution of the growth process, which is confirmed by both experiments and numerical simulations. The model allows us to link the characteristic time of the growth to the exchange rate between the "moving" and "static" grains. We show that this rate is proportional to the height of the flowing layer even for thick flows. The study of upstream traveling waves sheds new light on the BCRE model

A Back-to-Basics Empirical Study of Priority Queues

The theory community has proposed several new heap variants in the recent past which have remained largely untested experimentally. We take the field back to the drawing board, with straightforward implementations of both classic and novel structures using only standard, well-known optimizations. We study the behavior of each structure on a variety of inputs, including artificial workloads, workloads generated by running algorithms on real map data, and workloads from a discrete event simulator used in recent systems networking research. We provide observations about which characteristics are most correlated to performance. For example, we find that the L1 cache miss rate appears to be strongly correlated with wallclock time. We also provide observations about how the input sequence affects the relative performance of the different heap variants. For example, we show (both theoretically and in practice) that certain random insertion-deletion sequences are degenerate and can lead to misleading results. Overall, our findings suggest that while the conventional wisdom holds in some cases, it is sorely mistaken in others

The engineering geology of the Nottingham area, UK

Nottingham was built near a crossing point on the River Trent in the East Midlands of England. Initially, the City developed on a low sandstone hill close to the north bank of the river, which provided a secure, well-drained location above the marshes that bordered the river. Geologically, Nottingham stands at the boundary between Palaeozoic rocks to the north and west, and Mesozoic and Cainozoic strata to the south and east. The area is underlain by coal-bearing Carboniferous Coal Measures, Permian dolomitic limestones, Permo-Triassic mudstones and weak sandstones, Jurassic clays and Quaternary glacial and alluvial deposits. Artificial deposits, resulting from the social, industrial and mineral extraction activities of the past cover the natural deposits over much of the area. This geological environment has underpinned the economic development of the area through the mining of coal (now largely ceased), oil extraction that was important during the Second World War, brickmaking from clays, alluvial sand and gravel extraction from the Trent Valley and gypsum extraction from the Permo-Triassic mudstones. The Permo-Triassic sandstone is a nationally important aquifer and has also been exploited at the surface and from shallow mines for sand. However, this history of the use and exploitation of mineral deposits has created a number of environmental problems including rising groundwater levels, abandoned mine shafts and mining subsidence, and, within the City itself, the occasional collapse of artificial cavities in the sandstone and contaminated land left by industrial activities. Natural constraints on development include gypsum dissolution, landslides, rockfalls, swell-shrink problems in Jurassic clays and flooding. Occasional minor earthquakes are attributed to movements due to coal mining or natural, deep geological structures. Thus, Nottingham’s geological context remains an important consideration when planning its future regeneration and development

Zipf and Heaps laws from dependency structures in component systems

Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of components emerges from architectural and specific constraints in such systems. On the other hand, general regularities may unify different systems, such as the broadly studied Zipf and Heaps laws, respectively concerning the distribution of component frequencies and their number as a function of system size. Dependency structures (i.e., directed networks encoding the dependency relations between the components in a system) were proposed recently as a possible organizing principles underlying some of the regularities observed. However, the consequences of this assumption were explored only in binary component systems, where solely the presence or absence of components is considered, and multiple copies of the same component are not allowed. Here, we consider a simple model that generates, from a given ensemble of dependency structures, a statistical ensemble of sets of components, allowing for components to appear with any multiplicity. Our model is a minimal extension that is memoryless, and therefore accessible to analytical calculations. A mean-field analytical approach (analogous to the "Zipfian ensemble" in the linguistics literature) captures the relevant laws describing the component statistics as we show by comparison with numerical computations. In particular, we recover a power-law Zipf rank plot, with a set of core components, and a Heaps law displaying three consecutive regimes (linear, sub-linear and saturating) that we characterize quantitatively

Why some heaps support constant-amortized-time decrease-key operations, and others do not

A lower bound is presented which shows that a class of heap algorithms in the pointer model with only heap pointers must spend Omega(log log n / log log log n) amortized time on the decrease-key operation (given O(log n) amortized-time extract-min). Intuitively, this bound shows the key to having O(1)-time decrease-key is the ability to sort O(log n) items in O(log n) time; Fibonacci heaps [M.L. Fredman and R. E. Tarjan. J. ACM 34(3):596-615 (1987)] do this through the use of bucket sort. Our lower bound also holds no matter how much data is augmented; this is in contrast to the lower bound of Fredman [J. ACM 46(4):473-501 (1999)] who showed a tradeoff between the number of augmented bits and the amortized cost of decrease-key. A new heap data structure, the sort heap, is presented. This heap is a simplification of the heap of Elmasry [SODA 2009: 471-476] and shares with it a O(log log n) amortized-time decrease-key, but with a straightforward implementation such that our lower bound holds. Thus a natural model is presented for a pointer-based heap such that the amortized runtime of a self-adjusting structure and amortized lower asymptotic bounds for decrease-key differ by but a O(log log log n) factor

THE EFFECTS OF ISOPROPYL N-PHENYL CARBAMATE ON THE GREEN ALGA OEDOGONIUM CARDIACUM : I. Cell Division

Cell division in vegetative filaments of the green alga Oedogonium cardiacum is presented as an experimental system. We report on how we have used this system to study the effects of isopropyl N-phenylcarbamate (IPC) on the mitotic apparatus and on the phycoplast, a planar array of cytokinetic microtubules. Polymerization of microtubules was prevented when filaments, synchronized by a light/dark regime and chilled (2°C) while in metaphase or just before phycoplast formation, were exposed to 5.5 x 10-4 M IPC and then returned to room temperature. Spindles reformed or phycoplasts formed when these filaments were transferred to growth medium free of IPC. However, the orientation of both microtubular systems was disturbed: the mitotic apparatus often contained three poles, frequently forming three daughter nuclei upon karyokinesis; the phycoplast was often stellate rather than planar, and it sometimes was displaced to the side of both daughter nuclei, resulting in a binucleate and an anucleate cell upon cytokinesis. Our results suggest that IPC (a) prevents the assembly of microtubules, (b) increases the number of functional polar bodies, and (c) affects the orientation of microtubules in O. cardiacum. High voltage (1,000 kV) electron microscopy of 0.5-µm thick sections allowed us to visualize the polar structures, which were not discernible in thin sections