An incremental algorithm for generating all minimal models

AbstractThe task of generating minimal models of a knowledge base is at the computational heart of diagnosis systems like truth maintenance systems, and of nonmonotonic systems like autoepistemic logic, default logic, and disjunctive logic programs. Unfortunately, it is NP-hard. In this paper we present a hierarchy of classes of knowledge bases, Ψ1,Ψ2,… , with the following properties: first, Ψ1 is the class of all Horn knowledge bases; second, if a knowledge base T is in Ψk, then T has at most k minimal models, and all of them may be found in time O(lk2), where l is the length of the knowledge base; third, for an arbitrary knowledge base T, we can find the minimum k such that T belongs to Ψk in time polynomial in the size of T; and, last, where K is the class of all knowledge bases, it is the case that ⋃i=1∞Ψi=K, that is, every knowledge base belongs to some class in the hierarchy. The algorithm is incremental, that is, it is capable of generating one model at a time

Reasoning with minimal models: efficient algorithms and applications

AbstractReasoning with minimal models is at the heart of many knowledge-representation systems. Yet it turns out that this task is formidable, even when very simple theories are considered. In this paper, we introduce the elimination algorithm, which performs, in linear time, minimal model finding and minimal model checking for a significant subclass of positive CNF theories which we call positive head-cycle-free (HCF) theories. We also prove that the task of minimal entailment is easier for positive HCF theories than it is for the class of all positive CNF theories. Finally, we show how variations of the elimination algorithm can be applied to allow queries posed on disjunctive deductive databases and disjunctive default theories to be answered in an efficient way

Genetic variation at flowering time loci in wild and cultivated barley

The worldwide spread of barley cultivation required adaptation to agricultural environments far distant from those found in its centre of domestication. An important component of this adaptation is the timing of flowering, achieved predominantly in response to day length and temperature. Here, we use a collection of cultivars, landraces and wild barley accessions to investigate the origins and distribution of allelic diversity at four major flowering time loci, mutations at which have been under selection during the spread of barley cultivation into Europe. Our findings suggest that while mutant alleles at the PPD-H1 and PPD-H2 photoperiod loci occurred pre-domestication, the mutant vernalization non-responsive alleles utilized in landraces and cultivars at the VRN-H1 and VRN-H2 loci occurred post-domestication. The transition from wild to cultivated barley is associated with a doubling in the number of observed multi-locus flowering-time haplotypes, suggesting that the resulting phenotypic variation has aided adaptation to cultivation in the diverse ecogeographic locations encountered. Despite the importance of early-flowering alleles during the domestication of barley in Europe, we show that novel VRN alleles associated with early flowering in wild barley have been lost in domesticates, highlighting the potential of wild germplasm as a source of novel allelic variation for agronomic traits

On the ecology of hyperscum-forming Microsystis aeruginosa in a hypertrophic African lake.

Thesis (Ph.D.)-University of Natal, Pietermaritzburg, 1987.Light is the primary source of energy in most of earth's ecosystems . In freshwater ecosystems the major interacting factors that determine the abundance and species composition of planktonic phototrophs, the primary utilizers of light, are nutrients, temperature and light. With increasing eutrophication and declining geographical latitude, nutrient availability becomes in excess of the organisms' requirements, water temperature is more favourable for growth, and community structure depends to a greater extent on light availability. This study focuses on the population dynamics of the bloom-forming cyanobacterium Microcystis aeruginosa Kutz. emend. Elenkin in subtropical Hartbeespoort Dam, South Africa. The objectives of the study were: to investigate the annual cycle, and the factors leading to the dominance and success of the cyanobacterium in this hypertrophic, warm monomictic lake, where light availability is the major factor limiting phytoplankton growth rates; to study the surface blooms and ultimately hyperscums that this species forms; and to assess the ecological significance of hyperscums. A 4. 5-years field study of phytoplankton abundance and species composition in relation to changes in the physical environment, was undertaken. The hypothesis was that M. aeruginosa dominated the phytoplankton population (> 80 % by volume) up to 10 months of every year because it maintained itself within shallow diurnal mixed layers and was thus ensured access to light. It was shown that wind speeds over Hartbeespoort Dam were strong enough to mix the epilimnion (7 - 18 m depth) through Langmuir circulations only 12 % of the time. At other times solar heating led to the formation of shallow ( < 2 m) diurnal mixed layers (Z[1]) that were usually shallower than the euphotic zone (Zeu; x = 3.5 m), while the seasonal mixed layer (zrn) was always deeper than Zeu. From the correspondence between vertical gradients of chlorophyll a concentrations and density gradients, when M. aeruginosa was dominant, it was implied that this species maintained the bulk of its population within Z[1]. Under the same mixing conditions non-buoyant species sank into dark layers. These data point out the importance of distinguishing between Zrn and Z[1], and show the profound effect that the daily pattern of Z[1], as opposed to the seasonal pattern of Zrn can have on phytoplankton species composition Adaptation to strong light intensities at the surface was implicated from low cellular chlorophyll a content (0.132 μg per 10[6] cells) and high I[k ](up to 1230 μE m⁻² S¯¹). Ensured access to light, the postmaximum summer populations persisted throughout autumn and winter, despite suboptimal winter temperatures, by sustaining low losses. Sedimentation caused a sharp decline of the population at the end of winter each year and a short ( 2-3 months) successional episode follCMed, rut by late spring M. aeruginosa. was again dominant. The mixing regime in Hartbeespoort Dam and the buoyancy mechanism of M. aeruginosa led to frequent formation of surface bloons and ultimately hyperscums. Hyperscums were defined as thick (decimeters), crusted, buoyant cyanobacterial mats, in which the organisms are so densely packed that free water is not evident. In Hartbeespoort Dam in winter M. aeruginosa formed hyperscums that measured up to 0.75 m in thickness, covered more than a hectare, contained up to 2 tonnes of chlorophyll a, and persisted for 2 - 3 monnths. Hyperscum formation was shown to depend upon the coincidence of the following preconditions: a large, pre-existing standing crop of positively buoyant cyanobacteria; turbulent mixing that is too weak to overcome the tendency of the cells to float, over prolonged periods (weeks); lake morphometry with wind-protected sites on lee shores; and high incident solar radiation. The infrequent occurrence of hyperscums can be attributed to the rare co-occurrence of these conditions. Colonies in the hyperscum were arranged in a steep vertical gradient, where colony compaction increased exponentially with decreasing distance form the surface. This structure was caused by evaporative dehydration at the surface, and by the buoyancy regulation mechanism of M. aeruginosa., which results with cells being unable to lose boyancy when deprived access to light from above. The mean chlorophyll a concentration and water content were 3.0 g 1¯¹ and 14 % at the surface crust, 1.0 g 1¯¹ and 77 % at a few mm depth, and 0.3 g 1¯¹ and 94 % at 10 cm depth, where M. aeruginosa cell concentration exceeded 109 ml¯¹. A consequence of the high cell and pigment concentrations was that light penetrated only 3 mm or less, below which anaerobic, highly reduced conditions developed. Nutrient concentrations in hyperscum interstitial water, collected by dialysis, increased dramatically with time (phosphate: 30-fold over 3 months; ammonia: 260-fold). Volatile fatty acids, intermediate metabolites in anaerobic decomposition processes, were present. Gas bubbles trapped within the hyperscum contained methane (28 %) , and CO[2] (19 %), the major end products of anaerobic decomposition, and no oxygen. The structure and function of M. aeruginosa in hyperscum was examined in relation to the vertical position of colonies and the duration of exposure to hyperscum condition. Colonies and cells collected from 10 em depth in the hyperscum were similar in their morphology (light and fluorescent microscopy) and ultrastructure (transmission and scanning electron microscopy) to those of colonies from surface blooms in the main basin of the lake. With declining depth over the uppermost 10 mm of the hyperscum cells appeared increasingly dehydrated, decomposed and' colonized by bacteria. studies employing microelectrode techniques demonstrated that photosynthetic activity of colonies at the surface of a newly accumulated hyperscum rapidly photoinhibited, substrate-limited, and then ceased within hours of exposure to light intensities > 625 μE m⁻² S¯¹. Photooxidative death followed. The dead cells dehydrated to form the dry crust, from underneath. and space was thus created for colonies rising Cells collected from 10 cm depth retained their photosynthetic capacity ([14]C-uptake experiments) throughout the hyperscum season, although a considerable decline in this capacity was noted over the last (third) month. Altogether the data indicated that spatial separation developed within the hyperscum, between a zone at the surface of lethal physical conditions, a zone beneath the surface of stressful and probably lethal chemical conditions, and a deeper zone of more moderate conditions, which nevertheless, deteriorated after 2 - 3 months. A conceptual model describing the fate of a colony entering a hyperscum was then proposed. According to this model, a colony that arrives below a hyperscum and is not carried away by currents, becomes over-buoyant in the dark and floats into the bottom of the hyperscum. With time it migrates towards, due to its own positive buoyancy, the buoyancy of colonies rising from underneath, and the collapse of cells at the top. It survives in the dark, anaerobic environment by maintaining low levels of basal metabolism while utilizing stored reserves. Depending on weather conditions, the colony mayor may not remain within the hyperscum long enough to reach the zone of decomposition near the surface, where it would die. With the aging of the hyperscum and the accumulation of trapped decomposition products, the zone of decomposition expands. Thus, a hyperscum is essentially a site of a continuous cycle of death and dehydration at the surface and upward migration of colonies from below to replace those that died, although not all colonies entering the hyperscum necessarily reach the lethal zone. The formation of hyperscums was shown to have no major influence on the annual cycle of M. aeruginosa in Hartbeespoort Dam. The seasonality of increase and decline of the planktonic population was similar from year to year, irrespective of whether or not hyperscums formed. The phenomenon of hyperscums demonnstrated that, as Reynolds and Walsby (1975) claimed, thick cyanobacterial water-blooms do form incidentally and have no vital function in the biology of the organism. water temperature did have a major effect on the annual cycle of this species in Hartbeespoort Dam. In temperate lakes the low water temperatures in autumn and winter (<10° C) cause M. aeruginosa to lose its ability to regain buoyancy in the dark, and consequently it sinks to bottom sediments. The higher ( > l2°C) minimum winter temperature in Hartbeespoort Dam leads to the maintenance of a relatively large residual planktonic population throughout the winter. Unlike the case in temperate lakes, the long-term survival of M. aeruginosa in warm-water lakes probably does not depend on winter benthic stocks for the provision of an inoculum for the following growth season

Inter-trial neuronal activity in inferior temporal cortex: a putative vehicle to generate long-term visual associations.

When monkeys perform a delayed match-to-sample task, some neurons in the anterior inferotemporal cortex show sustained activity following the presentation of specific visual stimuli, typically only those that are shown repeatedly. When sample stimuli are shown in a fixed temporal order, the few images that evoke delay activity in a given neuron are often neighboring stimuli in the sequence, suggesting that this delay activity may be the neural correlate of associative long-term memory. Here we report that stimulus-selective sustained activity is also evident following the presentation of the test stimulus in the same task. We use a neural network model to demonstrate that persistent stimulus-selective activity across the intertrial interval can lead to similar mnemonic representations (distributions of delay activity across the neural population) for neighboring visual stimuli. Thus, inferotemporal cortex may contain neural machinery for generating long-term stimulus-stimulus associations

Response of Spiking Neurons to Correlated Inputs

The effect of a temporally correlated afferent current on the firing rate of a leaky integrate-and-fire (LIF) neuron is studied. This current is characterized in terms of rates, auto and cross-correlations, and correlation time scale $\tau_c$ of excitatory and inhibitory inputs. The output rate $\nu_{out}$ is calculated in the Fokker-Planck (FP) formalism in the limit of both small and large $\tau_c$ compared to the membrane time constant $\tau$ of the neuron. By simulations we check the analytical results, provide an interpolation valid for all $\tau_c$ and study the neuron's response to rapid changes in the correlation magnitude.Comment: 4 pages, 3 figure