The arithmetic of receiver scheduling for electronic support

In Electronic Support, it is well known that periodic search strategies for swept-frequency superheterodyne receivers (SHRs) can cause synchronisation with the radar it seeks to detect. Synchronisation occurs when the periods governing the search strategies of the SHR and radar are commensurate. The result may be that the radar is never detected. This paper considers the synchronisation problem in depth. We find that there are usually a finite number of synchronisation ratios between the radar’s scan period and the SHR’s sweep period. We develop three geometric constructions by which these ratios can be found and we relate them to the Farey series. The ratios may be used to determine the intercept time for any combination of scan and sweep period. This theory can assist the operator of an SHR in selecting a sweep period that minimises the intercept time against a number of radars in a threat emitter list.

Cognitive deficits, length of illness and symptom severity in schizophrenia

Background Research using neuropsychological testing has demonstrated that patients with schizophrenia show deficits in multiple neurocognitive domains. The aim of this study is to identify cognitive deficits that correlate with length of illness and symptom severity. Method Twenty clinically stable outpatients with chronic schizophrenia (18M : 2F) and 14 healthy controls (13M : 1F), matched on age, gender and parental education, were administered a neuropsychological battery consisting of the Hayling Sentence Completion Test (HSCT), WMS-III Verbal Paired Associates & Letter Number Sequencing, Modified Card Sort Test (MCST), Pyramids & Palm Trees Test, National Adult Reading Test (NART), Controlled Oral Word Association Test (COWAT), and WAIS-III. Severity of symptoms was rated with the Structured Clinical Interview – Positive and Negative Syndromes Scale (SCI-PANSS). Results In comparison to controls, patients showed significant deficits on all of the neuropsychological tasks except for the COWAT. MCST total categories, NART, Verbal IQ and arithmetic, similarities & digit symbol of the WAIS-III had the largest effect size between the groups. The longer the illness duration, the poorer the performance on WAISIII block design and the lower the performance IQ score. The poorer the performance on WMS-III letter number sequencing, the greater the positive symptoms, negative symptoms and general psychopathology. Conclusion Compared to controls, patients showed large effect sizes on measures of executive functioning, intelligence, working memory, verbal comprehension and speed of processing. The findings suggest that impairment in executive functioning and performance IQ is associated with length of illness, while impairment in working memory is associated with heightened symptom severity.

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

Patchy populations in stochastic environments: Critical number of patches for persistence

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be greater than or equal to1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the persistence of the population. As the magnitude of environmental fluctuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested decreases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environmental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily distributed organisms that are restricted to a small number of habitat patches.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

A real-time asymmetric multiprocessor-reconfigurable system-on-chip architecture

We propose an asymmetric multi-processor SoC architecture, featuring a master CPU running uClinux, and multiple loosely-coupled slave CPUs running real-time threads assigned by the master CPU. Real-time SoC architectures often demand a compromise between a generic platform for different applications, and application-specific customizations to achieve performance requirements. Our proposed architecture offers a generic platform running a conventional embedded operating system providing a traditional software-oriented development approach, while multiple slave CPUs act as a dedicated independent real-time threads execution unit running in parallel of master CPU to achieve performance requirements. In this paper, the architecture is described, including the application / threading development environment. The performance of the architecture with several standard benchmark routines is also analysed.