Search PubMed⌕ Search

Biomedical subjects

H M Hastings

Publications and source records attributed to H M Hastings.

14 recordsLinked to original sources
PubMed1996

Nonlinear dynamics in ventricular fibrillation.

Electrogram recordings of ventricular fibrillation appear complex and possibly chaotic. However, sequences of beat-to-beat intervals obtained from these recordings are generally short, making it difficult to explicitly demonstrate nonlinear dynamics. Motivated by the work of Sugihara on atmospheric dynamics and the Durbin-Watson test for nonlinearity, we introduce a new statistical test that recovers significant dynamical patterns from smoothed lag plots. This test is used to show highly significant nonlinear dynamics in a stable canine model of ventricular fibrillation.

Algorithms↗
PubMed1996

The spatial distribution of pancreatic islets follows a universal power law.

In a previous report we quantified the apparently complex and irregular distribution of pancreatic islets in the guinea pig by showing that they formed a set of cluster or correlation dimension approximately 2.5. Here we show that this distribution holds in a wide range of mammalian species and through ontogenetic development in the guinea pig. These results strongly suggest that islet formation follows an iterative or fractal rule which is universal among mammals.

Animals↗
PubMed1996

Scatter factor protein levels in human breast cancers: clinicopathological and biological correlations.

Scatter factor (SF) is an invasogenic and angiogenic cytokine the cellular receptor of which is encoded by a proto-oncogene (c-met). We measured the immunoreactive SF content (nanograms of SF per milligram of protein) in tissue extracts from 166 breast cancers and correlated the values with various known prognostic parameters. Invasive cancers had nearly four times greater SF content than did ductal carcinoma in situ, and the difference was statistically significant (P < 0.02, two-tailed t-test). However, there were no significant differences in SF content among different histological types of invasive cancer. Invasive cancers that had spread to axillary lymph nodes exhibited higher SF content than did invasive cancers without regional spread (P < 0.02), but the difference in SF content between node-positive and node-negative tumors was not as great as that between invasive and ductal carcinoma in situ tumors. There was a trend toward increased SF content in larger primary tumors as compared with smaller tumors, but statistical comparison revealed borderline significance (0.05 < P < 1.0). There was no significant correlation between SF content and other parameters, including estrogen receptor, progesterone receptor, DNA ploidy, S phase, or Scarff-Bloom-Richardson score. We also measured the content of von Willebrand factor (a marker of blood vessels) and interleukin-1 beta (a pro-inflammatory cytokine) in the same tumor extracts. SF content showed a strong positive correlation with von Willebrand factor content (P < 0.001) but did not appear to be correlated with interleukin-1 beta. These findings suggest that SF is correlated with several other clinicopathological indicators of aggressive tumor behavior, consistent with the hypothesis that SF is a biological factor that may play a role in breast cancer pathogenesis.

Biomarkers, Tumor↗
PubMed1992

Statistical geometry of pancreatic islets.

Quantitative histomorphometric studies of the dynamics of growth and development of pancreatic islets in normal and pathological states pose substantial methodological and conceptual problems. We address these problems with the geometry of random fractals, and apply our methods to the analysis of islet regeneration in the alloxan-treated guinea-pig. In both experimental islet-regenerated and control animals, islet centres are found to cluster in similar fractal subsets of dimension strictly less than 3, in agreement with the postulated origin of islets along a system of ductules, and suggesting that regeneration follows the same mathematical dynamics as original islet formation.

Alloxan↗
PubMed1991

Remarks on population planning and control.

We investigate the use of control theory in population planning and show how the use of age at first birth, birth interval, and sex ratio as control variables leads to a practical, fault tolerant approach to population planning and control.

Age Factors↗
PubMed1989

Evolutionary learning and hierarchical Markov systems.

The observation is made that various forms of evolutionary learning systems and classical evolutionary processes can be formally described as hierarchical systems of Markov processes. This leads to a simplification of issues such as convergence criteria and limiting behavior of such systems. The hierarchical structures in question are derived from the notion of rules and meta-rules for moving on graphs studied previously.

Biological Evolution↗
PubMed1989

Sixty million connections per second.

The purpose of this note is to report processing in a feedforward neural network at a peak speed of 59.9 million connections per second. The network algorithm was coded in Fortran and executed on a CRAY XMP-1, a high speed general purpose vector machine.

Artificial Intelligence↗
PubMed1986

Sex and computing.

The computational power of asexual and sexual reproduction is explored with the conclusion that sexual reproduction probably offers significantly greater computational power. This at least partially explains the evolution of sex.

Biological Evolution↗
PubMed1985

Low dissipation computing in biological systems.

Biological systems frequently need to solve many computationally hard decision and optimization problems. The solution of these problems by digital computers as presently understood requires exponentially large energy dissipation. This severely restricts the ability of digital computers to attack such problems. We shall show that only polynomial dissipation is required to solve these problems adequately by "physical annealing", as realized in the genetic system, making these problems tractable energetically.

Biometry↗
PubMed1984

Stability of large systems.

We use the May-Wigner Stability Theorem (Geman (1984) preprint, Brown University; Hastings (1984) preprint, Hofstra University), to study the Lyapunov and structural stability of "real" large systems. Here are our new main results. For large systems which satisfy certain natural scaling relations (Harrison, Am. Natur., 113 (1979) 659; May (1979) Blackwell Scientific, Oxford), Lyapunov stability tends to increase with increasing complexity. However, at least one aspect of structural stability decreases: both competitive and cooperative effects can rapidly destabilize such a system. Finally, we observe that random matrices which satisfy the hypotheses and stability criterion of the May-Wigner theorem are asymptotically of the form 'rotation followed by multiplication by lambda,lambda less than 1'. This allows an easy analysis of the effects of noise in these systems. We conclude by briefly discussing applications to analysis of stability of systems such as the world economy, power networks, and the immune system.

Cybernetics↗
PubMed1982

Stochastic information processing biological systems.

We propose a simple, biochemically-based model for stochastic information processing in brain, genetic, and, consequently, evolutionary modelling. The essential features of reaction-diffusion processes are realized by intrinsically stochastic probabilistic automata (Shannon and Weaver, 1948; see also Ashby, 1958, von Neumann, 1966; Burks, 1970; Paz, 1971) whose definition extends that of classical automata. (Classical automata are deterministic; earlier work on probabilistic automata focused on error correction and at least approximating deterministic behavior.) We call these probabilistic automata biochemical to emphasize the role of intrinsically stochastic process in biological information processing. Our model yields descriptions of gradualism (Conrad, 1974), learning, and apparent inefficiencies in the brain, and partially resolves the near impossibility of simultaneous point mutations (Conrad, 1972, 1978) in genetics. The genetic model implies an evolutionary dynamics of punctuated equilibria (Gould and Eldredge, 1977).

Animals↗
PubMed1982

Time scales, persistence and patchiness.

We consider competition in patch-dynamical and more general diffusion-extinction models. These models identify three time scales in ecology. We begin with a reformulation of Levin's 1978 basic model, using a geometric description of diffusion. As in Levin's model, diffusion drives short-term dynamics, and longer-term dynamics depends upon a diffusion-extinction ratio; maximizing this ratio is shown to be an Evolutionarily Stable Strategy. Over still longer times, the effect of organisms upon their environments becomes paramount. We use Mandelbrot's 1977 fractals to develop these models, and thus relate persistence with relative patchiness. Finally, we propose a numerical measure, the fractal exponent H, of successional stage.

Biological Evolution↗