How many photons are needed to distinguish two transparencies?

We give a bound on the minimum number of photons that must be absorbed by any quantum protocol to distinguish between two transparencies. We show how a quantum Zeno method in which the angle of rotation is varied at each iteration can attain this bound in certain situations.Comment: 5 pages, 4 figure

Learning from Minimum Entropy Queries in a Large Committee Machine

In supervised learning, the redundancy contained in random examples can be avoided by learning from queries. Using statistical mechanics, we study learning from minimum entropy queries in a large tree-committee machine. The generalization error decreases exponentially with the number of training examples, providing a significant improvement over the algebraic decay for random examples. The connection between entropy and generalization error in multi-layer networks is discussed, and a computationally cheap algorithm for constructing queries is suggested and analysed.Comment: 4 pages, REVTeX, multicol, epsf, two postscript figures. To appear in Physical Review E (Rapid Communications

The time-profile of cell growth in fission yeast: model selection criteria favoring bilinear models over exponential ones

BACKGROUND: There is considerable controversy concerning the exact growth profile of size parameters during the cell cycle. Linear, exponential and bilinear models are commonly considered, and the same model may not apply for all species. Selection of the most adequate model to describe a given data-set requires the use of quantitative model selection criteria, such as the partial (sequential) F-test, the Akaike information criterion and the Schwarz Bayesian information criterion, which are suitable for comparing differently parameterized models in terms of the quality and robustness of the fit but have not yet been used in cell growth-profile studies. RESULTS: Length increase data from representative individual fission yeast (Schizosaccharomyces pombe) cells measured on time-lapse films have been reanalyzed using these model selection criteria. To fit the data, an extended version of a recently introduced linearized biexponential (LinBiExp) model was developed, which makes possible a smooth, continuously differentiable transition between two linear segments and, hence, allows fully parametrized bilinear fittings. Despite relatively small differences, essentially all the quantitative selection criteria considered here indicated that the bilinear model was somewhat more adequate than the exponential model for fitting these fission yeast data. CONCLUSION: A general quantitative framework was introduced to judge the adequacy of bilinear versus exponential models in the description of growth time-profiles. For single cell growth, because of the relatively limited data-range, the statistical evidence is not strong enough to favor one model clearly over the other and to settle the bilinear versus exponential dispute. Nevertheless, for the present individual cell growth data for fission yeast, the bilinear model seems more adequate according to all metrics, especially in the case of wee1Δ cells

The Virulence in the Guinea-pig of Tubercle Bacilli Isolated before Treatment from South Indian Patients with Pulmonary Tuberculosis: 1. Homogeneity of the Investigation and a Critique of the Virulence Test

A series of studies on the virulence in the guinea-pig of tubercle bacilli isolated before treatment from Indian tuberculous patients admitted to a controlled comparison of different regimens of domiciliary chemotherapy has recently been undertaken by the Tuberculosis Chemotherapy Centre, Madras. The main object of these studies was to determine whether the differences in virulence of the tubercle bacilli obtained from Indian patients before the start of chemotherapy were related to the severtiy or type of the patients’ disease at that time and to the subsequent response to treatment. Before these relationships could be‘ investigated, however, it was necessary to find out whether the results of the virulence tests, which were carried out over a period of two-and-a-half years at the Centre and at the Microbiological Research Establishment, Porton, England, could be considered as a unified whole-that, is, as if they had all been done on the same day in the same laboratory. A proportion of the cultures was stored at – 20°C for 44-78 weeks, but this did not affect their virulence. Inter-experimental variation was found to be small in the Porton series of tests and undetectable in the Madras series, and the results in the latter series could be successfully adjusted to those in the former by allowing for differences in the means and standard deviations of the distributions for the two series. The measure of virulence used was found to be reasonably acceptable for the analysis of variance technique. Suggestions are made as to ways of improving the efficiency of the experimental design in future studies

Analytical and Numerical Study of Internal Representations in Multilayer Neural Networks with Binary Weights

We study the weight space structure of the parity machine with binary weights by deriving the distribution of volumes associated to the internal representations of the learning examples. The learning behaviour and the symmetry breaking transition are analyzed and the results are found to be in very good agreement with extended numerical simulations.Comment: revtex, 20 pages + 9 figures, to appear in Phys. Rev.

Storage capacity of correlated perceptrons

We consider an ensemble of $K$ single-layer perceptrons exposed to random inputs and investigate the conditions under which the couplings of these perceptrons can be chosen such that prescribed correlations between the outputs occur. A general formalism is introduced using a multi-perceptron costfunction that allows to determine the maximal number of random inputs as a function of the desired values of the correlations. Replica-symmetric results for $K=2$ and $K=3$ are compared with properties of two-layer networks of tree-structure and fixed Boolean function between hidden units and output. The results show which correlations in the hidden layer of multi-layer neural networks are crucial for the value of the storage capacity.Comment: 16 pages, Latex2

Modeling oscillatory Microtubule--Polymerization

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates as well as typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold a so--called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure

The Virulence in the Guinea-pig of Tubercle Bacilli Isolated before Treatment from South Indian Patients with Pulmonary Tuberculosis 3. Virulence related to Pretreatment Status of Disease and to Response to Chemotherapy

This is the last of a series of three reports from the Tuberculosis Chemotherapy Centre Madras, on a study undertaken with the object of finding out whether differences in the virulence in the guinea-pig of tubercle bacilli isolated from South Indian tuberculous patients before the start of chemotherapy are related to the severity of the patients’ disease on admission to treatment and to the subsequent response to chemotherapy. The 281 patients in this study were drawn from the patients admitted to a l-year comparison of four domiciliary chemotherapeutic regimens : (a) 3.9-5.5 mg/kg isoniazid plus 0.2-0.3 g/kg sodium PAS daily, divided into two doses (PH series) ; (b) 7.8-9.6 mg/kg isoniazid alone daily in one dose (HI-I series) ; (c) 7.8-9.6 mg/kg isoniazid alone daily, divided into two doses (HI-2 series) ; (d) 3.9-5.5 mg/kg isoniazid alone daily, divided into two doses (H series). No evidence was found of an association between the virulence of the organisms and any pretreatment condition of known prognostic importance. There was no association between pretreatment virulence and progress during treatment in the PH series (the most effective regimen). In the other series, however, the progress was more satisfactory in patients infected with organisms of low virulence than in those infected with organisms of high virulence, the association between virulence and progress attaining statistical significance in the combined HI-2 and H series (the least effective regimens) and only just failing to do so in the smaller HI-1 series. Possible explanations are put forward both for the absence of an association between virulence and severity of disease on admission and for the presence of an association between virulence and response in the patients treated with isoniazid alone

Multilayer neural networks with extensively many hidden units

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is performed by general symmetric Boolean functions whereas the hidden layer is connected to the output by either discrete or continuous couplings. Introducing an overlap in the space of Boolean functions as order parameter the storage capacity if found to scale with the logarithm of the number of implementable Boolean functions. The generalization behaviour is smooth for continuous couplings and shows a discontinuous transition to perfect generalization for discrete ones.Comment: 4 pages, 2 figure

Islands of conformational stability for Filopodia

Filopodia are long, thin protrusions formed when bundles of fibers grow outwardly from a cell surface while remaining closed in a membrane tube. We study the subtle issue of the mechanical stability of such filopodia and how this depends on the deformation of the membrane that arises when the fiber bundle adopts a helical configuration. We calculate the ground state conformation of such filopodia, taking into account the steric interaction between the membrane and the enclosed semiflexible fiber bundle. For typical filopodia we find that a minimum number of fibers is required for filopodium stability. Our calculation elucidates how experimentally observed filopodia can obviate the classical Euler buckling condition and remain stable up to several tens of . We briefly discuss how experimental observation of the results obtained in this work for the helical-like deformations of enclosing membrane tubes in filopodia could possibly be observed in the acrosomal reactions of the sea cucumber Thyone, and the horseshoe crab Limulus. Any realistic future theories for filopodium stability are likely to rely on an accurate treatment of such steric effects, as analysed in this work