Novel steady state of a microtubule assembly in a confined geometry

We study the steady state of an assembly of microtubules in a confined volume, analogous to the situation inside a cell where the cell boundary forms a natural barrier to growth. We show that the dynamical equations for growing and shrinking microtubules predict the existence of two steady states, with either exponentially decaying or exponentially increasing distribution of microtubule lengths. We identify the regimes in parameter space corresponding to these steady states. In the latter case, the apparent catastrophe frequency near the boundary was found to be significantly larger than that in the interior. Both the exponential distribution of lengths and the increase in the catastrophe frequency near the cell margin is in excellent agreement with recent experimental observations.Comment: 8 pages, submitted to Phys. Rev.

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

Altered Cerebellar Short-Term Plasticity but No Change in Postsynaptic AMPA-Type Glutamate Receptors in a Mouse Model of Juvenile Batten Disease

Juvenile Batten disease is the most common progressive neurodegenerative disorder of childhood. It is associated with mutations in the CLN3 gene, causing loss of function of CLN3 protein and degeneration of cerebellar and retinal neurons. It has been proposed that changes in granule cell AMPA-type glutamate receptors (AMPARs) contribute to the cerebellar dysfunction. In this study we compared AMPAR properties and synaptic transmission in cerebellar granule cells from wild-type and Cln3 knockout mice. In Cln3Δex1–6 cells the amplitude of AMPA-evoked whole-cell currents was unchanged. Similarly, we found no change in the amplitude, kinetics, or rectification of synaptic currents evoked by individual quanta, or in their underlying single-channel conductance. We found no change in cerebellar expression of GluA2 or GluA4 protein. By contrast, we observed a reduced number of quantal events following mossy-fiber stimulation in Sr2+, altered short-term plasticity in conditions of reduced extracellular Ca2+, and reduced mossy fiber vesicle number. Thus, while our results suggest early presynaptic changes in the Cln3Δex1–6 mouse model of juvenile Batten disease, they reveal no evidence for altered postsynaptic AMPARs

Finite size scaling in neural networks

We demonstrate that the fraction of pattern sets that can be stored in single- and hidden-layer perceptrons exhibits finite size scaling. This feature allows to estimate the critical storage capacity \alpha_c from simulations of relatively small systems. We illustrate this approach by determining \alpha_c, together with the finite size scaling exponent \nu, for storing Gaussian patterns in committee and parity machines with binary couplings and up to K=5 hidden units.Comment: 4 pages, RevTex, 5 figures, uses multicol.sty and psfig.st

One-and-a-half quantum de Finetti theorems

We prove a new kind of quantum de Finetti theorem for representations of the unitary group U(d). Consider a pure state that lies in the irreducible representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained in the tensor product of U_mu and U_nu; let xi be the state obtained by tracing out U_nu. We show that xi is close to a convex combination of states Uv, where U is in U(d) and v is the highest weight vector in U_mu. When U_{mu+nu} is the symmetric representation, this yields the conventional quantum de Finetti theorem for symmetric states, and our method of proof gives near-optimal bounds for the approximation of xi by a convex combination of product states. For the class of symmetric Werner states, we give a second de Finetti-style theorem (our 'half' theorem); the de Finetti-approximation in this case takes a particularly simple form, involving only product states with a fixed spectrum. Our proof uses purely group theoretic methods, and makes a link with the shifted Schur functions. It also provides some useful examples, and gives some insight into the structure of the set of convex combinations of product states.Comment: 14 pages, 3 figures, v4: minor additions (including figures), published versio

The detection of airborne transmission of tuberculosis from HIV-infected patients, using an in vivo air sampling model

Background. Nosocomial transmission of tuberculosis remains an important public health problem. We created an in vivo air sampling model to study airborne transmission of tuberculosis from patients coinfected with human immunodeficiency virus (HIV) and to evaluate environmental control measures. Methods. An animal facility was built above a mechanically ventilated HIV‐tuberculosis ward in Lima, Peru. A mean of 92 guinea pigs were continuously exposed to all ward exhaust air for 16 months. Animals had tuberculin skin tests performed at monthly intervals, and those with positive reactions were removed for autopsy and culture for tuberculosis. Results. Over 505 consecutive days, there were 118 ward admissions by 97 patients with pulmonary tuberculosis, with a median duration of hospitalization of 11 days. All patients were infected with HIV and constituted a heterogeneous group with both new and existing diagnoses of tuberculosis. There was a wide variation in monthly rates of guinea pigs developing positive tuberculin test results (0%–53%). Of 292 animals exposed to ward air, 159 developed positive tuberculin skin test results, of which 129 had laboratory confirmation of tuberculosis. The HIV‐positive patients with pulmonary tuberculosis produced a mean of 8.2 infectious quanta per hour, compared with 1.25 for HIV‐negative patients with tuberculosis in similar studies from the 1950s. The mean monthly patient infectiousness varied greatly, from production of 0–44 infectious quanta per hour, as did the theoretical risk for a health care worker to acquire tuberculosis by breathing ward air. Conclusions. HIV‐positive patients with tuberculosis varied greatly in their infectiousness, and some were highly infectious. Use of environmental control strategies for nosocomial tuberculosis is therefore a priority, especially in areas with a high prevalence of both tuberculosis and HIV infection

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