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

Minimal Absorption Measurements

We show that it is not possible to discriminate two close transparencies without a certain number of photons being absorbed. We extend this to the discrimination of patterns of transparency (images).Comment: 11 pages (latex

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

Measuring Energy, Estimating Hamiltonians, and the Time-Energy Uncertainty Relation

Suppose that the Hamiltonian acting on a quantum system is unknown and one wants to determine what is the Hamiltonian. We show that in general this requires a time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta H \gtrsim 1$ where $\Delta H$ is a measure of how accurately the unknown Hamiltonian must be estimated. We then apply this result to the problem of measuring the energy of an unknown quantum state. It has been previously shown that if the Hamiltonian is known, then the energy can in principle be measured in an arbitrarily short time. On the other hand we show that if the Hamiltonian is not known then an energy measurement necessarily takes a minimum time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta E \gtrsim 1$ where $\Delta E$ is the precision of the energy measurement. Several examples are studied to address the question of whether it is possible to saturate these uncertainty relations. Their interpretation is discussed in detail.Comment: 12pages, revised version with small correction

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

Gastro-intestinal flora and diarrhoea after Vagotomy

Twenty patients, 7 of whom had diarrhoea after vagotomy and drainage, were  investigated by culture of gastric and jejunal aspirates and measurements of faecal  fat, free bile acids in jejunal fluid, urinary indican excretion, serum folate and serum vitamin B,2. The haematological findings were compared with those in 20 patients  with duodenal ulcer who had not undergone surgery and in 25 healthy controls. The pattern of small bowel flora was normal after vagotomy; this was consistent where the normal results of the urinary indican estimations. There was no relationship between diarrhoea and the bacteriological results. Steatorrhoea occurred in 6 of the 7 patients with  diarrhoea and in only 1 of 13 without diarrhoea, suggesting a relationship between diarrhoea and faecal fat excretion after vagotomy and drainage. The mean serum folate and vitamin B'2 levels of the patients after vagotomy were significantly lower than thosein healthy controls. Some of the folate levels in the duodenal ulcer controls were subnormal

Serial counts of Mycobacterium tuberculosis in sputum as surrogate markers of the sterilising activity of rifampicin and pyrazinamide in treating pulmonary tuberculosis

BACKGROUND: Since the sterilising activity of new antituberculosis drugs is difficult to assess by conventional phase III studies, surrogate methods related to eventual relapse rates are required. METHODS: A suitable method is suggested by a retrospective analysis of viable counts of Mycobacterium tuberculosis in 12-hr sputum collections from 122 newly diagnosed patients with pulmonary tuberculosis in Nairobi, done pretreatment and at 2, 7, 14 and 28 days. Treatment was with isoniazid and streptomycin, supplemented with either thiacetazone (SHT) or rifampicin + pyrazinamide (SHRZ). RESULTS: During days 0–2, a large kill due to isoniazid occurred, unrelated to treatment or HIV status; thereafter it decreased exponentially. SHRZ appeared to have greater sterilising activity than SHT during days 2–7 (p = 0.044), due to rifampicin, and during days 14–28, probably due mainly to pyrazinamide. The greatest discrimination between SHRZ and SHT treatments was found between regression estimates of kill over days 2–28 (p = 0.0005) in patients who remained positive up to 28 days with homogeneous kill rates. No associations were found between regression estimates and the age, sex, and extent of disease or cavitation. An increased kill in HIV seropositive patients, unrelated to the treatment effect, was evident during days 2–28 (p = 0.007), mainly during days 2–7. CONCLUSIONS: Surrogate marker studies should either be in small groups treated with monotherapy during days 2 to about 7 or as add-ons or replacements in isoniazid-containing standard regimens from days 2 to 28 in large groups

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.