Non-additive dissipation in open quantum networks out of equilibrium

We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We show that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, we identify an additional interference term that generates coherences in the energy eigenbasis, associated with the current of conserved particles flowing in the steady state. Notably, non-additivity arises even for wide-band reservoirs coupled arbitrarily weakly to the system. Our results shed light on the non-trivial interplay between multiple thermal noise sources in modular open quantum systems.Comment: Final author version, including new Appendix A explaining the connection between conserved currents and energy-eigenbasis coherence in open network

Sequential weak measurement

The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When these observables do not commute, we may obtain information about joint properties of a quantum system that would be forbidden in the usual strong measurement scenario. As an application, we provide a physically compelling characterisation of the notion of counterfactual quantum computation

The Susceptibility to Hydrogen Peroxide of Indian and British Isoniazid-Sensitive and Isoniazid- Resistant Tubercle Bacilli

The present work describes an attempt to modify the method of Kreis and Le Joubioux (1957a) so that it would accurately estimate the relative proportions of catalase-positive and catalase-negative organisms in strains containing mixtures of the two types. A bactericidal test was chosen in preference to a bacteriostatic test, since it is difficult to obtain quantitative measurement with the latter technique. In performing a bactericidal test residual peroxide must be inactivated or removed by dilution so that it does not inhibit the growth of surviving organisms. Knox, Meadow and Worssam (1956) removed peroxide by centrifugation and washing, but this method was considered impracticable if this test were to be used on a large scale, and likely to produce inaccurate counts on the surviving organisms. In the present work the method of removal of peroxide was studied as well as the determination of the optimal peroxide concentration and period of exposure which would kill all catalase-negative organisms, but would leave catalase-positive organisms unaffected. In addition, the method of Kreis & Le Joubioux (1957a) was modified by reducing the inoculum of organisms exposed to peroxide so that catalase-positive bacilli would not be able to destroy peroxide during the test itself. The standardised bactericidal test was then employed in comparing the susceptibility to peroxide of isoniazid-sensitive strains from British and Indian patients, and in investigating the relationship between the peroxide susceptibility and the catalase activity of their isoniazid-resistant mutant strains

On the Calibration of a Size-Structured Population Model from Experimental Data

The aim of this work is twofold. First, we survey the techniques developed in (Perthame, Zubelli, 2007) and (Doumic, Perthame, Zubelli, 2008) to reconstruct the division (birth) rate from the cell volume distribution data in certain structured population models. Secondly, we implement such techniques on experimental cell volume distributions available in the literature so as to validate the theoretical and numerical results. As a proof of concept, we use the data reported in the classical work of Kubitschek [3] concerning Escherichia coli in vitro experiments measured by means of a Coulter transducer-multichannel analyzer system (Coulter Electronics, Inc., Hialeah, Fla, USA.) Despite the rather old measurement technology, the reconstructed division rates still display potentially useful biological features

Weak measurement takes a simple form for cumulants

A weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wavefunction for the pointer is real, the mean displacement of the pointer is proportional to the so-called weak value of the observable being measured. This gives an intuitively direct way of understanding weak measurement. However, if the initial pointer wavefunction takes complex values, the relationship between pointer displacement and weak value is not quite so simple, as pointed out recently by R. Jozsa. This is even more striking in the case of sequential weak measurements. These are carried out by coupling several pointers at different stages of evolution of the system, and the relationship between the products of the measured pointer positions and the sequential weak values can become extremely complicated for an arbitrary initial pointer wavefunction. Surprisingly, all this complication vanishes when one calculates the cumulants of pointer positions. These are directly proportional to the cumulants of sequential weak values. This suggests that cumulants have a fundamental physical significance for weak measurement

Multiple mechanisms determine ER network morphology during the cell cycle in Xenopus egg extracts

In metazoans the endoplasmic reticulum (ER) changes during the cell cycle, with the nuclear envelope (NE) disassembling and reassembling during mitosis and the peripheral ER undergoing extensive remodeling. Here we address how ER morphology is generated during the cell cycle using crude and fractionated Xenopus laevis egg extracts. We show that in interphase the ER is concentrated at the microtubule (MT)-organizing center by dynein and is spread by outward extension of ER tubules through their association with plus ends of growing MTs. Fusion of membranes into an ER network is dependent on the guanosine triphosphatase atlastin (ATL). NE assembly requires fusion by both ATL and ER-soluble N-ethyl-maleimide–sensitive factor adaptor protein receptors. In mitotic extracts, the ER converts into a network of sheets connected by ER tubules and loses most of its interactions with MTs. Together, these results indicate that fusion of ER membranes by ATL and interaction of ER with growing MT ends and dynein cooperate to generate distinct ER morphologies during the cell cycle

Deterministic mechanical model of T-killer cell polarization reproduces the wandering of aim between simultaneously engaged targets

T-killer cells of the immune system eliminate virus-infected and tumorous cells through direct cell-cell interactions. Reorientation of the killing apparatus inside the T cell to the T-cell interface with the target cell ensures specificity of the immune response. The killing apparatus can also oscillate next to the cell-cell interface. When two target cells are engaged by the T cell simultaneously, the killing apparatus can oscillate between the two interface areas. This oscillation is one of the most striking examples of cell movements that give the microscopist an unmechanistic impression of the cell's fidgety indecision. We have constructed a three-dimensional, numerical biomechanical model of the molecular-motor-driven microtubule cytoskeleton that positions the killing apparatus. The model demonstrates that the cortical pulling mechanism is indeed capable of orienting the killing apparatus into the functional position under a range of conditions. The model also predicts experimentally testable limitations of this commonly hypothesized mechanism of T-cell polarization. After the reorientation, the numerical solution exhibits complex, multidirectional, multiperiodic, and sustained oscillations in the absence of any external guidance or stochasticity. These computational results demonstrate that the strikingly animate wandering of aim in T-killer cells has a purely mechanical and deterministic explanation. © 2009 Kim, Maly

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

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