Assessing T cell clonal size distribution: a non-parametric approach

Clonal structure of the human peripheral T-cell repertoire is shaped by a number of homeostatic mechanisms, including antigen presentation, cytokine and cell regulation. Its accurate tuning leads to a remarkable ability to combat pathogens in all their variety, while systemic failures may lead to severe consequences like autoimmune diseases. Here we develop and make use of a non-parametric statistical approach to assess T cell clonal size distributions from recent next generation sequencing data. For 41 healthy individuals and a patient with ankylosing spondylitis, who undergone treatment, we invariably find power law scaling over several decades and for the first time calculate quantitatively meaningful values of decay exponent. It has proved to be much the same among healthy donors, significantly different for an autoimmune patient before the therapy, and converging towards a typical value afterwards. We discuss implications of the findings for theoretical understanding and mathematical modeling of adaptive immunity.Comment: 13 pages, 3 figures, 2 table

Josephson charge-phase qubit with radio frequency readout: coupling and decoherence

The charge-phase Josephson qubit based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-frequency driven tank circuit enabling the readout of the qubit states by measuring the effective Josephson inductance of the transistor. The effect of qubit dephasing and relaxation due to electric and magnetic control lines as well as the measuring system is evaluated. Recommendations for operation of the qubit in magic points producing minimum decoherence are given.Comment: 11 pages incl. 6 fig

Radio-frequency Bloch-transistor electrometer

A quantum-limited electrometer based on charge modulation of the Josephson supercurrent in the Bloch transistor inserted into a superconducting ring is proposed. As this ring is inductive coupled to a high-Q resonance tank circuit, the variations of the charge on the transistor island (input signal) are converted into variations of amplitude and phase of radio-frequency oscillations in the tank. These variations are amplified and then detected. The output noise, the back-action fluctuations and their cross-correlation are computed. It is shown that our device enables measurements of the charge with a sensitivity which is determined by the energy resolution of its amplifier, that can be reduced down to the standard quantum limit of \hbar/2. On the basis of this setup a "back-action-evading" scheme of the charge measurements is proposed.Comment: 5 pages incl. 2 figure

Towards the observation of phase locked Bloch oscillations in arrays of small Josephson junctions

We have designed an experiment and performed extensive simulations and preliminary measurements to identify a set of realistic circuit parameters that should allow the observation of constant-current steps at I=2ef in short arrays of small Josephson junctions under external AC drive of frequency f. Observation of these steps demonstrating phase lock of the Bloch oscillations with the external drive requires a high-impedance environment for the array, which is provided by on-chip resistors close to the junctions. We show that the width and shape of the steps crucially depend on the shape of the drive and the electron temperature in the resistors

Decoherence of a Josephson qubit due to coupling to two level systems

Noise and decoherence are major obstacles to the implementation of Josephson junction qubits in quantum computing. Recent experiments suggest that two level systems (TLS) in the oxide tunnel barrier are a source of decoherence. We explore two decoherence mechanisms in which these two level systems lead to the decay of Rabi oscillations that result when Josephson junction qubits are subjected to strong microwave driving. (A) We consider a Josephson qubit coupled resonantly to a two level system, i.e., the qubit and TLS have equal energy splittings. As a result of this resonant interaction, the occupation probability of the excited state of the qubit exhibits beating. Decoherence of the qubit results when the two level system decays from its excited state by emitting a phonon. (B) Fluctuations of the two level systems in the oxide barrier produce fluctuations and 1/f noise in the Josephson junction critical current I_o. This in turn leads to fluctuations in the qubit energy splitting that degrades the qubit coherence. We compare our results with experiments on Josephson junction phase qubits.Comment: 23 pages, Latex, 6 encapsulated postscript figure

Zero Order Estimates for Analytic Functions

The primary goal of this paper is to provide a general multiplicity estimate. Our main theorem allows to reduce a proof of multiplicity lemma to the study of ideals stable under some appropriate transformation of a polynomial ring. In particular, this result leads to a new link between the theory of polarized algebraic dynamical systems and transcendental number theory. On the other hand, it allows to establish an improvement of Nesterenko's conditional result on solutions of systems of differential equations. We also deduce, under some condition on stable varieties, the optimal multiplicity estimate in the case of generalized Mahler's functional equations, previously studied by Mahler, Nishioka, Topfer and others. Further, analyzing stable ideals we prove the unconditional optimal result in the case of linear functional systems of generalized Mahler's type. The latter result generalizes a famous theorem of Nishioka (1986) previously conjectured by Mahler (1969), and simultaneously it gives a counterpart in the case of functional systems for an important unconditional result of Nesterenko (1977) concerning linear differential systems. In summary, we provide a new universal tool for transcendental number theory, applicable with fields of any characteristic. It opens the way to new results on algebraic independence, as shown in Zorin (2010).Comment: 42 page

Communicating Josephson Qubits

We propose a scheme to implement a quantum information transfer protocol with a superconducting circuit and Josephson charge qubits. The information exchange is mediated by an L-C resonator used as a data bus. The main decoherence sources are analyzed in detail.Comment: 4 pages, 2 figure

Asymmetric Upwarp of the Asthenosphere beneath the Baikal Rift Zone, Siberia

In the summer of 1991 we installed 27 seismic stations about lake Baikal, Siberia, aimed at obtaining accurately timed digital seismic data to investigate the deep structure and geodynamics of the Baikal rift zone and adjacent regions. Sixty-six teleseismic events with high signal-to-noise ratio were recorded. Travel time and Q analysis of teleseisms characterize an upwarp of the lithosphere-asthenosphere boundary under Baikal. Theoretical arrival times were calculated by using the International Association of Seismology and Physics of the Earth\u27s interior 1991 Earth model, and travel time residuals were found by subtracting computed arrival times from observed ones. A three-dimensional downward projection inversion method is used to invert the P wave velocity structure with constraints from deep seismic sounding data. Our results suggest that (1) the lithosphere-asthenosphere transition upwarps beneath the rift zone, (2) the upwarp has an asymmetric shape, (3) the velocity contrast is -4.9% in the asthenosphere, (4) the density contrast is -0.6%, and (5) the P wave attenuation contrast t* is 0.1 s

S K S Splitting beneath Continental Rift Zones

We present measurements of S K S splitting at 28 digital seismic stations and 35 analog stations in the Baikal rift zone, Siberia, and adjacent areas, and at 17 stations in the East African Rift in Kenya and compare them with previous measurements from the Rio Grande Rift of North America. Fast directions in the inner region of the Baikal rift zone are distributed in two orthogonal directions, NE and NW, approximately parallel and perpendicular to the NE strike of the rift. In the adjacent Siberian platform and northern Mongolian fold belt, only the rift-orthogonal fast direction is observed. In southcentral Mongolia, the dominant fast direction changes to rift-parallel again, although a small number of measurements are still rift-orthogonal. For the axial zones of the East African and Rio Grande Rifts, fast directions are oriented on average NNE, that is, rotated clockwise from the N-S trending rift. All three rifts are underlain by low-velocity upper mantle as determined from teleseismic tomography. Rift-related mantle flow provides a plausible interpretation for the rift-orthogonal fast directions. The rift-parallel fast directions near the rift axes can be interpreted by oriented magmatic cracks in the mantle or small-scale mantle convection with rift-parallel flow. The agreement between stress estimates and corresponding crack orientations lends some weight to the suggestion that the rift-parallel fast directions are caused by oriented magmatic cracks