On Generalizations of Network Design Problems with Degree Bounds

Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1) by handling more complex degree constraints in the minimum spanning tree problem (namely, laminar crossing spanning tree), and (2) by incorporating `degree bounds' in other combinatorial optimization problems such as matroid intersection and lattice polyhedra. We give new or improved approximation algorithms, hardness results, and integrality gaps for these problems.Comment: v2, 24 pages, 4 figure

Ground-state characterization of Nb charge-phase Josephson qubits

We present investigations of Josephson charge-phase qubits inductively coupled to a radio-frequency driven tank-circuit enabling the readout of the states by measuring the Josephson inductance of the qubit. The circuits including junctions with linear dimensions of 60 nm and 80 nm are fabricated from Nb trilayer and allowing the determination of relevant sample parameters at liquid helium temperature. The observed partial suppression of the circulating supercurrent at 4.2 K is explained in the framework of a quantum statistical model. We have probed the ground-state properties of qubit structures with different ratios of the Josephson coupling to Coulomb charging energy at 20 mK, demonstrating both the magnetic control of phase and the electrostatic control of charge on the qubit island.Comment: 8 pages, 8 figure

Zeeman energy and spin relaxation in a one-electron quantum dot

We have measured the relaxation time, T1, of the spin of a single electron confined in a semiconductor quantum dot (a proposed quantum bit). In a magnetic field, applied parallel to the two-dimensional electron gas in which the quantum dot is defined, Zeeman splitting of the orbital states is directly observed by measurements of electron transport through the dot. By applying short voltage pulses, we can populate the excited spin state with one electron and monitor relaxation of the spin. We find a lower bound on T1 of 50 microseconds at 7.5 T, only limited by our signal-to-noise ratio. A continuous measurement of the charge on the dot has no observable effect on the spin relaxation.Comment: Replaced with the version published in Phys. Rev. Let

Influence of smoking and obesity on alveolar-arterial gas pressure differences and dead space ventilation at rest and peak exercise in healthy men and women

SummaryBackground and aimsBesides exercise intolerance, the assessment of ventilatory and perfusion adequacy allows additional insights in the disease pathophysiology in many cardiovascular or pulmonary diseases. Valid measurements of dead space/tidal volume ratios (VD/VT), arterial (a′) – end-tidal (et) carbon dioxide (CO2) and oxygen (O2) pressure differences (p(a′-et)CO2) and (p(et-a′)O2), and alveolar (A)–a′ O2 pressure differences (p(A-a′)O2) require using blood samples in addition to gas exchange analyses on a breath-by-breath-basis. Smoking and nutritional status are also important factors in defining disorders. Using a large healthy population we considered the impact of these factors to develop useful prediction equations.Methods and resultsIncremental cycle exercise protocols were applied to apparently healthy volunteer adults who did not have structural heart disease or echocardiographic or lung function pathologies. Age, height, weight, and smoking were analysed for their influence on the target parameters in each gender. Reference values were determined by regression analyses. The final study sample consisted of 476 volunteers (190 female), aged 25–85 years. Smoking significantly influences p(A-a′)O2 and p(a′-et)CO2 at rest and peak exercise, and VD/VT during exercise. Obesity influences upper limits of VD/VT, p(a′-et)CO2 and p(et-a′)O2 at rest as well as p(A-a′)O2 and p(et-a′)O2 at exercise. Reference equations for never-smokers as well as for apparently healthy smokers considering influencing factors are given.ConclusionGender, age, height, weight, and smoking significantly influence gas exchange. Considering all of these factors this study provides a comprehensive set of reference equations derived from a large number of participants of a population-based study

Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(\min\{\sqrt{n}, \sqrt{k}\})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {\em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $\epsilon>0$, removes at most $m-k$ demands and has cost no more than $O(1/\epsilon^{2})$ times the cost of an optimal algorithm that removes at most $(1-\epsilon)(m-k)$ demands

Correlation-function spectroscopy of inelastic lifetime in heavily doped GaAs heterostructures

Measurements of resonant tunneling through a localized impurity state are used to probe fluctuations in the local density of states of heavily doped GaAs. The measured differential conductance is analyzed in terms of correlation functions with respect to voltage. A qualitative picture based on the scaling theory of Thouless is developed to relate the observed fluctuations to the statistics of single particle wavefunctions. In a quantitative theory correlation functions are calculated. By comparing the experimental and theoretical correlation functions the effective dimensionality of the emitter is analyzed and the dependence of the inelastic lifetime on energy is extracted.Comment: 41 pages, 14 figure

Terahertz photoresponse of AlInSb/InSb/AlInSb quantum well structures

We have studied the photoresponse (transmission and photoconductivity of Corbino-shaped devices) of structures with InSb quantum wells (AlInSb barriers). To characterize the devices, the Shubnikov-de Haas (SdH) effect up to magnetic fields B of 7 T and current-voltage (I-V) characteristics at various magnetic fields were measured. Some of the samples showed clearly resolvable SdH oscillations. The I-V curves showed pronounced nonlinearities. The phototransmission and the photoconductivity at various terahertz (THz) frequencies were measured around 2.5 THz generated by a p-Ge laser. From the cyclotron resonance (transmission measurements) we deduced a cyclotron mass of 0.022m0. We also performed photoconductivity measurements on Corbino-shaped devices in the THz frequency range. Oscillations of the photoconductivity with maxima near the minima of the conductivity in the dark were observed. Thus, these devices are potentially suitable for the detection of THz radiation

Strong quantum memory at resonant Fermi edges revealed by shot noise

Studies of non-equilibrium current fluctuations enable assessing correlations involved in quantum transport through nanoscale conductors. They provide additional information to the mean current on charge statistics and the presence of coherence, dissipation, disorder, or entanglement. Shot noise, being a temporal integral of the current autocorrelation function, reveals dynamical information. In particular, it detects presence of non-Markovian dynamics, i.e., memory, within open systems, which has been subject of many current theoretical studies. We report on low-temperature shot noise measurements of electronic transport through InAs quantum dots in the Fermi-edge singularity regime and show that it exhibits strong memory effects caused by quantum correlations between the dot and fermionic reservoirs. Our work, apart from addressing noise in archetypical strongly correlated system of prime interest, discloses generic quantum dynamical mechanism occurring at interacting resonant Fermi edges.Comment: 6 pages, 3 figure