Parametric Oscillation with Squeezed Vacuum Reservoirs

Employing the quantum Hamiltonian describing the interaction of two-mode light (signal-idler modes) generated by a nondegenerate parametric oscillator (NDPO) with two uncorrelated squeezed vacuum reservoirs (USVR), we derive the master equation. The corresponding Fokker-Planck equation for the Q-function is then solved employing a propagator method developed in Ref. \cite{1}. Making use of this Q-function, we calculate the quadrature fluctuations of the optical system. From these results we infer that the signal-idler modes are in squeezed states and the squeezing occurs in the first quadrature. When the NDPO operates below threshold we show that, for a large squeezing parameter, a squeezing amounting to a noise suppression approaching 100% below the vacuum level in the first quadrature can be achieved.Comment: 16 page

The Stable Roommates problem with short lists

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists SRI that are degree constrained, i.e., preference lists are of bounded length. The first variant, EGAL d-SRI, involves finding an egalitarian stable matching in solvable instances of SRI with preference lists of length at most d. We show that this problem is NP-hard even if d=3. On the positive side we give a (2d+3)/7-approximation algorithm for d={3,4,5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of SRI, called d-SRTI, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-SRTI admits a stable matching is NP-complete even if d=3. We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d=3 case. However for d=2 we show that the latter problem can be solved in polynomial time.Comment: short version appeared at SAGT 201

Functional renormalization group with a compactly supported smooth regulator function

The functional renormalization group equation with a compactly supported smooth (CSS) regulator function is considered. It is demonstrated that in an appropriate limit the CSS regulator recovers the optimized one and it has derivatives of all orders. The more generalized form of the CSS regulator is shown to reduce to all major type of regulator functions (exponential, power-law) in appropriate limits. The CSS regulator function is tested by studying the critical behavior of the bosonized two-dimensional quantum electrodynamics in the local potential approximation and the sine-Gordon scalar theory for d<2 dimensions beyond the local potential approximation. It is shown that a similar smoothing problem in nuclear physics has already been solved by introducing the so called Salamon-Vertse potential which can be related to the CSS regulator.Comment: JHEP style, 11 pages, 2 figures, proofs corrected, accepted for publication by JHE

Dilated Convolutional Neural Networks for Cardiovascular MR Segmentation in Congenital Heart Disease

We propose an automatic method using dilated convolutional neural networks (CNNs) for segmentation of the myocardium and blood pool in cardiovascular MR (CMR) of patients with congenital heart disease (CHD). Ten training and ten test CMR scans cropped to an ROI around the heart were provided in the MICCAI 2016 HVSMR challenge. A dilated CNN with a receptive field of 131x131 voxels was trained for myocardium and blood pool segmentation in axial, sagittal and coronal image slices. Performance was evaluated within the HVSMR challenge. Automatic segmentation of the test scans resulted in Dice indices of 0.80$\pm$0.06 and 0.93$\pm$0.02, average distances to boundaries of 0.96$\pm$0.31 and 0.89$\pm$0.24 mm, and Hausdorff distances of 6.13$\pm$3.76 and 7.07$\pm$3.01 mm for the myocardium and blood pool, respectively. Segmentation took 41.5$\pm$14.7 s per scan. In conclusion, dilated CNNs trained on a small set of CMR images of CHD patients showing large anatomical variability provide accurate myocardium and blood pool segmentations

Fidelity analysis of topological quantum phase transitions

We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical models; we exploit this mapping to obtain the scaling of the fidelity metric tensor near criticality. The topological phase transitions manifest themselves in divergences of the fidelity metric across the phase boundaries. These results provide evidence that the fidelity approach is a valuable tool to investigate novel phases lacking a clear characterization in terms of local order parameters

Popular matchings with two-sided preferences and one-sided ties

We are given a bipartite graph $G = (A \cup B, E)$ where each vertex has a preference list ranking its neighbors: in particular, every $a \in A$ ranks its neighbors in a strict order of preference, whereas the preference lists of $b \in B$ may contain ties. A matching $M$ is popular if there is no matching $M'$ such that the number of vertices that prefer $M'$ to $M$ exceeds the number of vertices that prefer $M$ to~$M'$. We show that the problem of deciding whether $G$ admits a popular matching or not is NP-hard. This is the case even when every $b \in B$ either has a strict preference list or puts all its neighbors into a single tie. In contrast, we show that the problem becomes polynomially solvable in the case when each $b \in B$ puts all its neighbors into a single tie. That is, all neighbors of $b$ are tied in $b$'s list and $b$ desires to be matched to any of them. Our main result is an $O(n^2)$ algorithm (where $n = |A \cup B|$) for the popular matching problem in this model. Note that this model is quite different from the model where vertices in $B$ have no preferences and do not care whether they are matched or not.Comment: A shortened version of this paper has appeared at ICALP 201

Further evidence for the planet around 51 Pegasi

The discovery of the planet around the solar-type star 51 Pegasi marked a watershed in the search for extrasolar planets. Since then seven other solar-type stars have been discovered, of which several have surprisingly short orbital periods, like the planet around 51 Peg. These planets were detected using the indirect technique of measuring variations in the Doppler shifts of lines in the spectra of the primary stars. But it is possible that oscillations of the stars themselves (or other effects) could mimic the signature of the planets, particularly around the short-period planets. The apparent lack of spectral and brightness variations, however, led to widespread acceptance that there is a planet around 51 Peg. This conclusion was challenged by the observation of systematic variations in the line profile shapes of 51 Peg, which suggested stellar oscillations. If these observations are correct, then there is no need to invoke a planet around 51 Peg to explain the data. Here we report observations of 51 Peg at a much higher spectral resolution than those in ref.9, in which we find no evidence for systematic changes in the line shapes. The data are most consistent with a planetary companion to 51 Peg.Comment: LaTeX, 6 pages, 2 figures. To appear in 8 January 1998 issue of Natur

A multicentre trial of voltaren in the treatment of rheumatoid arthritis

Voltaren, a compound with analgesic, anti-inflammatory and antipyretic properties, has been compared at two dose levels-25 mg t.d.s. and 50 mg t.d.s. with indomethacin 25 mg t.d.s. and acetylsalicylic acid 1 500 mg t.d.s. Ninety-one patients with definite or classical rheumatoid arthritis took part in this study. The trial was a doubleblind cross-over study, with each  medication being given for one week. Patients were washed out for one week prior to the first active treatment. Each patient received only two of the four possible treatments. Voltaren in a dose of 25 mg t.d.s. was found to improve the symptoms of rheumatoid arthritis to a greater degree than indomethacin or acetylsalicylic acid. Voltaren 50 mg t.d.s. evoked a greater response than acetylsalicylic acid and was at least as efficacious as indomethacin. Voltaren was better tolerated than either indomethacin or acetylsalicylic acid. The incidence of gastro-intestinal side-effects was similar with Voltaren and indomethacin, and half that produced by acetylsalicylic acid. Some evidence of possible drug interaction was found.S. Afr. Med. J., 48, 2013 (1974)

GeNN: a code generation framework for accelerated brain simulations

Large-scale numerical simulations of detailed brain circuit models are important for identifying hypotheses on brain functions and testing their consistency and plausibility. An ongoing challenge for simulating realistic models is, however, computational speed. In this paper, we present the GeNN (GPU-enhanced Neuronal Networks) framework, which aims to facilitate the use of graphics accelerators for computational models of large-scale neuronal networks to address this challenge. GeNN is an open source library that generates code to accelerate the execution of network simulations on NVIDIA GPUs, through a flexible and extensible interface, which does not require in-depth technical knowledge from the users. We present performance benchmarks showing that 200-fold speedup compared to a single core of a CPU can be achieved for a network of one million conductance based Hodgkin-Huxley neurons but that for other models the speedup can differ. GeNN is available for Linux, Mac OS X and Windows platforms. The source code, user manual, tutorials, Wiki, in-depth example projects and all other related information can be found on the project website http://genn-team.github.io/genn/