A plane graph representation of triconnected graphs

AbstractGiven a graph G=(V,E), a set S={s1,s2,…,sk} of k vertices of V, and k natural numbers n1,n2,…,nk such that ∑i=1kni=|V|, the k-partition problem is to find a partition V1,V2,…,Vk of the vertex set V such that |Vi|=ni, si∈Vi, and Vi induces a connected subgraph of G for each i=1,2,…,k. For the tripartition problem on a triconnected graph, a naive algorithm can be designed based on a directional embedding of G in the two-dimensional Euclidean space. However, for graphs of large number of vertices, the implementing of this algorithm requires high precision real arithmetic to distinguish two close vertices in the plane. In this paper, we propose an algorithm for dealing with the tripartition problem by introducing a new data structure called the region graph, which represents a kind of combinatorial embedding of the given graph in the plane. The algorithm constructs a desired tripartition combinatorially in the sense that it does not require any geometrical computation with actual coordinates in the Euclidean space

Double-Free-Layer Stochastic Magnetic Tunnel Junctions with Synthetic Antiferromagnets

Stochastic magnetic tunnel junctions (sMTJ) using low-barrier nanomagnets have shown promise as fast, energy-efficient, and scalable building blocks for probabilistic computing. Despite recent experimental and theoretical progress, sMTJs exhibiting the ideal characteristics necessary for probabilistic bits (p-bit) are still lacking. Ideally, the sMTJs should have (a) voltage bias independence preventing read disturbance (b) uniform randomness in the magnetization angle between the free layers, and (c) fast fluctuations without requiring external magnetic fields while being robust to magnetic field perturbations. Here, we propose a new design satisfying all of these requirements, using double-free-layer sMTJs with synthetic antiferromagnets (SAF). We evaluate the proposed sMTJ design with experimentally benchmarked spin-circuit models accounting for transport physics, coupled with the stochastic Landau-Lifshitz-Gilbert equation for magnetization dynamics. We find that the use of low-barrier SAF layers reduces dipolar coupling, achieving uncorrelated fluctuations at zero-magnetic field surviving up to diameters exceeding ($D\approx 100$ nm) if the nanomagnets can be made thin enough ($\approx 1$-$2$ nm). The double-free-layer structure retains bias-independence and the circular nature of the nanomagnets provides near-uniform randomness with fast fluctuations. Combining our full sMTJ model with advanced transistor models, we estimate the energy to generate a random bit as $\approx$ 3.6 fJ, with fluctuation rates of $\approx$ 3.3 GHz per p-bit. Our results will guide the experimental development of superior stochastic magnetic tunnel junctions for large-scale and energy-efficient probabilistic computation for problems relevant to machine learning and artificial intelligence

Experimental Verification of a One-Dimensional Diffraction-Limit Coronagraph

We performed an experimental verification of a coronagraph. As a result, we confirmed that, at the focal region where the planetary point spread function exists, the coronagraph system mitigates the raw contrast of a star-planet system by at least $1\times10^{-5}$ even for the 1-$\lambda/D$ star-planet separation. In addition, the verified coronagraph keeps the shapes of the off-axis point spread functions when the setup has the source angular separation of 1$\lambda/D$. The low-order wavefront error and the non-zero extinction ratio of the linear polarizer may affect the currently confirmed contrast. The sharpness of the off-axis point spread function generated by the sub-$\lambda/D$ separated sources is promising for the fiber-based observation of exoplanets. The coupling efficiency with a single mode fiber exceeds 50% when the angular separation is greater than 3--4$\times 10^{-1}\lambda/D$. For sub-$\lambda/D$ separated sources, the peak positions (obtained with Gaussian fitting) of the output point spread functions are different from the angular positions of sources; the peak position moved from about $0.8\lambda/D$ to $1.0\lambda/D$ as the angular separation of the light source varies from $0.1\lambda/D$ to $1.0\lambda/D$. The off-axis throughput including the fiber-coupling efficiency (with respect to no focal plane mask) is about 40% for 1-$\lambda/D$ separated sources and 10% for 0.5-$\lambda/D$ separated ones (excluding the factor of the ratio of pupil aperture width and Lyot stop width), where we assumed a linear-polarized-light injection. In addition, because this coronagraph can remove point sources on a line in the sky, it has another promising application for high-contrast imaging of exoplanets in binary systems.Comment: 18 pages, 10 figures, accepted for the Publications of the Astronomical Society of the Pacifi

Multimodality imaging to identify lipid-rich coronary plaques and predict periprocedural myocardial injury: Association between near-infrared spectroscopy and coronary computed tomography angiography

BackgroundThis study compares the efficacy of coronary computed tomography angiography (CCTA) and near-infrared spectroscopy intravascular ultrasound (NIRS–IVUS) in patients with significant coronary stenosis for predicting periprocedural myocardial injury during percutaneous coronary intervention (PCI).MethodsWe prospectively enrolled 107 patients who underwent CCTA before PCI and performed NIRS–IVUS during PCI. Based on the maximal lipid core burden index for any 4-mm longitudinal segments (maxLCBI4mm) in the culprit lesion, we divided the patients into two groups: lipid-rich plaque (LRP) group (maxLCBI4mm ≥ 400; n = 48) and no-LRP group (maxLCBI4mm < 400; n = 59). Periprocedural myocardial injury was a postprocedural cardiac troponin T (cTnT) elevation of ≥5 times the upper limit of normal.ResultsThe LRP group had a significantly higher cTnT (p = 0.026), lower CT density (p < 0.001), larger percentage atheroma volume (PAV) by NIRS–IVUS (p = 0.036), and larger remodeling index measured by both CCTA (p = 0.020) and NIRS–IVUS (p < 0.001). A significant negative linear correlation was found between maxLCBI4mm and CT density (rho = −0.552, p < 0.001). Multivariable logistic regression analysis identified maxLCBI4mm [odds ratio (OR): 1.006, p = 0.003] and PAV (OR: 1.125, p = 0.014) as independent predictors of periprocedural myocardial injury, while CT density was not an independent predictor (OR: 0.991, p = 0.22).ConclusionCCTA and NIRS–IVUS correlated well to identify LRP in culprit lesions. However, NIRS–IVUS was more competent in predicting the risk of periprocedural myocardial injury

Coulomb-mediated antibunching of an electron pair surfing on sound

Electron flying qubits are envisioned as potential information link within a quantum computer, but also promise -- alike photonic approaches -- a self-standing quantum processing unit. In contrast to its photonic counterpart, electron-quantum-optics implementations are subject to Coulomb interaction, which provide a direct route to entangle the orbital or spin degree of freedom. However, the controlled interaction of flying electrons at the single particle level has not yet been established experimentally. Here we report antibunching of a pair of single electrons that is synchronously shuttled through a circuit of coupled quantum rails by means of a surface acoustic wave. The in-flight partitioning process exhibits a reciprocal gating effect which allows us to ascribe the observed repulsion predominantly to Coulomb interaction. Our single-shot experiment marks an important milestone on the route to realise a controlled-phase gate for in-flight quantum manipulations

Generation of a single-cycle acoustic pulse: a scalable solution for transport in single-electron circuits

The synthesis of single-cycle, compressed optical and microwave pulses sparked novel areas of fundamental research. In the field of acoustics, however, such a generation has not been introduced yet. For numerous applications, the large spatial extent of surface acoustic waves (SAW) causes unwanted perturbations and limits the accuracy of physical manipulations. Particularly, this restriction applies to SAW-driven quantum experiments with single flying electrons, where extra modulation renders the exact position of the transported electron ambiguous and leads to undesired spin mixing. Here, we address this challenge by demonstrating single-shot chirp synthesis of a strongly compressed acoustic pulse. Employing this solitary SAW pulse to transport a single electron between distant quantum dots with an efficiency exceeding 99%, we show that chirp synthesis is competitive with regular transduction approaches. Performing a time-resolved investigation of the SAW-driven sending process, we outline the potential of the chirped SAW pulse to synchronize single-electron transport from many quantum-dot sources. By superimposing multiple pulses, we further point out the capability of chirp synthesis to generate arbitrary acoustic waveforms tailorable to a variety of (opto)nanomechanical applications. Our results shift the paradigm of compressed pulses to the field of acoustic phonons and pave the way for a SAW-driven platform of single-electron transport that is precise, synchronized, and scalable.Comment: To be published in Physical Review