On Murty-Simon Conjecture II

A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter two edge-critical graph on $n$ vertices is at most $\lfloor \frac{n^{2}}{4} \rfloor$ and the extremal graph is the complete bipartite graph $K_{\lfloor \frac{n}{2} \rfloor, \lceil \frac{n}{2} \rceil}$. In the series papers [7-9], the Murty-Simon Conjecture stated by Haynes et al. is not the original conjecture, indeed, it is only for the diameter two edge-critical graphs of even order. In this paper, we completely prove the Murty-Simon Conjecture for the graphs whose complements have vertex connectivity $\ell$, where $\ell = 1, 2, 3$; and for the graphs whose complements have an independent vertex cut of cardinality at least three.Comment: 9 pages, submitted for publication on May 10, 201

Translation of EEG spatial filters from resting to motor imagery using independent component analysis.

Electroencephalogram (EEG)-based brain-computer interfaces (BCIs) often use spatial filters to improve signal-to-noise ratio of task-related EEG activities. To obtain robust spatial filters, large amounts of labeled data, which are often expensive and labor-intensive to obtain, need to be collected in a training procedure before online BCI control. Several studies have recently developed zero-training methods using a session-to-session scenario in order to alleviate this problem. To our knowledge, a state-to-state translation, which applies spatial filters derived from one state to another, has never been reported. This study proposes a state-to-state, zero-training method to construct spatial filters for extracting EEG changes induced by motor imagery. Independent component analysis (ICA) was separately applied to the multi-channel EEG in the resting and the motor imagery states to obtain motor-related spatial filters. The resultant spatial filters were then applied to single-trial EEG to differentiate left- and right-hand imagery movements. On a motor imagery dataset collected from nine subjects, comparable classification accuracies were obtained by using ICA-based spatial filters derived from the two states (motor imagery: 87.0%, resting: 85.9%), which were both significantly higher than the accuracy achieved by using monopolar scalp EEG data (80.4%). The proposed method considerably increases the practicality of BCI systems in real-world environments because it is less sensitive to electrode misalignment across different sessions or days and does not require annotated pilot data to derive spatial filters

The influence of a single defect in composite gate insulators on the performance of nanotube transistors

The current through a carbon nanotube field-effect transistor (CNFET) with cylindrical gate electrode is calculated using the nonequilibrium Greens function method in a tight-binding approximation. The obtained result is in good agreement with the experimental data. The space radiation and nuclear radiation are known to cause defects in solids. The theoretical approach is used to calculate the amplitude of the random-telegraph-signal (RTS) noise due to a single defect in the gate oxide of a long channel p-type CNFET. We investigate how the amplitude of the RTS noise is affected by the composite structure of gate insulators, which contains an inner insulator with a dielectric constant larger than 3.9 and an outer insulator with a dielectric constant of 3.9 (as for SiO2). It is found that the RTS amplitude increases apparently with the decreasing thickness of the inner gate insulator. If the inner insulator is too thin, even though its dielectric constant is as large as 80, the amplitude of the RTS noise caused by the charge of Q = +1e may amount to around 80% in the turn-on region. Due to strong effects of defects in CNFETs, CNFETs have a potential to be used for detecting the space radiation or nuclear radiation.Comment: 8 Figure

Inverse spectral problems for Sturm–Liouville operators with partial information

[[abstract]]In this paper, we study the inverse spectral problems for Sturm–Liouville operators with Robin boundary conditions and show that if the potential q on the interval [0,α] for some α∈[0,1) is given a priori, then the potential q on the whole interval [0,1] can be uniquely determined by a subset of pairs of eigenvalues and the weight numbers of the corresponding eigenvalues or by parts of two spectra.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]GB

A Tale of Two Portals: Testing Light, Hidden New Physics at Future e+e−e^+ e^- Colliders

We investigate the prospects for producing new, light, hidden states at a future $e^+ e^-$ collider in a Higgsed dark $U(1)_D$ model, which we call the Double Dark Portal model. The simultaneous presence of both vector and scalar portal couplings immediately modifies the Standard Model Higgsstrahlung channel, $e^+ e^- \to Zh$, at leading order in each coupling. In addition, each portal leads to complementary signals which can be probed at direct and indirect detection dark matter experiments. After accounting for current constraints from LEP and LHC, we demonstrate that a future $e^+ e^-$ Higgs factory will have unique and leading sensitivity to the two portal couplings by studying a host of new production, decay, and radiative return processes. Besides the possibility of exotic Higgs decays, we highlight the importance of direct dark vector and dark scalar production at $e^+ e^-$ machines, whose invisible decays can be tagged from the recoil mass method.Comment: 47 pages, 9 figures, 1 table. v2: references added, version matched to JHE