Improvement of Uncertainty Relations for Mixed States

We study a possible improvement of uncertainty relations. The Heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables. The Schroedinger uncertainty relation improves the Heisenberg uncertainty relation by adding the correlation in terms of anti-commutator. However both relations are insensitive whether the state used is pure or mixed. We improve the uncertainty relations by introducing additional terms which measure the mixtureness of the state. For the momentum and position operators as conjugate observables and for the thermal state of quantum harmonic oscillator, it turns out that the equalities in the improved uncertainty relations hold

LDPC Code Design for Distributed Storage: Balancing Repair Bandwidth, Reliability and Storage Overhead

Distributed storage systems suffer from significant repair traffic generated due to frequent storage node failures. This paper shows that properly designed low-density parity-check (LDPC) codes can substantially reduce the amount of required block downloads for repair thanks to the sparse nature of their factor graph representation. In particular, with a careful construction of the factor graph, both low repair-bandwidth and high reliability can be achieved for a given code rate. First, a formula for the average repair bandwidth of LDPC codes is developed. This formula is then used to establish that the minimum repair bandwidth can be achieved by forcing a regular check node degree in the factor graph. Moreover, it is shown that given a fixed code rate, the variable node degree should also be regular to yield minimum repair bandwidth, under some reasonable minimum variable node degree constraint. It is also shown that for a given repair-bandwidth requirement, LDPC codes can yield substantially higher reliability than currently utilized Reed-Solomon (RS) codes. Our reliability analysis is based on a formulation of the general equation for the mean-time-to-data-loss (MTTDL) associated with LDPC codes. The formulation reveals that the stopping number is closely related to the MTTDL. It is further shown that LDPC codes can be designed such that a small loss of repair-bandwidth optimality may be traded for a large improvement in erasure-correction capability and thus the MTTDL.Comment: 32 page

Shannon entropy as an indicator of spatial resolution for morphology of mode pattern in dielectric microcavity

We present the Shannon entropy as an indicator of spatial resolution for morphology of resonance mode pattern in dielectric micro cavity. We obtain two types of optimized mesh point for the minimum and maximum sizes, respectively. The critical mesh point for the minimum size is determined by the barely identifiable quantum number through chi square test whereas the saturation of difference of the Shannon entropy corresponds to the maximum size. We can also show that the critical mesh point increases as the (real) wave number of eigenvalue trajectory increases and estimate the proportional constant between them.

A New Extension of Ho\v{r}ava-Lifshitz Gravity and Curing Pathologies of the Scalar Graviton

We consider an extension of the Ho\v{r}ava-Lifshitz gravity with extra conformal symmetry by introducing a scalar field with higher order curvature terms. Relaxing the exact local Weyl symmetry, we construct an action with three free parameters which breaks local anisotropic Weyl symmetry but still preserves residual global Weyl symmetry. At low energies, it reduces to a Lorentz-violating scalar-tensor gravity. With a constant scalar field background and particular choices of the parameters, it reduces to the Ho\v{r}ava-Lifshitz (HL) gravity, but any perturbation from these particular configurations produces some non-trivial extensions of HL gravity. The perturbation analysis of the new extended HL gravity in the Minkowski background shows thatthe pathological behaviors of scalar graviton, i.e., ghost or instability problem, and strong coupling problem do not emerge up to cubic order as well as quadratic order.Comment: 14 pages, version to appear in JHE

Adversarial Dropout for Supervised and Semi-supervised Learning

Recently, the training with adversarial examples, which are generated by adding a small but worst-case perturbation on input examples, has been proved to improve generalization performance of neural networks. In contrast to the individually biased inputs to enhance the generality, this paper introduces adversarial dropout, which is a minimal set of dropouts that maximize the divergence between the outputs from the network with the dropouts and the training supervisions. The identified adversarial dropout are used to reconfigure the neural network to train, and we demonstrated that training on the reconfigured sub-network improves the generalization performance of supervised and semi-supervised learning tasks on MNIST and CIFAR-10. We analyzed the trained model to reason the performance improvement, and we found that adversarial dropout increases the sparsity of neural networks more than the standard dropout does.Comment: submitted to AAAI-1

Non-target Structural Displacement Measurement Using Reference Frame Based Deepflow

Structural displacement is crucial for structural health monitoring, although it is very challenging to measure in field conditions. Most existing displacement measurement methods are costly, labor intensive, and insufficiently accurate for measuring small dynamic displacements. Computer vision (CV) based methods incorporate optical devices with advanced image processing algorithms to accurately, cost-effectively, and remotely measure structural displacement with easy installation. However, non-target based CV methods are still limited by insufficient feature points, incorrect feature point detection, occlusion, and drift induced by tracking error accumulation. This paper presents a reference frame based Deepflow algorithm integrated with masking and signal filtering for non-target based displacement measurements. The proposed method allows the user to select points of interest for images with a low gradient for displacement tracking and directly calculate displacement without drift accumulated by measurement error. The proposed method is experimentally validated on a cantilevered beam under ambient and occluded test conditions. The accuracy of the proposed method is compared with that of a reference laser displacement sensor for validation. The significant advantage of the proposed method is its flexibility in extracting structural displacement in any region on structures that do not have distinct natural features

Emergent Localization in Dodecagonal Bilayer Quasicrystals

A new type of long-range ordering in the absence of translational symmetry gives rise to drastic revolution of our common knowledge in condensed matter physics. Quasicrystal, as such unconventional system, became a plethora to test our insights and to find exotic states of matter. In particular, electronic properties in quasicrystal have gotten lots of attention along with their experimental realization and controllability in twisted bilayer systems. In this work, we study how quasicrystalline order in bilayer systems can induce unique localization of electrons without any extrinsic disorders. We focus on dodecagonal quasicrystal that has been demonstrated in twisted bilayer graphene system in recent experiments. In the presence of small gap, we show the localization generically occurs due to non-periodic nature of quasicrystal, which is evidenced by the inverse participation ratio and the energy level statistics. We understand the origin of such localization by approximating the dodecagonal quasicrystals as an impurity scattering problem.Comment: 4 pages, 5 figure

Probing unconventional superconductivity in inversion symmetric doped Weyl semimetal

Unconventional superconductivity has been predicted to arise in the topologically non-trivial Fermi surface of doped inversion symmetric Weyl semimetals (WSM). In particular, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and nodal BCS states are theoretically predicted to be possible superconductor pairing states in inversion symmetric doped WSM. In an effort to resolve preferred pairing state, we theoretically study two separate four terminal quantum transport methods that each exhibit a unique electrical signature in the presence of FFLO and nodal BCS states in doped WSMs. We first introduce a Josephson junction that consists of a doped WSM and an s-wave superconductor in which we show that the application of a transverse uniform current in s-wave superconductor effectively cancels the momentum carried by FFLO states in doped WSM. From our numerical analysis, we find a peak in Josephson current amplitude at finite uniform current in s-wave superconductor that serves as an indicator of FFLO states in doped WSMs. Furthermore, we show using a four terminal measurement configuration that the nodal points may be shifted by an application of transverse uniform current in doped WSM. We analyze the topological phase transitions induced by nodal pair annihilation in non-equilibrium by constructing the phase diagram and we find a characteristic decrease in the density of states that serves as a signature of the quantum critical point in the topological phase transition, thereby identifying nodal BCS states in doped WSM.Comment: 8 pages, 4 figures (5 pages, 2 figures for supplementary material

Einstein-singleton theory and its power spectra in de Sitter inflation

We study the Einstein-singleton theory during de Sitter inflation since it provides a way of degenerate fourth-order scalar theory. We obtain an exact solution expressed in terms of the exponential-integral function by solving the degenerate fourth-order scalar equation in de Sitter spacetime. Furthermore, we find that its power spectrum blows negatively up in the superhorizon limit, while it is negatively scale-invariant in the subhorizon limit. This suggests that the Einstein-singleton theory contains the ghost-instability and thus, it is not suitable for developing a slow-roll inflation model.Comment: 1+15 pages, 3 figures, version to appear in Int. J. Mod. Phys.

THz radiation by the frequency down-shift of Nd:YAG lasers

The interaction between an intense laser and a relativistic dense electron beam propagating in the same direction could down-shift the laser frequency. This process, which can be used to generate a coherent THz radiation, is theoretically analyzed. With a set of practically relevant parameters, it is suggested that the radiation energy could reach the order of 1 mJ per shot in the duration of 100 pico-second, or the temporal radiation power of 10 MW