EigenGP: Gaussian Process Models with Adaptive Eigenfunctions

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both basis dictionary elements--eigenfunctions of a GP prior--and prior precisions in a sparse finite model. It is well known that, among all orthogonal basis functions, eigenfunctions can provide the most compact representation. Unlike other sparse Bayesian finite models where the basis function has a fixed form, our eigenfunctions live in a reproducing kernel Hilbert space as a finite linear combination of kernel functions. We learn the dictionary elements--eigenfunctions--and the prior precisions over these elements as well as all the other hyperparameters from data by maximizing the model marginal likelihood. We explore computational linear algebra to simplify the gradient computation significantly. Our experimental results demonstrate improved predictive performance of EigenGP over alternative sparse GP methods as well as relevance vector machine.Comment: Accepted by IJCAI 201

f(T)f(T) Theories and Varying Fine Structure Constant

In analogy to $f(R)$ theory, recently a new modified gravity theory, namely the so-called $f(T)$ theory, has been proposed to drive the current accelerated expansion without invoking dark energy. In the present work, by extending Bisabr's idea, we try to constrain $f(T)$ theories with the varying fine structure "constant", $\alpha\equiv e^2/\hbar c$. We find that the constraints on $f(T)$ theories from the observational $\Delta\alpha/\alpha$ data are very severe. In fact, they make $f(T)$ theories almost indistinguishable from $\Lambda$CDM model.Comment: 12 pages, 4 figures, 1 table, revtex4; v2: discussions added, Phys. Lett. B in press; v3: published versio

Energy-storage properties and electrocaloric effects of Pb(1-3x/2)LaxZr0.85Ti0.15O3 antiferroelectric thick films

1-µm-Pb(1-3x/2)LaxZr0.85Ti0.15O3 (PLZT) antiferroelectric (AFE) thick films with x = 0.08, 0.10, 0.12, and 0.14 were deposited on LaNiO3/Si (100) substrates by a sol-gel method. The dielectric properties, energy-storage performance, electrocaloric effect, and leakage current behavior were investigated in detail. With increasing La content, dielectric constant and saturated polarizations of the thick films were gradually decreased. A maximum recoverable energy-storage density of 38 J/cm3 and efficiency of 71% were achieved in the thick films with x = 0.12 at room temperature. Moreover, a large reversible adiabatic temperature change ∆T = 25.0 o C was presented in the thick films with x = 0.08 at 127 o C at 990 kV/cm. All the samples had a lower leakage current density below 10- 6 A/cm2 at room temperature. These results indicated that the PLZT AFE thick films could be a potential candidate for applications in high energy-storage density capacitors and cooling devices

A giant electrocaloric effect of a Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3 antiferroelectric thick film at room temperature

A 2-µm-Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3 (PLZST) antiferroelectric (AFE) thick film with tetragonal structure was deposited on LaNiO3/Si (100) substrates via a sol-gel technique. The electrocaloric effect (ECE) of the PLZST thick film is investigated under the functions of external electric field and temperature. Giant ECEs (∆T = 53.8 oC and ∆S = 63.9 J·K-1·kg-1) are received at 5 oC, which is attributed to a field-induced AFE to ferroelectric (FE) phase transition. Moreover, a large ∆T of above 30 oC is remains at temperature range from 5 oC to 25 oC. The maximum electrocaloric coefficient (ξmax = 0.060 K·cm/kV) and refrigeration efficiency (COP = 18) of the film are also obtained at 5 oC. At room temperature, the values of ∆T, ∆S, COP and ξmax are 35.0 oC, 39.0 J·K-1·kg-1, 14 and 0.039 K·cm/kV at 900 kV/cm, respectively. The AFE thick films with giant ECEs are promising candidates for applications in cooling systems at room temperature

Enhanced energy-storage performance and electrocaloric effect in compositionally graded Pb(1−3x/2)LaxZr0.85Ti0.15O3 antiferroelectric thick films

The compositionally graded multilayer Pb(1−3x/2)LaxZr0.85Ti0.15O3 (PLZT) antiferroelectric (AFE) thick films were deposited on LaNiO3/Si (100) substrates by using a sol–gel method. The effect of gradient sequence on dielectric properties, energy-storage performance, and electrocaloric effect (ECE) was investigated in detail. It is found that the compositionally graded films exhibited a significant enhancement in dielectric properties, energy-storage performance and ECE, which was, in contrast to the single-composition PLZT film, contributed by the strain and the gradient of polarization near the interfaces between the adjacent layers. A recoverable energy-storage density of 44 J/cm3 and efficiency of 71% was obtained in the up-graded PLZT AFE thick film at 1950 kV/cm. A giant reversible adiabatic temperature change of ∆T=28 °C at room temperature at 900 kV/cm was also achieved in the up-graded film. Moreover, all the thick films displayed a small leakage current density below 10−6 A/cm2 at room temperature. Thus, the compositionally graded PLZT AFE thick films with a large recoverable energy-storage density and a giant ECE could be a potential candidate for the applications in high energy-storage density capacitors and cooling devices

Momentum polarization: an entanglement measure of topological spin and chiral central charge

Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin $\theta_a=2\pi h_a$ is an important property of a topological quasi-particle, which is the Berry phase obtained in the adiabatic self-rotation of the quasi-particle by $2\pi$. For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge $c$. In this paper we propose a new approach to compute the topological spin and chiral central charge in lattice models by defining a new quantity named as the momentum polarization. Momentum polarization is defined on the cylinder geometry as a universal subleading term in the average value of a "partial translation operator". We show that the momentum polarization is a quantum entanglement property which can be computed from the reduced density matrix, and our analytic derivation based on edge conformal field theory shows that the momentum polarization measures the combination $h_a-\frac{c}{24}$ of topological spin and central charge. Numerical results are obtained for two example systems, the non-Abelian phase of the honeycomb lattice Kitaev model, and the $\nu=1/2$ Laughlin state of a fractional Chern insulator described by a variational Monte Carlo wavefunction. The numerical results verifies the analytic formula with high accuracy, and further suggests that this result remains robust even when the edge states cannot be described by a conformal field theory. Our result provides a new efficient approach to characterize and identify topological states of matter from finite size numerics.Comment: 13 pages, 8 figure