Majorana phases in neutrino-antineutrino oscillations

If the massive neutrinos are Majorana particles, neutrinoless double beta ($0\nu\beta\beta$) decay experiments are not enough to determine the Majorana phases. We carry out a systematic study of CP violation in neutrino-antineutrino oscillations. In these processes, CP-conserving parts involve six independent $0\nu\beta\beta$-like mass terms $\langle m\rangle_{\alpha\beta}$ and CP-violating parts are associated with nine independent Jarlskog-like parameters ${\cal V}^{ij}_{\alpha\beta}$ (for $\alpha, \beta = e, \mu, \tau$ and $i, j = 1, 2,3$). With the help of current neutrino oscillation data, we illustrate the salient features of six independent CP-violating asymmetries between $\nu_\alpha \to \bar{\nu}_\beta$ and $\bar{\nu}_\alpha \to \nu_\beta$ oscillations.Comment: 4 pages, 4 figures, NUFACT 2013 proceeding

Higher-order expansions of powered extremes of normal samples

In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall (1980). Furthermore, it is shown that the rate of convergence of distributions/densities of normalized extremes depends in principle on the power index

Totally Real Flat Minimal Surfaces in Quaternionic Projective Spaces

In this paper, we study totally real minimal surfaces in the quaternionic projective space $\mathbb{H}P^n$. We prove that the linearly full totally real flat minimal surfaces of isotropy order $n$ in $\mathbb{H}P^n$ are two surfaces in $\mathbb{C}P^n$, one of which is the Clifford solution, up to symplectic congruence

Quantum state complexity and the thermodynamic arrow of time

Why time is a one-way corridor? What's the origin of the arrow of time? We attribute the thermodynamic arrow of time as the direction of increasing quantum state complexity. Inspired by the work of Nielsen, Susskind and Micadei, we checked this hypothesis on both a simple two qubit and a three qubit quantum system. The result shows that in the two qubit system, the thermodynamic arrow of time always points in the direction of increasing quantum state complexity. For the three qubit system, the heat flow pattern among subsystems is closely correlated with the quantum state complexity of the subsystems. We propose that besides its impact on macroscopic spatial geometry, quantum state complexity might also generate the thermodynamic arrow of time.Comment: 4 pages, 4 figure

Understanding over-parameterized deep networks by geometrization

A complete understanding of the widely used over-parameterized deep networks is a key step for AI. In this work we try to give a geometric picture of over-parameterized deep networks using our geometrization scheme. We show that the Riemannian geometry of network complexity plays a key role in understanding the basic properties of over-parameterizaed deep networks, including the generalization, convergence and parameter sensitivity. We also point out deep networks share lots of similarities with quantum computation systems. This can be regarded as a strong support of our proposal that geometrization is not only the bible for physics, it is also the key idea to understand deep learning systems.Comment: 6 page

Quantifying Nonlocality Based on Local Hidden Variable Models

We introduce a fresh scheme based on the local hidden variable models to quantify nonlocality for arbitrarily high-dimensional quantum systems. Our scheme explores the minimal amount of white noise that must be added to the system in order to make the system local and realistic. Moreover, the scheme has a clear geometric significance and is numerically computable due to powerful computational and theoretical methods for the class of convex optimization problems known as semidefinite programs.Comment: 4page

Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff

We give quantitative estimates on the asymptotics of the linearized Boltzmann collision operator and its associated equation from angular cutoff to non cutoff. On one hand, the results disclose the link between the hyperbolic property resulting from the Grad's cutoff assumption and the smoothing property due to the long-range interaction. On the other hand, with the help of the localization techniques in the phase space, we observe some new phenomenon in the asymptotic limit process. As a consequence, we give the affirmative answer to the question that there is no jump for the property that the collision operator with cutoff does not have the spectrum gap but the operator without cutoff does have for the moderate soft potentials

Multi-dimensional central limit theorems and laws of large numbers under sublinear expectations

In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.Comment: 18 pages. arXiv admin note: text overlap with arXiv:1002.4546 by other author

Spreading in a shifting environment modeled by the diffusive logistic equation with a free boundary

We investigate the influence of a shifting environment on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When the environment is homogeneous and favourable, this model was first studied in Du and Lin \cite{DL}, where a spreading-vanishing dichotomy was established for the long-time dynamics of the species, and when spreading happens, it was shown that the species invades the new territory at some uniquely determined asymptotic speed $c_0>0$. Here we consider the situation that part of such an environment becomes unfavourable, and the unfavourable range of the environment moves into the favourable part with speed $c>0$. We prove that when $c\geq c_0$, the species always dies out in the long-run, but when $0<c<c_0$, the long-time behavior of the species is determined by a trichotomy described by (a) {\it vanishing}, (b) {\it borderline spreading}, or (c) {\it spreading}. If the initial population is writen in the form $u_0(x)=\sigma \phi(x)$ with $\phi$ fixed and $\sigma>0$ a parameter, then there exists $\sigma_0>0$ such that vanishing happens when $\sigma\in (0,\sigma_0)$, borderline spreading happens when $\sigma=\sigma_0$, and spreading happens when $\sigma>\sigma_0$

How deep learning works --The geometry of deep learning

Why and how that deep learning works well on different tasks remains a mystery from a theoretical perspective. In this paper we draw a geometric picture of the deep learning system by finding its analogies with two existing geometric structures, the geometry of quantum computations and the geometry of the diffeomorphic template matching. In this framework, we give the geometric structures of different deep learning systems including convolutional neural networks, residual networks, recursive neural networks, recurrent neural networks and the equilibrium prapagation framework. We can also analysis the relationship between the geometrical structures and their performance of different networks in an algorithmic level so that the geometric framework may guide the design of the structures and algorithms of deep learning systems.Comment: 16 pages, 13 figure