DeepWriter: A Multi-Stream Deep CNN for Text-independent Writer Identification

Text-independent writer identification is challenging due to the huge variation of written contents and the ambiguous written styles of different writers. This paper proposes DeepWriter, a deep multi-stream CNN to learn deep powerful representation for recognizing writers. DeepWriter takes local handwritten patches as input and is trained with softmax classification loss. The main contributions are: 1) we design and optimize multi-stream structure for writer identification task; 2) we introduce data augmentation learning to enhance the performance of DeepWriter; 3) we introduce a patch scanning strategy to handle text image with different lengths. In addition, we find that different languages such as English and Chinese may share common features for writer identification, and joint training can yield better performance. Experimental results on IAM and HWDB datasets show that our models achieve high identification accuracy: 99.01% on 301 writers and 97.03% on 657 writers with one English sentence input, 93.85% on 300 writers with one Chinese character input, which outperform previous methods with a large margin. Moreover, our models obtain accuracy of 98.01% on 301 writers with only 4 English alphabets as input.Comment: This article will be presented at ICFHR 201

General Reynolds Analogy for Blunt-nosed Bodies in Hypersonic Flows

In this paper, the relation between skin friction and heat transfer along windward sides of blunt-nosed bodies in hypersonic flows is investigated. The self-similar boundary layer analysis is accepted to figure out the distribution of the ratio of skin friction to heat transfer coefficients along the wall. It is theoretically obtained that the ratio depends linearly on the local slope angle of the wall surface, and an explicit analogy expression is presented for circular cylinders, although the linear distribution is also found for other nose shapes and even in gas flows with chemical reactions. Furthermore, based on the theoretical modelling of the second order shear and heat transfer terms in Burnett equations, a modified analogy is derived in the near continuum regime by considering the rarefied gas effects. And a bridge function is also constructed to describe the nonlinear analogy in the transition flow regime. At last, the direct simulation Monte Carlo method is used to validate the theoretical results. The general analogy, beyond the classical Reynolds analogy, is applicable to both flat plates and blunt-nosed bodies, in either continuous or rarefied hypersonic flows

Piezoelectricity and Topological Quantum Phase Transitions in Two-Dimensional Spin-Orbit Coupled Crystals with Time-Reversal Symmetry

Finding new physical responses that signal topological quantum phase transitions is of both theoretical and experimental importance. Here, we demonstrate that the piezoelectric response can change discontinuously across a topological quantum phase transition in two-dimensional time-reversal invariant systems with spin-orbit coupling, thus serving as a direct probe of the transition. We study all gap closing cases for all 7 plane groups that allow non-vanishing piezoelectricity and find that any gap closing with 1 fine-tuning parameter between two gapped states changes either the $Z_2$ invariant or the locally stable valley Chern number. The jump of the piezoelectric response is found to exist for all these transitions, and we propose the HgTe/CdTe quantum well and BaMnSb$_2$ as two potential experimental platforms. Our work provides a general theoretical framework to classify topological quantum phase transitions and reveals their ubiquitous relation to the piezoelectric response.Comment: Close to the published versio

Order-Preservation for Multidimensional Stochastic Functional Differential Equations with Jump

Sufficient and necessary conditions are presented for the order-preservation of stochastic functional differential equations on $\R^d$ with non-Lipschitzian coefficients driven by the Brownian motion and Poisson processes. The sufficiency of the conditions extends and improves some known comparison theorems derived recently for one-dimesional equations and multidimensional equations without delay, and the necessity is new even in these special situations.Comment: 18page

Spin Susceptibility, Upper Critical Field and Disorder Effect in j=32j=\frac{3}{2} Superconductors with Singlet-Quintet Mixing

Recently, a new pairing state with the mixing between s-wave singlet channel and isotropic d-wave quintet channel induced by centrosymmetric spin-orbit coupling has been theoretically proposed in the superconducting materials with $j=\frac{3}{2}$ electrons. In this work, we derive the expressions of the zero-temperature spin susceptibility, the upper critical field close to the zero-field critical temperature $T_c$ and the critical temperature with weak random non-magnetic disorders for the singlet-quintet mixed state based on the Luttinger model. Our study revealed the following features of the singlet-quintet mixing. (1) The zero-temperature spin susceptibility remains zero for the singlet-quintet mixed state if only the centrosymmetric spin-orbit coupling is taken into account, and will deviate from zero when the non-centrosymmetric spin-orbit coupling is introduced. (2) The singlet-quintet mixing can help enhance the upper critical field roughly because it can increase $T_c$. (3) Although the quintet channel is generally suppressed by the non-magnetic disorder scattering, we find the strong mixing between singlet and quintet channels can help to stabilize the quintet channel. As a result, we still find a sizable quintet component mixed into the singlet channel in the presence of weak random non-magnetic disorders. Our work provides the guidance for future experiments on spin susceptibility and upper critical field of the singlet-quintet mixed superconducting states, and illustrates the stability of the singlet-quintet mixing against the weak random non-magnetic disorder.Comment: 23 pages and 6 figure

Distribution Dependent SDEs with Singular Coefficients

Under integrability conditions on distribution dependent coefficients, existence and uniqueness are proved for McKean-Vlasov type SDEs with non-degenerate noise. When the coefficients are Dini continuous in the space variable, gradient estimates and Harnack type inequalities are derived. These generalize the corresponding results derived for classical SDEs, and are new in the distribution dependent setting.Comment: 28page

Classification of topological crystalline insulators based on representation theory

Topological crystalline insulators define a new class of topological insulator phases with gapless surface states protected by crystalline symmetries. In this work, we present a general theory to classify topological crystalline insulator phases based on the representation theory of space groups. Our approach is to directly identify possible nontrivial surface states in a semi-infinite system with a specific surface, of which the symmetry property can be described by 17 two-dimensional space groups. We reproduce the existing results of topological crystalline insulators, such as mirror Chern insulators in the $pm$ or $pmm$ groups, $C_{nv}$ topological insulators in the $p4m$, $p31m$ and $p6m$ groups, and topological nonsymmorphic crystalline insulators in the $pg$ and $pmg$ groups. Aside from these existing results, we also obtain the following new results: (1) there are two integer mirror Chern numbers ($\mathbb{Z}^2$) in the $pm$ group but only one ($\mathbb{Z}$) in the $cm$ or $p3m1$ group for both the spinless and spinful cases; (2) for the $pmm$ ($cmm$) groups, there is no topological classification in the spinless case but $\mathbb{Z}^4$ ($\mathbb{Z}^2$) classifications in the spinful case; (3) we show how topological crystalline insulator phase in the $pg$ group is related to that in the $pm$ group; (4) we identify topological classification of the $p4m$, $p31m$, and $p6m$ for the spinful case; (5) we find topological non-symmorphic crystalline insulators also existing in $pgg$ and $p4g$ groups, which exhibit new features compared to those in $pg$ and $pmg$ groups. We emphasize the importance of the irreducible representations for the states at some specific high-symmetry momenta in the classification of topological crystalline phases. Our theory can serve as a guide for the search of topological crystalline insulator phases in realistic materials

Deep-learning based numerical BSDE method for barrier options

As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic differential equation (BSDE). We can either solve the PDE to obtain option prices or solve its associated BSDE. Recently a deep learning technique has been applied to solve option prices using the BSDE approach. In this approach, deep learning is used to learn some deterministic functions, which are used in solving the BSDE with terminal conditions. In this paper, we extend the deep-learning technique to solve a PDE with both terminal and boundary conditions. In particular, we will employ the technique to solve barrier options using Brownian motion bridges

Leptonic Unitarity Triangles and Effective Mass Triangles of the Majorana Neutrinos

Given the best-fit results of six neutrino oscillation parameters, we plot the Dirac and Majorana unitarity triangles (UTs) of the 3\times 3 lepton flavor mixing matrix to show their real shapes for the first time. The connections of the Majorana UTs with neutrino-antineutrino oscillations and neutrino decays are explored, and the possibilities of right or isosceles UTs are discussed. In the neutrino mass limit of m_1 \to 0 or m_3 \to 0, which is allowed by current experimental data, we show how the six triangles formed by the effective Majorana neutrino masses \langle m\rangle_{\alpha\beta} (for \alpha, \beta = e, \mu, \tau) and their corresponding component vectors look like in the complex plane. The relations of such triangles to the Majorana phases and to the lepton-number-violating decays H^{++} \to \alpha^+ \beta^+ in the type-II seesaw mechanism are also illustrated.Comment: 18 pages, 4 figures, more discussions added. Invited contribution to the Special Issue on Neutrino Oscillations for celebrating the Nobel Prize in Physics 2015 (Nucl. Phys. B in press

Neutrino mass ordering and \mu-\tau reflection symmetry breaking

If the neutrino mass spectrum turns out to be m^{}_3 < m^{}_1 < m^{}_2, one may choose to relabel it as m^{\prime}_1 < m^{\prime}_2 < m^{\prime}_3 such that all the masses of fundamental fermions with the same electrical charges are in order. In this case the columns of the 3\times 3 lepton flavor mixing matrix U should be reordered accordingly, and the resulting pattern U^\prime may involve one or two large mixing angles in the standard parametrization or its variations. Since the Majorana neutrino mass matrix keeps unchanged in such a mass relabeling, a possible \mu-\tau reflection symmetry is respected in this connection and its breaking effects are model-independently constrained at the 3\sigma level by using current experimental data.Comment: 17 pages, 5 figures, some changes made, new figures and discussions added, and accepted for publication in Chinese Phys.