Unified parametrization of quark and lepton mixing matrices in tri-bimaximal pattern

Parametrization of the quark and lepton mixing matrices is the first attempt to understand the mixing of fermions. In this work, we parameterize the quark and lepton matrices with the help of quark-lepton complementarity (QLC) in a tri-bimaximal pattern of lepton mixing matrix. In this way, we combine the parametrization of the two matrices with each other. We apply this new parametrization to several physical quantities, and show its simplicity in the expression of, e.g., the Jarlskog parameter of CP violation.Comment: 12 latex page

Bosonization of quantum sine-Gordon field with a boundary

Boundary operators and boundary ground states in sine-Gordon model with a fixed boundary condition are studied using bosonization and q-deformed oscillators.We also obtain the form-factors of this model.Comment: Latex 25page

Improved ACD-based financial trade durations prediction leveraging LSTM networks and Attention Mechanism

The liquidity risk factor of security market plays an important role in the formulation of trading strategies. A more liquid stock market means that the securities can be bought or sold more easily. As a sound indicator of market liquidity, the transaction duration is the focus of this study. We concentrate on estimating the probability density function p({\Delta}t_(i+1) |G_i) where {\Delta}t_(i+1) represents the duration of the (i+1)-th transaction, G_i represents the historical information at the time when the (i+1)-th transaction occurs. In this paper, we propose a new ultra-high-frequency (UHF) duration modelling framework by utilizing long short-term memory (LSTM) networks to extend the conditional mean equation of classic autoregressive conditional duration (ACD) model while retaining the probabilistic inference ability. And then the attention mechanism is leveraged to unveil the internal mechanism of the constructed model. In order to minimize the impact of manual parameter tuning, we adopt fixed hyperparameters during the training process. The experiments applied to a large-scale dataset prove the superiority of the proposed hybrid models. In the input sequence, the temporal positions which are more important for predicting the next duration can be efficiently highlighted via the added attention mechanism layer

Triminimal Parametrization of Quark Mixing Matrix

Starting from a new zeroth order basis for quark mixing (CKM) matrix based on the quark-lepton complementarity and the tri-bimaximal pattern of lepton mixing, we derive a triminimal parametrization of CKM matrix with three small angles and a CP-violating phase as its parameters. This new triminimal parametrization has the merits of fast convergence and simplicity in application. With the quark-lepton complementary relations, we derive relations between the two unified triminimal parametrizations for quark mixing obtained in this work and for lepton mixing obtained by Pakvasa-Rodejohann-Weiler. Parametrization deviating from quark-lepton complementarity is also discussed.Comment: 9 pages, no figur