Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks

Event sequence, asynchronously generated with random timestamp, is ubiquitous among applications. The precise and arbitrary timestamp can carry important clues about the underlying dynamics, and has lent the event data fundamentally different from the time-series whereby series is indexed with fixed and equal time interval. One expressive mathematical tool for modeling event is point process. The intensity functions of many point processes involve two components: the background and the effect by the history. Due to its inherent spontaneousness, the background can be treated as a time series while the other need to handle the history events. In this paper, we model the background by a Recurrent Neural Network (RNN) with its units aligned with time series indexes while the history effect is modeled by another RNN whose units are aligned with asynchronous events to capture the long-range dynamics. The whole model with event type and timestamp prediction output layers can be trained end-to-end. Our approach takes an RNN perspective to point process, and models its background and history effect. For utility, our method allows a black-box treatment for modeling the intensity which is often a pre-defined parametric form in point processes. Meanwhile end-to-end training opens the venue for reusing existing rich techniques in deep network for point process modeling. We apply our model to the predictive maintenance problem using a log dataset by more than 1000 ATMs from a global bank headquartered in North America.Comment: Accepted at Thirty-First AAAI Conference on Artificial Intelligence (AAAI17

Freeze-in Dirac neutrinogenesis: thermal leptonic CP asymmetry

We present a freeze-in realization of the Dirac neutrinogenesis in which the decaying particle that generates the lepton-number asymmetry is in thermal equilibrium. As the right-handed Dirac neutrinos are produced non-thermally, the lepton-number asymmetry is accumulated and partially converted to the baryon-number asymmetry via the rapid sphaleron transitions. The necessary CP-violating condition can be fulfilled by a purely thermal kinetic phase from the wavefunction correction in the lepton-doublet sector, which has been neglected in most leptogenesis-based setup. Furthermore, this condition necessitates a preferred flavor basis in which both the charged-lepton and neutrino Yukawa matrices are non-diagonal. To protect such a proper Yukawa structure from the basis transformations in flavor space prior to the electroweak gauge symmetry breaking, we can resort to a plethora of model buildings aimed at deciphering the non-trivial Yukawa structures. Interestingly, based on the well-known tri-bimaximal mixing with a minimal correction from the charged-lepton or neutrino sector, we find that a simultaneous explanation of the baryon-number asymmetry in the Universe and the low-energy neutrino oscillation observables can be attributed to the mixing angle and the CP-violating phase introduced in the minimal correction.Comment: 28 pages and 7 figures; more discussions and one figure added, final version published in the journa

Proof of some conjectural congruences involving Domb numbers

In this paper, we mainly prove the following conjectures of Z.-H. Sun \cite{SH2}: Let $p>3$ be a prime. If $p\equiv1\pmod3$ and $p=x^2+3y^2$, then we have $$\sum_{k=0}^{p-1}\frac{D_k}{4^k}\equiv\sum_{k=0}^{p-1}\frac{D_k}{16^k}\equiv4x^2-2p-\frac{p^2}{4x^2}\pmod{p^3},$$ and if $p\equiv2\pmod3$, then $$\sum_{k=0}^{p-1}\frac{D_k}{4^k}\equiv-2\sum_{k=0}^{p-1}\frac{D_k}{16^k}\equiv\frac{p^2}2\binom{\frac{p-1}2}{\frac{p-5}6}^{-2} \pmod{p^3},$$ where $D_n=\sum_{k=0}^n\binom{n}k^2\binom{2k}k\binom{2n-2k}{n-k}$ stands for the $n$th Domb number.Comment: 26 pages. (1.2) in Theorem 1.3 is added. arXiv admin note: text overlap with arXiv:2111.0877

Comprehension of Conversational Implicature in L2 Chinese

This study examined the ability to comprehend conventional and non-conventional implicatures, and the effect of proficiency and learning context (foreign language learners vs. heritage learners) on comprehension of implicature in L2 Chinese. Participants were three groups of college students of Chinese: elementary-level foreign language learners (n=21), advanced-level foreign language learners (n=25), and advanced-level heritage learners (n=25). They completed a 36-item computer-delivered listening test measuring their ability to comprehend three types of implicature: conventional indirect refusals, conventional indirect opinions, and non-conventional indirect opinions. Comprehension was analyzed for accuracy (scores on a multiple-choice measure) and comprehension speed (average time taken to answer items correctly). There was a significant effect of implicature type on accuracy, but not on comprehension speed. A significant effect of participant group was observed on accuracy, but the effect was mixed on comprehension speed

The two‐ to three‐second time window of shot durations in movies

Movie shots of singular scenes have a preferential duration of 2 to 3 s regardless of producers, movie types, and cultural environments. This observation suggests that the temporal structure of movies matches a neural mechanism of information processing in the time domain