Fast Escaping Sets of meromorphic functions

In this paper, we give a definition of Eremenko's point of a meromorphic function with infinitely many poles and a condition for its existence in narrow annuli in terms of a covering theorem of annulus.Comment: some further work will be don

A Fast Quantum-safe Asymmetric Cryptosystem Using Extra Superincreasing Sequences

This paper gives the definitions of an extra superincreasing sequence and an anomalous subset sum, and proposes a fast quantum-safe asymmetric cryptosystem called JUOAN2. The new cryptosystem is based on an additive multivariate permutation problem (AMPP) and an anomalous subset sum problem (ASSP) which parallel a multivariate polynomial problem and a shortest vector problem respectively, and composed of a key generator, an encryption algorithm, and a decryption algorithm. The authors analyze the security of the new cryptosystem against the Shamir minima accumulation point attack and the LLL lattice basis reduction attack, and prove it to be semantically secure (namely IND-CPA) on the assumption that AMPP and ASSP have no subexponential time solutions. Particularly, the analysis shows that the new cryptosystem has the potential to be resistant to quantum computing attack, and is especially suitable to the secret communication between two mobile terminals in maneuvering field operations under any weather. At last, an example explaining the correctness of the new cryptosystem is given.Comment: 8 Pages. arXiv admin note: text overlap with arXiv:1408.622

Lyapunov exponents and related concepts for entire functions

Let $f$ be an entire function and denote by $f^\#$ be the spherical derivative of $f$ and by $f^n$ the $n$-th iterate of $f$. For an open set $U$ intersecting the Julia set $J(f)$, we consider how fast $\sup_{z\in U} (f^n)^\#(z)$ and $\int_U (f^n)^\#(z)^2 dx\:dy$ tend to $\infty$. We also study the growth rate of the sequence $(f^n)^\#(z)$ for $z\in J(f)$.Comment: 20 page

Investigation of Multimodal Features, Classifiers and Fusion Methods for Emotion Recognition

Automatic emotion recognition is a challenging task. In this paper, we present our effort for the audio-video based sub-challenge of the Emotion Recognition in the Wild (EmotiW) 2018 challenge, which requires participants to assign a single emotion label to the video clip from the six universal emotions (Anger, Disgust, Fear, Happiness, Sad and Surprise) and Neutral. The proposed multimodal emotion recognition system takes audio, video and text information into account. Except for handcraft features, we also extract bottleneck features from deep neutral networks (DNNs) via transfer learning. Both temporal classifiers and non-temporal classifiers are evaluated to obtain the best unimodal emotion classification result. Then possibilities are extracted and passed into the Beam Search Fusion (BS-Fusion). We test our method in the EmotiW 2018 challenge and we gain promising results. Compared with the baseline system, there is a significant improvement. We achieve 60.34% accuracy on the testing dataset, which is only 1.5% lower than the winner. It shows that our method is very competitive.Comment: 9 pages, 11 figures and 4 Tables. EmotiW2018 challeng

Band modification in (Ga, Mn)As evidenced by new measurement scheme --- magnetic photoresistance circular dichroism

The expected features of diluted magnetic semiconductors still remain in controversial issue, concerning whether or not s, p-d (f) exchange interactions indeed modify the host semiconductor band structure. To solve this doubt, a new scheme for measuring magneto-optical (MO) effect is developed, called magnetic photoresistance circular dichroism (PR-MCD), which detects the differential photoresistance of materials between two circularly polarized excitations. That allows us to detect the MO effect induced only by interband transitions, and provide unambiguous evidence that the host semiconductor band structure is indeed modified by the strong exchange interactions. Our PR-MCD spectra also disclose intrigue features which may come from strong coupling correlation effect at very high manganese concentration limit

On the iterations and the argument distribution of meromorphic functions

This paper consists of tow parts. One is to study the existence of a point $a$ in the intersection of Julia set and escaping set such that $\arg z=\theta$ is a singular direction if $\theta$ is a limit point of $\{\arg f^n(a)\}$ under some growth condition of a meromorphic function. The other is to study the connection between the Fatou set and singular direction. We prove that the absent of singular direction deduces the non-existence of annuli in the Fatou set.Comment: 28 page

Studies of Differences from the point of view of Nevanlinna Theory

This paper consists of three parts. First, we give so far the best condition under which the shift invariance of the counting function, and of the characteristic of a subharmonic function, holds. Second, a difference analogue of logarithmic derivative of a $\delta$-subharmonic function is established allowing the case of hyper-order equal to one and minimal hyper-type, which improves the condition of the hyper-order less than one. Finally, we make a careful discussion of a well-known difference equation and give out the possible forms of the equation under a growth condition for the solutions.Comment: 36 pages. To appear in the Transactions of the American Mathematical Society: https://doi.org/10.1090/tran/806

Second main theorem with tropical hypersurfaces and defect relation

The tropical Nevanlinna theory is Nevanlinna theory for tropical functions or maps over the max-plux semiring by using the approach of complex analysis. The main purpose of this paper is to study the second main theorem with tropical hypersurfaces into tropical projective spaces and give a defect relation which can be regarded as a tropical version of the Shiffman's conjecture. On the one hand, our second main theorem improves and extends the tropical Cartan's second main theorem due to Korhonen and Tohge [Advances Math. 298(2016), 693-725]. The growth of tropical holomorphic curve is also improved to $\limsup_{r\rightarrow\infty}\frac{\log T_{f}(r)}{r}=0$ (rather than just hyperorder strictly less than one) by obtaining an improvement of tropical logarithmic derivative lemma. On the other hand, we obtain a new version of tropical Nevanlinna's second main theorem which is different from the tropical Nevanlinna's second main theorem obtained by Laine and Tohge [Proc. London Math. Soc. 102(2011), 883-922]. The new version of the tropical Nevanlinna's second main theorem implies an interesting defect relation that $\delta_{f}(a)=0$ holds for a nonconstant tropical meromorphic function $f$ with $\limsup_{r\rightarrow\infty}\frac{\log T_{f}(r)}{r}=0$ and any $a\in\mathbb{R}$ such that $f\oplus a\not\equiv a.$Comment: 33 page

Hierarchical equations of motion for impurity solver in dynamical mean-field theory

A nonperturbative quantum impurity solver is proposed based on a formally exact hierarchical equations of motion (HEOM) formalism for open quantum systems. It leads to quantitatively accurate evaluation of physical properties of strongly correlated electronic systems, in the framework of dynamical mean-field theory (DMFT). The HEOM method is also numerically convenient to achieve the same level of accuracy as that using the state-of-the-art numerical renormalization group impurity solver at finite temperatures. The practicality of the novel HEOM+DMFT method is demonstrated by its applications to the Hubbard models with Bethe and hypercubic lattice structures. We investigate the metal-insulator transition phenomena, and address the effects of temperature on the properties of strongly correlated lattice systems.Comment: 14 pages, 11 figures, updated version accepted to be published in PR

Estimating Number of Factors by Adjusted Eigenvalues Thresholding

Determining the number of common factors is an important and practical topic in high dimensional factor models. The existing literatures are mainly based on the eigenvalues of the covariance matrix. Due to the incomparability of the eigenvalues of the covariance matrix caused by heterogeneous scales of observed variables, it is very difficult to give an accurate relationship between these eigenvalues and the number of common factors. To overcome this limitation, we appeal to the correlation matrix and show surprisingly that the number of eigenvalues greater than $1$ of population correlation matrix is the same as the number of common factors under some mild conditions. To utilize such a relationship, we study the random matrix theory based on the sample correlation matrix in order to correct the biases in estimating the top eigenvalues and to take into account of estimation errors in eigenvalue estimation. This leads us to propose adjusted correlation thresholding (ACT) for determining the number of common factors in high dimensional factor models, taking into account the sampling variabilities and biases of top sample eigenvalues. We also establish the optimality of the proposed methods in terms of minimal signal strength and optimal threshold. Simulation studies lend further support to our proposed method and show that our estimator outperforms other competing methods in most of our testing cases.Comment: 35 pages; 4 figure