Abstract:
This paper establishes the income and risk model in financial investment based on multi-objective programming theory, aiming to analyze the relationship between risk and return in financial investment and discuss the relationship between the risk the investor shall bear and decentralization degree of investment project. MATLAB software is used to analyze the investor’s optimized return under fixed risk level and the minimized risk with defined benefit. In addition, it chooses the optimal portfolio under such risk level with respect to the bearing capacity of different risks. This paper performs sensitivity analysis of risk in income model using LINGO software, and puts forward the optimal portfolio for the investor without special preference. Calculations show that the model established is satisfactory in determining the optimal portfolio.

In this paper, based on existing results, decision making about portfolio investment
schemes is discussed, ordering method of fuzzy numbers of interval
value is shown, corresponding auxiliary models are established and solutions
are provided with theories of fuzzy mathematics, optimization theory and
numerical calculation, etc. Then it applies software programming to solve the
portfolio investment situation between investors in savings and four securities
according to the established models. The result shows that investors can
choose the risk coefficient that they can bear to reach the maximum value of
expected returns. The greater the risk coefficient, the greater the income, the
smaller the risk coefficient and the smaller the income. Investors can determine
their own portfolio strategy according to their own conditions in order
to meet their own interests.

Abstract:
Traditional international trade theory is mainly based on comparative advantage. In fact, structure of international trade is more complicated than what is illustrated by theory, which affects illustrating ability of traditional international trade theory. By introducing organizational capital and combing it with specialization and scale economy, this paper interpreted intra-industry and inter-industry trade and put forward relevant suggestions for policy.

Abstract:
We present a local representation of the electronic dielectric response function, based on a spatial partition of the dielectric response into contributions from each Wannier function using a generalized density functional perturbation theory. This procedure is fully ab initio, and therefore allows us to rigorously define local metrics, such as "bond polarizability," on Wannier centers. We show that the locality of the response function is determined by the locality of three quantities: Wannier functions of the occupied manifold, the density matrix, and the Hamiltonian matrix. In systems with a gap, the bare dielectric response is exponentially localized, which supports the physical picture of the dielectric response function as a collection of interacting local response that can be captured by a tight-binding model.

Abstract:
Let $\tau_3(n)$ be the triple divisor function which is the number of solutions of the equation $d_1d_2d_3=n$ in natural numbers. It is shown that $$ \sum_{1\leq n_1,n_2,n_3\leq \sqrt{x}}\tau_3(n_1^2+n_2^2+n_3^2)=c_1x^{\frac{3}{2}}(\log x)^2+ c_2x^{\frac{3}{2}}\log x +c_3x^{\frac{3}{2}} +O_{\varepsilon}(x^{\frac{11}{8}+\varepsilon}) $$ for some constants $c_1$, $c_2$ and $c_3$.

Abstract:
The low-rank matrix factorization as a L1 norm minimization problem has recently attracted much attention due to its intrinsic robustness to the presence of outliers and missing data. In this paper, we propose a new method, called the divide-and-conquer method, for solving this problem. The main idea is to break the original problem into a series of smallest possible sub-problems, each involving only unique scalar parameter. Each of these subproblems is proved to be convex and has closed-form solution. By recursively optimizing these small problems in an analytical way, efficient algorithm, entirely avoiding the time-consuming numerical optimization as an inner loop, for solving the original problem can naturally be constructed. The computational complexity of the proposed algorithm is approximately linear in both data size and dimensionality, making it possible to handle large-scale L1 norm matrix factorization problems. The algorithm is also theoretically proved to be convergent. Based on a series of experiment results, it is substantiated that our method always achieves better results than the current state-of-the-art methods on $L1$ matrix factorization calculation in both computational time and accuracy, especially on large-scale applications such as face recognition and structure from motion.

Abstract:
The maximum mean discrepancy (MMD) is a recently proposed test statistic for two-sample test. Its quadratic time complexity, however, greatly hampers its availability to large-scale applications. To accelerate the MMD calculation, in this study we propose an efficient method called FastMMD. The core idea of FastMMD is to equivalently transform the MMD with shift-invariant kernels into the amplitude expectation of a linear combination of sinusoid components based on Bochner's theorem and Fourier transform (Rahimi & Recht, 2007). Taking advantage of sampling of Fourier transform, FastMMD decreases the time complexity for MMD calculation from $O(N^2 d)$ to $O(L N d)$, where $N$ and $d$ are the size and dimension of the sample set, respectively. Here $L$ is the number of basis functions for approximating kernels which determines the approximation accuracy. For kernels that are spherically invariant, the computation can be further accelerated to $O(L N \log d)$ by using the Fastfood technique (Le et al., 2013). The uniform convergence of our method has also been theoretically proved in both unbiased and biased estimates. We have further provided a geometric explanation for our method, namely ensemble of circular discrepancy, which facilitates us to understand the insight of MMD, and is hopeful to help arouse more extensive metrics for assessing two-sample test. Experimental results substantiate that FastMMD is with similar accuracy as exact MMD, while with faster computation speed and lower variance than the existing MMD approximation methods.

Abstract:
Self-paced learning (SPL) has been attracting increasing attention in machine learning and computer vision. Albeit empirically substantiated to be effective, the investigation on its theoretical insight is still a blank. It is even unknown that what objective a general SPL regime converges to. To this issue, this study attempts to initially provide some new insights under this "heuristic" learning scheme. Specifically, we prove that the solving strategy on SPL exactly accords with a majorization minimization algorithm, a well known technique in optimization and machine learning, implemented on a latent objective. A more interesting finding is that, the loss function contained in this latent objective has a similar configuration with non-convex regularized penalty, an attractive topic in statistics and machine learning. In particular, we show that the previous hard and linear self-paced regularizers are equivalent to the capped norm and minimax concave plus penalties, respectively, both being widely investigated in statistics. Such connections between SPL and previous known researches enhance new insightful comprehension on SPL, like convergence and parameter setting rationality. The correctness of the proposed theory is substantiated by experimental results on synthetic and UCI data sets.

To analyze the clinical symptoms and signs in cases of
oral submucous fibrosis which has transformed into squamous cell carcinoma, twenty-nine
patients with squamous cell carcinoma correlated with oral submucous fibrosis,
leukoplakia, lichen planus were taken biopsy for positive diagnosis. The
clinical and pathological diagnosis of oral submucous fibrosis depended on
clinical and pathological diagnostic standards. The oral submucous fibrosis
involving different portions and size in the mouth was observed and recorded.
The portions of oral cancer, clinical findings and symptoms, cancerous size,
the conditions of the local lymphatic nodes and of oral submucous fibrosis
correlated with squamous cell carcinoma in the mouth, oral leukoplakia, lichen planus were also observed
and recorded. In twenty-nine patients with oral squamous cell carcinoma,
duration from oral submucous fibrosis transformed into oral cancer ranged
from 2 to 15 years with an average year of 6.69. The serious degrees of oral
submucous fibrosis in the patients with oral cancer were that the moderately
advanced stage was found in 3 cases (10.34%) and the advanced stage was found
in 26 cases (89.65%). The cancerous portion was that the buccal mucosa was
found in 9 cases (31.03%); the tongue was found in 14 cases (48.27%); the other
portion was found in the rest 6 cases (20.68%). Among the twenty-nine patients
twenty-three patients with squamous cell carcinoma were associated with leukoplakia
(79.31%), five patients were associated with lichen planus (17.24%). Twenty-seven
patients (93.1%) had habits of betel quid chewing, smoked cigarette and drank
alcohol, the rest two patients had habits of betel quid chewing and cigarette
smoking. The present study demonstrates that oral submucous fibrosis is a real
precancerous lesion and may transform into squamous cell carcinoma in the
mouth.

Abstract:
p21 CIP1/WAF1 is a p53-target gene in response to cellular DNA damage. Here we report the development of a fish cell biosensor system for high throughput genotoxicity detection of new drugs, by stably integrating two reporter plasmids of pGL 3-p21-luc (human p21 promoter linked to firefly luciferase) and pRL-CMV-luc (CMV promoter linked to Renilla luciferase) into marine flatfish flounder gill (FG) cells, referred to as p21FGLuc. Initial validation of this genotoxicity biosensor system showed that p21FGLuc cells had a wild-type p53 signaling pathway and responded positively to the challenge of both directly acting genotoxic agents (bleomycin and mitomycin C) and indirectly acting genotoxic agents (cyclophosphamide with metabolic activation), but negatively to cyclophosphamide without metabolic activation and the non-genotoxic agents ethanol and D-mannitol, thus confirming a high specificity and sensitivity, fast and stable response to genotoxic agents for this easily maintained fish cell biosensor system. This system was especially useful in the genotoxicity detection of Di(2-ethylhexyl) phthalate (DEHP), a rodent carcinogen, but negatively reported in most non-mammalian in vitro mutation assays, by providing a strong indication of genotoxicity for DEHP. A limitation for this biosensor system was that it might give false positive results in response to sodium butyrate and any other agents, which can trans-activate the p21 gene in a p53-independent manner.