A possible method for non-Hermitian and non-PTPT-symmetric Hamiltonian systems

A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator $\eta_+$ and defining the annihilation and creation operators to be $\eta_+$-pseudo-Hermitian adjoint to each other. The operator $\eta_+$ represents the $\eta_+$-pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-$PT$-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator $\eta_+$ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-$PT$-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.Comment: 15 pages, no figures; v2: clarifications added; v3: 16 pages, 1 figure, clarifications made clearer; v4: 19 pages, the main context is completely rewritten; v5: 25 pages, title slightly changed, clarifications added, the final version to appear in PLOS ON

A Family of Maximum Margin Criterion for Adaptive Learning

In recent years, pattern analysis plays an important role in data mining and recognition, and many variants have been proposed to handle complicated scenarios. In the literature, it has been quite familiar with high dimensionality of data samples, but either such characteristics or large data have become usual sense in real-world applications. In this work, an improved maximum margin criterion (MMC) method is introduced firstly. With the new definition of MMC, several variants of MMC, including random MMC, layered MMC, 2D^2 MMC, are designed to make adaptive learning applicable. Particularly, the MMC network is developed to learn deep features of images in light of simple deep networks. Experimental results on a diversity of data sets demonstrate the discriminant ability of proposed MMC methods are compenent to be adopted in complicated application scenarios.Comment: 14 page

High-efficiency orange and yellow organic light-emitting devices using platinum(II) complexes containing extended π -conjugated cyclometalated ligands as dopant materials

Two luminescent platinum(II) complexes 1 and 2 containing extended π -conjugated cyclometalated ligands have been used as dopant materials for the construction of two high-efficiency organic light-emitting devices I and II. Device I (containing dopant 1) emits orange emission and exhibits a maximum external quantum efficiency of 12.4%, a maximum luminous efficiency of 32.3 cdA, and a maximum power efficiency of 11.2 lmW. Device II (containing dopant 2) emits yellow light and exhibits a maximum external quantum efficiency of 16.1%, a maximum luminous efficiency of 51.8 cdA, and a maximum power efficiency of 23.2 lmW. © 2007 American Institute of Physics.published_or_final_versio

The Journal of Mathematical Chemistry: A Bibliometric Profile

This paper describes the bibliometric characteristics of 2,398 articles published in the Journal of Mathematical Chemistry in the period 1987-2015. These articles have been analysed using data from the Web of Science Core Collection and demonstrate the contribution of the journal not only to mathematical chemistry but also to science more generally

Fracturing ranked surfaces

Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially allocating these elements according to their ranks and systematically preventing the occupation of bridges, namely elements that, if occupied, would provide global connectivity, we disclose that bridges hide a new tricritical point at an occupation fraction $p=p_{c}$, where $p_{c}$ is the percolation threshold of random percolation. For any value of $p$ in the interval $p_{c}< p \leq 1$, our results show that the set of bridges has a fractal dimension $d_{BB} \approx 1.22$ in two dimensions. In the limit $p \rightarrow 1$, a self-similar fracture is revealed as a singly connected line that divides the system in two domains. We then unveil how several seemingly unrelated physical models tumble into the same universality class and also present results for higher dimensions

Factors related to children’s caries: a structural equation modeling approach

BACKGROUND: Dental caries among preschool children is highly prevalent in many less-developed countries. METHODS: A model which explored the factors related to children’s dental caries was tested in this study using structural equation modeling. Caregivers of children aged 5 years were surveyed on their socioeconomic status, and their oral health knowledge, attitudes and practices. In addition, information on their children’s oral health practices, dental insurance and dental service utilization were collected. Examination of caries was conducted on all children who returned fully completed questionnaires. RESULTS: The results showed that socioeconomic factors influenced children’s oral health practices through the impact of caregivers’ oral health knowledge and practices; that caregivers’ oral health knowledge affected children’s oral health practices through the influence of caregivers’ oral health attitudes and practices; and finally, that children’s oral health practices were linked directly to their caries. CONCLUSION: The findings have important applications for promoting policies aimed at advancing children’s oral health

The cytotoxic effects of lipidic formulated gold porphyrin nanoparticles for the treatment of neuroblastoma

Objective: Nanotechnology has been identified as a promising platform in the improvement of the design and development of drug delivery systems. In the present study we investigated the potential of lipidic nanoparticles consisting of gold porphyrin for the treatment of neuroblastoma. Materials and methods: To characterize the size of the lipidic gold porphyrin nanoparticles, we used transmission electron microscopy (TEM). The in vitro cytotoxic effect on neuroblastoma activity was examined using XTT cell proliferation assay, then IC50 values were calculated. In vivo safety and toxicity were studied using intraperitoneal injection of gold porphyrin nanoparticles into normal animals. Finally, tumor size measurement and animal survival were studied to investigate the therapeutic effect of lipidic gold porphyrin nanoparticles on neuroblastoma growth. Results: We found that incorporation of gold porphyrin into lipidic nanoparticles resulted in a 16-fold increase in size. Subsequent in vitro and in vivo cytotoxicity studies further showed that the lipidic gold porphyrin nanoparticles could decrease systemic toxicity, as well as inhibiting tumor growth following administration into the neuroblastoma bearing mice. Conclusion: The delivery of lipidic gold porphyrin nanoparticles by incorporation with lipidic formulation is feasible approach to treat neuroblastoma. We await further studies to evaluate tumor killing kinetics. © 2010 Lee et al, publisher and licensee Dove Medical Press Ltd.published_or_final_versio

Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure

Linear-T resistivity and change in Fermi surface at the pseudogap critical point of a high-Tc superconductor

A fundamental question of high-temperature superconductors is the nature of the pseudogap phase which lies between the Mott insulator at zero doping and the Fermi liquid at high doping p. Here we report on the behaviour of charge carriers near the zero-temperature onset of that phase, namely at the critical doping p* where the pseudogap temperature T* goes to zero, accessed by investigating a material in which superconductivity can be fully suppressed by a steady magnetic field. Just below p*, the normal-state resistivity and Hall coefficient of La1.6-xNd0.4SrxCuO4 are found to rise simultaneously as the temperature drops below T*, revealing a change in the Fermi surface with a large associated drop in conductivity. At p*, the resistivity shows a linear temperature dependence as T goes to zero, a typical signature of a quantum critical point. These findings impose new constraints on the mechanisms responsible for inelastic scattering and Fermi surface transformation in theories of the pseudogap phase.Comment: 24 pages, 6 figures. Published in Nature Physics. Online at http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys1109.htm

Gene and protein expression of glucose transporter 1 and glucose transporter 3 in human laryngeal cancer—the relationship with regulatory hypoxia-inducible factor-1α expression, tumor invasiveness, and patient prognosis

Increased glucose uptake mediated by glucose transporters and reliance on glycolysis are common features of malignant cells. Hypoxia-inducible factor-1α supports the adaptation of hypoxic cells by inducing genes related to glucose metabolism. The contribution of glucose transporter (GLUT) and hypoxia-inducible factor-1α (HIF-1α) activity to tumor behavior and their prognostic value in head and neck cancers remains unclear. The aim of this study was to examine the predictive value of GLUT1, GLUT3, and HIF-1α messenger RNA (mRNA)/protein expression as markers of tumor aggressiveness and prognosis in laryngeal cancer. The level of hypoxia/metabolic marker genes was determined in 106 squamous cell laryngeal cancer (SCC) and 73 noncancerous matched mucosa (NCM) controls using quantitative realtime PCR. The related protein levels were analyzed by Western blot. Positive expression of SLC2A1, SLC2A3, and HIF-1α genes was noted in 83.9, 82.1, and 71.7 % of SCC specimens and in 34.4, 59.4, and 62.5 % of laryngeal cancer samples. Higher levels of mRNA/protein for GLUT1 and HIF-1α were noted in SCC compared to NCM (p<0.05). SLC2A1 was found to have a positive relationship with grade, tumor front grading (TFG) score, and depth and mode of invasion (p<0.05). SLC2A3 was related to grade and invasion type (p<0.05). There were also relationships of HIF-1α with pTNM, TFG scale, invasion depth and mode, tumor recurrences, and overall survival (p<0.05). In addition, more advanced tumors were found to be more likely to demonstrate positive expression of these proteins. In conclusion, the hypoxia/metabolic markers studied could be used as molecular markers of tumor invasiveness in laryngeal cancer.This work was supported, in part, by the statutory fund of the Department of Cytobiochemistry, University of Łódź, Poland (506/811), and by grant fromtheNational Science Council, Poland (N403 043 32/2326)