Fractional derivatives hold memory effects, and they are extensively used in various real-world applications. However, they also need large storage space and cause poor efficiency. In this paper, ...some standard definitions are revisited. Then, short memory fractional derivatives and a short memory fractional modeling approach are introduced. Numerical solutions are given by the use of the predictor–corrector method. The short memory is adopted for fractional modeling of memristor, neural networks and materials’ relaxation property. Global stability conditions of variable-order neural networks are derived. The new features of short memory fractional differential equations are used to improve the performance of networks. The results are illustrated in comparison with standard ones. Finally, discussions are made about potential applications.
A general fractional calculus is described using fractional operators with respect to another function, and some often used propositions are presented in this framework. Together with the continuous ...time random walk (CTRW), a general time-fractional Fokker–Planck equation is derived and the governing equation meets the general fractional derivative. Finally, various new probability density functions are proposed in this paper.
Premise
Pollination in many aquatic plants takes place on the water surface, and the male flowers or stamens often produce gas bubbles underwater; however, the generation mechanism and function of ...these bubbles are unknown.
Methods
A common submerged plant, Hydrilla verticillata, was used as experimental material to observe the structure of male flowers, analyze the process of bubble generation, and simulate the movement process of the male flower with attached gas bubble in water.
Results
The aerenchyma inside the male plants of H. verticillata transported the gas produced by the plant's branches during photosynthesis to the male flower, and the formed gas bubbles became attached to the edge of the perianth. The gas accumulation rate in the attached bubbles increased with light intensity. Once the bubble diameter increased to approximately 3.3 mm, the male flowers with the bubble detached from the plant and floated to the water surface. The removal of the attached bubbles did not affect the male flower detached from the plant; however, the surfacing of male flowers without gas bubbles was easily prevented by the plant's branches in the water, and they could not reach the water surface to complete pollen dispersal.
Conclusions
The gas bubbles produced by male flowers of H. verticillata came from the gas produced by branches under light. These bubbles can help ascending male flowers bypass the obstacles in water and reach the surface to complete pollination.
The Dahutang deposit is a newly discovered tungsten deposit, which is within the largest ones in the world with an estimated WO3 reserve of 2 million tones. W-mineralization is considered to be ...related with the Late Mesozoic granites in the district. However, the precise emplacement ages, sources of these granites, and their relationship with mineralization are not well understood. In this study, four mineralization-related granite bodies (G1 to G4) were identified in the Dahutang mining area, including the porphyritic-like two-mica granite (G1) (the size of its phenocrysts is from 0.2×0.2cm2 to 0.7×0.3cm2), middle- to fine-grained muscovite granite (G2), porphyritic two-mica granite (G3) (the size of its phenocrysts is from 0.3×0.2cm2 to 0.9×0.6cm2), and fine-grained two-mica granite (G4). LA-ICP-MS U–Pb dating of zircon grains from these four granite bodies yields emplacement ages of 144.0±0.6Ma, 133.7±0.5Ma, 130.3±1.1Ma and 130.7±1.1Ma, respectively. Granites contain quartz, K-feldspar and plagioclase as the principal phases, accompanied by muscovite, minor biotite and accessory minerals. Geochemically, the granites are strongly peraluminous, have high contents of alkalis, high Ga/Al ratios, enrichment in LILEs (such as Rb) and depletion in HFSEs (such as Zr, Nb, Ti). The granites formed at relatively low temperatures (679°C to 760°C) according to zircon saturation temperatures. Geochemical fractionation trends recorded by whole rocks and minerals permit to distinguish and model the two fractional crystallization series G1 and G2–G4. Fractional crystallization of orthoclase and albite in G1 and G4, and orthoclase and oligoclase in G2 and G3 was the principal process of magmatic differentiation that controlled Rb, Sr and Ba concentrations, whereas rare earth elements were fractionated by accessory minerals, such as apatite, zircon and monazite. The geochemical data suggest that the rocks are highly fractionated S-type granites. The granites show bulk rock εNd(t) values in the range of −9.37 to −5.92 and zircon εHf(t) values from −8.44 to −2.13, with late Mesoproterozoic TDMC ages for both Nd and Hf isotopes. Geochemical and isotopic data suggest that these highly fractionated S-type granites G1 and G2–G4 were originated from two episodes of partial melting of different protoliths which have analogous components of metamorphosed pelitic rocks from the Neoproterozoic Shuangqiaoshan Group, which are enriched in tungsten. Extreme fractional crystallization resulted in further enrichment of tungsten in the evolved granitic magma. The new presented data together with previously published data suggest that the Dahutang granitic complex was likely to be formed during lithospheric thinning and asthenospheric upwelling process in Eastern China.
•Dahutang deposit is a new discovered largest tungsten deposit in the world.•The granites at Duhutang are highly fractionated S-type granites.•The granites were originated from two episodes of partial melting of different protoliths.•The G1 granite intruded during the first stage of 144Ma.•The G2–G4 granites intruded during the second stage of 130–134Ma.
This study investigates linear fractional difference equations with respect to interval–valued functions. Caputo and Riemann–Liouville differences are defined. w–monotonicity is introduced and ...discrete Leibniz integral laws are provided. Then exact solutions of two linear equations are obtained by Picard's iteration. In comparison with the deterministic initial problems, the solutions are given in discrete Mittag–Leffler functions with and without delay, respectively. This paper provides a novel tool to understand fractional uncertainty problems on discrete time domains.
Discrete fractional calculus is suggested to describe neural networks with memory effects. Fractional discrete-time recurrent neural network is proposed on an isolated time scale. Stability results ...are investigated via Banach fixed point technique. The attractive solution space is constructed and stability conditions are provided. Furthermore, short memory and variable-order fractional neural networks are given according to the stability conditions. Two and three dimensional numerical examples are used to demonstrate the theoretical results.
•Variable-order fractional discrete-time neural network is proposed.•Stability conditions are provided by fixed point theorems.•Numerical examples are given to illustrate the theoretical results.
Dysfunctions of long non-coding RNA (lncRNAs) have been associated with the initiation and progression of hepatocellular carcinoma (HCC), but the clinicopathologic significance and potential role of ...lncRNA PTTG3P (pituitary tumor-transforming 3, pseudogene) in HCC remains largely unknown.
We compared the expression profiles of lncRNAs in 3 HCC tumor tissues and adjacent non-tumor tissues by microarrays. In situ hybridization (ISH) and quantitative real-time polymerase chain reaction (qRT-PCR) were applied to assess the level of PTTG3P and prognostic values of PTTG3P were assayed in two HCC cohorts (n = 46 and 90). Artificial modulation of PTTG3P (down- and over-expression) was performed to explore the role of PTTG3P in tumor growth and metastasis in vitro and in vivo. Involvement of PTTG1 (pituitary tumor-transforming 1), PI3K/AKT signaling and its downstream signals were validated by qRT-PCR and western blot.
We found that PTTG3P was frequently up-regulated in HCC and its level was positively correlated to tumor size, TNM stage and poor survival of patients with HCC. Enforced expression of PTTG3P significantly promoted cell proliferation, migration, and invasion in vitro, as well as tumorigenesis and metastasis in vivo. Conversely, PTTG3P knockdown had opposite effects. Mechanistically, over-expression of PTTG3P up-regulated PTTG1, activated PI3K/AKT signaling and its downstream signals including cell cycle progression, cell apoptosis and epithelial-mesenchymal transition (EMT)-associated genes.
Our findings suggest that PTTG3P, a valuable marker of HCC prognosis, promotes tumor growth and metastasis via up-regulating PTTG1 and activating PI3K/AKT signaling in HCC and might represent a potential target for gene-based therapy.
The limitations of current anti-angiogenic therapies necessitate other targets with complimentary mechanisms. Here, we show for the first time that soluble E-cadherin (sE-cad) (an 80-kDa soluble ...form), which is highly expressed in the malignant ascites of ovarian cancer patients, is a potent inducer of angiogenesis. In addition to ectodomain shedding, we provide further evidence that sE-cad is abundantly released in the form of exosomes. Mechanistically, sE-cad-positive exosomes heterodimerize with VE-cadherin on endothelial cells and transduce a novel sequential activation of β-catenin and NFκB signaling. In vivo and clinical data prove the relevance of sE-cad-positive exosomes for malignant ascites formation and widespread peritoneal dissemination. These data advance our understanding of the molecular regulation of angiogenesis in ovarian cancer and support the therapeutic potential of targeting sE-cad. The exosomal release of sE-cad, which represents a common route for externalization in ovarian cancer, could potentially be biomarkers for diagnosis and prognosis.
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