Mean-squared displacement and variance for confined Brownian motion

For one-dimension Brownian motion in the confined system with the size $L$, the mean-squared displacement(MSD) defined by $\left \langle (x-x_0)^2 \right\rangle$ should be proportional to $t^{\alpha(t)}$. The power $\alpha(t)$ should range from $1$ to $0$ over time, and the MSD turns from $2Dt$ to $c L^2$, here the coefficient $c$ independent of $t$, $D$ being the diffusion coefficient. The paper aims to quantitatively solve the MSD in the intermediate confinement regime. The key to this problem is how to deal with the propagator and the normalization factor of the Fokker-Planck equation(FPE) with the Dirichlet Boundaries. Applying the Euler-Maclaurin approximation(EMA) and integration by parts for the small $t$, we obtain the MSD being $2Dt(1-\frac{2\sqrt{\xi} }{3\pi\sqrt{\pi}})$, with $t_{ch}=\frac{L^2}{4\pi^2D},\xi\equiv \frac{t}{t_{ch}}$, and the power $\alpha(t)$ being $\frac{1-0.18\sqrt{\xi}}{1-0.12\sqrt{\xi}}$. Further, we analysis the MSD and the power for the $d$-dimension system with $\gamma$-dimension confinement. In the case of $\gamma< d$, there exists the sub-diffusive behavior in the intermediate time. The universal description is consistent with the recent experiments and simulations in the micro-nano systems. Finally, we calculate the position variance(PV) meaning $\left\langle (x-\left\langle x \right\rangle)^2 \right\rangle$. Under the initial condition referring to the different probability density function(PDF) being $p_{0}(x)$, MSD and PV should exhibit different dependencies on time, which reflect corresponding diffusion behaviors.As examples, the paper discusses the representative initial PDFs reading $p_{0}(x)=\delta(x-x_0)$, with the midpoint $x_0=\frac{L}{2}$ and the endpoint $x_0=\epsilon$(or $0^+$).The MSD(equal to PV) reads $2Dt(1-\frac{5\pi^3 Dt}{L^2})$,and $\frac{4}{\pi}(2Dt)[1+\frac{2\sqrt{\pi Dt}}{L}]$for the small $t$,respectively.Comment: 18 pages, 4 figure

3-(4-Bromo­phen­yl)-4-[2-(4-nitro­phen­yl)hydrazin­yl]furan-2(5H)-one

In the title compound, C16H12BrN3O4, the furan-2(5H)-one ring forms a dihedral angle of 33.19 (9)° with the 4-bromo­benzene unit and is nearly perpendicular to the 4-nitro­benzene segment, making a dihedral angle of 89.93 (10)°. In the crystal, N—H⋯O hydrogen bonds link the mol­ecules, generating an infinite chain along [010]. The chains are linked into a three-dimensional network by C—H⋯O, C—H⋯π and π–π contacts [centroid–centroid separation = 3.805 (2) Å]

8-Chloro-4-cyclo­hexyl-2H-1,4-benzoxazin-3(4H)-one

In the crystal structure of title compound, C14H16ClNO2, the cyclo­hexyl ring is in a chair conformation. The molecules are connected into centrosymmetric dimers via weak C—H⋯O hydrogen bonds

Highly Efficient White Organic Light-Emitting Diodes with Controllable Excitons Behavior by a Mixed Interlayer between Fluorescence Blue and Phosphorescence Yellow-Emitting Layers

A highly efficient hybrid white organic light-emitting diode (HWOLED) has been demonstrated with a mixed interlayer between fluorescent blue and phosphorescent yellow-emitting layers. The device structure is simplified by using a controllable fluorescence-mixed interlayer-phosphorescence emission layer structure. The electroluminance (EL) performance can be modulated easily by adjusting the ratio of the hole-predominated material to the electron-predominated material in the interlayer. It is found that the HWOLED with a ratio of 3 : 2 exhibits a current efficiency of 34 cd/A and a power efficiency of 29 lm/W at 1000 cd/m2 with warm white Commission Internationale de l’Eclairage (CIE1931) coordinates of (0.4273, 0.4439). The improved efficiency and adaptive CIE coordinates are attributed to the controllable mixed interlayer with enhanced charge carrier transport, optimized excitons distribution, and improved harvestings of singlet and triplet excitons

The effect of water temperature on the pathogenicity of decapod iridescent virus 1 (DIV1) in Litopenaeus vannamei

Decapod iridescent virus 1 (DIV1) has caused huge losses to the shrimp breeding industry in recent years as a new shrimp virus. In this study, white leg shrimp, Litopenaeus vannamei, were cultured at different temperatures (26 ± 1 °C and 32 ± 1 °C) and the same salinity, then infected with DIV1 by intramuscular injection to determine the effects of water temperature on viral infection. The DIV1 copy counts in the gills, hepatopancreas, pleopods, intestines, and muscles of L. vannamei were measured in samples collected at 6, 12, and 24 h post-infection (hpi), and the survival rate of L. vannamei was assessed every 6 h after infection. At 96 hpi, the survival rates of L. vannamei in the high (32 ± 1 ℃) and standard (26 ± 1 ℃) water temperature groups were 2.22% and 4.44%, respectively. The peak time of mortality in the high-water temperature group was 6 h earlier than in the standard water temperature group. After 24 hours of DIV1 infection, the DIV1 copy counts in the standard water temperature treatment group were significantly higher than those in the high-water temperature treatment group. The tissues with the highest virus copy counts in the standard and high-temperature groups were the intestines (2.9×1011 copies/g) and muscles (7.0×108 copies/g). The effect of temperature on the pathogenicity of DIV1 differs from that of other previously studied viruses, such as white spot syndrome virus, Taura syndrome virus, and infectious hypodermal and hematopoietic necrosis virus, because the high-water temperature did not mitigate the damage caused by DIV1 infection

BPLLDA: Predicting lncRNA-Disease Associations Based on Simple Paths With Limited Lengths in a Heterogeneous Network

In recent years, it has been increasingly clear that long noncoding RNAs (lncRNAs) play critical roles in many biological processes associated with human diseases. Inferring potential lncRNA-disease associations is essential to reveal the secrets behind diseases, develop novel drugs, and optimize personalized treatments. However, biological experiments to validate lncRNA-disease associations are very time-consuming and costly. Thus, it is critical to develop effective computational models. In this study, we have proposed a method called BPLLDA to predict lncRNA-disease associations based on paths of fixed lengths in a heterogeneous lncRNA-disease association network. Specifically, BPLLDA first constructs a heterogeneous lncRNA-disease network by integrating the lncRNA-disease association network, the lncRNA functional similarity network, and the disease semantic similarity network. It then infers the probability of an lncRNA-disease association based on paths connecting them and their lengths in the network. Compared to existing methods, BPLLDA has a few advantages, including not demanding negative samples and the ability to predict associations related to novel lncRNAs or novel diseases. BPLLDA was applied to a canonical lncRNA-disease association database called LncRNADisease, together with two popular methods LRLSLDA and GrwLDA. The leave-one-out cross-validation areas under the receiver operating characteristic curve of BPLLDA are 0.87117, 0.82403, and 0.78528, respectively, for predicting overall associations, associations related to novel lncRNAs, and associations related to novel diseases, higher than those of the two compared methods. In addition, cervical cancer, glioma, and non-small-cell lung cancer were selected as case studies, for which the predicted top five lncRNA-disease associations were verified by recently published literature. In summary, BPLLDA exhibits good performances in predicting novel lncRNA-disease associations and associations related to novel lncRNAs and diseases. It may contribute to the understanding of lncRNA-associated diseases like certain cancers