On the spectral moments of trees with a given bipartition

For two given positive integers $p$ and $q$ with $p\leqslant q$, we denote \mathscr{T}_n^{p, q}={T: T is a tree of order $n$ with a $(p, q)$-bipartition}. For a graph $G$ with $n$ vertices, let $A(G)$ be its adjacency matrix with eigenvalues $\lambda_1(G), \lambda_2(G), ..., \lambda_n(G)$ in non-increasing order. The number $S_k(G):=\sum_{i=1}^{n}\lambda_i^k(G)\,(k=0, 1, ..., n-1)$ is called the $k$th spectral moment of $G$. Let $S(G)=(S_0(G), S_1(G),..., S_{n-1}(G))$ be the sequence of spectral moments of $G$. For two graphs $G_1$ and $G_2$, one has $G_1\prec_s G_2$ if for some $k\in {1,2,...,n-1}$, $S_i(G_1)=S_i(G_2) (i=0,1,...,k-1)$ and $S_k(G_1)<S_k(G_2)$ holds. In this paper, the last four trees, in the $S$-order, among $\mathscr{T}_n^{p, q} (4\leqslant p\leqslant q)$ are characterized.Comment: 11 pages, 7 figure

Mercury and Polychlorinated Biphenyl Bioaccumulation Dynamics in Fish

Global contamination by mercury (Hg) and polychlorinated biphenyls (PCBs) coupled with high health risks to humans requires exposure models. The models must correctly predict Hg and PCB concentrations in fish, which in turn, requires accurate estimates of model parameters. This dissertation first quantified assimilation efficiencies (AE) and elimination coefficients (ktot) of Hg and PCBs in Goldfish (Carassius auratus). Then, a non-steady state toxicokinetic model, combined with a Wisconsin bioenergetics model, was developed to simulate Hg and PCB bioaccumulation in Silver Carp (Hypophthalmichthys molitrix), Bighead Carp (Hypophthalmichthys nobilis), and Bluegill (Lepomis macrochirus) from multiple locations. Finally, a sensitivity analysis was performed for these three modeled species to evaluate the relative contribution of each parameter to the model outcomes. The results indicated that dietary AEs were 98±10 % and 40±9 % for MeHg and PCBs, respectively, thus, Hg had a higher AE compared to PCBs. The ktot of MeHg was 0.010±0.002 d-1, which was equivalent to those measured for highly hydrophobic PCBs with log KOW =7.2. In addition, using the tissue specific growth rate, the non-steady state bioenergetics/kinetics model was generally able to simulate differences in the bioaccumulation trends of PCBs and Hg for the study species. The sensitivity analysis indicated that toxicokinetic parameters representing tissue growth rate are as influential as model parameters associated with ontogenetic diet shifts in terms of explaining age specific Hg and PCB bioaccumulation. Overall, this dissertation was the first to directly compare chemical toxicokinetics between Hg and PCBs within the same organism, and to quantify the effect of tissue specific growth rate on bioaccumulation of these contaminants by fish using a non-steady state bioenergetics/ toxicokinetics model. It was concluded that Hg has a higher bioaccumulation potential than PCBs, and suggested tissue growth rates should be incorporated in future bioaccumulation models especially as they apply to modelling PCB dynamics in fish

Achilles Is a Circadian Clock-controlled Gene That Regulates the Immune System and Its Rhythmicity in Drosophila

Circadian clock is a transcriptional/translational feedback loop that drives the rhythmic expression of downstream mRNAs. Termed “clock-controlled genes,” these molecular outputs of the circadian clock orchestrate cellular, metabolic, and behavioral rhythms. As part of our on-going work to characterize key upstream regulators of circadian mRNA expression, we have identified a novel clock-controlled gene in Drosophila melanogaster, Achilles (Achl), which is rhythmic at the mRNA level in the brain and represses expression of immune response genes, especially anti-microbial peptides in the immune system. Achl knock-down in the brain dramatically elevates expression of crucial immune response genes, including IM1 (Immune induced molecule 1), Mtk (Metchnikowin), and Drs (Drosomysin). As a result, flies with knocked-down Achl expression are more resistant to bacterial challenges. Meanwhile, no significant change in core clock gene expression and locomotor activity is observed, suggesting that Achl influences rhythmic mRNA outputs rather than directly regulating the core timekeeping mechanism. Additionally, Achl knock-down in the brain disrupts the rhythmicity of the immune system. Flies with knocked-down Achl show altered rhythmicity in both survival towards infection and sensitivity of immune response gene induction upon infection. Using high-throughput RNA-sequencing, we also identified candidate clock controlled genes that are downstream of Achl. Notably, Achl knock-down in the absence of immune challenge significantly diminishes the fly’s overall lifespan and resistance towards starvation, indicating a behavioral or metabolic cost of constitutively activating this pathway. Together, our data demonstrate that (1) Achl is a novel clock-controlled gene that (2) regulates the immune system in a repressive manner. (3) Achl regulates the rhythmicity of the immune system, and (4) Achl participates in signaling from the brain to immunological tissues

Barrier-free Assistant

With the rapid development of the Internet in recent years, social media is also changing and influencing people\u27s social ways. Become an indispensable part of people\u27s social life. Social contact should belong to the whole people, and daily communication is the demand of everyone. However, some particular groups still need to face many obstacles when using social media. For Pre-lingually deaf people, sign language is their first language, and English is their second language. Sometimes when they read some information in the second language, they can\u27t fully understand it, which leads to obstacles when they use social media. Secondly, in addition to text and pictures, voice and video are frequently used in social media. However, voice and video are difficult for deaf people to deal with, which significantly reduces the user experience of deaf people. Therefore, to solve these problems and improve the user experience of deaf people is what we need to do at present. This article will start with a discussion on what difficulties and obstacles deaf people encounter when using social media. It will then further explore how technology can be used to solve previous problems and how to improve deaf people\u27s user experience