The graphs which are cospectral with the generalized pineapple graph

Let $p, k, q$ be positive integers with $p\geqslant 4,$ $p-2 \geqslant k$ and let $K_{p,k}^{q}$ be the generalized pineapple graph which is obtained by joining independent set of $q$ vertices with $k$ vertices of a complete graph $K_{p}.$ In this paper, we determine all graphs which are cospectral with $K_{p,k}^{q}.$

Higher KK-Groups of Smooth Projective Curves Over Finite Fields

Let $X$ be a smooth projective curve over a finite field $\mathbb{F}$ with $q$ elements. For $m\geq 1,$ let $X_m$ be the curve $X$ over the finite field $\mathbb{F}_m$, the $m$-th extension of $\mathbb{F}.$ Let $K_n(m)$ be the $K$-group $K_n(X_m)$ of the smooth projective curve $X_m.$ In this paper, we study the structure of the groups $K_n(m).$ If $l$ is a prime, we establish an analogue of Iwasawa theorem in algebraic number theory for the orders of the $l$-primary part $K_n(l^m)\{l\}$ of $K_n(l^m)$. In particular, when $X$ is an elliptic curve $E$ defined over $\mathbb{F},$ our method determines the structure of $K_n(E).$ Our results can be applied to construct an efficient {\bf DL} system in elliptic cryptography.Comment: 20 page, 8 table

Measuring protected-area effectiveness using vertebrate distributions from leech iDNA

Protected areas are key to meeting biodiversity conservation goals, but direct measures of effectiveness have proven difficult to obtain. We address this challenge by using environmental DNA from leech-ingested bloodmeals to estimate spatially-resolved vertebrate occupancies across the 677 km 2 Ailaoshan reserve in Yunnan, China. From 30,468 leeches collected by 163 park rangers across 172 patrol areas, we identify 86 vertebrate species, including amphibians, mammals, birds and squamates. Multi-species occupancy modelling shows that species richness increases with elevation and distance to reserve edge. Most large mammals (e.g. sambar, black bear, serow, tufted deer) follow this pattern; the exceptions are the three domestic mammal species (cows, sheep, goats) and muntjak deer, which are more common at lower elevations. Vertebrate occupancies are a direct measure of conservation outcomes that can help guide protected-area management and improve the contributions that protected areas make towards global biodiversity goals. Here, we show the feasibility of using invertebrate-derived DNA to estimate spatially-resolved vertebrate occupancies across entire protected areas

Sciences for The 2.5-meter Wide Field Survey Telescope (WFST)

The Wide Field Survey Telescope (WFST) is a dedicated photometric survey facility under construction jointly by the University of Science and Technology of China and Purple Mountain Observatory. It is equipped with a primary mirror of 2.5m in diameter, an active optical system, and a mosaic CCD camera of 0.73 Gpix on the main focus plane to achieve high-quality imaging over a field of view of 6.5 square degrees. The installation of WFST in the Lenghu observing site is planned to happen in the summer of 2023, and the operation is scheduled to commence within three months afterward. WFST will scan the northern sky in four optical bands (u, g, r, and i) at cadences from hourly/daily to semi-weekly in the deep high-cadence survey (DHS) and the wide field survey (WFS) programs, respectively. WFS reaches a depth of 22.27, 23.32, 22.84, and 22.31 in AB magnitudes in a nominal 30-second exposure in the four bands during a photometric night, respectively, enabling us to search tremendous amount of transients in the low-z universe and systematically investigate the variability of Galactic and extragalactic objects. Intranight 90s exposures as deep as 23 and 24 mag in u and g bands via DHS provide a unique opportunity to facilitate explorations of energetic transients in demand for high sensitivity, including the electromagnetic counterparts of gravitational-wave events detected by the second/third-generation GW detectors, supernovae within a few hours of their explosions, tidal disruption events and luminous fast optical transients even beyond a redshift of 1. Meanwhile, the final 6-year co-added images, anticipated to reach g about 25.5 mag in WFS or even deeper by 1.5 mag in DHS, will be of significant value to general Galactic and extragalactic sciences. The highly uniform legacy surveys of WFST will also serve as an indispensable complement to those of LSST which monitors the southern sky.Comment: 46 pages, submitted to SCMP

Defining the Conformational Features of Anchorless, Poorly Neuroinvasive Prions

Infectious prions cause diverse clinical signs and form an extraordinary range of structures, from amorphous aggregates to fibrils. How the conformation of a prion dictates the disease phenotype remains unclear. Mice expressing GPI-anchorless or GPI-anchored prion protein exposed to the same infectious prion develop fibrillar or nonfibrillar aggregates, respectively, and show a striking divergence in the disease pathogenesis. To better understand how a prion's physical properties govern the pathogenesis, infectious anchorless prions were passaged in mice expressing anchorless prion protein and the resulting prions were biochemically characterized. Serial passage of anchorless prions led to a significant decrease in the incubation period to terminal disease and altered the biochemical properties, consistent with a transmission barrier effect. After an intraperitoneal exposure, anchorless prions were only weakly neuroinvasive, as prion plaques rarely occurred in the brain yet were abundant in extracerebral sites such as heart and adipose tissue. Anchorless prions consistently showed very high stability in chaotropes or when heated in SDS, and were highly resistant to enzyme digestion. Consistent with the results in mice, anchorless prions from a human patient were also highly stable in chaotropes. These findings reveal that anchorless prions consist of fibrillar and highly stable conformers. The additional finding from our group and others that both anchorless and anchored prion fibrils are poorly neuroinvasive strengthens the hypothesis that a fibrillar prion structure impedes efficient CNS invasion

Interplay of Nkx3.2, Sox9 and Pax3 Regulates Chondrogenic Differentiation of Muscle Progenitor Cells

Muscle satellite cells make up a stem cell population that is capable of differentiating into myocytes and contributing to muscle regeneration upon injury. In this work we investigate the mechanism by which these muscle progenitor cells adopt an alternative cell fate, the cartilage fate. We show that chick muscle satellite cells that normally would undergo myogenesis can be converted to express cartilage matrix proteins in vitro when cultured in chondrogenic medium containing TGFß3 or BMP2. In the meantime, the myogenic program is repressed, suggesting that muscle satellite cells have undergone chondrogenic differentiation. Furthermore, ectopic expression of the myogenic factor Pax3 prevents chondrogenesis in these cells, while chondrogenic factors Nkx3.2 and Sox9 act downstream of TGFß or BMP2 to promote this cell fate transition. We found that Nkx3.2 and Sox9 repress the activity of the Pax3 promoter and that Nkx3.2 acts as a transcriptional repressor in this process. Importantly, a reverse function mutant of Nkx3.2 blocks the ability of Sox9 to both inhibit myogenesis and induce chondrogenesis, suggesting that Nkx3.2 is required for Sox9 to promote chondrogenic differentiation in satellite cells. Finally, we found that in an in vivo mouse model of fracture healing where muscle progenitor cells were lineage-traced, Nkx3.2 and Sox9 are significantly upregulated while Pax3 is significantly downregulated in the muscle progenitor cells that give rise to chondrocytes during fracture repair. Thus our in vitro and in vivo analyses suggest that the balance of Pax3, Nkx3.2 and Sox9 may act as a molecular switch during the chondrogenic differentiation of muscle progenitor cells, which may be important for fracture healing

Genome-wide association analysis identifies 30 new susceptibility loci for schizophrenia

We conducted a genome-wide association study (GWAS) with replication in 36,180 Chinese individuals and performed further transancestry meta-analyses with data from the Psychiatry Genomics Consortium (PGC2). Approximately 95% of the genome-wide significant (GWS) index alleles (or their proxies) from the PGC2 study were overrepresented in Chinese schizophrenia cases, including ∼50% that achieved nominal significance and ∼75% that continued to be GWS in the transancestry analysis. The Chinese-only analysis identified seven GWS loci; three of these also were GWS in the transancestry analyses, which identified 109 GWS loci, thus yielding a total of 113 GWS loci (30 novel) in at least one of these analyses. We observed improvements in the fine-mapping resolution at many susceptibility loci. Our results provide several lines of evidence supporting candidate genes at many loci and highlight some pathways for further research. Together, our findings provide novel insight into the genetic architecture and biological etiology of schizophrenia

Lehmer's totient problem over Fq[x] {\mathbb{F}}_{q}[x]

In this paper, we consider the function field analogue of the Lehmer's totient problem. Let $p(x)\in\mathbb{F}_q[x]$ and $\varphi(q,p(x))$ be the Euler's totient function of $p(x)$ over $\mathbb{F}_q[x],$ where $\mathbb{F}_q$ is a finite field with $q$ elements. We prove that $\varphi(q,p(x))|(q^{{\rm deg}(p(x))}-1)$ if and only if (i) $p(x)$ is irreducible; or (ii) $q=3, \; p(x)$ is the product of any $2$ non-associate irreducibes of degree $1;$ or (iii) $q=2,\; p(x)$ is the product of all irreducibles of degree $1,$ all irreducibles of degree $1$ and $2,$ and the product of any $3$ irreducibles one each of degree $1, 2$ and $3$.Comment: 12 page