Maximum solutions of normalized Ricci flows on 4-manifolds

We consider maximum solution $g(t)$, $t\in [0, +\infty)$, to the normalized Ricci flow. Among other things, we prove that, if $(M, \omega)$ is a smooth compact symplectic 4-manifold such that $b_2^+(M)>1$ and let $g(t),t\in[0,\infty)$, be a solution to (1.3) on $M$ whose Ricci curvature satisfies that $|\text{Ric}(g(t))|\leq 3$ and additionally $\chi(M)=3 \tau (M)>0$, then there exists an $m\in \mathbb{N}$, and a sequence of points $\{x_{j,k}\in M\}$, $j=1, ..., m$, satisfying that, by passing to a subsequence, $$(M, g(t_{k}+t), x_{1,k},..., x_{m,k}) \stackrel{d_{GH}}\longrightarrow (\coprod_{j=1}^m N_j, g_{\infty}, x_{1,\infty}, ...,, x_{m,\infty}),$$ $t\in [0, \infty)$, in the $m$-pointed Gromov-Hausdorff sense for any sequence $t_{k}\longrightarrow \infty$, where $(N_{j}, g_{\infty})$, $j=1,..., m$, are complete complex hyperbolic orbifolds of complex dimension 2 with at most finitely many isolated orbifold points. Moreover, the convergence is $C^{\infty}$ in the non-singular part of $\coprod_1^m N_{j}$ and $\text{Vol}_{g_{0}}(M)=\sum_{j=1}^{m}\text{Vol}_{g_{\infty}}(N_{j})$, where $\chi(M)$ (resp. $\tau(M)$) is the Euler characteristic (resp. signature) of $M$.Comment: 23 page

A classification of smooth embeddings of 3-manifolds in 6-space

We work in the smooth category. If there are knotted embeddings S^n\to R^m, which often happens for 2m<3n+4, then no concrete complete description of embeddings of n-manifolds into R^m up to isotopy was known, except for disjoint unions of spheres. Let N be a closed connected orientable 3-manifold. Our main result is the following description of the set Emb^6(N) of embeddings N\to R^6 up to isotopy. The Whitney invariant W : Emb^6(N) \to H_1(N;Z) is surjective. For each u \in H_1(N;Z) the Kreck invariant \eta_u : W^{-1}u \to Z_{d(u)} is bijective, where d(u) is the divisibility of the projection of u to the free part of H_1(N;Z). The group Emb^6(S^3) is isomorphic to Z (Haefliger). This group acts on Emb^6(N) by embedded connected sum. It was proved that the orbit space of this action maps under W bijectively to H_1(N;Z) (by Vrabec and Haefliger's smoothing theory). The new part of our classification result is determination of the orbits of the action. E. g. for N=RP^3 the action is free, while for N=S^1\times S^2 we construct explicitly an embedding f : N \to R^6 such that for each knot l:S^3\to R^6 the embedding f#l is isotopic to f. Our proof uses new approaches involving the Kreck modified surgery theory or the Boechat-Haefliger formula for smoothing obstruction.Comment: 32 pages, a link to http://www.springerlink.com added, to appear in Math. Zei

Association analyses of the interaction between the ADSS and ATM genes with schizophrenia in a Chinese population

<p>Abstract</p> <p>Background</p> <p>The blood-derived RNA levels of the adenylosuccinate synthase (<it>ADSS</it>) and ataxia telangiectasia mutated (<it>ATM</it>) genes were found to be down- and up-regulated, respectively, in schizophrenics compared with controls, and <it>ADSS </it>and <it>ATM </it>were among eight biomarker genes to discriminate schizophrenics from normal controls. ADSS catalyzes the first committed step of AMP synthesis, while ATM kinase serves as a key signal transducer in the DNA double-strand breaks response pathway. It remains unclear whether these changes result from mutations or polymorphisms in the two genes.</p> <p>Methods</p> <p>Six SNPs in the <it>ADSS </it>gene and three SNPs in the <it>ATM </it>gene in a Chinese population of 488 schizophrenics and 516 controls were genotyped to examine their association with schizophrenia (SZ). Genotyping was performed using the Sequenom platform.</p> <p>Results</p> <p>There was no significant difference in the genotype, allele, or haplotype distributions of the nine SNPs between cases and controls. Using the Multifactor Dimensionality Reduction (MDR) method, we found that the interactions among rs3102460 in the <it>ADSS </it>gene and rs227061 and rs664143 in the <it>ATM </it>gene revealed a significant association with SZ. This model held a maximum testing accuracy of 60.4% and a maximum cross-validation consistency of 10 out of 10.</p> <p>Conclusion</p> <p>These findings suggest that the combined effects of the polymorphisms in the <it>ADSS </it>and <it>ATM </it>genes may confer susceptibility to the development of SZ in a Chinese population.</p

SalK/SalR, a Two-Component Signal Transduction System, Is Essential for Full Virulence of Highly Invasive Streptococcus suis Serotype 2

BACKGROUND: Streptococcus suis serotype 2 (S. suis 2, SS2) has evolved into a highly infectious entity, which caused the two recent large-scale outbreaks of human SS2 epidemic in China, and is characterized by a toxic shock-like syndrome. However, the molecular pathogenesis of this new emerging pathogen is still poorly understood. METHODOLOGY/PRINCIPAL FINDINGS: 89K is a newly predicted pathogenicity island (PAI) which is specific to Chinese epidemic strains isolated from these two SS2 outbreaks. Further bioinformatics analysis revealed a unique two-component signal transduction system (TCSTS) located in the candidate 89K PAI, which is orthologous to the SalK/SalR regulatory system of Streptococcus salivarius. Knockout of salKR eliminated the lethality of SS2 in experimental infection of piglets. Functional complementation of salKR into the isogenic mutant DeltasalKR restored its soaring pathogenicity. Colonization experiments showed that the DeltasalKR mutant could not colonize any susceptible tissue of piglets when administered alone. Bactericidal assays demonstrated that resistance of the mutant to polymorphonuclear leukocyte (PMN)-mediated killing was greatly decreased. Expression microarray analysis exhibited a transcription profile alteration of 26 various genes down-regulated in the DeltasalKR mutant. CONCLUSIONS/SIGNIFICANCE: These findings suggest that SalK/SalR is requisite for the full virulence of ethnic Chinese isolates of highly pathogenic SS2, thus providing experimental evidence for the validity of this bioinformatically predicted PAI

Genomic Relationships, Novel Loci, and Pleiotropic Mechanisms across Eight Psychiatric Disorders

Genetic influences on psychiatric disorders transcend diagnostic boundaries, suggesting substantial pleiotropy of contributing loci. However, the nature and mechanisms of these pleiotropic effects remain unclear. We performed analyses of 232,964 cases and 494,162 controls from genome-wide studies of anorexia nervosa, attention-deficit/hyper-activity disorder, autism spectrum disorder, bipolar disorder, major depression, obsessive-compulsive disorder, schizophrenia, and Tourette syndrome. Genetic correlation analyses revealed a meaningful structure within the eight disorders, identifying three groups of inter-related disorders. Meta-analysis across these eight disorders detected 109 loci associated with at least two psychiatric disorders, including 23 loci with pleiotropic effects on four or more disorders and 11 loci with antagonistic effects on multiple disorders. The pleiotropic loci are located within genes that show heightened expression in the brain throughout the lifespan, beginning prenatally in the second trimester, and play prominent roles in neurodevelopmental processes. These findings have important implications for psychiatric nosology, drug development, and risk prediction.Peer reviewe