Qiuye Bao, Nicole Liling Tay, Christina Yingyan Lim
et al.
AbstractAdvanced molecular and cellular technologies provide promising tools for wildlife and biodiversity conservation. Induced pluripotent stem cell (iPSC) technology offers an easily accessible and infinite source of pluripotent stem cells, and have been derived from many threatened wildlife species. This paper describes the first successful integration-free reprogramming of adult somatic cells to iPSCs, and their differentiation, from three endangered Southeast Asian primates: the Celebes Crested Macaque (Macaca nigra), the Lar Gibbon (Hylobates lar), and the Siamang (Symphalangus syndactylus). iPSCs were also generated from the Proboscis Monkey (Nasalis larvatus). Differences in mechanisms could elicit new discoveries regarding primate evolution and development. iPSCs from endangered species provides a safety net in conservation efforts and allows for sustainable sampling for research and conservation, all while providing a platform for the development of further in vitro models of disease.
Fedor V. Fomin, Petr A. Golovach, Fahad Panolan
et al.
AbstractWe investigate the parameterized complexity of finding diverse sets of solutions to three fundamental combinatorial problems. The input to the Weighted Diverse Bases problem consists of a matroid $$M$$ M , a weight function $$\omega :E(M)\rightarrow \mathbb {N} $$ ω : E ( M ) → N , and integers $$k\ge 1, d\ge 1$$ k ≥ 1 , d ≥ 1 . The task is to decide if there is a collection of $$k$$ k bases$$B_{1}, \dotsc , B_{k}$$ B 1 , ⋯ , B k of $$M$$ M such that the weight of the symmetric difference of any pair of these bases is at least $$d$$ d . The input to the Weighted Diverse Common Independent Sets problem consists of two matroids $$M_{1},M_{2}$$ M 1 , M 2 defined on the same ground set $$E$$ E , a weight function $$\omega :E\rightarrow \mathbb {N} $$ ω : E → N , and integers $$k\ge 1, d\ge 1$$ k ≥ 1 , d ≥ 1 . The task is to decide if there is a collection of $$k$$ k common independent sets$$I_{1}, \dotsc , I_{k}$$ I 1 , ⋯ , I k of $$M_{1}$$ M 1 and $$M_{2}$$ M 2 such that the weight of the symmetric difference of any pair of these sets is at least $$d$$ d . The input to the Diverse Perfect Matchings problem consists of a graph $$G$$ G and integers $$k\ge 1, d\ge 1$$ k ≥ 1 , d ≥ 1 . The task is to decide if $$G$$ G contains $$k$$ k perfect matchings$$M_{1},\dotsc ,M_{k}$$ M 1 , ⋯ , M k such that the symmetric difference of any two of these matchings is at least $$d$$ d . We show that none of these problems can be solved in polynomial time unless $${{\,\mathrm{\textsf{P}}\,}} ={{\,\mathrm{\textsf{NP}}\,}} $$ P = NP . We derive fixed-parameter tractable ($${{\,\mathrm{\textsf{FPT}}\,}}$$ FPT ) algorithms for all three problems with $$(k,d)$$ ( k , d ) as the parameter, and present a $$poly(k,d)$$ p o l y ( k , d ) -sized kernel for Weighted Diverse Bases.
In this paper, we firstly generalize the Brunn-Minkowski type inequality for Ekeland-Hofer-Zehnder symplectic capacity of bounded convex domains established by Artstein-Avidan-Ostrover in 2008 to extended symplectic capacities of bounded convex domains constructed by authors based on a class of Hamiltonian non-periodic boundary value problems recently. Then we introduce a class of non-periodic billiards in convex domains, and for them we prove some corresponding results to those for periodic billiards in convex domains obtained by Artstein-Avidan-Ostrover in 2012.
In Kontsevich's graph calculus, internal vertices of directed graphs are inhabited by multi-vectors, e.g., Poisson bi-vectors; the Nambu-determinant Poisson brackets are differential-polynomial in the Casimir(s) and density $\varrho$ times Levi-Civita symbol. We resolve the old vertices into subgraphs such that every new internal vertex contains one Casimir or one Levi-Civita symbol${}\times\varrho$. Using this micro-graph calculus, we show that Kontsevich's tetrahedral $γ_3$-flow on the space of Nambu-determinant Poisson brackets over $\mathbb{R}^3$ is a Poisson coboundary: we realize the trivializing vector field $\smash{\vec{X}}$ over $\smash{\mathbb{R}^3}$ using micro-graphs. This $\smash{\vec{X}}$ projects to the known trivializing vector field for the $γ_3$-flow over $\smash{\mathbb{R}^2}$.
This paper details the geometry of the Kustaanheimo-Stiefel mapping, which regularizes the Hamiltonian of the Kepler problem. It leans heavily on the work of J.-C. van der Meer.
We note implications of the Cayley-Sylvester theory of invariants and covariants for the Hamilton equations generated by cubic and quartic Hamiltonian functions.
Under an assumption of normal genericity, we show that a stable J-holomorphic curve has, in the space of homologous curves of the same genus, a locally Euclidean neighbourhood of the expected dimension given by Riemann-Roch. In dimension 4, the normal genericity condition is satisfied in by every curve in CP2 (for an almost complex structure homotopic with the standard one) which has only nodes as singularities. This leads in particular to a solution of the symplectic isotopy problem for surfaces of degree 3.
In this paper, we develop a mini-max theory of the action functional over the semi-infinite cycles via the chain level Floer homology theory and construct spectral invariants of Hamiltonian diffeomorphisms on arbitrary, especially on {\it non-exact and non-rational}, compact symplectic manifold $(M,ω)$. To each given time dependent Hamiltonian function $H$ and quantum cohomology class $ 0 \neq a \in QH^*(M)$, we associate an invariant $ρ(H;a)$ which varies continuously over $H$ in the $C^0$-topology. This is obtained as the mini-max value over the semi-infinite cycles whose homology class is `dual' to the given quantum cohomology class $a$ on the covering space $\widetilde Ω_0(M)$ of the contractible loop space $Ω_0(M)$. We call them the {\it Novikov Floer cycles}. We apply the spectral invariants to the study of Hamiltonian diffeomorphisms in sequels of this paper.
We produce examples of generalized complex structures on manifolds by generalizing results from symplectic and complex geometry. We produce generalized complex structures on symplectic fibrations over a generalized complex base. We study in some detail different invariant generalized complex structures on compact Lie groups and provide a thorough description of invariant structures on nilmanifolds, achieving a classification on 6-nilmanifolds. We study implications of the `dd^c-lemma' in the generalized complex setting. Similarly to the standard dd^c-lemma, its generalized version induces a decomposition of the cohomology of a manifold and causes the degeneracy of the spectral sequence associated to the splitting d = \del + \delbar at E_1. But, in contrast with the dd^c-lemma, its generalized version is not preserved by symplectic blow-up or blow-down (in the case of a generalized complex structure induced by a symplectic structure) and does not imply formality.
In math.GT/0002110 the author's Theorems 1.1 and 1.2, combined, implied that iterated torus knots are transversally simple. This result is in error and this erratum pin points the error. In "An addendum on iterated torus knots" a more subtle result is proven resulting in giving a geometric realization of the Honda-Etnyre transverse (2,3)-cable of the (2,3)-torus knot example--Appendix joint with H. Matsuda. (See math.SG/0306330 and math.GT/0610566.)
This paper is devoted to studying some properties of the Courant algebroids: we explain the so-called "conducting bundle construction" and use it to attach the Courant algebroid to Dixmier-Douady gerbe (following ideas of P. Severa). We remark that WZNW-Poisson condition of Klimcik and Strobl (math.SG/0104189) is the same as Dirac structure in some particular Courant algebroid. We propose the construction of the Lie algebroid on the loop space starting from the Lie algebroid on the manifold and conjecture that this construction applied to the Dirac structure above should give the Lie algebroid of symmetries in the WZNW-Poisson $σ$-model, we show that it is indeed true in the particular case of Poisson $σ$-model.