Stable Secretaries

We define and study a new variant of the secretary problem. Whereas in the classic setting multiple secretaries compete for a single position, we study the case where the secretaries arrive one at a time and are assigned, in an on-line fashion, to one of multiple positions. Secretaries are ranked according to talent, as in the original formulation, and in addition positions are ranked according to attractiveness. To evaluate an online matching mechanism, we use the notion of blocking pairs from stable matching theory: our goal is to maximize the number of positions (or secretaries) that do not take part in a blocking pair. This is compared with a stable matching in which no blocking pair exists. We consider the case where secretaries arrive randomly, as well as that of an adversarial arrival order, and provide corresponding upper and lower bounds.Comment: Accepted for presentation at the 18th ACM conference on Economics and Computation (EC 2017

Hunter, Cauchy Rabbit, and Optimal Kakeya Sets

A planar set that contains a unit segment in every direction is called a Kakeya set. We relate these sets to a game of pursuit on a cycle ℤ_n. A hunter and a rabbit move on the nodes of ℤ_n without seeing each other. At each step, the hunter moves to a neighbouring vertex or stays in place, while the rabbit is free to jump to any node. Adler et al. (2003) provide strategies for hunter and rabbit that are optimal up to constant factors and achieve probability of capture in the first n steps of order 1/ log n. We show these strategies yield a Kakeya set consisting of 4n triangles with minimal area (up to constant), namely Θ(1/ log n). As far as we know, this is the first non-iterative construction of a boundary-optimal Kakeya set. Considering the continuum analog of the game yields a construction of a random Kakeya set from two independent standard Brownian motions {B(s) : s ≥ 0} and {W(s) : s ≥ 0}. Let τ_t := min{s ≥ 0 : B(s) = t}. Then X_t = W(τ_t) is a Cauchy process and K := {(ɑ,X_t + ɑt) : ɑ, t ∈ [0, 1]} is a Kakeya set of zero area. The area of the ε-neighbourhood of K is as small as possible, i.e., almost surely of order Θ(1/| log ε|)

Hunter, Cauchy Rabbit, and Optimal Kakeya Sets

A planar set that contains a unit segment in every direction is called a Kakeya set. We relate these sets to a game of pursuit on a cycle $\Z_n$. A hunter and a rabbit move on the nodes of $\Z_n$ without seeing each other. At each step, the hunter moves to a neighbouring vertex or stays in place, while the rabbit is free to jump to any node. Adler et al (2003) provide strategies for hunter and rabbit that are optimal up to constant factors and achieve probability of capture in the first $n$ steps of order $1/\log n$. We show these strategies yield a Kakeya set consisting of $4n$ triangles with minimal area, (up to constant), namely $\Theta(1/\log n)$. As far as we know, this is the first non-iterative construction of a boundary-optimal Kakeya set. Considering the continuum analog of the game yields a construction of a random Kakeya set from two independent standard Brownian motions $\{B(s): s \ge 0\}$ and $\{W(s): s \ge 0\}$. Let $\tau_t:=\min\{s \ge 0: B(s)=t\}$. Then $X_t=W(\tau_t)$ is a Cauchy process, and $K:=\{(a,X_t+at) : a,t \in [0,1]\}$ is a Kakeya set of zero area. The area of the $\epsilon$-neighborhood of $K$ is as small as possible, i.e., almost surely of order $\Theta(1/|\log \epsilon|)$

A new role of hindbrain boundaries as pools of neural stem/progenitor cells regulated by Sox2

Background: Compartment boundaries are an essential developmental mechanism throughout evolution, designated to act as organizing centers and to regulate and localize differently fated cells. The hindbrain serves as a fascinating example for this phenomenon as its early development is devoted to the formation of repetitive rhombomeres and their well-defined boundaries in all vertebrates. Yet, the actual role of hindbrain boundaries remains unresolved, especially in amniotes. Results: Here, we report that hindbrain boundaries in the chick embryo consist of a subset of cells expressing the key neural stem cell (NSC) gene Sox2. These cells co-express other neural progenitor markers such as Transitin (the avian Nestin), GFAP, Pax6 and chondroitin sulfate proteoglycan. The majority of the Sox2+ cells that reside within the boundary core are slow-dividing, whereas nearer to and within rhombomeres Sox2+ cells are largely proliferating. In vivo analyses and cell tracing experiments revealed the contribution of boundary Sox2+ cells to neurons in a ventricular-to-mantle manner within the boundaries, as well as their lateral contribution to proliferating Sox2+ cells in rhombomeres. The generation of boundary-derived neurospheres from hindbrain cultures confirmed the typical NSC behavior of boundary cells as a multipotent and self-renewing Sox2+ cell population. Inhibition of Sox2 in boundaries led to enhanced and aberrant neural differentiation together with inhibition in cell-proliferation, whereas Sox2 mis-expression attenuated neurogenesis, confirming its significant function in hindbrain neuronal organization. Conclusions: Data obtained in this study deciphers a novel role of hindbrain boundaries as repetitive pools of neural stem/progenitor cells, which provide proliferating progenitors and differentiating neurons in a Sox2-dependent regulation. Electronic supplementary material The online version of this article (doi:10.1186/s12915-016-0277-y) contains supplementary material, which is available to authorized users

A Universal Expression/Silencing Vector in Plants[C][OA]

A universal vector (IL-60 and auxiliary constructs), expressing or silencing genes in every plant tested to date, is described. Plants that have been successfully manipulated by the IL-60 system include hard-to-manipulate species such as wheat (Triticum duram), pepper (Capsicum annuum), grapevine (Vitis vinifera), citrus, and olive (Olea europaea). Expression or silencing develops within a few days in tomato (Solanum lycopersicum), wheat, and most herbaceous plants and in up to 3 weeks in woody trees. Expression, as tested in tomato, is durable and persists throughout the life span of the plant. The vector is, in fact, a disarmed form of Tomato yellow leaf curl virus, which is applied as a double-stranded DNA and replicates as such. However, the disarmed virus does not support rolling-circle replication, and therefore viral progeny single-stranded DNA is not produced. IL-60 does not integrate into the plant's genome, and the construct, including the expressed gene, is not heritable. IL-60 is not transmitted by the Tomato yellow leaf curl virus's natural insect vector. In addition, artificial satellites were constructed that require a helper virus for replication, movement, and expression. With IL-60 as the disarmed helper “virus,” transactivation occurs, resulting in an inducible expressing/silencing system. The system's potential is demonstrated by IL-60-derived suppression of a viral-silencing suppressor of Grapevine virus A, resulting in Grapevine virus A-resistant/tolerant plants