Friday the 13th: The Empirics of Bad Luck

We use the UK Labor Force survey to investigate whether the socio-economic outcomes of people born on the 13th day of the month, and of those born on Friday the 13th, differ from the outcomes of people born on more auspicious days. In many European countries, including the UK, number 13 is considered unlucky and Friday the 13th is seen as an especially unlucky day. We find little evidence that people born on the 13th or those born on Friday the 13th are significantly less likely to be employed, earn lower wages or that they are more likely to stay unmarried compared to people born on other days

The mechanisms of calcium homeostasis and signalling in the lens

Excessive Ca2+ can be detrimental to cells and raised levels of Ca2+ in human lenses with cortical cataract have been found to play a major role in the opacification process. Ca2+ homeostasis is therefore, recognised as having fundamental importance in lens pathophysiology. Furthermore, Ca2+ plays a central role as a second messenger in cell signalling and mechanisms have evolved which give cells exquisite control over intracellular Ca2+ ([Ca2+]i) via an array of specialised regulatory and signalling proteins. In this review we discuss these mechanisms as they apply to the lens. Ca2+ levels in human aqueous humour are approximately 1 mM and there is a large, 10,000 fold, inwardly directed gradient across the plasma membrane. In the face of such a large gradient highly efficient mechanisms are needed to maintain low [Ca2+]i. The Na+/Ca2+ exchanger (NCX) and plasma membrane Ca2+-ATPase (PMCA) actively remove Ca2+ from the cells, whereas the sarco(endo)plasmic reticulum Ca2+-ATPase (SERCA) sequesters Ca2+ in the endoplasmic reticulum (ER) Ca2+ store. In lens epithelial cells the dominant role is played by the ATPases, whilst in the fibre cells NCX activity appears to be more important. Usually, [Ca2+]i can be increased in a number of ways. Ca2+ influx through the plasma membrane, for example, is mediated by an array of channels with evidence in the lens for the presence of voltage-operated Ca2+ channels (VOCCs), receptor-operated Ca2+ channels (ROCCs) and channels mediating store-operated Ca2+ entry (SOCE). Ca2+ signalling is initiated via activation of G-protein-coupled receptors (GPCRs) and receptor tyrosine kinases (RTK) of which the lens expresses a surprisingly diverse array responding to various neurotransmitters, hormones, growth factors, autocoids and proteases. Downstream of plasma membrane receptors are IP3-gated channels (IP3Rs) and ryanodine receptors (RYRs) located in the ER, which when activated cause a rapid increase in [Ca2+]i and these have also been identified in the lens. Through an appreciation of the diversity and complexity of the mechanisms involved in Ca2+ homeostasis in normal lens cells we move closer to an understanding of the mechanisms which mediate pathological Ca2+ overload as occurs in the process of cataract formation

A competition between N---O and C---O through space interactions in the crystal structures of 3,3'-dinitro-2,2'-bipyridine N-oxides and N,N'-dioxides

The crystal structures of a series of 3,3’-dinitro-2,2’-bipyridine N-oxides and N,N’-dioxides consistently show 1,5 interactions between nitro oxygen atoms and aromatic carbon atoms ((ON)O---C: 2.623(2)-2.839(2) Å) while there are also 1,6 interactions between N-oxide oxygen atoms and nitro nitrogen atoms in most cases (O---N(O2): 2.737(2)-2.874(3) Å). The O---C interactions appears to be a common feature in ortho-nitro-biphenyl systems, and there is some evidence that the effect is cooperative when there are ortho nitro groups on both rings. The O---N interactions are considerably longer than the corresponding 1,5 N---O interaction measured here in 8-nitroquinoline-1-oxide (O---N(O2): 2.5418(17) Å), which in turn is longer than the corresponding N---O interaction in the corresponding 8-diazonium-1-oxide analogue

1,6-Interactions between dimethylamino and aldehyde groups in two biphenyl derivatives

The title compounds, 2-(dimethylamino)biphenyl-2'-carboxaldehyde, C15H15NO, and 2-(dimethylamino)biphenyl-2',6'-dicarboxaldehyde, C16H15NO2, show similar 1,6-interactions [N...C=O 2.929 (3) to 3.029 (3) Å] between the dimethylamino and aldehyde groups located in the ortho positions of the two rings, which lie at 58.1 (1)-62.4 (1)° to each other

Root data with group actions

Suppose $k$ is a field, $G$ is a connected reductive algebraic $k$-group, $T$ is a maximal $k$-torus in $G$, and $\Gamma$ is a finite group that acts on $(G,T)$. From the above, one obtains a root datum $\Psi$ on which $\text{Gal}(k)\times\Gamma$ acts. Provided that $\Gamma$ preserves a positive system in $\Psi$, not necessarily invariant under $\text{Gal}(k)$, we construct an inverse to this process. That is, given a root datum on which $\text{Gal}(k)\times\Gamma$ acts appropriately, we show how to construct a pair $(G,T)$, on which $\Gamma$ acts as above. Although the pair $(G,T)$ and the action of $\Gamma$ are canonical only up to an equivalence relation, we construct a particular pair for which $G$ is $k$-quasisplit and $\Gamma$ fixes a $\text{Gal}(k)$-stable pinning of $G$. Using these choices, we can define a notion of taking "$\Gamma$-fixed points" at the level of equivalence classes, and this process is compatible with a general "restriction" process for root data with $\Gamma$-action.Comment: v2: one word inserted, one citation inserted, one reference updated, one misspelling correcte

Structural studies of peri-interactions and bond formation between electron-rich atomic centres and N-phenylcarboxamides or nitroalkenyl groups

Structural studies of peri-interactions with dimethylamino groups in naphthalene systems indicate that the N-phenylcarboxamide group has a through-space electron attracting power closer to that of a carboxylic ester than a N,N-dialkylcarboxamide, while 2-nitroalkenyl groups have a lower through-space electron attracting power. However, addition of a benzoyl group to the 2-position of the nitroethenyl group leads to cyclisation to give a zwitterion, in which the carbanion is stabilised by full conjugation with the nitro group and partial conjugation with the carbonyl group. An interesting case where a steric interaction overrides an electrophile/nucleophile attraction is also described. The limitations to the interpretation of short contact distances from crystallographic measurements are discussed

Improved Algorithms for Decremental Single-Source Reachability on Directed Graphs

Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the number of nodes in the graph [Henzinger et al. STOC 2014]. The algorithm is a combination of several different algorithms, each for a different $m$ vs. $n$ trade-off. For the case of $m = \Theta(n^{1.5})$ the running time is $O(n^{2.47})$, just barely below $mn = \Theta(n^{2.5})$. In this paper we simplify the previous algorithm using new algorithmic ideas and achieve an improved running time of $\tilde O(\min(m^{7/6} n^{2/3}, m^{3/4} n^{5/4 + o(1)}, m^{2/3} n^{4/3+o(1)} + m^{3/7} n^{12/7+o(1)}))$. This gives, e.g., $O(n^{2.36})$ for the notorious case $m = \Theta(n^{1.5})$. We obtain the same upper bounds for the problem of maintaining the strongly connected components of a directed graph undergoing edge deletions. Our algorithms are correct with high probabililty against an oblivious adversary.Comment: This paper was presented at the International Colloquium on Automata, Languages and Programming (ICALP) 2015. A full version combining the findings of this paper and its predecessor [Henzinger et al. STOC 2014] is available at arXiv:1504.0795