Shintani cocycles and vanishing order of pp-adic Hecke LL-series at s=0s=0

Let $\chi$ be a Hecke character of finite order of a totally real number field $F$. By using Hill's Shintani cocyle we provide a cohomological construction of the $p$-adic $L$-series $L_p(\chi, s)$ associated to $\chi$. This is used to show that $L_p(\chi, s)$ has a trivial zero at $s=0$ of order at least equal to the number of places of $F$ above $p$ where the local component of $\chi$ is trivial

On special zeros of pp-adic LL-functions of Hilbert modular forms

Let $E$ be a modular elliptic curve over a totally real number field $F$. We prove the weak exceptional zero conjecture which links a (higher) derivative of the $p$-adic $L$-function attached to $E$ to certain $p$-adic periods attached to the corresponding Hilbert modular form at the places above $p$ where $E$ has split multiplicative reduction. Under some mild restrictions on $p$ and the conductor of $E$ we deduce the exceptional zero conjecture in the strong form (i.e.\ where the automorphic $p$-adic periods are replaced by the \cL-invariants of $E$ defined in terms of Tate periods) from a special case proved earlier by Mok. Crucial for our method is a new construction of the $p$-adic $L$-function of $E$ in terms of local data

Solution of a uniqueness problem in the discrete tomography of algebraic Delone sets

We consider algebraic Delone sets $\varLambda$ in the Euclidean plane and address the problem of distinguishing convex subsets of $\varLambda$ by X-rays in prescribed $\varLambda$-directions, i.e., directions parallel to nonzero interpoint vectors of $\varLambda$. Here, an X-ray in direction $u$ of a finite set gives the number of points in the set on each line parallel to $u$. It is shown that for any algebraic Delone set $\varLambda$ there are four prescribed $\varLambda$-directions such that any two convex subsets of $\varLambda$ can be distinguished by the corresponding X-rays. We further prove the existence of a natural number $c_{\varLambda}$ such that any two convex subsets of $\varLambda$ can be distinguished by their X-rays in any set of $c_{\varLambda}$ prescribed $\varLambda$-directions. In particular, this extends a well-known result of Gardner and Gritzmann on the corresponding problem for planar lattices to nonperiodic cases that are relevant in quasicrystallography.Comment: 21 pages, 1 figur

Application of Incident Command Structure to clinical trial management in the academic setting: principles and lessons learned

Background Clinical trial success depends on appropriate management, but practical guidance to trial organisation and planning is lacking. The Incident Command System (ICS) is the ‘gold standard’ management system developed for managing diverse operations in major incident and public health arenas. It enables effective and flexible management through integration of personnel, procedures, resources, and communications within a common hierarchical organisational structure. Conventional ICS organisation consists of five function modules: Command, Planning, Operations, Logistics, and Finance/Administration. Large clinical trials will require a separate Regulatory Administrative arm, and an Information arm, consisting of dedicated data management and information technology staff. We applied ICS principles to organisation and management of the Prehospital Use of Plasma in Traumatic Haemorrhage (PUPTH) trial. This trial was a multidepartmental, multiagency, randomised clinical trial investigating prehospital administration of thawed plasma on mortality and coagulation response in severely injured trauma patients. We describe the ICS system as it would apply to large clinical trials in general, and the benefits, barriers, and lessons learned in utilising ICS principles to reorganise and coordinate the PUPTH trial. Results Without a formal trial management structure, early stages of the trial were characterised by inertia and organisational confusion. Implementing ICS improved organisation, coordination, and communication between multiple agencies and service groups, and greatly streamlined regulatory compliance administration. However, unfamiliarity of clinicians with ICS culture, conflicting resource allocation priorities, and communication bottlenecks were significant barriers. Conclusions ICS is a flexible and powerful organisational tool for managing large complex clinical trials. However, for successful implementation the cultural, psychological, and social environment of trial participants must be accounted for, and personnel need to be educated in the basics of ICS

Brief of Amicus Curiae, Michael E. Spiess, et al, in Support of Lisa M. Avagliano, et al

https://digitalcommons.nyls.edu/sumitomo_briefs/1000/thumbnail.jp