The Berry-Keating Hamiltonian and the Local Riemann Hypothesis

The local Riemann hypothesis states that the zeros of the Mellin transform of a harmonic-oscillator eigenfunction (on a real or p-adic configuration space) have real part 1/2. For the real case, we show that the imaginary parts of these zeros are the eigenvalues of the Berry-Keating hamiltonian H=(xp+px)/2 projected onto the subspace of oscillator eigenfunctions of lower level. This gives a spectral proof of the local Riemann hypothesis for the reals, in the spirit of the Hilbert-Polya conjecture. The p-adic case is also discussed.Comment: 9 pages, no figures; v2 included more mathematical background, v3 has minor edits for clarit

The a-number of hyperelliptic curves

It is known that for a smooth hyperelliptic curve to have a large $a$-number, the genus must be small relative to the characteristic of the field, $p>0$, over which the curve is defined. It was proven by Elkin that for a genus $g$ hyperelliptic curve $C$ to have $a_C=g-1$, the genus is bounded by $g<\frac{3p}{2}$. In this paper, we show that this bound can be lowered to $g <p$. The method of proof is to force the Cartier-Manin matrix to have rank one and examine what restrictions that places on the affine equation defining the hyperelliptic curve. We then use this bound to summarize what is known about the existence of such curves when $p=3,5$ and $7$.Comment: 7 pages. v2: revised and improved the proof of the main theorem based on suggestions from the referee. To appear in the proceedings volume of Women in Numbers Europe-

Power-Law Distributions in a Two-sided Market and Net Neutrality

"Net neutrality" often refers to the policy dictating that an Internet service provider (ISP) cannot charge content providers (CPs) for delivering their content to consumers. Many past quantitative models designed to determine whether net neutrality is a good idea have been rather equivocal in their conclusions. Here we propose a very simple two-sided market model, in which the types of the consumers and the CPs are {\em power-law distributed} --- a kind of distribution known to often arise precisely in connection with Internet-related phenomena. We derive mostly analytical, closed-form results for several regimes: (a) Net neutrality, (b) social optimum, (c) maximum revenue by the ISP, or (d) maximum ISP revenue under quality differentiation. One unexpected conclusion is that (a) and (b) will differ significantly, unless average CP productivity is very high

Complete quantization of a diffeomorphism invariant field theory

In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not correspond to a subset of Einstein's gravity it has the advantage that the programme of canonical quantization can be carried out completely and explicitly, both, via the reduced phase space approach or along the lines of the algebraic quantization programme. This model stands in close correspondence to the frequently treated cylindrically symmetric waves. In contrast to other models that have been looked at up to now in terms of the new variables the reduced phase space is infinite dimensional while the scalar constraint is genuinely bilinear in the momenta. The infinite number of Dirac observables can be expressed in compact and explicit form in terms of the original phase space variables. They turn out, as expected, to be non-local and form naturally a set of countable cardinality.Comment: 32p, LATE

A comparison of the cost-effectiveness of treatment of prolonged acute convulsive epileptic seizures in children across Europe

In the majority of children and adolescents with epilepsy, optimal drug therapy adequately controls their condition. However, among the remaining patients who are still uncontrolled despite mono-, bi- or tri-therapy with chronic anti-epileptic treatment, a rescue medication is required. In Western Europe, the licensed medications available for first-line treatment of prolonged acute convulsive seizures (PACS) vary widely, and so comparators for clinical and economic evaluation are not consistent. No European guidelines currently exist for the treatment of PACS in children and adolescents and limited evidence is available for the effectiveness of treatments in the community setting. The authors present cost-effectiveness data for BUCCOLAM® (midazolam oromucosal solution) for the treatment of PACS in children and adolescents in the context of the treatment pathway in seven European countries in patients from 6 months to 18 years. For each country, the health economic model consisted of a decision tree, with decision nodes informed by clinical data and expert opinion obtained via a Delphi methodology. The events modelled are those associated with a patient experiencing a seizure in the community setting. The model assessed the likelihood of medication being administered successfully and of seizure cessation. The associated resource use was also modelled, and ambulance call-outs and hospitalisations were considered. The patient's quality of life was estimated by clinicians, who completed a five-level EuroQol five dimensions questionnaire from the perspective of a child or adolescent suffering a seizure. Despite differences in current therapy, treatment patterns and healthcare costs in all countries assessed, BUCCOLAM was shown to be cost saving and offered increased health-related benefits for patients in the treatment of PACS compared with the current local standard of care

Development of photocrosslinking probes based on Huwentoxin-IV to map the site of interaction on Nav1.7

Voltage-gated sodium (Nav) channels respond to changes in the membrane potential of excitable cells through the concerted action of four voltage-sensor domains (VSDs). Subtype Nav1.7 plays an important role in the propagation of signals in pain-sensing neurons and is a target for the clinical development of novel analgesics. Certain inhibitory cystine knot (ICK) peptides produced by venomous animals potently modulate Nav1.7, however the molecular mechanisms underlying their selective binding and activity remain elusive. This study reports on the design of a library of photoprobes based on the potent spider toxin Huwentoxin-IV and the determination of the toxin binding interface on VSD2 of Nav1.7 through a photocrosslinking and tandem mass spectrometry approach. Our Huwentoxin-IV probes selectively crosslink to extracellular loop S1-2 and helix S3 of VSD2 in a chimeric channel system. Our results provide a strategy that will enable mapping of sites of interaction of other ICK peptides on Nav channels

The Anatomy of Memory Politics: A Formalist Analysis of Tate Britain’s ‘Artist and Empire’ and the Struggle over Britain’s Imperial Past

In this paper, I propose a new approach for understanding the meaning of memory politics, which draws upon the archetypal literary criticism of Northrop Frye. I suggest that the four archetypes elaborated by Frye—comedy, romance, tragedy, and satire—can be used as a heuristic device for interpreting the contested historical narratives that are associated with the politics of memory. I illustrate this approach through a case-study of Artists and Empire: Facing Britain’s Imperial Past, an exhibition held at Tate Britain in 2016, amidst increasing contestation over the meaning of the British Empire. In sum, I find that the exhibit narrated Britain’s imperial past as a comedy, in which a key theme was the progressive cultural mixing of the British and the people they colonized. To conclude, I discuss the implications of such a narrative for constructing an inclusive, postcolonial British identity. As an alternative, I draw on Aristotle to suggest that a tragic narrative would have been more propitious

Effects of the Selective Serotonin Reuptake Inhibitor Fluoxetine on Counterregulatory Responses to Hypoglycemia in Individuals With Type 1 Diabetes

OBJECTIVE—Previous work has demonstrated that chronic administration of the serotonin reuptake inhibitor (SSRI) fluoxetine augments counterregulatory responses to hypoglycemia in healthy humans. However, virtually no information exists regarding the effects of fluoxetine on integrated physiological counterregulatory responses during hypoglycemia in type 1 diabetes. Therefore, the specific aim of this study was to test the hypothesis that 6-week use of the SSRI fluoxetine would amplify autonomic nervous system (ANS) counterregulatory responses to hypoglycemia in individuals with type 1 diabetes

Time-of-arrival in quantum mechanics

We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the ``time-of-arrival'' operator. We discuss the general properties of this operator. We construct the operator explicitly in the simple case of a free nonrelativistic particle, and compare the probabilities it yields with the ones estimated indirectly in terms of the flux of the Schr\"odinger current. We derive a well defined uncertainty relation between time-of-arrival and energy; this result shows that the well known arguments against the existence of such a relation can be circumvented. Finally, we define a ``time-representation'' of the quantum mechanics of a free particle, in which the time-of-arrival is diagonal. Our results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics.Comment: Latex/Revtex, 20 pages. 2 figs included using epsf. Submitted to Phys. Rev.

Protein multi-scale organization through graph partitioning and robustness analysis: Application to the myosin-myosin light chain interaction

Despite the recognized importance of the multi-scale spatio-temporal organization of proteins, most computational tools can only access a limited spectrum of time and spatial scales, thereby ignoring the effects on protein behavior of the intricate coupling between the different scales. Starting from a physico-chemical atomistic network of interactions that encodes the structure of the protein, we introduce a methodology based on multi-scale graph partitioning that can uncover partitions and levels of organization of proteins that span the whole range of scales, revealing biological features occurring at different levels of organization and tracking their effect across scales. Additionally, we introduce a measure of robustness to quantify the relevance of the partitions through the generation of biochemically-motivated surrogate random graph models. We apply the method to four distinct conformations of myosin tail interacting protein, a protein from the molecular motor of the malaria parasite, and study properties that have been experimentally addressed such as the closing mechanism, the presence of conserved clusters, and the identification through computational mutational analysis of key residues for binding.Comment: 13 pages, 7 Postscript figure