Comparison of measured and predicted performance of a SIS waveguide mixer at 345 GHz

The measured gain and noise of a SIS waveguide mixer at 345 GHz have been compared with theoretical values, calculated from the quantum mixer theory using a three port model. As a mixing element, we use a series array of two Nb-Al2O3-Nb SIS junctions. The area of each junction is 0.8 sq microns and the normal state resistance is 52 omega. The embedding impedance of the mixer has been determined from the pumped DC-IV curves of the junction and is compared to results from scale model measurements (105 x). Good agreement was obtained. The measured mixer gain, however, is a factor of 0.45 plus or minus 0.5 lower than the theoretical predicted gain. The measured mixer noise temperature is a factor of 4-5 higher than the calculated one. These discrepancies are independent on pump power and are valid for a broad range of tuning conditions

Extortion in the United Kingdom

Extortion racketeering has been long pointed out as the “defining activity of organised crime” (Konrad & Skaperdas, 1998). Although in recent years this crime has not been among the top listed organised crime threats in the strategic EU policy documents, it still remains ever present in European countries. The seriousness of the phenomenon has been recognised at the EU level and the crime has been listed in a number of EU legal acts in the field of police and judicial cooperation in criminal matters. In this section of the report, Dr Bonino discusses the legal status of extortion in the UK and the specifics of organised crime in that country

How large are the level sets of the Takagi function?

Let T be Takagi's continuous but nowhere-differentiable function. This paper considers the size of the level sets of T both from a probabilistic point of view and from the perspective of Baire category. We first give more elementary proofs of three recently published results. The first, due to Z. Buczolich, states that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states that the average number of points in a level set is infinite. The third result, also due to Lagarias and Maddock, states that the average number of local level sets contained in a level set is 3/2. In the second part of the paper it is shown that, in contrast to the above results, the set of ordinates y with uncountably infinite level sets is residual, and a fairly explicit description of this set is given. The paper also gives a negative answer to a question of Lagarias and Maddock by showing that most level sets (in the sense of Baire category) contain infinitely many local level sets, and that a continuum of level sets even contain uncountably many local level sets. Finally, several of the main results are extended to a version of T with arbitrary signs in the summands.Comment: Added a new Section 5 with generalization of the main results; some new and corrected proofs of the old material; 29 pages, 3 figure

Patterns in rational base number systems

Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\'ele ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums

Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Determinants of pain interference and headache impact in patients who have chronic migraine with medication overuse: Results from the MOTS trial

OBJECTIVE: Pain interference and headache impact refer to negative consequences that pain and headache have on one\u27s life. This study investigated determinants of these negative impacts in a large patient cohort who have chronic migraine with medication overuse. METHODS: Six hundred and eleven adults were enrolled from 34 headache, neurology, and primary care clinics. Negative consequences of chronic migraine with medication overuse were determined using the Patient-Reported Outcomes Measurement Information System (PROMIS) Pain Interference 6b questionnaire and the Headache Impact Test 6. Relationships between PROMIS-6b and Headache Impact Test 6 scores with demographics, headache characteristics, medication use, anxiety symptoms, and depression symptoms were assessed with linear regression. Elastic Net regression was used to develop a multiple regression model. RESULTS: PROMIS-6b T-Scores averaged 65.2 (SD 5.4) and Headache Impact Test 6 scores averaged 65.0 (SD 5.3), indicating severe negative consequences of chronic migraine with medication overuse. Chronic migraine with medication overuse interfered with enjoyment of life, concentration, daily activities, doing tasks away from home, and socializing. Depression symptom severity had the strongest relationship with pain interference and headache impact. Moderate-to-severe headache frequency, headache intensity, and anxiety symptoms were also associated with pain interference and headache impact. CONCLUSIONS: Chronic migraine with medication overuse is associated with substantial negative consequences, the extent of which is most strongly related to depression symptoms

Metabolic engineering of the iodine content in Arabidopsis

Plants are a poor source of iodine, an essential micronutrient for human health. Several attempts of iodine biofortification of crops have been carried out, but the scarce knowledge on the physiology of iodine in plants makes results often contradictory and not generalizable. In this work, we used a molecular approach to investigate how the ability of a plant to accumulate iodine can be influenced by different mechanisms. In particular, we demonstrated that the iodine content in Arabidopsis thaliana can be increased either by facilitating its uptake with the overexpression of the human sodium-iodide symporter (NIS) or through the reduction of its volatilization by knocking-out HOL-1, a halide methyltransferase. Our experiments show that the iodine content in plants results from a balance between intake and retention. A correct manipulation of this mechanism could improve iodine biofortification of crops and prevent the release of the ozone layer-threatening methyl iodide into the atmosphere