The Absolute and the Relative Dimension of Constitutional Rights

The principle of proportionality is necessary if it can claim validity in all legal systems. What can claim validity in all legal systems has absolute validity. On the other hand, what can only claim to have validity in some legal systems has merely relative validity. This distinction is applicable not only to the principle of proportionality as a norm about the application of constitutional rights but also to the constitutional rights themselves, and the institutionalization of the protection of constitutional rights by means of judicial review. This leads to three questions, which are connected systematically: (1) Do constitutional rights have an absolute character? (2) Does the principle of proportionality have an absolute character? (3) Does constitutional review have an absolute character? In this chapter the first two questions are discussed.

Relative, local and global dimension in complex networks

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogeneities, or to intrinsically discrete systems such as networks. To take into account locality, finiteness and discreteness, dynamical processes can be used to probe the space geometry and define its dimension. Here we show that each point in space can be assigned a relative dimension with respect to the source of a diffusive process, a concept that provides a scale-dependent definition for local and global dimension also applicable to networks. To showcase its application to physical systems, we demonstrate that the local dimension of structural protein graphs correlates with structural flexibility, and the relative dimension with respect to the active site uncovers regions involved in allosteric communication. In simple models of epidemics on networks, the relative dimension is predictive of the spreading capability of nodes, and identifies scales at which the graph structure is predictive of infectivity.

Apparent Measure, Integral of Real Order, and Relative Dimension

In this chapter, the author introduces a concept of apparent measure in R^n and associates the concept of relative dimension (of real order) that depends on the geometry of the object to measure and on the distance that separates it from an observer. At the end, the author discusses the relative dimension of a Cantor set. This measure enables us to provide a geometric interpretation of the Riemann-Liouville's integral of order αϵ├]0,1], and based on this interpretation, the author introduces a modification on the Riemann-Liouville's integral to make it symmetrical and then introduces a new fractional derivative that exploits at the same time the right and the left fractional derivatives.

TATE’S CONJECTURE AND THE TATE–SHAFAREVICH GROUP OVER GLOBAL FUNCTION FIELDS

Let ${\mathcal{X}}$ be a regular variety, flat and proper over a complete regular curve over a finite field such that the generic fiber $X$ is smooth and geometrically connected. We prove that the Brauer group of ${\mathcal{X}}$ is finite if and only Tate’s conjecture for divisors on $X$ holds and the Tate–Shafarevich group of the Albanese variety of $X$ is finite, generalizing a theorem of Artin and Grothendieck for surfaces to arbitrary relative dimension. We also give a formula relating the orders of the group under the assumption that they are finite, generalizing the known formula for a surface.

Self-Controlled Feedback and Learner Impulsivity in Sequential Motor Learning

Many studies have attributed self-controlled feedback benefits associated with motor learning to learners' greater information processing during practice. However, individual learner characteristics like their impulsivity can also influence how people engage cognitively during learning. We investigated possible dissociations between the types of interaction in self-controlled knowledge of results (KR) and learner impulsivity levels in learning a sequential motor task. Ninety volunteers responded to the self-restraint section of the Barkley deficits in executive functioning scale, and those 60 participants with the highest ( n = 30) and lowest ( n = 30) impulsivity scores practiced a motor task involving sequential pressing of four keys in predetermined absolute and relative times. We further divided participants into four experimental groups by assigning the high- and low-impulsivity groups to two forms of KR—self-controlled absolute and yoked. Study results showed no interaction effect between impulsivity and self-controlled KR, and, contrary to expectation, self-controlled KR did not benefit learning, independently of impulsivity. However, low-impulsivity participants performed better than high-impulsivity participants on the absolute dimension of the transfer task, while high-impulsivity learners were better at the relative dimension. Cognitive characteristics of automatic and reflexive processing were expressed by the strategies used to direct attention to relative and absolute task dimensions, respectively. Low-impulsivity learners switched their attention to both dimensions at the end of practice, while high-impulsivity learners did not switch their attention or directed it only to the relative dimension at the end of the practice. These results suggest that the cognitive styles of high- and low-impulsive learners differentially favor learning distinct dimensions of a motor task, regardless of self-controlled KR.

Where is the information on USD/Bitcoin hourly prices?

This paper analyses the price discovery in the USD/Bitcoin market since Mar‑2014 to Nov‑2016. The results show a positive relationship between the informational relevance of exchanges and their market shares. Information is mostly transmitted between exchanges within an hour, at least for the main exchanges, although lagged feedbacks occur from the major exchanges. Minor exchanges are merely satellite ones and react to price information with some delay. Bitfinex is the most important exchange: the lagged feedback from this exchange to the market is 18.3%, while the reverse feedback accounts only for 0.6% of the total feedback. Volatility in the major exchanges is the main factor explaining the feedback measures, which sustains the claim that the relative importance of the information-based component of volatility increases with the relative dimension of the exchange.

The Influence of Texture and Firing on Thermal and Elastic Properties of Illite-Based Ceramics

The texture in illite-based ceramics was introduced by spreading a large number of thin layers of a wet plastic mass one on top of the other. The basal planes of the plate-like illite crystals are predominantly oriented parallely with the direction of spreading. The samples were fired at different temperatures ranging from room temperature up to 1100 °C with a heating rate of 5 °C/min, then freely cooled and measured at room temperature. We determined Young modulus (E), thermal diffusivity (a) and relative dimension changes (Δl/l0) in two directions: parallely to the basal planes (a subscript ||) of the illite crystals and perpendicularly to these planes (a subscript ⊥). It was found that the ratio E|| / E⊥ ≈ 2.9 and a|| / a⊥ ≈ 2.0 up to 900 °C. Above 900 °C, the values of E and a increase due to sintering, and the differences between the values measured in the two directions decrease. In the case of the thermal diffusivity these differences do not disappear even after firing at the temperature of 1200 °C.