Gyrations: The Missing Link Between Classical Mechanics with its Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying Hyperbolic Geometry

Being neither commutative nor associative, Einstein velocity addition of relativistically admissible velocities gives rise to gyrations. Gyrations, in turn, measure the extent to which Einstein addition deviates from commutativity and from associativity. Gyrations are geometric automorphisms abstracted from the relativistic mechanical effect known as Thomas precession

Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns

An asymptotic interface equation for directional solidification near the absolute stabiliy limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts destabilizing on a planar interface. Moreover, linear stability analysis suggests that the morphology diagram is modified by the flow near the onset of the Mullins-Sekerka instability. Via numerical analysis, the bifurcation structure of the system is shown to change. Besides the known hexagonal cells, structures consisting of stripes arise. Due to its symmetry-breaking properties, the flow term induces a lateral drift of the whole pattern, once the instability has become active. The drift velocity is measured numerically and described analytically in the framework of a linear analysis. At large flow strength, the linear description breaks down, which is accompanied by a transition to flow-dominated morphologies, described in a companion paper. Small and intermediate flows lead to increased order in the lattice structure of the pattern, facilitating the elimination of defects. Locally oscillating structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review

On the relation of Thomas rotation and angular velocity of reference frames

In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing concepts, introduced in \cite{rindler}, is to consider a rotating reference frame co-moving with the gyroscope, and relate the precession of the gyroscope to the angular velocity of the reference frame. A recent paper \cite{herrera}, however, applies this principle to three different co-moving rotating reference frames and arrives at three different Thomas rotation angles. The reason for this apparent paradox is that the principle of \cite{rindler} is used for a situation to which it does not apply. In this paper we rigorously examine the theoretical background and limitations of applicability of the principle of \cite{rindler}. Along the way we also establish some general properties of {\it rotating reference frames}, which may be of independent interest.Comment: 14 pages, 2 figure

A Derivation of Three-Dimensional Inertial Transformations

The derivation of the transformations between inertial frames made by Mansouri and Sexl is generalised to three dimensions for an arbitrary direction of the velocity. Assuming lenght contraction and time dilation to have their relativistic values, a set of transformations kinematically equivalent to special relativity is obtained. The ``clock hypothesis'' allows the derivation to be extended to accelerated systems. A theory of inertial transformations maintaining an absolute simultaneity is shown to be the only one logically consistent with accelerated movements. Algebraic properties of these transformations are discussed. Keywords: special relativity, synchronization, one-way velocity of light, ether, clock hypothesis.Comment: 16 pages (A5), Latex, one figure, to be published in Found. Phys. Lett. (1997

The value of social media language for the assessment of wellbeing: a systematic review and meta-analysis

Wellbeing is predominantly measured through self-reports, which is time-consuming and costly. It can also be measured by automatically analysing language expressed on social media platforms, through social media text mining (SMTM). We present a systematic review based on 45 studies, and a meta-analysis of 32 convergent validities from 18 studies reporting correlations between SMTM and survey-based wellbeing. We find that (1) studies were mostly limited to the English language, (2) Twitter was predominantly used for data collection, (3) word-level and data-driven methods were similarly prominent, and (4) life satisfaction was the most common outcome studied. We found that SMTM-based estimates of wellbeing correlated with survey-reported scores across studies at a meta-analytic average of r = .33(95% CI [.25, .40]) for individual-level assessments of wellbeing, and at r = .54(95% CI [.37, .67]) for regional measures of well-being. We provide recommendations for future SMTM wellbeing studies

Category-Based Filtering and User Stereotype Cases to Reduce the Latency Problem in Recommender Systems

Abstract. Collaborative filtering is an often successful method for personalized item selection in Recommender systems. However, in domains where items are frequently added, collaborative filtering encounters the latency problem. Characterized by the system’s inability to select recently added items, the latency problem appears because new items in a collaborative filtering system must be reviewed before they can be recommended. Content-based filtering may help to counteract this problem, but runs the risk of only recommending items almost identical to the ones the user has appreciated before. In this paper, a combination of category-based filtering and user stereotype cases is proposed as a novel approach to reduce the latency problem. Category-based filtering puts emphasis on categories as meta-data to enable quicker personalization. User stereotype cases, identified by clustering similar users, are utilized to decrease response times and improve the accuracy of recommendations when user information is incomplete.