172 research outputs found
Perception, Prestige and PageRank
Academic esteem is difficult to quantify in objective terms. Network theory
offers the opportunity to use a mathematical formalism to model both the esteem
associated with an academic and the relationships between academic colleagues.
Early attempts using this line of reasoning have focused on intellectual
genealogy as constituted by supervisor student networks. The process of
examination is critical in many areas of study but has not played a part in
existing models. A network theoretical "social" model is proposed as a tool to
explore and understand the dynamics of esteem in the academic hierarchy. It is
observed that such a model naturally gives rise to the idea that the esteem
associated with a node in the graph (the esteem of an individual academic) can
be viewed as a dynamic quantity that evolves with time based on both local and
non-local changes in the properties in the network. The toy model studied here
includes both supervisor-student and examiner-student relationships. This gives
an insight into some of the key features of academic genealogies and naturally
leads to a proposed model for "esteem propagation" on academic networks. This
propagation is not solely directed forward in time (from teacher to progeny)
but sometimes also flows in the other direction. As collaborators do well, this
reflects well on those with whom they choose to collaborate and those that
taught them. Furthermore, esteem as a quantity continues to be dynamic even
after the end of a relationship or career. In other words, esteem can be
thought of as flowing both forward and backward in time.Comment: 40 page
Infinitely many inequivalent field theories from one Lagrangian
Logarithmic time-like Liouville quantum field theory has a generalized PT
invariance, where T is the time-reversal operator and P stands for an S-duality
reflection of the Liouville field . In Euclidean space the Lagrangian of
such a theory, , is analyzed
using the techniques of PT-symmetric quantum theory. It is shown that L defines
an infinite number of unitarily inequivalent sectors of the theory labeled by
the integer n. In one-dimensional space (quantum mechanics) the energy spectrum
is calculated in the semiclassical limit and the mth energy level in the nth
sector is given by .Comment: 5 pages, 7 figure
Dimensions: Building Context for Search and Evaluation
Dimensions is a new scholarly search database that focuses on the broader set of use cases that academics now face. By including awarded grants, patents, and clinical trials alongside publication and Altmetric attention data, Dimensions goes beyond the standard publication-citation ecosystem to give the user a much greater sense of context of a piece of research. All entities in the graph may be linked to all other entities. Thus, a patent may be linked to a grant, if an appropriate reference is made. Books, book chapters, and conference proceedings are included in the publication index. All entities are treated as first-class objects and are mapped to a database of research institutions and a standard set of research classifications via machine-learning techniques. This article gives an overview of the methodology of construction of the Dimensions dataset and user interface
Probability Density in the Complex Plane
The correspondence principle asserts that quantum mechanics resembles
classical mechanics in the high-quantum-number limit. In the past few years
many papers have been published on the extension of both quantum mechanics and
classical mechanics into the complex domain. However, the question of whether
complex quantum mechanics resembles complex classical mechanics at high energy
has not yet been studied. This paper introduces the concept of a local quantum
probability density in the complex plane. It is shown that there
exist infinitely many complex contours of infinite length on which is real and positive. Furthermore, the probability integral is finite. Demonstrating the existence of such contours is the essential
element in establishing the correspondence between complex quantum and
classical mechanics. The mathematics needed to analyze these contours is subtle
and involves the use of asymptotics beyond all orders.Comment: 38 pages, 17figure
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