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 $\phi$. In Euclidean space the Lagrangian of such a theory, $L=\frac{1}{2}(\nabla\phi)^2-ig\phi\exp(ia\phi)$, 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 $E_{m,n}\sim(m+1/2)^2a^2/(16n^2)$.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 $\rho(z)$ in the complex plane. It is shown that there exist infinitely many complex contours $C$ of infinite length on which $\rho(z) dz$ is real and positive. Furthermore, the probability integral $\int_C\rho(z) dz$ 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

On optimum Hamiltonians for state transformations

For a prescribed pair of quantum states |psi_I> and |psi_F> we establish an elementary derivation of the optimum Hamiltonian, under constraints on its eigenvalues, that generates the unitary transformation |psi_I> --> |psi_F> in the shortest duration. The derivation is geometric in character and does not rely on variational calculus.Comment: 5 page