Generalized Weierstrass-Enneper inducing, conformal immersions, and gravity

Basic quantities related to 2-D gravity, such as Polyakov extrinsic action, Nambu-Goto action, geometrical action, and Euler characteristic are studied using generalized Weierstrass-Enneper (GWE) inducing of surfaces. Connection of the GWE inducing with conformal immersion is made and varius aspects of the theory are shown to be invariant under the modified Veselov-Novikov hierarchy of flows. The geometry of certain surfaces is shown to be connected with the dynamics of infinite and finite dimensional integrable systems. Connections to Liouville-Beltrami gravity are indicated.Comment: Latex, 37 page

A filtering approach to tracking volatility from prices observed at random times

This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $S=(S_{t})_{t\geq0}$ is given by $$dS_{t}=r(\theta_{t})S_{t}dt+v(\theta_{t})S_{t}dB_{t},$$ where $B=(B_{t})_{t\geq0}$ is a Brownian motion, $v$ is a positive function, and $\theta=(\theta_{t})_{t\geq0}$ is a c\'{a}dl\'{a}g strong Markov process. The random process $\theta$ is unobservable. We assume also that the asset price $S_{t}$ is observed only at random times $0<\tau_{1}<\tau_{2}<....$ This is an appropriate assumption when modelling high frequency financial data (e.g., tick-by-tick stock prices). In the above setting the problem of estimation of $\theta$ can be approached as a special nonlinear filtering problem with measurements generated by a multivariate point process $(\tau_{k},\log S_{\tau_{k}})$. While quite natural, this problem does not fit into the standard diffusion or simple point process filtering frameworks and requires more technical tools. We derive a closed form optimal recursive Bayesian filter for $\theta_{t}$, based on the observations of $(\tau_{k},\log S_{\tau_{k}})_{k\geq1}$. It turns out that the filter is given by a recursive system that involves only deterministic Kolmogorov-type equations, which should make the numerical implementation relatively easy

near field to far field tranfsormation of bipolar measurements by equivalent magnetic current approach

An equivalent magnetic current (EMC) approach has been proposed as an alternative method to the classical modal formulation for computing the far-field pattern of a radiating antenna from planar near-field measurements. The attractiveness of this EMC approach includes the possibility of producing the correct far-field pattern in all regions in front of a planar antenna under test (AUT), a drawback of the classical modal formulation due to its dependence on the Fourier transform and assumptions which must be made about the field outside of the measurement zone, and its adaptability to both irregularly sampled and non-canonical near-field measurement surfaces. A drawback of the EMC approach, however, is its significantly larger computational requirements. A comparison of the EMC and classical modal approaches for near-field to far-field transformation is examined in terms of the resultant far-field patterns. Measurement results for a waveguide-fed slot array using the UCLA bi-polar planar near-field measurement scanner are presented. An implementation of the EMC approach for the bi-polar geometry is described and results obtained using different subsets of the measured bi-polar near-field data are presented and compared to that obtained using the classical modal approach.Peer ReviewedPostprint (published version

Cyberbullying - when does a school authority\u27s liability in tort end?

Cyberbullying in schools is increasing on an alarming rate. The development of the Internet and smartphone technology have increased the potential scope of a school authority’s duty of care for its students. A question frequently asked by educators is “Where does a school authority’s duty of care end in the interconnected, 24/7 world of the Internet?” This paper argues that a duty of care will be owed where the school is in a school/student relationship with its students. That relationship can exist outside the school gates and outside of school hours. There are no decisions of senior appellate courts that deal with a school authority’s liability for cyberbullying. The authors, therefore, analyse the nature of the relationship to identify the key features that must be present to establish the existence of a duty of care. Three features are identified as critical to the existence of the duty of care outside of the normal school hours. They are the extent to which the school authority controls or ought to control a given situation, the extent to which it has encouraged students to participate in a particular activity and the extent to which a school authority is aware or ought to be aware of risks associated with the relevant activity of its students

Combining Rewriting and Incremental Materialisation Maintenance for Datalog Programs with Equality

Materialisation precomputes all consequences of a set of facts and a datalog program so that queries can be evaluated directly (i.e., independently from the program). Rewriting optimises materialisation for datalog programs with equality by replacing all equal constants with a single representative; and incremental maintenance algorithms can efficiently update a materialisation for small changes in the input facts. Both techniques are critical to practical applicability of datalog systems; however, we are unaware of an approach that combines rewriting and incremental maintenance. In this paper we present the first such combination, and we show empirically that it can speed up updates by several orders of magnitude compared to using either rewriting or incremental maintenance in isolation.Comment: All proofs contained in the appendix. 7 pages + 4 pages appendix. 7 algorithms and one table with evaluation result

Consequences of Pure Point Diffraction Spectra for Multiset Substitution Systems

There is a growing body of results in the theory of discrete point sets and tiling systems giving conditions under which such systems are pure point diffractive. Here we look at the opposite direction: what can we infer about a discrete point set or tiling, defined through a primitive substitution system, given that it is pure point diffractive? Our basic objects are Delone multisets and tilings, which are self-replicating under a primitive substitution system of affine mappings with a common expansive map $Q$. Our first result gives a partial answer to a question of Lagarias and Wang: we characterize repetitive substitution Delone multisets that can be represented by substitution tilings using a concept of "legal cluster". This allows us to move freely between both types of objects. Our main result is that for lattice substitution multiset systems (in arbitrary dimensions) being a regular model set is not only sufficient for having pure point spectrum--a known fact--but is also necessary. This completes a circle of equivalences relating pure point dynamical and diffraction spectra, modular coincidence, and model sets for lattice substitution systems begun by the first two authors of this paper.Comment: 36 page

High directivity modes in the koch island fractal patch antenna

The article shows that a patch antenna with fractal boundary exhibits, at a frequencies above the fundamental mode, localized modes. These modes can have broadside directive patterns. As an example of this phenomenon experimental data on the Koch island patch antenna is presented.Peer ReviewedPostprint (published version

Spectral statistics in disordered metals: a trajectories approach

We show that the perturbative expansion of the two-level correlation function, $R(\omega)$, in disordered conductors can be understood semiclassically in terms of self-intersecting particle trajectories. This requires the extension of the standard diagonal approximation to include pairs of paths which are non-identical but have almost identical action. The number of diagrams thus produced is much smaller than in a standard field-theoretical approach. We show that such a simplification occurs because $R(\omega)$ has a natural representation as the second derivative of free energy $F(\omega)$. We calculate $R(\omega)$ to 3-loop order, and verify a one-parameter scaling hypothesis for it in 2d. We discuss the possibility of applying our ``weak diagonal approximation'' to generic chaotic systems.Comment: 9 pages in REVTeX two-column format including 4 figures; submitted to Phys.Rev.

Capacity building in economics : education and research in transition economies

The development of the institutional capacity to create and evaluate economic policies remains a critical need-and constraint-in most transition economies if they are to complete the successful passage to fully functioning market economies. To take an active role in the transition process, economic policymakers, business leaders, government officials, and others need a thorough grounding in market-based economics. This requires strengthening economics education and providing support for qualified economists to teach economics at all levels and to carry out high-quality research and policy analysis. Although the education systems in a handful of countries have already risen to the challenge, in many other transition countries, the structure of educational and research institutes remains grounded in the Communist model. This paper presents findings from a comprehensive study assessing the state of economics education and research in 24 countries in East-Central Europe and the former Soviet Union. While 20 countries were initially included because preliminary assessments showed that they lacked the capability to offer high-quality economics education, four additional countries-the Czech Republic, Hungary, Russia, and Ukraine-were included to highlight five centers of excellence that they already host. Based on the experience of these successful centers, the study's findings, and information gathered from a series of donor meetings in Berlin, New York, and Washington, D.C., this paper presents an approach to building new indigenous capacity for teaching and research on market-based economics in regions where the need is particularly critical-the Caucasus, Central Asia, and Southeast Europe.Curriculum&Instruction,Decentralization,Agricultural Knowledge&Information Systems,Teaching and Learning,Public Health Promotion,Tertiary Education,Health Monitoring&Evaluation,Agricultural Knowledge&Information Systems,Teaching and Learning,Curriculum&Instruction