The Maxwell equations as a B\"acklund transformation

Backlund transformations (BTs) are a useful tool for integrating nonlinear partial differential equations (PDEs). However, the significance of BTs in linear problems should not be ignored. In fact, an important linear system of PDEs in Physics, namely, the Maxwell equations of Electromagnetism, may be viewed as a BT relating the wave equations for the electric and the magnetic field, these equations representing integrability conditions for solution of the Maxwell system. We examine the BT property of this system in detail, both for the vacuum case and for the case of a linear conducting medium.Comment: 7 pages; minor corrections; see also arXiv:0803.3688 and references therei

Infinitesimal symmetry transformations of matrix-valued differential equations: An algebraic approach

The study of symmetries of partial differential equations (PDEs) has been traditionally treated as a geometrical problem. Although geometrical methods have been proven effective with regard to finding infinitesimal symmetry transformations, they present certain conceptual difficulties in the case of matrix-valued PDEs; for example, the usual differential-operator representation of the symmetry-generating vector fields is not possible in this case. An algebraic approach to the symmetry problem of PDEs is described, based on abstract operators (characteristic derivatives) which admit a standard differential-operator representation in the case of scalar-valued PDEs.Comment: 17 pages; minor corrections; see also arXiv:0803.368

Symmetry, Conserved Charges, and Lax Representations of Nonlinear Field Equations: A Unified Approach

A certain non-Noetherian connection between symmetry and integrability properties of nonlinear field equations in conservation-law form is studied. It is shown that the symmetry condition alone may lead, in a rather straightforward way, to the construction of a Lax pair, a doubly infinite set of (generally nonlocal) conservation laws, and a recursion operator for symmetries. Applications include the chiral field equation and the self-dual Yang-Mills equation.Comment: 15 page

Venture Capital and Innovation in Europe

This paper examines the direction of causality between Venture Capital (VC) and innovation (proxied by patents) in Europe. We test whether causality runs from patents to VC by estimating a linear dynamic panel model and causality from VC to patents by estimating a panel count model. Evidence from a European sample indicates that causality runs from patents to VC suggesting that, in Europe, innovation seems to create a demand for VC and not VC a supply of innovation. In this sense, innovative ideas seem to lack more than funds in EuropeVenture Capital; Dynamic Panel Data; Innovation; Patents

On the demand for lotteries in Greece

Demand for lotteries has been estimated in several countries, an important issue being whether operators set lottery payouts optimally. The question is tackled by means of a traditional demand equation in effective price and recently by a demand equation variant in jackpots, both specifications indicating that in many countries operators set their payout ratio more or less correctly and slightly on the generous side. The objective of this paper is to provide evidence on the lottery demand parameters in Greece and to assess the optimality of the current payout-allocating rulesdemand elasticity; payout policy

Electromotive Force: A Guide for the Perplexed

The concept of electromotive force (emf) may be introduced in various ways in an undergraduate course of theoretical electromagnetism. The multitude of alternate expressions for the emf is often the source of confusion to the student. We summarize the main ideas, adopting a pedagogical logic that proceeds from the general to the specific. The emf of a "circuit" is first defined in the most general terms. The expressions for the emf of some familiar electrodynamical systems are then derived in a rather straightforward manner. A diversity of physical situations is thus unified within a common theoretical framework.Comment: 11 pages, 5 figures; added example & appendi

Unveiling connectivity patterns of categories in complex systems: an application to human needs in urban places

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of mathematical sociology on 06/09/2016, available online: http://www.tandfonline.com/doi/full/10.1080/0022250X.2016.1219855We present a methodology based on weighted networks and dependence coefficients aimed at revealing connectivity patterns between categories. As a case study, it is applied to an urban place and at two spatial levels—neighborhood and square—where categories correspond to human needs. Our results show that diverse spatial levels present different and nontrivial patterns of need emergence. A numerical model indicates that these patterns depend on the probability distribution of weights. We suggest that this way of analyzing the connectivity of categories (human needs in our case study) in social and ecological systems can be used to define new strategies to cope with complex processes, such as those related to transition management and governance, urban-making, and integrated planning.Peer ReviewedPostprint (author's final draft

A hybrid architecture for the implementation of the Athena neural net model

The implementation of an earlier introduced neural net model for pattern classification is considered. Data flow principles are employed in the development of a machine that efficiently implements the model and can be useful for real time classification tasks. Further enhancement with optical computing structures is also considered