Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.Comment: 13 page

Generalized modularity matrices

Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various modularity matrices and shed light on their spectral properties that are at the basis of various theoretical results and practical spectral-type algorithms for community detection

Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of {\it Genius loci}. Global structural properties of a city can be characterized by the thermodynamical parameters calculated in the random walks problem.Comment: 44 pages, 22 figures, 2 table

A measure of centrality based on the spectrum of the Laplacian

We introduce a family of new centralities, the k-spectral centralities. k-Spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information. We explore this centrality in the context of several examples. While for sparse unweighted networks 1-spectral centrality behaves similarly to other standard centralities, for dense weighted networks they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) distinct from other known measures.Comment: 12 pages, 6 figures, 2 table

Molecular Clock on a Neutral Network

The number of fixed mutations accumulated in an evolving population often displays a variance that is significantly larger than the mean (the overdispersed molecular clock). By examining a generic evolutionary process on a neutral network of high-fitness genotypes, we establish a formalism for computing all cumulants of the full probability distribution of accumulated mutations in terms of graph properties of the neutral network, and use the formalism to prove overdispersion of the molecular clock. We further show that significant overdispersion arises naturally in evolution when the neutral network is highly sparse, exhibits large global fluctuations in neutrality, and small local fluctuations in neutrality. The results are also relevant for elucidating the topological structure of a neutral network from empirical measurements of the substitution process.Comment: 10 page

Concept of an efficient self-startup voltage converter with dynamic maximum power point tracking for microscale thermoelectric generators

Microscale Thermoelectric Generators (microTEGs) have a high application potential for energy harvesting for autonomous microsystems. In contrast to conventional thermoelectric generators, microTEGs can only supply small output-voltages. Therefore, voltage converters are required to provide supply-voltages that are sufficiently high to power microelectronics. However, for high conversion efficiency, voltage converters need to be optimized for the limited input voltage range and the typically high internal resistance of microTEGs. To overcome the limitations of conventional voltage converters we present an optimized self-startup voltage converter with dynamic maximum power point tracking. The performance potential of our concept is theoretically and experimentally analyzed. The voltage conversion interface demonstrates energy harvesting from open-circuit voltages as low as 30.7 mV, and enables independent and full start-up from 131 mV. No additional external power supply is required at any time during operation. It can be operated with a wide range of internal resistances from 20.6 to − 4 kΩ with a conversation efficiency between η = 68–79%

Dynamic Computation of Network Statistics via Updating Schema

In this paper we derive an updating scheme for calculating some important network statistics such as degree, clustering coefficient, etc., aiming at reduce the amount of computation needed to track the evolving behavior of large networks; and more importantly, to provide efficient methods for potential use of modeling the evolution of networks. Using the updating scheme, the network statistics can be computed and updated easily and much faster than re-calculating each time for large evolving networks. The update formula can also be used to determine which edge/node will lead to the extremal change of network statistics, providing a way of predicting or designing evolution rule of networks.Comment: 17 pages, 6 figure

Evaluation of resistive-plate-chamber-based TOF-PET applied to in-beam particle therapy monitoring

Particle therapy is a highly conformal radiotherapy technique which reduces the dose deposited to the surrounding normal tissues. In order to fully exploit its advantages, treatment monitoring is necessary to minimize uncertainties related to the dose delivery. Up to now, the only clinically feasible technique for the monitoring of therapeutic irradiation with particle beams is Positron Emission Tomography (PET). In this work we have compared a Resistive Plate Chamber (RPC)-based PET scanner with a scintillation-crystal-based PET scanner for this application. In general, the main advantages of the RPC-PET system are its excellent timing resolution, low cost, and the possibility of building large area systems. We simulated a partial-ring scannerbeam monitoring, which has an intrinsically low positron yield compared to diagnostic PET. In addition, for in-beam PET there is a further data loss due to the partial ring configuration. In order to improve the performance of the RPC-based scanner, an improved version of the RPC detector (modifying the thickness of the gas and glass layers), providing a larger sensitivity, has been simulated and compared with an axially extended version of the crystal-based device. The improved version of the RPC shows better performance than the prototype, but the extended version of the crystal-based PET outperforms all other options. based on an RPC prototype under construction within the Fondazione per Adroterapia Oncologica (TERA). For comparison with the crystal-based PET scanner we have chosen the geometry of a commercially available PET scanner, the Philips Gemini TF. The coincidence time resolution used in the simulations takes into account the current achievable values as well as expected improvements of both technologies. Several scenarios (including patient data) have been simulated to evaluate the performance of different scanners. Initial results have shown that the low sensitivity of the RPC hampers its application to hadro

What next for Shared Lives? Family-based support as a potential option for older people

With an ageing population and limited resources the challenge for policy makers and practitioners is how best to provide for the care and support needs of older people. This article draws on findings from two studies, a scoping study of the personalisation of care services and another which aimed to generate evidence about the potential use of family-based support schemes (Shared Lives, SL) for certain groups of older people. Forty-three schemes participated in a survey to gather information about services provided and the extent to which this included older people and their carers, and six staffs were interviewed across two schemes about issues for expanding provision for older people in their local areas. It was evident that SL schemes were already supporting a number of older people and there was support for expansion from both schemes and local authorities. Adequate resources, awareness raising, management commitment, and a pool of suitable carers would be needed to support any expansion effort. There is also still a need for SL to be more widely known and understood by care managers if it is to be considered part of mainstream provision for older people