Weak Polynomial Identities for M1,1(E)

* Partially supported by Universita` di Bari: progetto “Strutture algebriche, geometriche e descrizione degli invarianti ad esse associate”.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

* The authors thank the “Swiss National Science Foundation” for its support.

Regular and Other Kinds of Extensions of Topological Spaces

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.

Case-Based Reasoning Tools from Shells to Object-Oriented Frameworks

A Case-Based Reasoning (CBR) tool is software that can be used to develop several applications that require cased-based reasoning methodology. CBR shells are kind of application generators with graphical user interface. They can be used by non-programmer users but the extension or integration of new components in these tools is not possible. In this paper we analyzed three CBR object-oriented framework development environments CBR*Tools, CAT-CBR, and JColibri. These frameworks work as open software development environment and facilitate the reuse of their design as well as implementations.

Credibility theory-based available transfer capability assessment

Since the development of large scale power grid interconnections and power markets, research on available transfer capability (ATC) has attracted great attention. The challenges for accurate assessment of ATC originate from the numerous uncertainties in electricity generation, transmission, distribution and utilization sectors. Power system uncertainties can be mainly described as two types: randomness and fuzziness. However, the traditional transmission reliability margin (TRM) approach only considers randomness. Based on credibility theory, this paper firstly built models of generators, transmission lines and loads according to their features of both randomness and fuzziness. Then a random fuzzy simulation is applied, along with a novel method proposed for ATC assessment, in which both randomness and fuzziness are considered. The bootstrap method and multi-core parallel computing technique are introduced to enhance the processing speed. By implementing simulation for the IEEE-30-bus system and a real-life system located in Northwest China, the viability of the models and the proposed method is verified.

A Note on Elementary Derivations

2000 Mathematics Subject Classification: Primary: 14R10. Secondary: 14R20, 13N15.

Probabilistic Models in Cryptography, Coding Theory and Tests for PRNG

2000 Mathematics Subject Classification: 94A29, 94B70

(2,3)-generation of the groups PSL6(q)

2010 Mathematics Subject Classification: 20F05, 20D06.

Source localization methods

One of the most pressing demands on electrophysiology applied to the diagnosis of epilepsy is the non-invasive localization of the neuronal generators responsible for brain electrical and magnetic fields (the so-called inverse problem). These neuronal generators produce primary currents in the brain, which together with passive currents give rise to the EEG signal. Unfortunately, the signal we measure on the scalp surface doesn't directly indicate the location of the active neuronal assemblies. This is the expression of the ambiguity of the underlying static electromagnetic inverse problem, partly due to the relatively limited number of independent measures available. A given electric potential distribution recorded at the scalp can be explained by the activity of infinite different configurations of intracranial sources. In contrast, the forward problem, which consists of computing the potential field at the scalp from known source locations and strengths with known geometry and conductivity properties of the brain and its layers (CSF/meninges, skin and skull), i.e. the head model, has a unique solution. The head models vary from the computationally simpler spherical models (three or four concentric spheres) to the realistic models based on the segmentation of anatomical images obtained using magnetic resonance imaging (MRI). Realistic models – computationally intensive and difficult to implement – can separate different tissues of the head and account for the convoluted geometry of the brain and the significant inter-individual variability. In real-life applications, if the assumptions of the statistical, anatomical or functional properties of the signal and the volume in which it is generated are meaningful, a true three-dimensional tomographic representation of sources of brain electrical activity is possible in spite of the ‘ill-posed’ nature of the inverse problem (Michel et al., 2004). The techniques used to achieve this are now referred to as electrical source imaging (ESI) or magnetic source imaging (MSI). The first issue to influence reconstruction accuracy is spatial sampling, i.e. the number of EEG electrodes. It has been shown that this relationship is not linear, reaching a plateau at about 128 electrodes, provided spatial distribution is uniform. The second factor is related to the different properties of the source localization strategies used with respect to the hypothesized source configuration.

Message passing for distributed optimisation of power allocation with renewable resources

The increase in renewable energy generators introduced into the electricity grid is putting pressure on its stability and management as predictions of renewable energy sources cannot be accurate or fully controlled. This, with the additional pressure of fluctuations in demand, presents a problem more complex than the current methods of controlling electricity distribution were designed for. A global approximate and distributed optimisation method for power allocation that accommodates uncertainties and volatility is suggested and analysed. It is based on a probabilistic method known as message passing [1], which has deep links to statistical physics methodology. This principled method of optimisation is based on local calculations and inherently accommodates uncertainties; it is of modest computational complexity and provides good approximate solutions.We consider uncertainty and fluctuations drawn from a Gaussian distribution and incorporate them into the message-passing algorithm. We see the effect that increasing uncertainty has on the transmission cost and how the placement of volatile nodes within a grid, such as renewable generators or consumers, effects it.

Lie-szimmetriák egy közgazdasági alkalmazása (An economic application of the Lie symmetries)

Ebben a tanulmányban ismertetjük a Nöther-tétel lényegi vonatkozásait, és kitérünk a Lie-szimmetriák értelmezésére abból a célból, hogy közgazdasági folyamatokra is alkalmazzuk a Lagrange-formalizmuson nyugvó elméletet. A Lie-szimmetriák dinamikai rendszerekre történő feltárása és viselkedésük jellemzése a legújabb kutatások eredményei e területen. Például Sen és Tabor (1990), Edward Lorenz (1963), a komplex kaotikus dinamika vizsgálatában jelent®s szerepet betöltő 3D modelljét, Baumann és Freyberger (1992) a két-dimenziós Lotka-Volterra dinamikai rendszert, és végül Almeida és Moreira (1992) a három-hullám interakciós problémáját vizsgálták a megfelelő Lie-szimmetriák segítségével. Mi most empirikus elemzésre egy közgazdasági dinamikai rendszert választottunk, nevezetesen Goodwin (1967) ciklusmodelljét. Ennek vizsgálatát tűztük ki célul a leírandó rendszer Lie-szimmetriáinak meghatározásán keresztül. / === / The dynamic behavior of a physical system can be frequently described very concisely by the least action principle. In the centre of its mathematical presentation is a specic function of coordinates and velocities, i.e., the Lagrangian. If the integral of the Lagrangian is stationary, then the system is moving along an extremal path through the phase space, and vice versa. It can be seen, that each Lie symmetry of a Lagrangian in general corresponds to a conserved quantity, and the conservation principle is explained by a variational symmetry related to a dynamic or geometrical symmetry. Briey, that is the meaning of Noether's theorem. This paper scrutinizes the substantial characteristics of Noether's theorem, interprets the Lie symmetries by PDE system and calculates the generators (symmetry vectors) on R. H. Goodwin's cyclical economic growth model. At first it will be shown that the Goodwin model also has a Lagrangian structure, therefore Noether's theorem can also be applied here. Then it is proved that the cyclical moving in his model derives from its Lie symmetries, i.e., its dynamic symmetry. All these proofs are based on the investigations of the less complicated Lotka Volterra model and those are extended to Goodwin model, since both models are one-to-one maps of each other. The main achievement of this paper is the following: Noether's theorem is also playing a crucial role in the mechanics of Goodwin model. It also means, that its cyclical moving is optimal. Generalizing this result, we can assert, that all dynamic systems' solutions described by first order nonlinear ODE system are optimal by the least action principle, if they have a Lagrangian.

Development and verification of control and protection strategies in hybrid AC/DC power systems for smart grid applications

Modern power networks incorporate communications and information technology infrastructure into the electrical power system to create a smart grid in terms of control and operation. The smart grid enables real-time communication and control between consumers and utility companies allowing suppliers to optimize energy usage based on price preference and system technical issues. The smart grid design aims to provide overall power system monitoring, create protection and control strategies to maintain system performance, stability and security. This dissertation contributed to the development of a unique and novel smart grid test-bed laboratory with integrated monitoring, protection and control systems. This test-bed was used as a platform to test the smart grid operational ideas developed here. The implementation of this system in the real-time software creates an environment for studying, implementing and verifying novel control and protection schemes developed in this dissertation. Phasor measurement techniques were developed using the available Data Acquisition (DAQ) devices in order to monitor all points in the power system in real time. This provides a practical view of system parameter changes, system abnormal conditions and its stability and security information system. These developments provide valuable measurements for technical power system operators in the energy control centers. Phasor Measurement technology is an excellent solution for improving system planning, operation and energy trading in addition to enabling advanced applications in Wide Area Monitoring, Protection and Control (WAMPAC). Moreover, a virtual protection system was developed and implemented in the smart grid laboratory with integrated functionality for wide area applications. Experiments and procedures were developed in the system in order to detect the system abnormal conditions and apply proper remedies to heal the system. A design for DC microgrid was developed to integrate it to the AC system with appropriate control capability. This system represents realistic hybrid AC/DC microgrids connectivity to the AC side to study the use of such architecture in system operation to help remedy system abnormal conditions. In addition, this dissertation explored the challenges and feasibility of the implementation of real-time system analysis features in order to monitor the system security and stability measures. These indices are measured experimentally during the operation of the developed hybrid AC/DC microgrids. Furthermore, a real-time optimal power flow system was implemented to optimally manage the power sharing between AC generators and DC side resources. A study relating to real-time energy management algorithm in hybrid microgrids was performed to evaluate the effects of using energy storage resources and their use in mitigating heavy load impacts on system stability and operational security.

Algorithms for efficient transaction management and consistent queries in client -server semantic object-oriented parallel databases

Large read-only or read-write transactions with a large read set and a small write set constitute an important class of transactions used in such applications as data mining, data warehousing, statistical applications, and report generators. Such transactions are best supported with optimistic concurrency, because locking of large amounts of data for extended periods of time is not an acceptable solution. The abort rate in regular optimistic concurrency algorithms increases exponentially with the size of the transaction. The algorithm proposed in this dissertation solves this problem by using a new transaction scheduling technique that allows a large transaction to commit safely with significantly greater probability that can exceed several orders of magnitude versus regular optimistic concurrency algorithms. A performance simulation study and a formal proof of serializability and external consistency of the proposed algorithm are also presented.^ This dissertation also proposes a new query optimization technique (lazy queries). Lazy Queries is an adaptive query execution scheme which optimizes itself as the query runs. Lazy queries can be used to find an intersection of sub-queries in a very efficient way, which does not require full execution of large sub-queries nor does it require any statistical knowledge about the data.^ An efficient optimistic concurrency control algorithm used in a massively parallel B-tree with variable-length keys is introduced. B-trees with variable-length keys can be effectively used in a variety of database types. In particular, we show how such a B-tree was used in our implementation of a semantic object-oriented DBMS. The concurrency control algorithm uses semantically safe optimistic virtual "locks" that achieve very fine granularity in conflict detection. This algorithm ensures serializability and external consistency by using logical clocks and backward validation of transactional queries. A formal proof of correctness of the proposed algorithm is also presented. ^