Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations $d\leq n^2/4$
and $d\geq n^2/2$, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to $n(n-1)/2$ was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for $d \geq 4(n2+n)/9$ and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related
asymptotic results.

Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Characterization of Transmission Losses

In this paper, characterizing transmission losses according to their origin is carried out. Transmission loss is decomposed into three components. The first is due to the current flow from generators to loads. The second is due to the circulating current between generators. The third represents the contribution of network structure and controls to increasing or decreasing transmission losses. Analytical proofs of the proposed loss decomposition are presented along with methods of allocating each component to the parties contributing to it. Illustration on simple dc and ac systems is presented. Results of application of the proposed method compared with other methods are also presented.

Rapid design of application specific FFT cores

Methods are presented for developing synthesizable FFT cores. These are based on a modular approach in which parameterized commutator and processor blocks are cascaded to implement the computations required in many important FFT signal flow graphs. In addition, it is shown how the use of a digital serial data organization can be used to produce systems that offer 100% processor utilization along with reductions in storage requirements. The approach has been used to create generators for the automated synthesis of FFT cores that are portable across a broad range of silicon technologies. Resulting chip designs are competitive with ones created using manual methods but with significant reductions in design times.

Systolic VLSI compiler (SVC) for high performance vector quantisation chips

An overview is given of a systolic VLSI compiler (SVC) tool currently under development for the automated design of high performance digital signal processing (DSP) chips. Attention is focused on the design of systolic vector quantization chips for use in both speech and image coding systems. The software in question consists of a cell library, silicon assemblers, simulators, test pattern generators, and a specially designed graphics shell interface which makes it expandable and user friendly. It allows very high performance digital coding systems to be rapidly designed in VLSI.

Synthesizable FFT cores

Methods are presented for developing synthesizable FFT cores. These are based on a modular approach in which parameterizable blocks are cascaded to implement the computations required across a range of typical FFT signal flow graphs. The underlying architectural approach combines the use of a digital serial data organization with generic commutator blocks to produce systems that offer 100% processor utilization with storage requirements less than previous designs. The approach has been used to create generators for the automated synthesis of FFT cores that are portable across a broad range of silicon technologies. Resulting chip designs are competitive with manual methods but with significant reductions in design times.

Analysis of Two-Speed Wind Farm Operation From Grid-Side Measurements

This paper analyzes data captured by a phasor measurement unit at a wind farm, employing two-speed induction generators, and investigates aspects of the control system's interaction with the power system. Composite superimposed transient events are proposed as a method to improve the quality of the analysis and reduce errors caused by unknowns, such as wind speed variation. A Mathworks SimPowerSystems model validates the inertia contribution of the wind farm, which is an important parameter in power systems with high wind penetration. Transients caused by turbine speed transitions are identified and explained. The analysis also highlights areas where wind farm control should be improved if useful inertia contribution is to be provided.

Simulations of magnetic microstructure in thin film elements used for programmable motion of magnetic particles

The results of two-dimensional micromagnetic modeling of magnetization patterns in Permalloy ellipses under the influence of rotating constant-amplitude magnetic fields are discussed. Ellipses of two different lateral sizes have been studied, 0.5m x 1.5m and 1m x 3m. The amplitude of the rotating magnetic field was varied between simulations with the condition that it must be large enough to saturate or nearly saturate the ellipse with the field applied along the long axis of the ellipse. For the smaller ellipse size it is found that the magnetization pattern forms an S state and the direction of the net magnetization lags behind the direction of the applied field. At a critical angle of the rotating magnetic field the direction of the magnetization switches by a large angle to a new S state. Both the critical angle and the angle interval of the switch depend on field amplitude. For this new state, it is instead the applied field direction that lags behind the magnetization direction. The transient magnetization patterns correspond to multi-domain patterns including two vortices, but this state never exists for the equilibrated magnetization patterns. The behavior of the larger ellipse in rotating field is different. With the field applied along the long-axis of the ellipse, the magnetization of the ellipse is nearly saturated with a vortex close to each apex of the ellipse. As the field is rotated, this magnetization pattern remains and the net-magnetization direction lags behind the direction of the field until for a certain angle of the applied field an equilibrium multi-domain state is created. Comparisons are made with corresponding experimental results obtained by performing in-field magnetic force microscopy on Permalloy ellipses.

Exotic Domain States in Ferroelectrics: Searching for Vortices and Skyrmions

Very recent experimental and theoretical work has sought to find out whether or not complex arrangements of dipoles (such as flux-closure, vortex or skyrmion patterns) exist in ferroelectrics. While there is undoubtedly still considerable work to be done, enough insight has now been gained to warrant a brief discussion of progress to date. This review article attempts to undertake such a discussion.

A simple bioanalytical method for the quantification of antiepileptic drugs in dried blood spots

An increasing number of publications on the dried blood spot (DBS) sampling approach for the quantification of drugs and metabolites have been spurred on by the inherent advantages of this sampling technique. In the present research, a selective and sensitive high-performance liquid chromatography method for the concurrent determination of multiple antiepileptic drugs (AEDs) [levetiracetam (LVT), lamotrigine (LTG), phenobarbital (PHB)], carbamazepine (CBZ) and its active metabolite carbamazepine-10,11 epoxide (CBZE)] in a single DBS has been developed and validated. Whole blood was spotted onto Guthrie cards and dried. Using a standard punch (6. mm diameter), a circular disc was punched from the card and extracted with methanol: acetonitrile (3:1, v/v) containing hexobarbital (Internal Standard) and sonicated prior to evaporation. The extract was then dissolved in water and vortex mixed before undergoing solid phase extraction using HLB cartridges. Chromatographic separation of the AEDs was achieved using Waters XBridge™ C18 column with a gradient system. The developed method was linear over the concentration ranges studied with r=0.995 for all compounds. The lower limits of quantification (LLOQs) were 2, 1, 2, 0.5 and 1. µg/mL for LVT, LTG, PHB, CBZE and CBZ, respectively. Accuracy (%RE) and precision (%CV) values for within and between day were

Self-Similar Nested Flux Closure Structures in a Tetragonal Ferroelectric

In specific solid-state materials, under the right conditions, collections of magnetic dipoles are known to spontaneously form into a variety of rather complex geometrical patterns, exemplified by vortex and skyrmion structures. While theoretically, similar patterns should be expected to form from electrical dipoles, they have not been clearly observed to date: the need for continued experimental exploration is therefore clear. In this Letter we report the discovery of a rather complex domain arrangement that has spontaneously formed along the edges of a thin single crystal ferroelectric sheet, due to surface-related depolarizing fields. Polarization patterns are such that nanoscale “flux-closure” loops are nested within a larger mesoscale flux closure object. Despite the orders of magnitude differences in size, the geometric forms of the dual-scale flux closure entities are rather similar.

Capability Curve Based Enhanced Reactive Power Control Strategy for Stability Enhancement and Network Voltage Management

Reactive power has become a vital resource in modern electricity networks due to increased penetration of distributed generation. This paper examines the extended reactive power capability of DFIGs to improve network stability and capability to manage network voltage profile during transient faults and dynamic operating conditions. A coordinated reactive power controller is designed by considering the reactive power capabilities of the rotor-side converter (RSC) and the grid-side converter (GSC) of the DFIG in order to maximise the reactive power support from DFIGs. The study has illustrated that, a significant reactive power contribution can be obtained from partially loaded DFIG wind farms for stability enhancement by using the proposed capability curve based reactive power controller; hence DFIG wind farms can function as vital dynamic reactive power resources for power utilities without commissioning additional dynamic reactive power devices. Several network adaptive droop control schemes are also proposed for network voltage management and their performance has been investigated during variable wind conditions. Furthermore, the influence of reactive power capability on network adaptive droop control strategies has been investigated and it has also been shown that enhanced reactive power capability of DFIGs can substantially improve the voltage control performance.

Day-Ahead Optimal Charging/Discharging Scheduling for Electric Vehicles in Micro-Grids

A micro-grid is an autonomous system which can be operated and connected to an external system or isolated with the help of energy storage systems (ESSs). While the daily output of distributed generators (DGs) strongly depends on the temporal distribution of natural resources such as wind and solar, unregulated electric vehicle (EV) charging demand will deteriorate the imbalance between the daily load and generation curves. In this paper, a statistical model is presented to describe daily EV charging/discharging behaviour. An optimisation problem is proposed to obtain economic operation for the micro-grid based on this model. In day-ahead scheduling, with estimated information of power generation and load demand, optimal charging/discharging of EVs during 24 hours is obtained. A series of numerical optimization solutions in different scenarios is achieved by serial quadratic programming. The results show that optimal charging/discharging of EVs, a daily load curve can better track the generation curve and the network loss and required ESS capacity are both decreased. The paper also demonstrates cost benefits for EVs and operators.

Determination of Power System Response during Small Load Fluctuations

This paper proposes a calculation method to determine power system response during small load perturbations or minor disturbances. The method establishes the initial value of active power transient using traditional reduction technique on admittance matrix, which incorporates voltage variations in the determination. The method examines active power distribution among generators when several loads simultaneously change, and verifies that the superposition principle is applicable for this scenario. The theoretical derivation provided in the paper is validated by numerical simulations using a 3-generator 9-bus benchmark model. The results indicate that the inclusion of voltage variation renders an independent and precise measure of active power response during transient conditions.

Measurement-based Method for Wind Farm Power System Oscillation Monitoring

The global increase in the penetration of renewable energy is pushing electrical power systems into uncharted territory, especially in terms of transient and dynamic stability. In particular, the greater penetration of wind generation in European power networks is, at times, displacing a significant capacity of conventional synchronous generation with fixed-speed induction generation and now more commonly, doubly-fed induction generators. The impact of such changes in the generation mix requires careful monitoring to assess the impact on transient and dynamic stability. This paper presents a measurement based method for the early detection of power system oscillations, with attention to mode damping, in order to raise alarms and develop strategies to actively improve power system dynamic stability and security. A method is developed based on wavelet transform and support vector data description (SVDD) to detect oscillation modes in wind farm output power, which may excite dynamic instabilities in the wider system. The wavelet transform is used as a filter to identify oscillations in different frequency bands, while SVDD is used to extract dominant features from different scales and generate an assessment boundary according to the extracted features. Poorly damped oscillations of a large magnitude or that are resonant can be alarmed to the system operator, to reduce the risk of system instability. Method evaluation is exemplified used real data from a chosen wind farm.