Quantum computing and polynomial equations over the finite field Z(2)

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z(2). This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP subset of P-#P and BQP subset of PP.

Master and apprentice or difference and complementarity? Local government practioners, doctoral studies and co-produced research

In their search for innovative policy solutions to complex social problematics, local governance practitioners will look to synergising specific policy guidance from government departments with conceptual scientific research outputs. UK academics are also now expected to emphasise the relevance of their research and to increase its utilisation by practitioners. Away from utilitarian pressures, academics from applied discipline, such as Public Administration and Local Government Studies are increasingly drawn to the benefits of co-produced research. Despite the pressure for more co-research there are few opportunities for practitioners and academics to nurture relationships that would support close collaboration. This paper looks at the opportunity for closer collaboration when practitioners undertake research degrees, in order to enhance their cognitive skills and develop greater scientific knowledge of particular policy domains. If this route to closer collaboration is to succeed, it will require academics to think differently about their relationship with practitioner-students.

Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation?

Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата.

Time-Dependent Differential Inclusions and Viability

AMS subject classification: Primary 34A60, Secondary 49J52.

SG Pseudo-Differential Operators and Weak Hyperbolicity

2002 Mathematics Subject Classification: 35S05, 47G30, 58J42.

Diversity, difference and nation: indigenous peoples on screen in Mexico

This paper draws on constructivist theories of identity that regard the self as, paradoxically, coming into existence through interaction with the other, to investigate the discursive formation of indigenous people in the forging of Mexican national identity. The aim of the essay is to show how difference has been managed and deployed in the establishment of national Mexican identities from independence until the present. This is done with reference to visual culture and film and illustrated with examples from the ‘Golden Age’ as well as ‘the New Mexican Cinema’.

Differential ability and attainment in language and arithmetic of Dutch primary school pupils.

Background. In pre-school and primary education pupils differ in many abilities and competences (‘giftedness’). Yet mainstream educational practice seems rather homogeneous in providing age-based or grade-class subject matter approaches. Aims. To clarify whether pupils scoring initially at high ability level do develop and attain differently at school with respect to language and arithmetic compared with pupils displaying other initial ability levels. To investigate whether specific individual, family or educational variables co-vary with the attainment of these different types of pupils in school. Samples. Data from the large-scale PRIMA cohort study including a total of 8258 grade 2 and 4 pupils from 438 primary schools in The Netherlands. Methods. Secondary analyses were carried out to construct gain scores for both language and arithmetic proficiency and a number of behavioural, attitudinal, family and educational characteristics. The pupils were grouped into different ability categories (highly able; able; above average; average and below). Further analyses used Pearson correlations and analyses of variance both between and within ability categories. Cross-validation was done by introducing a cohort of younger pupils in pre-school and grouping both cohorts into decile groups based on initial ability in language and arithmetic. Results. Highly able pupils generally decreased in attainment in both language and arithmetic, whereas pupils in average and below average groups improved their language and arithmetic scores. Only with highly able pupils were some educational characteristics correlated with the pupils’ development in achievement, behaviour and attitudes. Conclusions. Pre-school and primary education should better match pupils’ differences in abilities and competences from their start in pre-school to improve their functioning, learning processes and outcomes. Recommendations for educational improvement strategies are presented in closing.

Using the interaural time difference and cross-correlation to localise short-term complex noises

The mammalian binaural cue of interaural time difference (ITD) and cross-correlation have long been used to determine the point of origin of a sound source. The ITD can be defined as the different points in time at which a sound from a single location arrives at each individual ear [1]. From this time difference, the brain can calculate the angle of the sound source in relation to the head [2]. Cross-correlation compares the similarity of each channel of a binaural waveform producing the time lag or offset required for both channels to be in phase with one another. This offset corresponds to the maximum value produced by the cross-correlation function and can be used to determine the ITD and thus the azimuthal angle θ of the original sound source. However, in indoor environments, cross-correlation has been known to have problems with both sound reflections and reverberations. Additionally, cross-correlation has difficulties with localising short-term complex noises when they occur during a longer duration waveform, i.e. in the presence of background noise. The crosscorrelation algorithm processes the entire waveform and the short-term complex noise can be ignored. This paper presents a technique using thresholding which enables higher-localisation abilities for short-term complex sounds in the midst of background noise. To determine the success of this thresholding technique, twenty-five sounds were recorded in a dynamic and echoic environment. The twenty-five sounds consist of hand-claps, finger-clicks and speech. The proposed technique was compared to the regular cross-correlation function for the same waveforms, and an average of the azimuthal angles determined for each individual sample. The sound localisation ability for all twenty-five sound samples is as follows: average of the sampled angles using cross-correlation: 44%; cross-correlation technique with thresholding: 84%. From these results, it is clear that this proposed technique is very successful for the localisation of short-term complex sounds in the midst of background noise and in a dynamic and echoic indoor environment.

A rare case of postpartum thrombocytosis. Differential diagnosis and management

This is a case of a 43-year-old primigravida primipara woman who presented in our Department in 36 weeks gestational age and underwent caesarean section due to preeclampsia. From her history, it was known that her pregnancy was an in vitro fertilization (IVF) result. She also received low molecular weight heparin because of thrombophilia (protein S insufficiency). We present this case of postpartum thrombocytosis and discuss the differential diagnosis of this condition through the presentation of its management.