Genus for knots and links in renormalizable templates with several branch nodes

We apply kneading theory to describe the knots and links generated by the iteration of renormalizable nonautonomous dynamical systems with reducible kneading invariants, in terms of the links corresponding to each factor. As a consequence we obtain explicit formulas for the genus for this kind of knots and links.

Design of the ISePorto robocup Middle-Size League Robotic Soccer Team: Control, Localisation and Coordination

Proceedings of the 10th Mediterranean Conference on Control and Automation - MED2002 Lisbon, Portugal, July 9-12, 2002

A topological invariant to predict the three-dimensional writhe of ideal configurations of knots and links.

We present herein a topological invariant of oriented alternating knots and links that predicts the three-dimensional (3D) writhe of the ideal geometrical configuration of the considered knot/link. The fact that we can correlate a geometrical property of a given configuration with a topological invariant supports the notion that the ideal configuration contains important information about knots and links. The importance of the concept of ideal configuration was already suggested by the good correlation between the 3D writhe of ideal knot configurations and the ensemble average of the 3D writhe of random configurations of the considered knots. The values of the new invariant are quantized: multiples of 4/7 for links with an odd number of components (including knots) and 2/7 plus multiples of 4/7 for links with an even number of components.

Linear relations between writhe and minimal crossing number in Conway families of ideal knots and links

We showed earlier how to predict the writhe of any rational knot or link in its ideal geometric configuration, or equivalently the average of the 3D writhe over statistical ensembles of random configurations of a given knot or link (Cerf and Stasiak 2000 Proc. Natl Acad. Sci. USA 97 3795). There is no general relation between the minimal crossing number of a knot and the writhe of its ideal geometric configuration. However, within individual families of knots linear relations between minimal crossing number and writhe were observed (Katritch et al 1996 Nature 384 142). Here we present a method that allows us to express the writhe as a linear function of the minimal crossing number within Conway families of knots and links in their ideal configuration. The slope of the lines and the shift between any two lines with the same

Auditory localisation and recognition after left inferior collicular lesion: effects of work load on cortical activation patterns (fMRI study)

Evidence from neuropsychological and activation studies (Clarke et al., 2oo0, Maeder et al., 2000) suggests that sound recognitionand localisation are processed by two anatomically and functionally distinct cortical networks. We report here on a case of a patientthat had an interruption of auditory information and we show: i) the effects of this interruption on cortical auditory processing; ii)the effect of the workload on activation pattern.A 36 year old man suffered from a small left mesencephalic haemotrhage, due to cavernous angioma; the let% inferior colliculuswas resected in the surgical approach of the vascular malformation. In the acute stage, the patient complained of auditoryhallucinations and of auditory loss in right ear, while tonal audiometry was normal. At 12 months, auditory recognition, auditorylocalisation (assessed by lTD and IID cues) and auditory motion perception were normal (Clarke et al., 2000), while verbal dichoticlistening was deficient on the right side.Sound recognition and sound localisation activation patterns were investigated with fMRI, using a passive and an activeparadigm. In normal subjects, distinct cortical networks were involved in sound recognition and localisation, both in passive andactive paradigm (Maeder et al., 2OOOa, 2000b).Passive listening of environmental and spatial stimuli as compared to rest strongly activated right auditory cortex, but failed toactivate left primary auditory cortex. The specialised networks for sound recognition and localisation could not be visual&d onthe right and only minimally on the left convexity. A very different activation pattern was obtained in the active condition wherea motor response was required. Workload not only increased the activation of the right auditory cortex, but also allowed theactivation of the left primary auditory cortex. The specialised networks for sound recognition and localisation were almostcompletely present in both hemispheres.These results show that increasing the workload can i) help to recruit cortical region in the auditory deafferented hemisphere;and ii) lead to processing auditory information within specific cortical networks.References:Clarke et al. (2000). Neuropsychologia 38: 797-807.Mae.der et al. (2OOOa), Neuroimage 11: S52.Maeder et al. (2OOOb), Neuroimage 11: S33

A partial ordering of knots and links through diagrammatic unknotting

In this paper we de. ne a partial ordering of knots and links using a special property derived from their minimal diagrams. A link K' is called a predecessor of a link K if Cr(K') < Cr(K) and a diagram of K' can be obtained from a minimal diagram D of K by a single crossing change. In such a case, we say that K' < K. We investigate the sets of links that can be obtained by single crossing changes over all minimal diagrams of a given link. We show that these sets are specific for different links and permit partial ordering of all links. Some interesting results are presented and many questions are raised.

Carcinoembryonic antigen expression, antibody localisation and immunophotodetection of human colon cancer liver metastases in nude mice: a model for radioimmunotherapy.

Colorectal cancer frequently disseminates through the portal vein into the liver. In this study, outbred Swiss nude mice were adapted to facilitate the induction of liver metastases by a pre-grafting treatment with 6 Gy total body irradiation and i.v. injection of anti-asialo GM1 antibody. One day later, cultured LS 174T human colon cancer cells were injected into the surgically exposed spleen, which was resected 3 min later. In 48 of 65 mice, a few to several hundred liver metastases were macroscopically observed at dissection 3 to 4 weeks after transplantation. Ten of 10 mice, followed-up for survival, died with multiple large confluent liver metastases. By reducing the radiation dose to 4 or 0 Gy, or omitting the anti-asialo GM1 antibody injection, only 60%, 37% or 50% of mice, respectively, had visible metastases 3 weeks after transplantation. Carcinoembryonic antigen (CEA) measured in tumour extracts was in the mean 25.6 micrograms/g in liver metastases compared with 9.2 micrograms/g in s.c. tumours. Uptake of radiolabelled anti-CEA monoclonal antibody (MAb) in the metastases 12, 24 and 48 hr after injection gave a mean value of 39% of the injected dose per gram of tissue (ID/g). In comparison, MAb uptake in s.c. and intrasplenic tumours or lung metastases gave a mean percentage ID/g of 20, 18 and 15, respectively. Laser-induced fluorescence after injection of indocyanin-MAb conjugate allowed direct visual detection of small liver metastases, including some that were not visible under normal light. Preliminary results showed that mice, pre-treated with 4 Gy irradiation and the anti-asialo GM1 injection, were tolerant to radioimmunotherapy with a total dose of 500 muCi 131I labeled anti-CEA intact MAbs given in 3 injections.

Mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

CV Exemplar and Links

a pdf and word format document which level 1 students can use as an examplar or template for their CV. Also includes links to example CVs and sites which help of creating CVs

notes and links related computer misuse act 1990

collectively edited resource for INFO2009 initially created as a demonstrator

Technical Report Background Reading Guidance and Links

Handout which contains a set of links to a variety of background resources associated with the topics for a technical report coursework. Resources are clustered into three overview areas, but contain links which be used to address each of the six questions scenarios.