Partial spreads and vector space partitions

Constant-dimension codes with the maximum possible minimum distance have been studied under the name of partial spreads in Finite Geometry for several decades. Not surprisingly, for this subclass typically the sharpest bounds on the maximal code size are known. The seminal works of Beutelspacher and Drake \& Freeman on partial spreads date back to 1975, and 1979, respectively. From then until recently, there was almost no progress besides some computer-based constructions and classifications. It turns out that vector space partitions provide the appropriate theoretical framework and can be used to improve the long-standing bounds in quite a few cases. Here, we provide a historic account on partial spreads and an interpretation of the classical results from a modern perspective. To this end, we introduce all required methods from the theory of vector space partitions and Finite Geometry in a tutorial style. We guide the reader to the current frontiers of research in that field, including a detailed description of the recent improvements.Comment: 30 pages, 1 tabl

Asymptotic bounds for the sizes of constant dimension codes and an improved lower bound

We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show relations between them. A slightly improved version of the so-called linkage construction is presented which is e.g. used to construct constant dimension codes with subspace distance $d=4$, dimension $k=3$ of the codewords for all field sizes $q$, and sufficiently large dimensions $v$ of the ambient space, that exceed the MRD bound, for codes containing a lifted MRD code, by Etzion and Silberstein.Comment: 30 pages, 3 table

High Resolution Spectral Domain Optical Coherence Tomography (SD-OCT) in Multiple Sclerosis: The First Follow Up Study over Two Years

“Non-invasive, faster and less expensive than MRI” and “the eye is a window to the brain” are recent slogans promoting optical coherence tomography (OCT) as a new surrogate marker in multiple sclerosis (MS). Indeed, OCT allows for the first time a non-invasive visualization of axons of the central nervous system (CNS). Reduction of retina nerve fibre layer (RNFL) thickness was suggested to correlate with disease activity and duration. However, several issues are unclear: Do a few million axons, which build up both optic nerves, really resemble billions of CNS neurons? Does global CNS damage really result in global RNFL reduction? And if so, does global RNFL reduction really exist in all MS patients, and follow a slowly but steadily ongoing pattern? How can these (hypothesized) subtle global RNFL changes be reliably measured and separated from the rather gross RNFL changes caused by optic neuritis? Before generally being accepted, this interpretation needs further critical and objective validation.We prospectively studied 37 MS patients with relapsing remitting (n = 27) and secondary progressive (n = 10) course on two occasions with a median interval of 22.4±0.5 months [range 19–27]. We used the high resolution spectral domain (SD-)OCT with the Spectralis 3.5 mm circle scan protocol with locked reference images and eye tracking mode. Patients with an attack of optic neuritis within 12 months prior to the onset of the study were excluded.Although the disease was highly active over the observation period in more than half of the included relapsing remitting MS patients (19 patients/32 relapses) and the initial RNFL pattern showed a broad range, from normal to markedly reduced thickness, no significant changes between baseline and follow-up examinations could be detected.These results show that caution is required when using OCT for monitoring disease activity and global axonal injury in MS

Altered Antioxidant-Oxidant Status in the Aqueous Humor and Peripheral Blood of Patients with Retinitis Pigmentosa

Retinitis Pigmentosa is a common form of hereditary retinal degeneration constituting the largest Mendelian genetic cause of blindness in the developed world. It has been widely suggested that oxidative stress possibly contributes to its pathogenesis. We measured the levels of total antioxidant capacity, free nitrotyrosine, thiobarbituric acid reactive substances (TBARS) formation, extracellular superoxide dismutase (SOD3) activity, protein, metabolites of the nitric oxide/cyclic GMP pathway, heme oxygenase-I and inducible nitric oxide synthase expression in aqueous humor or/and peripheral blood from fifty-six patients with retinitis pigmentosa and sixty subjects without systemic or ocular oxidative stress-related disease. Multivariate analysis of covariance revealed that retinitis pigmentosa alters ocular antioxidant defence machinery and the redox status in blood. Patients with retinitis pigmentosa present low total antioxidant capacity including reduced SOD3 activity and protein concentration in aqueous humor. Patients also show reduced SOD3 activity, increased TBARS formation and upregulation of the nitric oxide/cyclic GMP pathway in peripheral blood. Together these findings confirmed the hypothesis that patients with retinitis pigmentosa present reduced ocular antioxidant status. Moreover, these patients show changes in some oxidative-nitrosative markers in the peripheral blood. Further studies are needed to clarify the relationship between these peripheral markers and retinitis pigmentosa

Efficient Explicit Constructions of Multipartite Secret Sharing Schemes

Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. Secret sharing schemes for multipartite access structures have received considerable attention due to the fact that multipartite secret sharing can be seen as a natural and useful generalization of threshold secret sharing. This work deals with efficient and explicit constructions of ideal multipartite secret sharing schemes, while most of the known constructions are either inefficient or randomized. Most ideal multipartite secret sharing schemes in the literature can be classified as either hierarchical or compartmented. The main results are the constructions for ideal hierarchical access structures, a family that contains every ideal hierarchical access structure as a particular case such as the disjunctive hierarchical threshold access structure and the conjunctive hierarchical threshold access structure, the constructions for three families of compartmented access structures, and the constructions for two families compartmented access structures with compartments. On the basis of the relationship between multipartite secret sharing schemes, polymatroids, and matroids, the problem of how to construct a scheme realizing a multipartite access structure can be transformed to the problem of how to find a representation of a matroid from a presentation of its associated polymatroid. In this paper, we give efficient algorithms to find representations of the matroids associated to several families of multipartite access structures. More precisely, based on know results about integer polymatroids, for each of those families of access structures above, we give an efficient method to find a representation of the integer polymatroid over some finite field, and then over some finite extension of that field, we give an efficient method to find a presentation of the matroid associated to the integer polymatroid. Finally, we construct ideal linear schemes realizing those families of multipartite access structures by efficient methods

The RESET project: constructing a European tephra lattice for refined synchronisation of environmental and archaeological events during the last c. 100 ka

This paper introduces the aims and scope of the RESET project (. RESponse of humans to abrupt Environmental Transitions), a programme of research funded by the Natural Environment Research Council (UK) between 2008 and 2013; it also provides the context and rationale for papers included in a special volume of Quaternary Science Reviews that report some of the project's findings. RESET examined the chronological and correlation methods employed to establish causal links between the timing of abrupt environmental transitions (AETs) on the one hand, and of human dispersal and development on the other, with a focus on the Middle and Upper Palaeolithic periods. The period of interest is the Last Glacial cycle and the early Holocene (c. 100-8 ka), during which time a number of pronounced AETs occurred. A long-running topic of debate is the degree to which human history in Europe and the Mediterranean region during the Palaeolithic was shaped by these AETs, but this has proved difficult to assess because of poor dating control. In an attempt to move the science forward, RESET examined the potential that tephra isochrons, and in particular non-visible ash layers (cryptotephras), might offer for synchronising palaeo-records with a greater degree of finesse. New tephrostratigraphical data generated by the project augment previously-established tephra frameworks for the region, and underpin a more evolved tephra 'lattice' that links palaeo-records between Greenland, the European mainland, sub-marine sequences in the Mediterranean and North Africa. The paper also outlines the significance of other contributions to this special volume: collectively, these illustrate how the lattice was constructed, how it links with cognate tephra research in Europe and elsewhere, and how the evidence of tephra isochrons is beginning to challenge long-held views about the impacts of environmental change on humans during the Palaeolithic. © 2015 Elsevier Ltd.RESET was funded through Consortium Grants awarded by the Natural Environment Research Council, UK, to a collaborating team drawn from four institutions: Royal Holloway University of London (grant reference NE/E015905/1), the Natural History Museum, London (NE/E015913/1), Oxford University (NE/E015670/1) and the University of Southampton, including the National Oceanography Centre (NE/01531X/1). The authors also wish to record their deep gratitude to four members of the scientific community who formed a consultative advisory panel during the lifetime of the RESET project: Professor Barbara Wohlfarth (Stockholm University), Professor Jørgen Peder Steffensen (Niels Bohr Institute, Copenhagen), Dr. Martin Street (Romisch-Germanisches Zentralmuseum, Neuwied) and Professor Clive Oppenheimer (Cambridge University). They provided excellent advice at key stages of the work, which we greatly valued. We also thank Jenny Kynaston (Geography Department, Royal Holloway) for construction of several of the figures in this paper, and Debbie Barrett (Elsevier) and Colin Murray Wallace (Editor-in-Chief, QSR) for their considerable assistance in the production of this special volume.Peer Reviewe