Some closure operations in Zariski-Riemann spaces of valuation domains: a survey

In this survey we present several results concerning various topologies that were introduced in recent years on spaces of valuation domains

Protein multi-scale organization through graph partitioning and robustness analysis: Application to the myosin-myosin light chain interaction

Despite the recognized importance of the multi-scale spatio-temporal organization of proteins, most computational tools can only access a limited spectrum of time and spatial scales, thereby ignoring the effects on protein behavior of the intricate coupling between the different scales. Starting from a physico-chemical atomistic network of interactions that encodes the structure of the protein, we introduce a methodology based on multi-scale graph partitioning that can uncover partitions and levels of organization of proteins that span the whole range of scales, revealing biological features occurring at different levels of organization and tracking their effect across scales. Additionally, we introduce a measure of robustness to quantify the relevance of the partitions through the generation of biochemically-motivated surrogate random graph models. We apply the method to four distinct conformations of myosin tail interacting protein, a protein from the molecular motor of the malaria parasite, and study properties that have been experimentally addressed such as the closing mechanism, the presence of conserved clusters, and the identification through computational mutational analysis of key residues for binding.Comment: 13 pages, 7 Postscript figure

Conformal blocks and generalized theta functions

Let M(r) be the moduli space of rank r vector bundles with trivial determinant on a Riemann surface X . This space carries a natural line bundle, the determinant line bundle L . We describe a canonical isomorphism of the space of global sections of L^k with a space known in conformal field theory as the ``space of conformal blocks", which is defined in terms of representations of the Lie algebra sl(r, C((z))).Comment: 43 pages, Plain Te

Please mind the gap: students’ perspectives of the transition in academic skills between A-level and degree level geography

This paper explores first-year undergraduates’ perceptions of the transition from studying geography at pre-university level to studying for a degree. This move is the largest step students make in their education, and the debate about it in the UK has been reignited due to the government’s planned changes to A-level geography. However, missing from most of this debate is an appreciation of the way in which geography students themselves perceive their transition to university. This paper begins to rectify this absence. Using student insights, we show that their main concern is acquiring the higher level skills required for university learning

Time-of-arrival in quantum mechanics

We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the ``time-of-arrival'' operator. We discuss the general properties of this operator. We construct the operator explicitly in the simple case of a free nonrelativistic particle, and compare the probabilities it yields with the ones estimated indirectly in terms of the flux of the Schr\"odinger current. We derive a well defined uncertainty relation between time-of-arrival and energy; this result shows that the well known arguments against the existence of such a relation can be circumvented. Finally, we define a ``time-representation'' of the quantum mechanics of a free particle, in which the time-of-arrival is diagonal. Our results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics.Comment: Latex/Revtex, 20 pages. 2 figs included using epsf. Submitted to Phys. Rev.

Upregulation of the voltage-gated sodium channel beta2 subunit in neuropathic pain models: characterization of expression in injured and non-injured primary sensory neurons

The development of abnormal primary sensory neuron excitability and neuropathic pain symptoms after peripheral nerve injury is associated with altered expression of voltage-gated sodium channels (VGSCs) and a modification of sodium currents. To investigate whether the beta2 subunit of VGSCs participates in the generation of neuropathic pain, we used the spared nerve injury (SNI) model in rats to examine beta2 subunit expression in selectively injured (tibial and common peroneal nerves) and uninjured (sural nerve) afferents. Three days after SNI, immunohistochemistry and Western blot analysis reveal an increase in the beta2 subunit in both the cell body and peripheral axons of injured neurons. The increase persists for >4 weeks, although beta2 subunit mRNA measured by real-time reverse transcription-PCR and in situ hybridization remains unchanged. Although injured neurons show the most marked upregulation,beta2 subunit expression is also increased in neighboring non-injured neurons and a similar pattern of changes appears in the spinal nerve ligation model of neuropathic pain. That increased beta2 subunit expression in sensory neurons after nerve injury is functionally significant, as demonstrated by our finding that the development of mechanical allodynia-like behavior in the SNI model is attenuated in beta2 subunit null mutant mice. Through its role in regulating the density of mature VGSC complexes in the plasma membrane and modulating channel gating, the beta2 subunit may play a key role in the development of ectopic activity in injured and non-injured sensory afferents and, thereby, neuropathic pain

Wearable Haptic Devices for Gait Re-education by Rhythmic Haptic Cueing

This research explores the development and evaluation of wearable haptic devices for gait sensing and rhythmic haptic cueing in the context of gait re-education for people with neurological and neurodegenerative conditions. Many people with long-term neurological and neurodegenerative conditions such as Stroke, Brain Injury, Multiple Sclerosis or Parkinson’s disease suffer from impaired walking gait pattern. Gait improvement can lead to better fluidity in walking, improved health outcomes, greater independence, and enhanced quality of life. Existing lab-based studies with wearable devices have shown that rhythmic haptic cueing can cause immediate improvements to gait features such as temporal symmetry, stride length, and walking speed. However, current wearable systems are unsuitable for self-managed use for in-the-wild applications with people having such conditions. This work aims to investigate the research question of how wearable haptic devices can help in long-term gait re-education using rhythmic haptic cueing. A longitudinal pilot study has been conducted with a brain trauma survivor, providing rhythmic haptic cueing using a wearable haptic device as a therapeutic intervention for a two-week period. Preliminary results comparing pre and post-intervention gait measurements have shown improvements in walking speed, temporal asymmetry, and stride length. The pilot study has raised an array of issues that require further study. This work aims to develop and evaluate prototype systems through an iterative design process to make possible the self-managed use of such devices in-the-wild. These systems will directly provide therapeutic intervention for gait re-education, offer enhanced information for therapists, remotely monitor dosage adherence and inform treatment and prognoses over the long-term. This research will evaluate the use of technology from the perspective of multiple stakeholders, including clinicians, carers and patients. This work has the potential to impact clinical practice nationwide and worldwide in neuro-physiotherapy

The Tate conjecture for K3 surfaces over finite fields

Artin's conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin's conjecture over fields of characteristic p>3. This implies Tate's conjecture for K3 surfaces over finite fields of characteristic p>3. Our results also yield the Tate conjecture for divisors on certain holomorphic symplectic varieties over finite fields, with some restrictions on the characteristic. As a consequence, we prove the Tate conjecture for cycles of codimension 2 on cubic fourfolds over finite fields of characteristic p>3.Comment: 20 pages, minor changes. Theorem 4 is stated in greater generality, but proofs don't change. Comments still welcom