Differential Calculi on Some Quantum Prehomogeneous Vector Spaces

This paper is devoted to study of differential calculi over quadratic algebras, which arise in the theory of quantum bounded symmetric domains. We prove that in the quantum case dimensions of the homogeneous components of the graded vector spaces of k-forms are the same as in the classical case. This result is well-known for quantum matrices. The quadratic algebras, which we consider in the present paper, are q-analogues of the polynomial algebras on prehomogeneous vector spaces of commutative parabolic type. This enables us to prove that the de Rham complex is isomorphic to the dual of a quantum analogue of the generalized Bernstein-Gelfand-Gelfand resolution.Comment: LaTeX2e, 51 pages; changed conten

Rendezvous of Distance-aware Mobile Agents in Unknown Graphs

We study the problem of rendezvous of two mobile agents starting at distinct locations in an unknown graph. The agents have distinct labels and walk in synchronous steps. However the graph is unlabelled and the agents have no means of marking the nodes of the graph and cannot communicate with or see each other until they meet at a node. When the graph is very large we want the time to rendezvous to be independent of the graph size and to depend only on the initial distance between the agents and some local parameters such as the degree of the vertices, and the size of the agent's label. It is well known that even for simple graphs of degree $\Delta$, the rendezvous time can be exponential in $\Delta$ in the worst case. In this paper, we introduce a new version of the rendezvous problem where the agents are equipped with a device that measures its distance to the other agent after every step. We show that these \emph{distance-aware} agents are able to rendezvous in any unknown graph, in time polynomial in all the local parameters such the degree of the nodes, the initial distance $D$ and the size of the smaller of the two agent labels $l = \min(l_1, l_2)$. Our algorithm has a time complexity of $O(\Delta(D+\log{l}))$ and we show an almost matching lower bound of $\Omega(\Delta(D+\log{l}/\log{\Delta}))$ on the time complexity of any rendezvous algorithm in our scenario. Further, this lower bound extends existing lower bounds for the general rendezvous problem without distance awareness

Almost optimal asynchronous rendezvous in infinite multidimensional grids

Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ> 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δ-dimensional Euclidean space and that each agent knows the Cartesian coordinates of its own initial position (but not the one of the other agent). We design an algorithm permitting the agents to meet after traversing a trajectory of length O(d δ polylog d). This bound for the case of 2d-grids subsumes the main result of [12]. The algorithm is almost optimal, since the Ω(d δ) lower bound is straightforward. Further, we apply our rendezvous method to the following network design problem. The ports of the δ-dimensional grid have to be set such that two anonymous agents starting at distance at most d from each other will always meet, moving in an asynchronous manner, after traversing a O(d δ polylog d) length trajectory. We can also apply our method to a version of the geometric rendezvous problem. Two anonymous agents move asynchronously in the δ-dimensional Euclidean space. The agents have the radii of visibility of r1 and r2, respectively. Each agent knows only its own initial position and its own radius of visibility. The agents meet when one agent is visible to the other one. We propose an algorithm designing the trajectory of each agent, so that they always meet after traveling a total distance of O( ( d)), where r = min(r1, r2) and for r ≥ 1. r)δpolylog ( d r

From 2D conformal to 4D self-dual theories: quaternionic analyticity

It is shown that self-dual theories generalize to four dimensions both the conformal and analytic aspects of two-dimensional conformal field theories. In the harmonic space language there appear several ways to extend complex analyticity (natural in two dimensions) to quaternionic analyticity (natural in four dimensions). To be analytic, conformal transformations should be realized on $CP^3$, which appears as the coset of the complexified conformal group modulo its maximal parabolic subgroup. In this language one visualizes the twistor correspondence of Penrose and Ward and consistently formulates the analyticity of Fueter.Comment: 24 pages, LaTe

Gathering in Dynamic Rings

The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares the same fundamental assumption: the topological structure does not change during the rendezvous or the gathering; this is true also for those investigations that consider faulty nodes. In other words, they only consider static graphs. In this paper we start the investigation of gathering in dynamic graphs, that is networks where the topology changes continuously and at unpredictable locations. We study the feasibility of gathering mobile agents, identical and without explicit communication capabilities, in a dynamic ring of anonymous nodes; the class of dynamics we consider is the classic 1-interval-connectivity. We focus on the impact that factors such as chirality (i.e., a common sense of orientation) and cross detection (i.e., the ability to detect, when traversing an edge, whether some agent is traversing it in the other direction), have on the solvability of the problem. We provide a complete characterization of the classes of initial configurations from which the gathering problem is solvable in presence and in absence of cross detection and of chirality. The feasibility results of the characterization are all constructive: we provide distributed algorithms that allow the agents to gather. In particular, the protocols for gathering with cross detection are time optimal. We also show that cross detection is a powerful computational element. We prove that, without chirality, knowledge of the ring size is strictly more powerful than knowledge of the number of agents; on the other hand, with chirality, knowledge of n can be substituted by knowledge of k, yielding the same classes of feasible initial configurations

Large scale three-dimensional modelling for wave and tidal energy resource and environmental impact : methodologies for quantifying acceptable thresholds for sustainable exploitation

We describe a modelling project to estimate the potential effects of wave & tidal stream renewables on the marine environment. • Realistic generic devices to be used by those without access to the technical details available to developers are described. • Results show largely local sea bed effects at the level of the currently proposed renewables developments in our study area. • Large scale 3D modelling is critical to quantify the direct, indirect and cumulative effects of renewable energy extraction. • This is critical to comply with planning & environmental impact assessment regulations and achieve Good Environmental Status

Twistors and Black Holes

Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex coordinates adapted to the Heisenberg symmetries. The results bear a simple relation to the Hesse potential \Sigma of the special Kahler manifold M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We explicitly construct the ``covariant c-map'' and the ``twistor map'', which relate real coordinates on M x CP^1 (resp. M x R^4/Z_2) to complex coordinates on Z (resp. S). As applications, we solve for the general BPS geodesic motion on M, and provide explicit integral formulae for the quaternionic Penrose transform relating elements of H^1(Z,O(-k)) to massless fields on M annihilated by first or second order differential operators. Finally, we compute the exact radial wave function (in the supergravity approximation) for BPS black holes with fixed electric and magnetic charges.Comment: 47 pages, v2: typos corrected, reference added, v3: minor change

Mobile agent rendezvous: A survey

Abstract. Recent results on the problem of mobile agent rendezvous on distributed networks are surveyed with an emphasis on outlining the various approaches taken by researchers in the theoretical computer science community.

EPidemiology Of Cardiogenic sHock in Scotland (EPOCHS):a multicentre, prospective observational study of the prevalence, management and outcomes of cardiogenic shock in Scotland

BackgroundDespite high rates of cardiovascular disease in Scotland, the prevalence and outcomes of patients with cardiogenic shock are unknown.MethodsWe undertook a prospective observational cohort study of consecutive patients with cardiogenic shock admitted to the intensive care unit (ICU) or coronary care unit at 13 hospitals in Scotland for a six-month period. Denominator data from the Scottish Intensive Care Society Audit Group were used to estimate ICU prevalence; data for coronary care units were unavailable. We undertook multivariable logistic regression to identify factors associated with in-hospital mortality.ResultsIn total, 247 patients with cardiogenic shock were included. After exclusion of coronary care unit admissions, this comprised 3.0% of all ICU admissions during the study period (95% confidence interval [CI] 2.6 to 3.5%). Aetiology was acute myocardial infarction (AMI) in 48%. The commonest vasoactive treatment was noradrenaline (56%) followed by adrenaline (46%) and dobutamine (40%). Mechanical circulatory support was used in 30%. Overall in-hospital mortality was 55%. After multivariable logistic regression, age (odds ratio [OR] 1.04, 95% CI 1.02 to 1.06), admission lactate (OR 1.10, 95% CI 1.05 to 1.19), Society for Cardiovascular Angiographic Intervention stage D or E at presentation (OR 2.16, 95% CI 1.10 to 4.29), and use of adrenaline (OR 2.73, 95% CI 1.40 to 5.40) were associated with mortality.ConclusionsIn Scotland the prevalence of cardiogenic shock was 3% of all ICU admissions; more than half died prior to discharge. There was significant variation in treatment approaches, particularly with respect to vasoactive support strategy. <br/

The Vital Role of Social Workers in Community Partnerships: The Alliance for Gay, Lesbian, Bisexual, Transgender and Questioning Youth

The account of The Alliance for Gay, Lesbian, Bisexual, Transgender, and Questioning (GLBTQ) Youth formation offers a model for developing com- munity-based partnerships. Based in a major urban area, this university-community collaboration was spearheaded by social workers who were responsible for its original conceptualization, for generating community support, and for eventual staffing, administration, direct service provision, and program evaluation design. This article presents the strategic development and evolution of this community- based service partnership, highlighting the roles of schools of social work, academics, and social work students in concert with community funders, practitioners and youth, in responding to the needs of a vulnerable population