A new strategy to improve proactive route updates in mobile ad hoc networks

This paper presents two new route update strategies for performing proactive route discovery in mobile ad hoc networks (MANETs). The first strategy is referred to as minimum displacement update routing (MDUR). In this strategy, the rate at which route updates are sent into the network is controlled by how often a node changes its location by a required distance. The second strategy is called minimum topology change update (MTCU). In this strategy, the route updating rate is proportional to the level of topology change each node experiences. We implemented MDUR and MTCU on top of the fisheye state routing (FSR) protocol and investigated their performance by simulation. The simulations were performed in a number of different scenarios, with varied network mobility, density, traffic, and boundary. Our results indicate that both MDUR and MTCU produce significantly lower levels of control overhead than FSR and achieve higher levels of throughput as the density and the level of traffic in the network are increased

Flow Matching on General Geometries

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes its target vector field in closed-form. The key ingredient behind RFM is the construction of a relatively simple premetric for defining target vector fields, which encompasses the existing Euclidean case. To extend to general geometries, we rely on the use of spectral decompositions to efficiently compute premetrics on the fly. Our method achieves state-of-the-art performance on many real-world non-Euclidean datasets, and we demonstrate tractable training on general geometries, including triangular meshes with highly non-trivial curvature and boundaries

Long-Term Consequences of Congestion Pricing: A Small Cordon in the Hand Is Worth Two in the Bush

We evaluate and compare the long-term economic effects of three cordon-based road pricing schemes applied to the Washington, DC, metropolitan area. To conduct this analysis, we employ a spatially disaggregated general equilibrium model of a regional economy that incorporates the decisions of residents, firms, and developers, integrated with a spatially disaggregated strategic transportation planning model that features mode, time period, and route choice. We find that all cordon pricing schemes increase welfare of the residents, as well as lead to GDP growth. At the optimum, the larger cordon and a double cordon lead to higher benefits than the small cordon encompassing downtown core. Nevertheless, the small cordon seems to be a safer bet because when the toll charge is set suboptimally, the net benefits from the small cordon compared to the optimum change negligibly, while the net benefits from the larger cordon decline sharply as the charge deviates from the optimal level.traffic congestion, cordon tolls, land use, welfare analysis, road pricing, general equilibrium, simulation, Washington DC

HIV-associated multi-centric Castleman’s disease with multiple organ failure: cuccessful treatment with rituximab

Introduction: Multicentric Castleman's Disease (MCD), a lymphoproliferative disorder associated with Human Herpes Virus-8 (HHV-8) infection, is increasing in incidence amongst HIV patients. This condition is associated with lymphadenopathy, polyclonal gammopathy, hepato-splenomegaly and systemic symptoms. A number of small studies have demonstrated the efficacy of the anti-CD20 monoclonal antibody, rituximab, in treating this condition. Case presentation: We report the case of a 46 year old Zambian woman who presented with pyrexia, diarrhoea and vomiting, confusion, lymphadenopathy, and renal failure. She rapidly developed multiple organ failure following the initiation of treatment of MCD with rituximab. Following admission to intensive care (ICU), she received prompt multi-organ support. After 21 days on the ICU she returned to the haematology medical ward, and was discharged in remission from her disease after 149 days in hospital. Conclusion: Rituximab, the efficacy of which has thus far been examined predominantly in patients outside the ICU, in conjunction with extensive organ support was effective treatment for MCD with associated multiple organ failure. There is, to our knowledge, only one other published report of its successful use in an ICU setting, where it was combined with cyclophosphamide, adriamycin and prednisolone. Reports such as ours support the notion that critically unwell patients with HIV and haematological disease can benefit from intensive care

Algorithms to automatically quantify the geometric similarity of anatomical surfaces

We describe new approaches for distances between pairs of 2-dimensional surfaces (embedded in 3-dimensional space) that use local structures and global information contained in inter-structure geometric relationships. We present algorithms to automatically determine these distances as well as geometric correspondences. This is motivated by the aspiration of students of natural science to understand the continuity of form that unites the diversity of life. At present, scientists using physical traits to study evolutionary relationships among living and extinct animals analyze data extracted from carefully defined anatomical correspondence points (landmarks). Identifying and recording these landmarks is time consuming and can be done accurately only by trained morphologists. This renders these studies inaccessible to non-morphologists, and causes phenomics to lag behind genomics in elucidating evolutionary patterns. Unlike other algorithms presented for morphological correspondences our approach does not require any preliminary marking of special features or landmarks by the user. It also differs from other seminal work in computational geometry in that our algorithms are polynomial in nature and thus faster, making pairwise comparisons feasible for significantly larger numbers of digitized surfaces. We illustrate our approach using three datasets representing teeth and different bones of primates and humans, and show that it leads to highly accurate results.Comment: Changes with respect to v1, v2: an Erratum was added, correcting the references for one of the three datasets. Note that the datasets and code for this paper can be obtained from the Data Conservancy (see Download column on v1, v2

Headache in an HIV positive patient: diagnostic challenges and approach to treatment

Headaches are a common complaint in HIV positive patients attending emergency services. A thorough understanding of the differential diagnoses, initial investigations and empirical management of this presentation is essential for the assessing physician. We discuss a case of a patient with known advanced HIV infection presenting with headache to the emergency department. Given the range of possible diagnoses, broad-spectrum antimicrobial therapy was initially commenced. This was stopped when magnetic resonance imaging confirmed a diagnosis of venous sinus thrombosis. Anticoagulation therapy was started in accordance with current clinical guidelines after discussing the rationale and options for treatment with the patient. Here, we review the guidelines and supporting evidence for management of venous sinus thrombosis, and consider the challenges and strategies for engaging a patient with previous poor attendance in their ongoing care

Neural Conservation Laws: A Divergence-Free Perspective

We investigate the parameterization of deep neural networks that by design satisfy the continuity equation, a fundamental conservation law. This is enabled by the observation that any solution of the continuity equation can be represented as a divergence-free vector field. We hence propose building divergence-free neural networks through the concept of differential forms, and with the aid of automatic differentiation, realize two practical constructions. As a result, we can parameterize pairs of densities and vector fields that always exactly satisfy the continuity equation, foregoing the need for extra penalty methods or expensive numerical simulation. Furthermore, we prove these models are universal and so can be used to represent any divergence-free vector field. Finally, we experimentally validate our approaches by computing neural network-based solutions to fluid equations, solving for the Hodge decomposition, and learning dynamical optimal transport maps

Local syzygies of multiplier ideals

In recent years, multiplier ideals have found many applications in local and global algebraic geometry. Because of their importance, there has been some interest in the question of which ideals on a smooth complex variety can be realized as multiplier ideals. Other than integral closure no local obstructions have been known up to now, and in dimension two it was established by Favre-Jonsson and Lipman-Watanabe that any integrally closed ideal is locally a multiplier ideal. We prove the somewhat unexpected result that multiplier ideals in fact satisfy some rather strong algebraic properties involving higher syzygies. It follows that in dimensions three and higher, multiplier ideals are very special among all integrally closed ideals.Comment: 8 page

Equivariant Polynomials for Graph Neural Networks

Graph Neural Networks (GNN) are inherently limited in their expressive power. Recent seminal works (Xu et al., 2019; Morris et al., 2019b) introduced the Weisfeiler-Lehman (WL) hierarchy as a measure of expressive power. Although this hierarchy has propelled significant advances in GNN analysis and architecture developments, it suffers from several significant limitations. These include a complex definition that lacks direct guidance for model improvement and a WL hierarchy that is too coarse to study current GNNs. This paper introduces an alternative expressive power hierarchy based on the ability of GNNs to calculate equivariant polynomials of a certain degree. As a first step, we provide a full characterization of all equivariant graph polynomials by introducing a concrete basis, significantly generalizing previous results. Each basis element corresponds to a specific multi-graph, and its computation over some graph data input corresponds to a tensor contraction problem. Second, we propose algorithmic tools for evaluating the expressiveness of GNNs using tensor contraction sequences, and calculate the expressive power of popular GNNs. Finally, we enhance the expressivity of common GNN architectures by adding polynomial features or additional operations / aggregations inspired by our theory. These enhanced GNNs demonstrate state-of-the-art results in experiments across multiple graph learning benchmarks