Degeneracy loci, virtual cycles and nested Hilbert schemes II

We express nested Hilbert schemes of points and curves on a smooth projective surface as "virtual resolutions" of degeneracy loci of maps of vector bundles on smooth ambient spaces. We show how to modify the resulting obstruction theories to produce the virtual cycles of Vafa-Witten theory and other sheaf-counting problems. The result is an effective way of calculating invariants (VW, SW, local PT and local DT) via Thom-Porteous-like Chern class formulae.Comment: 42 pages. Two referees' corrections. To appear in Compositi

Degeneracy loci, virtual cycles and nested Hilbert schemes I

Given a map of vector bundles on a smooth variety, consider the deepest degeneracy locus where its rank is smallest. We show it carries a natural perfect obstruction theory whose virtual cycle can be calculated by the Thom-Porteous formula. We show nested Hilbert schemes of points on surfaces can be expressed as degeneracy loci. We show how to modify the resulting obstruction theories to recover the virtual cycles of Vafa-Witten and reduced local DT theories. The result computes some Vafa-Witten invariants in terms of Carlsson-Okounkov operators. This proves and extends a conjecture of Gholampour-Sheshmani-Yau and generalises a vanishing result of Carlsson-Okounkov.Comment: Published version. 29 page

Current iodine status and progress over the last decade towards elimination of iodine deficiency in Rajkot District, Gujarat

Objective: To find out prevalence of goitre in primary school children; to compare prevalence with previous survey; to determine median urinary iodine concentration; to assess level of iodine in salt samples at household and retail shop level; and to study profile of salt sold at retail shops. Design & Settings: 30 cluster survey study in primary schools of Rajkot district. Subjects: Children studying in 1st to 7th standard. Methods: Total 70 students including five boys and five girls from 1st to 7th standard present in class on the day of visit were selected randomly for Goitre examination, so, total 2100 students were examined in schools. Urine sample was collected from one boy & one girl from each standard in each cluster. From community, 28 students including two boys and two girls from each standard in same age group were examined and also salt samples were tested from their households. From each village, one retail shop was visited and salts were purchased and tested for iodine on the spot with spot kit. Results: Goitre prevalence was found 8.8% among primary school children compare to 5.6% in 1999. As the age increases the Goitre prevalence also increases except in age group of 12 years. Median urinary iodine excretion level was found 110 µg/L. Iodine level >15 ppm was found in 81% salts samples tested at household level. Conclusion: Present study showed mild Goitre prevalence in primary school children in Rajkot district of Gujarat but still iodine content of salt found inadequate at household level

Active transport in a channel: stabilisation by flow or thermodynamics

Recent experiments on active materials, such as dense bacterial suspensions and microtubule-kinesin motor mixtures, show a promising potential for achieving self-sustained flows. However, to develop active microfluidics it is necessary to understand the behaviour of active systems confined to channels. Therefore here we use continuum simulations to investigate the behaviour of active fluids in a two-dimensional channel. Motivated by the fact that most experimental systems show no ordering in the absence of activity, we concentrate on temperatures where there is no nematic order in the passive system, so that any nematic order is induced by the active flow. We systematically analyze the results, identify several different stable flow states, provide a phase diagram and show that the key parameters controlling the flow are the ratio of channel width to the length scale of active flow vortices, and whether the system is flow aligning or flow tumbling

A Learning-based Stochastic MPC Design for Cooperative Adaptive Cruise Control to Handle Interfering Vehicles

Vehicle to Vehicle (V2V) communication has a great potential to improve reaction accuracy of different driver assistance systems in critical driving situations. Cooperative Adaptive Cruise Control (CACC), which is an automated application, provides drivers with extra benefits such as traffic throughput maximization and collision avoidance. CACC systems must be designed in a way that are sufficiently robust against all special maneuvers such as cutting-into the CACC platoons by interfering vehicles or hard braking by leading cars. To address this problem, a Neural- Network (NN)-based cut-in detection and trajectory prediction scheme is proposed in the first part of this paper. Next, a probabilistic framework is developed in which the cut-in probability is calculated based on the output of the mentioned cut-in prediction block. Finally, a specific Stochastic Model Predictive Controller (SMPC) is designed which incorporates this cut-in probability to enhance its reaction against the detected dangerous cut-in maneuver. The overall system is implemented and its performance is evaluated using realistic driving scenarios from Safety Pilot Model Deployment (SPMD).Comment: 10 pages, Submitted as a journal paper at T-I