A GIT interpretration of the Harder-Narasimhan filtration

An unstable torsion free sheaf on a smooth projective variety gives a GIT unstable point in certain Quot scheme. To a GIT unstable point, Kempf associates a "maximally destabilizing" 1-parameter subgroup, and this induces a filtration of the torsion free sheaf. We show that this filtration coincides with the Harder-Narasimhan filtration.Comment: 19 pages; Comments of the referees and references added. The construction for holomorphic pairs (Sections 6 and 7 from previous version) will appear in a further publication. To appear in Rev. Mat Complutens

Transmission pricing of distributed multilateral energy transactions to ensure system security and guide economic dispatch

In this paper we provide a simulations-based demonstration of a hybrid electricity market that combines the distributed competitive advantages of decentralized markets with the system security guarantees of centralized markets. In this market, the transmission service provider (TSP) guides an electricity market towards the optimal power flow (OPF) solution, even when maximizing its own revenue. End users negotiate with each other to determine an energy price and then submit separate bids for transmission to the TSP. The TSP returns with prices for transmission, allowing end users to respond. In simulations, this hybrid-decentralized market approaches the near-optimal results of fully coordinated and constrained markets. Additionally, this market exhibits properties that remove incentives for the TSP to withhold capacity. This hybrid market leads a market towards the optimum while allowing the TSP and the end users to act out of self-interest. Index Terms₇Electricity markets, transmission, optimum power flow.Supported by the MIT Center for Energy and Environmental Policy Research

Frobenius Splittings

We give a gentle introduction to Frobenius splittings. Then we recall a few results that have been obtained with the method.Comment: 21 pages, typos correcte

Influence of Different Irrigants on the Accuracy of Two Electronic Apex Locators: An In Vivo study

INTRODUCTION: Working length (WL) is defined as the distance from a coronal reference point to the point at which the canal preparation and obturation should terminate (American association of Endodontists 2003). As per the definition the endodontic therapy is mainly concerned with the WL within which all the procedures must terminate without any violation for a successful outcome. According to American Association of endodontists (1984), The radiographic apex is defined as the anatomical end of the root as seen on the radiograph, while the apical foramen is the region where the canal leaves the root surface next to the periodontal ligament. The success of the RCT is mainly dependent on proper cleaning and shaping of the canal space. To effectively clean and shape the root canal space the apical target i.e. apical constriction should be determined accuratel. Traditional methods for establishing working length have been (a) the use of anatomical averages and knowledge of anatomy, (b) tactile sensation, (c) moisture on a paper point and (d) radiography. AIM OF THE STUDY: The aim of the study was to evaluate the accuracy of two electronic apex locators in wet and dry conditions. Dry canal was considered as control and the presence of irrigation solution was considered as experimental groups. The apex locator used were: 1. Root ZX Mini, 2. Propex II. The irrigation solution used were: 1. Dry canal (control), 2. Normal saline 0.9%, 3. Sodium hypochlorite 5.25%, 4. QMix. MATERIALS AND METHODS: 33 patients with 60 maxillary anterior teeth (60 canals) scheduled for endodontic treatment participated in this In vivo study. Previous approval was obtained from the Institutional Review Board/ Ethical committee (2018-STU-BrIV-SVR-07) for this study. Informed consent was obtained from the patient. Inclusion criteria were teeth that are planned for non-surgical endodontic treatment and Exclusion criteria were Teeth with cracks, undefinable coronal reference points, periapical lesions, immature apices, root canal obliteration, perforation, internal resorption, curved canals and periodontally compromised teeth. A standardized preoperative diagnostic periapical radiograph was taken for each tooth. Under Local anesthesia and rubber dam isolation initial access cavity preparation was done using ½ round diamond bur and highspeed dental handpiece. Pulp extirpation done and initial apical file was selected according to the snug fit that is evident at the apex. EWL measurements were recorded accordingly with the two apex locators - Root ZX Mini and Propex II, in dry canal (control) and in the presence of three irrigant solutions – Normal saline 0.9%; Sodium Hypochlorite 5.25% and QMix. In between change of irrigation solution, the canal is flushed with saline and dried with paper points to eliminate any reaction between the solutions. The measurement taken in dry canal was co-related with those measurement taken with the three different irrigants. The data collected were compiled using MS-Office Excel and was subjected to Statistical analysis using IBM corp. SPSS (Statistical package for social sciences) Statistics for windows, version 20.0 (Armonk, NY) Statistical significance was set at P < 0.05. Descriptive and inferential statistics were used to analyse the data. Normality of the data was assessed. Independent t-test was done to assess the statistical difference between Group A and Group B.ANOVA with bonferroni posthoc was done for within group comparison. RESULTS: Descriptive analysis of mean values shows that the correlation between the dry canal and other groups, Root ZX Mini was found be in accordance with the dry canal measurements rather than Propex II group mean values. CONCLUSION: Within the limitations of the study the specificity of the apex locators found to be the same but on major comparison with the mean data accuracy of Root ZX mini has been proved again

Capturing the sporting heroes of our past by extracting 3D movements from legacy video content

Sports are a key part of cultural identity, and it is necessary to preserve them as important intangible Cultural Heritage, especially the human motion techniques specific to individual sports. In this paper we present a method for extracting 3D athlete motion from video broadcast sources, providing an important tool for preserving the heritage represented by these movements. Broadcast videos include camera motion, multiple player interaction, occlusions and noise, presenting significant challenges to solve the reconstruction. The approach requires initial definition of some key-frames and setting of 2D key-points in those frames manually. Thereafter an automatic process estimates the poses and positions of the players in the key-frames, and in the frames between key-frames, taking into account collisions with the environment and human kinematic constraints. Initial results are extremely promising and this data could be used to analyze the sport's evolution over time, or even to generate animations for interactive applications

Two-dimensional enrichment analysis for mining high-level imaging genetic associations

Enrichment analysis has been widely applied in the genome-wide association studies (GWAS), where gene sets corresponding to biological pathways are examined for significant associations with a phenotype to help increase statistical power and improve biological interpretation. In this work, we expand the scope of enrichment analysis into brain imaging genetics, an emerging field that studies how genetic variation influences brain structure and function measured by neuroimaging quantitative traits (QT). Given the high dimensionality of both imaging and genetic data, we propose to study Imaging Genetic Enrichment Analysis (IGEA), a new enrichment analysis paradigm that jointly considers meaningful gene sets (GS) and brain circuits (BC) and examines whether any given GS-BC pair is enriched in a list of gene-QT findings. Using gene expression data from Allen Human Brain Atlas and imaging genetics data from Alzheimer's Disease Neuroimaging Initiative as test beds, we present an IGEA framework and conduct a proof-of-concept study. This empirical study identifies 12 significant high level two dimensional imaging genetics modules. Many of these modules are relevant to a variety of neurobiological pathways or neurodegenerative diseases, showing the promise of the proposal framework for providing insight into the mechanism of complex diseases

Multilayer electronic component systems and methods of manufacture

Multilayer electronic component systems and methods of manufacture are provided. In this regard, an exemplary system comprises a first layer of liquid crystal polymer (LCP), first electronic components supported by the first layer, and a second layer of LCP. The first layer is attached to the second layer by thermal bonds. Additionally, at least a portion of the first electronic components are located between the first layer and the second layer