Central limit theorem for exponentially quasi-local statistics of spin models on Cayley graphs

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs and taking values in a countable space but under the stronger assumptions of {\alpha}-mixing (for local statistics) and exponential {\alpha}-mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.Comment: Minor changes incorporated based on suggestions by referee

The Effectiveness of Internet Advertising on Consumer Behaviour

Advertising is a communication medium where companies made to know the consumers about the product or it is a medium where companies tries to increase the sales and branding the product and many other definitions proposed by various researches, as days past on advertising medium was classified into 2 modes 1. Online advertising and 2. Offline advertising. In this paper, internet advertising mode was explained. The objective populace becomes the publicizing companies and their customers. The research applied a defined testing strategy to pick 60 exam respondents every day.  Content research turned into utilized to dissect subjective facts simultaneously as the quantitative facts changed into broke down utilizing clean measurements utilizing SPSS. Relapse and Correlation examination changed into applied to reveal the connections among the elements. The statistics were brought via rates, implies, fashionable deviations and frequencies. The research found that web promoting turned into a hit on attain and making of mindfulness because of diverse use, and set up that its dependability as a publicizing media was low contrasted with TV. Web publicizing has huge courting with the consumers' purchase desire and along those lines is a critical determinant in impacting purchaser behaviour

Study on Torsional Behaviour of Retrofitted Rectangular RC Beams with Web Openings

In modern building construction web openings become necessary to provide utility ducts like water supply lines, air conditioning ducts etc. These ducts cause potential weakness in any construction hence affecting strength, serviceability and stability of the structure. There will be more adverse impact on structures if web opening has to pass through the beams or columns. Sometime in unavoidable situations openings are essential to pass through existing load bearing elements of structure hence required to strengthen externally to restore the strength. External jacketing by glass, carbon, basalt fibre fabrics provides a popular, simple and effective method for restoring the strength capacity of such elements. Many research works have been published on behaviour of retrofitted RCC beams with opening of different size and shapes especially under shear and flexure. Very few works are published to study the effect of beams with opening in torsion. The aim of the present work is to experimentally investigate the behaviour of rectangular RCC beams with rectangular small and large openings. The beams are retrofitted with GFRP fabrics of different orientations and width. GFRP strips of widths 10cm and 20cm fiber orientations (90/90/90/90/90) and (45/90/45/90/45) are used for retrofitting. The behaviour of beams were studied in terms of collapse load, torsional moment vs angle of twist, failure patterns

Entropy-difference based stereo error detection

Stereo depth estimation is error-prone; hence, effective error detection methods are desirable. Most such existing methods depend on characteristics of the stereo matching cost curve, making them unduly dependent on functional details of the matching algorithm. As a remedy, we propose a novel error detection approach based solely on the input image and its depth map. Our assumption is that, entropy of any point on an image will be significantly higher than the entropy of its corresponding point on the image's depth map. In this paper, we propose a confidence measure, Entropy-Difference (ED) for stereo depth estimates and a binary classification method to identify incorrect depths. Experiments on the Middlebury dataset show the effectiveness of our method. Our proposed stereo confidence measure outperforms 17 existing measures in all aspects except occlusion detection. Established metrics such as precision, accuracy, recall, and area-under-curve are used to demonstrate the effectiveness of our method

Development of oligomer-specific antibodies against tau protein and testing of therapeutic potential in a cell model of tau pathology

Tau, a microtubule associated protein, forms abnormal aggregates in many neurodegenerative diseases such as Alzheimer disease (AD). There is an urgent need for disease-modifying therapies of AD and related tauopathies. Inhibiting the aggregation of tau and the accumulation of neurofibrillary tangles (NFTs) could be helpful in combating tau pathology. Recent studies show that tau induced toxicity is mainly due to the presence of oligomers of tau rather than the monomers and fibrillar aggregates (Kaniyappan et al., 2017, Flach et al., 2012, Lasagna-Reeves et al., 2010). To combat the toxicity of tau oligomers we developed antibodies against the purified low-n tau oligomers (dimers to hexamers) of TauRDΔK, the strongly aggregating repeat domain of tau. Monoclonal antibodies were tested by various biochemical and biophysical methods for their specificity to bind to the toxic oligomers. Some antibodies show specificity to aggregates of tau while others detect all forms of tau. Antibodies 2B10 and 6H1, described as representative examples, bind to tau oligomers with high specificity as judged by dotblot, dynamic light scattering (DLS) and immunofluorescence analysis. As these antibodies are dependent on tau conformations, they appear non-specific in denaturing methods like western blotting. 2B10 and 6H1 antibodies are able to inhibit the tau aggregation up to ~90% in vitro (TauRDΔK, hTauP301L), as judged by the Thioflavin S fluorescence assay which is sensitive to ß-structure. In the presence of antibodies tau protein forms only up to low-n oligomers as judged by light scattering and atomic force microscopy (AFM). The choice of the pH of the column elution buffer of the antibodies plays a key role in determining the activity of the antibodies, as antibodies eluted at low pH have a higher activity compared to the same antibodies eluted at high pH. The ability of antibodies to inhibit the aggregation of tau was tested in an N2a cell model of tau pathology which expresses the pro-aggregant tau repeat domain TauRDΔK. Antibodies were added to the extracellular medium, without or with protein transfection reagent (Xfect) which stimulates cellular uptake. In this assay, 2B10 antibody failed to inhibit tau aggregation (ThS signal) and failed to prevent aggregation induced apoptosis (Annexin V signal). By contrast, in the split-luciferase complementation assay the antibody 2B10, applied extracellularly, was able to prevent the dimerization/oligomerization of tau. Surprisingly this antibody has only a relatively low affinity to tau but is still very active in inhibiting tau aggregation in vitro. Antibodies added extracellularly were taken up by the cells and sorted into lysosomes. Their inhibitory effect can be explained by the fact that the internalized antibody recruits the toxic tau protein or oligomers to the lysosomes for degradation. In summary, a subset of antibodies raised against the purified low-n oligomers of TauRDΔK are able to inhibit tau aggregation both in vitro and in a cell model of tau pathology