Query Complexity of Search Problems

We relate various complexity measures like sensitivity, block sensitivity, certificate complexity for multi-output functions to the query complexities of such functions. Using these relations, we provide the following improvements upon the known relationship between pseudo-deterministic and deterministic query complexity for total search problems: - We show that deterministic query complexity is at most the third power of its pseudo-deterministic query complexity. Previously, a fourth-power relation was shown by Goldreich, Goldwasser and Ron (ITCS\u2713). - We improve the known separation between pseudo-deterministic and randomized decision tree size for total search problems in two ways: (1) we exhibit an exp(??(n^{1/4})) separation for the SearchCNF relation for random k-CNFs. This seems to be the first exponential lower bound on the pseudo-deterministic size complexity of SearchCNF associated with random k-CNFs. (2) we exhibit an exp(?(n)) separation for the ApproxHamWt relation. The previous best known separation for any relation was exp(?(n^{1/2})). We also separate pseudo-determinism from randomness in And and (And,Or) decision trees, and determinism from pseudo-determinism in Parity decision trees. For a hypercube colouring problem, that was introduced by Goldwasswer, Impagliazzo, Pitassi and Santhanam (CCC\u2721) to analyze the pseudo-deterministic complexity of a complete problem in TFNP^{dt}, we prove that either the monotone block-sensitivity or the anti-monotone block sensitivity is ?(n^{1/3}); Goldwasser et al. showed an ?(n^{1/2}) bound for general block-sensitivity

Detection of Brain Tumor in MRI Image through Fuzzy-Based Approach

The process of accurate detection of edges of MRI images of a brain is always a challenging but interesting problem. Accurate detection is very important and critical for the generation of correct diagnosis. The major problem that comes across while analyzing MRI images of a brain is inaccurate data. The process of segmentation of brain MRI image involves the problem of searching anatomical regions of interest, which can help radiologists to extract shapes, appearance, and other structural features for diagnosis of diseases or treatment evaluation. The brain image segmentation is composed of many stages. During the last few years, preprocessing algorithms, techniques, and operators have emerged as a powerful tool for efficient extraction of regions of interest, performing basic algebraic operations on images, enhancing specific image features, and reducing data on both resolution and brightness. Edge detection is one of the techniques of image segmentation. Here from image segmentation, tumor is located. Finally, we try to retrieve tumor from MRI image of a brain in the form of edge more accurately and efficiently, by enhancing the performance of diffe rent kinds of edge detectors using fuzzy approach

Online Covariate Shift Detection based Adaptive Brain-Computer Interface to Trigger Hand Exoskeleton Feedback for Neuro-Rehabilitation

A major issue in electroencephalogram (EEG) based brain-computer interfaces (BCIs) is the intrinsic non-stationarities in the brain waves, which may degrade the performance of the classifier, while transitioning from calibration to feedback generation phase. The non-stationary nature of the EEG data may cause its input probability distribution to vary over time, which often appear as a covariate shift. To adapt to the covariate shift, we had proposed an adaptive learning method in our previous work and tested it on offline standard datasets. This paper presents an online BCI system using previously developed covariate shift detection (CSD)-based adaptive classifier to discriminate between mental tasks and generate neurofeedback in the form of visual and exoskeleton motion. The CSD test helps prevent unnecessary retraining of the classifier. The feasibility of the developed online-BCI system was first tested on 10 healthy individuals, and then on 10 stroke patients having hand disability. A comparison of the proposed online CSD-based adaptive classifier with conventional non-adaptive classifier has shown a significantly (p<0.01) higher classification accuracy in both the cases of healthy and patient groups. The results demonstrate that the online CSD-based adaptive BCI system is superior to the non-adaptive BCI system and it is feasible to be used for actuating hand exoskeleton for the stroke-rehabilitation applications