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

MultiFusionNet: Multilayer Multimodal Fusion of Deep Neural Networks for Chest X-Ray Image Classification

Chest X-ray imaging is a critical diagnostic tool for identifying pulmonary diseases. However, manual interpretation of these images is time-consuming and error-prone. Automated systems utilizing convolutional neural networks (CNNs) have shown promise in improving the accuracy and efficiency of chest X-ray image classification. While previous work has mainly focused on using feature maps from the final convolution layer, there is a need to explore the benefits of leveraging additional layers for improved disease classification. Extracting robust features from limited medical image datasets remains a critical challenge. In this paper, we propose a novel deep learning-based multilayer multimodal fusion model that emphasizes extracting features from different layers and fusing them. Our disease detection model considers the discriminatory information captured by each layer. Furthermore, we propose the fusion of different-sized feature maps (FDSFM) module to effectively merge feature maps from diverse layers. The proposed model achieves a significantly higher accuracy of 97.21% and 99.60% for both three-class and two-class classifications, respectively. The proposed multilayer multimodal fusion model, along with the FDSFM module, holds promise for accurate disease classification and can also be extended to other disease classifications in chest X-ray images.Comment: 19 page

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