5,564 research outputs found

    Counting Humps in Motzkin paths

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    In this paper we study the number of humps (peaks) in Dyck, Motzkin and Schr\"{o}der paths. Recently A. Regev noticed that the number of peaks in all Dyck paths of order nn is one half of the number of super Dyck paths of order nn. He also computed the number of humps in Motzkin paths and found a similar relation, and asked for bijective proofs. We give a bijection and prove these results. Using this bijection we also give a new proof that the number of Dyck paths of order nn with kk peaks is the Narayana number. By double counting super Schr\"{o}der paths, we also get an identity involving products of binomial coefficients.Comment: 8 pages, 2 Figure

    Data-Driven Rational Drug Design

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    Vast amount of experimental data in structural biology has been generated, collected and accumulated in the last few decades. This rich dataset is an invaluable mine of knowledge, from which deep insights can be obtained and practical applications can be developed. To achieve that goal, we must be able to manage such Big Data\u27\u27 in science and investigate them expertly. Molecular docking is a field that can prominently make use of the large structural biology dataset. As an important component of rational drug design, molecular docking is used to perform large-scale screening of putative associations between small organic molecules and their pharmacologically relevant protein targets. Given a small molecule (ligand), a molecular docking program simulates its interaction with the target protein, and reports the probable conformation of the protein-ligand complex, and the relative binding affinity compared against other candidate ligands. This dissertation collects my contributions in several aspects of molecular docking. My early contribution focused on developing a novel metric to quantify the structural similarity between two protein-ligand complexes. Benchmarks show that my metric addressed several issues associated with the conventional metric. Furthermore, I extended the functionality of this metric to cross different systems, effectively utilizing the data at the proteome level. After developing the novel metric, I formulated a scoring function that can extract the biological information of the complex, integrate it with the physics components, and finally enhance the performance. Through collaboration, I implemented my model into an ultra-fast, adaptive program, which can take advantage of a range of modern parallel architectures and handle the demanding data processing tasks in large scale molecular docking applications

    Dissection of the mitotic and nuclear functions of Chromator, a nuclear-derived spindle matrix component in Drosophila

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    A spindle matrix has long been proposed to serve as a stationary or elastic molecular matrix substrate for the organization and activities of microtubules and motors, based on the consideration of a mechanical and functional support for the stabilization of microtubule spindle during force generation from mitotic motors. Recently, the identification of four Drosophila proteins, Skeletor, Megator, EAST and Chromator has provided molecular evidence for the existence of this macromolecular matrix structure during mitosis. All of these four proteins have been shown to interact with each other within a protein complex and redistribute from the nucleus at interphase to form a fusiform spindle-like structure that does not rely on polymerized microtubules from prophase until telophase. Especially, the discovery of the large coiled-coil domain in Megator suggests that Megator may provide the structural element of this matrix. Characterizations of these molecules all indicate their potential to constitute a bona fide spindle matrix. However, functional analysis is missing due to the limitation of existing mutant alleles and the multiple essential roles played by at least some of these proteins at different stages of the cell cycle.;Taking advantage of newly generated hypomorphic alleles of the Chro gene, different functional roles of Chromator were dissected and the results are presented in this dissertation. In transheterozygous Chro71/Chro612 mutants, interphase polytene chromosome structures are disrupted with misalignment of the band/interband pattern and numerous ectopic contacts between non-homologous regions. During mitosis a dramatically disorganized spindles and chromosome segregation defects are observed in dividing neuroblasts from mutant third instar larval brains. In addition, an interphase-specific interaction between Chromator and the H3 Serine 10 kinase JIL-1 as well as mitotic interactions of Chromator with the molecular motor Ncd and microtubules are described.;This dissertation provides the first reported detailed functional analysis of one spindle matrix candidate, Chromator, in animal system. Impaired Chromator function in the mutant allele causes improper spindle assembly and chromosome segregation during mitosis as well as defective interphase polytene chromosome structures. These findings, with the characteristic cell-cycle dependent distribution pattern of Chromator reveal that Chromator is a nuclear-derived multifunctional protein that performs its essential functions from interphase to mitosis

    Support Neighbor Loss for Person Re-Identification

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    Person re-identification (re-ID) has recently been tremendously boosted due to the advancement of deep convolutional neural networks (CNN). The majority of deep re-ID methods focus on designing new CNN architectures, while less attention is paid on investigating the loss functions. Verification loss and identification loss are two types of losses widely used to train various deep re-ID models, both of which however have limitations. Verification loss guides the networks to generate feature embeddings of which the intra-class variance is decreased while the inter-class ones is enlarged. However, training networks with verification loss tends to be of slow convergence and unstable performance when the number of training samples is large. On the other hand, identification loss has good separating and scalable property. But its neglect to explicitly reduce the intra-class variance limits its performance on re-ID, because the same person may have significant appearance disparity across different camera views. To avoid the limitations of the two types of losses, we propose a new loss, called support neighbor (SN) loss. Rather than being derived from data sample pairs or triplets, SN loss is calculated based on the positive and negative support neighbor sets of each anchor sample, which contain more valuable contextual information and neighborhood structure that are beneficial for more stable performance. To ensure scalability and separability, a softmax-like function is formulated to push apart the positive and negative support sets. To reduce intra-class variance, the distance between the anchor's nearest positive neighbor and furthest positive sample is penalized. Integrating SN loss on top of Resnet50, superior re-ID results to the state-of-the-art ones are obtained on several widely used datasets.Comment: Accepted by ACM Multimedia (ACM MM) 201

    Entries and late entries for GCSE and A Level : 2014/15 academic year

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    Access arrangements for GCSE and A Level : 2014/15 academic year

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