553 research outputs found

    Fluctuations of TASEP and LPP with general initial data

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    We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to a point. We also consider variants of last passage percolation with inhomogeneous parameter geometric weights and provide variational formulas of a similar nature. This proves one aspect of the conjectural description of the renormalization fixed point of the Kardar-Parisi-Zhang universality class.Comment: 44 pages, 6 figure

    Fluctuations of TASEP and LPP with general initial data

    Get PDF
    We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to a point. We also consider variants of last passage percolation with inhomogeneous parameter geometric weights and provide variational formulas of a similar nature. This proves one aspect of the conjectural description of the renormalization fixed point of the Kardar-Parisi-Zhang universality clas

    ULTRALOW-FREQUENCY MUTATIONAL VARIATIONS REFLECT SPATIAL HETEROGENEITY OF GLIOBLASTOMAS

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    Glioblastoma multiforme (GBM) is the most common and aggressive type of brain tumor in adults, hallmarked by inter and intratumoral heterogeneity. Current treatment incorporates several biomarkers at the genomic and epigenomic levels. However, the efficacy of prognosis based on single biopsy was often undermined by the heterogeneous nature of GBM. Studies have highlighted the need for multi-sector biopsies to minimize the effect of intratumoral heterogeneity in clinical decision-making. In this project, we investigated mutations of geographically different regions of 20 primary glioblastoma specimens from seven patients for the selected regions of 13 genes using a novel targeted deep sequencing technology, Duplex Sequencing (DS). We have focused on subclonal (ultralow- and low-frequency) mutations that are not detectable by conventional next generation sequencing (NGS) methodologies but are accurately detectable by DS. Our findings indicate the heterogeneity of known GBM biomarkers, TERT promoter C228T mutation and IDH1 nonsynonymous mutations (R132H, R132G) in codon 132, in different regions of the GBM. Intratumoral heterogeneity of subclonal mutations are mainly found in EGFR, TERT, MSH6, PIK3CA, and PIK3R1 genes in most patients (six out of seven). Our results reveal that the similarity in mutation sequence context was not significantly higher in closely located specimens compared with distally located specimens. These findings could provide information on clinically relevant mutations that are unique to different regions of the tumors, and help guide future studies that seek to develop multi-sector biopsies for GBM prognosis

    zkFL: Zero-Knowledge Proof-based Gradient Aggregation for Federated Learning

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    Federated Learning (FL) is a machine learning paradigm, which enables multiple and decentralized clients to collaboratively train a model under the orchestration of a central aggregator. Traditional FL solutions rely on the trust assumption of the centralized aggregator, which forms cohorts of clients in a fair and honest manner. However, a malicious aggregator, in reality, could abandon and replace the client's training models, or launch Sybil attacks to insert fake clients. Such malicious behaviors give the aggregator more power to control clients in the FL setting and determine the final training results. In this work, we introduce zkFL, which leverages zero-knowledge proofs (ZKPs) to tackle the issue of a malicious aggregator during the training model aggregation process. To guarantee the correct aggregation results, the aggregator needs to provide a proof per round. The proof can demonstrate to the clients that the aggregator executes the intended behavior faithfully. To further reduce the verification cost of clients, we employ a blockchain to handle the proof in a zero-knowledge way, where miners (i.e., the nodes validating and maintaining the blockchain data) can verify the proof without knowing the clients' local and aggregated models. The theoretical analysis and empirical results show that zkFL can achieve better security and privacy than traditional FL, without modifying the underlying FL network structure or heavily compromising the training speed
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