1,559 research outputs found

    Symmetrized models of last passage percolation and non-intersecting lattice paths

    Get PDF
    It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups U(l)U(l), Sp(2l)Sp(2l) and O(l)O(l). We present a theory of such results based on non-intersecting lattice paths, and integration techniques familiar from the theory of random matrices. Detailed derivations of probabilities relating to two further symmetrizations are also given.Comment: 21 pages, 5 figure

    Random walks and random fixed-point free involutions

    Full text link
    A bijection is given between fixed point free involutions of {1,2,...,2N}\{1,2,...,2N\} with maximum decreasing subsequence size 2p2p and two classes of vicious (non-intersecting) random walker configurations confined to the half line lattice points l≥1l \ge 1. In one class of walker configurations the maximum displacement of the right most walker is pp. Because the scaled distribution of the maximum decreasing subsequence size is known to be in the soft edge GOE (random real symmetric matrices) universality class, the same holds true for the scaled distribution of the maximum displacement of the right most walker.Comment: 10 page

    Vicious Walkers and Hook Young Tableaux

    Full text link
    We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of walker's movements. Applying the saddle point method, we reveal that the scaling limit gives the Tracy--Widom distribution, which is same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.Comment: 23 pages, 5 figure

    Safety and efficacy of pralsetinib in RET fusion–positive non-small-cell lung cancer including as first-line therapy: update from the ARROW trial

    Get PDF
    RET inhibition; Pralsetinib; Targeted therapyInhibición de RET; Pralsetinib; Terapia dirigidaInhibició de RET; Pralsetinib; Teràpia dirigidaBackground RET fusions are present in 1%-2% of non-small-cell lung cancer (NSCLC). Pralsetinib, a highly potent, oral, central nervous system-penetrant, selective RET inhibitor, previously demonstrated clinical activity in patients with RET fusion–positive NSCLC in the phase I/II ARROW study, including among treatment-naive patients. We report an updated analysis from the ARROW study. Patients and methods ARROW is a multi-cohort, open-label, phase I/II study. Eligible patients were ≥18 years of age with locally advanced or metastatic solid tumours and an Eastern Cooperative Oncology Group performance status of 0-2 (later 0-1). Patients initiated pralsetinib at the recommended phase II dose of 400 mg once daily until disease progression, intolerance, consent withdrawal, or investigator’s decision. The co-primary endpoints (phase II) were overall response rate (ORR) by blinded independent central review and safety. Results Between 17 March 2017 and 6 November 2020 (data cut-off), 281 patients with RET fusion–positive NSCLC were enrolled. The ORR was 72% [54/75; 95% confidence interval (CI) 60% to 82%] for treatment-naive patients and 59% (80/136; 95% CI 50% to 67%) for patients with prior platinum-based chemotherapy (enrolment cut-off for efficacy analysis: 22 May 2020); median duration of response was not reached for treatment-naive patients and 22.3 months for prior platinum-based chemotherapy patients. Tumour shrinkage was observed in all treatment-naive patients and in 97% of patients with prior platinum-based chemotherapy; median progression-free survival was 13.0 and 16.5 months, respectively. In patients with measurable intracranial metastases, the intracranial response rate was 70% (7/10; 95% CI 35% to 93%); all had received prior systemic treatment. In treatment-naive patients with RET fusion–positive NSCLC who initiated pralsetinib by the data cut-off (n = 116), the most common grade 3-4 treatment-related adverse events (TRAEs) were neutropenia (18%), hypertension (10%), increased blood creatine phosphokinase (9%), and lymphopenia (9%). Overall, 7% (20/281) discontinued due to TRAEs. Conclusions Pralsetinib treatment produced robust efficacy and was generally well tolerated in treatment-naive patients with advanced RET fusion–positive NSCLC. Results from the confirmatory phase III AcceleRET Lung study (NCT04222972) of pralsetinib versus standard of care in the first-line setting are pending.This work was supported by Blueprint Medicines Corporation and F. Hoffmann-La Roche, Ltd, Switzerland (no grant number)

    Growth models, random matrices and Painleve transcendents

    Full text link
    The Hammersley process relates to the statistical properties of the maximum length of all up/right paths connecting random points of a given density in the unit square from (0,0) to (1,1). This process can also be interpreted in terms of the height of the polynuclear growth model, or the length of the longest increasing subsequence in a random permutation. The cumulative distribution of the longest path length can be written in terms of an average over the unitary group. Versions of the Hammersley process in which the points are constrained to have certain symmetries of the square allow similar formulas. The derivation of these formulas is reviewed. Generalizing the original model to have point sources along two boundaries of the square, and appropriately scaling the parameters gives a model in the KPZ universality class. Following works of Baik and Rains, and Pr\"ahofer and Spohn, we review the calculation of the scaled cumulative distribution, in which a particular Painlev\'e II transcendent plays a prominent role.Comment: 27 pages, 5 figure

    The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class

    Full text link
    We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ universality class, not only as regards to scaling exponents but also as regards to the full probability distribution of the height in the long time limit.Comment: Proceedings StatPhys 2

    An Efficient Anomaly Recognition Framework Using an Attention Residual LSTM in Surveillance Videos

    Get PDF
    Video anomaly recognition in smart cities is an important computer vision task that plays a vital role in smart surveillance and public safety but is challenging due to its diverse, complex, and infrequent occurrence in real-time surveillance environments. Various deep learning models use significant amounts of training data without generalization abilities and with huge time complexity. To overcome these problems, in the current work, we present an efficient light-weight convolutional neural network (CNN)-based anomaly recognition framework that is functional in a surveillance environment with reduced time complexity. We extract spatial CNN features from a series of video frames and feed them to the proposed residual attention-based long short-term memory (LSTM) network, which can precisely recognize anomalous activity in surveillance videos. The representative CNN features with the residual blocks concept in LSTM for sequence learning prove to be effective for anomaly detection and recognition, validating our model’s effective usage in smart cities video surveillance. Extensive experiments on the real-world benchmark UCF-Crime dataset validate the effectiveness of the proposed model within complex surveillance environments and demonstrate that our proposed model outperforms state-of-the-art models with a 1.77%, 0.76%, and 8.62% increase in accuracy on the UCF-Crime, UMN and Avenue datasets, respectively
    • …
    corecore