A Bayesian adaptive marker‐stratified design for molecularly targeted agents with customized hierarchical modeling

It is well known that the treatment effect of a molecularly targeted agent (MTA) may vary dramatically, depending on each patient's biomarker profile. Therefore, for a clinical trial evaluating MTA, it is more reasonable to evaluate its treatment effect within different marker subgroups rather than evaluating the average treatment effect for the overall population. The marker‐stratified design (MSD) provides a useful tool to evaluate the subgroup treatment effects of MTAs. Under the Bayesian framework, the beta‐binomial model is conventionally used under the MSD to estimate the response rate and test the hypothesis. However, this conventional model ignores the fact that the biomarker used in the MSD is, in general, predictive only for the MTA. The response rates for the standard treatment can be approximately consistent across different subgroups stratified by the biomarker. In this paper, we proposed a Bayesian hierarchical model incorporating this biomarker information into consideration. The proposed model uses a hierarchical prior to borrow strength across different subgroups of patients receiving the standard treatment and, therefore, improve the efficiency of the design. Prior informativeness is determined by solving a “customized” equation reflecting the physician's professional opinion. We developed a Bayesian adaptive design based on the proposed hierarchical model to guide the treatment allocation and test the subgroup treatment effect as well as the predictive marker effect. Simulation studies and a real trial application demonstrate that the proposed design yields desirable operating characteristics and outperforms the existing designs

Rumba : a Python framework for automating large-scale recursive internet experiments on GENI and FIRE+

It is not easy to design and run Convolutional Neural Networks (CNNs) due to: 1) finding the optimal number of filters (i.e., the width) at each layer is tricky, given an architecture; and 2) the computational intensity of CNNs impedes the deployment on computationally limited devices. Oracle Pruning is designed to remove the unimportant filters from a well-trained CNN, which estimates the filters’ importance by ablating them in turn and evaluating the model, thus delivers high accuracy but suffers from intolerable time complexity, and requires a given resulting width but cannot automatically find it. To address these problems, we propose Approximated Oracle Filter Pruning (AOFP), which keeps searching for the least important filters in a binary search manner, makes pruning attempts by masking out filters randomly, accumulates the resulting errors, and finetunes the model via a multi-path framework. As AOFP enables simultaneous pruning on multiple layers, we can prune an existing very deep CNN with acceptable time cost, negligible accuracy drop, and no heuristic knowledge, or re-design a model which exerts higher accuracy and faster inferenc

Hankel determinants, Pad\'e approximations, and irrationality exponents

The irrationality exponent of an irrational number $\xi$, which measures the approximation rate of $\xi$ by rationals, is in general extremely difficult to compute explicitly, unless we know the continued fraction expansion of $\xi$. Results obtained so far are rather fragmentary, and often treated case by case. In this work, we shall unify all the known results on the subject by showing that the irrationality exponents of large classes of automatic numbers and Mahler numbers (which are transcendental) are exactly equal to $2$. Our classes contain the Thue--Morse--Mahler numbers, the sum of the reciprocals of the Fermat numbers, the regular paperfolding numbers, which have been previously considered respectively by Bugeaud, Coons, and Guo, Wu and Wen, but also new classes such as the Stern numbers and so on. Among other ingredients, our proofs use results on Hankel determinants obtained recently by Han.Comment: International Mathematics Research Notices 201

A New Method for Fast Computation of Moments Based on 8-neighbor Chain CodeApplied to 2-D Objects Recognition

2D moment invariants have been successfully applied in pattern recognition tasks. The main difficulty of using moment invariants is the computational burden. To improve the algorithm of moments computation through an iterative method, an approach for fast computation of moments based on the 8-neighbor chain code is proposed in this paper. Then artificial neural networks are applied for 2D shape recognition with moment invariants. Compared with the method of polygonal approximation, this approach shows higher accuracy in shape representation and faster recognition speed in experiment

Multiparty quantum secret splitting and quantum state sharing

A protocol for multiparty quantum secret splitting is proposed with an ordered $N$ EPR pairs and Bell state measurements. It is secure and has the high intrinsic efficiency and source capacity as almost all the instances are useful and each EPR pair carries two bits of message securely. Moreover, we modify it for multiparty quantum state sharing of an arbitrary $m$-particle entangled state based on quantum teleportation with only Bell state measurements and local unitary operations which make this protocol more convenient in a practical application than others.Comment: 7 pages, 1 figure. The revision of the manuscript appeared in PLA. Some procedures for detecting cheat have been added. Then the security loophole in the original manuscript has been eliminate