GHZ Test
Zero-knowledge and multi-prover systems are both central notions in classical and quantum complexity theory. There is, however, little research in quantum multi-prover zero-knowledge systems. This paper studies complexity-theoretical aspects of the quantum multi-prover zero-knowledge systems. This paper has two results: 1.QMIP* systems with honest zero-knowledge can be converted into general zero-knowledge systems without any assumptions. 2.QMIP* has computational quantum zero-knowledge systems if a natural computational conjecture holds. One of the main tools is a test (called the GHZ test) that uses GHZ states shared by the provers, which prevents the verifier’s attack in the above two results. Another main tool is what we call the Local Hamiltonian based Interactive protocol (LHI protocol). The LHI protocol makes previous research for Local Hamiltonians applicable to check the history state of interactive proofs, and we then apply Broadbent et al.’s zero-knowledge protocol for QMA \cite{BJSW} to quantum multi-prover systems in order to obtain the second result. …

Clubmark
There is a great diversity of clustering and community detection algorithms, which are key components of many data analysis and exploration systems. To the best of our knowledge, however, there does not exist yet any uniform benchmarking framework, which is publicly available and suitable for the parallel benchmarking of diverse clustering algorithms on a wide range of synthetic and real-world datasets. In this paper, we introduce Clubmark, a new extensible framework that aims to fill this gap by providing a parallel isolation benchmarking platform for clustering algorithms and their evaluation on NUMA servers. Clubmark allows for fine-grained control over various execution variables (timeouts, memory consumption, CPU affinity and cache policy) and supports the evaluation of a wide range of clustering algorithms including multi-level, hierarchical and overlapping clustering techniques on both weighted and unweighted input networks with built-in evaluation of several extrinsic and intrinsic measures. Our framework is open-source and provides a consistent and systematic way to execute, evaluate and profile clustering techniques considering a number of aspects that are often missing in state-of-the-art frameworks and benchmarking systems. …

Model-Implied Instrumental Variable – Generalized Method of Moments (MIIV-GMM)
The common maximum likelihood (ML) estimator for structural equation models (SEMs) has optimal asymptotic properties under ideal conditions (e.g., correct structure, no excess kurtosis, etc.) that are rarely met in practice. This paper proposes model-implied instrumental variable – generalized method of moments (MIIV-GMM) estimators for latent variable SEMs that are more robust than ML to violations of both the model structure and distributional assumptions. Under less demanding assumptions, the MIIV-GMM estimators are consistent, asymptotically unbiased, asymptotically normal, and have an asymptotic covariance matrix. They are ‘distribution-free,’ robust to heteroscedasticity, and have overidentification goodness-of-fit J-tests with asymptotic chi-square distributions. In addition, MIIV-GMM estimators are ‘scalable’ in that they can estimate and test the full model or any subset of equations, and hence allow better pinpointing of those parts of the model that fit and do not fit the data. An empirical example illustrates MIIV-GMM estimators. Two simulation studies explore their finite sample properties and find that they perform well across a range of sample sizes. …

Trimmed Ensemble Kalman Filter (TEnKF)
We study the ensemble Kalman filter (EnKF) algorithm for sequential data assimilation in a general situation, that is, for nonlinear forecast and measurement models with non-additive and non-Gaussian noises. Such applications traditionally force us to choose between inaccurate Gaussian assumptions that permit efficient algorithms (e.g., EnKF), or more accurate direct sampling methods which scale poorly with dimension (e.g., particle filters, or PF). We introduce a trimmed ensemble Kalman filter (TEnKF) which can interpolate between the limiting distributions of the EnKF and PF to facilitate adaptive control over both accuracy and efficiency. This is achieved by introducing a trimming function that removes non-Gaussian outliers that introduce errors in the correlation between the model and observed forecast, which otherwise prevent the EnKF from proposing accurate forecast updates. We show for specific trimming functions that the TEnKF exactly reproduces the limiting distributions of the EnKF and PF. We also develop an adaptive implementation which provides control of the effective sample size and allows the filter to overcome periods of increased model nonlinearity. This algorithm allow us to demonstrate substantial improvements over the traditional EnKF in convergence and robustness for the nonlinear Lorenz-63 and Lorenz-96 models. …