We consider a high-dimensional linear regression problem, where the covariates (features) are ordered in some meaningful way, and the number of covariates p can be much larger than the sample size n. The fused lasso of Tibshirani et al. (2005) is designed especially to tackle this type of problems; it yields sparse coefficients and selects grouped variables, and encourages local constant coefficient profile within each group. However, in some applications, the effects of different features within a group might be different and change smoothly. In this paper, we propose a new spline-lasso or more generally, spline-MCP to better capture the different effects within the group. The newly proposed method is very easy to implement since it can be easily turned into a lasso or MCP problem. Simulations show that the method works very effectively both in feature selection and prediction accuracy. A real application is also given to illustrate the benefits of the method.

In recent years, a significant amount of attention has been paid to solve partial differential equations (PDEs) by deep learning. For example, deep Galerkin method (DGM) uses the PDE residual in the least-squares sense as the loss function and a deep neural network (DNN) to approximate the PDE solution. In this work, we propose a deep mixed residual method (MIM) to solve PDEs with high-order derivatives. Notable examples include Poisson equation, Monge-Ampére equation, biharmonic equation, and Korteweg-de Vries equation. In MIM, we first rewrite a high-order PDE into a first-order system, very much in the same spirit as local discontinuous Galerkin method and mixed finite element method in classical numerical methods for PDEs. We then use the residual of first-order system in the least-squares sense as the loss function, which is in close connection with least-squares finite element method. For aforementioned classical numerical methods, the choice of trail and test functions is important for stability and accuracy issues in many cases. MIM shares this property when DNNs are employed to approximate unknowns functions in the first-order system. In one case, we use nearly the same DNN to approximate all unknown functions and in the other case, we use totally different DNNs for different unknown functions. Numerous results of MIM with different loss functions and different choice

Stochastic model checking is a technique for analyzing systems that possess probabilistic characteristics. However, its scalability is limited as probabilistic models of real-world applications typically have very large or infinite state space. This paper presents a new infinite state CTMC model checker, STAMINA, with improved scalability. It uses a novel state space approximation method to reduce large and possibly infinite state CTMC models to finite state representations that are amenable to existing stochastic model checkers. It is integrated with a new property-guided state expansion approach that improves the analysis accuracy. Demonstration of the tool on several benchmark examples shows promising results in terms of analysis efficiency and accuracy compared with a state-of-theart CTMC model checker that deploys a similar approximation method.

Quantitative verification tools compute probabilities, expected rewards, or steady-state values for formal models of stochastic and timed systems. Exact results often cannot be obtained efficiently, so most tools use floating-point arithmetic in iterative algorithms that approximate the quantity of interest. Correctness is thus defined by the desired precision and determines performance. In this paper, we report on the experimental evaluation of these trade-offs performed in QComp 2020: the second friendly competition of tools for the analysis of quantitative formal models. We survey the precision guarantees-ranging from exact rational results to statistical confidence statements-offered by the nine participating tools. They gave rise to a performance evaluation using five tracks with varying correctness criteria, of which we present the results.

The design of modern network-on-chip (NoC) systems faces reliability challenges due to process and environmental variations. Peak power supply noise (PSN) in the power delivery network of a NoC device plays a critical role in determining reliable operations: PSN typically leads to voltage droop, which can cause timing errors in the NoC router pipelines. Existing simulation-based approaches cannot provide rigorous, worst-case reliability guarantees on the probabilistic behaviors of PSN. To address this problem, this paper takes a significant step in formally analyzing PSN in modern NoCs. Specifically, we present a probabilistic model checking approach for the rigorous characterization of PSN for a generic central router of a large mesh-NoC system, under the Round Robin scheduling mechanism with a uniform random network traffic load. Defining features for PSN are extracted at the behavioral level to facilitate property formulation. Several abstract models have been derived for the central router's concrete model based on the observations of its arbiter's conflict resolution behavior. Probabilistic modeling and verification are performed using the Modest Toolset. Results show significant scalability of our abstract models, and reveal key PSN characteristics that are indicative of NoC design and optimization.