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We consider a linear model which can have a large number of explanatory variables, the errors with an asymmetric distribution or some values of the explained variable are missing at random. In order to take in account these several situations, we consider the non parametric empirical likelihood (EL) estimation method. Because a constraint in EL contains an indicator function then a smoothed function instead of the indicator will be considered. Two smoothed expectile maximum EL methods are proposed, one of which will automatically select the explanatory variables. For each of the methods we obtain the convergence rate of the estimators and their asymptotic normality. The smoothed expectile empirical log-likelihood ratio process follow asymptotically a chi-square distribution and moreover the adaptive LASSO smoothed expectile maximum EL estimator satisfies the sparsity property which guarantees the automatic selection of zero model coefficients. In order to implement these methods, we propose four algorithms.

Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution. Developing efficient and accurate solution strategies that account for errors on the space, time and parameter domains simultaneously is highly challenging. Indeed, it is well known that standard polynomial-based approximations on the parameter domain can incur errors that grow in time. In this work, we focus on advection-diffusion problems with parameter-dependent wind fields. A novel adaptive solution strategy is proposed that allows users to combine stochastic collocation on the parameter domain with off-the-shelf adaptive timestepping algorithms with local error control. This is a non-intrusive strategy that builds a polynomial-based surrogate that is adapted sequentially in time. The algorithm is driven by a so-called hierarchical estimator for the parametric error and balances this against an estimate for the global timestepping error which is derived from a scaling argument.

The emerging concept of Over-the-Air (OtA) computation has shown great potential for achieving resource-efficient data aggregation across large wireless networks. However, current research in this area has been limited to the standard many-to-one topology, where multiple nodes transmit data to a single receiver. In this study, we address the problem of applying OtA computation to scenarios with multiple receivers, and propose a novel communication design that exploits joint precoding and decoding over multiple time slots. To determine the optimal precoding and decoding vectors, we formulate an optimization problem that aims to minimize the mean squared error of the desired computations while satisfying the unbiasedness condition and power constraints. Our proposed multi-slot design is shown to be effective in saving communication resources (e.g., time slots) and achieving smaller estimation errors compared to the baseline approach of separating different receivers over time.

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to second-order methods that are computationally more expensive. In this work we aim to approximate a nonlinear model with a linear one and correct the resulting approximation error. We develop a sequential method that iteratively solves a linear inverse problem and updates the approximation error by evaluating it at the new solution. This treatment convexifies the problem and allows us to benefit from established convex optimization methods. We separately consider cases where the approximation is fixed over iterations and where the approximation is adaptive. In the fixed case we show theoretically under what assumptions the sequence converges. In the adaptive case, particularly considering the special case of approximation by first-order Taylor expansion, we show that with certain assumptions the sequence converges to a critical point of the original nonconvex functional. Furthermore, we show that with quadratic objective functions the sequence corresponds to the Gauss-Newton method. Finally, we showcase numerical results superior to the conventional model correction method. We also show, that a fixed approximation can provide competitive results with considerable computational speed-up.

We introduce new techniques for the parameterized verification of disjunctive timed networks (DTNs), i.e., networks of timed automata (TAs) that communicate via location guards that enable a transition only if at least one process is in a given location. This computational model has been considered in the literature before, and example applications are gossiping clock synchronization protocols or planning problems. We address the minimum-time reachability problem (minreach) in DTNs, and show how to efficiently solve it based on a novel zone-graph algorithm. We further show that solving minreach allows us to construct a summary TA capturing exactly the possible behaviors of a single TA within a DTN of arbitrary size. The combination of these two results enables the parameterized verification of DTNs, while avoiding the construction of an exponential-size cutoff-system required by existing results. Our techniques are also implemented, and experiments show their practicality.

Deadlocks are one of the most notorious concurrency bugs, and significant research has focused on detecting them efficiently. Dynamic predictive analyses work by observing concurrent executions, and reason about alternative interleavings that can witness concurrency bugs. Such techniques offer scalability and sound bug reports, and have emerged as an effective approach for concurrency bug detection, such as data races. Effective dynamic deadlock prediction, however, has proven a challenging task, as no deadlock predictor currently meets the requirements of soundness, high-precision, and efficiency. In this paper, we first formally establish that this tradeoff is unavoidable, by showing that (a) sound and complete deadlock prediction is intractable, in general, and (b) even the seemingly simpler task of determining the presence of potential deadlocks, which often serve as unsound witnesses for actual predictable deadlocks, is intractable. The main contribution of this work is a new class of predictable deadlocks, called sync(hronization)-preserving deadlocks. Informally, these are deadlocks that can be predicted by reordering the observed execution while preserving the relative order of conflicting critical sections. We present two algorithms for sound deadlock prediction based on this notion. Our first algorithm SPDOffline detects all sync-preserving deadlocks, with running time that is linear per abstract deadlock pattern, a novel notion also introduced in this work. Our second algorithm SPDOnline predicts all sync-preserving deadlocks that involve two threads in a strictly online fashion, runs in overall linear time, and is better suited for a runtime monitoring setting. We implemented both our algorithms and evaluated their ability to perform offline and online deadlock-prediction on a large dataset of standard benchmarks.

The single-source shortest path (SSSP) problem is a well-studied problem that is used in many applications. In the parallel setting, a work-efficient algorithm that additionally attains $o(n)$ parallel depth has been elusive. Alternatively, various approaches have been developed that take advantage of specific properties of a particular class of graphs. On a graphics processing unit (GPU), the current state-of-the-art SSSP algorithms are implementations of the Delta-stepping algorithm, which does not perform well for graphs with large diameters. The main contribution of this work is to provide an algorithm designed for GPUs that runs efficiently for such graphs. We present the parallel bucket heap, a parallel cache-efficient data structure adapted for modern GPU architectures that supports standard priority queue operations, as well as bulk update. We analyze the structure in several well-known computational models and show that it provides both optimal parallelism and is cache-efficient. We implement the parallel bucket heap and use it in a parallel variant of Dijkstra's algorithm to solve the SSSP problem. Experimental results indicate that, for sufficiently large, dense graphs with high diameter, we outperform the current state-of-the-art SSSP implementations on an NVIDIA RTX 2080 Ti and Quadro M4000 by up to a factor of 2.8 and 5.4, respectively.

Understanding superfluidity remains a major goal of condensed matter physics. Here we tackle this challenge utilizing the recently developed Fermionic neural network (FermiNet) wave function Ansatz for variational Monte Carlo calculations. We study the unitary Fermi gas, a system with strong, short-range, two-body interactions known to possess a superfluid ground state but difficult to describe quantitively. We demonstrate key limitations of the FermiNet Ansatz in studying the unitary Fermi gas and propose a simple modification that outperforms the original FermiNet significantly, giving highly accurate results. We prove mathematically that the new Ansatz is a strict generalization of the original FermiNet architecture, despite the use of fewer parameters. Our approach shares several advantanges with the FermiNet: the use of a neural network removes the need for an underlying basis set; and the flexiblity of the network yields extremely accurate results within a variational quantum Monte Carlo framework that provides access to unbiased estimates of arbitrary ground-state expectation values. We discuss how the method can be extended to study other superfluids.

We develop a method for hybrid analyses that uses external controls to augment internal control arms in randomized controlled trials (RCT) where the degree of borrowing is determined based on similarity between RCT and external control patients to account for systematic differences (e.g. unmeasured confounders). The method represents a novel extension of the power prior where discounting weights are computed separately for each external control based on compatibility with the randomized control data. The discounting weights are determined using the predictive distribution for the external controls derived via the posterior distribution for time-to-event parameters estimated from the RCT. This method is applied using a proportional hazards regression model with piecewise constant baseline hazard. A simulation study and a real-data example are presented based on a completed trial in non-small cell lung cancer. It is shown that the case weighted adaptive power prior provides robust inference under various forms of incompatibility between the external controls and RCT population.

We study the complexity of reductions for weighted reachability in parametric Markov decision processes. That is, we say a state p is never worse than q if for all valuations of the polynomial indeterminates it is the case that the maximal expected weight that can be reached from p is greater than the same value from q. In terms of computational complexity, we establish that determining whether p is never worse than q is coETR-complete. On the positive side, we give a polynomial-time algorithm to compute the equivalence classes of the order we study for Markov chains. Additionally, we describe and implement two inference rules to under-approximate the never-worse relation and empirically show that it can be used as an efficient preprocessing step for the analysis of large Markov decision processes.