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1. Assume(), Capture(), Verify(), Establish(): A Vocabulary for Static Program Analysis

   https://doi.org/10.1109/QRS-C60940.2023.00067  

   Mohammadi, Hessamaldin; Ghardallou, Wided; Brick, Elijah; Mili, Ali (October 2023, IEEE)

   We propose a set of functions that a user can invoke to analyze a program written in a C-like language: Assume() refers to a label in the source code or to a program part, and enables the user to make an assumption about the state of the program at some label or the function of some program part; Capture() refers to a label or a program part and returns an assertion about the state of the program at the label or the function of the program part; Verify() refers to a label or a program part and tests a unary assertion about the state of the program at the label or a binary assertion about the function of the program part; Establish() refers to a label or a program part and modifies the program code to make Verify() return TRUE at that label or program part, if it did not originally. We discuss the foundations of this tool as well as a preliminary implementation. 

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2. Polynomial Chaos-Based Controller Design for Uncertain Linear Systems With State and Control Constraints

   https://doi.org/10.1115/1.4038800  

   Nandi, Souransu; Migeon, Victor; Singh, Tarunraj; Singla, Puneet (July 2018, Journal of Dynamic Systems, Measurement, and Control)

   For linear dynamic systems with uncertain parameters, design of controllers which drive a system from an initial condition to a desired final state, limited by state constraints during the transition is a nontrivial problem. This paper presents a methodology to design a state constrained controller, which is robust to time invariant uncertain variables. Polynomial chaos (PC) expansion, a spectral expansion, is used to parameterize the uncertain variables permitting the evolution of the uncertain states to be written as a polynomial function of the uncertain variables. The coefficients of the truncated PC expansion are determined using the Galerkin projection resulting in a set of deterministic equations. A transformation of PC polynomial space to the Bernstein polynomial space permits determination of bounds on the evolving states of interest. Linear programming (LP) is then used on the deterministic set of equations with constraints on the bounds of the states to determine the controller. Numerical examples are used to illustrate the benefit of the proposed technique for the design of a rest-to-rest controller subject to deformation constraints and which are robust to uncertainties in the stiffness coefficient for the benchmark spring-mass-damper system. 

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3. A stepped-sine curve-fit algorithm for finding cantilever resonance shifts in AFM

   https://doi.org/10.23919/ACC.2019.8814403  

   Kang, Zhixin; Saygin, Verda; Brown, Keith A.; Andersson, Sean (July 2019, 2019 American Control Conference (ACC))

   Atomic force microscopes (AFMs) are used not only to image with nanometer-scale resolution, but also to nanofabricate structures on a surface using methods such as dip-pen nanolithography (DPN). DPN involves using the tip of the AFM to deposit a small amount of material on the surface. Typically, this process is done in open loop, leading to large variations in the amount of material transferred. One of the first steps to closing this loop is to be able to accurately and rapidly measure the amount of deposition. This can be done by measuring the change in the resonance frequency of the cantilever before and after a write as that shift is directly related to the change in mass on the cantilever. Currently, this is done using a thermal-based system identification, a technique which uses the natural Brownian excitation of the cantilever as a white noise excitation combined with a fast Fourier transform to extract a Bode plot. However, thermal-based techniques do not have a good signal to noise ratio at typical cantilever resonance frequencies and thus do not provide the needed resolution in the DPN application. Here we develop a scheme that iteratively uses a stepped-sine approach. At each step of the iteration, three frequencies close to the approximate location of the resonance are injected and used to fit a model of the magnitude of the transfer function. The identified peak is used to select three new frequencies in a smaller range in a binary search to reduce the uncertainty of the measured resonance peak location. The scheme is demonstrated through simulation and shown to produce an accuracy of better than 0.5 Hz on a cantilever with a 14 kHz resonance in a physically realistic noise scenario. 

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4. RePBubLik: Reducing Polarized Bubble Radius with Link Insertions

   https://doi.org/10.1145/3437963.3441825  

   Haddadan, Shahrzad; Menghini, Cristina; Riondato, Matteo; Upfal, Eli (March 2021, WSDM)

   Liane, Lewin-Eytan; David, Carmel; Elad, Yom-Tov (Ed.)

   The topology of the hyperlink graph among pages expressing different opinions may influence the exposure of readers to diverse content. Structural bias may trap a reader in a 'polarized' bubble with no access to other opinions. We model readers' behavior as random walks. A node is in a 'polarized' bubble if the expected length of a random walk from it to a page of different opinion is large. The structural bias of a graph is the sum of the radii of highly-polarized bubbles. We study the problem of decreasing the structural bias through edge insertions. 'Healing' all nodes with high polarized bubble radius is hard to approximate within a logarithmic factor, so we focus on finding the best k edges to insert to maximally reduce the structural bias. We present RePBubLik, an algorithm that leverages a variant of the random walk closeness centrality to select the edges to insert. RePBubLik obtains, under mild conditions, a constant-factor approximation. It reduces the structural bias faster than existing edge-recommendation methods, including some designed to reduce the polarization of a graph. 

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5. A Global-Local Approximation Framework for Large-Scale Gaussian Process Modeling

   https://doi.org/10.1080/00401706.2023.2296451  

   Vakayil, Akhil; Joseph, V Roshan (April 2024, Technometrics)

   In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ a combined global-local approach in building the approximation. Our framework uses a subset-of-data approach where the subset is a union of a set of global points designed to capture the global trend in the data, and a set of local points specific to a given testing location to capture the local trend around the testing location. The correlation function is also modeled as a combination of a global, and a local kernel. The predictive performance of our framework, which we refer to as TwinGP, is comparable to the state-of-the-art GP modeling methods, but at a fraction of their computational cost. 

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