On the mixing time of coordinate Hit-and-Run

We obtain a polynomial upper bound on the mixing time $T_{CHR}(\epsilon)$ of the coordinate Hit-and-Run (CHR) random walk on an $n-$ dimensional convex body, where $T_{CHR}(\epsilon)$ is the number of steps needed to reach within $\epsilon$ of the uniform distribution with respect to the total variation distance, starting from a warm start (i.e., a distribution which has a density with respect to the uniform distribution on the convex body that is bounded above by a constant). Our upper bound is polynomial in n, R and $\frac{1}{\epsilon}$ , where we assume that the convex body contains the unit $\Vert\cdot\Vert_\infty$ -unit ball $B_\infty$ and is contained in its R-dilation $R\cdot B_\infty$ . Whether CHR has a polynomial mixing time has been an open question.

Warm Start Method for Solving Chance Constrained Optimal Control Problems Using Biased Kernel Density Estimators

A warm start method is developed for efficiently solving complex chance constrained optimal control problems. The warm start method addresses the computational challenges of solving chance constrained optimal control problems using biased kernel density estimators and Legendre-Gauss-Radau collocation with an $hp$ adaptive mesh refinement method. To address the computational challenges, the warm start method improves both the starting point for the chance constrained optimal control problem, as well as the efficiency of cycling through mesh refinement iterations. The improvement is accomplished by tuning a parameter of the kernel density estimator, as well as implementing a kernel switch as part of the solution process. Additionally, the number of samples for the biased kernel density estimator is set to incrementally increase through a series of mesh refinement iterations. Thus, the warm start method is a combination of tuning a parameter, a kernel switch, and an incremental increase in sample size. This warm start method is successfully applied to solve two challenging chance constrained optimal control problems in a computationally efficient manner using biased kernel density estimators and Legendre-Gauss-Radau collocation.

A high-resolution search for the Hα emission line of the accreting companion GQ Lup b with ESPRESSO

<p>In the current theories of planet formation, the amount of energy that a forming gas giant retains from its accretion flow is still unknown. This unconstrained parameter has a large impact on the post-formation evolution of the new planet, as it defines its initial temperature and luminosity. Models have been developed, ranging from “hot-start” models assuming that all the energy is retained internally, to “cold-start” ones assuming that everything is radiated away, and "warm-start" ones in between. Their coexistence introduces large degeneracies on the determination of age and mass in direct imaging observations, as these studies use the cold or hot-start models to infer these parameters from the observed luminosity of a planet. A promising way of solving this problem is the study of atomic emission lines originating from the hot gas shocked by the accretion flow. Recently, Aoyama et al. (2018, 2020) presented simulations of hydrogen lines emitted by the accretion shock onto the circumplanetary disk and the planetary surface. They showed that the line luminosity and width can be used to infer the protoplanet mass, thus giving an estimation that is independent from the evolution models. They applied it to the case of PDS70 b and c (Aoyama & Ikoma 2019, Hashimoto et al. 2020), but were ultimately limited by the spectral resolution of the MUSE observations they used (R ~ 2500). In this context, our team recently proposed and carried out a pilot program using the VLT/ESPRESSO fiber-fed spectrograph, equipped with very high resolution (R = 190 000), to characterize the Hα line of the young substellar companion GQ Lup b. We will present in this poster how these observations were conducted, the methods used to remove the contamination from the host star, and the results we obtained.</p>

Explaining inference queries with bayesian optimization

Obtaining an explanation for an SQL query result can enrich the analysis experience, reveal data errors, and provide deeper insight into the data. Inference query explanation seeks to explain unexpected aggregate query results on inference data; such queries are challenging to explain because an explanation may need to be derived from the source, training, or inference data in an ML pipeline. In this paper, we model an objective function as a black-box function and propose BOExplain, a novel framework for explaining inference queries using Bayesian optimization (BO). An explanation is a predicate defining the input tuples that should be removed so that the query result of interest is significantly affected. BO --- a technique for finding the global optimum of a black-box function --- is used to find the best predicate. We develop two new techniques (individual contribution encoding and warm start) to handle categorical variables. We perform experiments showing that the predicates found by BOExplain have a higher degree of explanation compared to those found by the state-of-the-art query explanation engines. We also show that BOExplain is effective at deriving explanations for inference queries from source and training data on a variety of real-world datasets. BOExplain is open-sourced as a Python package at https://github.com/sfu-db/BOExplain.

Warm-starting quantum optimization

There is an increasing interest in quantum algorithms for problems of integer programming and combinatorial optimization. Classical solvers for such problems employ relaxations, which replace binary variables with continuous ones, for instance in the form of higher-dimensional matrix-valued problems (semidefinite programming). Under the Unique Games Conjecture, these relaxations often provide the best performance ratios available classically in polynomial time. Here, we discuss how to warm-start quantum optimization with an initial state corresponding to the solution of a relaxation of a combinatorial optimization problem and how to analyze properties of the associated quantum algorithms. In particular, this allows the quantum algorithm to inherit the performance guarantees of the classical algorithm. We illustrate this in the context of portfolio optimization, where our results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth. Likewise, Recursive QAOA for MAXCUT problems shows a systematic increase in the size of the obtained cut for fully connected graphs with random weights, when Goemans-Williamson randomized rounding is utilized in a warm start. It is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.

A Warm-start Digital CRISPR-based Method for the Quantitative Detection of Nucleic Acids

Nucleic acids-based molecular diagnostic tools incorporating the CRISPR/Cas system are being developed as rapid and sensitive methods for pathogen detection. However, most CRISPR/Cas-based diagnostics lack quantitative detection ability. Here, we report Warm-Start RApid DIgital Crispr Approach (WS-RADICA), which uses commercially available digital chips for the rapid, sensitive, and quantitative detection of nucleic acids. WS-RADICA detected as little as 1 copy/μL SARS-CoV-2 RNA in 40 min (qualitative detection) or 60 min (quantitative detection). WS-RADICA can be easily adapted to various digital devices: two digital devices were evaluated for both DNA and RNA quantification, with linear dynamic ranges of 0.8-12777 copies/μL for DNA and 1.2-18391 copies/μL for RNA (both R2 values > 0.99). Moreover, WS-RADICA had greater sensitivity and inhibitor tolerance than a bulk RT-LAMP-Cas12b reaction and similar performance to RT-qPCR and RT-dPCR. Given its speed, sensitivity, quantification capability, and inhibitor tolerance, WS-RADICA shows great promise for a variety of applications requiring nucleic acid quantification.