Building surrogate models is one common approach when we attempt to learn unknown black-box functions. Bayesian optimization provides a framework which allows us to build surrogate models based on sequential samples drawn from the function and find t
he optimum. Tuning algorithmic parameters to optimize the performance of large, complicated black-box application codes is a specific important application, which aims at finding the optima of black-box functions. Within the Bayesian optimization framework, the Gaussian process model produces smooth or continuous sample paths. However, the black-box function in the tuning problem is often non-smooth. This difficult tuning problem is worsened by the fact that we usually have limited sequential samples from the black-box function. Motivated by these issues encountered in tuning, we propose a novel additive Gaussian process model called clustered Gaussian process (cGP), where the additive components are induced by clustering. In the examples we studied, the performance can be improved by as much as 90% among repetitive experiments. By using this surrogate model, we want to capture the non-smoothness of the black-box function. In addition to an algorithm for constructing this model, we also apply the model to several artificial and real applications to evaluate it.
This paper studies controlling segregation in social networks via exogenous incentives. We construct an edge formation game on a directed graph. A user (node) chooses the probability with which it forms an inter- or intra- community edge based on a u
tility function that reflects the tradeoff between homophily (preference to connect with individuals that belong to the same group) and the preference to obtain an exogenous incentive. Decisions made by the users to connect with each other determine the evolution of the social network. We explore an algorithmic recommendation mechanism where the exogenous incentive in the utility function is based on weak ties which incentivizes users to connect across communities and mitigates the segregation. This setting leads to a submodular game with a unique Nash equilibrium. In numerical simulations, we explore how the proposed model can be useful in controlling segregation and echo chambers in social networks under various settings.
Exotic spin-dependent interactions may be generated by exchanging hypothetical bosons that have been proposed to solve some mysteries in physics by theories beyond the standard model of particle physics. The search for such interactions can be conduc
ted by tabletop scale experiments using high precision measurement techniques. Here we report an experiment to explore the parity-odd interaction between moving polarized electrons and unpolarized nucleons using a magnetic force microscope. The polarized electrons are provided by the magnetic tip at the end of a silicon cantilever, and their polarizations are approximately magnetized in the plane of the magnetic coating on the tip. A periodic structure with alternative gold and silicon dioxide stripes provides unpolarized nucleons with periodic number density modulation. The exotic forces are expected to change the oscillation amplitude of the cantilever which is measured by a fiber laser interferometer. Data has been taken by scanning the tip over the nucleon source structure at constant separation, and no exotic signal related to the density modulation has been observed. Thus, the experiment sets a limit on the electron-nucleon coupling constant, $g_A^eg_V^Nleq 9times 10^{-15}$ for 15 $mu$m $le lambda le$ 180 $mu$m, using a direct force measurement method.
We report three new FRBs discovered by the Five-hundred-meter Aperture Spherical radio Telescope (FAST), namely FRB 181017.J0036+11, FRB 181118 and FRB 181130, through the Commensal Radio Astronomy FAST Survey (CRAFTS). Together with FRB 181123 that
was reported earlier, all four FAST-discovered FRBs share the same characteristics of low fluence ($leq$0.2 Jy ms) and high dispersion measure (DM, $>1000$ dmu), consistent with the anti-correlation between DM and fluence of the entire FRB population. FRB 181118 and FRB 181130 exhibit band-limited features. FRB 181130 is prominently scattered ($tau_ssimeq8$ ms) at 1.25 GHz. FRB 181017.J0036+11 has full-bandwidth emission with a fluence of 0.042 Jy ms, which is one of the faintest FRB sources detected so far. CRAFTS starts to built a new sample of FRBs that fills the region for more distant and fainter FRBs in the fluence-$rm DM_E$ diagram, previously out of reach of other surveys. The implied all sky event rate of FRBs is $1.24^{+1.94}_{-0.90} times 10^5$ sky$^{-1}$ day$^{-1}$ at the $95%$ confidence interval above 0.0146 Jy ms. We also demonstrate here that the probability density function of CRAFTS FRB detections is sensitive to the assumed intrinsic FRB luminosity function and cosmological evolution, which may be further constrained with more discoveries.
Optimizing k-space sampling trajectories is a challenging topic for fast magnetic resonance imaging (MRI). This work proposes to optimize a reconstruction algorithm and sampling trajectories jointly concerning image reconstruction quality. We paramet
erize trajectories with quadratic B-spline kernels to reduce the number of parameters and enable multi-scale optimization, which may help to avoid sub-optimal local minima. The algorithm includes an efficient non-Cartesian unrolled neural network-based reconstruction and an accurate approximation for backpropagation through the non-uniform fast Fourier transform (NUFFT) operator to accurately reconstruct and back-propagate multi-coil non-Cartesian data. Penalties on slew rate and gradient amplitude enforce hardware constraints. Sampling and reconstruction are trained jointly using large public datasets. To correct the potential eddy-current effect introduced by the curved trajectory, we use a pencil-beam trajectory mapping technique. In both simulations and in-vivo experiments, the learned trajectory demonstrates significantly improved image quality compared to previous model-based and learning-based trajectory optimization methods for 20x acceleration factors. Though trained with neural network-based reconstruction, the proposed trajectory also leads to improved image quality with compressed sensing-based reconstruction.
Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An important aspect
of these methods is how to preserve relative distances between points in the higher-dimensional space after reducing rows and columns to fit in a lower dimensional space. This aspect is important because conclusions based on faulty visual reasoning can be harmful. Judging dissimilar points as similar or similar points as dissimilar on the basis of a visualization can lead to false conclusions. To ameliorate this bias and to make visualizations of very large datasets feasible, we introduce two new algorithms that respectively select a subset of rows and columns of a rectangular matrix. This selection is designed to preserve relative distances as closely as possible. We compare our matrix sketch to more traditional alternatives on a variety of artificial and real datasets.
This paper proposes a new method for joint design of radiofrequency (RF) and gradient waveforms in Magnetic Resonance Imaging (MRI), and applies it to the design of 3D spatially tailored saturation and inversion pulses. The joint design of both wavef
orms is characterized by the ODE Bloch equations, to which there is no known direct solution. Existing approaches therefore typically rely on simplified problem formulations based on, e.g., the small-tip approximation or constraining the gradient waveforms to particular shapes, and often apply only to specific objective functions for a narrow set of design goals (e.g., ignoring hardware constraints). This paper develops and exploits an auto-differentiable Bloch simulator to directly compute Jacobians of the (Bloch-simulated) excitation pattern with respect to RF and gradient waveforms. This approach is compatible with emph{arbitrary} sub-differentiable loss functions, and optimizes the RF and gradients directly without restricting the waveform shapes. For computational efficiency, we derive and implement explicit Bloch simulator Jacobians (approximately halving computation time and memory usage). To enforce hardware limits (peak RF, gradient, and slew rate), we use a change of variables that makes the 3D pulse design problem effectively unconstrained; we then optimize the resulting problem directly using the proposed auto-differentiation framework. We demonstrate our approach with two kinds of 3D excitation pulses that cannot be easily designed with conventional approaches: Outer-volume saturation (90{deg} flip angle), and inner-volume inversion.
Topological data analysis (TDA) allows us to explore the topological features of a dataset. Among topological features, lower dimensional ones have recently drawn the attention of practitioners in mathematics and statistics due to their potential to
aid the discovery of low dimensional structure in a data set. However, lower dimensional features are usually challenging to detect from a probabilistic perspective. In this paper, lower dimensional topological features occurring as zero-density regions of density functions are introduced and thoroughly investigated. Specifically, we consider sequences of coverings for the support of a density function in which the coverings are comprised of balls with shrinking radii. We show that, when these coverings satisfy certain sufficient conditions as the sample size goes to infinity, we can detect lower dimensional, zero-density regions with increasingly higher probability while guarding against false detection. We supplement the theoretical developments with the discussion of simulated experiments that elucidate the behavior of the methodology for different choices of the tuning parameters that govern the construction of the covering sequences and characterize the asymptotic results.
Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow
the framework of circular coordinate representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular coordinate framework to take into account the roughness of circular coordinates in change-point and high-dimensional applications. We use a generalized penalty function instead of an $L_{2}$ penalty in the traditional circular coordinate algorithm. We provide simulation experiments and real data analysis to support our claim that circular coordinates with generalized penalty will detect the change in high-dimensional datasets under different sampling schemes while preserving the topological structures.
We report the discovery of a highly dispersed fast radio burst, FRB~181123, from an analysis of $sim$1500~hr of drift-scan survey data taken using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The pulse has three distinct emission
components, which vary with frequency across our 1.0--1.5~GHz observing band. We measure the peak flux density to be $>0.065$~Jy and the corresponding fluence $>0.2$~Jy~ms. Based on the observed dispersion measure of 1812~cm$^{-3}$~pc, we infer a redshift of $sim 1.9$. From this, we estimate the peak luminosity and isotropic energy to be $lesssim 2times10^{43}$~erg~s$^{-1}$ and $lesssim 2times10^{40}$~erg, respectively. With only one FRB from the survey detected so far, our constraints on the event rate are limited. We derive a 95% confidence lower limit for the event rate of 900 FRBs per day for FRBs with fluences $>0.025$~Jy~ms. We performed follow-up observations of the source with FAST for four hours and have not found a repeated burst. We discuss the implications of this discovery for our understanding of the physical mechanisms of FRBs.
