blog
Predictive Synthesis of Control Barrier Functions and its Application to Time-Varying Constraints
This paper presents a systematic method for synthesizing a Control Barrier Function (CBF) that encodes predictive information into a CBF. Unlike other methods, the synthesized CBF can account for changes and time-variations in the constraints even when constructed for time-invariant constraints. This...
Eccentric or circular? A reanalysis of binary black hole gravitational wave events for orbital eccentricity signatures
We present a reanalysis of 17 gravitational-wave events detected with Advanced LIGO and Advanced Virgo in their first three observing runs, using the new IMRPhenomTEHM model — a phenomenological time-domain multipolar waveform model for aligned-spin black-hole binaries in elliptical orbits with two...
Causal machine learning for high-dimensional mediation analysis using interventional effects mapped to a target trial
Causal mediation analysis examines causal pathways linking exposures to disease. The estimation of interventional effects, which are mediation estimands that overcome certain identifiability problems of natural effects, has been advanced through causal machine learning methods, particularly for high-dimensional mediators. Recently, it has...
Hyperbolic nonlinear Schrödinger equations on $\mathbb{R}\times \mathbb{T}$
In this paper, we consider the hyperbolic nonlinear Schr\”odinger equations (HNLS) on $\mathbb{R}\times\mathbb{T}$. We obtain the sharp local well-posedness up to the critical regularity for cubic nonlinearity and in critical spaces for higher odd nonlinearities. Moreover, when the initial data is small,...
Gaussian behaviors: representations and data-driven control
We propose a modeling framework for stochastic systems based on Gaussian processes. Finite-length trajectories of the system are modeled as random vectors from a Gaussian distribution, which we call a Gaussian behavior. The proposed model naturally quantifies the uncertainty in the trajectories,...
On commuting integer matrices
Given $d, N \in \mathbb{N}$, we define $\mathfrak{C}_d(N)$ to be the number of pairs of $d\times d$ matrices $A,B$ with entries in $[-N,N] \cap \mathbb{Z}$ such that $AB = BA$. We prove that $$ N^{10} \ll \mathfrak{C}_3(N) \ll N^{10},$$ thus confirming a...
Quantum Discrete Variable Representations
We present a fault-tolerant quantum algorithm for implementing the Discrete Variable Representation (DVR) transformation, a technique widely used in simulations of quantum-mechanical Hamiltonians. DVR provides a diagonal representation of local operators and enables sparse Hamiltonian structures, making it a powerful alternative to...
Radiative equilibrium boundary condition and correlation analysis on catalytic surfaces in DSMC
This study integrates radiative equilibrium boundary conditions on a catalytic surface within the Direct Simulation Monte Carlo (DSMC) method. The radiative equilibrium boundary condition is based on the principle of energy conservation at each surface element, enabling the accurate capture of spatially...
Adaptive PCA-Based Outlier Detection for Multi-Feature Time Series in Space Missions
Analyzing multi-featured time series data is critical for space missions making efficient event detection, potentially onboard, essential for automatic analysis. However, limited onboard computational resources and data downlink constraints necessitate robust methods for identifying regions of interest in real time. This work...
Recovering Nesterov accelerated dynamics from Heavy Ball dynamics via time rescaling
In a real Hilbert space, we consider two classical problems: the global minimization of a smooth and convex function $f$ (i.e., a convex optimization problem) and finding the zeros of a monotone and continuous operator $V$ (i.e., a monotone equation). Attached to...