Blog
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...
Generating heterogeneous data on gene trees
We introduce GenPhylo, a Python module that simulates nucleotide sequence data along a phylogeny avoiding the restriction of continuous-time Markov processes. GenPhylo uses directly a general Markov model and therefore naturally incorporates heterogeneity across lineages. We solve the challenge of generating transition...
FailLite: Failure-Resilient Model Serving for Resource-Constrained Edge Environments
Model serving systems have become popular for deploying deep learning models for various latency-sensitive inference tasks. While traditional replication-based methods have been used for failure-resilient model serving in the cloud, such methods are often infeasible in edge environments due to significant resource...
Positive-tone Nanolithography of Antimony Trisulfide with Femtosecond Laser Wet-etching
Antimony trisulfide ($Sb_{2}S_{3}$), as an emerging material for integrated photonic devices, has attracted significant attention due to its high index, low loss, and phase-changing property in the optical regime. However, conventional lithography-based fabrication methods involve complex, time-consuming, multistep processes, rendering the photonic...
The area of spheres in the Brownian plane
We consider the area of spheres centered at the distinguished point in the Brownian plane. As a function of the radius, the resulting process has continuously differentiable sample paths. Furthermore, the pair consisting of the process and its derivative is time-homogeneous Markov...
The effects of pressure loads in the dimension reduction of elasticity models
We study the dimensional reduction from three to two dimensions in hyperelastic materials subject to a live load, modeled as a constant pressure force. Our results demonstrate that this loading has a significant impact in higher-order scaling regimes, namely those associated with...