Research
Research
Research
Research
338+ open-access research outputs.
Under what condition is a random constraint satisfaction problem hard to refute by the sum-of-squares (SoS) algorithm? A sufficient condition is t-wise uniformity, that is, each constraint has a t-wis…
Electron backscatter diffraction is a powerful tool for mapping crystallographic microstructures. However, the primary crux to improving orientation accuracy and applying the technique to challenging …
High-Resolution Electron Backscatter Diffraction (HR-EBSD) has advanced rapidly in recent years, significantly improving elastic strain measurements and dislocation density evaluation with submicron s…
This paper extends the Kikuchi method to give algorithms for decisional $k$-sparse Learning With Errors (LWE) and $k$-sparse Learning Parity with Noise (LPN) problems for higher moduli $q$. We create …
Transmission Kikuchi diffraction in the scanning electron microscope has gained popularity as a materials characterization technique for its high throughput and nanometer-level spatial resolution. Whi…
Suppose $E, F$ are Borel sets in the plane, $\dim_{\mathcal{H}} E>1$, $\dim_{\mathcal{H}} E+\dim_{\mathcal{H}} F>2$, and $F$ has equal Hausdorff and packing dimension. We prove that there exists $y\in…
Exchange of two neutrinos (as well as other fermions) generates a long-range parity-violating (PV) potential of the form $\sim G^2/r^5$, with characteristic range $\hbar/(2m_\nu c)$. In atomic systems…
Data-parallel (DP) training with synchronous all-reduce is a dominant paradigm for full-parameter fine-tuning of large language models (LLMs). While parameter synchronization guarantees numerical equi…
The singularity theory of rational functions, i.e., the quotient of two polynomials, has been investigated in the past two decades. The Bernstein-Sato polynomial of a rational function has recently be…
Let $H$ be a Hopf algebra over a field $k$ with a bijective antipode. It is proved that the Gorenstein global dimension of $H$ coincides with the Gorenstein projective dimension of the trivial left (o…
In the technique of Electron Backscatter Diffraction (EBSD), the accurate detection and identification of different phases existing in a sample is often limited by overlapping Kikuchi diffraction patt…
In the present study, correlative transmission Kikuchi diffraction transmission electron microscopy (TKD-TEM) measurements, atom probe tomography (APT), and density functional theory (DFT) calculation…
Electron backscatter diffraction is one of the most prevalent techniques used for microstructural characterization. In recent years, there has been an increase in the use of data-driven methods to ana…
This paper presents several efficient decision procedures for trace equivalence of GKAT automata, which make use of on-the-fly symbolic techniques via SAT solvers. To demonstrate applicability of our …
The search for suitable datasets is the critical "first step" in data-driven research, but it remains a great challenge. Researchers often need to search for datasets based on high-level task descript…
We consider the Lotka-Volterra system and provide necessary conditions for an equilibrium to be stable. Our results naturally complement earlier fundamental results by N. Adachi, Y. Takeuchi, and H. T…
We find a family of compact $C^k$ hypersurfaces where the local Mizohata-Takeuchi Conjecture fails with a power loss of $R^{\alpha}$ for any $\alpha<\frac{n-1}{n-1+k}$. Moreover, this family is dense …
The $k$-$\mathsf{XOR}$ problem is one of the most well-studied problems in classical complexity. We study a natural quantum analogue of $k$-$\mathsf{XOR}$, the problem of computing the ground energy o…
Let $R^{\frac{1}{2}}$ be a large integer, and $\omega$ be a nonnegative weight in the $R$-ball $B_R=[0,R]^2$ such that $\omega(B_R)\le R$. For any complex sequence $\{a_n\}$, define the quadratic expo…
Electron back-scatter diffraction (EBSD) has traditionally relied upon methods such as the Hough transform and dictionary Indexing to interpret diffraction patterns and extract crystallographic orient…
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