Research
Research
Research
Research
2,302+ open-access research outputs.
We consider a class of nonlinear parabolic equations \[ \dfrac{\partial}{\partial t} b(u)-\nabla \cdot (A(x,t,u,\nabla u))+H(x,t,\nabla u)=f , \] where $H$ is a nonlinear lower order term sati…
Let $\mathcal{OP}_n$ be the monoid of all orientation-preserving full transformations on $X_n=\{1,\dots, n\}$ with the natural order. For $\alpha \in \mathcal{OP}_n$, let $F(\alpha)=\{y\in X_n: y\alph…
Adversarial Training (AT) is one of the most effective methods for developing robust deep neural networks (DNNs). However, AT faces a trade-off problem between clean accuracy and adversarial robustnes…
Robust uncertainty quantification is increasingly important in modern data analysis and is often formalized under Huber's model, which allows an $\varepsilon$-fraction of arbitrary corruptions. In man…
We study a game-theoretic model of epidemic control in a large population with finitely many groups and non-cooperative individuals. In the model, individuals jointly choose their socialization levels…
Let $G$ be a graph and $S \subseteq V(G)$. In the cycle convexity, we say that $S$ is \textit{cycle convex} if for any $u\in V(G)\setminus S$, the induced subgraph of $S\cup\{u\}$ contains no cycle th…
For a simple graph $G$ with $n$ vertices, let $A_G$ denote the adjacency matrix of $G$, and let $\lambda_1(G) \geq \lambda_2(G) \geq \dots \geq \lambda_n(G)$ be its eigenvalues. For an integer $p \geq…
On generalized Heisenberg-type groups $\mathbb{G}(2n,m,\mathbb{U},\mathbb{W})$, we give uniform volume estimates for the ball defined by a large class of Carnot-Carath\'{e}odory distances, and establi…
The present work is a continuation of our earlier investigation with the primary objective to systematically calculate the $E2$ matrix elements using the microscopic approach of the triaxial projected…
Reliable position and attitude sensing is critical for highly automated vehicles that operate on conventional roadways. Lidar sensors are increasingly incorporated into pose-estimation systems. Despit…
This is an extended version of our publication Learning state machines from data streams: A generic strategy and an improved heuristic, International Conference on Grammatical Inference (ICGI) 2023, R…
Since the breakthrough superpolynomial multilinear formula lower bounds of Raz (Theory of Computing 2006), proving such lower bounds against multilinear algebraic branching programs (mABPs) has been a…
Black hole thermodynamics in Lorentz-violating gravity is subtle because different excitations propagate at different speeds and hence identify different causal horizons. We revisit Einstein--AEther g…
Finite families of biorthogonal rational functions and orthogonal polynomials of Racah-type are studied within a unified algebraic framework based on the meta Racah algebra and its finite-dimensional …
The $k$-means problem is a classic objective for modeling clustering in a metric space. Given a set of points in a metric space, the goal is to find $k$ representative points so as to minimize the sum…
Retrieval-Augmented Generation (RAG) enhances Large Language Models (LLMs) with external knowledge but remains vulnerable to low-authority sources that can propagate misinformation. We investigate whe…
Individual head-related transfer functions (HRTFs) are essential for accurate spatial audio binaural rendering but remain difficult to obtain due to measurement complexity. This study investigates whe…
We determine the optimal universal growth scale for the integral means of normalized logarithmic derivatives in the Carath\'eodory class. This resolves a problem of D.~K.~Thomas.…
We prove an asymptotic formula for the second moment of the first derivative of quadratic twists of modular $L$-functions with three leading order main terms. It improves the previous result of Kumar …
Approaches to calculate SU(N) colored knot invariants (HOMFLY-PT polynomials) are well and widely developed. However, SO(N) case is mostly forgotten. With this paper we want to start the discusion of …
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