Duy Ho

Duy Ho

We study the Hermitian hull-variation problem for vector rank-metric codes. Except for one parameter pair, we show that the Hermitian hull dimension of such a code can be reduced to any smaller value within its equivalence class, and in particular every such code is equivalent to a Hermitian LCD code. We then address the existence of maximum rank distance (MRD) codes with prescribed Hermitian hull dimension. To this end, we introduce the notion of a \emph{scaled trace-self-dual basis} of a finite field extension, which exists in all cases, and use it to construct Hermitian self-orthogonal generalized Gabidulin codes for every prime power. Combined with the hull-variation theorem, this yields MRD codes attaining every admissible Hermitian hull dimension.

Kanat Abdukhalikov, Duy Ho

Additive codes have attracted considerable attention for their potential to outperform linear codes. However, distinguishing strictly additive codes from those that are equivalent to linear codes remains a fundamental challenge. To resolve this ambiguity, we introduce a deterministic test that requires only the generator matrix of the code. We apply this test to verify the strict additivity of several quaternary additive codes recently reported in the literature. Conversely, we demonstrate that a previously known additive complementary dual (ACD) code is equivalent to a linear Hermitian LCD code, thereby improving the best-known bounds for such linear codes.

Udiptaman Das, Krishnasai B. Atmakuri, Duy Ho et al.

Large language models (LLMs) offer new opportunities for constructing knowledge graphs (KGs) from unstructured clinical narratives. However, existing approaches often rely on structured inputs and lack robust validation of factual accuracy and semantic consistency, limitations that are especially problematic in oncology. We introduce an end-to-end framework for clinical KG construction and evaluation directly from free text using multi-agent prompting and a schema-constrained Retrieval-Augmented Generation (KG-RAG) strategy. Our pipeline integrates (1) prompt-driven entity, attribute, and relation extraction; (2) entropy-based uncertainty scoring; (3) ontology-aligned RDF/OWL schema generation; and (4) multi-LLM consensus validation for hallucination detection and semantic refinement. Beyond static graph construction, the framework supports continuous refinement and self-supervised evaluation, enabling iterative improvement of graph quality. Applied to two oncology cohorts (PDAC and BRCA), our method produces interpretable, SPARQL-compatible, and clinically grounded knowledge graphs without relying on gold-standard annotations. Experimental results demonstrate consistent gains in precision, relevance, and ontology compliance over baseline methods.

Duy Ho, Trygve Johnsen

The intersection of a linear code with its dual is called the hull of the code. It is known that, for classical linear codes under the Hamming-metric, the dimension of the hull can be reduced up to equivalence. This phenomenon leads to the so-called hull-variation problem formulated by Hao Chen in 2023. In this paper, we consider the analogous problem for vector rank-metric codes, along with their associated matrix codes and extended block codes. Our results include the fact that every vector rank-metric code over any finite field $\mathbb{F}_q$, in particular when $q=2$ or $q=3$, is equivalent to an LCD code.

Ahmed Alanazi, Duy Ho, Yugyung Lee

Robots navigating dynamic, cluttered, and semantically complex environments must integrate perception, symbolic reasoning, and spatial planning to generalize across diverse layouts and object categories. Existing methods often rely on static priors or limited memory, constraining adaptability under partial observability and semantic ambiguity. We present GRIP, Grid-based Relay with Intermediate Planning, a unified, modular framework with three scalable variants: GRIP-L (Lightweight), optimized for symbolic navigation via semantic occupancy grids; GRIP-F (Full), supporting multi-hop anchor chaining and LLM-based introspection; and GRIP-R (Real-World), enabling physical robot deployment under perceptual uncertainty. GRIP integrates dynamic 2D grid construction, open-vocabulary object grounding, co-occurrence-aware symbolic planning, and hybrid policy execution using behavioral cloning, D* search, and grid-conditioned control. Empirical results on AI2-THOR and RoboTHOR benchmarks show that GRIP achieves up to 9.6% higher success rates and over $2\times$ improvement in path efficiency (SPL and SAE) on long-horizon tasks. Qualitative analyses reveal interpretable symbolic plans in ambiguous scenes. Real-world deployment on a Jetbot further validates GRIP's generalization under sensor noise and environmental variation. These results position GRIP as a robust, scalable, and explainable framework bridging simulation and real-world navigation.