Research
Research
Research
Research
2,547+ open-access research outputs.
We classify fillable contact structures on all negative-definite star-shaped plumbings. Along the way, we show that such Seifert fibred spaces admit a unique negative maximal twisting number, and comp…
We adapt the Ozsv\'ath-Szab\'o full path algorithm to every star-shaped graph and establish a correspondence between negative-twisting tight contact structures on any Seifert fibred space over $S^2$, …
Knots and links represent a fundamental motif of non-local connectivity that permeates the physical sciences from string theory to protein folds. While spectral braiding has been explored in two-band …
We develop a Koszul-theoretic framework for comparing classical Alexander-type invariants with infinitesimal invariants arising from finite-type commutative differential graded algebra models. The cen…
\textbf{Background:} Regulatory frameworks for AI in healthcare, including the EU AI Act and FDA guidance on AI/ML-based medical devices, require clinical decision support to demonstrate not only accu…
Let $Y_-$ and $Y_+$ be two compact 3-manifolds with empty or toroidal boundary. A 4-dimensional ribbon homology cobordism is a homologically trivial cobordism built with 1-handles and 2-handles. In th…
The Nobel Prize in literature 1965 was awarded Mikhail Sholokhov (1905-1984), for the epic novel Tikhij Don about Cossack life and the birth of a new Soviet society (And Quiet Flows the Don, or The Qu…
Recent advancements in self-supervised learning have led to powerful surgical vision encoders capable of spatiotemporal understanding. However, extending these visual foundations to multi-modal reason…
We prove a suitable fibration theorem over quasi-trivial tori that, through an approach developed by Harpaz and Wittenberg, implies so-called solvable descent. In particular, this gives a positive ans…
In this paper, we investigate a quandle structure induced by an augmented rack arising from a gauge transformation group. We construct a quandle from a principal bundle and its discrete generalization…
In this paper, we investigate structural properties of the Cayley graph of a quandle and describe this graph for several important classes of quandles, including conjugation, Takasaki, dihedral, and A…
Masking-based post-hoc explanation methods, such as KernelSHAP and LIME, estimate local feature importance by querying a black-box model under randomized perturbations. This paper formulates this proc…
Functional connectivity analysis is an important tool for characterizing interactions among brain regions, particularly in studies of neurodegenerative disorders such as Alzheimer's disease (AD). Gaus…
The widespread use of clickbait headlines, crafted to mislead and maximize engagement, poses a significant challenge to online credibility. These headlines employ sensationalism, misleading claims, an…
Deep neural networks can predict human judgments, but this does not imply that they rely on human-like information or reveal the cues underlying those judgments. Prior work has addressed this issue us…
We determine the irreducible ${\rm SL}(2,\mathbb{C})$-character variety of the 3-chain link exterior which is called the `magic $3$-manifold', and deduce a formula for the twisted Alexander polynomial…
Post-hoc feature attribution methods are widely deployed in safety-critical vision systems, yet their stability under realistic input perturbations remains poorly characterized. Existing metrics evalu…
It is well known that for $m\geq 2$ there are at most two non-equivalent $m$-knots with diffeomorphic exterior. Such pair of knots will be called $\textit{ non-reflexive knot pair}$. A classical probl…
For arborescent links, we present an efficient method of computing their Alexander polynomials. Applying this method, we express the Alexander polynomials of Montesinos links in terms of certain funct…
Random subspace method has wide security applications such as providing certified defenses against adversarial and backdoor attacks, and building robustly aligned LLM against jailbreaking attacks. How…
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