Research
Research
Research
Research
828+ open-access research outputs.
Stoquasticity, originating in sign-problem-free physical systems, gives rise to $\sf StoqMA$, introduced by Bravyi, Bessen, and Terhal (2006), a quantum-inspired intermediate class between $\sf MA$ an…
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…
Ternary coherent configurations are, on the one hand, a special case of multidimensional coherent configurations introduced by L. Babai (2016), and, on the other hand, a natural generalization of asso…
The most important architectural problem in AI is not the size of the model but the absence of a layer that carries forward what the model has come to understand. Sessions end. Context windows fill. M…
Source localization in complex networks is a rapidly advancing field with numerous real-world applications, including determining the source of misinformation. In this work, we model information sprea…
In this paper, we exhibit $\textsf{AC}^{3}$ isomorphism tests for coprime extensions $H \ltimes N$ where $H$ is elementary Abelian and $N$ is Abelian; and groups where $\text{Rad}(G) = Z(G)$ is elemen…
ATANT v1.0 (arXiv:2604.06710) defined continuity as a system property with 7 required properties and introduced a 10-checkpoint, LLM-free evaluation methodology validated on a 250-story corpus. Since …
We present ATANT (Automated Test for Acceptance of Narrative Truth), an open evaluation framework for measuring continuity in AI systems: the ability to persist, update, disambiguate, and reconstruct …
Cardiac magnetic resonance (CMR) is a cornerstone for diagnosing cardiovascular disease. However, it remains underutilized due to complex, time-consuming interpretation across multi-sequences, phases,…
Let $G$ be a strongly regular graph of prime order $p$ with connection degree $k \geq 6$. We prove that the \emph{quantum walk characteristic polynomial} $\chi_q(G,\lambda) \coloneqq \det(\lambda I - …
Determining the randomized (or distributional) communication complexity of disjointness is a central problem in communication complexity, having roots in the foundational work of Babai, Frankl, and Si…
We prove a multilevel non-shadow refinement of the Alon--Babai--Suzuki (ABS) nonuniform restricted-intersection theorem. Let $K=\{k_1,\dots,k_r\}$ and let $L$ be a set with $|L|=s$. If $\mathcal{F}\su…
Targeted hub removal is known to weaken connectivity in heterogeneous networks. We show that in Barab\'asi--Albert networks the same intervention can also shift Watts threshold dynamics across the cas…
We study the empirical spectral distribution of the normalized Laplacian of linear preferential attachment graphs in the Barab{\'a}si-Albert regime with fixed out-degree. For the resulting sequence of…
In the modelling of social systems, opinion latency is the idea that once an agent changes its opinion, there will be a period of time where it is immune to other changes. When added to the voter mode…
In multiphase flows, kinetic and interfacial energies coexist, and their mutual conversion can strongly influence the overall energy balance. However, in statistically steady flows these energy reserv…
One of the most well-known conjectures concerning Hamiltonicity in graphs asserts that any sufficiently large connected vertex transitive graph contains a Hamilton cycle. In this form, it was first wr…
Large-scale video repositories are increasingly available for modern video understanding and generation tasks. However, transforming raw videos into high-quality, task-specific datasets remains costly…
There are a number of existing studies analysing the convergence behaviour of graph neural networks on large random graphs. Unfortunately, the majority of these studies do not model correlations betwe…
Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially wh…
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