Research
Research
Research
Research
185+ open-access research outputs.
In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) published a thought experiment that is entirely correct, has been demonstrated in real experiments, and is now the most famous in quantu…
We provide a positive answer to an old problem of Jonathan K. Simon: if $K$ and $K'$ are two knots such that there is an epimorphism from the knot group of $K$ to the knot group of $K'$, then the genu…
Tensegrity robots possess lightweight and resilient structures but present significant challenges for state estimation due to compliant and distributed ground contacts. This paper introduces a symmetr…
The world of primes has many gaps between evidence and theorems. Here, we review Legendre's conjecture on primes between consecutive squares and recent progress on the weaker question of primes betwee…
About 40 years ago Jonathan and Peter Borwein discovered the series identity $$ \sum_{n=0}^\infty \frac{(-1)^n(6n)!}{(3n)!(n!)^3} \frac{(A+nB)}{C^{n+1/2}} = \frac{1}{12\pi} $$ where \begin{align*} A&=…
Large Language Models (LLMs) can simulate person-like things which at least appear to have stable behavioural and psychological dispositions. Call these things characters. Are characters minded and ps…
Glacial segmentation is essential for reconstructing past glacier dynamics and evaluating climate-driven landscape change. However, weak optical contrast and the limited availability of high-resolutio…
Motion prediction has been studied in different contexts with models trained on narrow distributions and applied to downstream tasks in human motion prediction and robotics. Simultaneously, recent eff…
Let $(M^5,g)$ be a five-dimensional non-trivial simply-connected compact quasi-Einstein manifold with boundary. If $M$ has constant scalar $R$, Johnatan Costa, Ernani Ribeiro Jr, and Detang Zhou show …
We present a randomized polynomial-time simplex algorithm with higher probability and tighter bounds for linear programming by applying improved quasi-convex properties, a logarithmic rounding on a gi…
Large language models are increasingly being used in critical domains of politics, business, and education, but the nature of their normative ethical judgment remains opaque. Alignment research has, t…
For a set $E \subseteq \mathbb{F}_q^d$, the distance set is defined as $\Delta(E) := \{\|\mathbf{x} - \mathbf{y}\| : \mathbf{x}, \mathbf{y} \in E\}$, where $\|\cdot\|$ denotes the standard quadratic f…
The rapid advancement of Generative AI has raised significant questions regarding its ability to produce creative and novel outputs. Our recent work investigates this question within the domain of che…
We introduce a new group action on set systems, constructed as a semidirect product of a permutation group and a group generated by twist and loop complementation operations on a single element. This …
In this paper, we propose a new heteroskedasticity and autocorrelation consistent covariance matrix estimator based on the prewhitened kernel estimator and a localized leave-one-out frequency domain c…
We address a problem posed by Nathan Kaplan in the 2014 Combinatorial and Additive Number Theory session: finding the largest subset $H \subseteq (\mathbb{Z}/4\mathbb{Z})^n$ with no distinct $x, y, z …
This oral history interview provides Yakir Aharonov's perspective on the theoretical discovery of the Aharonov-Bohm effect in 1959, during his PhD studies in Bristol with David Bohm, the reception of …
The purpose of this paper is to translate the expression of rank 2 cluster scattering diagrams via dilogarithm elements into via formal power series. As a corollary, we prove some conjectures introduc…
In recent work, the author, in collaboration with Allen, Long, and Tu, developed the Explicit Hypergeometric Modularity Method (EHMM), which establishes the modularity of a large class of hypergeometr…
Recent work (Nathan et al, arXiv:2405.05671) proposed an architecture for a dissipatively stabilized GKP qubit, and protocols for protected Clifford gates. Here we propose a protocol for a protected n…
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