Research
Research
Research
Research
242+ 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…
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…
The POEMMA-Balloon with Radio (PBR) is a NASA mission designed to study Ultra-High-Energy Cosmic Rays and Very-High-Energy Neutrinos from a balloon platform. Serving as a precursor to the planned POEM…
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…
We investigate the feasibility of detecting extensive air showers via their geo-synchrotron X-ray emission from high-altitude platforms. Starting from first principles, we derive a differential expres…
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 …
Integrating Information and Communications Technology (ICT) devices into the power grid brings many benefits. However, it also exposes the grid to new potential cyber threats. Many control and protect…
The increasing integration of IoT-connected devices in smart grids has introduced new vulnerabilities at the distribution level. Of particular concern is the potential for cyberattacks that exploit hi…
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