Research
Research
Research
Research
3,923+ open-access research outputs.
In a wireless network, the spatial location of the transmitters has a large impact on the achievable rate at each user location. The optimal placement of -- for example -- cellular base stations is a …
We consider the modular action of the symmetric group $S_n$ on $R = k[x_1,\ldots,x_n]$ when $\mathrm{char}(k) = p \leq n$. We show that the image of the transfer map $R\to R^{S_n}$ is an elimination i…
We develop a geometric procedure for finding the Ap\'ery set of any numerical semigroup with embedding dimension four. We use this method to find the Frobenius numbers, genera, Betti elements, minimal…
We consider a Ziegler pair of plane arrangements, that is two plane arrangements $\mathcal{A}:f=0$ and $\mathcal{A}':f'=0$ in the projective space $\mathbb{P}^3$, such that the intersection lattices $…
Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise while distorting gl…
Electromagnetic signals propagating across interstellar distances are subject to simultaneous distortion by seven distinct physical mechanisms: relativistic Doppler shift, stellar aberration, interste…
Explicit formulas determining the dimension and the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$ are given in terms of the graded Betti numbers of the minimal free resolution o…
Gorenstein toric contact manifolds are good toric contact manifolds with zero first Chern class that are completely determined by certain integral convex polytopes called toric diagrams. The Ehrhart p…
The Dyson Minds 2025 Workshop, held at the Center for Brains, Minds & Machines at MIT and organized by Penn State, MIT, and The Ultraintelligence Foundation, brought together researchers in astrophysi…
We prove that any closed, convex hypersurface in an $(n+1)$-dimensional Riemannian manifold with $\lceil \frac{n}{2} \rceil$-positive curvature operator is a rational homology sphere with finite funda…
Let $X_t = B_t + \mu t$, $t \geq 0$, be planar Brownian motion with nonzero drift, and let $K_t^r = \{x \in \mathbb{R}^2 : {\rm dist}(x, X[0,t]) \leq r\}$ be the radius-$r$ Wiener sausage up to time $…
This paper presents DDF2Pol, a lightweight dual-domain convolutional neural network for PolSAR image classification. The proposed architecture integrates two parallel feature extraction streams, one r…
We present the second paper in our program characterizing the impact of massive neutrinos on the multiscale cosmic web using global topology and persistent homology. Building on the methodology establ…
The spectral kernel field equation R[k] = T[k] lacks a conservation-law analog. We prove (i) the fixed-point flow is strictly volume-expanding (tr DF > 0), precluding automatic conservation, and (ii) …
We introduce and study small covers that are pullbacks from the simplex, extending pullbacks from the linear model. Our main result gives several equivalent characterizations of this class, including …
Rapid growth in electric-vehicle (EV) charging demand is placing increasing stress on distribution power networks (DPNs), whose hosting capacity is often limited and spatially uneven. Beyond demonstra…
Chang'E-4 (CE4), the first mission to soft-land on the lunar farside, provides a unique opportunity for astronomical observations from an environment shielded from terrestrial radio interference, and …
Perimeter control is an effective urban traffic management strategy that regulates inflow to congested urban regions using aggregate network dynamics. While existing approaches primarily optimize syst…
We prove central limit theorems (CLTs) for topological functionals of Bernoulli bond percolation on infinite graphs beyond the Euclidean lattice $\mathbb{Z}^{d}$. For quasi-transitive graphs of subexp…
P. Di Francesco first introduced the "Aztec triangle" in his study of the relationship between the twenty-vertex model and domino tilings. He conjectured an exact formula for the number of tilings of …
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