Research
Research
Research
Research
801+ open-access research outputs.
We estimate the maximum ratio between the $\sigma_t$- and $\sigma$-irregularity for graphs and trees of order $n$, which are respectively bounded by $\Theta(n^{5/2})$ and $n-2$. This answers a questio…
The cross-ratio degree problem is about counting rational curves with $n$ marked points satisfying $n-3$ cross-ratio conditions. This problem has a tropical analogue which provides the same number, as…
We show that there is no universal upper bound for the systolic ratio of Bott-integrable contact forms on closed 3-manifolds, thus providing further evidence for the relative flexibility of integrable…
The number $\sigma_k(G)$ of induced subgraphs with size $k$ of a graph $G$ was introduced recently as the number of $k$-nearly independent vertex subsets of $G$. Results highlighting similarity and di…
The concept of input-independent computational time for chemistry-based analog computers was introduced in Anderson-Joshi (2025), where it was shown that arithmetic operations can be computed in a fix…
We show that the geometric aspect ratio of the Twin Dragon equals $1/\varphi$, where $\varphi = (1+\sqrt{5})/2$ is the golden ratio. The result follows by solving the covariance fixed-point equation f…
This work uses mostly model-theoretic methods to establish new proof-theoretic theorems about several axiomatic theories of truth over KP (Kripke-Platek set theory) and stronger theories, especially Z…
Affine geometry is usually regarded as a framework in which metric notions such as distance and angle are absent. However, just as projective geometry produces various metric geometries by introducing…
We explain how the spectrum of a closed embedded surface $\Sigma \subset \mathbb{R}^3$ relates to the Dirichlet spectrum of the bounded domain $\Omega \subset \mathbb{R}^3$ with $\partial \Omega = \Si…
We show exactness of the homotopy sequence for the logarithmic fundamental group in the case of log smooth, finitely presented, proper and saturated morphisms of fs log schemes over a field. This gene…
The transversal ratio of a polytope $P$ is the minimum proportion of vertices of $P$ required to intersect each facet of $P$. The weak chromatic number of $P$ is the minimum number of colors required …
We study recovery from incomplete random spatial samples for discretized fields arising as fixed-time snapshots of partial differential equations. The organizing parameter is the Fourier ratio $$ FR(g…
By exploiting the arithmetic homotopy of the moduli spaces of curves, Galois-Teichm\"uller theory stands at the interface of braid-mapping class groups and of anabelian geometry. Starting from the cla…
We revisit the golden sieve, a self-referential deletion process on increasing sequences of positive integers introduced by the author in 2002. Applied to the natural numbers, the sieve produces the W…
We study density estimation in Kullback-Leibler divergence: given an i.i.d. sample from an unknown density $p^\star$, the goal is to construct an estimator $\widehat{p}$ such that $\mathrm{KL}(p^\star…
Adaptive systems must strike a balance between prediction and surprise to thrive in uncertain environments. We propose an information-theoretic balance function, $ f(p) = -(1 - p)\ln(1 - p) + \ln p $,…
This paper develops a unified framework for asymptotically minimax robust hypothesis testing under distributional uncertainty, applicable to both Bayesian and Neyman--Pearson formulations (Type-I and …
Let $K$ be a square in the plane and $\rho_K(x,y)$ be the hyperbolic distance between $x$, $y\in K$. Denote by $s_K(x,y)$ the triangular ratio metric in $K$; for $x\neq y$ the value of $s_K(x,y)$ equa…
Policy-gradient methods are widely used in reinforcement learning, yet training often becomes unstable or slows down as learning progresses. We study this phenomenon through the noise-to-signal ratio …
In this paper we focus on providing sufficient conditions for some transform orders for which the quantile densities ratio is non-monotone and, therefore, the convex transform order does not hold. The…
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