Research
Research
Research
Research
28+ open-access research outputs.
We reprove the generalized Nandakumar-Ramana Rao conjecture for the prime case using representation ring-graded Bredon cohomology. Our approach relies solely on the $RO(C_p)$-graded cohomology of conf…
The notion of a normal bit sequence was introduced by Borel in 1909; it was the first definition of an individual random object. Normality is a weak notion of randomness requiring only that all $2^n$ …
In order to investigate the chemical history of the entire MilkyWay, it is imperative to also study the dust-obscured regions, where most of the mass lies. The Galactic Center is an example of such a …
A decade ago two groups of authors, Karasev, Hubard and Aronov, and Blagojevi\'c and Ziegler, have shown that the regular convex partitions of a Euclidean space into $n$ parts yield a solution to the …
Given a triangle $\Delta$, we study the problem of determining the smallest enclosing and largest embedded isosceles triangles of $\Delta$ with respect to area and perimeter. This problem was initiall…
Learning in general-sum games is unstable and frequently leads to socially undesirable (Pareto-dominated) outcomes. To mitigate this, Learning with Opponent-Learning Awareness (LOLA) introduced oppone…
Motivated by a question of R.\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex pentagons of the same area and the same perimeter.…
Arabshahi, Singh, and Anandkumar (2018) propose a method for creating a dataset of symbolic mathematical equations for the tasks of symbolic equation verification and equation completion. Unfortunatel…
Thrombocytopenia in coronavirus disease-2019 (COVID-19) can be attributed to multiple factors. Most often it is disease related. It is usually mild and if severe often associated with severe COVID-19 …
Given side information that an Ising tree-structured graphical model is homogeneous and has no external field, we derive the exact asymptotics of learning its structure from independently drawn sample…
Motivated by a question of R.\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex quadrangles of the same area and the same perimeter. As a byproduct we obt…
We show that every minimum area isosceles triangle containing a given triangle $T$ shares a side and an angle with $T$. This proves a conjecture of Nandakumar motivated by a computational problem. We …
R. Nandakumar asked whether there is a tiling of the plane by pairwise incongruent triangles of equal area and equal perimeter. Recently a negative answer was given by Kupavskii, Pach and Tardos. Stil…
Let $\cal T$ be a tiling of the plane with equilateral triangles no two of which share a side. We prove that if the side lengths of the triangles are bounded from below by a positive constant, then $\…
There exist tilings of the plane with pairwise noncongruent triangles of equal area and bounded perimeter. Analogously, there exist tilings with triangles of equal perimeter, the areas of which are bo…
We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise noncongruent triangles of equal area and equal perimeter. We also show that no convex polygon with mor…
In this paper we study the frequentist convergence rate for the Latent Dirichlet Allocation (Blei et al., 2003) topic models. We show that the maximum likelihood estimator converges to one of the fini…
We study the task of maximizing rewards from recommending items (actions) to users sequentially interacting with a recommender system. Users are modeled as latent mixtures of C many representative use…
Nandakumar asked whether there is a tiling of the plane by pairwise non-congruent triangles of equal area and equal perimeter. Here a weaker result is obtained: there is a tiling of the plane by pairw…
Variational inference is a very efficient and popular heuristic used in various forms in the context of latent variable models. It's closely related to Expectation Maximization (EM), and is applied wh…
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