Search
Search Results
-
A Markovian and Roe-algebraic approach to asymptotic expansion in measure
In this paper, we conduct further studies on geometric and analytic properties of asymptotic expansion in measure. More precisely, we develop a...
-
Expansions in multiple bases
Expansion of real numbers is a basic research topic in number theory. Usually we expand real numbers in one given base. In this paper, we begin to...
-
Expansion, Divisibility and Parity: An Explanation
After seeing how questions on the finer distribution of prime factorization—considered inaccessible until recently—reduce to bounding the norm of an...
-
Boolean Function Analysis on High-Dimensional Expanders
We initiate the study of Boolean function analysis on high-dimensional expanders. We give a random-walk based definition of high-dimensional...
-
Isoperimetric Inequalities and Supercritical Percolation on High-Dimensional Graphs
It is known that many different types of finite random subgraph models undergo quantitatively similar phase transitions around their percolation...
-
-
Sparse expanders have negative curvature
We prove that bounded-degree expanders with non-negative Ollivier–Ricci curvature do not exist, thereby solving a long-standing open problem...
-
Expansions in multiple bases over general alphabets
Expansions in non-integer bases have been extensively investigated since a pioneering work of Rényi. We introduce a more general framework of...
-
Mixing times and hitting times for general Markov processes
The hitting and mixing times are two fundamental quantities associated with Markov chains. In Peres and Sousi [PS15] and Oliveira [Oli12], the...
-
A revised monotonicity-based method for computing tight image enclosures of functions
The computation of tight interval image enclosures of functions over bounded variable domains is in the heart of interval-based branch and bound...
-
Local Spectral Expansion Approach to High Dimensional Expanders Part II: Mixing and Geometrical Overlap**
We further explore the local-to-global approach for expansion of simplicial complexes that we call local spectral expansion. Specifically, we prove...
-
Simplicial branching random walks
We study a model of branching random walks on simplicial complexes, which can be seen as a natural generalization of random walks on graphs....
-
Fast Gradient Method for Low-Rank Matrix Estimation
Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new...
-
-
A solution framework for linear PDE-constrained mixed-integer problems
We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or...
-
Free boundary dimers: random walk representation and scaling limit
We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly...
-
On the Structure of Solutions to the Key Gosper Equation in Problems of Symbolic Summation
AbstractThe structure of polynomial solutions to the Gosper’s key equation is analyzed. A method for rapid “extraction” of simple high-degree factors...
-
Comparative Analysis of Lung Sac Inflation
Inflated lung sacs are a serious medical condition that may be fatal to people. An infectious agent, most likely a virus or bacterium, is responsible...
-
Non-uniform Expansions of Real Numbers
We introduce and study non-uniform expansions of real numbers, given by two non-integer bases.
-
An integrated rolling horizon and adaptive-refinement approach for disjoint trajectories optimization
Planning for multiple commodities simultaneously is a challenging task arising in divers applications, including robot motion or various forms of...
