Related papers: The W. Thurston Algorithm for Real Quadratic Ratio…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
Thurston parameterized quadratic invariant laminations with a non-invariant lamination, the quotient of which yields a combinatorial model for the Mandelbrot set. As a step toward generalizing this construction to cubic polynomials, we…
We develop the theory of Thurston maps that are defined everywhere on the topological sphere $S^2$ with a possible exception of a single essential singularity. We establish an analog of the celebrated W. Thurston's characterization theorem…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the…
We study canonical decompositions of postcritically finite branched coverings of the 2-sphere, as defined by K.~Pilgrim. We show that every hyperbolic cycle in the decomposition does not have a Thurston obstruction. It is thus Thurston…
This paper introduces the concept of quasi $\alpha$-firmly nonexpansive mappings in Wasserstein spaces over $\mathbb R^d$ and analyzes properties of these mappings. We prove that for quasi $\alpha$-firmly nonexpansive mappings satisfying a…
The monotonicity of entropy is investigated for real quadratic rational maps on the real circle $\mathbb{R}\cup\{\infty\}$ based on the natural partition of the corresponding moduli space $\mathcal{M}_2(\mathbb{R})$ into its monotonic,…
In this paper we prove that the monotonicity of kneading sequences and topological entropy, a fundamental structural property of the quadratic family, extends to the class of power-law unimodal maps $f_a(x)=a-|x|^r$ for arbitrary critical…
Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…
Motion planning in high-dimensional space is a challenging task. In order to perform dexterous manipulation in an unstructured environment, a robot with many degrees of freedom is usually necessary, which also complicates its motion…
It has been known for some time that the topological entropy is a nondecreasing function of the parameter in the real quadratic family, which corresponds to the intuitive idea that more nonlinearity induces more complex dynamical behavior.…
The tomographic histories approach is presented. As an inverse problem, we recover in an operational way the effective topology of the extended configuration space of a system. This means that from a series of experiments we get a set of…
We consider Milnor's "tower algorithm" in the space of piecewise monotone maps, an iterative algorithm on the space of metrics which unifies, on the one hand, Thurston's iterative scheme which converges to holomorphic models, and, on the…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
William Thurston (1946-2012) gave a combinatorial characterization for generic branched self-coverings of the two-sphere by associating a planar graph to them 10.48550/arXiv.1502.04760. By generalizing the notion of local balancing, the…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
This paper constructs a combinatorial model for all postcritically finite rational maps arising as the Newton's method of a complex polynomial. This model is used in [LMS] to give a combinatorial classification of postcritically finite…
Sampling-based motion planning techniques have emerged as an efficient algorithmic paradigm for solving complex motion planning problems. These approaches use a set of probing samples to construct an implicit graph representation of the…