Related papers: Universality in symbolic dynamics constrained by M…
Finite subdivision rules in high dimensions can be difficult to visualize and require complex topological structures to be constructed explicitly. In many applications, only the history graph is needed. We characterize the history graph of…
We prove several results about the relationship between the word complexity function of a subshift and the set of Turing degrees of points of the subshift, which we call the Turing spectrum. Among other results, we show that a Turing…
We review (and extend) the analysis of general theories of all interactions (gravity included) where the mass scales are due to dimensional transmutation. Quantum consistency requires the presence of terms in the action with four…
We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra\"{\i}ss\'{e} limit) embeds all countable semigroups. This approach provides us not only…
It is proved that if $D$ is a $UFD$ and $R$ is a $D$-algebra, such that $U(R)\cap D\neq U(D)$, then $R$ has a maximal subring. In particular, if $R$ is a ring which either contains a unit $x$ which is not algebraic over the prime subring of…
The limited distinctness of physical systems is roughly expressed by uncertainty relations. Here we show distinctness is a finite resource we can exactly count to define basic physical quantities, limits to the resolution of space and time,…
We consider ergodic families of Verblunsky coefficients generated by minimal aperiodic subshifts. Simon conjectured that the associated probability measures on the unit circle have essential support of zero Lebesgue measure. We prove this…
This paper studies properties of a subdifferential defined using a generalized conjugation scheme. We relate this subdifferential together with the domain of an appropriate conjugate function and the {\epsilon}-directional derivative. In…
In the nice recent work [48], S. Wang established uniform log-Sobolev inequalities for mean field particles when the energy is flat convex. In this note we comment how to extend his proof to some semi-convex energies provided the curvature…
An analysis of necessary conditions for the existence of controlled dynamics with an attractor of a specified topological type is given. It uses the Hopf classification by degree for Gauss maps of manifolds to spheres of the same dimension,…
The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays…
Global control offers a promising route to scalable quantum computing. A recent conjecture by Hu et al. (arXiv:2508.19075) proposes that any connected qubit graph equipped with global Ising-type interactions and tunable global transverse…
For $1\le d\le \ell< k$, we give a new lower bound for the minimum $d$-degree threshold that guarantees a Hamilton $\ell$-cycle in $k$-uniform hypergraphs. When $k\ge 4$ and $d< \ell=k-1$, this bound is larger than the conjectured minimum…
The principle of optimality is a fundamental aspect of dynamic programming, which states that the optimal solution to a dynamic optimization problem can be found by combining the optimal solutions to its sub-problems. While this principle…
For any even integer $k\ge 6$, integer $d$ such that $k/2\le d\le k-1$, and sufficiently large $n\in (k/2)\mathbb N$, we find a tight minimum $d$-degree condition that guarantees the existence of a Hamilton $(k/2)$-cycle in every…
In [2], the authors prove Stillman's conjecture in all characteristics and all degrees by showing that, independent of the algebraically closed field $K$ or the number of variables, $n$ forms of degree at most $d$ in a polynomial ring $R$…
Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky's univalence axiom. This makes many extensionality principles, like function and propositional extensionality, directly…
We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics.…
We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study makes use of a "Universality Hypothesis" for the relevant energy scales of a many-body system at unitarity. This Hypothesis is supported…
This paper unifies problems and results related to (embedding) universal and homomorphism universal structures. On the one side we give a new combinatorial proof of the existence of universal objects for homomorphism defined classes of…