Tootfinder

Weakly o-minimal types
Slavko Moconja, Predrag Tanovi\'c
https://arxiv.org/abs/2404.08260 https://arxiv.org/pdf/2404.08260…

Weakly o-minimal types
We introduce and study weak o-minimality in the context of complete types in an arbitrary first-order theory. A type $p\in S(A)$ is weakly o-minimal with respect to $<$, a relatively $A$-definable linear order on $p(\mathfrak C)$, if every relatively definable subset has finitely many convex components; we prove that in that case the latter holds for all orders. Notably, we prove: (i) a monotonicity theorem for relatively definable functions on the locus of a weakly o-minimal type; (ii) weakly …

Edge coloring lattice graphs
Joris Kattem\"olle
https://arxiv.org/abs/2402.08752 https://arxiv.org/pdf/2402.08752

Edge coloring lattice graphs
We develop the theory of the edge coloring of infinite lattice graphs, proving a necessary and sufficient condition for a proper edge coloring of a patch of a lattice graph to induce a proper edge coloring of the entire lattice graph by translation. This condition forms the cornerstone of a method that finds nearly minimal or minimal edge colorings of infinite lattice graphs. In case a nearly minimal edge coloring is requested, the running time is $O(μ^2 D^4)$, where $μ$ is the number of edge…

Quaternion-Based Attitude Stabilization Using Synergistic Hybrid Feedback With Minimal Potential Functions
Xin Tong, Qingpeng Ding, Haiyang Fang, Shing Shin Cheng
https://arxiv.org/abs/2404.08326

Quaternion-Based Attitude Stabilization Using Synergistic Hybrid Feedback With Minimal Potential Functions
This paper investigates the robust global attitude stabilization problem for a rigid-body system using quaternion-based feedback. We propose a novel synergistic hybrid feedback with the following notable features: (1) It demonstrates central synergism by utilizing a minimal number of potential functions; (2) It ensures consistency with respect to the unit quaternion representation of rigid-body attitude; (3) Its state-feedback laws incorporate a shared action term that steers the system toward …

This https://arxiv.org/abs/2404.03860 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimal hyperbolic polynomials and ranks of homogeneous cones
The starting point of this paper is the computation of minimal hyperbolic polynomials of duals of cones arising from chordal sparsity patterns. From that, we investigate the relation between ranks of homogeneous cones and their minimal polynomials. Along the way, we answer in the negative a question posed in an earlier paper and show examples of homogeneous cones that cannot be realized as rank-one generated (ROG) hyperbolicity cones.

On closed definable subsets in Hensel minimal structures
Krzysztof Jan Nowak
https://arxiv.org/abs/2403.08039 https://arxiv.org/pdf/2…

On closed definable subsets in Hensel minimal structures
This paper deals with Hensel minimal structures on non-trivially valued fields $K$. The main aim is to establish the following two properties of closed 0-definable subsets $A$ in the affine spaces $K^{n}$. Every such subset $A$ is the zero locus of a continuous 0-definable function $f:K^{n} \to K$, and there exists a 0-definable retraction $r: K^{n} \to A$. While the former property is a non-Archimedean counterpart of the one from o-minimal geometry, the former does not hold in real geometry in…

This https://arxiv.org/abs/2404.03860 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimal hyperbolic polynomials and ranks of homogeneous cones
The starting point of this paper is the computation of minimal hyperbolic polynomials of duals of cones arising from chordal sparsity patterns. From that, we investigate the relation between ranks of homogeneous cones and their minimal polynomials. Along the way, we answer in the negative a question posed in an earlier paper and show examples of homogeneous cones that cannot be realized as rank-one generated (ROG) hyperbolicity cones.

This https://arxiv.org/abs/2208.00954 has been replaced.
link: https://scholar.google.com/scholar?q=a

Spectral Spaces in o-minimal and other NIP theories
We study some model-theoretic notions in NIP by means of spectral topology. In the o-minimal setting we relate the o-minimal spectrum with other topological spaces such as the real spectrum and the space of infinitesimal types of Peterzil and Starchenko. In particular, we prove for definably compact groups that the space of closed points is homeomorphic to the space of infinitesimal types. We also prove that with the spectral topology the set of invariant types concentrated in a definably compa…

This https://arxiv.org/abs/2208.00954 has been replaced.
link: https://scholar.google.com/scholar?q=a

Spectral Spaces in o-minimal and other NIP theories
We study some model-theoretic notions in NIP by means of spectral topology. In the o-minimal setting we relate the o-minimal spectrum with other topological spaces such as the real spectrum and the space of infinitesimal types of Peterzil and Starchenko. In particular, we prove for definably compact groups that the space of closed points is homeomorphic to the space of infinitesimal types. We also prove that with the spectral topology the set of invariant types concentrated in a definably compa…

This https://arxiv.org/abs/2403.08039 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On closed definable subsets in Hensel minimal structures
This paper deals with Hensel minimal structures on non-trivially valued fields $K$. The main aim is to establish the following two properties of closed 0-definable subsets $A$ in the affine spaces $K^{n}$. Every such subset $A$ is the zero locus of a continuous 0-definable function $f:K^{n} \to K$, and there exists a 0-definable retraction $r: K^{n} \to A$. While the former property is a non-Archimedean counterpart of the one from o-minimal geometry, the former does not hold in real geometry in…

This https://arxiv.org/abs/2403.08039 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On closed definable subsets in Hensel minimal structures
This paper deals with Hensel minimal structures on non-trivially valued fields $K$. The main aim is to establish the following two properties of closed 0-definable subsets $A$ in the affine spaces $K^{n}$. Every such subset $A$ is the zero locus of a continuous 0-definable function $f:K^{n} \to K$, and there exists a 0-definable retraction $r: K^{n} \to A$. While the former property is a non-Archimedean counterpart of the one from o-minimal geometry, the former does not hold in real geometry in…