Related papers: Stable $\A^1$-connectedness
In this note, we prove the coherence of Frobenius stable direct images in a new case. We also show a generation theorem regarding to it. Furthermore, we prove a corresponding theorem in characteristic zero.
We consider the following property of a first order theory T with a distinguished unary predicate P: every model of the theory of P occurs as the P-part of some model of T. We call this property the Gaifman property. Gaifman conjectured…
We study Tao's finitary viewpoint of convergence in metric spaces, as captured by the notion of metastability. We adopt the perspective of continuous model theory. We show that, in essence, metastable convergence with a given rate is the…
D. Bailey and R. E. Crandall recently formulated a "Hypothesis A", which provides a general principle to explain the (conjectured) normality of constants like pi or log 2 and other related numbers, to base 2 or other integer bases. This…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
The theoretical motivations to perform experimental tests of the stationary state fluctuation relation are reviewed. The difficulties involved in such tests, evidenced by numerical simulations, are also discussed.
We introduce the problem of stability verification of quantum sources which are non-i.i.d.. The problem consists in ascertaining whether a given quantum source is stable or not, in the sense that it produces always a desired quantum state…
Periodic orbits for the classical $\phi^4$ theory on the one dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, fixed and free boundary conditions. Through the process, we…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
The steady states of an isotone electric system are described by an isotone function with respect to the componentwise order. When there are steady states, we highlight a dominant steady state and we study its domain of attraction for the…
In this paper, the incremental stability of interconnected switched nonlinear systems is discussed. The nature of switching considered is state-dependent. The incremental stability of the switched interconnected system is a stronger…
We consider nonlinear scalar conservation laws posed on a network. We establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and…
If a real scalar field is dominated by non-relativistic modes, then it approximately conserves its particle number and obeys an equation that governs a complex scalar field theory with a conserved global U(1) symmetry. From this fact, it is…
We study one way in which stable phenomena can exist in an NIP theory. We start by defining a notion of 'pure instability' that we call 'distality' in which no such phenomenon occurs. O-minimal theories and the p-adics for example are…
Persistence diagrams, which summarize the birth and death of homological features extracted from data, are employed as stable signatures for applications in image analysis and other areas. Besides simply considering the multiset of…
If a linear combination of k smooth vector fields is zero at a point, then, generically, near this point there are small cycles comprised of segments from the flow of each vector field. This answers a question posed in arXiv:math/0504365.
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
We discuss stabilization around trajectories of the continuity equation with nonlocal vector fields, where the control is localized, i.e., it acts on a fixed subset of the configuration space. We first show that the correct definition of…
Taking a representation-theoretic viewpoint, we construct a continuous associahedron motivated by the realization of the generalized associahedron in the physical setting. We show that our associahedron shares important properties with the…
This letter concerns the reliability of coupled oscillator networks in response to fluctuating inputs. Reliability means that (following a transient) an input elicits identical responses upon repeated presentations, regardless of the…