相关论文: On the classification of planar constrained differ…
Recently, concepts from the emerging field of tropical geometry have been used to identify different scaling regimes in chemical reaction networks where dimension reduction may take place. In this paper, we try to formalize these ideas…
Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this work, we propose an alternative approach to assessing topologically induced edge states in free…
Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…
In this paper, we have studied 'absorbing' and 'balanced' sets in an Exponential Vector Space (\emph{evs} in short) over the field $\mathbb K$ of real or complex. These sets play pivotal role to describe several aspects of a topological…
We characterize the limit periodic sets of families of polynomial planar vector fields up to homeomorphisms. We show that any limit periodic set is topologically equivalent to a compact and connected semialgebraic set of the sphere with…
We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and…
Let E be a locally compact second countable Hausdorff space and F the pertaining family of all closed sets. We endow F respectively with the Fell-topology, the upper Fell topology or the upper Vietoris-topology and investigate weak…
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…
We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…
In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
Modulated symmetries are internal symmetries which do not commute with spatial symmetries; dipolar symmetries are a prime example. We give a general recipe for constructing topological phases protected by modulated symmetries via a defect…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $ N $ variables, as binary neural networks and cellular automata. The main difficulty is the…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
We introduce a notion of discrete topological complexity in the setting of simplicial complexes, using only the combinatorial structure of the complex by means of the concept of contiguous simplicial maps. We study the links of this new…
$Vect(N)$, the algebra of vector fields in $N$ dimensions, is studied. Some aspects of local differential geometry are formulated as $Vect(N)$ representation theory. There is a new class of modules, {\it conformal fields}, whose…
Topological insulators are a new class of materials that have engendered considerable research interest among the condensed matter community owing primarily to their application prospects in quantum computations and spintronics. Many of the…
This paper deals with the characterization, in terms of closedness of certain sets regarding other sets, of Farkas lemmas determining when the upperlevel set of a given convex function contains the intersection, say F, of a convex set of a…
We prove the existence of a finite temperature Z_{2} phase transition for the topological charge ordering within the Fully Frustrated XY Model. Our method enables a proof of the topological charge confinement within the conventional XY…