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We find the explicit local models of isolated singularities of conformal hyperbolic metrics by Complex Analysis, which is interesting in its own and could potentially be extended to high-dimensional case.
Rank one transformations serve as a source of examples in ergodic theory, showing variety of algebraic, asymptotic and spectral properties of dynamical systems. The properties of a rank one transformation are closely related to the weak…
Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of…
Some basic geometric properties related to connectedness and topological dimension 0 are discussed, especially in connection with the ultrametric version of the triangle inequality.
We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincar\'e property, we produce a well-behaved relaxation theory via approximation by…
Weak measurements may result in extra quantity of quantumness of correlations compared with standard projective measurement on a bipartite quantum state. We show that the quantumness of correlations by weak measurements can be consumed for…
Quantum statistical models (i.e., families of normalized density matrices) and quantum measurements (i.e., positive operator-valued measures) can be regarded as linear maps: the former, mapping the space of effects to the space of…
We show that self-similar measures on $\mathbb{R}^d$ satisfying the weak separation condition are uniformly scaling. Our approach combines elementary ergodic theory with geometric analysis of the structure given by the weak separation…
We consider the trace map associated with the Fibonacci Hamiltonian as a diffeomorphism on the invariant surface associated with a given coupling constant and prove that the non-wandering set of this map is hyperbolic if the coupling is…
For any geodesic metric space $X$, we give a complete cohomological characterisation of the hyperbolicity of $X$ in terms of vanishing of its second $\ell^{\infty}$-cohomology. We extend this result to the relative setting of $X$ with a…
Measurements are crucial in quantum mechanics, in fundamental research as well as in applicative fields like quantum metrology, quantum-enhanced measurements and other quantum technologies. In the recent years, weak-interaction-based…
Spatial statistics is an area of study devoted to the statistical analysis of data that have a spatial label associated with them. Geographers often refer to the "location information" associated with the "attribute information," whose…
Quantum measurement is physically realized through a finite dynamical interaction between a system and a measuring apparatus, giving rise to a continuous transition from weak to strong regimes. While this crossover is well understood under…
The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…
The article recapitulates the concept of weak measurement in its broader sense encapsulating the trade between asymptotically weak measurement precision and asymptotically large measurement statistics. Essential applications in…
The use of weak measurements for performing quantum tomography is enjoying increased attention due to several recent proposals. The advertised merits of using weak measurements in this context are varied, but are generally represented by…
Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…
Observations in quantum weak measurements are determined by complex numbers called weak values. We present a geometrical interpretation of the argument of weak values of general Hermitian observables in $N$-dimensional quantum systems in…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…