Results 1 - 10 of 22277
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[en] We build a Morse function by a density estimator from optical flow sampled data, by using the Morse function and the nudged elastic band method we establish one-dimensional cell complexes, we study 8×8 and 9×9 optical flow patches to discover their topological features from the cell complexes. We discover that spaces of 8×8 and 9×9 patches have same topology as a circle, which spreads some known results to larger optical flow patches. (paper)
[en] Local symmetries are spatial symmetries present in a subdomain of a complex system. By using and extending a framework of so-called non-local currents that has been established recently, we show that one can gain knowledge about the structure of eigenstates in locally symmetric setups through a Kirchhoff-type law for the non-local currents. The framework is applicable to all discrete planar Schrödinger setups, including those with non-uniform connectivity. Conditions for spatially constant non-local currents are derived and we explore two types of locally symmetric subsystems in detail, closed-loops and one-dimensional open ended chains. We find these systems to support locally similar or even locally symmetric eigenstates. - Highlights: • We extend the framework of non-local currents to discrete planar systems. • Structural information about the eigenstates is gained. • Conditions for the constancy of non-local currents are derived. • We use the framework to design two types of example systems featuring locally symmetric eigenstates.
[en] We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one-dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non-integer N and for 3D Laplacian problems. (fast track communication)
[en] Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions provide us with the solutions of various hydrodynamic type equations. Integrable one dimensional systems in terms of Riemann invariants and its extensions, multidimensional equations describing isoenthalpic and polytropic motions and shallow water type equations are among them. (paper)
[en] In the one-dimensional case, for a function satisfying the Gurov-Reshetnyak condition, the infimum of the indices of the Muckenhoupt classes containing this function is found. It is also shown that each Muckenhoupt class lies in some Gurov-Reshetnyak class
[en] We investigate parking in a one-dimensional lot, where cars enter at a rate λ and each attempts to park close to a target at the origin. Parked cars also depart at rate 1. An entering driver cannot see beyond the parked cars for more desirable open spots. We analyze a class of strategies in which a driver ignores open spots beyond τL, where τ is a risk threshold and L is the location of the most distant parked car, and attempts to park at the first available spot encountered closer than τL. When all drivers use this strategy, the probability to park at the best available spot is maximal when , and parking at the best available spot occurs with probability . (paper)
[en] The three-spectral inverse problem for a Stieltjes string (a thread bearing finite number of point masses) is solved. The inverse problem for a Stieltjes string damped at an interior point with the ends fixed appears to be closely connected to the corresponding three-spectral problem. Conditions obtained are necessary and sufficient for a set of complex numbers to be the spectrum of a Stieltjes string damped at an interior point
[en] We provide a necessary and sufficient condition under which the quenched central limit theorem without random centering holds for one-dimensional random systems that are uniformly expanding. This condition holds in particular when all the maps preserve a common measure. We also give a counter example which shows that this condition is not necessarily satisfied when the maps do not preserve a common measure. (paper)
[en] A method is presented for the implementation of edge local complementation (ELC) in graph states, based on the application of two Hadamard operations and a single controlled-phase (CZ) gate. As an application, we demonstrate an efficient scheme for constructing a one-dimensional logical cluster state based on the five-qubit quantum error-correcting code, using a sequence of ELCs. A single physical CZ operation, together with local operations, is sufficient to create a logical CZ operation between two logical qubits. This approach in concatenation may allow one to create a hierarchical quantum network for quantum information tasks.