arXiv subjects

Grzegorz Jablonski

Publications and source records attributed to Grzegorz Jablonski.

3 recordsLinked to original sources

arXiv2020

Čech-Delaunay gradient flow and homology inference for self-maps

We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspace of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.

math.AT↗

arXiv2018

High-power Piezoelectric Tuner Driver for Lorentz Force Compensation

Superconducting Radio Frequency (SRF) cavities are used in modern accelerators to efficiently accelerate particles. When cavity is supplied with pulsed RF field it undergoes a mechanical strain due to the Lorentz force. The resulting deformation causes dynamic detuning whose amplitude depends on mechanical properties of the cavity, RF pulse rate and their profile. This effect causes considerable loss of acceleration performance. Therefore, it is usually actively compensated, most commonly with fast piezoelectric actuators. MicroTCA.4 standard was developed to accommodate control and data acquisition electronic systems of large-scale physics applications. The paper presents a design of high-power amplifier implemented using the MicroTCA.4 technology. The design of the driver was optimized for driving large-capacitance piezo actuators. Several possible architectures of the driver are presented and compared, taking into consideration the power and cooling limitations of MicroTCA.4. The design of a two-channel piezo driver and its initial laboratory test results are also discussed.

physics.ins-det↗

arXiv2016

Combining persistent homology and invariance groups for shape comparison

In many applications concerning the comparison of data expressed by $\mathbb{R}^m$-valued functions defined on a topological space $X$, the invariance with respect to a given group $G$ of self-homeomorphisms of $X$ is required. While persistent homology is quite efficient in the topological and qualitative comparison of this kind of data when the invariance group $G$ is the group $\mathrm{Homeo}(X)$ of all self-homeomorphisms of $X$, this theory is not tailored to manage the case in which $G$ is a proper subgroup of $\mathrm{Homeo}(X)$, and its invariance appears too general for several tasks. This paper proposes a way to adapt persistent homology in order to get invariance just with respect to a given group of self-homeomorphisms of $X$. The main idea consists in a dual approach, based on considering the set of all $G$-invariant non-expanding operators defined on the space of the admissible filtering functions on $X$. Some theoretical results concerning this approach are proven and two experiments are presented. An experiment illustrates the application of the proposed technique to compare 1D-signals, when the invariance is expressed by the group of affinities, the group of orientation-preserving affinities, the group of isometries, the group of translations and the identity group. Another experiment shows how our technique can be used for image comparison.

math.AT↗