Metric Graph Approximations of Geodesic Spaces

A standard result in metric geometry is that every compact geodesic metric space can be approximated arbitrarily well by finite metric graphs in the Gromov-Hausdorff sense. It is well known that the first Betti number of the approximating graphs may blow up as the approximation gets finer. In our work, given a compact geodesic metric space $X$, we define a sequence $(\delta^X_n)_{n \geq 0}$ of non-negative real numbers by $$\delta^X_n:=\inf \{d_{\mathrm{GH}}(X,G): G \text{ a finite metric graph, } \beta_1(G)\leq n \} .$$ By construction, and the above result, this is a non-increasing sequence with limit $0$. We study this sequence and its rates of decay with $n$. We also identify a precise relationship between the sequence and the first Vietoris-Rips persistence barcode of $X$. Furthermore, we specifically analyze $\delta_0^X$ and find upper and lower bounds based on hyperbolicity and other metric invariants. As a consequence of the tools we develop, our work also provides a Gromov-Hausdorff stability result for the Reeb construction on geodesic metric spaces with respect to the function given by distance to a reference point

Radiated Immunity Testing of a Device with an External Wire: Repeatibility of Reverberation Chamber Results and Correlation with Anechoic Chamber Results

We present the experimental radiated immunity results of an electronic device with an external wire obtained in reverberation and anechoic chambers. Repeatability and reproducibility of reverberation chamber measurements are investigated by repeating the test in three reverberation chambers with different characteristics. We show how the current state of the art allows a statistical control of RC measurement repeatability within an industrial installation, and that a statistical correlation with AC results frequency by frequency is possible in particular cases relevant to automotive application

Operasyonun adı:Unut

Taha Toros Arşivi, Dosya No: 200-Cavit Orhan TütengilUnutma İstanbul projesi İstanbul Kalkınma Ajansı'nın 2016 yılı "Yenilikçi ve Yaratıcı İstanbul Mali Destek Programı" kapsamında desteklenmiştir. Proje No: TR10/16/YNY/010

Spreadsheet optimization of flow for WIP goods at a yarn and tire cord manufacturer:

We developed a spreadsheet optimization model to find the optimal material handling policy at a leading yarn and tire cord manufacturer’s facility. The focus of the study is to optimize the movement of looms of yarn and tire cord between two major manufacturing steps. The considered flow network within the manufacturing facility is a miniature two-stage supply chain, including the middle layer of depots. Movement of material takes place through forklift trucks and cranes, which impose electricity, labor, maintenance, and depreciation costs. After introducing the company, the facility, and the project goals, we present the underlying linear programming (LP) model and our spreadsheet implementation. The results of our model suggest an annual saving of approximately $22,000 for the facility