40 research outputs found
Green's function of a finite chain and the discrete Fourier transform
A new expression for the Green's function of a finite one-dimensional lattice
with nearest neighbor interaction is derived via discrete Fourier transform.
Solution of the Heisenberg spin chain with periodic and open boundary
conditions is considered as an example. Comparison to Bethe ansatz clarifies
the relation between the two approaches.Comment: preprint of the paper published in Int. J. Modern Physics B Vol. 20,
No. 5 (2006) 593-60
Infinite Simple 3D Cubic Lattice of Identical Resistors (Two Missing Bonds)
An infinite regular three-dimensional network is composed of identical
resistors each of resistance joining adjacent nodes. What is the equivalent
resistance between the lattice site and the lattice site, when two bonds are
removed from the perfect network? Three cases are considered here, and some
numerical values are calculated. Finally, the asymptotic behavior of the
equivalent resistance is studied for large distances between the two sites.Comment: 11 pages, 3 figures, published in EPJ-A
Infinite Networks of Identical Capacitors
The capacitance between the origin and any other lattice site in an infinite
square lattice of identical capacitors is studied. The method is generalized to
infinite Simple Cubic (SC) lattice. We make use of the superposition principle
and the symmetry of the infinite gridComment: 16 pages, 5 figures, 2 table
Deep learning identifies cardiac coupling between mother and fetus during gestation
In the last two decades, stillbirth has caused around 2 million fetal deaths worldwide. Although current ultrasound tools are reliably used for the assessment of fetal growth during pregnancy, it still raises safety issues on the fetus, requires skilled providers, and has economic concerns in less developed countries. Here, we propose deep coherence, a novel artificial intelligence (AI) approach that relies on 1 min non-invasive electrocardiography (ECG) to explain the association between maternal and fetal heartbeats during pregnancy. We validated the performance of this approach using a trained deep learning tool on a total of 941 one minute maternal-fetal R-peaks segments collected from 172 pregnant women (20–40 weeks). The high accuracy achieved by the tool (90%) in identifying coupling scenarios demonstrated the potential of using AI as a monitoring tool for frequent evaluation of fetal development. The interpretability of deep learning was significant in explaining synchronization mechanisms between the maternal and fetal heartbeats. This study could potentially pave the way toward the integration of automated deep learning tools in clinical practice to provide timely and continuous fetal monitoring while reducing triage, side-effects, and costs associated with current clinical devices