We present a novel mapping for studying 2D many-body quantum systems by solving an effective, one-dimensional long-range model in place of the original two-dimensional short-range one. In particular, we address the problem of choosing an efficient mapping from the 2D lattice to a 1D chain that optimally preserves the locality of interactions within the TN structure. By using Matrix Product States (MPS) and Tree Tensor Network (TTN) algorithms, we compute the ground state of the 2D quantum Ising model in transverse field with lattice size up to 64×64, comparing the results obtained from different mappings based on two space-filling curves, the snake curve and the Hilbert curve. We show that the locality-preserving properties of the Hilbert curve leads to a clear improvement of numerical precision, especially for large sizes, and turns out to provide the best performances for the simulation of 2D lattice systems via 1D TN structures.
International Society of Peritoneal Dialysis (ISPD) guidelines suggest that in case of bacterial peritonitis in peritoneal dialysis patients, antibiotic therapy failure, and/or the absence of clinical improvement after 4‐7 days should induce catheter removal. We present an atypical case of recurrent bacterial peritonitis, 2 episodes, during a 35‐day treatment. The second episode occurred after therapy modifi cation. In addition to having constant abnormal laboratory (increased C‐reactive protein values, leukocyte cell count, serum ferritin, etc.) and clinical (fever) findings, patients' subjective well‐being and fulfi lled dialysis effi ciency remained unchanged during the treatment period; these data induced further therapy modifi cation without catheter removal. One month later laboratory parameters returned to normal, whereas echotomography control revealed the absence of the previously observed infl ammatory signs. In conclusion, our case provides evidence that patients' clinical conditions may be more predictive than laboratory findings of outcome following bacterial peritonitis.
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