Encoding for the Blackwell Channel with Reinforced Belief Propagation

A key idea in coding for the broadcast channel (BC) is binning, in which the transmitter encode information by selecting a codeword from an appropriate bin (the messages are thus the bin indexes). This selection is normally done by solving an appropriate (possibly difficult) combinatorial problem. Recently it has been shown that binning for the Blackwell channel --a particular BC-- can be done by iterative schemes based on Survey Propagation (SP). This method uses decimation for SP and suffers a complexity of O(n^2). In this paper we propose a new variation of the Belief Propagation (BP) algorithm, named Reinforced BP algorithm, that turns BP into a solver. Our simulations show that this new algorithm has complexity O(n log n). Using this new algorithm together with a non-linear coding scheme, we can efficiently achieve rates close to the border of the capacity region of the Blackwell channel.Comment: 5 pages, 8 figures, submitted to ISIT 200

Spin-fermion mappings for even Hamiltonian operators

We revisit the Jordan-Wigner transformation, showing that --rather than a non-local isomorphism between different fermionic and spin Hamiltonian operators-- it can be viewed in terms of local identities relating different realizations of projection operators. The construction works for arbitrary dimension of the ambient lattice, as well as of the on-site vector space, generalizing Jordan-Wigner's result. It provides direct mapping of local quantum spin problems into local fermionic problems (and viceversa), under the (rather physical) requirement that the latter are described by Hamiltonian's which are even products of fermionic operators. As an application, we specialize to mappings between constrained-fermions models and spin 1 models on chains, obtaining in particular some new integrable spin Hamiltonian, and the corresponding ground state energies.Comment: 7 pages, ReVTeX file, no figure

Diagnosis of BPH and treatment of LUTS

Summary Aims of the study:  This survey was conducted in France, Germany, Italy, Spain and UK, with the aim to assess diagnosis and therapy of BPH patients in clinical practice. Methods used to conduct the study:  A selected cohort of 455 general practitioners (GPs) in Europe were asked to report information on BPH patients with lower urinary tract symptoms (LUTS), including patient characteristics, diagnostic procedures, severity of illness, symptoms duration and underlying conditions. The GPs provided data relating to 886 patients. Results of the study:  The diagnostic work-up included description of symptoms (74.9–85.1%), rectal examination (55.4–82.1%) and the determination of PSA (79.1–94.7%). Transrectal sonography was popular in Italy and France (51.1% and 55.9%, respectively), less so in Germany (15.3%) and Spain (13.1%) and not at all in the UK (2.3%). At diagnosis, the most common symptom was nocturia (71–88%), followed by frequency (15–79%), urgency (43–68%) and weak stream (47–64%). The most common combination was the triad nocturia–frequency–feeling of incomplete emptying (22–31%). The mean ± SD LUTS severity score was similar in all countries: The main aim of treatment was the resolution of nocturia, which had an average score that reflected an important need (> 3.5) closely followed by frequency (3.3–3.9). Conclusions drawn from the study and clinical implications:  This survey has shown that the most common LUTS is nocturia. Analyses of the symptoms' pattern revealed that the most common combination appears to be the triad nocturia-frequency-feeling of incomplete emptying. An association between LUTS and heart disease, diabetes and hypertension suggests that the pharmacological treatment should be devoid of effects on the cardiovascular system. With alpha blockers as first line treatment of LUTS, respondents were more concerned with hypotensive episodes resulting in falls, rather than about other typical side effects (e.g. ejaculation disorders and lowered libido). The survey highlights educational needs in diagnostics

Hubbard model on triangular N -leg cylinders: Chiral and nonchiral spin liquids

The existence of a gapped chiral spin liquid has been recently suggested in the vicinity of the metal-insulator transition of the Hubbard model on the triangular lattice, by intensive density-matrix renormalization group (DMRG) simulations [A. Szasz, J. Motruk, M. P. Zaletel, and J. E. Moore, Phys. Rev. X 10, 021042 (2020)10.1103/PhysRevX.10.021042]. Here, we report the results obtained within the variational Monte Carlo technique based upon Jastrow-Slater wave functions, implemented with backflow correlations. As in DMRG calculations, we consider N-leg cylinders. For N=4 and in the presence of a next-nearest-neighbor hopping, a chiral spin liquid emerges between the metal and the insulator with magnetic quasi-long-range order. Within our approach, the chiral state is gapped and breaks the reflection symmetry. By contrast, for both N=5 and 6, the chiral spin liquid is not the state with the lowest variational energy: in the former case, a nematic spin liquid is found in the entire insulating regime, while for the less frustrated case with N=6 the results are very similar to that obtained on two-dimensional clusters [L. F. Tocchio, A. Montorsi, and F. Becca, Phys. Rev. B 102, 115150 (2020)2469-995010.1103/PhysRevB.102.115150], with an antiferromagnetic phase close to the metal-insulator transition and a nematic spin liquid in the strong-coupling regime

Magnetic and spin-liquid phases in the frustrated t-t′ Hubbard model on the triangular lattice

The Hubbard model and its strong-coupling version, the Heisenberg one, have been widely studied on the triangular lattice to capture the essential low-temperature properties of different materials. One example is given by transition metal dichalcogenides, as 1T-TaS$_2$, where a large unit cell with 13 Ta atoms forms weakly coupled layers with an isotropic triangular lattice. By using accurate variational Monte Carlo calculations, we report the phase diagram of the $t-t′$ Hubbard model on the triangular lattice, highlighting the differences between positive and negative values of $t′/t$; this result can be captured only by including the charge fluctuations that are always present for a finite electron-electron repulsion. Two spin-liquid regions are detected: one for $t′/t0$. The spin-liquid phase appears to be gapless, though the variational wave function has a nematic character, in contrast to the Heisenberg limit. We do not find any evidence for nonmagnetic Mott phases in the proximity of the metal-insulator transition, at variance with the predictions (mainly based upon strong-coupling expansions in $t/U$) that suggest the existence of a weak-Mott phase that intrudes between the metal and the magnetically ordered insulator

Hubbard model on triangular N-leg cylinders: Chiral and nonchiral spin liquids

The existence of a gapped chiral spin liquid has been recently suggested in the vicinity of the metal-insulator transition of the Hubbard model on the triangular lattice, by intensive density-matrix renormalization group (DMRG) simulations [A. Szasz, J. Motruk, M. P. Zaletel, and J. E. Moore, Phys. Rev. X 021042 (2020)]. Here, we report the results obtained within the variational Monte Carlo technique based upon Jastrow-Slater wave functions, implemented with backflow correlations. As in DMRG calculations, we consider N-leg cylinders. For N = 4 and in the presence of a next-nearest-neighbor hopping, a chiral spin liquid emerges between the metal and the insulator with magnetic quasi-long-range order. Within our approach, the chiral state is gapped and breaks the reflection symmetry. By contrast, for both N = 5 and 6, the chiral spin liquid is not the state with the lowest variational energy: in the former case, a nematic spin liquid is found in the entire insulating regime, while for the less frustrated case with N = 6 the results are very similar to that obtained on two-dimensional clusters [L. F. Tocchio, A. Montorsi, and F. Becca, Phys. Rev. B 102, 115150 (2020)], with an antiferromagnetic phase close to the metal-insulator transition and a nematic spin liquid in the strong-coupling regime

Classical realization of two-site Fermi-Hubbard systems

A classical wave optics realization of the two-site Hubbard model, describing the dynamics of interacting fermions in a double-well potential, is proposed based on light transport in evanescently-coupled optical waveguides.Comment: 4 page

Development of a Numerical Approach for the CFD Simulation of a Gear Pump under Actual Operating Conditions

The geometric complexity and high-pressure gradients that characterize the design of the flow field of gear pumps make it very difficult to obtain an accurate CFD simulation of the component. Usually, assumptions are made both in terms of geometrical features and physics being included in the analysis. The contact between the teeth, which is a key factor for the correct functioning of these pumps, represents a critical challenge in 3D CFD simulations, mainly due to the intrinsic limits of the dynamic meshing techniques that can hardly effectively manage a zero or close to zero gap point forming during gear rotation. The geometric complexity and high-pressure gradients that characterize the gear pump flow field make a CFD analysis quite difficult, and the contact between the gear teeth is usually avoided, thus being an extremely important feature. In this paper, a gear pump composed of inlet and outlet pipes was considered, and the contact between the gear's teeth was modeled in two different ways, one where it is effectively implemented and one where it is avoided using distancing and a proper casing modification. Herein, a new methodology is proposed for the application of the dynamic mesh method in the Simcenter STAR-CCM+ environment using an adaptive remeshing technique. The proposed methodology is compared with the alternative overset meshing method available in the software. The new meshing method is implemented using a user-routing that reproduces the real geometry of the gears while rotating during the pump operation, with teeth contact included. The routine is optimized in order to limit the additional computation and time needed for the remeshing process. The results that can be obtained using the two meshing approaches for the gear pump are compared in terms of computational effort and the accuracy of the results. The two methods showed opposite results in almost all the reported results, with the overset being more precise in the radial pressure evaluation and the dynamic being more reliable in the cavitation/aeration extension cloud