585 research outputs found
Determination of Boundary Scattering, Intermagnon Scattering, and the Haldane Gap in Heisenberg Chains
Low-lying magnon dispersion in a S=1 Heisenberg antiferromagnetic (AF) chain
is analyzed using the non-Abelian DMRG method. The scattering length of the boundary coupling and the inter-magnon scattering length are
determined. The scattering length is found to exhibit a
characteristic diverging behavior at the crossover point. In contrast, the
Haldane gap , the magnon velocity , and remain constant at the
crossover. Our method allowed estimation of the gap of the S=2 AF chain to be
using a chain length longer than the correlation length
.Comment: 6 pages, 3 figures, 1 table, accepted in Phys. Rev.
Extracting a function encoded in amplitudes of a quantum state by tensor network and orthogonal function expansion
There are quantum algorithms for finding a function satisfying a set of
conditions, such as solving partial differential equations, and these achieve
exponential quantum speedup compared to existing classical methods, especially
when the number of the variables of is large. In general, however,
these algorithms output the quantum state which encodes in the amplitudes,
and reading out the values of as classical data from such a state can be so
time-consuming that the quantum speedup is ruined. In this study, we propose a
general method for this function readout task. Based on the function
approximation by a combination of tensor network and orthogonal function
expansion, we present a quantum circuit and its optimization procedure to
obtain an approximating function of that has a polynomial number of degrees
of freedom with respect to and is efficiently evaluable on a classical
computer. We also conducted a numerical experiment to approximate a
finance-motivated function to demonstrate that our method works.Comment: 16 pages, 8 figure
Conformance Testing as Falsification for Cyber-Physical Systems
In Model-Based Design of Cyber-Physical Systems (CPS), it is often desirable
to develop several models of varying fidelity. Models of different fidelity
levels can enable mathematical analysis of the model, control synthesis, faster
simulation etc. Furthermore, when (automatically or manually) transitioning
from a model to its implementation on an actual computational platform, then
again two different versions of the same system are being developed. In all
previous cases, it is necessary to define a rigorous notion of conformance
between different models and between models and their implementations. This
paper argues that conformance should be a measure of distance between systems.
Albeit a range of theoretical distance notions exists, a way to compute such
distances for industrial size systems and models has not been proposed yet.
This paper addresses exactly this problem. A universal notion of conformance as
closeness between systems is rigorously defined, and evidence is presented that
this implies a number of other application-dependent conformance notions. An
algorithm for detecting that two systems are not conformant is then proposed,
which uses existing proven tools. A method is also proposed to measure the
degree of conformance between two systems. The results are demonstrated on a
range of models
Decreased plasma postheparin lipolytic activity in systemic lupus erythematosus
Plasma postheparin lipolytic activity (PHLA) was measured on 50 patients with systemic lupus erythematosus (SLE). Plasma PHLA was significantly decreased in SLE patients. This decrease was most striking in the acute phase of the disease. There was a close relationship between decreased PHLA and immunologic factors indicative of the acute phase of SLE. These immunologic factors included shaggy antinuclear antibody pattern, low serum complement titer, high DNA antibody titer, mixed cryoglobulin and lumpy glomerular pattern by immunofluorescent staining.</p
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