1,496 research outputs found
On the correlation measure of a family of commuting Hermitian operators with applications to particle densities of the quasi-free representations of the CAR and CCR
Let be a locally compact, second countable Hausdorff topological space.
We consider a family of commuting Hermitian operators indexed by
all measurable, relatively compact sets in (a quantum stochastic
process over ). For such a family, we introduce the notion of a correlation
measure. We prove that, if the family of operators possesses a correlation
measure which satisfies some condition of growth, then there exists a point
process over having the same correlation measure. Furthermore, the
operators can be realized as multiplication operators in the
-space with respect to this point process. In the proof, we utilize the
notion of -positive definiteness, proposed in [Y. G. Kondratiev and T.\
Kuna, {\it Infin. Dimens. Anal. Quantum Probab. Relat. Top.} {\bf 5} (2002),
201--233]. In particular, our result extends the criterion of existence of a
point process from that paper to the case of the topological space , which
is a standard underlying space in the theory of point processes. As
applications, we discuss particle densities of the quasi-free representations
of the CAR and CCR, which lead to fermion, boson, fermion-like, and boson-like
(e.g. para-fermions and para-bosons of order 2) point processes.
In particular, we prove that any fermion point process corresponding to a
Hermitian kernel may be derived in this way
Radar Cross Section of Orbital Debris Objects
This discussion is concerned with the radar-data analysis and usage involved in the building of model orbital debris (OD) populations in the near-Earth environment, focusing on radar cross section (RCS). While varying with radar wavelength, physical dimension, material composition, overall shape and structure, the RCS of an irregular object is also strongly dependent on its spatial orientation. The historical records of observed RCSs for cataloged OD objects in the Space Surveillance Network are usually distributed over an RCS range, forming respective characteristic patterns. The National Aeronautics and Space Administration (NASA) Size Estimation Model provides an empirical probability-density function of RCS as a function of effective diameter (or characteristic length), which makes it feasible to predict possible RCS distributions for a given model OD population and to link data with model from a statistical perspective. The discussion also includes application of the widely used method of moments (MoM) and the Generalized Multi-particle Mie-solution (GMM) in the prediction of the RCS of arbitrarily shaped objects. Theoretical calculation results for an aluminum cube are compared with corresponding experimental measurements
Long-term Effects of Temperature Variations on Economic Growth: A Machine Learning Approach
This study investigates the long-term effects of temperature variations on
economic growth using a data-driven approach. Leveraging machine learning
techniques, we analyze global land surface temperature data from Berkeley Earth
and economic indicators, including GDP and population data, from the World
Bank. Our analysis reveals a significant relationship between average
temperature and GDP growth, suggesting that climate variations can
substantially impact economic performance. This research underscores the
importance of incorporating climate factors into economic planning and
policymaking, and it demonstrates the utility of machine learning in uncovering
complex relationships in climate-economy studies
Predicting the epidemic threshold of the susceptible-infected-recovered model
Researchers have developed several theoretical methods for predicting
epidemic thresholds, including the mean-field like (MFL) method, the quenched
mean-field (QMF) method, and the dynamical message passing (DMP) method. When
these methods are applied to predict epidemic threshold they often produce
differing results and their relative levels of accuracy are still unknown. We
systematically analyze these two issues---relationships among differing results
and levels of accuracy---by studying the susceptible-infected-recovered (SIR)
model on uncorrelated configuration networks and a group of 56 real-world
networks. In uncorrelated configuration networks the MFL and DMP methods yield
identical predictions that are larger and more accurate than the prediction
generated by the QMF method. When compared to the 56 real-world networks, the
epidemic threshold obtained by the DMP method is closer to the actual epidemic
threshold because it incorporates full network topology information and some
dynamical correlations. We find that in some scenarios---such as networks with
positive degree-degree correlations, with an eigenvector localized on the high
-core nodes, or with a high level of clustering---the epidemic threshold
predicted by the MFL method, which uses the degree distribution as the only
input parameter, performs better than the other two methods. We also find that
the performances of the three predictions are irregular versus modularity
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