Rough sets and matroidal contraction

Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to matroids and study the contraction of the dual of the corresponding matroid. First, for an equivalence relation on a universe, a matroidal structure of the rough set is established through the lower approximation operator. Second, the dual of the matroid and its properties such as independent sets, bases and rank function are investigated. Finally, the relationships between the contraction of the dual matroid to the complement of a single point set and the contraction of the dual matroid to the complement of the equivalence class of this point are studied.Comment: 11 page

The influence of tropospheric biennial oscillation on mid-tropospheric CO_2

Mid-tropospheric CO_2 retrieved from the Atmospheric Infrared Sounder (AIRS) was used to investigate CO_2 interannual variability over the Indo-Pacific region. A signal with periodicity around two years was found for the AIRS mid-tropospheric CO_2 for the first time, which is related to the Tropospheric Biennial Oscillation (TBO) associated with the strength of the monsoon. During a strong (weak) monsoon year, the Western Walker Circulation is strong (weak), resulting in enhanced (diminished) CO_2 transport from the surface to the mid-troposphere. As a result, there are positive (negative) CO2 anomalies at mid-troposphere over the Indo-Pacific region. We simulated the influence of the TBO on the mid-tropospheric CO_2 over the Indo-Pacific region using the MOZART-2 model, and results were consistent with observations, although we found the TBO signal in the model CO_2 is to be smaller than that in the AIRS observations

Influence of Stratospheric Sudden Warming on AIRS Midtropospheric CO_2

Midtropospheric CO_2 retrievals from the Atmospheric Infrared Sounder (AIRS) were used to explore the influence of stratospheric sudden warming (SSW) on CO_2 in the middle to upper troposphere. To choose the SSW events that had strong coupling between the stratosphere and troposphere, the authors applied a principal component analysis to the NCEP/Department of Energy Global Reanalysis 2 (NCEP-2) geopotential height data at 17 pressure levels. Two events (April 2003 and March 2005) that have strong couplings between the stratosphere and troposphere were chosen to investigate the influence of SSW on AIRS midtropospheric CO_2. The authors investigated the temporal and spatial variations of AIRS midtropospheric CO_2 before and after the SSW events and found that the midtropospheric CO_2 concentrations increased by 2–3 ppm within a few days after the SSW events. These results can be used to better understand how the chemical tracers respond to the large-scale dynamics in the high latitudes

CO_2 semiannual oscillation in the middle troposphere and at the surface

Using in situ measurements, we find a semiannual oscillation (SAO) in the midtropospheric and surface CO_2. Chemistry transport models (2-D Caltech/JPL model, 3-D GEOS-Chem, and 3-D MOZART-2) are used to investigate possible sources for the SAO signal in the midtropospheric and surface CO_2. From model sensitivity studies, it is revealed that the SAO signal in the midtropospheric CO_2 originates mainly from surface CO_2 with a small contribution from transport fields. It is also found that the source for the SAO signal in surface CO_2 is mostly related to the CO_2 exchange between the biosphere and the atmosphere. By comparing model CO_2 with in situ CO_2 measurements at the surface, we find that models are able to capture both annual and semiannual cycles well at the surface. Model simulations of the annual and semiannual cycles of CO_2 in the tropical middle troposphere agree reasonably well with aircraft measurements

Influence of El Niño on Midtropospheric CO_2 from Atmospheric Infrared Sounder and Model

The authors investigate the influence of El Niño on midtropospheric CO_2 from the Atmospheric Infrared Sounder (AIRS) and the Model for Ozone and Related Chemical Tracers, version 2 (MOZART-2). AIRS midtropospheric CO_2 data are used to study the temporal and spatial variability of CO_2 in response to El Niño. CO_2 differences between the central and western Pacific Ocean correlate well with the Southern Oscillation index. To reveal the temporal and spatial variability of the El Niño signal in the AIRS midtropospheric CO_2, a multiple regression method is applied to the CO_2 data from September 2002 to February 2011. There is more (less) midtropospheric CO_2 in the central Pacific and less (more) midtropospheric CO_2 in the western Pacific during El Niño (La Niña) events. Similar results are seen in the MOZART-2 convolved midtropospheric CO_2, although the El Niño signal in the MOZART-2 is weaker than that in the AIRS data

El Niño–Southern Oscillation in Tropical and Midlatitude Column Ozone

The impacts of El Niño–Southern Oscillation (ENSO) on the tropical total column ozone, the tropical tropopause pressure, and the 3.5-yr ozone signal in the midlatitude total column ozone were examined using the Goddard Earth Observing System Chemistry–Climate Model (GEOS CCM). Observed monthly mean sea surface temperature and sea ice between 1951 and 2004 were used as boundary conditions for the model. Since the model includes no solar cycle, quasi-biennial oscillation, or volcanic forcing, the ENSO signal was found to dominate the tropical total column ozone variability. Principal component analysis was applied to the detrended, deseasonalized, and low-pass filtered model outputs. The first mode of model total column ozone captured 63.8% of the total variance. The spatial pattern of this mode was similar to that in Total Ozone Mapping Spectrometer (TOMS) observations. There was also a clear ENSO signal in the tropical tropopause pressure in the GEOS CCM, which is related to the ENSO signal in the total column ozone. The regression coefficient between the model total column ozone and the model tropopause pressure was 0.71 Dobson units (DU) hPa^(−1). The GEOS CCM was also used to investigate a possible mechanism for the 3.5-yr signal observed in the midlatitude total column ozone. The 3.5-yr signal in the GEOS CCM column ozone is similar to that in the observations, which suggests that a model with realistic ENSO can reproduce the 3.5-yr signal. Hence, it is likely that the 3.5-yr signal was caused by ENSO

A Resonant Lorentz-Force Magnetometer Exploiting Blue Sideband Actuation to Enhance Sensitivity and Resolution

This paper reports a miniaturized resonant Lorentz-force magnetometer that exploits blue-sideband actuation to attain a better sensitivity and resolution. The resonant magnetometer consists of a double-ended tuning fork (DETF) resonator with cavity slots to optimize thermoelastic dissipation, as well as a Lorentz-force generator structure to transduce the magnetic force to the axial of the resonator. The proposed device demonstrates a Lorentz-force sensitivity of 5.5 mV/nN, a noise floor of 1.25 μV/ √ Hz, and a resolution of 0.23 pN/ √ Hz. In comparison with a conventional drive scheme, the blue- sideband actuation achieves approximately two orders of magnitude improvement regarding sensitivity and resolution than that of the amplitude modulation (AM) readout and 3.6-fold enhancement than that of the frequency modulation (FM) readout. The results affirm the merit of the novel excitation method and provide solid evidence of its effectiveness in practical applications