Mixed Integer Linear Programming for Feature Selection in Support Vector Machine

This work focuses on support vector machine (SVM) with feature selection. A MILP formulation is proposed for the problem. The choice of suitable features to construct the separating hyperplanes has been modelled in this formulation by including a budget constraint that sets in advance a limit on the number of features to be used in the classification process. We propose both an exact and a heuristic procedure to solve this formulation in an efficient way. Finally, the validation of the model is done by checking it with some well-known data sets and comparing it with classical classification methods.Comment: 37 pages, 20 figure

Ultradeep Infrared Array Camera Observations of sub-L* z~7 and z~8 Galaxies in the Hubble Ultra Deep Field: the Contribution of Low-Luminosity Galaxies to the Stellar Mass Density and Reionization

We study the Spitzer Infrared Array Camera (IRAC) mid-infrared (rest-frame optical) fluxes of 14 newly WFC3/IR-detected z=7 z_{850}-dropout galaxies and 5 z=8 Y_{105}-dropout galaxies. The WFC3/IR depth and spatial resolution allow accurate removal of contaminating foreground light, enabling reliable flux measurements at 3.6 micron and 4.5 micron. None of the galaxies are detected to [3.6]=26.9 (AB, 2 sigma), but a stacking analysis reveals a robust detection for the z_{850}-dropouts and an upper limit for the Y_{105}-dropouts. We construct average broadband SEDs using the stacked ACS, WFC3, and IRAC fluxes and fit stellar population synthesis models to derive mean redshifts, stellar masses, and ages. For the z_{850}-dropouts, we find z=6.9^{+0.1}_{-0.1}, (U-V)_{rest}=0.4, reddening A_V=0, stellar mass M*=1.2^{+0.3}_{-0.6} x 10^9 M_sun (Salpeter IMF). The best-fit ages ~300Myr, M/L_V=0.2, and SSFR=1.7Gyr^{-1} are similar to values reported for luminous z=7 galaxies, indicating the galaxies are smaller but not younger. The sub-L* galaxies observed here contribute significantly to the stellar mass density and under favorable conditions may have provided enough photons for sustained reionization at 7<z<11. In contrast, the z=8.3^{+0.1}_{-0.2} Y_{105}-dropouts have stellar masses that are uncertain by 1.5 dex due to the near-complete reliance on far-UV data. Adopting the 2 sigma upper limit on the M/L(z=8), the stellar mass density to M_{UV,AB} < -18 declines from rho*(z=7)=3.7^{+1.0}_{-1.8} x 10^6 M_sun Mpc^{-3} to rho*(z=8) < 8 x 10^5 M_sun Mpc^{-3}, following (1+z)^{-6} over 3<z<8. Lower masses at z=8 would signify more dramatic evolution, which can be established with deeper IRAC observations, long before the arrival of the James Webb Space Telescope.Comment: 6 pages, 3 figures, 2 tables, emulateapj, accepted for publication in ApJ

Deep infrared studies of massive high redshift galaxies

LEI Universiteit LeidenUBL - phd migration 201

The GREATS Hβ\beta+[OIII] Luminosity Function and Galaxy Properties at z∼8\mathbf{z\sim8}: Walking the Way of JWST

The James Webb Space Telescope will allow to spectroscopically study an unprecedented number of galaxies deep into the reionization era, notably by detecting [OIII] and H$\beta$ nebular emission lines. To efficiently prepare such observations, we photometrically select a large sample of galaxies at $z\sim8$ and study their rest-frame optical emission lines. Combining data from the GOODS Re-ionization Era wide-Area Treasury from Spitzer (GREATS) survey and from HST, we perform spectral energy distribution (SED) fitting, using synthetic SEDs from a large grid of photoionization models. The deep Spitzer/IRAC data combined with our models exploring a large parameter space enables to constrain the [OIII]+H$\beta$ fluxes and equivalent widths for our sample, as well as the average physical properties of $z\sim8$ galaxies, such as the ionizing photon production efficiency with $\log(\xi_\mathrm{ion}/\mathrm{erg}^{-1}\hspace{1mm}\mathrm{Hz})\geq25.77$. We find a relatively tight correlation between the [OIII]+H$\beta$ and UV luminosity, which we use to derive for the first time the [OIII]+H$\beta$ luminosity function (LF) at $z\sim8$. The $z\sim8$ [OIII]+H$\beta$ LF is higher at all luminosities compared to lower redshift, as opposed to the UV LF, due to an increase of the [OIII]+H$\beta$ luminosity at a given UV luminosity from $z\sim3$ to $z\sim8$. Finally, using the [OIII]+H$\beta$ LF, we make predictions for JWST/NIRSpec number counts of $z\sim8$ galaxies. We find that the current wide-area extragalactic legacy fields are too shallow to use JWST at maximal efficiency for $z\sim8$ spectroscopy even at 1hr depth and JWST pre-imaging to $\gtrsim30$ mag will be required.Comment: 13 pages, 9 figures, accepted for publication in MNRA

The Outstanding Decisions of the United States Supreme Court in 1954

We perform a kinematic and morphological analysis of 44 star-forming galaxies at z ̃ 2 in the COSMOS legacy field using near-infrared spectroscopy from Keck/MOSFIRE and F160W imaging from CANDELS/3D-HST as part of the ZFIRE survey. Our sample consists of cluster and field galaxies from 2.0 &lt; z &lt; 2.5 with K-band multi-object slit spectroscopic measurements of their Hα emission lines. Hα rotational velocities and gas velocity dispersions are measured using the Heidelberg Emission Line Algorithm (HELA), which compares directly to simulated 3D data cubes. Using a suite of simulated emission lines, we determine that HELA reliably recovers input S 0.5 and angular momentum at small offsets, but V 2.2/σ g values are offset and highly scattered. We examine the role of regular and irregular morphology in the stellar mass kinematic scaling relations, deriving the kinematic measurement S 0.5, and finding {log}({S}0.5)=(0.38+/- 0.07){log}(M/{M}☉ -10)+(2.04+/- 0.03) with no significant offset between morphological populations and similar levels of scatter (̃0.16 dex). Additionally, we identify a correlation between M ⋆ and V 2.2/σ g for the total sample, showing an increasing level of rotation dominance with increasing M ⋆, and a high level of scatter for both regular and irregular galaxies. We estimate the specific angular momenta (j disk) of these galaxies and find a slope of 0.36 ± 0.12, shallower than predicted without mass-dependent disk growth, but this result is possibly due to measurement uncertainty at M ⋆ &lt; 9.5 However, through a Kolmogorov-Smirnov test we find irregular galaxies to have marginally higher j disk values than regular galaxies, and high scatter at low masses in both populations

Expanded Search for z~10 Galaxies from HUDF09, ERS, and CANDELS Data: Evidence for Accelerated Evolution at z>8?

We search for z~10 galaxies over ~160 arcmin^2 of WFC3/IR data in the Chandra Deep Field South, using the public HUDF09, ERS, and CANDELS surveys, that reach to 5sigma depths ranging from 26.9 to 29.4 in H_160 AB mag. z>~9.5 galaxy candidates are identified via J_125-H_160>1.2 colors and non-detections in any band blueward of J_125. Spitzer IRAC photometry is key for separating the genuine high-z candidates from intermediate redshift (z~2-4) galaxies with evolved or heavily dust obscured stellar populations. After removing 16 sources of intermediate brightness (H_160~24-26 mag) with strong IRAC detections, we only find one plausible z~10 galaxy candidate in the whole data set, previously reported in Bouwens et al. (2011). The newer data cover a 3x larger area and provide much stronger constraints on the evolution of the UV luminosity function (LF). If the evolution of the z~4-8 LFs is extrapolated to z~10, six z~10 galaxies are expected in our data. The detection of only one source suggests that the UV LF evolves at an accelerated rate before z~8. The luminosity density is found to increase by more than an order of magnitude in only 170 Myr from z~10 to z~8. This increase is >=4x larger than expected from the lower redshift extrapolation of the UV LF. We are thus likely witnessing the first rapid build-up of galaxies in the heart of cosmic reionization. Future deep HST WFC3/IR data, reaching to well beyond 29 mag, can enable a more robust quantification of the accelerated evolution around z~10.Comment: 13 pages, 11 figures, ApJ resubmitted after referee repor

Mean Hα+[N ii]+[S ii] EW inferred for star-forming galaxies at z ∼ 5.1–5.4 using high-quality Spitzer /IRAC photometry

Recent Spitzer/InfraRed Array Camera (IRAC) photometric observations have revealed that rest-frame optical emission lines contribute significantly to the broad-band fluxes of high-redshift galaxies. Specifically, in the narrow redshift range z ∼ 5.1–5.4 the [3.6]–[4.5] colour is expected to be very red, due to contamination of the 4.5 μm band by the dominant Hα line, while the 3.6 μm filter is free of nebular emission lines. We take advantage of new reductions of deep Spitzer/IRAC imaging over the Great Observatories Origins Deep Survey-North+South fields (Labbé et al. 2015) to obtain a clean measurement of the mean Hα equivalent width (EW) from the [3.6]–[4.5] colour in the redshift range z = 5.1–5.4. The selected sources either have measured spectroscopic redshifts (13 sources) or lie very confidently in the redshift range z = 5.1–5.4 based on the photometric redshift likelihood intervals (11 sources). Our zphot = 5.1–5.4 sample and zspec = 5.10–5.40 spectroscopic sample have a mean [3.6]–[4.5] colour of 0.31 ± 0.05 and 0.35 ± 0.07 mag, implying a rest-frame EW (Hα+[N II]+[S II]) of 665 ± 53 and 707 ± 74 Å, respectively, for sources in these samples. These values are consistent albeit slightly higher than derived by Stark et al. at z ∼ 4, suggesting an evolution to higher values of the Hα+[N II]+[S II] EW at z > 2. Using the 3.6 μm band, which is free of emission line contamination, we perform robust spectral energy distribution fitting and find a median specific star formation rate of sSFR = 17+2−517−5+2 Gyr−1, 7+1−2×7−2+1× higher than at z ∼ 2. We find no strong correlation (<2σ) between the Hα+[N II]+[S II] EW and the stellar mass of sources. Before the advent of JWST, improvements in these results will come through an expansion of current spectroscopic samples and deeper Spitzer/IRAC measurements

UV Luminosity Functions from 132 z~7 and z~8 Lyman-Break Galaxies in the ultra-deep HUDF09 and wide-area ERS WFC3/IR Observations

We identify 73 z~7 and 59 z~8 candidate galaxies in the reionization epoch, and use this large 26-29.4 AB mag sample of galaxies to derive very deep luminosity functions to <-18 AB mag and the star formation rate density at z~7 and z~8. The galaxy sample is derived using a sophisticated Lyman-Break technique on the full two-year WFC3/IR and ACS data available over the HUDF09 (~29.4 AB mag, 5 sigma), two nearby HUDF09 fields (~29 AB mag, 14 arcmin) and the wider area ERS (~27.5 AB mag) ~40 arcmin**2). The application of strict optical non-detection criteria ensures the contamination fraction is kept low (just ~7% in the HUDF). This very low value includes a full assessment of the contamination from lower redshift sources, photometric scatter, AGN, spurious sources, low mass stars, and transients (e.g., SNe). From careful modelling of the selection volumes for each of our search fields we derive luminosity functions for galaxies at z~7 and z~8 to <-18 AB mag. The faint-end slopes alpha at z~7 and z~8 are uncertain but very steep at alpha = -2.01+/-0.21 and alpha=-1.91+/-0.32, respectively. Such steep slopes contrast to the local alpha<~-1.4 and may even be steeper than that at z~4 where alpha=-1.73+/-0.05. With such steep slopes (alpha<~-1.7) lower luminosity galaxies dominate the galaxy luminosity density during the epoch of reionization. The star formation rate densities derived from these new z~7 and z~8 luminosity functions are consistent with the trends found at later times (lower redshifts). We find reasonable consistency, with the SFR densities implied from reported stellar mass densities, being only ~40% higher at z<7. This suggests that (1) the stellar mass densities inferred from the Spitzer IRAC photometry are reasonably accurate and (2) that the IMF at very high redshift may not be very different from that at later times.Comment: 38 pages, 21 figures, 20 tables, ApJ, accepted for publicatio

Relations among several nuclear and electronic density functional reactivity indexes

A set of connections among several nuclear and electronic indexes of reactivity in the framework of the conceptual Density Functional Theory by using an expansion ofthe energy functional in terms of the total number of electrons and the normal coordinates within a canonical ensemble was derived. The relations obtained provided explicit links between important quantities related to the chemical reactivity of a system. This paper particularly demonstrates that the derivative of the electronic energy with respect to the external potential of a system in its equilibrium geometry was equal to the negative of the nuclear repulsion derivative with respect to the external potentia