Instance Space of the Number Partitioning Problem

Within the replica framework we study analytically the instance space of the number partitioning problem. This classic integer programming problem consists of partitioning a sequence of N positive real numbers \{a_1, a_2,..., a_N} (the instance) into two sets such that the absolute value of the difference of the sums of $a_j$ over the two sets is minimized. We show that there is an upper bound $\alpha_c N$ to the number of perfect partitions (i.e. partitions for which that difference is zero) and characterize the statistical properties of the instances for which those partitions exist. In particular, in the case that the two sets have the same cardinality (balanced partitions) we find $\alpha_c=1/2$. Moreover, we show that the disordered model resulting from hte instance space approach can be viewed as a model of replicators where the random interactions are given by the Hebb rule.Comment: 7 page

Comment on "Evidence for the Droplet/Scaling Picture of Spin Glasses"

In a recent letter Moore et al. claim to exhibit evidence for a non-mean-field behavior of the $3d$ Ising spin glass. We show that their claim is insubstantial, and by analyzing in detail the behavior of the Migdal-Kadanoff approximation (MKA) as compared to the behavior of the Edwards-Anderson (EA) spin glass we find further evidence of a mean-field like behavior of the $3d$ spin glass.Comment: 1 page comment including one postscript figur

Two 2MASS-Selected Young Stellar Clusters: Photometry, Spectroscopy, and the IMF

We present near-infrared J, H, and K_s images and K-band spectroscopy of two newly discovered stellar clusters at different stages of evolution. Our spectra suggest the presence of massive YSOs in the heavily embedded cluster in the star-forming region near radio source G353.4-0.4 and an O5-O6V star in the cluster near radio source G305+00.2. We determine a K-band luminosity function (KLF) for both clusters and an initial mass function (IMF) for the cluster near G305+00.2. The derived IMF slope is -1.5 if the KLF is used to derive the IMF and is -0.98 if the color-magnitude diagram and spectra are used. The more reliable CMD-based slope is flatter than the Salpeter value usually found for stellar clusters. We find that using the KLF alone to derive an IMF is likely to produce an overly steep slope in stellar clusters subject to variable extinction.Comment: 16 pages, 18 figures, accepted to A

Storage of correlated patterns in a perceptron

We calculate the storage capacity of a perceptron for correlated gaussian patterns. We find that the storage capacity $\alpha_c$ can be less than 2 if similar patterns are mapped onto different outputs and vice versa. As long as the patterns are in general position we obtain, in contrast to previous works, that $\alpha_c \geq 1$ in agreement with Cover's theorem. Numerical simulations confirm the results.Comment: 9 pages LaTeX ioplppt style, figures included using eps

5cm OH masers as diagnostics of physical conditions in star-forming regions

We demonstrate that the observed characteristics of the 5 cm OH masers in star-forming regions can be explained with the same model and the same parameters as the 18 cm and the 6 cm OH masers. In our already published study of the 18 cm and the 6 cm OH masers in star-forming regions we had examined the pumping of the 5 cm masers, but did not report the results we had found because of some missing collision rate coefficients, which in principle could be important. The recently published observations on the 5 cm masers of OH encourage us to report our old calculations along with some new ones that we have performed. These calculations, in agreement with the observations, reveal the main lines at 5 cm as strong masers, the 6049 MHz satellite line as a weak maser, and the 6017 MHz satellite line as never inverted for reasonable values of the parametersComment: TeX 15 pages, 30 postscript figures, accepted by Ap

CH 3 GHz Observations of the Galactic Center

A 3 $\times$ 3 map of the Galactic Center was made at 9\arcmin resolution and 10\arcmin spacing in the CH $^2\Pi_{1/2}$, J=1/2, F=1-1 transition at 3335 MHz. The CH emission shows a velocity extent that is nearly that of the CO(1-0) line, but the CH line profiles differ markedly from the CO. The 3335 MHz CH transition primarily traces low-density molecular gas and our observations indicate that the mass of this component within $\sim$ 30 pc of the Galactic Center is $\sim$ 9 $\times$ 10$^6$ M$_\odot$. The CO-H$_2$ conversion factor obtained for the low-density gas in the mapped region is greater than that thought to apply to the dense molecular gas at the Galactic Center. In addition to tracing the low-density molecular gas at the Galactic Center, the CH spectra show evidence of emission from molecular clouds along the line of sight both in the foreground and background. The scale height of these clouds ranges from 27 - 109 pc, consistent with previous work based on observations of molecular clouds in the inner Galaxy.Comment: 29 pages, 12 figure

Do divorcing couples become happier by breaking up?

Divorce is a leap in the dark. The paper investigates whether people who split up actually become happier. Using the British Household Panel Survey, we can observe an individual's level of psychological well-being in the years before and after divorce. Our results show that divorcing couples reap psychological gains from the dissolution of their marriages. Men and women benefit equally. The paper also studies the effects of bereavement, of having dependant children and of remarriage. We measure well-being by using general health questionnaire and life satisfaction scores

A Deep Multicolor Survey. VI. Near-Infrared Observations, Selection Effects, and Number Counts

I present near-infrared J (1.25um), H (1.65um), and K (2.2um) imaging observations of 185 square arcminutes in 21 high galactic latitude fields. These observations reach limiting magnitudes of J ~ 21 mag, H ~ 20 mag and K ~ 18.5 mag. The detection efficiency, photometric accuracy and selection biases as a function of integrated object brightness, size, and profile shape are quantified in detail. I evaluate several popular methods for measuring the integrated light of faint galaxies and show that only aperture magnitudes provide an unbiased measure of the integrated light that is independent of apparent magnitude. These J, H, and K counts and near-infrared colors are in best agreement with passive galaxy formation models with at most a small amount of merging (for Omega_M = 0.3, Omega_Lambda = 0.7).Comment: AJ Accepted (Feb 2001). 28 pages, 7 embedded ps figures, AASTEX5. Minor changes to submitted version. Also available at http://www.astronomy.ohio-state.edu/~martini/pubs

Effelsberg Observations of Excited-State (6.0 GHz) OH in Supernova Remnants and W3(OH)

While masers in the 1720 MHz transition of OH are detected toward many supernova remnants (SNRs), no other OH transition is seen as a maser in SNRs. We present a search for masers at 6049 MHz, which has recently been predicted to produce masers by pure collisional excitation at conditions similar to that required for 1720 MHz masing. The Effelsberg 100 m telescope was used to observe the excited-state 6016, 6030, 6035, and 6049 MHz lines of OH toward selected SNRs, most of which have previously-detected bright 1720 MHz masers. No excited-state masers are found toward SNRs, consistent with previous observations of the 6049 MHz and other excited-state transitions. We do not see clear evidence of absorption toward SNR target positions, although we do see evidence of absorption in the molecular cloud at +50 km/s near Sgr A East. Weak absorption is detected at 6016 MHz toward W3(OH), while stronger, narrower emission is seen at 6049 MHz, suggesting that the 6049 MHz emission is a low-gain maser. We conclude that conditions in SNRs are not conducive to excited-state maser emission, especially in excited-state satellite lines.Comment: 4 pages using emulateapj.cls including 2 tables and 1 figure, accepted to ApJ