The Hamilton-Waterloo Problem with even cycle lengths

The Hamilton-Waterloo Problem HWP$(v;m,n;\alpha,\beta)$ asks for a 2-factorization of the complete graph $K_v$ or $K_v-I$, the complete graph with the edges of a 1-factor removed, into $\alpha$ $C_m$-factors and $\beta$ $C_n$-factors, where $3 \leq m < n$. In the case that $m$ and $n$ are both even, the problem has been solved except possibly when $1 \in \{\alpha,\beta\}$ or when $\alpha$ and $\beta$ are both odd, in which case necessarily $v \equiv 2 \pmod{4}$. In this paper, we develop a new construction that creates factorizations with larger cycles from existing factorizations under certain conditions. This construction enables us to show that there is a solution to HWP$(v;2m,2n;\alpha,\beta)$ for odd $\alpha$ and $\beta$ whenever the obvious necessary conditions hold, except possibly if $\beta=1$; $\beta=3$ and $\gcd(m,n)=1$; $\alpha=1$; or $v=2mn/\gcd(m,n)$. This result almost completely settles the existence problem for even cycles, other than the possible exceptions noted above

Barriers to the Employment of Welfare Recipients

Dramatic reductions in welfare caseloads since passage of the Personal Responsibility and WorkOpportunity Reconciliation Act of 1996 have not allayed policy concerns about the employability of recipients remaining on the rolls. Analysis of potential barriers to employment can address whether current recipients have problems that either singly or in combination make it difficult for them to comply with the new requirements for getting and keeping jobs. In this paper, we explore the prevalence and work effects of 14 potential barriers in a new survey of a representative sample of 753 urban single-mother recipients. We report the prevalence of the barriers and how their number predicts employment rates, controlling for demographic characteristics. We also analyze which individual barriers are associated with employment and how a model inclusive of a comprehensive array of barriers improves upon a traditional human capital model of the work effects of education and work and welfare history. Single mothers who received welfare in 1997 had higher rates of personal health and mental health problems, domestic violence, and children’s health problems than do women in national samples, but they were no more likely than the general population to be drug or alcohol dependent. Only 15 percent of respondents had none of the barriers and almost two-thirds had two or more barriers. The numbers of multiple barriers were strongly and negatively associated with working, and among the individual barriers, low education, lack of access to transportation, poor health, having drug dependence or a major depressive disorder, and several experiences of workplace discrimination reduced employment. Welfare-to-work programs need to be more finely targeted with respect to exemptions and service provision, and states should consider providing longer-term and enhanced supports for those who face low prospects of leaving welfare for employment.

IUE observations of oxygen-rich supernova remnants

The IUE observations were used to determine the composition of the ejecta (especially C and Si abundances) and to test models for the ionization and excitation of the ejecta of two oxygen-rich supernova remnants (N132D in the Large Magellanic Cloud and 1E 0102-7219 in the Small Magellanic Cloud). Time-dependent photoionization by the EUV and X-ray radiation from 1E 0102-7219 can qualitatively explain its UV and optical line emission, but the density and ionization structures are complex and prevent a unique model from being specified. Many model parameters are poorly constrained, including the time dependence and shape of the ionizing spectrum. Moreover, the models presented are not self-consistent in that the volumes and densities of the optically emitting gas imply optical depths of order unity in the EUV, but absorption of the ionizing radiation was ignored. It is possible that these shortcomings reflect a more fundamental limitation of the model assumptions. It is assumed that the electron velocity distribution is Maxwellian and that the energy deposited by photoionization heats the electrons directly. The 500 eV electrons produced by the Auger process may excite or ionize other ions before they slow down enough to share their energy with other electrons. Many of the excitations would produce photons that could ionize lower ionization stages

Age is associated with reduced urethral pressure and afferent activity in rat

Age-related changes in the lower urinary tract (LUT) can affect the coordination of reflexes and increase the incidence of bladder disorders in elderly. This study examines the age-related loss of urethral signaling capability by measuring the afferent activity directly. We find that less urethral pressure develops in response to fluid flow in old rats compared to young rats and that pressure and flow evoke less urethral afferent activation. These findings are consistent with our previous study demonstrating that the urethra-to-bladder reflex, which is required for efficient voiding, becomes weaker with age. We measured the pudendal afferent response in young (4–7 months) and old (18–24 months) rats to fluid flow in the urethra across a range of flow rates. We used paraffin embedding and hematoxylin and eosin staining to quantify age-related changes in the sensory branch of the pudendal nerve. Urethral afferent signaling in response to the same urethral flow rates was weaker in older animals. That is, the sensitivity of urethra afferents to flow decreased with age, and higher flow rates were required in older animals to recruit urethra afferents. There was also a reduction in the myelin thickness of pudendal afferents in old rats, which is a possible contributing factor to the sensory activity. Furthermore, the same flow rates evoked less pressure in the urethras of old animals, indicating there is an age-related change of the urethral tissue that reduces the pressure stimulus to which these afferents respond. These results help characterize the underlying changes in LUT system with age

Sensory Motor Remapping of Space in Human-Machine Interfaces

Studies of adaptation to patterns of deterministic forces have revealed the ability of the motor control system to form and use predictive representations of the environment. These studies have also pointed out that adaptation to novel dynamics is aimed at preserving the trajectories of a controlled endpoint, either the hand of a subject or a transported object. We review some of these experiments and present more recent studies aimed at understanding how the motor system forms representations of the physical space in which actions take place. An extensive line of investigations in visual information processing has dealt with the issue of how the Euclidean properties of space are recovered from visual signals that do not appear to possess these properties. The same question is addressed here in the context of motor behavior and motor learning by observing how people remap hand gestures and body motions that control the state of an external device. We present some theoretical considerations and experimental evidence about the ability of the nervous system to create novel patterns of coordination that are consistent with the representation of extrapersonal space. We also discuss the perspective of endowing human–machine interfaces with learning algorithms that, combined with human learning, may facilitate the control of powered wheelchairs and other assistive devices

Constructing uniform 2-factorizations via row-sum matrices: solutions to the Hamilton-Waterloo problem

In this paper, we formally introduce the concept of a row-sum matrix over an arbitrary group $G$. When $G$ is cyclic, these types of matrices have been widely used to build uniform 2-factorizations of small Cayley graphs (or, Cayley subgraphs of blown-up cycles), which themselves factorize complete (equipartite) graphs. Here, we construct row-sum matrices over a class of non-abelian groups, the generalized dihedral groups, and we use them to construct uniform $2$-factorizations that solve infinitely many open cases of the Hamilton-Waterloo problem, thus filling up large parts of the gaps in the spectrum of orders for which such factorizations are known to exist

High Resolution mid-Infrared Imaging of SN 1987A

Using the Thermal-Region Camera and Spectrograph (T-ReCS) attached to the Gemini South 8m telescope, we have detected and resolved 10 micron emission at the position of the inner equatorial ring (ER) of supernova SN 1987A at day 6067. ``Hot spots'' similar to those found in the optical and near-IR are clearly present. The morphology of the 10 micron emission is globally similar to the morphology at other wavelengths from X-rays to radio. The observed mid-IR flux in the region of SN1987A is probably dominated by emission from dust in the ER. We have also detected the ER at 20 micron at a 4 sigma level. Assuming that thermal dust radiation is the origin of the mid-IR emission, we derive a dust temperature of 180^{+20}_{-10} K, and a dust mass of 1.- 8. 10^{-5} Mo for the ER. Our observations also show a weak detection of the central ejecta at 10 micron. We show that previous bolometric flux estimates (through day 2100) were not significantly contaminated by this newly discovered emission from the ER. If we assume that the energy input comes from radioactive decays only, our measurements together with the current theoretical models set a temperature of 90 leq T leq 100 K and a mass range of 10^{-4} - 2. 10^{-3} Mo for the dust in the ejecta. With such dust temperatures the estimated thermal emission is 9(+/-3) 10^{35} erg s^{-1} from the inner ring, and 1.5 (+/-0.5) 10^{36} erg s^{-1} from the ejecta. Finally, using SN 1987A as a template, we discuss the possible role of supernovae as major sources of dust in the Universe.Comment: aastex502, 14 pages, 4 figures; Accepted for publication in ApJ Content changed: new observations, Referee's comments and suggestion

Deep Chandra and multicolor HST observations of the jets of 3C 371 and PKS 2201+044

This paper presents multiwavelength imaging and broad-band spectroscopy of the relativistic jets in the two nearby radio galaxies 3C 371 and PKS 2201+044, acquired with Chandra, HST, VLA, and Merlin. Radio polarization images are also available. The two sources stand out as "intermediate'' between FRIs and FRIIs; their cores are classified as BL Lacs, although broad and narrow optical emission lines were detected at times. The multiwavelength images show jet morphologies with the X-ray emission peaking closer to the nucleus than the longer wavelengths. The jets are resolved at all wavelengths in a direction perpendicular to the jet axis. The jets SEDs are consistent with a single spectral component from radio to X-rays, interpreted as synchrotron emission. The SEDs show a progressive softening from the inner to the outer regions of the jet, indicating that the electron break energy moves to lower energies with distance from the core. Overall, the X-ray and multiwavelength properties of the jets of 3C 371 and PKS 2201+044 appear intermediate between those of FRIs and FRIIs.Comment: Accepted for publication in ApJ; 28 pages (emulateapj5), 17 figure