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.

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