Pattern avoidance in compositions and multiset permutations

We study pattern avoidance by combinatorial objects other than permutations, namely by ordered partitions of an integer and by permutations of a multiset. In the former case we determine the generating function explicitly, for integer compositions of n that avoid a given pattern of length 3 and we show that the answer is the same for all such patterns. We also show that the number of multiset permutations that avoid a given three-letter pattern is the same for all such patterns, thereby extending and refining earlier results of Albert, Aldred et al., and by Atkinson, Walker and Linton. Further, the number of permutations of a multiset S, with a_i copies of i for i = 1, ..., k, that avoid a given permutation pattern in S_3 is a symmetric function of the a_i's, and we will give here a bijective proof of this fact first for the pattern (123), and then for all patterns in S_3 by using a recently discovered bijection of Amy N. Myers.Comment: 8 pages, no figur

Training health professionals in patient-centered communication during magnetic resonance imaging to reduce patients’ perceived anxiety

Objective: We examined how a patient-centered communication training program for magnetic resonance imaging (MRI) affected health professional (HP) practice and patients’ perceived anxiety (PA). Methods: We implemented an intervention program. Six of the 17 eligible HPs completed the study. The proportion of observed desired behaviors (PODBs), including MRI procedure explanation (MRI-PE), communication, and MRI checking procedures was measured using an observation grid. We tested 182 patients (85 pre-, 58 post-, and 39 at follow-up) for PA pre- and post-MRI. Results: The Bayesian ANOVA effect size suggested moderate evidence of improvement in HP PODBs, preto post-intervention. Use of MRI-PE declined between post-intervention and follow-up (6 months later). Observed changes in PA, pre- to post-MRI, could be related to time constraints and perceived pressure to explain the exam in detail once institutional routines are reestablished. Conclusion: In MRI units, time constraints condition the performance of HPs who address patients’ PA. Practice implications: “Real workplace” interventions that promote better patient-centered communication and provide each patient with a comprehensive explanation of MRI procedures also appear to improve HP PODBs

Remittances, Liquidity Constraints and Human Capital Investments in Ecuador

Over the last decade Ecuador has experienced a strong increase in financial transfers from migrated workers, amounting to 6.4 percent of GDP and 31.5 percent of total exports of goods and services in 2005. This paper investigates how remittances via trans-national networks affect human capital investments through relaxing resource constraints and facilitate households in consumption smoothing by reducing vulnerability to economic shocks. In particular, we explore the effects of remittances on school enrolment and child work in Ecuador. Identification relies on instrumental variables, exploiting information on source countries of remittances and regional variation in the availability of bank offices that function as formal channels for sending remittances. Our results show that remittances increase school enrolment and decrease incidence of child work, especially for girls and in rural areas. Furthermore, we find that aggregate shocks are associated with increased work activities, while remittances are used to finance education when households are faced with these shocks. This suggests that liquidity constraints and vulnerability to covariate risk are especially relevant in rural areas, as it affects household’s investments in human capital of school age children. In this context both child labour supply and transnational remittances serve as coping mechanisms.migration, remittances, trans-national networks, education, child labour, Ecuador

Regularly spaced subsums of integer partitions

For integer partitions $\lambda :n=a_1+...+a_k$, where $a_1\ge a_2\ge >...\ge a_k\ge 1$, we study the sum $a_1+a_3+...$ of the parts of odd index. We show that the average of this sum, over all partitions $\lambda$ of $n$, is of the form $n/2+(\sqrt{6}/(8\pi))\sqrt{n}\log{n}+c_{2,1}\sqrt{n}+O(\log{n}).$ More generally, we study the sum $a_i+a_{m+i}+a_{2m+i}+...$ of the parts whose indices lie in a given arithmetic progression and we show that the average of this sum, over all partitions of $n$, is of the form $n/m+b_{m,i}\sqrt{n}\log{n}+c_{m,i}\sqrt{n}+O(\log{n})$, with explicitly given constants $b_{m,i},c_{m,i}$. Interestingly, for $m$ odd and $i=(m+1)/2$ we have $b_{m,i}=0$, so in this case the error term is of lower order. The methods used involve asymptotic formulas for the behavior of Lambert series and the Zeta function of Hurwitz. We also show that if $f(n,j)$ is the number of partitions of $n$ the sum of whose parts of even index is $j$, then for every $n$, $f(n,j)$ agrees with a certain universal sequence, Sloane's sequence \texttt{#A000712}, for $j\le n/3$ but not for any larger $j$

In-plane structure and ordering at liquid sodium surfaces and interfaces from ab initio molecular dynamics

Atoms at liquid metal surfaces are known to form layers parallel to the surface. We analyze the two-dimensional arrangement of atoms within such layers at the surface of liquid sodium, using ab initio molecular dynamics (MD) simulations based on density functional theory. Nearest neighbor distributions at the surface indicate mostly 5-fold coordination, though there are noticeable fractions of 4-fold and 6-fold coordinated atoms. Bond angle distributions suggest a movement toward the angles corresponding to a six-fold coordinated hexagonal arrangement of the atoms as the temperature is decreased towards the solidification point. We rationalize these results with a distorted hexagonal order at the surface, showing a mixture of regions of five and six-fold coordination. The liquid surface results are compared with classical MD simulations of the liquid surface, with similar effects appearing, and with ab initio MD simulations for a model solid-liquid interface, where a pronounced shift towards hexagonal ordering is observed as the temperature is lowered