The dropout problem and the attitudes of dropouts of junior high schools in Jefferson County, Colorado

Call number: LD2668 .R4 1963 V47

Faster Exponential-Time Approximation Algorithms Using Approximate Monotone Local Search

We generalize the monotone local search approach of Fomin, Gaspers,Lokshtanov and Saurabh [J.ACM 2019], by establishing a connection betweenparameterized approximation and exponential-time approximation algorithms formonotone subset minimization problems. In a monotone subset minimizationproblem the input implicitly describes a non-empty set family over a universeof size $n$ which is closed under taking supersets. The task is to find aminimum cardinality set in this family. Broadly speaking, we use approximatemonotone local search to show that a parameterized $\alpha$-approximationalgorithm that runs in $c^k \cdot n^{O(1)}$ time, where $k$ is the solutionsize, can be used to derive an $\alpha$-approximation randomized algorithm thatruns in $d^n \cdot n^{O(1)}$ time, where $d$ is the unique value in $d \in(1,1+\frac{c-1}{\alpha})$ such that$\mathcal{D}(\frac{1}{\alpha}\|\frac{d-1}{c-1})=\frac{\ln c}{\alpha}$ and$\mathcal{D}(a \|b)$ is the Kullback-Leibler divergence. This running timematches that of Fomin et al. for $\alpha=1$, and is strictly better when$\alpha >1$, for any $c > 1$. Furthermore, we also show that this result can bederandomized at the expense of a sub-exponential multiplicative factor in therunning time. We demonstrate the potential of approximate monotone local search by derivingnew and faster exponential approximation algorithms for Vertex Cover,$3$-Hitting Set, Directed Feedback Vertex Set, Directed Subset Feedback VertexSet, Directed Odd Cycle Transversal and Undirected Multicut. For instance, weget a $1.1$-approximation algorithm for Vertex Cover with running time $1.114^n\cdot n^{O(1)}$, improving upon the previously best known $1.1$-approximationrunning in time $1.127^n \cdot n^{O(1)}$ by Bourgeois et al. [DAM 2011].<br

Approximate Monotone Local Search for Weighted Problems

In a recent work, Esmer et al. describe a simple method - ApproximateMonotone Local Search - to obtain exponential approximation algorithms fromexisting parameterized exact algorithms, polynomial-time approximationalgorithms and, more generally, parameterized approximation algorithms. In thiswork, we generalize those results to the weighted setting. More formally, we consider monotone subset minimization problems over aweighted universe of size $n$ (e.g., Vertex Cover, $d$-Hitting Set and FeedbackVertex Set). We consider a model where the algorithm is only given access to asubroutine that finds a solution of weight at most $\alpha \cdot W$ (and ofarbitrary cardinality) in time $c^k \cdot n^{O(1)}$ where $W$ is the minimumweight of a solution of cardinality at most $k$. In the unweighted setting,Esmer et al. determine the smallest value $d$ for which a $\beta$-approximationalgorithm running in time $d^n \cdot n^{O(1)}$ can be obtained in this model.We show that the same dependencies also hold in a weighted setting in thismodel: for every fixed $\varepsilon>0$ we obtain a $\beta$-approximationalgorithm running in time $O\left((d+\varepsilon)^{n}\right)$, for the same $d$as in the unweighted setting. Similarly, we also extend a $\beta$-approximate brute-force search (in amodel which only provides access to a membership oracle) to the weightedsetting. Using existing approximation algorithms and exact parameterizedalgorithms for weighted problems, we obtain the first exponential-time$\beta$-approximation algorithms that are better than brute force for a varietyof problems including Weighted Vertex Cover, Weighted $d$-Hitting Set, WeightedFeedback Vertex Set and Weighted Multicut.<br

Optimally Repurposing Existing Algorithms to Obtain Exponential-Time Approximations

The goal of this paper is to understand how exponential-time approximationalgorithms can be obtained from existing polynomial-time approximationalgorithms, existing parameterized exact algorithms, and existing parameterizedapproximation algorithms. More formally, we consider a monotone subsetminimization problem over a universe of size $n$ (e.g., Vertex Cover orFeedback Vertex Set). We have access to an algorithm that finds an$\alpha$-approximate solution in time $c^k \cdot n^{O(1)}$ if a solution ofsize $k$ exists (and more generally, an extension algorithm that canapproximate in a similar way if a set can be extended to a solution with $k$further elements). Our goal is to obtain a $d^n \cdot n^{O(1)}$ time$\beta$-approximation algorithm for the problem with $d$ as small as possible.That is, for every fixed $\alpha,c,\beta \geq 1$, we would like to determinethe smallest possible $d$ that can be achieved in a model where ourproblem-specific knowledge is limited to checking the feasibility of a solutionand invoking the $\alpha$-approximate extension algorithm. Our resultscompletely resolve this question: (1) For every fixed $\alpha,c,\beta \geq 1$, a simple algorithm(``approximate monotone local search'') achieves the optimum value of $d$. (2) Given $\alpha,c,\beta \geq 1$, we can efficiently compute the optimum $d$up to any precision $\varepsilon > 0$. Earlier work presented algorithms (but no lower bounds) for the special case$\alpha = \beta = 1$ [Fomin et al., J. ACM 2019] and for the special case$\alpha = \beta > 1$ [Esmer et al., ESA 2022]. Our work generalizes theseresults and in particular confirms that the earlier algorithms are optimal inthese special cases.<br

Sources of variation in preschoolers’ relational reasoning: The interaction between language use and working memory

Previous research has suggested the importance of relational language and working memory in children’s relational reasoning. The tendency to use language (e.g., using more relational than object-focused language, prioritizing focal objects over background in linguistic descriptions) could reflect children’s biases toward the relational versus object-based solutions in a relational match-to-sample (RMTS) task. In the lack of any apparent object match as a foil option, object-focused children might rely on other cognitive mechanisms (i.e., working memory) to choose a relational match in the RMTS task. The current study examined the interactive roles of language- and working memory-related sources of variation in Turkish-learning preschoolers’ relational reasoning. We collected data from 4- and 5-year-olds (N = 41) via Zoom in the RMTS task, a scene description task, and a backward word span task. Generalized binomial mixed effects models revealed that children who used more relational language and background-focused scene descriptions performed worse in the relational reasoning task. Furthermore, children with less frequent relational language use and focal object descriptions of the scenes benefited more from working memory to succeed in the relational reasoning task. These results suggest additional working memory demands for object-focused children to choose relational matches in the RMTS task, highlighting the importance of examining the interactive effects of different cognitive mechanisms on relational reasoning

Sexuality throughout all the stages of pregnancy: experiences of expectant mothers

Objective: To explore and understand the sexual experiences of expectant mothers during their pregnancy. Methods: The study was carried out in two healthcare centers in the Almería Health District, in southern Spain. The participants included pregnant women who received prenatal care and/or maternity education. The inclusion criteria were being pregnant, maintaining sexual activity and agreeing to participate in the study. The exclusion criteria were having limitations on sexual activity by medical prescription. The sample consisted of 15 expectant women selected using a convenience sample, of which 5 took part in a focus group (FG) and 10 in in-depth interviews (IDI). Data was collected between the months of June and December 2016. Participants were contacted by the main researcher and an appointment was made to carry out the FGs or the IDIs. Results: Three main categories emerged: False beliefs and a holistic approach to sexuality during pregnancy, which is related to the concept of sexuality, false beliefs, and limited sexual counseling during pregnancy. Limitations: From fear at the beginning to physical diffi culty at the end, referring to the fluctuations in sexual desire as well as the physical changes that limit sexual activity. Adapting to changes: safe practices and satisfaction with one’s body image, which encompasses concerns about the risks and the relationship between body image and self-esteem. Conclusion: A lack of sexual counseling during pregnancy leads to the creation of false beliefs, which, together with physical changes, concerns about the risk, and fl uctuations in sexual desire and interest, bring about a decrease in sexual activity. But sexuality remains an important aspect of pregnancy, toward which the participants must adopt a broader approach, not limited to intercourse, and adopt sexual practices that are adapted to the physical and emotional changes that happen during this time

Can we rate public support for democracy in a comparable way? Cross-national equivalence of democratic attitudes in the World Value Survey

In this study we examine the cross-cultural equivalence of two scales that measure attitudes toward democracy across 36 countries in the World Value Survey (WVS) 2000. We examine the equivalence of these scales in order to explore if we can meaningfully compare democratic attitudes across countries. Multiple group confirmatory factor analyses (MGCFA) is applied to answer this question. The analyses indicate that the scales may be compared but only to a certain extent and not across all the countries. We close this article by discussing the implications of the findings

Transit timing variation analysis of the low-mass brown dwarf KELT-1 b

We investigate whether there is a variation in the orbital period of the short-period brown dwarf-mass KELT-1 b, which is one of the best candidates to observe orbital decay. We obtain 19 high-precision transit light curves of the target using six different telescopes. We add all precise and complete transit light curves from open databases and the literature, as well as the available Transiting Exoplanet Survey Satellite (TESS) observations from sectors 17 and 57, to form a transit timing variation (TTV) diagram spanning more than 10 yr of observations. The analysis of the TTV diagram, however, is inconclusive in terms of a secular or periodic variation, hinting that the system might have synchronized. We update the transit ephemeris and determine an informative lower limit for the reduced tidal quality parameter of its host star of Q ′⋆&gt;(8.5±3.9)×106 assuming that the stellar rotation is not yet synchronized. Using our new photometric observations, published light curves, the TESS data, archival radial velocities, and broadband magnitudes, we also update the measured parameters of the system. Our results are in good agreement with those found in previous analyses