The use of feedback in web-based instruction : achievement, feedback study time, and efficiency

The purpose of this research study is to compare the effects of an instructional treatment that presented adaptive feedback based on students’ perceptions about their answer correctness with a nonadaptive treatment on student performance, feedback study time, and lesson efficiency in a computer-based environment. Because of advances in technology, the instruction was delivered in a Web-based environment. Two versions of the Web-based lesson were designed. The lesson consisted of a pretest, a tutorial, and a posttest. The pre- and posttest were similar in that they tested students’ ability to classify defined concepts, a higher cognitive task. The tutorial presented instructional text with inserted verbal information questions. Undergraduate volunteers enrolled in entry level education courses in the Watson School of Education were randomly assigned to one of the two treatment groups. One group received varied feedback information based upon the combined assessment of response correctness and the student’s response certitude. The other group received feedback information that did not vary. Results indicate that the effects of adaptive feedback were not significantly different from the effects of nonadaptive feedback on concept learning. In the adaptive group, high certitude wrongs, low certitude corrects, and low certitude wrong responses resulted in higher feedback study time than high certitude correct responses. High certitude significantly correlated with fine discrimination errors in concept learning. In terms of feedback efficiency, adaptive feedback was significantly more efficient than nonadaptive feedback; however, for overall lesson efficiency, there were no significant differences between the two treatment groups. These results are discussed in terms of cost-benefit implications for the design of effective Web-based instruction. Implications for future research are discussed in reference to results of this study and past research

Subfunctionalization reduces the fitness cost of gene duplication in humans by buffering dosage imbalances

<p>Abstract</p> <p>Background</p> <p>Driven essentially by random genetic drift, subfunctionalization has been identified as a possible non-adaptive mechanism for the retention of duplicate genes in small-population species, where widespread deleterious mutations are likely to cause complementary loss of subfunctions across gene copies. Through subfunctionalization, duplicates become indispensable to maintain the functional requirements of the ancestral locus. Yet, gene duplication produces a dosage imbalance in the encoded proteins and thus, as investigated in this paper, subfunctionalization must be subject to the selective forces arising from the fitness bottleneck introduced by the duplication event.</p> <p>Results</p> <p>We show that, while arising from random drift, subfunctionalization must be inescapably subject to selective forces, since the diversification of expression patterns across paralogs mitigates duplication-related dosage imbalances in the concentrations of encoded proteins. Dosage imbalance effects become paramount when proteins rely on obligatory associations to maintain their structural integrity, and are expected to be weaker when protein complexation is ephemeral or adventitious. To establish the buffering effect of subfunctionalization on selection pressure, we determine the packing quality of encoded proteins, an established indicator of dosage sensitivity, and correlate this parameter with the extent of paralog segregation in humans, using species with larger population -and more efficient selection- as controls.</p> <p>Conclusions</p> <p>Recognizing the role of subfunctionalization as a dosage-imbalance buffer in gene duplication events enabled us to reconcile its mechanistic nonadaptive origin with its adaptive role as an enabler of the evolution of genetic redundancy. This constructive role was established in this paper by proving the following assertion: <it>If subfunctionalization is indeed adaptive, its effect on paralog segregation should scale with the dosage sensitivity of the duplicated genes</it>. Thus, subfunctionalization becomes adaptive in response to the selection forces arising from the fitness bottleneck imposed by gene duplication.</p

Superselectors: Efficient Constructions and Applications

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel conflict resolution and data security. We prove close upper and lower bounds on the size of superselectors and we provide efficient algorithms for their constructions. Albeit our bounds are very general, when they are instantiated on the combinatorial structures that are particular cases of superselectors (e.g., (p,k,n)-selectors, (d,\ell)-list-disjunct matrices, MUT_k(r)-families, FUT(k, a)-families, etc.) they match the best known bounds in terms of size of the structures (the relevant parameter in the applications). For appropriate values of parameters, our results also provide the first efficient deterministic algorithms for the construction of such structures

Partial Covering Arrays: Algorithms and Asymptotics

A covering array $\mathsf{CA}(N;t,k,v)$ is an $N\times k$ array with entries in $\{1, 2, \ldots , v\}$, for which every $N\times t$ subarray contains each $t$-tuple of $\{1, 2, \ldots , v\}^t$ among its rows. Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems. A central question is to determine or bound $\mathsf{CAN}(t,k,v)$, the minimum number $N$ of rows of a $\mathsf{CA}(N;t,k,v)$. The well known bound $\mathsf{CAN}(t,k,v)=O((t-1)v^t\log k)$ is not too far from being asymptotically optimal. Sensible relaxations of the covering requirement arise when (1) the set $\{1, 2, \ldots , v\}^t$ need only be contained among the rows of at least $(1-\epsilon)\binom{k}{t}$ of the $N\times t$ subarrays and (2) the rows of every $N\times t$ subarray need only contain a (large) subset of $\{1, 2, \ldots , v\}^t$. In this paper, using probabilistic methods, significant improvements on the covering array upper bound are established for both relaxations, and for the conjunction of the two. In each case, a randomized algorithm constructs such arrays in expected polynomial time

Facilitating flexible problem solving: A cognitive load perspective

The development of flexible, transferable problem-solving skills is an important aim of contemporary educational systems. Since processing limitations of our mind represent a major factor influencing any meaningful learning, the acquisition of flexible problem-solving skills needs to be based on known characteristics of our cognitive architecture in order to be effective and efficient. This paper takes a closer look at the processes involved in the acquisition of flexible problem-solving skills within a cognitive load framework. It concludes that (1) cognitive load theory can benefit from putting more emphasis on generalized knowledge structures; (2

Discovery of low-dimensional structure in high-dimensional inference problems

Many learning and inference problems involve high-dimensional data such as images, video or genomic data, which cannot be processed efficiently using conventional methods due to their dimensionality. However, high-dimensional data often exhibit an inherent low-dimensional structure, for instance they can often be represented sparsely in some basis or domain. The discovery of an underlying low-dimensional structure is important to develop more robust and efficient analysis and processing algorithms. The first part of the dissertation investigates the statistical complexity of sparse recovery problems, including sparse linear and nonlinear regression models, feature selection and graph estimation. We present a framework that unifies sparse recovery problems and construct an analogy to channel coding in classical information theory. We perform an information-theoretic analysis to derive bounds on the number of samples required to reliably recover sparsity patterns independent of any specific recovery algorithm. In particular, we show that sample complexity can be tightly characterized using a mutual information formula similar to channel coding results. Next, we derive major extensions to this framework, including dependent input variables and a lower bound for sequential adaptive recovery schemes, which helps determine whether adaptivity provides performance gains. We compute statistical complexity bounds for various sparse recovery problems, showing our analysis improves upon the existing bounds and leads to intuitive results for new applications. In the second part, we investigate methods for improving the computational complexity of subgraph detection in graph-structured data, where we aim to discover anomalous patterns present in a connected subgraph of a given graph. This problem arises in many applications such as detection of network intrusions, community detection, detection of anomalous events in surveillance videos or disease outbreaks. Since optimization over connected subgraphs is a combinatorial and computationally difficult problem, we propose a convex relaxation that offers a principled approach to incorporating connectivity and conductance constraints on candidate subgraphs. We develop a novel nearly-linear time algorithm to solve the relaxed problem, establish convergence and consistency guarantees and demonstrate its feasibility and performance with experiments on real networks

Bayesian Spatio-Temporal Modeling for Forecasting, Trend Assessment and Spatial Trend Filtering

This work develops Bayesian spatio-temporal modeling techniques specifically aimed at studying several aspects of our motivating applications, to include vector-borne disease incidence and air pollution levels. A key attribute of the proposed techniques are that they are scalable to extremely large data sets which consist of spatio-temporally oriented observations. The scalability of our modeling strategies is accomplished in two primary ways. First, through the introduction of carefully constructed latent random variables we are able to develop Markov chain Monte Carlo (MCMC) sampling algorithms that consist primarily of Gibbs steps. This leads to the fast and easy updating of the model parameters from common distributions. Second, for the spatio-temporal aspects of the models, a novel sampling strategy for Gaussian Markov random fields (GRMFs) that can be easily implemented (in parallel) within MCMC sampling algorithms is used. The performance of the proposed modeling strategies are demonstrated through extensive numerical studies and are further used to analyze vector-borne disease data measured on canines throughout the conterminous United States and PM 2.5 levels measured at weather stations throughout the Eastern United States. In particular, we begin by developing a Poisson regression model that can be used to forecast the incidence of vector-borne disease throughout a large geographic area. The proposed model accounts for spatio-temporal dependence through a vector autoregression and is fit through a Metropolis-Hastings based Markov chain Monte Carlo (MCMC) sampling algorithm. The model is used to forecast the prevalence of Lyme disease (Chapter 2) and Anaplasmosis (Chapter 3) in canines throughout the United States. As a part of these studies we also evaluate the significance of various climatic and socio-economic drivers of disease. We then present (Chapter 4) the development of the \u27chromatic sampler\u27 for GMRFs. The chromatic sampler is an MCMC sampling technique that exploits the Markov property of GMRFs to sample large groups of parameters in parallel. A greedy algorithm for finding such groups of parameters is presented. The methodology is found to be superior, in terms of computational effort, to both full block and single-site updating. For assessing spatio-temporal trends, we develop (Chapter 5) a binomial regression model with spatially varying coefficients. This model uses Gaussian predictive processes to estimate spatially varying coefficients and a conditional autoregressive structure embedded in a vector autoregression to account for spatio-temporal dependence in the data. The methodology is capable of estimating both widespread regional and small scale local trends. A data augmentation strategy is used to develop a Gibbs based MCMC sampling routine. The approach is made computationally feasible through adopting the chromatic sampler for GMRFs to sample the spatio-temporal random effects. The model is applied to a dataset consisting of 16 million test results for antibodies to Borrelia burgdoferi and used to identify several areas of the United States experiencing increasing Lyme disease risk. For nonparametric functional estimation, we develop (Chapter 6) a Bayesian multidimensional trend filter (BMTF). The BMTF is a flexible nonparameteric estimator that extends traditional one dimensional trend filtering methods to multiple dimensions. The methodology is computationally scalable to a large support space and the expense of fitting the model is nearly independent of the number of observations. The methodology involves discretizing the support space and estimating a multidimensional step function over the discretized support. Two adaptive methods of discretization which allows the data to determine the resolution of the resulting function is presented. The BMTF is then used (Chapter 7) to allow for spatially varying coefficients within a quantile regression model. A data augmentation strategy is introduced which facilitates the development of a Gibbs based MCMC sampling routine. This methodology is developed to study various meteorological drivers of high levels of PM 2.5, a particularly hazardous form of air pollution consisting of particles less than 2.5 micrometers in diameter