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Concept: How to Solve It


To investigate cognitive operations underlying sequential problem solving, we confronted ten Goffin’s cockatoos with a baited box locked by five different inter-locking devices. Subjects were either naïve or had watched a conspecific demonstration, and either faced all devices at once or incrementally. One naïve subject solved the problem without demonstration and with all locks present within the first five sessions (each consisting of one trial of up to 20 minutes), while five others did so after social demonstrations or incremental experience. Performance was aided by species-specific traits including neophilia, a haptic modality and persistence. Most birds showed a ratchet-like progress, rarely failing to solve a stage once they had done it once. In most transfer tests subjects reacted flexibly and sensitively to alterations of the locks' sequencing and functionality, as expected from the presence of predictive inferences about mechanical interactions between the locks.

Concepts: Psychology, Future, Educational psychology, Sequence, Demonstration, Problem solving, Problem, How to Solve It


Computer modeling, simulation and optimization are powerful tools that have seen increased use in biomechanics research. Dynamic optimizations can be categorized as either data-tracking or predictive problems. The data-tracking approach has been used extensively to address human movement problems of clinical relevance. The predictive approach also holds great promise, but has seen limited use in clinical applications. Enhanced software tools would facilitate the application of predictive musculoskeletal simulations to clinically-relevant research. The open-source software OpenSim provides tools for generating tracking simulations but not predictive simulations. However, OpenSim includes an extensive application programming interface that permits extending its capabilities with scripting languages such as MATLAB. In the work presented here, we combine the computational tools provided by MATLAB with the musculoskeletal modeling capabilities of OpenSim to create a framework for generating predictive simulations of musculoskeletal movement based on direct collocation optimal control techniques. In many cases, the direct collocation approach can be used to solve optimal control problems considerably faster than traditional shooting methods. Cyclical and discrete movement problems were solved using a simple 1 degree of freedom musculoskeletal model and a model of the human lower limb, respectively. The problems could be solved in reasonable amounts of time (several seconds to 1-2 hours) using the open-source IPOPT solver. The problems could also be solved using the fmincon solver that is included with MATLAB, but the computation times were excessively long for all but the smallest of problems. The performance advantage for IPOPT was derived primarily by exploiting sparsity in the constraints Jacobian. The framework presented here provides a powerful and flexible approach for generating optimal control simulations of musculoskeletal movement using OpenSim and MATLAB. This should allow researchers to more readily use predictive simulation as a tool to address clinical conditions that limit human mobility.

Concepts: Operations research, Computer program, Computer simulation, Optimization, Mathematical model, Application programming interface, Optimal control, How to Solve It


Herding of sheep by dogs is a powerful example of one individual causing many unwilling individuals to move in the same direction. Similar phenomena are central to crowd control, cleaning the environment and other engineering problems. Despite single dogs solving this ‘shepherding problem’ every day, it remains unknown which algorithm they employ or whether a general algorithm exists for shepherding. Here, we demonstrate such an algorithm, based on adaptive switching between collecting the agents when they are too dispersed and driving them once they are aggregated. Our algorithm reproduces key features of empirical data collected from sheep-dog interactions and suggests new ways in which robots can be designed to influence movements of living and artificial agents.

Concepts: Scientific method, Sociology, Science, Artificial intelligence, Problem solving, Individualism, How to Solve It, Intelligent agent


Previous research has shown that children benefit from gesturing during math instruction. We asked whether gesturing promotes learning because it is itself a physical action, or because it uses physical action to represent abstract ideas. To address this question, we taught third-grade children a strategy for solving mathematical-equivalence problems that was instantiated in one of three ways: (a) in a physical action children performed on objects, (b) in a concrete gesture miming that action, or © in an abstract gesture. All three types of hand movements helped children learn how to solve the problems on which they were trained. However, only gesture led to success on problems that required generalizing the knowledge gained. The results provide the first evidence that gesture promotes transfer of knowledge better than direct action on objects and suggest that the beneficial effects gesture has on learning may reside in the features that differentiate it from action.

Concepts: Idea, Learning, Knowledge, Object, Problem solving, Abstraction, Hand, How to Solve It


When animals encounter a task they have solved previously, or the same problem appears in a different apparatus, how does memory, alongside behavioural traits such as persistence, selectivity and flexibility, enhance problem-solving efficiency? We examined this question by first presenting grey squirrels with a puzzle 22 months after their last experience of it (the recall task). Squirrels were then given the same problem presented in a physically different apparatus (the generalisation task) to test whether they would apply the previously learnt tactics to solve the same problem but in a different apparatus. The mean latency to success in the first trial of the recall task was significantly different from the first exposure but not different from the last exposure of the original task, showing retention of the task. A neophobia test in the generalisation task suggested squirrels perceived the different apparatus as a different problem, but they quickly came to apply the same effective tactics as before to solve the task. Greater selectivity (the proportion of effective behaviours) and flexibility (the rate of switching between tactics) both enhanced efficiency in the recall task, but only selectivity enhanced efficiency in the generalisation task. These results support the interaction between memory and behavioural traits in problem-solving, in particular memory of task-specific tactics that could enhance efficiency. Squirrels remembered and emitted task-effective tactics more than ineffective tactics. As a result, they consistently changed from ineffective to effective behaviours after failed attempts at problem-solving.

Concepts: Psychology, Behavior, Human behavior, Problem solving, Behaviorism, Applied behavior analysis, How to Solve It, Eastern Gray Squirrel


α-Helical transmembrane proteins are a ubiquitous and important class of proteins, but present difficulties for crystallographic structure solution. Here, the effectiveness of the AMPLE molecular replacement pipeline in solving α-helical transmembrane-protein structures is assessed using a small library of eight ideal helices, as well as search models derived from ab initio models generated both with and without evolutionary contact information. The ideal helices prove to be surprisingly effective at solving higher resolution structures, but ab initio-derived search models are able to solve structures that could not be solved with the ideal helices. The addition of evolutionary contact information results in a marked improvement in the modelling and makes additional solutions possible.

Concepts: DNA, Protein, Molecular biology, Crystallography, Cell membrane, Membrane protein, Transmembrane protein, How to Solve It


Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Concepts: Time, Mathematics, Function, Calculation, The Domain, Sydney, Equations, Elementary algebra, How to Solve It


In social dilemmas, the ability of individuals to coordinate their actions is crucial to reach group optima [1]. Unless exacted by power or force, coordination in humans relies on a common understanding of the problem [2], which is greatly facilitated by communication [3, 4]. The lack of means of consultation about the nature of the problem and how to solve it may explain why multiagent coordination in nonhuman vertebrates has commonly been observed only when multiple individuals react instantaneously to a single stimulus, either natural or experimentally simulated [5, 6], for example a predator [7, 8], a prey [9, 10], or a neighboring group [11-14]. Here we report how vervet monkeys solved an experimentally induced coordination problem. In each of three groups, we trained a low-ranking female, the “provider,” to open a container holding a large amount of food, which the providers only opened when all individuals dominant to them (“dominants”) stayed outside an imaginary “forbidden circle” around it. Without any human guidance, the dominants learned restraint one by one, in hierarchical order from high to low. Once all dominants showed restraint immediately at the start of the trial, the providers opened the container almost instantly, saving all individuals opportunity costs due to lost foraging time. Solving this game required trial-and-error learning based on individual feedback from the provider to each dominant, and all dominants being patient enough to wait outside the circle while others learned restraint. Communication, social learning, and policing by high-ranking animals played no perceptible role.

Concepts: Human, Sociology, Primate, Learning, Knowledge, Problem solving, Coordination game, How to Solve It


To correct for scatter in kV cone-beam CT (CBCT) projection data on a clinical system using a new tool, Acuros®CTS, that estimates scatter images rapidly and accurately by deterministically solving the linear Boltzmann transport equation.

Concepts: Fundamental physics concepts, Tomographic reconstruction, How to Solve It, Ludwig Boltzmann


One of the greatest challenges in data mining is related to processing and analysis of massive data streams. Contrary to traditional static data mining problems, data streams require that each element is processed only once, the amount of allocated memory is constant and the models incorporate changes of investigated streams. A vast majority of available methods have been developed for data stream classification and only a few of them attempted to solve regression problems, using various heuristic approaches. In this paper, we develop mathematically justified regression models working in a time-varying environment. More specifically, we study incremental versions of generalized regression neural networks, called IGRNNs, and we prove their tracking properties - weak (in probability) and strong (with probability one) convergence assuming various concept drift scenarios. First, we present the IGRNNs, based on the Parzen kernels, for modeling stationary systems under nonstationary noise. Next, we extend our approach to modeling time-varying systems under nonstationary noise. We present several types of concept drifts to be handled by our approach in such a way that weak and strong convergence holds under certain conditions. Finally, in the series of simulations, we compare our method with commonly used heuristic approaches, based on forgetting mechanism or sliding windows, to deal with concept drift. Finally, we apply our concept in a real life scenario solving the problem of currency exchange rates prediction.

Concepts: Regression analysis, Statistics, Data, Model, Data mining, Problem solving, Convergence, How to Solve It