The Paradox of Time in Dynamic Causal Systems.

Recent work has shown that people use temporal information including order, delay, and variability to infer causality between events. In this study, we build on this work by investigating the role of time in dynamic systems, where causes take continuous values and also continually influence their effects. Recent studies of learning in these systems explored short interactions in a setting with rapidly evolving dynamics and modeled people as relying on simpler, resource-limited strategies to grapple with the stream of information. A natural question that arises from such an account is whether interacting with systems that unfold more slowly might reduce the systematic errors that result from these strategies. Paradoxically, we find that slowing the task indeed reduced the frequency of one type of error, albeit at the cost of increasing the overall error rate. To explain these results we posit that human learners analyze continuous dynamics into discrete events and use the observed relationships between events to draw conclusions about causal structure. We formalize this intuition in terms of a novel Causal Event Abstraction model and show that this model indeed captures the observed pattern of errors. We comment on the implications these results have for causal cognition.

Causal Information-Seeking Strategies Change Across Childhood and Adolescence.

Intervening on causal systems can illuminate their underlying structures. Past work has shown that, relative to adults, young children often make intervention decisions that appear to confirm a single hypothesis rather than those that optimally discriminate alternative hypotheses. Here, we investigated how the ability to make informative causal interventions changes across development. Ninety participants between the ages of 7 and 25 completed 40 different puzzles in which they had to intervene on various causal systems to determine their underlying structures. Each puzzle comprised a three- or four-node computer chip with hidden wires. On each trial, participants viewed two possible arrangements of the chip's hidden wires and had to select a single node to activate. After observing the outcome of their intervention, participants selected a wire configuration and rated their confidence in their selection. We characterized participant choices with a Bayesian measurement model that indexed the extent to which participants selected nodes that would best disambiguate the two possible causal structures versus those that had high causal centrality in one of the two causal hypotheses but did not necessarily discriminate between them. Our model estimates revealed that the use of a discriminatory strategy increased through early adolescence. Further, developmental improvements in intervention strategy were related to changes in the ability to accurately judge the strength of evidence that interventions revealed, as indexed by participants' confidence in their selections. Our results suggest that improvements in causal information-seeking extend into adolescence and may be driven by metacognitive sensitivity to the efficacy of previous interventions in discriminating competing ideas.

A Process Model of Causal Reasoning.

How do we make causal judgments? Many studies have demonstrated that people are capable causal reasoners, achieving success on tasks from reasoning to categorization to interventions. However, less is known about the mental processes used to achieve such sophisticated judgments. We propose a new process model-the mutation sampler-that models causal judgments as based on a sample of possible states of the causal system generated using the Metropolis-Hastings sampling algorithm. Across a diverse array of tasks and conditions encompassing over 1,700 participants, we found that our model provided a consistently closer fit to participant judgments than standard causal graphical models. In particular, we found that the biases introduced by mutation sampling accounted for people's consistent, predictable errors that the normative model by definition could not. Moreover, using a novel experimental methodology, we found that those biases appeared in the samples that participants explicitly judged to be representative of a causal system. We conclude by advocating sampling methods as plausible process-level accounts of the computations specified by the causal graphical model framework and highlight opportunities for future research to identify not just what reasoners compute when drawing causal inferences, but also how they compute it.

Causal Structure Learning in Continuous Systems.

Real causal systems are complicated. Despite this, causal learning research has traditionally emphasized how causal relations can be induced on the basis of idealized events, i.e., those that have been mapped to binary variables and abstracted from time. For example, participants may be asked to assess the efficacy of a headache-relief pill on the basis of multiple patients who take the pill (or not) and find their headache relieved (or not). In contrast, the current study examines learning via interactions with continuous dynamic systems, systems that include continuous variables that interact over time (and that can be continuously observed in real time by the learner). To explore such systems, we develop a new framework that represents a causal system as a network of stationary Gauss-Markov ("Ornstein-Uhlenbeck") processes and show how such OU networks can express complex dynamic phenomena, such as feedback loops and oscillations. To assess adult's abilities to learn such systems, we conducted an experiment in which participants were asked to identify the causal relationships of a number of OU networks, potentially carrying out multiple, temporally-extended interventions. We compared their judgments to a normative model for learning OU networks as well as a range of alternative and heuristic learning models from the literature. We found that, although participants exhibited substantial learning of such systems, they committed certain systematic errors. These successes and failures were best accounted for by a model that describes people as focusing on pairs of variables, rather than evaluating the evidence with respect to the full space of possible structural models. We argue that our approach provides both a principled framework for exploring the space of dynamic learning environments as well as new algorithmic insights into how people interact successfully with a continuous causal world.

Nanomechanical Plasmon Spectroscopy of Single Gold Nanoparticles.

We experimentally demonstrate the effect of the localized surface plasmon resonance (LSPR) of a single gold nanoparticle (AuNP) of 100 nm in diameter on the mechanical resonance frequency of a free-standing silicon nitride membrane by means of optomechanical transduction. We discover that a key effect to explain the coupling in these systems is the extinction cross section enhancement due to the excitation of the LSPR at selected wavelengths. In order to validate this coupling, we have developed a fixed wavelength interferometric readout system with an integrated tunable laser source, which allows us to perform the first experimental demonstration of nanomechanical spectroscopy of deposited AuNPs onto the membrane, discerning in between single particles and dimers by the mechanical frequency shift. We have also introduced three-axis mechanical scanners with nanometer-scale resolution in our experimental setup to selectively study single nanoparticles or small clusters. Whereas the single particles are polarization-insensitive, the gold dimers have a clearly defined polarization angle dependency as expected by theory. Finally, we found an unexpected long-distance (∼200 nm) coupling of the LSPR of separated AuNPs coming out from the guided light by the silicon nitride membrane.

Drift study of SU8 cantilevers in liquid and gaseous environments.

We present a study of the drift, in terms of cantilever deflections without probe/target interactions, of polymeric SU8 cantilevers. The drift is measured in PBS buffer (pH 7.4) and under vacuum (1mbar) conditions. We see that the cantilevers display a large drift in both environments. We believe this is because the polymer matrix absorbs liquid in one situation whereas it is being degassed in the other. An inhomogeneous expansion/contraction of the cantilever is seen because one surface of the cantilever may still have remains of the release layer from the fabrication. To further study the effect, we coat the cantilevers with a hydrophobic coating, perfluorodecyltrichlorosilane (FDTS). Fully encapsulating the SU8 cantilever greatly reduces the drift in liquid whereas a less significant change is seen in vacuum.

Micro-differential thermal analysis detection of adsorbed explosive molecules using microfabricated bridges.

Although micromechanical sensors enable chemical vapor sensing with unprecedented sensitivity using variations in mass and stress, obtaining chemical selectivity using the micromechanical response still remains as a crucial challenge. Chemoselectivity in vapor detection using immobilized selective layers that rely on weak chemical interactions provides only partial selectivity. Here we show that the very low thermal mass of micromechanical sensors can be used to produce unique responses that can be used for achieving chemical selectivity without losing sensitivity or reversibility. We demonstrate that this method is capable of differentiating explosive vapors from nonexplosives and is additionally capable of differentiating individual explosive vapors such as trinitrotoluene, pentaerythritol tetranitrate, and cyclotrimethylenetrinitromine. This method, based on a microfabricated bridge with a programmable heating rate, produces unique and reproducible thermal response patterns within 50 ms that are characteristic to classes of adsorbed explosive molecules. We demonstrate that this micro-differential thermal analysis technique can selectively detect explosives, providing a method for fast direct detection with a limit of detection of 600x10(-12) g.