Braden A. W. Brinkman

Experiments and Model for Serration Statistics in Low-Entropy, Medium-Entropy, and High-Entropy Alloys

High-entropy alloys (HEAs) are new alloys that contain five or more elements in roughly-equal proportion. We present new experiments and theory on the deformation behavior of HEAs under slow stretching (straining), and observe differences, compared to conventional alloys with fewer elements. For a specific range of temperatures and strain-rates, HEAs deform in a jerky way, with sudden slips that make it difficult to precisely control the deformation. An analytic model explains these slips as avalanches of slipping weak spots and predicts the observed slip statistics, stress-strain curves, and their dependence on temperature, strain-rate, and material composition. The ratio of the weak spots’ healing rate to the strain-rate is the main tuning parameter, reminiscent of the Portevin-LeChatellier effect and time-temperature superposition in polymers. Our model predictions agree with the experimental results. The proposed widely-applicable deformation mechanism is useful for deformation control and alloy design.

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes.

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or “quakes”. We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects “tuned critical” behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes.

Probing failure susceptibilities of earthquake faults using small-quake tidal correlations

Mitigating the devastating economic and humanitarian impact of large earthquakes requires signals for forecasting seismic events. Daily tide stresses were previously thought to be insufficient for use as such a signal. Recently, however, they have been found to correlate significantly with small earthquakes, just before large earthquakes occur. Here we present a simple earthquake model to investigate whether correlations between daily tidal stresses and small earthquakes provide information about the likelihood of impending large earthquakes. The model predicts that intervals of significant correlations between small earthquakes and ongoing low-amplitude periodic stresses indicate increased fault susceptibility to large earthquake generation. The results agree with the recent observations of large earthquakes preceded by time periods of significant correlations between smaller events and daily tide stresses. We anticipate that incorporating experimentally determined parameters and fault-specific details into the model may provide new tools for extracting improved probabilities of impending large earthquakes.

How Do Efficient Coding Strategies Depend on Origins of Noise in Neural Circuits

Neural circuits reliably encode and transmit signals despite the presence of noise at multiple stages of processing. The efficient coding hypothesis, a guiding principle in computational neuroscience, suggests that a neuron or population of neurons allocates its limited range of responses as efficiently as possible to best encode inputs while mitigating the effects of noise. Previous work on this question relies on specific assumptions about where noise enters a circuit, limiting the generality of the resulting conclusions. Here we systematically investigate how noise introduced at different stages of neural processing impacts optimal coding strategies. Using simulations and a flexible analytical approach, we show how these strategies depend on the strength of each noise source, revealing under what conditions the different noise sources have competing or complementary effects. We draw two primary conclusions: (1) differences in encoding strategies between sensory systems—or even adaptational changes in encoding properties within a given system—may be produced by changes in the structure or location of neural noise, and (2) characterization of both circuit nonlinearities as well as noise are necessary to evaluate whether a circuit is performing efficiently.

Probabilistic model of waiting times between large failures in sheared media.

Using a probabilistic approximation of a mean-field mechanistic model of sheared systems, we analytically calculate the statistical properties of large failures under slow shear loading. For general shear F(t), the distribution of waiting times between large system-spanning failures is a generalized exponential distribution, ρ_{T}(t)=λ(F(t))P(F(t))exp[-∫_{0}^{t}dτλ(F(τ))P(F(τ))], where λ(F(t)) is the rate of small event occurrences at stress F(t) and P(F(t)) is the probability that a small event triggers a large failure. We study the behavior of this distribution as a function of fault properties, such as heterogeneity or shear rate. Because the probabilistic model accommodates any stress loading F(t), it is particularly useful for modeling experiments designed to understand how different forms of shear loading or stress perturbations impact the waiting-time statistics of large failures. As examples, we study how periodic perturbations or fluctuations on top of a linear shear stress increase impact the waiting-time distribution.

Predicting how and when hidden neurons skew measured synaptic interactions

A major obstacle to understanding neural coding and computation is the fact that experimental recordings typically sample only a small fraction of the neurons in a circuit. Measured neural properties are skewed by interactions between recorded neurons and the “hidden” portion of the network. To properly interpret neural data and determine how biological structure gives rise to neural circuit function, we thus need a better understanding of the relationships between measured effective neural properties and the true underlying physiological properties. Here, we focus on how the effective spatiotemporal dynamics of the synaptic interactions between neurons are reshaped by coupling to unobserved neurons. We find that the effective interactions from a pre-synaptic neuron r′ to a post-synaptic neuron r can be decomposed into a sum of the true interaction from r′ to r plus corrections from every directed path from r′ to r through unobserved neurons. Importantly, the resulting formula reveals when the hidden units have—or do not have—major effects on reshaping the interactions among observed neurons. As a particular example of interest, we derive a formula for the impact of hidden units in random networks with “strong” coupling—connection weights that scale with 1/N, where N is the network size, precisely the scaling observed in recent experiments. With this quantitative relationship between measured and true interactions, we can study how network properties shape effective interactions, which properties are relevant for neural computations, and how to manipulate effective interactions.

Effective synaptic interactions in subsampled nonlinear networks with strong coupling

A major obstacle to understanding neural coding and computation is the fact that experimental recordings typically sample only a small fraction of the neurons in a circuit. Measured neural properties are skewed by interactions between recorded neurons and the “hidden” portion of the network. To properly interpret neural data, we thus need a better understanding of the relationships between measured effective neural properties and the true underlying physiological properties. Here, we focus on how the effective spatiotemporal dynamics of the synaptic interactions between neurons are reshaped by coupling to unobserved neurons. We find that the effective interactions from a pre-synaptic neuron r′ to a post-synaptic neuron r can be decomposed into a sum of the true interaction from r′ to r plus corrections from every directed path from r′ to r through unobserved neurons. Importantly, the resulting formula reveals when the hidden units have—or do not have—major effects on reshaping the interactions among observed neurons. As a prominent example, we derive a formula for strong impact of hidden units in random networks with connection weights that scale with 1/√N, where N is the network size—precisely the scaling observed in recent experiments.A major obstacle to understanding neural coding and computation is the fact that experimental recordings typically sample only a small fraction of the neurons in a circuit. Measured neural properties are skewed by interactions between recorded neurons and the “hidden” portion of the network. To properly interpret neural data and determine how biological structure gives rise to neural circuit function, we thus need a better understanding of the relationships between measured effective neural properties and the true underlying physiological properties. Here, we focus on how the effective spatiotemporal dynamics of the synaptic interactions between neurons are reshaped by coupling to unobserved neurons. We find that the effective interactions from a pre-synaptic neuron r ′ to a post-synaptic neuron r can be decomposed into a sum of the true interaction from r ′ to r plus corrections from every directed path from r ′ to r through unobserved neurons. Importantly, the resulting formula reveals when the hidden units have—or do not have—major effects on reshaping the interactions among observed neurons. As a particular example of interest, we derive a formula for the impact of hidden units in random networks with “strong” coupling—connection weights that scale with 1/√ N , where N is the network size, precisely the scaling observed in recent experiments. With this quantitative relationship between measured and true interactions, we can study how network properties shape effective interactions, which properties are relevant for neural computations, and how to manipulate effective interactions.

Noise- and stimulus-dependence of the optimal encoding nonlinearities in a simple ON/OFF retinal circuit model

Encoding of stimuli in the retina depends on the statistical properties of the input stimuli, neural noise, and circuit nonlinearities. Here, we present a simple model of a two-path ON/OFF RGC circuit (figure ​(figure1A).1A). We use variational methods to analytically calculate the optimal encoding nonlinearities in the presence of noise sources with two key biophysical properties: they have separate components that corrupt the stimulus (pre-nonlinearity) and the responses (post-nonlinearity), and they may be correlated across cells. We study qualitatively the effects of the competition between the stimulus and noise sources on the form of the encoding nonlinearities. We find that when both pre- and post-nonlinearity noises are low, the ON and OFF pathways each encode roughly half of the stimulus distribution (figure ​(figure1B).1B). However, the optimal nonlinearities rearrange at higher noise levels, introducing redundancy in signal encoding (figure ​(figure1C).1C). For very large post-nonlinearity noise, the best the circuit can do is encode the sign of the received stimulus (figure ​(figure1D).1D). The results of related studies are consistent with behavior observed in specific parameter regimes of the broad framework encompassed by this model [1,2]. Figure 1 A. Simple two-pathway retinal circuit model. A stimulus (s) is presented and transmitted to separate ON and OFF pathways, which receive correlated corrupting noises η+ and η-, respectively. The signals are passed through encoding nonlinearities ...