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In this paper, we use spectral analysis to investigate transfer learning and study model sensitivity to frequency shortcuts in medical imaging. By analyzing the power spectrum density of both pre-trained and fine-tuned model gradients, as well as artificially generated frequency shortcuts, we observe notable differences in learning priorities between models pre-trained on natural vs medical images, which generally persist during fine-tuning. We find that when a model's learning priority aligns with the power spectrum density of an artifact, it results in overfitting to that artifact. Based on these observations, we show that source data editing can alter the model's resistance to shortcut learning.

We introduce the notion of a "walk with jumps", which we conceive as an evolving process in which a point moves in a space (for us, typically $\mathbb{H}^2$) over time, in a consistent direction and at a consistent speed except that it is interrupted by a finite set of "jumps" in a fixed direction and distance from the walk direction. Our motivation is biological; specifically, to use walks with jumps to encode the activity of a neuron over time (a ``spike train``). Because (in $\mathbb{H}^2$) the walk is built out of a sequence of transformations that do not commute, the walk's endpoint encodes aspects of the sequence of jump times beyond their total number, but does so incompletely. The main results of the paper use the tools of hyperbolic geometry to give positive and negative answers to the following question: to what extent does the endpoint of a walk with jumps faithfully encode the walk's sequence of jump times?

Characterizing judgments of similarity within a perceptual or semantic domain, and making inferences about the underlying structure of this domain from these judgments, has an increasingly important role in cognitive and systems neuroscience. We present a new framework for this purpose that makes limited assumptions about how perceptual distances are converted into similarity judgments. The approach starts from a dataset of empirical judgments of relative similarities: the fraction of times that a subject chooses one of two comparison stimuli to be more similar to a reference stimulus. These empirical judgments provide Bayesian estimates of underling choice probabilities. From these estimates, we derive indices that characterize the set of judgments in three ways: compatibility with a symmetric dis-similarity, compatibility with an ultrametric space, and compatibility with an additive tree. Each of the indices is derived from rank-order relationships among the choice probabilities that, as we show, are necessary and sufficient for local consistency with the three respective characteristics. We illustrate this approach with simulations and example psychophysical datasets of dis-similarity judgments in several visual domains and provide code that implements the analyses at https://github.com/jvlab/simrank., Comment: Body: 64 pages; 16 figures; 7 supplementary figures, 3 appendices. This replacement is a major revision in response to peer reviews in Mathematical Neuroscience and Applications (MNA). Main changes are (i) reorganization to separate theory and implementation, (ii) addition of analyses of synthetic datasets, (iii) expanded discussion of alternatives and open issues

Animals use stereo sampling of odor concentration to localize sources and follow odor trails. We analyze the dynamics of a bilateral model that depends on the simultaneous comparison between odor concentrations detected by left and right sensors. The general model consists of three differential equations for the positions in the plane and the heading. When the odor landscape is an infinite trail, then we reduce the dynamics to a planar system whose dynamics have just two fixed points. Using an integrable approximation (for short sensors) we estimate the basin of attraction. In the case of a radially symmetric landscape, we again can reduce the dynamics to a planar system, but the behavior is considerably richer with multi-stability, isolas, and limit cycles. As in the linear trail case, there is also an underlying integrable system when the sensors are short. In odor landscapes that consist of multiple spots and trail segments, we find periodic and chaotic dynamics and characterize the behavior on trails with gaps and that turn corners.

We present the results from four stellar occultations by (486958) Arrokoth, the flyby target of the New Horizons extended mission. Three of the four efforts led to positive detections of the body, and all constrained the presence of rings and other debris, finding none. Twenty-five mobile stations were deployed for 2017 June 3 and augmented by fixed telescopes. There were no positive detections from this effort. The event on 2017 July 10 was observed by SOFIA with one very short chord. Twenty-four deployed stations on 2017 July 17 resulted in five chords that clearly showed a complicated shape consistent with a contact binary with rough dimensions of 20 by 30 km for the overall outline. A visible albedo of 10% was derived from these data. Twenty-two systems were deployed for the fourth event on 2018 Aug 4 and resulted in two chords. The combination of the occultation data and the flyby results provides a significant refinement of the rotation period, now estimated to be 15.9380 $\pm$ 0.0005 hours. The occultation data also provided high-precision astrometric constraints on the position of the object that were crucial for supporting the navigation for the New Horizons flyby. This work demonstrates an effective method for obtaining detailed size and shape information and probing for rings and dust on distant Kuiper Belt objects as well as being an important source of positional data that can aid in spacecraft navigation that is particularly useful for small and distant bodies., Comment: Submitted to Astronomical Journal (revised); 40 pages, 13 figures, 9 tables

Previously, in (Hermundstad et al., 2014), we showed that when sampling is limiting, the efficient coding principle leads to a "variance is salience" hypothesis, and that this hypothesis accounts for visual sensitivity to binary image statistics. Here, using extensive new psychophysical data and image analysis, we show that this hypothesis accounts for visual sensitivity to a large set of grayscale image statistics at a striking level of detail, and also identify the limits of the prediction. We define a 66-dimensional space of local grayscale light-intensity correlations, and measure the relevance of each direction to natural scenes. The "variance is salience" hypothesis predicts that two-point correlations are most salient, and predicts their relative salience. We tested these predictions in a texture-segregation task using un-natural, synthetic textures. As predicted, correlations beyond second order are not salient, and predicted thresholds for over 300 second-order correlations match psychophysical thresholds closely (median fractional error <0.13)., Comment: 33 pages, 12 figures

We describe a new, computationally simple method for analyzing the dynamics of neuronal spike trains driven by external stimuli. The goal of our method is to test the predictions of simple spike-generating models against extracellularly recorded neuronal responses. Through a new statistic called the power ratio, we distinguish between two broad classes of responses: (1) responses that can be completely characterized by a variable firing rate, (for example, modulated Poisson and gamma spike trains); and (2) responses for which firing rate variations alone are not sufficient to characterize response dynamics (for example, leaky integrate-and-fire spike trains as well as Poisson spike trains with long absolute refractory periods). We show that the responses of many visual neurons in the cat retinal ganglion, cat lateral geniculate nucleus, and macaque primary visual cortex fall into the second class, which implies that the pattern of spike times can carry significant information about visual stimuli. Our results also suggest that spike trains of X-type retinal ganglion cells, in particular, are very similar to spike trains generated by a leaky integrate-and-fire model with additive, stimulus-independent noise that could represent background synaptic activity., Comment: 2 Tables, 9 Figures. To appear in J. Neurosci. 18 (1998). Originally submitted to the neuro-sys archive which was never publicly announced (was 9905002)

We present the mathematical basis of a new approach to the analysis of temporal coding. The foundation of the approach is the construction of several families of novel distances (metrics) between neuronal impulse trains. In contrast to most previous approaches to the analysis of temporal coding, the present approach does not attempt to embed impulse trains in a vector space, and does not assume a Euclidean notion of distance. Rather, the proposed metrics formalize physiologically-based hypotheses for what aspects of the firing pattern might be stimulus-dependent, and make essential use of the point process nature of neural discharges. We show that these families of metrics endow the space of impulse trains with related but inequivalent topological structures. We show how these metrics can be used to determine whether a set of observed responses have stimulus-dependent temporal structure without a vector-space embedding. We show how multidimensional scaling can be used to assess the similarity of these metrics to Euclidean distances. For two of these families of metrics (one based on spike times and one based on spike intervals), we present highly efficient computational algorithms for calculating the distances. We illustrate these ideas by application to artificial datasets and to recordings from auditory and visual cortex., Comment: 16 Figures (not in this file). Originally submitted to the neuro-sys archive which was never publicly announced (was 9810001)