Transportation Distances on the Circle

Rabin, Julien; Delon, Julie; Gousseau, Yann

doi:10.1007/s10851-011-0284-0

Cited by 47 publications

(52 citation statements)

References 31 publications

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“…The Wasserstein distance w is used to compare the marginal distance distributions, it corresponds to the area between the cumulative probability distributions. The circular Wasserstein distance ∆ is used to compare the distribution of phases to another distribution with circular symmetry, it corresponds to the minimal distance from all linear Wasserstein distances on an unfolded circle for all possible starting points on the circle (Rabin et al, 2011). Circular and circular-linear kernel density estimations use von Mises and Gaussian kernels with adaptive concentration and smoothing parameters (García-Portugués et al, 2013).…”

Section: Discussionmentioning

confidence: 99%

Hippocampal spike-time correlations and place-field overlaps during open field foraging

Monsalve‐Mercado

Roudi²

2019

Preprint

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Phase precessing place cells encode spatial information on fine timescales via the timing of their spikes. This phase code has been extensively studied on linear tracks and for short runs in the open field. However, less is known about the phase code on unconstrained trajectories lasting tens of minutes, typical of open field foraging.In previous work (Monsalve-Mercado and Leibold, 2017), an analytic expression was derived for the spike-time cross-correlation between phase precessing place cells during natural foraging in the open field. This expression makes two predictions on how this phase code differs from the linear track case: cross-correlations are symmetric with respect to time, and they represent the distance between pairs of place fields in that the theta-filtered cross-correlations around zero time-lag are positive for cells with nearby fields while they are negative for those with fields further apart. Here we analyze several available open field recordings and show that these predictions hold for pairs of CA1 place cells. We also show that the relationship remains during remapping in CA1, and it is also present in place cells in area CA3. For CA1 place cells of Fmr1-null mice, which exhibit normal place fields but somewhat weaker temporal coordination with respect to theta compared to wild type, the cross-correlations still remain symmetric but the relationship to place field overlap is largely lost. The relationship discussed here describes how spatial information is communicated by place cells to downstream areas in a finer theta-timescale, relevant for learning and memory formation in behavioural tasks lasting tens of minutes in the open field.

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Section: Discussionmentioning

confidence: 99%

Hippocampal spike-time correlations and place-field overlaps during open field foraging

Monsalve‐Mercado

Roudi²

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…The Wasserstein distance w is used to compare the marginal distance distributions, it corresponds to the area between the cumulative probability distributions. The circular Wasserstein distance ∆ is used to compare the distribution of phases to another distribution with circular symmetry, it corresponds to the minimal distance from all linear Wasserstein distances on an unfolded circle for all possible starting points on the circle (Rabin et al, ). Circular and circular‐linear kernel density estimations (CLKDEs) use von Mises and Gaussian kernels with adaptive concentration and smoothing parameters (Garcıa‐Portugues, Crujeiras, & Gonzalez‐Manteiga, ).…”

Section: Methodsmentioning

confidence: 99%

Hippocampal spike‐time correlations and place field overlaps during open field foraging

Monsalve‐Mercado

Roudi²

2019

Hippocampus

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Phase precessing place cells encode spatial information on fine timescales via the timing of their spikes. This phase code has been extensively studied on linear tracks and for short runs in the open field. However, less is known about the phase code on unconstrained trajectories lasting tens of minutes, typical of open field foraging. In previous work (Monsalve‐Mercado and Leibold, Physical Review Letters, 119, 38101 (2017)), an analytic expression was derived for the spike‐time cross‐correlation between phase precessing place cells during natural foraging in the open field. This expression makes two predictions on how this phase code differs from the linear track case: cross‐correlations are symmetric with respect to time, and they represent the distance between pairs of place fields in that the theta‐filtered cross‐correlations around zero time lag are positive for cells with nearby fields while they are negative for those with fields further apart. Here we analyze several available open field recordings and show that these predictions hold for pairs of CA1 place cells. We also show that the relationship remains during remapping in CA1, and it is also present in place cells in area CA3. For CA1 place cells of Fmr1‐null mice, which exhibit normal place fields but somewhat weaker temporal coordination with respect to theta compared to wild type, the cross‐correlations still remain symmetric but the relationship to place field overlap is largely lost. The relationship discussed here describes how spatial information is communicated by place cells to downstream areas in a finer theta‐timescale, relevant for learning and memory formation in behavioral tasks lasting tens of minutes in the open field.

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“…We consider distributions on the real line, as well as periodic distributions, which are important for comparing histograms of orientations or of colors in some speci c color spaces, or directional spatial relations. This problem has been addressed using the Wasserstein distance in [19], but not using the Hausdor distance.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, existing methods for comparing histograms or probability distributions [11] are usually categorized into two classes: (i) bin-to-bin distances, and (ii) cross-bin distances, involving the distance on the support (or ground distance) [11,19,25]. In this paper, we only consider distances of the second class, keeping in mind the application to spatial relations.…”

Section: Introductionmentioning

confidence: 99%

Defining and computing Hausdorff distances between distributions on the real line and on the circle: link between optimal transport and morphological dilations

Bloch

Atif

2016

Mathematical Morphology - Theory and Applications

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Comparing probability or possibility distributions is important in many elds of information processing under uncertainty. In this paper we address the question of de ning and computing Hausdor distances between distributions in a general sense. We propose several dilations of distributions, and exhibit some links between Lévy-Prokhorov distances and dilation-based distances. In particular, mathematical morphology provides an elegant way to deal with periodic distributions. The case of possibility distributions is addressed using fuzzy mathematical morphology. As an illustration, the proposed approaches are applied to the comparison of spatial relations between objects in an image or a video sequence, when these relations are represented as distributions.

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Transportation Distances on the Circle

Cited by 47 publications

References 31 publications

Hippocampal spike-time correlations and place-field overlaps during open field foraging

Hippocampal spike-time correlations and place-field overlaps during open field foraging

Hippocampal spike‐time correlations and place field overlaps during open field foraging

Defining and computing Hausdorff distances between distributions on the real line and on the circle: link between optimal transport and morphological dilations

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