This paper proposes an approach to measure motion similarity between human-human and human-object interaction. The authors claim that human activities are usually defined by the interaction between individual characters, such as a high-five interaction.

As the interaction datasets are not available authors provide multiple small-scale interaction datasets:
https://i.imgur.com/P815TYu.png
where:
- 2C = a Character-Character (2C) database using kick-boxing motions
- CRC = Character-Retargeted Character where the size of characters is adjusted while maintaining the nature of the interaction
https://i.imgur.com/XX1WNpO.png
- HOI = Human-Object Interaction where a Chair is used as an object
https://i.imgur.com/Z6cxd7R.png
- 2PB = 2 People Boxing 
https://i.imgur.com/yUxmpY5.png
- 2PD = 2 People Daily Interaction where people represented as a surface point cloud
https://i.imgur.com/EzyELg3.png


**Methodology**
- *Customized Interaction Mesh Structure*. An interaction mesh is created by generating a volumetric mesh using Delaunay Tetrahedralization. Interaction is therefore represented by a series of interaction meshes. To reduce the bias of unequal number of points per human body part, synthetic points (shown in blue) are derived from available skeleton structure (shown in red):
 https://i.imgur.com/jtlrH49.png

 The edges after Delaunay Tetrahedralization are filtered in a way that all edges connecting to the same character are removed, as they do not contribute to the interaction.
 https://i.imgur.com/nWeUNl1.png
 The temporal sequence of interaction is a series of interaction meshes.

- *Distance between interaction meshes*.
   - Distance between two interaction meshes of two-character interactions:

   $d(e_i, e_j) = (|e_{i1} - e_{j1}| + |e_{i2} - e_{j2}|) \times \frac{1}{2} (1 - cos\theta),$
   https://i.imgur.com/jMHGx3o.png
   where $e_{i1}$ and $e_{i2}$ are two endpoints of an edge.

   - *Earth Mover's Distance*. Earth Mover’s Distance (EMD) is used to find the best correspondence between the input interaction meshes to achieve the comparison of two interactions with different semantic meaning:

    $EMD(E_I^{t_I}, E_J^{tJ}) = \frac{D(E_I^{t_I}, E_J^{tJ})}{\sum_{i=1}^{m} \sum_{j=1}^{n} f_{i,j}^*},$

    where $D(E_I^{t_I}, E_J^{tJ}) = \sum_{i=1}^{m} \sum_{j=1}^{n} d(e_i, e_j) f_{i,j}^*$ represents the minimum distance between two interaction meshes and $f_{i,j}^*$ is the optimal set of flow values returned by the mass transport solver that finds the optimal edge-level correspondence between two interaction meshes. The concept of the mass transport solver is visualized below:
    https://i.imgur.com/wmRhcxP.png


 - *Distance between interactions sequences*.
    - spatial normalization - removing its pelvis translation and its horizontal facing angle in each frame

    - temporal sampling - non-linear sampling strategy based on the frame distance measured by EMD. The sampling algorithm samples fewer in temporal regions with high similarity, which contribute less to the context of the interaction.

    - temporal alignment - keyframes are aligned using Dynamic Time Warping (DTW)

Possible functionality with the proposed method:
- Interaction motion similarity analysis
- Interaction motion retrieval

Notice:
>The pre-process took 1.5 hours, 0.5 hour and 4 hours for the 2C, CRC and HOI databases respectively. Given the meshes, computing the distance between two interactions took 0.2 seconds on average.

Discussion:
- the algorithm focuses on boxing/kickboxing as they have clear rules. Extending the proposed algorithm for measuring motion similarity for daily activities would require careful annotation.
- While the method, in theory, can be applied to single human activities, it quite clear that it would perform worse than other baselines for the task. This implies that it is better not applied for use cases where a comparison between two independent movements having no interaction with each other (dancing, yoga) is required.
- The method works best for close interaction activities as the edges in the interaction mesh would tend to have a similar structure (e.g. edge length) in case of distant interacting objects. 
- Application-wise, the algorithm is not suitable for online real-time use.

The Escherichia coli chemotaxis network is a model system for biological signal processing. In E. coli, transmembrane receptors responsible for signal transduction assemble into large clusters containing several thousand proteins. These sensory clusters have been observed at cell poles and future division sites. Despite extensive study, it remains unclear how chemotaxis clusters form, what controls cluster size and density, and how the cellular location of clusters is robustly maintained in growing and dividing cells. Here, we use photoactivated localization microscopy (PALM) to map the cellular locations of three proteins central to bacterial chemotaxis (the Tar receptor, CheY, and CheW) with a precision of 15 nm. We find that cluster sizes are approximately exponentially distributed, with no characteristic cluster size. One-third of Tar receptors are part of smaller lateral clusters and not of the large polar clusters. Analysis of the relative cellular locations of 1.1 million individual proteins (from 326 cells) suggests that clusters form via stochastic self-assembly. The super-resolution PALM maps of E. coli receptors support the notion that stochastic self-assembly can create and maintain approximately periodic structures in biological membranes, without direct cytoskeletal involvement or active transport.

The paper: "Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask" by Zhou et al., 2019 found that by just learning binary masks one can find random subnetworks that do much better than chance on a task. This new paper builds on this method by proposing a strong algorithm than Zhou et al. for finding these high-performing subnetworks.https://i.imgur.com/vxDqCKP.png

The intuition follows: "If a neural network with random weights (center) is sufficiently overparameterized, it will contain a subnetwork (right) that performs as well as a trained neural network (left) with the same number of parameters."

While Zhou et al. learned a probability for each weight this paper learns a score for each weight and takes the top k percent at evaluation. The scores are learned through their primary contribution that they call the edge-popup algorithm: 

https://i.imgur.com/9KcIbxd.png

"In the edge-popup Algorithm, we associate a score with each edge. On the forward pass we choose the top edges by score. On the backward pass we update the scores of all the edges with the straight-through estimator, allowing helpful edges that are “dead” to re-enter the subnetwork. *We never update the value of any weight in the network, only the score associated with each weight.*"

They're able to find higher-performing random subnetworks than Zhou et al.

https://i.imgur.com/T3D7OsZ.png

Updating the parameters in a LSTM language model based on the observed sequence during testing. A slice of text is first processed and then used for a gradient descent update step. A regularisation term is also proposed which draws the parameters back towards the original model.

https://i.imgur.com/zikOowE.png

The paper investigates compositional semantic models specialised for metaphors.

https://i.imgur.com/OnoJK3h.png

They construct a dataset of 8592 adjective-noun phrases, covering 23 different adjectives, annotated for being metaphorical or literal. They then train compositional models to predict the phrase vector based on the noun vector, as a linear combination with an adjective-specific weight matrix. They show that it’s better to learn separate adjective matrices for literal and metaphorical uses of each adjective, even though the amount of training data is smaller.