# Peripheral Network Connectivity Analyses for the Real-Time Tracking of Coupled Bodies in Motion

^{*}

## Abstract

**:**

But there’s nothing more profound than creating something out of nothing.—Rainbow Rowell

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Motivation: Deliberate vs. Consequential Motions Self-Generated by the Nervous Systems

#### 2.2. Data Acquisition and Signal Processing

#### 2.3. Instrumentation Specs

#### 2.4. Pre-Processing

#### 2.5. First Parameterization: The Micro-Movements

#### 2.6. Distance Estimation in Probability Space

#### 2.7. Second Parameterization: Coherence-Phase-Frequency (CPF)

#### 2.8. A Measure of Physical Entrainment

## 3. Results

#### 3.1. Connectivity Metrics: Body-Body Networks Degree Distributions

#### 3.2. Connectivity Metrics: Body-Body Networks Leading-Lagging Profiles

#### 3.3. Dynamically Coupled Body-Body Networks

#### 3.4. Automatic Identification of Connectivity and Coordination Patterns

#### 3.5. Individualized Noise-Body-Map Profiles

#### 3.6. K/W Distance in Probability Space

## 4. Discussion

#### 4.1. Connecting Central and Peripheral Signals of the Nervous Systems

#### 4.2. Other Applications in AI and Robotics

#### 4.3. Closing the Feedback Loop: Shifting from Correlation to Causation in Statistical Inference

#### 4.4. Higher Frequencies and Their Possible Uses in Sensory-Substitution Interventions

## 5. Patents

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Automatically tracking who leads in the dyadic interaction taking place as the ADOS-2 test [60] unfolds (to diagnose autism spectrum disorders). Two frames depicting the clinician and child engaged in the test. Both participants are wearing a grid of APDM Opal IMUs 128 Hz, Portland OR, on the torso, lumbar, right and left wrists, and right and left ankles (along with positional head and wrist Polhemus Latus sensors, 188 Hz, Colchester VT). The 12 IMUs simultaneously co-register acceleration, gyroscope, magnetometer, and temperature data. Acceleration data is used here to demonstrate the minute-by-minute states of the network conformed by the 12 nodes (1–6 on the clinician and 7–12 on the child). The ADOS-2 Module 3 for the verbal child was administered with tasks in the order depicted and using the task initials to represent the minute-by-minute activity. The network outgoing strength (obtained from the weighted sum of the links outgoing from a node i, times the maximal coherence value to another node j) defines a profile revealing leading activity for the child and clinician. For simplicity, the network states for the corresponding minute-peak activity are shown. One is for the peak at minute 15—when the clinician leads the child (during the Description of a Picture, DP task) and the other is at minute 37—when the child leads the clinician during the Break, B task. Vertical lines delineate the tasks’ segments (denoted by the initials) in the order in which they occurred. The labeling and analyses are completely automated.

## Appendix B

**Figure A2.**Network connectivity analyses of salsa dancing using a grid of IMUs of a commercially available sampling resolution. (

**A**) Dancers in pose with sensors’ placement. (

**B**) Network state derived from 30 s worth of data (30 × 60 × 128 frames at 128 Hz sampling resolution) with similar representation as Figure 7 in main paper. MM spikes derived from the fluctuations in linear acceleration amplitude. Linear acceleration time-series obtained from triaxial acceleration using the Euclidean norm to compute the scalar acceleration amplitude. Node at locations represent two self-emerging modules (colored in magenta an d yellow). Circle size represents the strength of the connectivity (incoming and outgoing weighted directed links from the node). Circle edge represents the maximal cross-coherence value measured pairwise with the connecting node. Pairwise links between nodes represent node i leading node j (i → j) and thickness represents the phase shift (lower values are thinner dashed lines 0–60, 61–120, and higher values 121–180 are thicker continuous lines). Link colors represent inner connections (red female, blue male) and black links represent inter connections from coupled nodes. (

**C**) Similar representation as in (

**B**) using orientation data. Data comes from the angular speed derived from quaternions representing the rotations of gyroscopes. Insets above B localize the signatures on the Gamma parameter plane relative to the worst case scenario of exponential distribution shape = 1 with the highest possible noise (extracted from the session) for angular speed and linear acceleration. Corresponding distances from each point to the extreme (most random and noisiest) case are expressed as color-coded vectors above panel (

**C**). Notice the complementary patterns between the well-rehearsed routine (male body leads and has strongest predictive signal vs. spontaneous improvisation whereby female leads with a stronger predictive signal than male).

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**Figure 1.**Coordination of complex patterns of behavior in multiple settings. (

**A**,

**B**) Maintaining and controlling difficult postures. (

**C**) Building synchronous synergies in dyadic exchange. (

**D**) Maintaining a harmonious flow in a crowd of dancers performing a choreography.

**Figure 2.**The data collection and representation tools. (

**A**) Two professional dancers in T-pose while being calibrated within the Phase Space. Cameras capturing the motion are marked and suits contain 38 LEDs in each dancer’s body. Data is sampled at 960 Hz. (

**B**) (

**Left**) panel: Skeleton showing the distribution of LEDs from 1–38 across the body segments. (

**Right**) panel: Our avatar designed in Matlab using a forward kinematics model in [32] to track the various parameters of interest (see movie from the Phase Space and Bot and Dolly in Link 1 of the Appendix B.).

**Figure 3.**Building our new micro-movements data type from kinematic parameters extractable from positional movement trajectories. (

**A**) Two views of the movement trajectories from the two dancers (red female and blue male) while performing one segment of a dance routine. (

**B**) Sample trajectory from the female hand during one routine. Frenet-Serret frames along the trajectory to compute curvature and torsion parameters. (

**C**) Linear speed profile of the hand trajectory segment in (

**B**) to automatically extract the pauses from the speed’s local minima marked with dots (corresponding to the dots on the three-dimensional trajectory of (

**B**)). (

**D**) Speed profile of one LED sensor across 500 s of motion and (

**E**) corresponding trajectory bending profile. (

**F**) Micro-movements scaling linear speed profile in (

**D**) and bending profile in (

**E**) to obtain the standardized wave form representing a continuous random process as spikes in signals’ amplitude fluctuations depicted in

**F**–

**G**.

**Figure 4.**Pipeline of signal processing to obtain the micro-movement spikes of the bending amplitude as input to a Gamma process and cross-coherence analyses. (

**A**) Average bending of the peaks from female dancer (one motion LED) obtained from Equation (2) of the main text is Gamma-distributed. Similarly, the peaks of the bending (not shown) are Gamma-distributed. As such, the MM derived from the normalization formula in Equation (2) are also Gamma-distributed and can be modeled by a Gamma process. (

**B**) Extraction of MM from full bending profile of a routine, with inset showing the MM spikes corresponding to a segment automatically extracted from speed pauses (see Figure 3B,C). (

**C**) Sampled 350 peaks (in the order in which they were acquired) from the motion path curvature generated by one LED (on the female) during a routine registered with 10 K frames are normalized as per Equation (2). They provide the amplitude MM scaled between 0–1 and are then zero-padded to recover the original number of frames in that routine segment. This procedure applied to all LEDs from both dancers then provides equal length MM spike vectors for pairwise cross-coherence analyses across all body parts of the two dancers. (

**D**) Full MM spikes across all frames, zero-padded to retain equal number of frames for cross-coherence analyses.

**Figure 5.**General characterization of stochastic signatures and empirically-derived criteria for targeted performance. (

**A**) The Gamma parameter plane spanned by the shape and scale dimensions. Each point localizes the signatures of the person’s performance for a given segment of the routine. The quadrants defining regions of interest to track performance are defined by the median of the shape and scale parameters (dynamically changing over the routines) and empirically defining the good region by the right lower quadrant (RLQ) with probability distributions tending to the Gaussian (symmetric) with a low noise to signal ratio (low scale value). The left upper quadrant (LUQ) instead denotes regions of high randomness (towards 1, the shape value of the memoryless Exponential distribution) and with a high noise to signal ratio. (

**B**) The log-log Gamma Parameter plane yields a power low-like relation of the MM data. The arrow head represents one PDF in the RLQ, localizing it in in (

**D**–

**F**). (

**C**) Schematics representing the different stochastic states of the data, as they evolve over time. (

**D**) Empirically estimated Probability Density Functions (PDFs) from the data in (

**A**,

**B**). (

**E**) Different distance criteria to ascertain similarities and differences between points in the probability space of interest. One criterium uses theoretical limiting points (Exponential with high noise vs. Gaussian with low noise), while the other uses empirically-estimated limiting points, derived from extrema of the entire data set. (

**F**) The Gamma summary statistics providing the empirically-derived moments of the distributions fit. Regions of interest are color-coded as in the previous panels. Scale from 0–1 corresponds to speed MM range.

**Figure 6.**From the time to frequency domain. (

**A**) The MM frames from different body nodes are FFT to perform power spectral analyses (

**B**) and then pairwise cross-coherence analyses yield the frequency of the peaks (x-axis) and the phase shift (y-axis) in (

**C**). (

**D**) Frequency ranges studied in human motor control vs. other ranges studied in disciplines that ascertain levels of detectable vibration that may be in some cases harmful to the human nervous systems. Higher frequencies that are physiologically relevant to the vibro-tactile domain are of interest to build sensory-substitution devices.

**Figure 7.**The coherence, phase, and frequency (CPF) parameterization and the weighted directed graph representation of the data as dynamically changing networks. (

**A**) Adjacency matrix of 76 × 76 entries (38 for each dancer) representing the state of the two dancers in one block of MM data. Each dot represents a maximal value (a peak) of the cross-coherence, with the range of coherence values represented in the color bar. Entries with 0-values have 0 cross-coherence. Four quadrants provide the pairwise values for the female body parts (38 LEDs on the top left quadrant); for the female → male (top right quadrant); for the male → female (bottom left quadrant); and for the male body parts (bottom right quadrant.) Square, circle, diamond, and triangle in each quadrant have the corresponding values of phase lead in (

**B**) and frequency in (

**C**). (

**D**) Network representation for a frequency band and block of MM data (see text) highlighting the interconnectivity of each body (blue weighted directed arrows male and red weighted directed arrows female). Black weighted directed arrows are the coupled activities across the dyad (thicker arrows are higher weight given by the phase lead values). Circle size is the strength of the connectivity (in degree and out degree counting number of edges entering and leaving the node) and color is the module representing highly interconnected sub-nets that are sparsely connected to other clusters.

**Figure 8.**Sample use of the modularity metric across different 10-based frequency bands. (

**A**) Different modules (16) self-emerge for each data block of the dynamically evolving network, as the routine unfolds for the female and male. (

**B**) Counting the participation of each body node in each of the modules. The entry of the matrix (color map) gives the number of times (per units of time, e.g., minute) a node participates in a module (horizontal range from 1 to 16 from (

**A**)) for the female and male dancer, e.g., during the dancing condition in this case.

**Figure 9.**The automatic extraction of coupled synergistic behavior from the modules that self-emerge in the network’s dynamic evolution. (

**A**) Simultaneous node participation in a given network module is tallied and threshold set to ½ the minimum of maximal participation. Such points count as coupled behavior for body segments that are comprised of such nodes. (

**B**) Matrix representing the coupled behavior (yellow) across body regions of the two dancers. (

**C**) Avatar representation of the coupled behavior. Blue (male) and red (female) with yellow segments colored from module to module. See Videos S2 and S3 showing full movies module by module and Video S4 showing the real-time dance video segment with the avatar representation.

**Figure 10.**Sample degree distributions for different frequency bands in one snippet of data reflecting the state of the network differently for lower vs. higher frequencies. Each inset frequency histogram reflects the number of K edges on the x-axis and the number of nodes with k edges along the y-axis. The color of the frequency histogram corresponds to the color of the links. Red reflects the female inner links; blue the male inner links; and black the coupled network inter links. Arrows reflect the directionality and thickness the phase shift (thicker values are higher shifts). Note the differences in degree connectivity between lower and higher frequency bands for each of the subnetworks of interest.

**Figure 11.**Connectivity metrics measuring female, male, and coupled networks: (

**A**) Percentage of nodes with maximal coherence for the coupled network significantly differed from the networks of the male and female bodies; (

**B**) Pairwise K/W distance matrix reveals patterns for the female network, the male network, and the coupled network, relative to the ideal Gaussian signature; (

**C**) Patterns of betweenness centrality (

**D**) phase and (

**E**) modularity are also different for each network under consideration. Notice the female network the has highest percentage of nodes with 0 phase shift (fully synchronous) and the coupled network has the highest percentage of nodes with the highest number of modules.

**Figure 12.**Automatically detecting patterns of leadership in the cohesiveness of the coupled behavior (inter-connectivity in (

**A**) and intra-connectivity for each dancer in (

**B**). (

**A**) Leading patterns across the full network of spontaneously self-emerging coupled nodes across 10-based frequency bands. Patterns unveiled using the outdegree distributions and including cohesive activity in inter-connected nodes across the two dancers and (

**B**) Leading activity for the self-emerging synergies of the body of each dancer (intra-connectivity). Out-Degree per node (sensor) used to unveil the leading information for selected body regions (upper body including the head, trunk, arms and hands), lumbar region (including lumbar areas and the hips) and lower body region (including the legs and feet) of each dancer. For the dancing condition in (

**A**) the female tends to lead across frequencies with the male taking the lead for 90–100 Hz range. In contrast the non-dancing condition is primarily led by the male dancer, except in bands 90–100 Hz and 190–210 Hz. In (

**B**) the individual patterns reveal which bodily region leads within each dancer’s synergies and condition, per frequency band.

**Figure 13.**Network’s self-emerging connectivity patterns for different 10-based frequency bands uncover critical network states. (

**A**) The characteristic pathlength of the network measuring the average shortest distance path profiled for different frequency bands. (

**B**) Adjacency matrix denoting the weighted directed graph used to build the network states for the minimum and maximum characteristic pathlength revealing the frequency band for which they occur. (

**C**) The network pairwise shortest distance paths when the characteristic pathlength is at its minimum value (which happens to occur at 50 Hz). (

**D**) The network’s pairwise shortest-distance-path state when the characteristic pathlength is at its minimum value (occurring at 50 Hz). (

**E**) The network’s pairwise shortest-distance-path state when the characteristic pathlength is at its maximum value (occurring at 210 Hz).

**Figure 14.**Summary statistics for the empirically estimated continuous family of Gamma probability distributions for speed and bending profiles taken for each of the 76 body nodes for the female and for the male dancer, by pooling movement activity across the 14 dancing routines (

**A**) and non-dancing (calibration and planning) segments (

**B**). Color bars represent physical levels of fluctuations in linear speed (cm/s) and bending (cm) measured as departures from the overall estimated Gamma means. Axes are as explained in methods (x-axis Gamma mean, y-axis Gamma variance, z-axis skewness and kurtosis represented in the size of the marker; squares represent lower body, triangles upper body, and circles head LEDs; blue edges represent male and red edges female).

**Figure 15.**Bodily maps of noise (scale values) for the female and male using the bending profiles pooled across all routines for each body node. (

**A**) Dancing condition with insets showing estimated PDFs for female and male. Avatars color-coded for one frame with levels of noise for the physically entrained body parts as explained in Figure 8 (blue avatar male, red avatar female, and green color gradient as in color bar in (

**B**), also showing the non-dancing condition).

**Figure 16.**Dancing routine performances at a glance, measuring the K/W distance from each dancer’s empirically estimated probability frequency distribution to the best or to the worst empirically determined PDF, as ascertained by noise levels and distribution shape symmetry across the entire set. (

**A**) Profile of empirically estimated Gamma distribution shape from female dancer’s linear speed across 14 routines (horizontal axis) and 38 body nodes (vertical axis) readily reveals routine 6 as the one with the most symmetric distribution. Male profile as female’s. Averaged Gamma distribution shape values taken across all body nodes for each dancer confirm routine 6 as the one yielding the most symmetric distribution shape. (

**B**) Same as (

**A**) for the Gamma scale parameter, empirically estimated from the linear speed profiles of each routine and across the grid of body nodes. (

**C**) K/W distance from routine and body node to the best (and worst) values taken across entire data set as the highest shape (closest to Gaussian symmetric shape) and lowest scale (noise) used to define the best case vs. the most skewed shape (closest to Exponential) and highest noise used to define the worst case.

Parameter | Condition | p-Value |
---|---|---|

Shape (a) | Dancing vs. NonDancing | 1.3027 × 10^{−21} |

Scale (b) | Dancing vs. NonDancing | 2.4329 × 10^{−}^{18} |

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**MDPI and ACS Style**

Kalampratsidou, V.; Torres, E.B.
Peripheral Network Connectivity Analyses for the Real-Time Tracking of Coupled Bodies in Motion. *Sensors* **2018**, *18*, 3117.
https://doi.org/10.3390/s18093117

**AMA Style**

Kalampratsidou V, Torres EB.
Peripheral Network Connectivity Analyses for the Real-Time Tracking of Coupled Bodies in Motion. *Sensors*. 2018; 18(9):3117.
https://doi.org/10.3390/s18093117

**Chicago/Turabian Style**

Kalampratsidou, Vilelmini, and Elizabeth B. Torres.
2018. "Peripheral Network Connectivity Analyses for the Real-Time Tracking of Coupled Bodies in Motion" *Sensors* 18, no. 9: 3117.
https://doi.org/10.3390/s18093117