Vector Coding Research Articles

Lower limb gait joint coordination variability in people with diabetes-related foot ulcers

BackgroundDiabetes-related foot ulcers pose substantial health risks globally, yet the biomechanical intricacies underlying their development remain incompletely understood. This study aimed to evaluate lower limb gait joint coordination variability in individuals with diabetes-related foot ulcers compared to those with diabetes (without diabetes-related foot ulcers) and healthy controls. MethodsA total of 99 participants (diabetes-related foot ulcers cases – 16, Diabetes controls – 50, Health controls – 33) compared three self-paced walking trials. Vector coding, a technique quantifying movement coordination, was employed, analysing hip-knee, knee-ankle, and hip-angle joint couplings in the sagittal plane. FindingsNo significant differences in coordination variability were found among the groups. However, distinct coupling pattern frequencies emerged, with diabetes-related foot ulcers cases exhibiting unique anti-phase hip and ankle coupling frequency counts compared to healthy controls. InterpretationThese findings challenge conventional understandings of diabetes-related foot ulcers biomechanics and underscore the complexity of gait in this population.

Design of Credit Bond Default Risk Measurement Model Based on Spatio-Temporal Attention Network and Genetic Algorithm Driven by Digital Economy

With the rapid advancement of the digital economy, the financial market confronts unprecedented complexity and interconnectivity, rendering the precise prediction of credit bond default risk particularly crucial. This paper introduces a novel credit bond default risk measurement model (GST-GRU) predicated on a spatio-temporal attention network and genetic algorithm, designed to enhance the accuracy and robustness of risk prediction. Initially, data preprocessing is undertaken, encompassing time series data cleaning, completion of missing values for historical financial information and bond default statuses, and extraction of spatial discrete information through independent vector coding. Subsequently, a spatio-temporal attention mechanism is employed to amplify feature information in both domains, while the GRU network captures the long-term dependencies within the time series data. Thereafter, model parameters are refined using a genetic algorithm to ensure global optimality. Experimental results demonstrate that the GST–GRU model markedly improves prediction accuracy across multiple public and self-constructed datasets, surpassing traditional models. This research furnishes robust technical support for risk management in the financial market, fosters the evolution of credit bond default risk prediction technology, and lays the groundwork for the intelligence and automation of future financial systems.

Precise Orientation Estimation for Rotated Object Detection Based on a Unit Vector Coding Approach

Existing rotated object detection methods usually use angular parameters to represent the object orientation. However, due to the symmetry and periodicity of these angular parameters, a well-known boundary discontinuity problem often results. More specifically, when the object orientation angle approaches the periodic boundary, the predicted angle may change rapidly and adversely affect model training. To address this problem, this paper introduces a new method that can effectively solve the boundary discontinuity problem related to angle parameters in rotated object detection. Our approach involves a novel vector-based encoding and decoding technique for angular parameters, and a cosine distance loss function for angular accuracy evaluation. By utilizing the characteristics of unit vectors and cosine similarity functions, our method parameterizes the orientation angle as components of the unit vector during the encoding process and redefines the orientation angle prediction task as a vector prediction problem, effectively avoiding the boundary discontinuity problem. The proposed method achieved a mean average precision (mAP) of 87.48% and an average cosine similarity (CS) of 0.997 on the MVTec test set. It also achieved an mAP score of 90.54% on the HRSC2016 test set, which is better than several existing state-of-the-art methods and proves its accuracy and effectiveness.

Associations between pain-related fear and lumbar movement variability during activities of daily living in patients with chronic low back pain and healthy controls

Low back pain (LBP) is a global issue involving biological, psychological, and social factors. Pain-related fear has been shown to influence movement behavior, however, its association with some measures of movement behavior, such as spinal movement variability, remains inconclusive. To further investigate this, spinal kinematics during various activities of daily living (i.e., walking, running, lifting, and stair climbing) of 49 patients with chronic LBP and a group of 51 sex-, age-, and BMI-matched healthy controls were used to calculate lumbar spine movement variability which was quantified using different indices (i.e., coefficient of variation, coupling angle variability in vector coding, deviation phase of the continuous relative phase and an angle-angular velocity variability). General and task-specific pain-related fear was assessed using the Tampa Scale of Kinesiophobia and the Photograph Series of Daily Activities—Short Electronic Version, respectively. Linear regression analyses showed no significant association between movement variability and pain-related fear, however, the sample consisted of younger individuals with moderate disability and with low levels of pain and pain-related fear. In addition, the different variability indices were weakly correlated and varied greatly depending on the method used and the task performed. Therefore, comparisons between studies with different movement variability calculation methods or different activities should be treated with caution.

Breast-torso movement coordination during running in different breast support

To reduce breast motion with a bra, we need to understand what drives the motion of the breasts, and what variables change as support increases. Quantifying breast-torso coordination and movement complexity across the gait cycle may offer deeper insights than previously reported discrete time lag. We aimed to compare breast-torso coordination and mutual influence across breast support conditions during running. Twelve female participants ran on a treadmill at 10 km h−1 with an encapsulation and compression sports bra, and in no bra. Nipple and torso position was recorded. Vector coding, granger causality and transfer entropy were calculated within gait cycles. In both bra conditions, a greater percentage of gait cycles was spent with the breast and torso in-phase (> 90%) compared to no bra running (~ 66%, p < 0.001), with most time spent in-phase in the encapsulation versus compression bra (p = 0.006). There was a main effect of breast support condition on Granger causality (p < 0.001), both from breast to torso and torso to breast. Transfer of information was highest from torso to breast, compared to breast to torso in all conditions. Overall, these results provide novel insight into the mutual and complex interaction between the breast and the torso while running in different bra conditions. The approaches presented allow for a greater understanding of bra support conditions than existing discrete measures, which may relate to comfort and performance. Therefore, measures of coupling, predictability and transfer of complexity should be employed in future work examining these features.

Egocentric neural representation of geometric vertex in the retrosplenial cortex

Egocentric neural representations of environmental features, such as edges and vertices, are important for constructing a geometrically detailed egocentric cognitive map for goal-directed navigation and episodic memory. While egocentric neural representations of edges like egocentric boundary/border cells exist, those that selectively represent vertices egocentrically are yet unknown. Here we report that granular retrosplenial cortex (RSC) neurons in male mice generate spatial receptive fields exclusively near the vertices of environmental geometries during free exploration, termed vertex cells. Their spatial receptive fields occurred at a specific orientation and distance relative to the heading direction of mice, indicating egocentric vector coding of vertex. Removing physical boundaries defining the environmental geometry abolished the egocentric vector coding of vertex, and goal-directed navigation strengthened the egocentric vector coding at the goal-located vertex. Our findings suggest that egocentric vector coding of vertex by granular RSC neurons helps construct an egocentric cognitive map that guides goal-directed navigation.

Test-retest reliability and minimal detectable change in pelvis and lower limb coordination during running assessed with modified vector coding

The objective of this study was to evaluate the reliability of Modified Vector Coding in assessing the coordination and coordination variability of the lower limbs and pelvis during running and to determine the Minimal Detectable Change (MDC). Twenty-five healthy runners participated in a biomechanical analysis of treadmill running using a motion capture system. Modified vector coding was applied to assess the three-dimensional coordination among various pelvis and lower limb segmental couplings. Reliability was assessed using the Intraclass Correlation Coefficient (ICC), Standard Error of Measurement (SEM), MDC, and Bland-Altman analysis to ascertain measurement consistency, agreement, and the smallest clinically meaningful change that exceeds measurement error. The test–retest reliability for 33 of 42 segmental couplings analyzed was good to excellent, with ICC values ranging from 0.613 to 0.928 (p <0.05), which substantiates the robustness of modified vector coding in running biomechanics. However, nine couplings, particularly femur-tibia in the sagittal plane during midstance and foot in the frontal plane-tibia in the transverse plane during late stance, exhibited poor to moderate reliability. These findings underscore the need for cautious interpretation due to significant proportional bias (p <0.05). SEM and MDC provided insights into the precision and minimal clinically significant changes for each coupling. The findings confirm the reliability of modified vector coding for biomechanical analysis in running, with most couplings demonstrating consistent high reliability. Nevertheless, specific couplings should be interpreted with caution due to potential measurement errors. The application of MDC highlights the precision of modified vector coding in biomechanical analyses and emphasizes the importance of careful interpretation to improve clinical and research outcomes in running-related injuries.

Using continuous relative phase and modified vector coding analyses to quantify spinal coordination and coordinative variability for healthy and chronic low back pain patients: An exploratory comparative analysis

Differences in coordination and coordinative variability are common in people with low back pain. While differences may relate to the different analyses used to quantify these metrics, the preferred approach remains unclear. We aimed to compare coordination and coordinative variability, in people with and without low back pain performing a lifting/lowering task, using continuous relative phase and vector coding procedures, and to identify which technique better detects group differences. Upper lumbar (T12-L3), lower lumbar (L3-S1), and hip angular kinematics were measured using electromagnetic motion capture during 10 crate lifting/lowering repetitions from adults with (n = 47) and without (n = 17) low back pain. Coordination and coordinative variability for the Hip-Lower Lumbar and Lower Lumbar-Upper Lumbar joint pairs were quantified using mean absolute relative phase and deviation phase (continuous relative phase), and coupling angle and coupling angle variability (vector coding), respectively. T-tests examined group differences in coordination and variability. Cohen’s d bootstrapping analyses identified the more sensitive technique for detecting group differences. Less in-phase and more variable behavior was observed in the low back pain group, mostly independent of joint pair and analytical technique (P < 0.05, Cohen’s d range = 0.61 to 1.33). Qualitatively, the low back group limited motion at the lower lumbar spine during lifting/lowering. Continuous relative phase was more sensitive in detecting group differences in coordinative variability, while vector coding was more sensitive towards differences in coordination. These procedures convey distinct information and have their respective merits. Researchers should consider the choice of analytical techniques based on their study objectives.

Can training to dissociate trunk and pelvic motion influence thorax-pelvis coordination and lumbar spine dynamic stability?

BackgroundThe large number of articulating joints within the spinal column provides an abundance of options to control its movement. However, the ability of individuals to consciously manipulate these movement options is poorly understood. ObjectivesTo determine if short-term training can improve the ability to consciously dissociate motion between the pelvis and thorax during repetitive pelvic tilting movements. DesignCross-over design with young healthy individuals. MethodSeventeen participants performed trials consisting of 35 continuous lift/lowers followed by 35 continuous anterior/posterior pelvic tilts while spine kinematics were recorded. Participants then underwent a 20-min training protocol designed to improve the control of pelvic motion and in particular the dissociation of pelvic and trunk motion. Post-training, the continuous pelvic tilt and lift/lower trials were repeated. Thorax-pelvis movement coordination was analyzed via vector coding and lumbar spine local dynamic stability was analyzed via Lyapunov exponents. Participants were grouped as being either high or low skill movers based on their ability to perform the pre-training pelvic tilt movements. ResultsThe low skill movement group demonstrated statistically significant increases in the time spent using in-phase pelvic dominant (p = 0.028) and anti-phase pelvic dominant (p = 0.043) coordination patterns during the pelvic tilt movements after the completion of the training protocol. The high skill movement group showed no differences in their movement patterns post-training. ConclusionsShort-term training, targeted to improve the ability to dissociate pelvic from thorax motion, had a beneficial effect on the group of individuals who initially lacked skill performing the pelvic tilting task.

Vector Coding Optical Wireless Links

The quasi-static nature of the optical wireless channel means that the channel state information (CSI) can be readily available at the transmitter and receiver prior to data transmission. This implies that electrically band-limited optical wireless communication (OWC) systems can make use of optimal channel partitioning or vector coding based multi-channel modulation (MCM) to achieve high throughput by mitigating the non-linearities arising from the optical and electrical channel. This paper proposes a pulse amplitude modulation (PAM) based DC-biased optical vector coding (DCO-VC) MCM scheme for OWC. The throughput performance of DCO-VC is evaluated and compared to the well known DC-biased optical orthogonal frequency division multiplexing (DCO-OFDM) over hybrid (line-of-sight and diffuse) and diffuse (non line-of-sight only) visible light communication (VLC) channels with additive white Gaussian noise. For the completeness of the VLC physical layer, the performance comparison is based on an uncoded and a forward error correction transmission mode using well-known convolutional codes with Viterbi decoder. The results show that the coded DCO-VC outperforms DCO-OFDM system by achieving up to 2 and 3 dB signal to noise ratio gains over hybrid and diffuse VLC channels, respectively.

Learning the Vector Coding of Egocentric Boundary Cells from Visual Data.

The use of spatial maps to navigate through the world requires a complex ongoing transformation of egocentric views of the environment into position within the allocentric map. Recent research has discovered neurons in retrosplenial cortex and other structures that could mediate the transformation from egocentric views to allocentric views. These egocentric boundary cells respond to the egocentric direction and distance of barriers relative to an animal's point of view. This egocentric coding based on the visual features of barriers would seem to require complex dynamics of cortical interactions. However, computational models presented here show that egocentric boundary cells can be generated with a remarkably simple synaptic learning rule that forms a sparse representation of visual input as an animal explores the environment. Simulation of this simple sparse synaptic modification generates a population of egocentric boundary cells with distributions of direction and distance coding that strikingly resemble those observed within the retrosplenial cortex. Furthermore, some egocentric boundary cells learnt by the model can still function in new environments without retraining. This provides a framework for understanding the properties of neuronal populations in the retrosplenial cortex that may be essential for interfacing egocentric sensory information with allocentric spatial maps of the world formed by neurons in downstream areas, including the grid cells in entorhinal cortex and place cells in the hippocampus.SIGNIFICANCE STATEMENT The computational model presented here demonstrates that the recently discovered egocentric boundary cells in retrosplenial cortex can be generated with a remarkably simple synaptic learning rule that forms a sparse representation of visual input as an animal explores the environment. Additionally, our model generates a population of egocentric boundary cells with distributions of direction and distance coding that strikingly resemble those observed within the retrosplenial cortex. This transformation between sensory input and egocentric representation in the navigational system could have implications for the way in which egocentric and allocentric representations interface in other brain areas.

Inter-joint coordination variability is associated with pain severity and joint loading in persons with knee osteoarthritis.

As the lower extremity is a linked-joint system, the contribution of movements at the hip and ankle, in addition to the knee, to gait patterns should be considered for persons with knee osteoarthritis (OA).However, the relationships of joint coordination variability to OA symptoms, particularly knee pain, and joint loading is unknown. The purpose of this study was to determine the relationship of joint coordination variability to knee pain severity and joint loading in persons with knee OA. Thirty-fourparticipants with knee OA underwent gait analysis. Vector coding was used to assess coordination variability during the early, mid, and late stance phase. Hip-knee coupling angle variability (CAV)during midstance was associated with Knee Injury and Osteoarthritis Outcome Score (KOOS)pain (r = -0.50, p = 0.002) and Visual Analog Scalepain (r = 0.36, p = 0.04). Knee-ankle CAV during midstance was associated with KOOS pain (r = -0.34, p = 0.05). Hip-knee CAV during early and midstance were associated with knee flexion moment (KFM)impulses (r = -0.46, p = 0.01). Knee-ankle CAV during early and midstance were associated with peak KFM (r = -0.51, p < 0.01; r = -0.70, p < 0.01). Moreover, knee-ankle CAV during early, mid, and late stance phase were associated with KFM impulses (r = -0.53, p < 0.01; r = -0.70, p < 0.01; r = -0.54, p < 0.01). These findings suggest that joint coordination variability may be a factor that influences pain and knee joint loading in persons with knee OA. Statement of Clinical Significance: Movement coordination of the hip, knee, and ankle should be considered in the clinical management and future research related to knee OA.

Analysis of segmental coordination in the lower extremity using vector coding: a pilot return-to-play study of acute ankle sprain.

Purpose: Acute ankle sprain may affect ankle function during sport and daily activities. This study aimed to use vector coding technique to analyze the difference over time between injured and healthy lower limb during the first week of acute ankle sprain phase (P1) and post a 1-month recovery phase (P2) to understand the return-to-play coordination strategy in the lower extremity. Methods: Six females attended the gait experiments with attached 40 reflective markers using eight-camera Vicon motion capture system. All participants walked barefoot while turning in four directions (T0°, T45°, T90°, T135°) at their self-selected speed. Coordination patterns were classified as in-phase, anti-phase, proximal or distal dominancy between lower limb joints involving hip, knee, ankle, subtalar, metatarsophalangeal (MTP) joint and tarsometatarsal (TMT) joint. Results: P1 showed more proximal joint dominant in Hip-Knee coupling angles but P2 displayed more distal joint dominant in Knee-Ankle joint coordination pattern and mainly distal joint dominant in Ankle-MTP coupling angle mapping. The Ankle-TMT1 and Ankle-TMT5 coordination patterns matched best in straight walking but worst in T135 walking. Conclusions: Investigating inter-segmental coordination in different turning movements could provide insights into gait changes from acute ankle sprain from one-month return-to-play recovery. Knowledge of lower limb coordination pattern may provide clinical implications to improve dynamic balance and gait stability for individuals with acute ankle sprain.

Coordination of the Lower Limbs of Soccer Players after Anterior Cruciate Ligament Reconstruction with Allograft and Autograft during Landing.

Quantitative biomechanical tests, along with physical assessment, may be useful to understand kinematics associated with graft types in anterior cruciate ligament surgery, particularly in individuals aiming for a safe return to sport. Sixty male soccer players in three groups participated in this study. Three equal groups of healthy, auto transplanted and allotransplanted participants, matched for age, gender, activity level and functional status, landed with one foot on a force plate. Their kinematic information was recorded by the motion analyzer and used to describe coordination the variability by measuring coupling angles using vector coding. The coordination variability of the allograft group in the surgical limb was significantly greater than that of the healthy group at least 9 months after the reconstructive surgery of the ACL and at the stage of return to sports, (F (6, 35) = 2.79, p = 0.025; Wilk's Λ = 0.676, partial η2 = 0.32). The coordination pattern in the surgical and healthy limbs of the surgical groups also differed from that of the healthy people, which was more pronounced in the allograft group, (F (6, 35) = 2.61, p = 0.034; Wilk's Λ = 0.690, partial η2 = 0.31). These results show that the allograft group has a different coordination variability at return to sport than the healthy group, so they may need more time for excessive training and competition.

Sparse Vector Coding for Short-Packet Transmission on Industrial Communications: Reference Architecture and Design Challenges

Reliable, fast, and deterministic communications are fundamental for future industrial wireless systems. This goal requires multiple cooperating technologies that pertain to different areas of the communication arena. The weight of the waveform and coding technique choices are critical to match industrial use cases' reliability and latency requirements. Specifically, this article contributes to the field of channel coding in wireless fieldbus links. Classical block coding schemes were designed to maximize information bit rates without stringent latency requirements. Their performance in applications that use short messages degrades significantly. Recently, sparse vector coding (SVC) has been proposed as a coding approach suitable for short-packet communications with moderate complexity and low processing latency. This article presents a comprehensive analysis of SVC and a reference communication framework for its implementation on a wireless system. A set of simulations is also designed to establish the cross correlation between the different parameters involved in the code design. As a result, the coding matrix has been identified as a critical parameter that can improve coding performance. In addition, this article includes two new procedures for determining the matrix that could lead to a gain of up to 2 dB with respect to the current state of the art.

Collaborative Layout Optimization for Ship Pipes Based on Spatial Vector Coding Technique

Collaborative Layout Optimization for Ship Pipes Based on Spatial Vector Coding Technique

Vector coding reveals the underlying balance control strategies used by humans during translational perturbation

Postural control research has focused on standing balance experiments on platforms moving with relatively large amplitudes (0.1–0.2 m). This study investigated balance strategies while standing on a platform moving 4 mm in anterior-posterior direction with frequency scaled linearly from 0.4 to 6 Hz. Platform motion and kinematic and kinetic information for nine healthy participants were recorded using motion capture and force plate systems. Coordination between hip, knee and ankle joint torque, and centre of mass (COM) and centre of pressure (COP) motion was quantified by vector coding. Significant main effect of platform frequency for knee-ankle and COP-COM phase relationship was observed (p = 0.023, p = 0.016). At frequencies below 2.11 and 2.34 Hz, ankle strategy was recruited. With ankle strategy, in-phase COP-COM motion with COP dominancy occurred at frequencies below 2.19 and 2.23 Hz during scaling up and down, respectively. As platform frequency passed these values, COM dominated over COP which was followed by anti-phase knee-ankle torque, called a knee strategy, and anti-phase motion between the COP and COM that allowed COP to regain dominance over COM. Collectively, we reveal knee strategy as a new and relevant strategy in real-life settings, and transition between ankle and knee strategies that underpinned transition between COP-COM relative motion.

Comparison of Spine–Pelvis Kinematics Variability during Sit-to-Stand and Stand-to-Sit in People with &amp; without Chronic Low Back Pain: A Vector Coding and Statistical Parametric Mapping Approach

There is evidence in the literature to suggest that low back pain may change spine–pelvis coordination during activities of daily living. This study aimed to compare the variability of the spine–pelvis coordination during sit-to-stand in people with and without LBP. Ten healthy individuals with a history of LBP and ten individuals without history of LBP participated in this study. Three-dimensional kinematic data of the upper trunk (UT), lower trunk (LT), lower back (LB), and pelvis segments during sit-to-stand and stand-to-sit were recorded using a multi-segmental spine and pelvis models using a motion capture system. The coordination patterns and the variability of the adjacent segments (UT, LT, LB, and pelvis) were calculated using the modified vector coding method that was implemented through a custom MATLAB code. An independent sample t-test was utilized to assess the differences in the coordination pattern, and a statistical parametric mapping method was used to quantify the differences in coordination variability between the two groups. The results indicate that there are some differences in coordination patterns between groups during sit-to-stand and stand-to-sit. However, a significant difference in coordination variability was only observed during sit-to-stand. The results showed that LBP can alter the kinematics coordination even in the upper (pain-free) parts of the spine during sit-to-stand by changing the coordination between UT and LT in a way that can lead to an increase in the loading on these segments. Additionally, people with LBP showed more coordination variability during sit-to-stand, which can be associated with a coordination strategy that facilitates an optimal and possibly pain-free coordination pattern.

Coding of latent variables in sensory, parietal, and frontal cortices during closed-loop virtual navigation.

We do not understand how neural nodes operate and coordinate within the recurrent action-perception loops that characterize naturalistic self-environment interactions. Here, we record single-unit spiking activity and local field potentials (LFPs) simultaneously from the dorsomedial superior temporal area (MSTd), parietal area 7a, and dorsolateral prefrontal cortex (dlPFC) as monkeys navigate in virtual reality to 'catch fireflies'. This task requires animals to actively sample from a closed-loop virtual environment while concurrently computing continuous latent variables: (i) the distance and angle travelled (i.e., path integration) and (ii) the distance and angle to a memorized firefly location (i.e., a hidden spatial goal). We observed a patterned mixed selectivity, with the prefrontal cortex most prominently coding for latent variables, parietal cortex coding for sensorimotor variables, and MSTd most often coding for eye movements. However, even the traditionally considered sensory area (i.e., MSTd) tracked latent variables, demonstrating path integration and vector coding of hidden spatial goals. Further, global encoding profiles and unit-to-unit coupling (i.e., noise correlations) suggested a functional subnetwork composed by MSTd and dlPFC, and not between these and 7a, as anatomy would suggest. We show that the greater the unit-to-unit coupling between MSTd and dlPFC, the more the animals' gaze position was indicative of the ongoing location of the hidden spatial goal. We suggest this MSTd-dlPFC subnetwork reflects the monkeys' natural and adaptive task strategy wherein they continuously gaze toward the location of the (invisible) target. Together, these results highlight the distributed nature of neural coding during closed action-perception loops and suggest that fine-grain functional subnetworks may be dynamically established to subserve (embodied) task strategies.

Angular dynamics in vector coding: a new approach based on angular velocity

ABSTRACT The assessment of coordination variability in multi-joint human movements has traditionally started from angle—angle representations, and then used the angle change between subsequent time points as input for further analysis through vector coding. We propose an improvement to this approach, and suggest employing angular velocities as input data (Velocity Ellipse Method, VEM). We used experimental data and theoretical principles to contrast VEM with an existing standard (Difference Ellipse Method) and discuss its advantages and potential issues. Normalised cross-correlation was used to compare VEM and DEM in 36 angle couplings, from 20 participants running at 12 km/h on a treadmill. The hip flexion/extension—knee flexion/extension data were further investigated to discuss the robustness of the approach to measurement noise and outliers. Although DEM and VEM generally exhibited similar patterns (cross-correlation between 0.851 and 0.999), the variability curves from the two methods were noticeably different in some intervals. Also, using angular velocities as input appeared more robust to potential noise from raw data whilst retaining the following features: (a) more coherent with biomechanical conventions for calculating three-dimensional angular dynamics; (b) still suitable for coordination analysis; and, (c) more easily interpretable by practitioners when represented as relative motion plots.