Disposable and Flexible Paper‐Based Optoelectronic Synaptic Devices for Physical Reservoir Computing

Health monitoring using wearable artificial intelligence (AI) sensors with sensing and cognitive capabilities has garnered significant attention. The development of self‐contained AI sensors that can operate with low power consumption, akin to the human brain, is necessary. Physical reservoir computing (PRC), which mimics the human brain using physical phenomena, offers a low‐power consumption architecture. Nevertheless, creating a flexible and easily disposable sensors using PRC capable of processing optical signals with sub‐second response times suitable for biological signals presents a challenge. In this study, a disposable and flexible paper‐based optoelectronic synaptic devices are designed, which are composed of nanocellulose and ZnO nanoparticles, for PRC. This device exhibits synaptic photocurrent in response to optical input. To assess its performance, a classification and time‐series forecasting tasks are conducted. The memory capacity of short‐term memory task, indicating the device's ability to store past information, is 1.8. The device can recognize handwritten digits with an accuracy of 88%. These results highlight the potential of the device for PRC. In addition, subjecting the device to 1000 rounds of bending do not affect its accuracy. Furthermore, the device burn in a few seconds, much like regular office paper, demonstrating its disposability.


Introduction
Health monitoring through the continuous attachment of sensors to individuals has been a subject of interest in the field of healthcare. [1]Long-term health monitoring is a valuable tool for effective management of chronic conditions and health-related issues. [2]Notably, because artificial intelligence (AI) can be used to predict future diseases and health conditions, [3] the amalgamation of wearable sensor technology with AI capabilities has ushered in more sophisticated data processing and interpretation. [4]owever, the widespread adoption of AI-based wearable sensors DOI: 10.1002/aelm.202300749 may lead to an increased bandwidth overload and communication delays during data transmission. [5]Therefore, it is crucial to develop AI devices for precise biological diagnostics in edge regions to facilitate both sensing and AI processing without extensive data transmission.
Human brains are highly efficient in cognitive tasks with exceptionally low power consumption compared with silicon-based computers. [6]Hence, extensive research has been conducted on brain-inspired neuromorphic computing, aimed at achieving low power consumption and handling intelligent tasks. [7,8]Physical reservoir computing (PRC) seamlessly blends sensing and AI processing, including classification and prediction, with minimal power usage. [9]n addition, the PRC is a suitable computational architecture for handling timeseries data that are common in biological signals.Thus far, PRC has been realized in various reservoir layers using physical devices such as spintronic devices, [10,11] ionic devices, [12,13] and synaptic devices. [14]To realize PRC specialized for biological diagnostics, four requirements are necessary for the synaptic device as the reservoir layer of the PRC.First, the synaptic devices should exhibit a sub-second response time compatible with biological signals in the range of 0.1-1.8Hz. [15][16][17] Second, they should be able to handle optical input signals because light is a non-invasive probe for living organisms. [18]Third, they have to be flexible so that it can attach to human skin.Fourth, they should be easily fabricated and disposed of because they must be frequently replaced from a hygiene perspective.
Previously, synaptic devices that satisfy some of these requirements mentioned above have been reported.Some studies have reported that the response times of the synaptic device can be modified by material design. [19,20]For example, Nakajima et al. [20] fabricated synaptic device with response rates below 0.5 Hz by increasing the gap of the Ag 2 S island.Lao et al. [21] realized a perovskite-based PRC utilizing light as the input; however, it was not flexible because the substrate was glass.Wu et al. [22] fabricated a flexible and light-responsive PRC using a plastic substrate and a light-responsive semiconducting polymer.However, to the best of our knowledge, there are no reports on the disposability of the synaptic device.Thus, there are no reports on the synaptic device that satisfies all four requirements.This study focuses on paper-based synaptic devices to realize PRC that satisfy the above four requirements since paper is flexible and ease to dispose of.Here, we present a paper-based optoelectronic synaptic device, which is composed of ZnO nanoparticles (NPs) and cellulose nanofibers (CNFs).The device demonstrated a gradual change in photocurrent with a sub-second time constant during ultraviolet (UV) light exposure and extinction.Using this phenomenon, we observed synaptic features such as paired-pulse facilitation (PPF).Moreover, we could classify 4-bit optical pulses.To evaluate the PRC performance, we performed a short-term memory (STM) task, a parity-check (PC) task, and a handwritten character recognition task using sub-second optical pulses.This device exhibits the capability to perform classification tasks even when bent, and we have also demonstrated its incineration capability after use.

Results and Discussion
Figure 1a,b depicts the images of the ZnO-CNF films with inplane patterned gold (Au) electrodes and the measurement setup, respectively.The average thickness of our films was ≈10 μm, with an electrode gap of ≈75 μm.We have previously observed the morphology of composite films of ZnO NPs and CNFs by scanning electron microscope (SEM) and atomic force microscope (AFM). [23]SEM observation revealed that most of the film consisted of a homogeneous mixture of ZnO NPs and CNFs.Some of the film was dotted with aggregates of ZnO NPs with a diameter of several hundred nm.The surface roughness of the film (root-mean square (RMS) value) was ≈4 nm revealed by AFM, indicating that the films was flat.The film was translucent to the naked eye, and when characterized for optical properties by UVvis, it exhibited the optical transmittance of over 50% in the visible light range.Detailed analysis of the surface morphology and optical properties is described in our previous work. [23]s previously reported, when our films were irradiated with UV-pulsed light while a constant voltage was applied to them, the films showed photoresponsivity. [23]Figure 1c presents the typical photocurrent dynamics under UV light ( = 365 nm) while applying a constant voltage (V = 3 V).The current increased upon UV light irradiation and decreased upon turning off the UV light.Notably, we observed a slow rise and decay over the span of seconds.We initially attempted single exponential fitting for the rise and decay transients, but neither yielded a satisfactory fit.The photocurrent transients of ZnO can be more accurately fitted by double exponential functions. [24,25]Consequently, we applied a dou-ble exponential function to fit both the rise and decay processes, as shown in Equations ( 1) and (2), respectively.
)} : rise ( 1) In these equations, A 0 , A 1 , A 2 , B 0 , B 1 , and B 2 represent constants, while  r1 ,  r2 ,  d1 , and  d2 denote the time constants for rise and decay.The suffixes in the time constants, r, d, 1, and 2 denote rise, decay, fast transient, and slow transient, respectively.Based on the fitted curves, we estimated  r1 ,  r2 ,  d1 , and  d2 to be 0.14, 6.04, 0.17, and 1.24 s, respectively.For comparison, we examined the photocurrent dynamics of ZnO single crystals.From AFM observation, RMS value of ZnO single crystal was found to be ≈0.7 nm (not shown here).We deposited in-plane patterned Au electrodes to a single-crystalline ZnO (0001) wafer (Zn plane) and measured the photocurrent stimulated by the optical pulse.The estimated values for  r1 ,  r2 ,  d1 , and  d2 were 7.8 ms, 0.21, 2.4, and 0.15 s, respectively.Notably, the time constants of the ZnO-CNF film were found to be larger than those of the ZnO single crystal.
ZnO is generally known to exhibit a very slow photocurrent decay, called persistent photoconductivity (PPC). [26,27]The proposed mechanisms of PPC include a gradual change in the energy barrier height due to adsorption/desorption of oxygen molecules on the ZnO surface, [28] recapture of electrons in the metastable state, [29] and trapping of electrons by trap states in the bandgap. [30]Among them, we believe that the adsorption/desorption of oxygen molecules on the ZnO surface is one of the major reasons for our case because our film has a large effective surface area owing to the ZnO NPs.
Figure 2a illustrates the band diagram under UV light irradiation and in the dark state.When exposed to light, an electron is initially excited to the conduction band, forming electron-hole pairs.Subsequently, holes combine with adsorbed oxygen ions, leading to the neutralization and desorption of oxygen molecules.This desorption process reduces the energy barrier that typically obstructs carrier transport.As a result, electrons in the conduction band are extracted as photocurrent into the external circuit.
Transitioning from the illuminated state to the dark state involves two key processes.First, electrons in the conduction band promptly recombine with holes in the valence band.Second, oxygen molecules physisorbed on the ZnO gain boundary. [31,32]Oxygen molecules capture electrons, leading to the formation of a depletion layer.Consequently, the barrier height increases, obstructing carrier transport.With fewer electrons overcoming the potential barrier, the photocurrent subsequently diminishes.Subsequently, we measured the time constant of the ZnO-CNF films as a function of temperature, as depicted in Figure 2b.The time constant increased with rising temperature, and we assume that the relaxation time constant can be expressed by Equation (3): [33]  = Aexp In the equation, A, E a , k, and T represent the pre-exponential factor, activation energy, Boltzmann constant, and absolute temperature, respectively.The activation energy values extracted from the two decays in Figure 1c were E a1 = 50 meV and E a2 = 0.18 eV for  d1 and  d2 , respectively.Because previous studies reported that energy barriers at the grain boundary of ZnO are 0.03 -0.2 [34] and 0.005-0.11eV, [35] and the activation energy for the chemisorption of oxygen on ZnO is 0.25 eV, [36] the values obtained in this study might correspond to the energy barriers for oxygen adsorption.
ZnO-CNF films possess a larger surface area than ZnO single crystals, potentially leading to a higher oxygen adsorption on the grain boundary.Consequently, ZnO-CNF films could have more energy barriers than ZnO single crystals, as depicted in Figure 2c.The presence of numerous energy barriers scatters carriers, resulting in a decrease in mobility.Thus, ZnO-CNF films would exhibit a larger time constant than ZnO single crystals.
Human neural networks can intrinsically decode time-series data owing to the time-dependent changes in neural network states produced by short-term plasticity. [37]The PRC is an architecture that mimics human neural networks.Thus, short-term plasticity may be necessary to create a PRC that can process timeseries data.Figure 3a,b shows the normalized current dynamics of the ZnO-CNF films and ZnO single crystal, respectively, upon irradiation with two light pulses separated by a time interval ΔT of 1 s.The maximum current induced by the second optical pulse exceeded that of the first pulse.This phenomenon is similar to the PPF found in biological synapses. [38]The film exhibited PPF, which is a type of short-term plasticity; [14] thus, it should be able to be utilized as a reservoir layer of PRC.
PPF is quantitatively characterized by the PPF index, defined as I 2 /I 1 × 100, where I 1 and I 2 represent the maximum current values induced by the first and second optical pulses, respectively.A higher PPF index indicates a greater capacity to store past inputs.Figure 3c shows the PPF index of ZnO-CNF films and ZnO single crystals across varying time intervals, ranging from 0.1 to 50 s.The PPF index for ZnO single crystals was 108% for an interval of 0.1 s and remained below 110% within the 0.1 to 10 s range.In contrast, the PPF index for ZnO-CNF films reached up to 156% at an interval of 0.1 s and exceeded 120% within the 0.1 to 10 s range.[41][42][43][44][45][46] Interestingly, ZnO-CNF films exhibit a higher PPF index than ZnO single crystals.As discussed earlier, this high PPF index may be influenced by the presence of energy barriers at the grain boundaries.
The physisorption rate of oxygen on the ZnO surface is slower than the chemisorption rate. [47]Our ZnO-CNF films have many grain boundaries compared to the ZnO single crystal, suggesting that the energy barrier may play an important role in carrier transport.Upon the first light irradiation, chemisorbed oxygen ions transform into physisorbed oxygen molecules when they receive photogenerated holes.This results in the narrowing of the depletion layer and a decrease in the energy barrier, as depicted in Figure S1a,b (Supporting Information).Therefore, the rate at which the energy barrier height decreases may depend on the chemisorption rate.In the dark, oxygen molecules in the gas physisorb to the ZnO surface.Subsequently, these physisorbed oxygen molecules convert into chemisorbed oxygen ions upon receiving electrons in the conduction band.The rate at which the energy barrier height increases may depend on the slow physisorption rate.Thus, the rate of energy barrier height increase is slower than the rate of decrease.The high PPF index's origin may be attributed to the fact that the energy barrier height does not fully return to its initial state in the dark, as depicted in Figure S1c (Supporting Information).In the second light irradiation, the current is enhanced compared to the first light irradiation, as illustrated in Figure S1d (Supporting Information).This suggests that ZnO-CNF films, which feature numerous energy barriers, are more suitable for synaptic devices than ZnO single crystals.
It is known that a reservoir layer of PRC has the ability to distinguish different input signals within the reservoir's state space. [22,48]We investigated whether our ZnO-CNF film can distinguish 4-bit input optical pulses.Figure 3d shows the typical current dynamics induced by 4-bit optical pulses (1111) with the pulse width of 500 ms.The photocurrent was gradually increased by light irradiation, and it was observed that the current values were piled up with increasing the number of pulses.In addition, we measured the photocurrents induced by various 4-bit optical pulses, ranging from 0000 to 1111, as shown in Figure S2 (Supporting Information).From the results, the readout currents, which are photocurrent values 2 ms after the end of the pulse, were extracted as shown in Figure 3e.It was found that the values of readout currents were different depending on the 4bit pattern, meaning that our ZnO-CNF film is able to distinguish the time-series input data required for the reservoir layer.We also confirmed that the film can distinguish 4-bit patterns even with different pulse width (50 to 250 ms) as shown in Figure S3 (Supporting Information).
We performed time-series forecasting tasks and a classification task to confirm that the ZnO-CNF film worked as a physical reservoir layer of PRC.The time-series data forecasting was characterized using a STM task and a PC task.The STM task assesses the device's ability to retain past input, [11] indicating its fading memory capability.The PC task is used for characterizing the type of nonlinearity in the system. [49]As depicted in the schematic illustration in Figure 4a, the time-series forecasting task comprises two phases: a learning process and a test process.The objective in the learning process is to obtain W output , which is the weights of the output layer.Random binary input data y input was converted into time-series optical pulse.The optical pulses were then irradiated onto the ZnO-CNF film, and the time-series photocurrent waveform was measured.Output data y predict is obtained by multiplying the photocurrent waveform and the weight W output .The W output was determined so that the y predict approaches the predicted value y target .For each task, different y target were used, as shown in the following equation: [50] y target (t) = y input (t − d) : STM task (4) where t is the time, d is the delay, and d max denotes the maximum delay where the correlation coefficient approaches zero.
In the test process, the ZnO-CNF film was irradiated with time-series optical pulses obtained by random binary data y' input , which differs from the learning process dataset, and the photocurrent waveform was measured in the same way as described above.The predicted value y' predict was obtained from the measured photocurrent waveform and the W output calculated by the learning process.We then verified for each task whether the obtained y' predict reproduced the target waveform y' target , which can be expressed by the same Equations ( 4) and ( 5).Additionally, we estimated the memory capacity C as follows: where "Corr" means typical correlation coefficient. [51]A high value of C indicates the presence of STM or nonlinearity stored within the reservoir.For comparison, the same experiment was conducted using a ZnO single crystal.
Figure 4b shows the predicted and target values for the STM task, with the number of virtual nodes of 125, the delay of 1, and the pulse width of 500 ms.The predicted values were almost the same as the target values, indicating that our device has STM clearly.Figure 4c shows the square of the correlation coefficient as a function of the delay for the STM task in both the ZnO-CNF film and ZnO single crystal.The correlation coefficient in the STM task for ZnO-CNF film was found to be higher than that for the ZnO single crystal.The values of C in the STM task (C STM ) of ZnO-CNF film and ZnO single crystal were 1.8 and 1.3, respectively.This indicates that ZnO-CNF film exhibits a higher memory capacity than ZnO single crystal.This enhanced capacity can be attributed to the high PPF index observed in ZnO-CNF films, as shown in Figure 3c.The STM of ZnO-CNF films aligns with that of reported PRC, [50][51][52][53][54] indicating the utility of ZnO-CNF films as a reservoir layer for PRC.
Figure 4d shows the predicted and target values for the PC task, with the number of virtual nodes of 125, the delay of 1, and the pulse width of 500 ms.It was found that the predicted values were different from the target values.As shown in Figure 4e, the C in the PC task (C PC ) of the ZnO-CNF film was as small as 0.4.This value was smaller than that of ZnO single crystal (C PC = 0.8).In addition, the C PC is lower than those in previous studies. [50,53,54]his result indicates that the ZnO-CNF film has weak nonlinearity and needs to be improved to handle complex tasks in reservoir computing.
Furthermore, we performed the classification task.We demonstrated an image classification task on the Modified National Institute of Standards and Technology (MNIST) dataset, where the image data were converted into pseudo-time-series signals. [19,55]igure 4f shows a schematic illustration of the data-processing sequence for the handwritten digit recognition tasks.To simplify the calculation, binarized 28 × 28 pixels MNIST images were cropped into 20 × 20 pixels.The images were then divided into five strips of 4 × 20 pixels each.The strips were combined into 4 × 100 pixels images.Subsequently, each row was converted into 4-bit optical pulses.Four devices were irradiated with the optical pulses.The photocurrent values at readout times ranging from 2 to 500 ms were obtained when each 4-bit optical pulse was irradiated to the device, where the time at which the 4 th pulse ended was defined as the readout time of 0 s.The average values of photocurrent of the four devices (1 × 100  Figure 4g shows the confusion matrix for the classification task using our devices.Handwritten digits were correctly classified, with an accuracy of up to 88%.Furthermore, as shown in Figure 4h, the accuracy remained consistently above 80% even when the pulse width was increased from 50 to 500 ms.This outcome confirms that our films can effectively operate as a PRC in the sub-second regime.
The mechanical durabilities of this device were investigated assuming application to a curved surface such as a body surface.First, we investigated the effect of the curvature of the device on handwritten-digit recognition when the device is bent.Figure 5a shows the accuracy of the classification task as a function of bending radius.The accuracy remained nearly unchanged at bending radii of 9.5 and 16.1 mm when compared to the flat condition.Next, to demonstrate the durability of our device, handwrittendigit recognition test was conducted while the device was repeatedly bent and stretched up to 1000 times.[58] As shown in Figure 5b, the accuracy found to remain consistent even after 1000 bending cycles.These results underscore the suitability of our films for use in flexible configurations.After being attached to a human body, used devices must be properly disposed of because they may contain contaminants.Incineration is one of the typical disposal methods for biological waste. [59]Figure 5c shows that our film could be entirely incinerated in seconds with combustion process as simple as office paper.The combustion process was similar to that of paper, indicating that the device can be incinerated using commonly used combustion systems.

Conclusion
In this study, we developed a disposable and flexible optoelectronic synaptic device in which ZnO NPs are embedded in CNF film to realize PRC.Our measurements revealed that the increase and decrease of photocurrent in ZnO-CNF films can be accurately modeled by a double exponential function, with the time constant of ZnO-CNF films being larger than that of ZnO single crystals.This prolonged time constant in ZnO-CNF films is likely attributable to band bending induced by the adsorption/desorption of oxygen molecules at the grain boundaries.In addition, ZnO-CNF films exhibited a higher PPF index compared to ZnO single crystals, with the maximum PPF index estimated at 156%.A higher PPF index signifies a greater storage capacity, which led us to conduct a time-series forecasting task to assess short-term memory capacity.The results showed that ZnO-CNF films had a short-term memory capacity of 1.8, while ZnO single crystals had a capacity of 1.3, consistent with the observed trend in the PPF index.ZnO-CNF films proved capable of classifying 4-bit optical pulses, achieving an accuracy of up to 88% in handwritten digit recognition.Importantly, this accuracy remained consistently above 80% even when varying the pulse width from 50 ms to 500 ms.These findings confirm that our films can effectively function as a synaptic device for PRC in the sub-second regime.Notably, the accuracy of handwritten digit recognition remained unaltered even after repeated bending, and the film demonstrated easy combustibility.
This study highlights the potential of embedding semiconductor particles in flexible CNF films for use as flexible synaptic device for PRC.Leveraging the PPC effect, typically seen as undesirable, allowed us to create an optoelectronic synaptic device with a slow time constant suitable for biological diagnostics.This development paves the way for the realization of wearable sensors for health monitoring applications.

Experimental Section
Device Fabrication: The ZnO-CNF film was fabricated using the spray deposition method. [23]This film consisted of composite freestanding material comprising ZnO NPs (average diameter of 25 nm; FINEX-50, Sakai Chemical Industry Co., Ltd., Osaka, Japan) and bamboo-derived cellulose nanofibers (Bamboo #C, Chuetsu Pulp & Paper Co., Ltd., Toyama, Japan), which were disintegrated using the aqueous counter collision (ACC) method. [60]The ZnO-CNF film contains 60 wt.%ZnO.The film had an average thickness of ≈10 μm.To measure the photocurrent of the film, a 30 nm-thick gold (Au) film was deposited using a thermal evaporator (VPC-410, ULVAC, Kanagawa, Japan).The coplanar electrode distances were 75 μm.As a control experiment, ZnO (0001) single crystal (Zn plane) (Z Crystal LLC, Kyoto, Japan) with Au electrodes was also fabricated.

Time-Series Forecasting Task:
A time-series forecasting task was performed based on the method proposed by Tsunegi et al. [50] The input data consisted of 1000 random binary values, where 0 and 1 represented the ON and OFF states of the UV light, respectively.The pulse width was set to 500 ms, and a virtual node of 125 was employed, resulting in 125 current values per optical pulse.
In the learning process, weights w was calculated using a computer to minimize the squared error between the output of the ZnO-CNF reservoir film and the target value.This could be expressed as [w − Y] 2 , where the measured current value forms an n × M matrix, denoted by , and the target value was a 1 × M matrix, denoted by Y.In this case, the weight (w) required to minimize the error could be calculated as w =  −1 Y where  −1 represents the Moore-Penrose pseudo-inverse matrix.To eliminate the initial 200 pulses as a washout, the remaining 800 pulses were utilized for learning.
In the test process, 1000 different random binary data points were input, distinct from the learning process, and the current values were measured.Subsequently, prediction values were calculated using the weights w that were calculated in the learning process.
Classification Task: Handwritten digit recognition tasks were conducted using the Modified National Institute of Standards and Technology (MNIST) dataset to demonstrate the functionality of the films as synaptic device for PRC.The MNIST dataset was transformed into 4-bit time series data and irradiated onto the films as optical pulses.The readout time was defined as the period after the conclusion of the 4-bit optical pulse irradiation.The current values within the readout time of 2 to 500 ms constituted the reservoir input.These obtained photocurrents were input into a neural network to update the weights.The neural network had 1 × 100 input layers, 1 × 10 output layers, and no hidden layers.The activation function of the NN was SoftMax, and RMSprop was used as the optimizer.The model was trained using 60000 images and evaluated its accuracy using 10000 images.
Assessment of Flexibility and Disposability: To showcase the flexibility and disposability of these films, tests were conducted on handwritten-digit recognition under various bending conditions.The accuracy of handwritten digit recognition under bending was assessed with bending radii ranging from 9.5 mm to 16 mm.Furthermore, the accuracy of handwritten digit recognition was tested under bending and after undergoing up to 1000 bending cycles.

Figure 1 .
Figure 1.Device structure and transient photocurrent.a) Image of the fabricated ZnO-CNF films.b) Schematic illustration of the measurement setup.c) Photocurrent dynamics applying constant voltage induced by optical pulse ( = 365 nm, pulse width:15 s, V = 3 V).The electrode distance was 75 μm.

Figure 2 .
Figure 2. Proposed conduction mechanism of photocurrent in ZnO-CNF films.a) The energy band diagram of the ZnO surface under dark and UV light illumination.b) Time constants of the ZnO-CNF films as a function of temperature.c) Energy band diagram of our device under dark and UV light illumination.

Figure 3 .
Figure 3. Synaptic and separation characteristics of ZnO-CNF films.a) Current dynamics of ZnO-CNF films, and b) ZnO single crystal induced by two optical pulses ( = 365 nm, pulse width: 500 ms, light intensity: 10 mW cm − 2).The current was normalized with the maximum current value induced by the first optical pulse.c) PPF index as a function of the time interval.d) Typical current dynamic induced by 4-bit optical pulses ( = 365 nm, pulse width: 500 ms).e) Readout current as a function of 4-bit optical pulse patterns ( = 365 nm, pulse width: ms, read out: 2 ms).

Figure 4 .
Figure 4. Time-series forecasting task and classification task performance.a) Schematic illustration of the time-series forecasting task using ZnO-CNF films.b) Target and system output of STM task.c) The square of the correlation coefficient as a function of the delay for the STM tasks.d) Target and system output of PC task.e) The square of the correlation coefficient as a function of the delay for the PC tasks.f) Schematic illustration of the classification task.g) Confusion matrix of classification tasks (pulse width 50 ms, readout time 10 ms).h) Accuracy of the classification task as a function of the pulse width (readout time 10 ms).

Figure 5 .
Figure 5. a) Accuracy of handwritten-digit recognition as a function of bending radius (pulse width: 250 ms, readout: 10 ms).b) Repeated bending test with a bending radius of 9.5 mm.c) Disposability test by burning ZnO-CNF films and office paper.
matrix) were input into a simple neural network (NN) with one layer for training.