Underground Coal Gasification (UCG) requires monitoring of the gasification area because the gasification process is invisible and the reaction temperature exceeds 1000 °C. Many fracturing events that occurred due to coal heating can be captured with Acoustic Emission (AE) monitoring technique during UCG. However, the temperature conditions to generate fracturing events during UCG have not yet been clarified. Therefore, the coal heating experiment and small-scale UCG experiment are conducted by measuring the temperature and AE activities in this research to examine the applicability of the AE technique instead of temperature measurement as a monitoring method during UCG. As a result, many fracturing events are generated when the temperature of coal is changed drastically, especially during coal gasification. Besides, AE events increase in the sensor near the heat source and AE sources are expanded widely with the expansion of the high-temperature region. AE monitoring is an effective technique for the estimation of the gasification area during UCG instead of temperature monitoring. Therefore, UCG is a promising option to improve the recovery of coal energy as a clean coal technology. In UCG, the product gas can be enhanced by expanding the gasification area with high temperatures. On the other hand, the excessive expansion of the gasification area causes several environmental problems such as gas leakage, deformation of the surrounding ground, and underground water pollution6. Therefore, UCG requires a monitoring system to control the gasification area.The demand for energy increases day by day with economic and population growth worldwide. Coal is still an important energy resource as the primary energy due to the large reserves and less regional ubiquity. However, many coal resources are being left without excavation due to technological and economic reasons in conventional mining systems. Underground Coal Gasification (UCG) is a technique to recover coal energy from underground by in-situ gasification. UCG contributes to improving the energy recovery ratio from coal because it enables the recovery of energy from untapped coal. Additionally, the injection agents and temperature of the coal seam affect the product gas composition, e.g., the steam injection enhances hydrogen production8. However, it is practically difficult to measure the temperatures of coal seams in the actual UCG site. Instead of temperature measurement, some techniques have been introduced to monitor the gasification area of UCG. Application of geophysical monitoring techniques has been discussed such as electrical resistance tomography9, electrical resistivity method10, microgravity survey11, and ground penetrating radar13. The estimation of the cavity growth and the velocity of gasification flame by means of a mathematical model has been also described17. This research focuses on the application of acoustic emission (AE) to monitor the gasification area. AE monitoring can be an alternative technique to temperature measurement because the micro-seismic will be occurred due to the expansion or contraction of coal under heating. AE generates simultaneously when the material generates fractures, meaning that real-time monitoring can be achieved by AE monitoring. Besides, it is possible to identify the location of fracturing activity by calculating the difference in seismic arriving time and sensor coordination with source location analysis. Many scholars have reported the generation of fracture with coal heating due to the different thermal expansion coefficients of minerals19, changing the pore structure22, and thermal contraction25. Ding et al.26 measured the AE count and the evolution of cracks with coal heating. AE signal is active especially when the crack width expands under 300–500 °C. It has been also reported that AE signals increase with heating under the loading condition compared to without heating27.The gasification area of UCG can be assumed with the temperature of the coal31. However, it is still uncertain the temperature conditions that these AE activities occur during the UCG process. This study discusses the applicability of the AE technique instead of temperature measurement as monitoring of gasification area by means of coal heating experiment and small-scale UCG experiment.Our previous works have also indicated the possibility to utilize the AE technique as a monitoring method of the gasification area during the UCG process2 and the dead time is set as 10 ms because the dead time is usually several ms in brittle materials: rock, concrete, and coal. The threshold is AE signal data was also recorded using a multi-recorder  with a sampling time of 1 µs. The signals were filtered with a high-pass filter of 5 Hz and a low-pass filter of 10,000 Hz by the amplifiers . AE signal data were used for AE source location analysis to discuss the relationship between the AE source and temperature distribution.The coal heating experiment was carried out by using a coal block which is size of 200 mm × 200 mm × 100 mm. Table The schematic diagram of the small-scale UCG experiment is shown in Fig. 23 described the deformation behavior of coal changes from expansion to contraction above 500 °C, indicating that the contraction behavior of the coal may affect the fracturing activity. In addition, more AE events can be detected the closer the distance from the heat source: the total AE events are respectively 2382 and 1515 in the sensor near the heat source (90 mm away from the heat source) and far from the heat source (110 mm away from the heat source). During coal heating, fracturing activities occur at several locations that exhibit high temperatures, meaning that AE events detected by the two sensors are hardly the same source. However, sensors closer to the heat source can detect AE events without being affected by attenuation because they are closer to the high-temperature area to generate fracturing events. This means that the AE events can be used to identify the location of the temperature change in the coal from the position of the sensors. However, the distribution of the location to generate the fracturing activities cannot be grasped from AE events. Therefore, AE source location analysis by multiple sensors is adopted in the next step.The results of temperature and AE events are respectively shown in Fig. 32. Figure In this study, the source location of AE activities is calculated by the least-squares travel-time-difference methodFigure 33. The AE events in the initial stage are higher on the production side for 30% of oxygen concentration while they are higher on the injection side for 70% of oxygen concentration. These results are in harmony with the temperature distribution results, indicating that many AE events occur at the locations where high-temperature regions are formed. The clear differences of AE events in the injection/production side are not found in the later stage of the gasification. This may be due to the small scale of the experiment, meaning that the distance between the acceleration transducers is too close to detect the difference of fracturing events for the wide gasification area. Wave attenuation occurs in proportion to the propagation distance. AE events cannot be detected due to wave attenuation if the distance from the fracturing source to the sensors is far. In the initial stage of the gasification, differences in the detected number of AE events occur depending on the location of the sensor because the high-temperature is small. On the other hand, the number of events does not show the difference in the sensors because wave attenuation does not occur due to the close distance between the sensors and the source of fracturing activities with the expansion of the high-temperature area. AE events increase during 800–1200 L of oxygen injection in 50% of oxygen concentration while they decrease with elapsed time in 30% and 70% of oxygen concentration. This can be explained by the gas production by the gasification reaction. Figure 3 during 800–950 L of oxygen injection in 50% of oxygen concentration due to the increase of combustible gas components: H2 increases from 13.08 to 14.63%, CO increases from 19.13 to 22.52%, and CH4 increases from 1.30 to 4.00%. Besides, AE events also increase when the oxygen injection volume is from 800 to 1200 L. This finding suggests that the AE event is related to coal gasification. Therefore, AE monitoring is an effective way to evaluate the coal gasification in underground.Figure Figure Many fracture events are generated when the temperature of the heat source changes dramatically, indicating that AE events are related to the temperature change of the coal.The closer the distance between the sensor and the heat source, the larger the number of AE events. This fact indicates that the location of the temperature change can be identified based on the position of the sensors.The high-temperature region differs based on the oxygen concentration. This may be because the reaction rate of the oxidation reaction; the oxygen is consumed faster on the injection side when the oxygen concentration is high.AE events increase especially during coal gasification.The expansion of the gasification area can be estimated by analyzing the AE source location.This study investigates the applicability of the AE technique as a monitoring system of the gasification area of UCG through the coal heating experiment and the small-scale UCG experiment. We have obtained the following knowledge.


A novel scheme is proposed for realizing effective DC acceleration of charged particles in a circular ring. The key is to use an induction acceleration cell with multi-insulating gaps that allow forced short circuit using solid-state switching devices such as SiC-MOSFET or unforced short circuit using diodes. A baseline design of the induction acceleration cell is shown. A coasting beam is accelerated in the circular ring without bunching. As its possible application, a continuous-wave terahertz free-electron laser (FEL) is proposed with numerical parameters, where this effective DC acceleration compensates for energy loss of the electron beam occupying the entire isochronous storage ring due to synchrotron radiation and FEL interaction. As a result, FEL microbunching of a coasting beam can be created, resulting in a high average output power that has not been possible with existing linac-driven FELs or RF storage-ring FELs. Induction acceleration is made possible by an induced voltage across an insulating gap in the induction cell, as shown in Fig. So far the basic laws of physics have told us that it is impossible to accelerate repeatedly charged particles in DC mode in a circular ring. This paper describes how this long-believed restriction can be effectively overcome. To do this, induction acceleration is used. The induction acceleration device is employed, the working principle of which is governed by Maxwell’s equations not including the term of displacement current. The induction acceleration method has evolved, since it was first proposed by Widerøe in his doctor thesisThis paper proposes as an alternative an induction cell with multi-shielding gaps as shown in Fig. 2, where a beam injected from the CERN 28 GeV Proton Synchrotron to the ISR was accelerated to 31 GeV. Several undesirable features in RF displacement acceleration are worth noting. Large RF modulation on the coasting beam in the phase space is unavoidable; as a result, the energy spread in the beam rapidly expands when the RF bucket passes through the phase-space area occupied by the beam and an increase in emittance due to non-adiabatic beam handling accompanies this process. In addition, RF displacement acceleration takes time. Thus, the utility of RF displacement acceleration is limited.RF displacement acceleration of a coasting beam circulating in a circular ring is well known, where a vacant RF bucket is created in the longitudinal phase space accommodating the coasting beam and it is slowly moved into the lower energy region, in association with acceleration of the coasting beam due to Liouville's theorem. This process is repeated until the desired energy is achieved. This acceleration technique was employed in the Intersecting Storage Ring (ISR) at CERNThe present DC acceleration method can overcome these disadvantageous features and may be an attractive in a wider range of applications. Below, a representative example of possible applications for a continuous-wave (CW) free-electron laser (FEL) in an isochronous storage ring will be introduced, although its feasibility is not fully justified at the present stage.3. The internal structure of the present induction cell is similar to existing ones, in which a magnetic core  is encircled by a primary excitation coil and the inner vacuum duct for the beam connected to the cell’s metal cage is equivalent to a secondary loop. The accelerating voltage is induced across the ceramic gap that is part of the vacuum duct. When a voltage pulse is applied across the primary coil’s terminal, the accelerating voltage continues to be induced until the magnetic core is saturated. Core resetting is essential in order to generate the next accelerating voltage pulse. For this purpose, a negative voltage pulse with the same pulse length as that of the set-voltage pulse must be applied across the primary coil’s terminal. The charged beam cannot pass the acceleration gap during the resetting period. This has been a main restriction on the existing induction synchrotrons5 and other circular induction accelerators6.The induction cell is a kind of one-to-one transformer, as shown in Fig. 7. CST Studio simulations8 show that geometrically symmetric short circuits are important for field uniformity within the induction cell.In the proposed induction cell, another circular ceramic gap is introduced on the front cell-plate so as to shield the electrical conductance of the stainless-steel plate as shown in Fig. 3. The design is based on the relation of the time-integrated induced voltage and maximum magnetic flux, V is the induced voltage, T is the pulse length, ΔB is the magnetic flux swing, and S (d x Δr) is a cross section of the toroidal-shape magnetic core where d and Δr represent the core length and the difference between inner diameter and outer diameter, respectively.For the reader’s reference, typical parameters of the 4 kV induction acceleration cell are given in Table A required total number of rinduction cells depneds on acclerator parameters. In the example discussed below, it may be two cells from the requirement of energy recovery, assuming an output power of 2.4 kW by a beam of 300 mA.Figure  V. This is, in a practical sense, an undesirable feature for effective DC acceleration. However, it can be overcome by confining the circulating beam within a finite region by using the barrier voltage pulses employed in existing induction synchrotrons5. In the example of an isochronous storage ring discussed below, this external confinement is unnecessary. If the repetition rate of the induction acceleration fin satisfies f0 = n × fin where n is integer and f0 is the revolution frequency of the circulating beam, particles in the time region without accelerating voltage will be lost because of frozen phase motions in the isochronous storage ring. As a result, the circulating beam will become a coasting beam with a short gap of missing particles. The gap’s time period of 100 ns has different meanings, depending on the size of circular ring. If its circumference is 30 m, then the transient time period of 100 ns may correspond to simply the time for the circulating beam to make one revolution at the speed of light. This means that the energy compensation is insufficient for the entire beam length to occupy the ring every 100 turns.Here, two induction cells are introduced (Cells 1 and 2). If Cells 1 and 2 are continuously operated as a pair in the manner described above with a phase difference π in time, then the circulating beam will be continuously accelerated by the accelerating voltage profile shown in Fig. V. We will discuss the assessment of the deviation later. By contrast, the 100 ns gap may be rather convenient in the case of much bigger ring, where the third induction cell can be omitted.It is possible to avoid the accelerating voltage gap every 100 turns by refreshing the circulating beam every 10 ms or 100 turns. Otherwise, a third induction cell could be introduced that is triggered in the transient time period of 100 ns by an induced pulse with a triangular profile consisting of rising and falling so as to fill the lack of voltage. The corresponding reset pulse has no effects because it is triggered away from the transient time region. However, the superimposed voltage profile is expected to deviate slightly from the desired constant accelerating voltage 6. For the application introduced here, voltage requirements seem to determine the number of cells required.The required voltage height and repetition rate for switching will depend on the machine and beam parameters in applications. Practical parameters for the induction cell unit are limited to the following specification: voltage height of < 4 kV/cell due to withstand voltage in the switching device and cell’s inner structure, pulse width of less than a few tens of microseconds due to magnetic core size, and repetition rate of < 1 MHz due to switching loss in the switching device, as stated in the Fig. 9. A group at Tsinghua University10 is planning to construct an isochronous storage ring employing induction acceleration, where a flat long bunch with the FEL microbunch structure will be accelerated by the asymmetric induction acceleration technique11. In principle, this acceleration technique is similar to that of existing induction synchrotrons, where the accelerating voltage must be generated at the MHz revolution frequency of the beam bunch in most of cases. As the time profile of the amplified wave will inevitably reflect the long beam bunch structure with microstructures, the amplified FEL signal becomes far from a CW.A potential application employing this DC acceleration scheme in a circular ring would be a CW terahertz (THz) FEL driven by a coasting beam with an FEL microbunching structure. Observation of the microbunching structure on the RF macrobunch in the storage ring, which is generated as a result of FEL interaction, has been reported previously12, where two long straight sections are occupied by the wiggler and the induction cells; meanwhile, two short straight sections are used for injection and extraction. THz seed waves are introduced from upstream of the wiggler. FEL micro-bunching of the injected electron beam rapidly progresses, amplifying the injected seed waves. The system will reach a steady state. Thus, the CW THz FEL can be realized. An exhausted beam is extracted from the ring and the driving beam is refreshed. The process is repeated every 100 turns in the example described below. Typical FEL parameters are listed in Table 14. Evaluation of the numerical values in Table Energy loss due to synchrotron radiation and the FEL interaction is compensated by the DC voltage provided in the present induction acceleration scheme. A schematic view is shown in Fig. 16, where the driving beam is tightly bunched at the FEL frequency (17.1 GHz) as a result of strong FEL interaction propagating through more than 100 stages, and the amplified microwave with gigawatt output power is extracted by the microwave extraction bend at every stage, and energy loss is replenished in the induction acceleration cell with megavolt voltage placed at the end of a stage. A 1D FEL macroparticle simulation assuming 100 stages has been carried out17. At the very least, no fatal degradation was found in the FEL amplification. This finding may encourage feasibility studies of the present scheme for CW THz FELs in the isochronous induction storage ring.Here, it is emphasized that this CW FEL is operated not in the SASE mode or oscillator mode, but in amplifier mode. The present scheme is similar to that of the linear multi-stage microwave FEL extensively studied for two-beam acceleratorsBw/γ = const). More precise parameters must be evaluated using modern 3D FEL simulation codes in the context mentioned in the “The FEL parameters shown here should be considered just as a reference because the universal gain equation was used with simplified assumptions such as tight bunching, zero transverse emittance, and an intrinsic tapered wiggler  FEL in a similar but larger scale isochronous induction storage ring by increasing the beam energy to 400–500 MeV. The CW EUV-FEL that generates polarized EUV light and can provide an average power at the kilowatt level would be quite attractive as a next-generation EUV lithography source to replace the present laser ablation EUV source with low wall-plug efficiency of about 0.1%These research topics will be big challenges for our accelerator/FEL society to tackle.6. It is hoped that induction acceleration using the induction cell with multi-insulating gaps described in this paper will spur new developments in electron synchrotrons and storage rings.To date, the induction acceleration technique has been used in hadron synchrotrons, demonstrating a wide freedom of longitudinal beam handlingSupplementary Information.


People rely upon sensory information in the environment to guide their actions. Ongoing goal-directed arm movements are constantly adjusted to the latest estimate of both the target and hand’s positions. Does the continuous guidance of ongoing arm movements also consider the latest visual information of the position of obstacles in the surrounding? To find out, we asked participants to slide their finger across a screen to intercept a laterally moving virtual target while moving through a gap that was created by two virtual circular obstacles. At a fixed time during each trial, the target suddenly jumped slightly laterally while still continuing to move. In half the trials, the size of the gap changed at the same moment as the target jumped. As expected, participants adjusted their movements in response to the target jump. Importantly, the magnitude of this response depended on the new size of the gap. If participants were told that the circles were irrelevant, changing the gap between them had no effect on the responses. This shows that obstacles’ instantaneous positions can be considered when visually guiding goal-directed movements. We often make reaching and grasping movements in cluttered environments consisting of both target and non-target items. The presence of non-target items in the surrounding alters the spatial trajectories of both reach-to-grasp  were randomly assigned to the irrelevant item group. Despite the cost in statistical power, we used a between-groups design to make it easier for participants to follow the instructions regarding the nature of the items. The study was approved by the local ethics committee in accordance with the Declaration of Helsinki.Twenty-four participants took part in the experiment. Participants either volunteered to take part or took part in return for course credit. Twelve participants  were randomly assigned to the The experiment was conducted in a normally illuminated room. The stimuli were back-projected at 120 Hz with a resolution of 800 × 600 pixels onto a 1.25 × 1.0-m acrylic rear-projection screen  tilted backward by 30°. Participants stood in front of the screen. An infrared camera  that was placed at about shoulder height to the left of the screen measured the position of a marker (an infrared light emitting diode) attached to the nail of the index finger of the participant’s dominant hand at 500 Hz.In order to synchronise the movement data (i.e. the marker position) with the stimulus presentation, the camera also recorded the position of a second marker attached to the side of the screen. This marker did not move but it stopped emitting infrared light so that its position was registered as ‘missing’ when a flash was presented at the top left corner of the screen (where a light-sensor was placed to detect the flash). We used a simple four-point calibration to relate the position of the fingertip to the projected images, automatically correcting for the fact that the marker was attached to the nail rather than the tip of the finger Fig. .Fig. 1A Participants stood in front of the large screen and were free to move as they wished. The display consisted of four virtual items: a black target (2 cm diameter disc), a grey hitting zone  and two red items (5 cm diameter discs), separated by a gap.At the beginning of each trial, a green starting point (2 cm diameter disc) was presented 35 cm below the centre of the hitting zone. The gap between the red items was 5 cm wide and its centre was 5 cm below the centre of the hitting zone. To start a trial, participants placed the index finger of their dominant hand on the starting point. Between 500 and 700 ms after they did so, the starting point disappeared, and the black target appeared 10 cm to the left of the centre of the hitting zone, moving rightward at 20 cm/s. Exactly 300 ms after the target appeared, it jumped either leftward or rightward by 1 cm. We picked this time because it allowed participants to initiate their movement towards the target before the jump, but not be so close to the red items that they did not have time to respond. Figure positive auditory feedback and their score would increase by one point. If participants missed the target or hit it whilst it was outside of the hitting zone, they did not receive any auditory feedback. If participants in the obstacles group touched one of the red items, one point was deducted from their score and they received negative auditory feedback, irrespective of hitting the target or not. Within each group, all participants were subject to two timings of item movement  and two changes in gap size . Each participant completed one block of 400 trials  in a single session that took approximately 20 min. In the 100 trials of each condition, the target jumped to the left on 50 trials and to the right on the other 50 trials. All conditions were randomly interleaved. At the end of the experiment, participants were debriefed, including being told about the groups.On arrival, participants read written instructions. These instructions were then repeated verbally to ensure understanding. Specifically, participants were instructed to slide their finger through the target whilst it was within the hitting zone. Participants in the obstacles group were told to avoid the red items, whereas participants in the irrelevant item group were told that the red items were irrelevant to the task. At that moment, participants were not aware that there were different groups who received different instructions. All participants were told that every time they successfully followed the instruction, they would receive response to the target jump by subtracting the average velocity after leftward jumps from that after rightward jumps  when the gap size narrowed from that when it widened . After determining the individual responses and response modulations in each condition, the values were averaged across participants.To assess whether the response to the target jump was modulated by the change in gap size, we determined the ned Fig. e. We didt-test to evaluate whether the response modulation magnitude was significantly larger than zero. Since it was, we needed to determine whether this is really due to the continuous updating of obstacle positions, rather than being caused by the obstacles’ motion itself. This was done by evaluating whether the response modulation magnitude was larger for the late condition of the obstacle than for the late condition of the irrelevant item group . If the response modulation magnitude in the late obstacles group had not been significantly larger than zero, we would not have conducted this test, but we would have checked that the response to the target jump did differ if the gap size was known in advance. This would have been done by evaluating the response modulation magnitude for the early gap changes for the obstacle group .To determine whether the response to the target jump was modulated by the change in gap size when the obstacles changed position at the same moment that the target jumped (late), we used a one-tailed, one-sample Table t(11) = 4.00, p = 0.001. The response modulation was also significantly larger for late changes in the obstacles’ positions than for late changes in the irrelevant items’ positions (t(22) = 2.36, p = 0.014; purple curves in Fig. As was to be expected, there was a clear response of the hand to the target jump in all conditions, demonstrated by the response curves all clearly deviating from zero in the positive direction. The hand moved in the direction of the target jump .This experiment was a direct replication of the The overall pattern of results is consistent with the main experiment: participants hit less targets and collided with more obstacles when the gap narrowed compared with when it widened Table . Particit(11) = 2.60, p = 0.013). In the replication, two of the participants did not have a positive response modulation in the late condition, but the one that clearly responded more vigorously when the obstacles moved closer together also did so in the early condition. We have no explanation for this participant’s behaviour. Importantly, the response modulation effect between 150 and 200 ms after the target jump was replicated. In contrast, the early negative response modulation (before 100 ms) was not, supporting our interpretation that it was a coincidence.Again, there was a clear response of the hand to the target jump in all four conditions (left and central panels of Fig. t1 = 2.60,Our goal was to assess whether the positions of obstacles in the surrounding are constantly updated when moving to intercept a target. To do this, we designed a task in which participants had to respond to a sudden change in the target’s position and assessed whether the size of this response was dependent upon the gap size between two obstacles through which participants must pass. In the critical condition, the gap size changed at the same time as the target jumped. The response to the target jump was modulated by the size of the gap between the obstacles: the magnitude of the response to the target jump was smaller when the gap between the obstacles was smaller. This provides evidence that obstacle positions can be updated and incorporated into the adjustment of an ongoing reaching movement.Before discussing this interpretation further, we should rule out alternative explanations. The first is that the modulation of responses by changes in gap size have nothing to do with considering the latest positions of the obstacles, but are automatic responses to visual motion, as was suggested by Aivar et al. . Such auWe designed the study in a way that balanced the motion of nearby items to minimise the potential effect of any automatic responses to background motion. However, the finger moved further to the right when the red items were irrelevant, rather than moving straight between the items Fig. , and conIn the early conditions, when the gap changed at the time of the target appearance, the obstacle positions could be incorporated into the initial movement plan. The fact that the response to the target jump considered the position of the obstacles in the early condition is in line with an earlier study showing that obstacles affect arm movement adjustments (Chapman and Goodale The response modulation revealed in the obstacles group appears to be stronger when the gap changed size earlier. This is not the result of moving in a manner that increases the possible vigour when one knows the gap size in advance. We interleaved all the conditions, but participants could have responded to early motion of the obstacles by adjusting how they moved towards the target. However, it is evident from Fig. Here, we perturbed the target to enable us to assess whether the response to such a perturbation was modulated by the position of the obstacles. Other research has used mechanical perturbations whereby the arm is perturbed by applying a mechanical force to assess the effect of obstacles on adjustments to the ongoing movements. De Comite et al.  showed tTo successfully execute reaching movements, people continuously update the position of both their hand and of the target item they wish to interact with. Using an interception task with virtual objects, we here show that people can also continuously update the positions of obstacles in the surrounding when adjusting their movements. The short latency with which all this takes place provides evidence for a highly automatic system that uses the most recent information about both target and obstacle positions to guide ongoing arm movements. This presumably contributes to the fact that people rarely collide with the many obstacles that they encounter in their surroundings in daily life.


At present, the existing influence evaluation algorithms often ignore network structure attributes, user interests and the time-varying propagation characteristics of influence. To address these issues, this work comprehensively discusses users’ own influence, weighted indicators, users’ interaction influence and the similarity between user interests and topics, thus proposing a dynamic user influence ranking algorithm called UWUSRank. First, we determine the user’s own basic influence based on their activity, authentication information and blog response. This improves the problem of poor objectivity of initial value on user influence evaluation when using PageRank to calculate user influence. Next, this paper mines users’ interaction influence by introducing the propagation network properties of Weibo (a Twitter-like service in China) information and scientifically quantifies the contribution value of followers’ influence to the users they follow according to different interaction influences, thereby solving the drawback of equal value transfer of followers’ influence. Additionally, we analyze the relevance of users’ personalized interest preferences and topic content and realize real-time monitoring of users’ influence at various time periods during the process of public opinion dissemination. Finally, we conduct experiments by extracting real Weibo topic data to verify the effectiveness of introducing each attribute of users’ own influence, interaction timeliness and interest similarity. Compared to TwitterRank, PageRank and FansRank, the results show that the UWUSRank algorithm improves the rationality of user ranking by 9.3%, 14.2%, and 16.7%, respectively, which proves the practicality of the UWUSRank algorithm. This approach can serve as a guide for research on user mining, information transmission methods, and public opinion tracking in social network-related areas. The social network market has rapidly developed thanks to the digital economy era and the rapid growth of Mobile Internet use. It has become a significant channel and carrier for maintaining social relationships and distributing news in human society. Weibo, one of the most popular social networking platforms today, has emerged as a significant means for users to exchange and obtain information. Its openness, immediacy of contact, simplicity of content, and strong interaction make it an attractive platform for government operations , and itsGiven that social networks are important channels for social relationship maintenance and information dissemination and can have far-reaching effects on both national security and social development, many scholars at home and abroad have researched the influence of social network users and proposed evaluation algorithms on user influence. For example, the HIUD algorithm , which mAnalyzing the influence of users on Weibo topics is important for the study of social networks. Firstly, influential users are the driving force behind the continuous spread of topics and their expansion . By studThe UWUSRank algorithm proposed in this article provides a more systematic and comprehensive analysis of users’ own attribute factors and their interactive behavior. By improving the PageRank algorithm, we dynamically describe the user’s influence from two aspects: the user’s own influence and their interaction influence;When analyzing the structure of social networks, this paper innovatively incorporates two indicators: connection tightness and interaction timelines. The tightness of connections reflects the varying degrees of correlation between users; The interaction timelines can be used to calculate the contribution of interaction behavior at different times to blogs. By considering the degree of user association and time factors, different interaction contribution rates of users can be calculated, making the interaction influence value of users more accurate;We introduce the correlation between user interests and topic content in the context of the topic. By considering the significant differences in the diffusion of different types of topic information among users, our model can evaluate the actual influence of Weibo users more reasonably.Our main contributions are as follows:The incoming and outgoing links of online pages and the user interaction in social networks are comparable; hence, the link analysis principle has also been used to assess the influence of user nodes on Weibo. The PageRank algorithm, which effectively ranks the value of web pages, i.e., the importance of each node in the network, is currently the source of many important link relationship analyses. Existing research typically combines the link analysis method with social network characteristics to suggest better approaches for evaluating the influence of social network users. The algorithm is improved primarily from user node characteristics, user interaction patterns, and user interests.Influence studies based on user node characteristics typically employ metrics such as the number of followers, blogs, retweets, and mentions as indicators. For instance, Zhang et al.  proposedThe method based on user interaction behavior mainly estimates node influence based on graphical features such as node degree and position in social networks. Community Scale-Sensitive Maxdegree (CSSM)  aims to According to the feature that Weibo information dissemination has topic differentiation, users can be divided into different communities before influence calculation. Abd Al-Azim et al.  divided In conclusion, there are several issues that need to be addressed: (1) the inner rules of individual behavior are not fully revealed when starting from target user attributes; (2) the analysis based on social network structure fails to consider the connection density and interaction time difference of nodes; (3) the relevance of users’ interest preferences to the content of Weibo topics has not been explored; (4) the contribution of user interaction to user influence changes over time, which is often ignored. Therefore, this paper comprehensively considers the influence of Weibo users based on their own characteristic attributes and interaction behaviors. Meanwhile, we introduce user interest values in the context of topics. Finally, we propose a UWUSRank algorithm based on the user’s own influence and interaction influence while considering user interest. The user’s own influence replaces the initial influence distributed equally in the PageRank algorithm, solving the situation that each node has the same initial PR value in the PageRank algorithm and excluding the interference of fake followers on influence. The evaluation of interaction behavior can solve the problem of equal distribution of the PR value of the web page’s outgoing links in the PageRank algorithm, and users with strong interaction relationships will get a higher proportion of influence value. Additionally, we introduce the similarity between users’ interests and topics to measure the influence value of users more comprehensively and accurately in the process of topic dissemination.The majority of the hot events of recent social concern are transmitted in the form of topics on Weibo, one of the most popular social network media today . Users eThis paper collects and monitors trending topics from Weibo and examines the size of the communication network, the rate of information flow, and the strength of the social connections among users who are actively involved in the topic dissemination. Then we calculate the corresponding user influence. The Weibo user influence calculation approach proposed in this paper is shown in The user’s own influence value, as the initial influence value in the improved PageRank algorithm, is composed of user activity, blog response, and user credibility. The definitions of these three indicators will be detailed in The two weight indicators of connection tightness and interaction timeliness take into account the closeness of user relationships and the time factor of interaction behavior. They are used to calculate the interaction contribution rate of user influence for subsequent calculation of user interaction influence values. The weighted indicators will be defined in detail in For the calculation of users’ interaction influence, this paper considers forwarding behavior and adds interaction timeliness to dynamically obtain the value of the interaction contribution rate. This part is detailed in Weibo users tend to intuitively judge the influence of other users based on some of their attributes . So, it User activityUser activity describes how actively a user has promoted the topic in the most recent time frame, which can be measured by the number of blogs a user has published, forwarded or liked over time. The more influential users frequently participate more actively in hot events and contribute more to their dissemination. In this study, user activity is measured by the number of recent blogs and the number of likes and retweets. The calculation formula is presented in Formula (1).Response to blogsThe response to a blog represents the degree to which a user’s recent blog has triggered discussion among other users. In this paper, we measure this index by analyzing the number of recent comments, retweets and likes, which is shown in Formula (2).User credibilityThe credibility of the user can also reflect the influence of the user to a great extent . For exaThen, we analyze the Weibo user’s own features and define the influence score Optimal weight acquisitionBased on past experimental experience and social network reality, different values are assigned to the weights in Influence propagation by users is not equally distributed to surrounding nodes, and interactions with highly connected edge weights result in greater value or strength of influence transfer between users. The connection edge weight reflects the importance of the interaction to the user’s influence. By quantitatively evaluating the tightness of the connections between network nodes and the timeliness of information exchange, we can determine the path weights in the interaction network.Tightness of connectionWeibo contains several intricate, overlapping community structures and covers a wide range of topics. Intra-community linkages are relatively strong, with frequent information exchanges and higher connection densities . HoweverTherefore, as the number of common neighbor nodes among users increases, the possibility that users are from the same community also increases. The more frequently users interact, the closer their relationships are, and the more power users have in core positions. In social networks, the importance of a node can be measured by the influence of users who are directly adjacent to that node. However, there are differences in the influence generated by in-degree neighbors and out-degree neighbors. In-degree neighbors are users who interact with this user, and out-degree neighbors are users who this user interact with. In order to better reflect the influence of topology and interaction between nodes in social networks on users, this paper refines the influence of nodes’ in-degree neighbors and out-degree neighbors on influence propagation according to the method proposed by Fu et al. . And we 2.Interaction TimelinesUser Users’ focus on online public opinion can shift with time . At the α = 11 h . ti0 is On the Weibo social network, users can retweet, comment, and like blogs on various topics. Among these behaviors, only retweeting can achieve the function of direct information dissemination . The intUser interest is an important factor that influences the spread of information . DiffereGenerally speaking, a topic on Weibo is the collection of all blogs that address a single public opinion event . Users tUsing this approach, we compile all user blogs published within the same time period into a user document set. In this study, we filter the obtained document set to remove noise and unnecessary information from the text to the greatest extent possible and then create a corpus of filtered texts by separating words and extracting related text feature words. Then we apply the TF-IDF algorithm to calculate the weight of the feature words and filter the final short text feature word document .(10)tfiFinally, we calculate the interest level of user This paper defines a dynamic model for calculating user influence based on the user’s own influence and interaction influence while also considering the similarity between user interests and the topic. To facilitate the explanation, Through interactive behaviors, Weibo users connect with each other in the network, constructing a sophisticated information dissemination system based on social networks. In this paper, we investigate the extent of users’ effect on others in the social network by abstracting the Weibo social network into a dynamic network. Dynamic network I0u is user In the process of Weibo opinion dissemination, the user’s ability to influence the intensity of information dissemination can be explored through their own influence, while the breadth of their ability to disseminate information can be explored through their interaction behavior. In this paper, we propose a reconstructed user influence evaluation algorithm, which improves upon the PageRank algorithm by combining the user’s own influence with their interaction behavior. This approach enables the calculation of the propagation influence The original PageRank algorithm assumes that each user is equally important and assigns the same initial influence score to all users. Moreover, each fan distributes its own score equally to the users it follows, which is not in line with reality. First of all, the initial influence of each user is different, and it should be determined by the user’s own influence. Secondly, although a user follows many users, it is impossible to treat all users equally, and the user will always be more interested in some of them and more willing to interact with their tweets, so the interaction contribution rate is different. Our core idea is that if a user follows another user with active interactions, then the user’s contribution to another user’s influence value should be higher than the default contribution of 1/m (if the user follows m users). Therefore, the algorithm proposed in this paper takes into account different users’ own information to determine their basic influence values, as well as the varying levels of contribution from different followers to the user’s influence. The stronger the interaction, the larger the corresponding followers will assign a larger proportion of the contribution value to the user. Meanwhile, this paper introduces user interest relevance, which takes into account the significant differences in the diffusion of different types of topic information among users and can more reasonably assess the actual influence of Weibo users.A vast number of users’ communication behaviors constitute the general characteristics of information dissemination, and each user’s individual ability to disseminate information reflects their contribution to the process of disseminating Weibo topics . User inThe UWUSRank algorithm dynamically characterizes user influence by considering both their own influence and interactive influence while also taking into account the similarity of their interests to the topic. The algorithm constructs a Weibo interaction network graph based on user data and calculates the influence of each user in the graph in turn. First, we calculate the user’s own influence as the initial value of influence. Then we calculate the interactive influence contributed by each follower in turn and compare the resulting influence value with the influence value of the previous round. If the difference is less than the threshold value, we exit the cycle and obtain the user’s influence value at this time; otherwise, we continue the calculation. Finally, we calculate the similarity between the user’s interest and the topic and multiply it by the influence value to obtain the final user influence value.The main calculation process of the UWUSRank algorithm can be summarized as the following Algorithm 1.Algorithm 1: The UWUSRank AlgorithmInput: Dynamic User Interaction Network Output: UWUSRank for each user//Calculate the user’s own influencefor all  indoCompute Compute Compute Initialize the influence value of each user as end for//Calculate user influence considering the user’s own influence and Interaction behaviorfortodo       whileE       Compute        Compute                               if converged.Precision refers to the proportion of relevant instances among all retrieved instances. In the context of user influence mining, precision can be defined as the proportion of correctly identified influential users among all users identified as influential by the algorithm . Taking Recall measures the completeness of the results measured by the algorithm . Taking F-value is a comprehensive evaluation index that balances the impact of Precision and Recall. The definition of the F-value is shown in Formula (17).According to the findings of the precision comparison shown in From the comparison results of the recall rate in From the comparison results of comprehensive indexes in By empirically evaluating the average performance of these four methods under topics, The above results demonstrate the strong correlation between users’ influence and their own influence and capacity for interaction. UWUSRank performs better when measuring the influence of Weibo users and mining highly influential users. In addition, solely using the number of user followers as an evaluation indicator of user influence has poor practical results.Strong influencers in social networks are able to reach more users . AccordiAnalysis of the influence of user interest on blog disseminationIn order to study the impact of users’ interests on their communication behavior, this paper classifies users by calculating the similarity between the content of their blogs and the content of the topics. According to the research findings of Yang et al. , users wThe points in 2.Analysis of the influence of time factor on user influenceThe UWUSRank can track how user influences change over time. Here we take “The Itaewon Stampede Accident” topic as the data set, set a time period to 12 h, and have a total of seven time periods for the statistical cycle. Then we use the UWUSRank algorithm to calculate the user influence values under each of the seven time periods. Throughout the statistical cycle, a total of 10,049 users participated in the topic discussions, from which we extracted the top seven users in the overall ranking. These users have consistently maintained a sizable influence and fan base throughout the study period. The influence values of users vary with time, and highly influential individuals are not always more influential than other users. 3.Analysis of the influence of each user’s own attributes on user influenceThis section also uses “The Itaewon Stampede Accident” topic as the data set, with a time period of 48 h. We have calculated the user activity, blog response and user authentication of the top 10 users in the influence ranking in the standard set and have also calculated the user’s own influence value proposed in this paper. As shown in User influence evaluation is a crucial aspect of social network research, and it plays an active role in estimating social opinion and guiding social hotspots. In this paper, we explore the dissemination mode of Weibo public opinion in the new media era, analyzing both users’ own influence and interactive influence. At the same time, we introduce users’ interest preferences and propose a dynamic calculation model of user influence based on interest preferences by improving the PageRank algorithm based on the information dissemination process of users’ dynamic interaction mechanism.Our experiment results on a large-scale Weibo dataset demonstrate that the proposed method can effectively improve the accuracy of user influence calculation in Weibo communities and uncover highly influential user groups. In the future, we plan to use the public opinion information dissemination network as the basis of our research, from which we can explore the group sentiment characteristics in the process of event dissemination and find out the pattern of sentiment contagion. Furthermore, we will study the role of textual emotion in the process of change of Weibo users’ influence to effectively improve the level of public opinion guidance.


Parametric imaging of the attenuation coefficient We present a robust theoretical framework to determine accuracy and precision of the DRE of We derive and validate analytical expressions for the accuracy and precision of Our analytical expressions agree with the numerical simulations for high signal-to-noise ratios and qualitatively describe the dependence on noise otherwise. A commonly used simplification of the DRE method results in a systematic overestimation of the attenuation coefficient in the order of We derived and validated expressions for the accuracy and precision of DRE of  These lead to changes in the spatial distribution of the complex refractive index, which in turn leads to changes in the absorption and scattering properties that can be measured using optical techniques. The main hypothesis underlying many applications of biophotonics is that, by measuring the optical properties, diagnosis or monitoring of tissue disease state or treatment is possible. Consequently, knowledge of the accuracy and precision of the methods to assess these optical properties is paramount.,,The optical property accessible with optical coherence tomography (OCT) measurements is the attenuation coefficient, which describes the decay rate of the OCT signal with depth.CF suffers from the drawback, as can be inferred from Eq. (1), that a finite sized AFR is necessary to achieve sufficient precision, which may preclude measurement of the attenuation coefficient of thin layers, such as in the retina or the arterial wall, or regions near the basal membrane.2Under the assumption of single backscattering from a homogeneous medium with stationary optical properties, the OCT signal versus depth We proceed to compute the definite integral cient as : μ^OCT contains a regularization term The mean value Thus, 4) reads  μ^OCT[i]Often, a simplified version of Eq. (7) is used by linearization of the logarithmic and exponential terms [perhaps inspired by the closer visual resemblance to Eq. (4)] Moreover, some authors further omit the (linearized) regularization term We now seek the precision with which Comparing Eq. (9) to Eq. (1), we see that the precision in the DRE estimation method is directly proportional to the pixel-wise estimate of the attenuation coefficient, whereas it is independent of 3To validate the accuracy and precision derived in Eqs. (6) and (9), we performed numerical simulations based on OCT scans from a homogeneous medium. Details of our simulation procedure can be found in Ref. Each squared, averaged A-scan is processed using Eq. (7) to estimate the attenuation coefficient. To demonstrate the spurious effect of linearization, we also analyzed the data using Eq. (8) with the regularization term We used comparable simulation parameters as previously4The assessment of the accuracy of the DRE method is shown in The more realistic case, when noise is included, is depicted in We proceed to compare the standard deviation Finally, we compared our previously reported lower bounds for the CF method5Quantification of the attenuation coefficient requires thorough assessment of the accuracy and precision with which it can be estimated from OCT data. In recent years, the DRE method has emerged as an attractive alternative to the conventional approach of CF. We have derived expressions for the accuracy and precision of attenuation coefficient determined by the DRE method and validated those with numerical simulations.The accuracy of the DRE method is given by Eq. (6). This equation includes a regularization term that sets the attenuation coefficient The expression for precision [Eq. (9), The dependence of precision on 5.1Simulations can be performed quickly and at low cost compared to the time and resources required for phantom experiments. Manufacturing of phantoms with precise control of the scattering properties can be challenging whereas simulations can explore a much wider range of parameter space beyond what is feasible in experiments. Simulations allow for precise control and manipulation of individual parameters (or tuning correlation among them), leading to deeper understanding of the underlying mechanisms. Although we have included only a limited number of Performance of both the CF and DRE methods depends on the appropriateness of the underlying single-exponential decay model of Eq. (3) to describe the light–tissue interaction . In the this study, both the simulation generating OCT data and analysis were based on the same Eq. (3). Therefore, the accuracy and precision derived in this article represent the best values that can be obtained. This best-case scenario may not be true for experimental data, for instance when a small fraction of multiple scattering occurs. Multiple scattering models are available5.2Measurements of the attenuation coefficient complement the structural images that OCT provides. The main premise is that quantification of 6In this article, we derived and validated the accuracy and precision of the depth resolved estimation method of the attenuation coefficient 7We model the mean OCT signal intensity as function of depth in Eq. (3) using a single exponential decay function, assuming that the confocal point spread function and the sensitivity roll-off are fully compensated and that a constant mean noise floor is subtracted. We first compute the integral Taken together with Eq. (3), we can solve for the attenuation coefficient as In practice, data are only available over a finite range, up to Solving Eq. (12) for Finally, Eq. (13) can be rearranged to solve for the attenuation coefficient giving the finite-range equivalent of Eq. (11) When Equation (15) reveals that the estimate 8Vermeer et al.We can use Eq. (16) to obtain an expression for s before .Quite often, approximate forms of Eq. (7) / Eq. (17) are found in literature, which are obtained by linearization of the logarithmic and exponential terms. Then, factor 9We seek the precision of the DRE method in the presence of noise. We make use of the fact that the attenuation coefficient will be approximately normally distributed, and that the precision is given by the standard deviation After pre-averaging The variance is given as Fiske et al.Thus, upon averaging 10Let We will first work out the term without noise, then the term with noise, making use of the fact that the analysis is based on the exponential decay model so we can write inside the summations: Let Then, the mean of And the variance as Inserting the expressions for the SNR and regularization term To arrive at a more compact, albeit approximate expression we first linearize the exponentials Then assume Comparing to Eq. (22), we see that


Visual working memory (VWM) allows us to actively store, update, and manipulate visual information surrounding us. While the underlying neural mechanisms of VWM remain unclear, contralateral delay activity (CDA), a sustained negativity over the hemisphere contralateral to the positions of visual items to be remembered, is often used to study VWM. To investigate if the CDA is a robust neural correlate for VWM tasks, we reproduced eight CDA‐related studies with a publicly accessible EEG data set. We used the raw EEG data from these eight studies and analyzed all of them with the same basic pipeline to extract CDA. We were able to reproduce the results from all the studies and show that with a basic automated EEG pipeline we can extract a clear CDA signal. We share insights from the trends observed across the studies and raise some questions about the CDA decay and the CDA during the recall phase, which surprisingly, none of the eight studies did address. Finally, we also provide reproducibility recommendations based on our experience and challenges in reproducing these studies. Contralateral Delay Activity (CDA) has been studied for over two decades and yet its underlying role in Visual Working Memory (VWM) remains unclear. This study reproduced eight CDA‐related studies and shows the robustness of CDA across different tasks, research groups, participants, and EEG devices. Acting as a mental buffer for visual information, VWM has been an active area of research for several decades. While behavioral studies have shown that working memory (WM), of which VWM is a subset, has a limited capacity of only a few items, usually ranging between 3 to 5 . One such VWM neural measurement being studied is the contralateral delay activity (CDA)  a robust and consistent neural correlate for Visual Working Memory (VWM) tasks?. We wanted to know if CDA is a consistent measure across different tasks, subjects, and EEG recording devices, or if it requires a lot of manual cleaning and handcrafting of the data to obtain it. To investigate the robustness of the CDA EEG signal, we looked for CDA‐related EEG data sets available online and tried to reproduce their results using a basic independent automated pipeline with no human intervention on the data to extract the CDA. Given that robustness can be interpreted in different ways, we should mention that we use the same definition as in the Framework for Open and Reproducible Research Teaching (FORRT): The persistence of support for a hypothesis under perturbations of the methodological/analytical pipeline. In other words, applying different methods/analysis pipelines to examine if the same conclusion is supported under different analytical conditions  such as the P300 and N270, benefit from a large volume of studies and replications and are well understood .Replicability: Lastly, before we dive in, we should also define the terms repeatability, is also used although less often, referring to the same group repeating the same experiment with the same analysis and obtaining the same results.Simply put, one can replicate a study or an effect (outcome of a study) but reproduce results . A third term, computational reproducibility, as defined in the FORRT  have benefited tremendously from good reproducibility frameworks, standards and overall culture. The accelerated pace of innovation and breakthroughs in AI were mainly enabled by accessibility of both data and code. These best practices of sharing both data and code in a reproducible manner are not, unfortunately, the default behavior in psycho‐ and neuro‐related fields. Here, we share how a few groups of researchers have made their data and code available and we hope to inspire others to follow that path.2CDA, Contralateral Delay Activity, and EEG. From the bibliography section of these articles, a few additional relevant studies were added to the list. Open Science Framework (OSF) with the keywords previously listed was also used to search for additional studies and data sets. It is important to note that six out of the eight studies included here have Edward Awh and Edward Vogel as co‐authors, highlighting a lack of independent studies on CDA with openly available EEG data.After looking through CDA‐related literature, searching for available data sets and asking  a few researchers in the field if they were aware of open access CDA‐related EEG data sets, we ended up with eight recent CDA‐related studies published between 2018 and 2021 with different task paradigms . All the studies were reproduced using MNE‐Python . With their nomenclature 2:0 means 2 targets in one hemifield and 0 target in the other hemifield for a net load of 2. 4:2 represents 6 targets total, 4 in one hemifield and 2 in the other for a net load of 2. As we can see, the highest CDA is obtained with 4:0 for a net load of 4. Interestingly, the 5:1 condition shows a higher CDA than 3:1 and 4:2 however lower than 2:0 indicating that having targets in both hemifields reduces the overall CDA amplitude. On the graph, t = 0 s is when the memory display appeared on the screen with the targets, then they stayed visible for 500 ms after which the participant had to remember the targets for 1 second before the probe display appeared for the participant to provide their answer as to confirm if the item in the probe display was indeed part of the targets or not.In 2.2Perturbing neural representations of working memory with task‐irrelevant interruption  and in a second condition the colors were the relevant features . On the graph, the cognitive impact of the separation that happened for half the trials (at 400 ms) is clearly visible in the CDA signal around 200 ms as highlighted by the grayed region. The full 2.2 s epoch is displayed on Figure For Experiment 2 Figure , the epo2.4EEG dynamics reveal a dissociation between storage and selective attention within working memory  or 2 (at t = 700 ms). However, in Experiment 2 the probe display was modeled after Berggren and Eimer  various groups have used to obtained their CDA. Second we will discuss some trends we have observed across the reviewed studies.Note that we did not look at any eye‐tracking data and assumed that the subjects respected the instructions of fixating the middle of the screen. Many studies had the eye‐tracking data available, however we did not use it nor have we excluded any trials based on eye‐movement. This does certainly impact the results we obtained when compared to the original curves of the authors in their paper. Given that such data were not available for all data sets, we decided to not consider them at all.3.1The contralateral delay activity (CDA), as its name implies, is a difference in the activity between the left and right hemisphere. The signal is obtained by subtracting one or more contralateral channels to equivalent ipsilateral channel(s) to the attended side. Unsworth et al., mentioned in their 2015 paper that it is now standard procedure for measuring the CDA to use posterior parietal, lateral occipital, and posterior temporal electrodes , citing the work of Vogel and Machizawa  and VogeIn order to better understand the signal shape and amplitude coming from the various electrode pairs, we looked at each pair for each condition of each study. Regardless of what the study actually used for their analysis, we used all channel pairs available in the raw data. We included here only the breakdown for Balaban  and VillTo confirm our empirical estimation of PO7/8 being the best electrode pair for CDA, we calculated the effect size for each available pair of electrodes by comparing contralateral versus ipsilateral activity for each study. All the data sets had the PO7/8 pair available but Adam et al. . Aside fFinally, the approach for averaging the channel pairs also varied. Some groups subtracted the pairs first and then averaged across pairs, while others averaged one side first and then subtracted to the average on other side. The order in which the averaging and subtracting happens does not really matter if no other operation is done on the signal and if they are all referenced to the same reference. For example, if we are trying to use the pairs PO7‐PO8, P7‐P8, and PO3‐PO4, we could either start by subtracting each pair individually  and then averaging the 3 signals obtained, giving us the resulting CDA or we could average one side together  and subtract it from the average signal from the other side . Both approaches would give the same CDA for a given trial.3.2The EEG signal being an electric potential difference between two electrodes, namely the electrode of interest and the reference, it is no surprise that the reference plays an important role in EEG studies. Changing the reference can drastically change the signal obtained and therefore influence the conclusion of a study. The ideal reference would be a neutral point with no electrical activity to which we could measure a difference of potential being only the activity of interest. Unfortunately, no such point exists on the body, leaving the problem of finding a good reference unsolved or open to interpretation. Best practices in EEG studies include (1) using the average of left and right mastoids or (2) to re‐reference the signal offline to the average of all channels or (3) using one or multiple electrode(s) on the midline such as Cz or (4) using a mathematical reference such as the reference electrode standardization technique (REST) or a Laplacian approach  studies. The choice of reference will impact the visual inspection and the cleaning of the data, however, when it comes to obtaining the CDA itself, because we are subtracting one electrode to the other, the reference gets somewhat canceled and therefore does not impact the resulting CDA signal as much. For example, if the contralateral electrode is PO8(‐Ref) and the ipsilateral electrode is PO7(‐Ref), then CDA  is (PO8 ‐ Ref) ‐ (PO7 ‐ Ref) which is equivalent to PO8 ‐ PO7 as the Ref cancels out. It is therefore still important to consider the reference for cleaning the signal but to keep in mind that the CDA itself is not as affected as much by the reference as typical, non‐latelarized, ERPs. This actually makes the CDA signal even more robust to noise, assuming that most EEG noise would be visible on both channels, and be canceled out during the subtraction. A noise that would survive that subtraction would be a noise seen only by one electrode or one ‘side’ of the head.3.3If the amplitude of the CDA correlates with the number of items being tracked, one could expect the amplitude to remain somewhat stable for the whole retention or tracking duration. However, in all the replicated studies we can observe the amplitude of the CDA declining way before the end of the retention phase even when the participants did not lose track of the item(s).good performances only, meaning that the subjects did remember all the items for the whole duration of the trial and provided good answers at the end. As we can see on Figures In later section 3.6 we look at the CDA when subjects lost track of one of more item(s)  but all figures previously showed with the reproduced results and discussed in the methods section were generated from 3.4One interesting phenomenon that most studies did not mention in their paper is the recall, or response, period . Interestingly, in most studies, we are observing a re‐increase in the amplitude of the EEG signal, sharing similarities with the CDA observed during the identification and retention (or tracking) periods. One potential reason most studies do not look at that period is because eye movements are generally not controlled in this phase, introducing artifacts in the EEG signal. Moreover, the induced artifacts are most likely lateralized and not normally distributed as the participants might be fixating and moving their eyes to the side of interest, complicating the dissociation between eye movements and cognitive processes in the EEG signal.Figures 1 + 3 same condition, the F7‐F8 pair is not being impacted as much and have a similar amplitude as the parietal channels, suggesting that the activity observed from the parietal channels is mostly cognitive while being slightly affected by eye‐movement artifacts. It is not very likely that the eye‐movement artifacts would affect more the parietal channels than the frontal ones. In Hakim et al.  and concluded their study saying that CDA is a reliable and valid individual measure of working memory that predicts behavioral performance on visual working memory tasks. Of the studies reviewed here, only three looked at the direct correlation between individual working memory performance and CDA amplitude. Most studies looked at the relationship between task conditions and performance, as well as the relationship between task conditions and CDA amplitude; however, only three looked at the direct correlation between performance and CDA amplitude  and confidently holds and tracks the correct number of items, despite some of them being wrong, this kind of mistake would result in the same CDA amplitude as if the right items were kept in memory. While the current state of CDA literature lacks the trial‐by‐trial analysis to evaluate the role CDA plays in performance, several studies have looked at the individual differences in CDA amplitude versus working memory performance or capacity. For example, Unsworth and colleagues in 2015  work. With their EEG and behavioral data we were able to reproduce a similar result with a slightly higher and more significant correlation . It is important to note that the classes are quite unbalanced as there are very few trials with an accuracy score of 0/6  or 6/6  and two thirds (66%) of the trials have an accuracy of either 2/6 or 3/6.In Adam et al. , they usK = N ×  and reported a correlation r = −0.43, p = 0.026 in their study. With their EEG and behavioral data we were able to reproduce a similar result with a slightly higher correlation .In Feldmann‐Wüstefeld , they usK = S x ((H‐F)/(1‐F)), where H is the observed hit rate, F the false alarm rate, and S is the higher set size (maximum number of to‐be‐remembered items). In their study, instead of looking at the correlation with WMC and CDA amplitude, they looked at the increase in CDA amplitude between set size of two and set size of four items and reported r = 0.448; p = 0.0159 showing that participants with high WMC  showed larger amplitude increase in CDA between two and four items, compared with participants with low WMC. Unfortunately, their behavior files were not available with their EEG data, preventing us from calculating the WMC with the same formula. In the EEG files, a binary trigger identifying good and bad answers was available so we were able to calculate the accuracy for each participant. Unfortunately, when correlating the difference in amplitude between ss = 2 and ss = 4 with accuracy for each participant we found no significant correlation and therefore were unable to reproduce the effect of CDA on individual performance. It is worth noting that according to a recent study by Ngiam and colleagues, a substantial number of subjects and trials is required to detect a significant CDA difference between set sizes   Identifying the excluded participant in the documentation file. Sometimes that information is available somewhere in the code as a if statement like if fname == “participant_X”; however, this information should be brought forward and featured in the main documentation file. (d) Identifying the excluded participants in the published paper. This works well when one or two participants are excluded with a mention like “participant #12 was excluded because of …” but does not scale well for multiple participants. (3) Document triggers/events; the triggers/events allowing to epoch the data properly should be clearly identified. Such information is usually a mix of hardware triggers from the EEG file and information from a behavioral file . For example, in most studies the side and the set size of each trial is available in the EEG file  but the performance of the trial is available in a behavioral file. Such structure should be clearly described the main documentation file. (4) Performance scoring code; there are many ways to assess performance  and it would be beneficial to share the corresponding code to avoid confusion. In most studies, the formula is described in the article but the corresponding code is not available. (5) Online repository platform; we recommend using OSF to share the data. OSF is a free, open platform to support your research and enable collaboration, as stated on their website. There is a limit of 50GB for the free tier which might not be enough for most EEG studies; however, the cost of additional storage capacity is fairly low and has a one‐time payment which works well with grant funding. All of the reviewed studies, but one, used OSF to share both the data and the code. Villena‐Gonzalez used Mendeley Data instead. Another option is OpenNeuro, a free and open platform for validating and sharing BIDS‐compliant MRI, PET, MEG, EEG, and iEEG data, as one can read on their website. (6) README file; we recommend having a README.md or .pdf file in the root folder explaining the crucial information about the data with reproducibility in mind. We provide as good example from Adam et al. ((1) EEG preprocessing; in most published papers, the preprocessing steps are well described; however, many studies have a “visual inspection” part to remove some of the contaminated data. This subjective step can make reproducing the results difficult and we encourage researchers to also share the preprocessed EEG files of each participants in order to be able to compare where the results start diverging when failing to reproduce the results. This obviously increases the size of data being stored and shared but adds a lot of value. (2) Excluded subjects; in their documentation file , researchers should make clear which subjects have been excluded from the analysis. Usually, in the published paper there is a mention like “3 subjects were removed because of …”, while this informs the reader about the number of subjects that were included, if the raw data of these subjects are included in the data folder, it puts the burden on someone trying to reproduce the study to find the excluded ones. We have encountered four ways to deal with this issue while reproducing the studies for this review. (a) Not sharing the raw data of excluded subjects. In most cases we would not recommend this as there might be useful parts in the data. It really depends on the reason for excluding the participants from the study. (b) Making a specific m et al.  below. WFinally, our objective with this review, aside from better understanding the cognitive mechanisms at play during a VWM task and the key role of CDA, was to evaluate the CDA reliability as a potential candidate for brain‐computer interfaces (BCIs). Many other ERPs and neural correlates are being used in brain‐computer interface paradigms; however, to our knowledge, the CDA has never been used in a BCI context. We have, however, seen a recent interest in using machine learning for CDA classification with regard to the number of items held in WM . We bel5With this study we were able to look at CDA across different VWM tasks, from different groups of subjects, recorded by different groups of researchers using different EEG equipment. By using the same simple independent pipeline for all studies, we have shown that CDA is a robust neural correlate of visual working memory. As for its exact role and meaning, more research is required.Moreover, having access to all these data sets allowed us to look beyond the usual numerical CDA mean amplitude over a window of interest but to also observe two phenomena that are understudied and underdocumented. First, the decay happening shortly after the CDA peaks while the participant still has to maintain the information. Second, the CDA‐like signal during the response period. For the latter, it can be difficult to control efficiently in order to dissociate eye‐movements and other artifacts from cognitive processes in the EEG signal during the response period; however, we believe it deserves more investigation as it could help shed more light on the CDA and working memory.Finally, all the code and figures generated for this review are available online on our repository. Many more figures that we did not include in the manuscript to keep it as short and concise as possible for better readability, are available on the repository.Yannick Roy: Conceptualization; data curation; formal analysis; methodology; software; validation; visualization; writing – original draft. Jocelyn Faubert: Funding acquisition; investigation; project administration; supervision; writing – review and editing.This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERCRDC) (reference number: RDPJ 514052–17) and an NSERC Discovery fund.The authors declare that there is no conflict of interest.Appendix S1 Supporting InformationClick here for additional data file.


We show that the topological entropy of the billiard map in a Bunimovich stadium is at most  The Bunimovich stadium is a planar domain whose boundary consists of two semicircles joined by parallel segments as in Fig. In this article we will study the topological entropy of the billiard map in a Bunimovich stadium. The topological entropy of a topological dynamical system is a real nonnegative number that is a measure of the complexity of the system. Roughly, it measures the exponential growth rate of the number of distinguishable orbits as time advances. We will discuss its exact definition in our setting in the next section.The study of topological entropy of billiards was initiated in . In thisentclass1pt{minimaRecently, Misiurewicz and Zhang  have shomentclass2pt{minimmentclasspt{minimaTopological entropy of hyperbolic billiards has also been studied in several other articles , 11, 21.the Bunimovich stadium billiard tablephase space of this billiard map will be denoted by s in the boundary of angleThe billiard mapbilliard flowWe consider We remark that the map mentclass2pt{minimMcAndrew , 5 and DMcAndrew  can not McAndrew  topologiMcAndrew . We begin by calculating the derivative of Throughout the proof the functions under consideration are restricted to the domain [1, For W function; see [W function is a multivalued function which for a given complex number z gives all the complex numbers w which satisfy the equation z is a positive real number then there is a single real solution w of this equation which we denote W(z).To prove the next lemma we will use the Lambert ion; see  for an ia such that There exists a constant The equation a verifies The constant Notice that Combining Lemmas For x and To prove the next result we consider the gamma function For any even If Now we are ready to prove the main theorem of the paper.C is a positive constant. Recall that p(n) denotes the complexity of From Corollary entclass1pt{minimaAnother very natural definition of topological entropy was given by Pesin and Pitskel’ in  and the ally, in  the capaally, in , but it ally, in  and the Fl) from  still hoFor any