In this study, the effectiveness of the video modeling method in teaching basic basketball skills to students with Down syndrome was examined. Four students with Down syndrome, who were studying at the disability free living center in Dolayaba, participated in this study. The ages of the students diagnosed with Down syndrome were as follows: two of them were 13, the others were 14 and 16. In the study, the effectiveness of video modeling in teaching basic basketball skills was evaluated using the multiple probe model, one of the single-subject research methods. The experimental process of the study consisted of collecting baseline data, daily, conducting instructional sessions, maintenance and generalization stages. The findings of the study showed that video modeling was effective in teaching basic basketball skills to students with Down syndrome and that they maintained the skills in interpersonal and environmental differences after the end of the instruction. When the opinions of the basketball teacher and the students were evaluated, it was determined that the students’ self-confidence and peer relations were strengthened thanks to their active participation in the lessons. The students were not bored because they stated that they found the lessons interesting and fun. Down Syndrome (DS): It is a type of physical, mental, and functional disability caused by an extra copy of the twenty-first chromosome. ,2. Its cJust like individuals with a typical development, special-needs individuals need to learn a variety of skills required by societal life. In acquiring skills such as self-care, everyday routine skills, shopping, traveling, etc., the objectives of the institutions continue to depend on the regulation of content and the delivery of appropriate methods or approaches to content ,5. One oResearch has shown that fair play, sportsmanship, and knowledge of moral development of sporting individuals have an impact on the moral character development from sport, when continually taught . MobilitStudies have reported that children and youth with DS lead a more sedentary lifestyle than their peers with normal development and as a result, they are more affected by health problems such as overweight and obesity ,16, and Individuals with disabilities can learn individual or team sports with appropriate training and support, enjoy them and have a healthy body . One of Shooting: Attacking player aims to throw the ball directly into the basket. Shooting is used to conclude an attack .Pass-making: It is the method that the player uses to transfer the ball to his teammates in different ways with one or both hands .Dribbling: The ball bounces off the ground when it hits the ground. This is performed with the left or right hand. The ball is bounced and moved from place to place, by running or walking. It is called basketball dribbling .In sporting skills, as in all fields, when teaching special-needs individuals a new skill, process, or concept, students can have a successful learning life depending on the teaching method or approach the teacher uses. Teaching methods are used to teach skills and concepts to individuals with special needs, and the skills or concepts to be taught have advantages and limitations over their characteristics . New metThere are two fundamental processes of learning by observation. These are the abilities to model and imitate. This process is highlighted in the field as a whole. The student exhibits the target behavior, and this becomes a clue for other students .The literature shows that researchers worldwide have been extensively investigating the effectiveness of video modeling in recent years . Van LaaResearch has shown that video modeling is effective in the education of individuals with autism and intellectual disabilities. However, the fact that there are few studies on both gaining sports skills and modeling with video, in studies on individuals with Down syndrome, reveals the importance of this research.This study aims to determine the effectiveness of teaching to model with video in teaching basketball basic movement skills to individuals with Down syndrome. For this purpose, the research sought answers to the following questions.Could teaching by video model give students with Down syndrome the ability to shoot from viewing basic basketball skills?Could teaching by video model give students with Down syndrome the ability to pass upon viewing basic basketball skills?Could teaching with the video model give students with Down syndrome the ability to dribble from viewing basic basketball skills?With the video model, can teaching be provided to students with Down syndrome, if they master the basic movements of the basketball skills, to help them generalize the skills (with different people and in different environments)?If video modeling teaching provides basic basketball skills, can the permanence of this outcome be ensured ten days and twenty days after the learning ends?Is teaching with video modeling practical on the social development of students with Down syndrome?In this chapter, we cover the research model, the dependent and independent variables of the research, the data collection tools used, teaching materials, application reliability, experimental process, information on the collection and scoring of data, analysis, and interpretation of data, and calculation of trustworthiness among observers.In this study, in order to determine the effectiveness of video model instruction in teaching basic basketball skills to students with Down syndrome in the acquisition, maintenance, and generalization of these skills, a multiple probe between subjects with probe phase, one of the single-subject research methods, was used.Single-subject research is a research method that involves time series analysis based on repeated measurements or observations before, during, and after an experimental intervention on a subject, in order to reach a basic causal relationship ,36,37. TOne of the most important functions of single-subject research is that it helps to demonstrate that the changes in the target behavior are not due to other factors, but only due to the practice .Before the implementation of video instruction, the researcher told the students that they would watch a video on the computer and then the videos were shown to the students. In the videos, the modeling stages of each skill were shown. After the modeling stage, the video was stopped, and instructions were given to the student. In the third stage, the independent practice stage, the student was asked to perform the skill he/she saw and experienced in the video. The same steps were followed for each skill.Teaching sessions lasted approximately 20–25 min. In the independent practice phase, social reinforcement was provided by using expressions such as “Well done, now it is done” when the student responded correctly.The dependent variable of this research is basic basketball skills. The independent variable of research is the teaching to model with video.The study was conducted in the basketball hall of the Center for Accessible Life in Dolayaba, where the students received education. The baseline, instruction, maintenance, and generalization sessions of the study were conducted in the same environment. There were four fixed hoops, two free-standing hoops, twenty-five funnels, and thirty basketballs in the basketball hall. Video images prepared for the target skill, 8 Inc. tablet computer, 13 Inc. laptop computer, computer cable, camera, tripod, and data collection forms were used in the study.The experimental process included baseline session, instructional, mass probe, daily probe, maintenance and generalization sessions for each subject.Four subjects participated in the study, Yusuf and Mikail 13, Ismail Can 14, Salih Can 16 years old. All subjects have been diagnosed with Down syndrome since birth and all subjects receive education in a special education and rehabilitation center.Probe sessions were held in the form of mass probe sessions and daily probe sessions. Mass probe sessions were conducted at the commencement level and simultaneously in all subjects after the end of teaching in each subject. The daily probe sessions were implemented at the beginning of instructional sessions in all topics, excluding the primary education session, and only for the subject in teaching.Five mass probe sessions were held to determine the pre-teaching performance of subjects and to determine the performance of subjects after they perform at a benchmark level and after stable data is obtained. The first of the mass probe sessions was held to collect kick-off level data.Mass probe sessions were held one-on-one with students at the location of the practice. In the first subject, three consecutive sessions were continued until stable data were obtained. After stable data were obtained, a training session was initiated for the first student. When the criterion for the first subject was fully met, the second probe session was conducted for all subjects. Three consecutive sessions with the second subject were continued until stable data were obtained, and after stable data were obtained, the instruction session with the second subject was started. The third probe session was conducted for all subjects when the second subject performed at the level of meeting the criterion. Three sessions with the third subject were continued until stable data were obtained, and after stable data were obtained, the training session with the third subject was started. When the third subject also performed at a level to meet the criterion, a fourth probe session was conducted for all subjects. The training session was continued for three sessions with the fourth subject until stable data were obtained, and after stable data were obtained, the training session was started with the fourth subject. When the last student performed at a level to meet the criterion, a final probe session was organized for all students.It was held before the instructional session on other days, except for the day when instructional sessions started in the daily probe sessions. Only the student’s performance data was collected.Training sessions were conducted three days a week and one session per day. During the session, students were taken to the hall where the intervention would take place. In the hall, the laptop was kept stationary on a table and the tablet was used to allow the practitioner to watch videos of the student standing in critical situations. The student was told “we will watch a video with you and you will do the same thing you see” and “if you do the same thing you see in the video, I will give you a reward that you will like”. Then the video was opened and watched. After the student watched the video, a verbal reinforcement such as “well done, you watched it very well” was given. After watching the video, the student was given an instruction such as “take the ball and do the same”. The successful behavior of the subject was verbally reinforced. When the student made a mistake, the student was told “let’s watch the video again”. After watching the video again, the student was again given the instruction “let’s do the same”.Maintenance sessions were held 10 and 20 days after the instructional was ended. Generalization sessions were conducted in the form of interpersonal training in different settings. Generalization sessions have been convened by the pupils’ sports teacher who works at the institution. It has thus been investigated whether they generalize the skill gained against different individuals.The research collected data on reliability and application across observers. For analysis of trustworthiness data between observers, the consensus/consensus + difference of opinion X 100 “formula was used. For application reliability, the formula “Observed practitioner behavior/planned practitioner behavior X 100” was used .This section includes findings on the effectiveness, maintenance, and generalization of basic basketball skills. The effectiveness, maintenance, and generalization findings chart shows the number of horizontal axis sessions, vertical axis daily probe sessions, and the right response percentages in generalization, instructional sessions. The data on the shooting skills of the subjects are given in Yusuf showed an average performance of 15% in the pre-instructional process. At the end of the instruction and probe sessions, it was observed that he responded correctly to the target stimulus with an average of 90%. In the follow-up sessions, which were conducted ten and twenty days later, it was observed that he maintained 90%.Ismail Can showed an average performance of 25% in the pre-instructional process. At the end of the instruction and probe sessions, it was observed that he responded correctly to the target stimulus with an average of 85%. In the follow-up sessions, which were conducted ten and twenty days later, it was seen that he maintained a level of 85%.Mikail showed an average performance of 25% in the pre-instructional process. At the end of the instruction and probe sessions, it was seen that he responded correctly to the target stimulus with an average of 90%. It was seen that he maintained a level of 85% in the follow-up sessions, which were conducted ten and twenty days later.Salih Can showed an average performance of 20% in the pre-instructional process. At the end of the instruction and probe sessions, it was seen that he responded correctly to the target stimulus with an average of 95%. In the follow-up sessions, which were conducted ten and twenty days later, it was seen that he maintained a level of 85%. The data related to the pass throwing skills of the subjects are given in Yusuf showed an average performance of 15% in the pre-instructional process. At the end of the instruction and probe sessions, it was observed that he responded correctly to the target stimulus with an average of 95%. In the follow-up sessions, which were conducted ten and twenty days later, it was observed that he maintained 95%.Ismail Can showed an average performance of 20% in the pre-instructional process. At the end of the instruction and probe sessions, it was observed that he responded correctly to the target stimulus with an average of 80%. In the follow-up sessions, which were conducted ten and twenty days later, it was observed that he maintained 80%.Mikail showed an average performance of 20% in the pre-instructional process. At the end of the instruction and probe sessions, it was seen that he responded correctly to the target stimulus with an average of 85%. It was seen that he maintained a level of 90% in the follow-up sessions, which were conducted ten and twenty days later.Salih Can showed an average performance of 20% in the pre-instructional process. At the end of the instruction and probe sessions, it was seen that he responded correctly to the target stimulus with an average of 90%. In the follow-up sessions, which were conducted ten and twenty days later, it was seen that he maintained a level of 90%. The data on the dribbling skills of the subjects are given in Yusuf showed an average performance of 15% in the pre-instructional process. At the end of the instruction and probe sessions, it was observed that he responded correctly to the target stimulus with an average of 90%. In the follow-up sessions, which were conducted ten and twenty days later, it was observed that he maintained 90%.Ismail Can showed an average performance of 20% in the pre-instructional process. At the end of the instruction and probe sessions, it was observed that he responded correctly to the target stimulus with an average of 90%. In the follow-up sessions, which were conducted ten and twenty days later, it was observed that he maintained 90%.Mikail showed an average performance of 20% in the pre-instructional process. At the end of the instruction and probe sessions, it was seen that he responded correctly to the target stimulus with an average of 90%. It was seen that he maintained a level of 90% in the follow-up sessions, which were conducted ten and twenty days later.Salih Can showed an average performance of 20% in the pre-instructional process. At the end of the instruction and probe sessions, it was seen that he responded correctly to the target stimulus with an average of 90%. In the follow-up sessions, which were conducted ten and twenty days later, it was seen that he maintained a level of 90%.Generalization sessions of the research were conducted using the preliminary test-end test model. Instructional sessions on generalization were held after all mass probe sessions. There was an interpersonal generalization study with sessions with the sports teacher who worked at the institution. In addition, these sessions were conducted in a different environment and generalization was made between environments. Yusuf, Ismail Can, Mikail, and Salih Can’s performances in generalization sessions are shown in Looking at all the findings, Yusuf’s preliminary test session before teaching showed that his basic basketball skills were at a 15% level. The post-test session after teaching showed a 90% level of performance. The preliminary test session of Ismail Can before teaching showed that his basic basketball skills were at a 20% level. The post-test session after teaching showed a 90% level of performance. Mikail’s preliminary test session before teaching showed that his basic basketball skills were at a 20% level. The post-test session after teaching showed a 90% level of performance. Salih Can’s preliminary test session before teaching showed that his basic basketball skills were at 20% and his post-test session after teaching showed that he performed at a 90% level. When the opinions of the basketball teacher and the students were evaluated, it was determined that the students’ self-confidence and peer relations were strengthened thanks to their active participation in the lessons. The students were not bored because they stated that they found the lessons interesting and fun.In light of these findings, teaching studies using the teaching of video modeling can conclude that subjects can generalize the skills they have gained in different environments and with different people.It was observed that the students who participated in the study showed great interest in computers and video screenings from the beginning of the instructional sessions in which computer-assisted video modeling instruction was used. Therefore, it is thought that students’ interest in technologies, such as computers and videos, and thus their high motivation has an effect on their acquisition of the targeted skills. This situation is similar to the findings obtained from other studies.In the study conducted by Baglama, it was seen that teaching with a video model effectively taught subtraction and addition skills in mathematics . In the In this research, the effect of basic basketball movements on the effectiveness and persistence of teaching of video modeling was investigated for four students with Down syndrome. According to the research findings, teaching by video model was determined to be effective in giving Down syndrome individuals basic basketball skills, generalized alongside different environments and different people, and persistence after 10–20 days.With video, the effectiveness of teaching to model in teaching different types of obstacles can be explored.In skill teaching, video model and teaching method can be compared using a different teaching method.A different sports skill teaching effectiveness can be explored with the method of being a model by video.When curriculum development studies are carried out by curriculum development experts, studies suitable for teaching with a video model can be prepared.In future studies, researchers can look at the effectiveness of the viewpoint technique, which is a different technique from the video modeling teaching method, in teaching sports skills to disabled children.Teachers, experts who are working in the field, and families can be taught about how the video model should be implemented in teaching sports skills.Depending on the findings, the following recommendations have been made:


In our work, we studythe dynamics of a graphene Corbinodisk supportedby a gold mechanical resonator in the presence of a magnetic field.We demonstrate here that our graphene/gold mechanical structure exhibitsa nontrivial resonance frequency dependence on the applied magneticfield, showing how this feature is indicative of the de Haas–vanAlphen effect in the graphene Corbino disk. Relying on the mechanicalresonances of the Au structure, our detection scheme is essentiallyindependent of the material considered and can be applied for dHvAmeasurements on any conducting 2D material. In particular, the schemeis expected to be an important tool in studies of centrosymmetrictransition metal dichalcogenide (TMD) crystals, shedding new lighton hidden magnetization and interaction effects. Since, in this case, electronic motionbecomes quantized due to the formation of Landau levels, which areultimately responsible for the nontrivial properties of the consideredelectronic system, it is quite natural that the dHvA effect has servedas the central probe in studies of the shape of the Fermi surfacein normal metals.As theoreticallyshown by Landauand Peierls in the 1930s,4 Unlike the 3D case,where the field dependence of the magnetization is described by theclassical 3D Landau–Kosevich formula, for 2D samples, the magnetizationshows a characteristic sawtooth pattern both for massive and masslessDirac fermions.5Besides investigations of the dHvA effectin conventional three-dimensional(3D) materials, magnetic properties of two-dimensional (2D) materialshave been investigated actively.6 in a 2D electrongas (2DEG), while a clear sawtooth pattern for the magnetization vsinverse magnetic field predicted in ref  have extensively beenused for imaging of integer and fractional quantum Hall states (QH)16In our work, we report the dHvA measurementof graphene membranein a Corbino geometry coupled to a gold (Au) mechanical resonator.The central idea of our technique consists in relating the shift ofthe mechanical resonant frequency of a graphene/Au structure to theoscillations of the magnetic susceptibility that characterize thedHvA effect. The idea of using mechanical motion to measure the magneticproperties of a graphene membrane introduced here can be consideredas a part of the emerging field of sensing with 2D mechanical resonators.The investigation of the dHvA effect insuspended graphene membraneswas first discussed in ref  where thSupporting Information). Furthermore, our experimentalconfiguration with separated 2D sample and metallic resonator partsis an advancement of the device design employed in refs , avoiding the issues related to glued/depositedcantilevers. The method is thus applicable to any 2D material, manyof which can be fabricated into mechanical resonators.27Our approachis along the lines of cantilever sensing,Supporting Information. Device B2 consists of two Au beams, one graphene Corbino disk, and a back gateto which a voltage Vg is applied, controllingthe charge density n on the graphene disk. The grapheneCorbino disk couples the two Au beams together mechanically; the parallelAu beams are located at different heights, about 150 nm apart, supportedby a bend in the center of the upper Au beam. Device B1.5 consistsof one and a half Au beams: the top Au beam has beenreplaced by a gold cantilever. The specific choice of using gold (witha very thin layer of chromium) resonators stems from their low contactresistance to graphene and long-term stability.29 In contrast to more conventional geometries,19 the adopted Corbino disk geometry allows well-defined measurementsbased on pure σxx component, withoutproblematic mixing of σxx and σxy components. Furthermore, Corbino geometryfacilitates explorations over a wide range of Landau levels becauseof its capability of withstanding larger charge densities than deviceswith free edges. Transport via phonon-enhanced hopping conductionappears to be an additional useful characteristics that allows fordetection of interaction-governed states in these disks .Our experiments were carried out on two devices: B2 1b and B133 In the FM technique,an FM source-drain voltage VFM(t) in Imix), which can be shown33 to be related to the amplitude and phase of the mechanical motionof the resonator at the modulation frequency ωL as The mechanical resonance properties of the sampleswere investigatedusing the FM mixing technique.34 The low-frequency resonances (hereafter“Au modes”) are essentially governed by the gold structures,with the dynamics of the graphene membrane being dictated by the motionof the graphene/gold boundary conditions. For the latter, given thediamagnetic character of Au, the gold structure acts as a mechanicaldetector of the magnetic properties of the graphene disk. In addition,due to the mechanical properties of the Au beams, for the Au modes,there is a wider range of driving fields for which the linear detectionof the quantum Hall states in graphene is possible in comparison withpure graphene modes. For these modes, the linear regime is limitedto oscillation amplitudes around 100 pm.35 For these reasons, we focus here on the former ones.Owing tothe difference in effective mass between the Au and grapheneportions of the devices, two basic types of resonances were observed:(low-frequency 10–40 MHz) combined gold-graphene modes and(high-frequency ≳90 MHz) pure graphene resonances in the Corbinodisk.Gd  is lifted at fields B ≥ 0.5T , Gd bears the signature of the fractional QH stateν = 1/3 .Gdand the phaseof the mixing current Imix obtained throughthe FM technique were found to reflect the nontrivial B dependence of the electronic properties (see G coincide with theupward phase flips in Imix (see the Supporting Information). For this reason, thephase flips in Imix can be employed assensitive detectors of QH states in suspended graphene. In our case,a Landau level sequence up to ν = 30 can be resolved in At the mechanical resonance, both B. The first consequence of the finiteDOS of graphene is a reduction of the force between the plates ofthe movable capacitor F ≐ ∂Ω/∂z = 1/2Cg′ (Vg –μ/e)2, where Vg is the external applied voltage, μ the graphene chemicalpotential, Cg the (position-dependent)geometric capacitance of the structure, and Cg′ its derivativewith respect to the displacement of the graphene/gold electrode (seethe Supporting Information). This formulawell fits the measured gate voltage dependence of the lower Au beamresonance presented in Our graphene/gold mechanicalresonator can be modeledas a capacitorwith one movable plate coupled to an external voltage source. In additionto the conventional electromagnetic field energy between the capacitorplates, the system exhibits a contribution to its total energy derivingfrom the finite density of states (DOS) of graphene. The dependenceof the graphene energy level structure on the external magnetic field,allows us to infer the magnetic properties  from the measurement of the mechanical resonances as afunction of Vg = constant constraint,we consider the grand canonical potential Ω, where theelectrochemical potential eVg is, theglobal control parameter. If we now confine ourselves to the analysisof the graphene sheet, i.e., we exclude the field between resonatorand backgate from the definition of the system, we can assume thateither the particle number n or the chemical potentialμ are the control parameters. We can write the thermodynamicpotential associated with the Corbino disk as Ωdisk = Ω0(x) + Ωosc, with x = n, μ. The oscillatorydependence of the thermodynamic potential Ωosc on B is a directconsequence of the appearance of Landau levels in the energy spectrum.38 Central to our analysis, it ispossible to write the oscillating part of the magnetic susceptibilityeq S31b. χm,osc exhibits theoscillations characteristic of the dHvA effect, where N is Landau level degeneracy factor, q), with τq being the quantum scattering time  Lorentzian line width for the Landau levels. The assumptionfor the Landau levels structure is consistent with previous theoreticalwork  (see the Supporting Information). The connection between the full description givenby Ω andΩdisk canbe understood as though the external control parameter Vg determines, along with B, the controlparameter of the graphene disk. Since eVg = 2ne(B)/Cg + μ, the value of the geometric capacitance interpolatesbetween a situation in which Vg imposesthe charge on the graphene disk (Cg →0) and the case for which the external voltage fixes the chemicalpotential μ (Cg → ∞).For intermediate values of Cg, we shouldinterpret the chemical potential μ appearing in eVg). Since, for our devices, we have that eVg ≫ μ, we are essentially, from the perspectiveof the graphene sheet, in a charge-controlled setting  = Ωosc).The properties of the whole system (moveable capacitor+ graphenedisk) can be derived from the relevant thermodynamic potential. Inour case, given the  and ref ). As disple refs  and 39) Supporting Information), it is possible to showthat resonant frequencies of our structures fn exhibit a nontrivial dependence on B reflecting the emergence of Landau levels in the spectrumof graphene ,Λ2 = Λ2, and η = η aregiven in the Supporting Information. Theexplicit expression of Λ1 and Λ2 allows us to establish the optimal value of the gate voltage B in terms of χosc, we can, alternatively,express it in terms of quantum capacitance . The relation between the twointerpretations is rooted in the  thermodynamic relationthat holds between quantum capacitance and magnetic susceptibility,which can be expressed as Supporting Information), allowing us to access experimentally both magneticand charge properties of the system under consideration.Through a standardthermodynamic analysis, taking into accountthe charging, magnetic, and elastic energy for our devices  is at the heart of the determination of theLandau levelgap in torque magnetometry experiments.40The universal interdependence of 38 As anticipated,even though gold resonancesare heavily utilized, we are probing the magnetization propertiesof the graphene part of the structure: choosing the spectrum and Berryphase of 2D electron gas would result in a different spacing of thefrequency dips. In analogy to the GMR measurements presented in ref  is unchanged across the measured magnetic fieldrange. The fitting value of the scattering time is close to τS = 0.3 ps extracted previously from the Shubnikov–deHaas oscillations at Vg = 10 V in a similardevice,30 and also close to the data in In q obtained from the dHvA fits areplotted as a function of Vg along withthe values τS obtained from theShubnikov–de Haas oscillations, present in the Landau fan plotin S matches with thescattering time obtained in ref  indeed arise from the dHvA effectin graphene.In d in ref  for ultr19 our approach is differentas we probe the graphene via a Au beam resonator. In a way our workis similar to the cantilever experiments by Harris and co-workers;15 however, by using an upper gold beam, enablingthe contact with the inner edge of the Corbino geometry, we can facilitateoperation on any conducting 2D material and obtain extraordinary samplequality via current annealing. This achievement seems out of reachfor regular cantilever devices combined with the present state-of-the-artnanofabrication possibilities for 2D material. From this perspective,our setup opens up new possibilities in relation to the investigationof the magnetic properties of transition metal dichalcogenides , witVFM; the layer thickness of the Austructure allows for a larger drive voltage range for which the linearmechanical regime is valid.The specific advantage of our setup consists of the fact thattherelevant mechanical resonances are the gold mechanical resonances,with the “sample”, in this case graphene, mechanicalresonances not playing any significant role. This offers specificadvantages over a “sample-only” mechanical resonator:(1) Reproducibility of the mechanical resonant frequency is independentof the material considered, avoiding potential detrimental effectsrelated to impurities on the resonant properties of the structure.In fact, the graphene resonance in Corbino geometry did split in severallocal resonances, which made studies using ”pure” grapheneoscillation very challenging. (2) Larger ”dynamical range”for In conclusion, we have developeda versatile system of coupledresonators in which a Au resonator can be employed for sensing offorces originating in atomically thin suspended samples, made of graphenein the QH regime in our case. Owing to the free suspension of ourgraphene membrane, movement of the Au sensing element can be detectedvia displacement of the graphene, which facilitates force sensitivitysufficient to observe magnetization oscillations due to the de Haas–vanAlphen effect in integer QH states, and even in the fractional QHregime. The experimental approach developed in this work opens upthe possibility to investigate de Haas–van Alphen effect inother 2D materials, in particular transition metal dichalcogenidecrystals with hidden magnetic properties.


In addition, the switching threshold can be further reduced via increasing the graphene oxide thickness, hence paving a new way for achieving tunable optical bistable devices at visible light frequencies.Here, we propose an optical bistable device structure with a few layers of graphene oxide integrated in the metal-dielectric-metal based asymmetric nanocavity. Through the light confinement in the nanocavity, the third order nonlinear absorption of graphene oxide can be significantly enhanced, which experimentally delivers low-threshold optical bistability at the visible wavelength of 532 nm with only 267 KW/cm Graphene oxide, a graphene-like oxidation two-dimensional 2D) material, has been investigated extensively because of its extraordinary optical nonlinear properties, which have been shown to be superior to normal dielectrics . UsuallyD materia2) due to the low third-order susceptibility [2 can be obtained through utilizing the local field of defect mode to enhance the nonlinearity [2 can be achieved [2 scale with the operation band limited in the terahertz frequency. Therefore, it is of great significance to design a device structure with the low threshold optical bistability especially in the KW/cm2 scale and the operation band at visible light frequencies [Optical bistability (OB) means that an optical system has two possible output light intensity states under a given input light intensity, which realizes the recoverable switching transition between these two light intensity states ,9. Optictibility . It is stibility . To furttibility , includitibility , surfacetibility  and Fabrtibility . For exainearity . K.J. Ahachieved . Even thquencies ,21.2 laser power. The asymmetric nanocavity is based on metal-dielectric-metal (MDM) Fabry-Perot cavity with a plasmonic lossy ultrathin (~20 nm) metal film as the top layer. The multilayer graphene oxide (GO) is integrated in the dielectric layer by stacking 1 mg/mL solution of graphene oxide [2 at the wavelength of 532 nm can be achieved experimentally with six layers of graphene oxide (around 12 nm thick). We believe that both the large nonlinear response of graphene oxide and the strong field confinement in the asymmetric MDM nanocavity play the important roles in obtaining the low threshold optical bistability.In this paper, we proposed an optical bistable device with a few layers of graphene oxide integrated in the asymmetric nanocavity, which delivers low-threshold optical bistability at visible frequencies with only few hundreds of KW/cmne oxide ,23 and 22O3 dielectric layer thickness through finite-difference time-domain (FDTD) simulation, covering the whole visible light wavelength range. To apply this asymmetric nanocavity for the nonlinear absorption enhancement of the GO, a 2 nm thick GO layer (corresponding to one layer of GO) is inserted in the middle of the nanocavity. The thickness of the upper and lower Al2O3 layer is optimized to be 40 nm and 45 nm, respectively, to achieve the cavity resonance around 532 nm in the green light wavelength region for the experimental device characterization with lasers in the following section. The three-dimensional schematic diagram of the GO integrated nanocavity structure considered in this work is shown in 2 as shown in 2 for three layers of graphene oxide integrated nanocavity and for six-layer of graphene oxide, the optical bistable threshold of the device is as low as 243 KW/cm2 as shown in To simulate our cavity optical bistability behavior, the third-order nonlinear coefficients of the graphene oxide film need to be deduced first via fitting the measured curves by Z-scan system. Plus, then we build the optical bistability device model with the nonlinear parameters obtained by Z-scan for the COMSOL simulation. The wavelength is set to be 532 nm and the thicknesses of the GO layers are one layer, three layers and six layers for simulation. The optical bistability phenomenon of the three models can be achieved with the COMSOL simulation and the results of optical bistability hysteresis loops are shown in 2O3 film were sequentially deposited on the polished wafer substrate by magnetron sputtering as a pre-fabricated substrate for the preparation of multilayer graphene oxide. Then we prepared 1 mg/mL solution of graphene oxide and put it into an ultrasonic cleaner to ultrasonically disperse it into suspension. The 20% solution of pdda was diluted to 2% solution and then the pre-fabricated substrate was soaked in 2% solution of pdda for one minute. After the pdda solution was evenly adsorbed on the substrate, the excess pdda solution was blow-dried with a nitrogen gun. Then the substrate with pdda was soaked in 1 mg/mL solution of graphene oxide for one minute, and after the anions and cations are attracted to each other, the graphene oxide can be evenly adsorbed on the pdda. The multilayer graphene oxide film can be obtained on the pre-fabricated substrate by repeating the above deposition steps as shown in 2O3 film and the 20 nm gold film were sputtered sequentially on the surface of the multilayer graphene oxide to form a complete nanocavity. The measured and simulated reflection spectra for the GO integrated nanocavity with different layers of GO are illustrated in To experimentally validate our device optical bistability performance, the GO integrated nanocavity device is fabricated as shown in To experimentally demonstrate the device optical bistability behavior, the optical characterization system was built up using the laser with the wavelength of 532 nm. 2, while the switching-down threshold of the device is around 540 KW/cm2. These switching threshold values are much less than those with nonlinear graphene integrated between Bragg reflectors (around 10 GW/cm2) [2) [2 and 414 KW/cm2, respectively, for three layers of graphene oxide integrated nanocavity as shown in 2 and the switching-up threshold is only reduced to around 40 KW/cm2 as shown in The basic issue of optical bistable device is to achieve the switching threshold as low as possible. In  GW/cm2)  or two tcm2) [2) . This lo2. The findings of this paper have important implications for realizing optical storage, optical switches, and optical amplifiers under low-threshold visible light conditions.In conclusion, we have developed an optical bistability device by integrating graphene oxide layers into the metal-dielectric-metal asymmetric nanocavity. The nonlinear absorption of the graphene oxide in the nanocavity can be enhanced, leading to the optical bistability behavior at the wavelength of 532 nm demonstrated both by the simulation and experiment. It can also be found that with the increase of the number of graphene oxide layers, the required threshold for optical bistability decreased. For the first time, we obtained low-threshold visible light optical bistability using graphene oxide as a nonlinear material with a light intensity of 267 KW/cm


The molecular docking technique was used to obtain in silico confirmation of possible interactions between molecules of His6-OPH and Bacitracin as well as the absence of a significant influence of such interactions on the enzymatic catalysis. The in vitro experiments showed a sufficient catalytic efficiency of action of the His6-OPH/Bacitracin combination as compared to the native enzyme. The notable improvement (up to 3.3 times) of antibacterial efficiency of Bacitracin was revealed in relation to Gram-negative bacteria when it was used in combination with His6-OPH. For the first time, the action of the Bacitracin with and without His6-OPH was shown to be effective against various yeast strains, and the presence of the enzyme increased the antibiotic effect up to 8.5 times. To estimate the role of the enzyme in the success of His6-OPH/Bacitracin with yeast, in silico experiments (molecular docking) with various fungous lactone-containing molecules were undertaken, and the opportunity of their enzymatic hydrolysis by His6-OPH was revealed in the presence and absence of Bacitracin.The effect of Bacitracin as an antibiotic acting against Gram-positive bacterial cells was evaluated in combination with hexahistidine-containing organophosphate hydrolase (His Quorum Sensing (QS) is one of the obvious reasons for the formation of resistant microbial biosystems [Today, the search for an effective solution to the problem of resistance in microorganisms and the prevention of the formation of multicomponent microbial highly concentrated populations of cells resistant to various influences and conditions of existence, that are resistant to various influences and conditions of existence in a quorum state, is still relevant  bacterial cells and acts by inhibiting the synthesis of their cell walls, in particular, peptidoglycan [Today, it can be noted that there is maximum interest in AMPs with a wide spectrum of action in relation to Gram-negative (G(−)) and Gram-positive (G(+)) bacterial cells ,6,7. Fordoglycan ,10,11,122+ ions or other divalent cations [55-isoprenyl phosphate (C55-P) is not formed from C55-PP, which, in turn, is a membrane carrier of N-acetylglucosamine (NAG) involved in the construction of the bacterial cell wall, specifically peptidoglycan. Hence, the high efficiency of Bacitracin’s action is precisely in relation to G(+) bacterial cells.It should be noted that Bacitracin has an original mechanism of action: it modifies the substrate of the pyrophosphatase, lipid C55-isoprenyl pyrophosphate (C-PP), in the presence of Zn cations . As a reInterestingly, despite the differences in the structure of the cell wall of G(+) and G(−) bacterial cells, as well as in pro- and eukaryotic cells of microorganisms , all of them are characterized by the structural presence of NAG: chitin is the main component of the cell wall of fungi, and, in fact, peptidoglycan is the most important part of the bacterial cell wall, as well as pseudopeptidoglycan  which presents in archaea cells . Consequ6-OPH), which exhibits lactonase activity against various N-acyl homoserine lactones, which are QS inducer molecules of most G(−) bacteria [Taking into account the above, in this work we investigated the effect of Bacitracin as an antimicrobial substance on different yeast cells. Moreover, in this study we decided to compare the effectiveness of Bacitracin in combination with such QQE as hexahistidine-containing organophosphate hydrolase  bacterial cells, since we noted the interest in the possibility of expanding the spectrum of action of Bacitracin above. The same combination was studied in relation to some G(+) bacterial cells, to compare the Bacitracin action effectiveness alone and in combination with His6-OPH.We decided to test this combination of His6-OPH and various antimicrobial agents to obtain reliable and reproducible results at the first stage of the study was demonstrated earlier in the development of active antibacterial drugs [The effectiveness of using computer modeling methods in studying interactions between Hisal drugs ,4.6-OPH and bacitracin molecules, and the absence of the likelihood of a significant effect of such interactions on enzyme activity, was necessary as a first step in studies of the catalytic and antimicrobial efficacy of the His6-OPH/Bacitracin combination.In this work, the molecular docking method was also applied, which initially allows choosing the most suitable models of molecular interactions and taking into account the presence of a solvent in the reaction medium at different pH values. Obtaining models confirming possible interactions between His6-OPH and various antimicrobial agents to obtain reliable and reproducible results at the first stage of the study was demonstrated earlier in the development of active antibacterial drugs [6-OPH and Bacitracin molecules, and the absence of the likelihood of a significant effect of such interactions on enzyme activity, was necessary as a first step in studies of the catalytic and antimicrobial action efficacy of the His6-OPH/Bacitracin combination.The effectiveness of using computer modeling methods in studying interactions between Hisal drugs ,4. In thTo obtain a model of the interaction of a Bacitracin molecule with a dimeric enzyme molecule and to study the characteristics of this interaction, the molecular docking method was used.6-OPH/Bacitracin were analyzed. In particular, the localization of Bacitracin molecules on the surface of the enzyme dimer, the size of the areas occupied by the molecules of this AMP on the entire surface of the enzyme and near the active sites of the His6-OPH dimer, and the values of the interaction energy  between the molecules in question  and 10.5 . Furthequestion  were con6-OPH/Bacitracin combination in possible catalytic reactions. In this regard, it was concluded that a small negative effect of Bacitracin in the reaction medium on the manifestation of the catalytic activity of His6-OPH should be expected.It was found that Bacitracin has minimal localization near the active sites of the enzyme dimer, while the availability of the enzyme’s catalytic sites for its typical substrates is poorly screened when using the resulting His6-OPH at interaction with other AMPs [It should be noted that rather high total calculated values of affinity (interaction energy) were obtained between functional groups located on the surface of the enzyme molecule and Bacitracin at both studied pH values , which iher AMPs ,5.6-OPH/Bacitracin is the most appropriate for use in practice, from the point of view of stabilizing the catalytic activity of the enzyme, appropriate samples of the combination under study were obtained. Further, these samples of His6-OPH combinations with Bacitracin, formed at pH 7.5 and 10.5, were exposed at 8 °C for 2 h, then used for hydrolysis of a typical substrate of this enzyme and the residual activity was determined  the combination of Histermined .6-OPH/Bacitracin, formed precisely at pH 7.5. The study of the pH of the optimum action of the enzyme in the presence of Bacitracin (the combination was obtained at pH 7.5) and in the absence of AMP  turned out to be better than that of the native enzyme, providing a conformation with a higher rate of hydrolytic reaction with the substrate that has already entered the active site of His6-OPH and formed an enzyme-substrate complex. Interestingly, we have already observed a similar effect of some enzyme partners such as Temporin A and Indolicidin, which are also small AMP molecules, on the catalytic characteristics of His6-OPH [However, the catalytic constant  turned out to be comparable with the same parameter established for the native enzyme. The data are generally consistent with the results of molecular docking: the catalytic activity of the enzyme in the presence of Bacitracin relative to the native enzyme did not change notably.The value of the efficiency constant of the enzyme in the combination of His6-OPH/Bacitracin combination, varying by protein in an aqueous medium, but maintaining a constant ratio between the enzyme and the antibiotic, on the enzymatic activity of the combination itself and the stability of its catalytic properties was studied  bacterial cells  and G(+) bacterial cells , as well as cells of various yeasts , Cryptococcus albidus Y-16, Pachysolen tannophilus Y-475, Kluyveromyces marxianus Y-18, Torulopsis spp. Y-276 and Trichosporon beigelii Y-253) in the absence and presence of His6-OPH  and yeast Pachysolen tannophilus (~8.5 times).G(+) bacterial cells and yeast For many of the studied cultures of microorganisms, there was also a significant decrease in the values of inhibitory concentrations (3.2–3.9 times) necessary for the manifestation of effective antimicrobial activity for the combination of the enzyme with AMP in comparison with a single Bacitracin.6-OPH allowed to assume that the success of the function of the composition indicated that His6-OPH probably exhibits lactonase activity not only against lactone-containing molecules of the quorum of G(−) bacterial cells, but also and in relation to various lactones synthesized by different fungi, including yeast. Among such lactone-containing molecules, secondary metabolites are known, which are used by fungi as metabolism regulating and fighting agents (mycotoxins) and QS signaling molecules [The results obtained with yeast cells in the study of the antimicrobial activity of Bacitracin in the combination with Hisolecules ,18,19,206-OPH on yeast lactones was made based on the known properties of this enzyme, for which we had previously established the ability to effectively hydrolyze various lactone-containing mycotoxins  synthesized by fungi as their own means of protection against competitors using the same substrates [The assumption about the possible hydrolytic effect of Hisbstrates .6-OPH, an in silico study was conducted in which molecular docking of various lactone-containing fungal molecules to the surface of the His6-OPH dimer was performed , their localization in the catalytic sites of the enzyme was visible  bacterial cells. The latter is confirmed by the effectiveness of the enzyme in combination with APM  to the surface of the enzyme dimer molecule , which mn showed  that a h typical . The the6-OPH/Bacitracin against bacteria and yeast  bacterial cells than many analogues under similar conditions [6-OPH, its effect is significantly improved.A comparison of the effectiveness of Bacitracin action with other previously studied AMP variants in combination with Hisnditions . With re6-OPH/Bacitracin, as it turned out    from amoCandida [The possibility of spreading the applied approach, namely, combining QQE with antibiotics, to the development of highly effective antimicrobial drugs seems simple and attractive not only for use against bacteria, but also to cells of other microorganisms, including those involved in the formation of various heterogeneous consortia in the form of biofilms based on pro- and eukaryotes, in particular, bacteria and yeast of the genus Candida ,35.6-OPH dimer was prepared using known crystallographic structure of OPH (PDB: 1QW7) which was modified by His6-tag as described previously [The structure of His PDB: 1QW which waChemBioDraw software  and ChemBio3D were used to create ligands (Bacitracin and lactones) structure and to apply energy minimization with force field MM2.http://www.poissonboltzmann.org/, accessed on 18 August 2022) with PARSE forcefield and default settings were used to calculate the surface charge distribution of both His6-OPH and Bacitracin [http://mgltools.scripps.edu/, accessed on 18 August 2022) with atomic charges calculated with the Gasteiger-Marsili method [Adaptive Poisson-Boltzmann solver (APBS) and PDB2PQR servers , which includes several terms in its own scoring function  was used for docking [6-OPH dimer obtained at the same pH values. That was made on a desktop computer equipped with Intel Pentium Dual-Core CPU E5400 2.7 GHz and 3 GB of available memory. Briefly, the grid box was approximately centered on the center of mass of the His6-OPH dimer. The size of the grid box was chosen so that the enzyme surface was within the box with an additional margin . Calculations were performed with default program options. Based on our previous studies with His6-OPH and results obtained in the development of new effective antibacterials [AutoDockVina  was defined as the quantity of the enzyme necessary to hydrolyze 1 μmol of Paraoxon per min at 25 °C. The purity and specific activity of His6-OPH preparation obtained (MW ≈ 37 kDa) was ca. 98% and 6000 U/mg.His methods . In shor6-OPH were prepared according to the following procedure: solution of Bacitracin at concentration of 0.8 g/L in 50 mM K-phosphate buffer (pH 7.5) or 50 mM Na-carbonate buffer (pH 10.5) containing 150 mM NaCl, were mixed with solution of 1 g/L His6-OPH in the same buffer at 1:1 (v/v) ratio and exposed for 30 min at room temperature. The final concentrations of His6-OPH and Bacitracin were 41 mg/L and 32 mg/L, respectively. After that enzyme activity of the combination prepared was measured as described earlier while varying Paraoxon concentration in a reaction mixture from 10 to 200 µM to determine catalytic characteristics.Combinations of Bacitracin with Hism) and the maximum rate of enzymatic reaction (Vmax) were calculated by hyperbolic approximation using the least squares method in Origin Pro . The obtained Km and Vmax values were further used to calculate catalytic constant (Vmax/E0) and action efficiency constant (Vmax/(E0 × Km) values for enzymatic activity.The values of the Michaelis constant , 50 mM phosphate/100 mM carbonate buffer (pH 8.0) and 100 mM carbonate buffer .50) value of Bacitracin alone or in combination with His6-OPH (1 g/L) was determined as described previously [Agrobacterium tumefaciens B-8833, Escherichia coli DH5α, Pseudomonas sp. 78G, Bacillus subtilis B-522) and yeasts  were used.50% inhibitory concentration : glucose—10, yeast extract—5, tryptone—10, Na citrate—1, K2HPO4·3H2O—3, MgSO4·7H2O—0.5, ascorbic acid—3. The bacterial and yeast cells were cultivated using a thermostatically controlled Adolf Kuhner AG shaker  at 28 °C (for G(−), and yeasts) and 30 °C (for G(+)), with stirring at 150 rpm.To accumulate biomass, the cells of bacteria Cell growth was monitored with an Agilent UV-8453 spectrophotometer  at 540 nm.6 cells/mL) prepared on basis of 100 mM carbonate buffer (pH 8.0) with Zn2+ ions (10−5 M) to provide the His6-OPH conditions for activity realization were used in the experiments. The cells were exposed at room temperature for 24 h with Bacitracin added in a concentration range from 0 to 32 mg/L.All microorganisms were separated after cultivation from the nutrition media by centrifugation. Further, the cells as suspensions in a saline (ca. (1 ± 0.1) × 1050.The concentration of intracellular ATP was determined using a standard ATP reagent  and luciferin-luciferase method to evaluate the residual concentration of viable cells in exposed samples using published procedure . The intAll data are presented as means of at least three independent experiments ± standard deviation (±SD). Statistical analysis was realized using SigmaPlot .6-OPH enzyme and such AMP as Bacitracin was obtained and the expediency of combining them in silico and in vitro was demonstrated. To the best of our knowledge, the antimicrobial activity of Bacitracin against yeast cells was demonstrated for the first time and an increase in its effectiveness in the presence of His6-OPH was established. The results of in silico studies once again confirmed the appropriateness of using computational methods as relatively fast and reliable way to predict effectiveness of such combinations of His6-OPH. These studies have allowed to obtain data according to which the reason for the success of the action of the His6-OPH/Bacitracin combination on yeast cells can be associated, as in the case of G(−)-bacterial cells, not only with the universal action of the antibiotic itself, but also with the ability of the enzyme used in the work to catalyze the hydrolysis of microbial lactone-containing molecules important for the metabolic and functional activity of microorganisms, as well as for their stable viability.Thus, in this study, a new effective combination of His


We demonstrate that a neural network automatically solves, explains, and generates university-level problems from the largest Massachusetts Institute of Technology (MIT) mathematics courses at a human level. Our methods combine three innovations: 1) using recent neural networks pretrained on text and fine-tuned on code rather than pretrained on text; 2) few-shot learning synthesizing programs that correctly solve course problems automatically; and 3) a pipeline to solve questions, explain solutions, and generate new questions indistinguishable by students from course questions. Our work solves university-level mathematics courses and improves upon state-of-the-art, increasing automatic accuracy on randomly sampled questions on a benchmark by order of magnitude. Implications for higher education include roles of artificial intelligence (AI) in automated course evaluation and content generation. We demonstrate that a neural network pretrained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI’s Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a dataset of questions from Massachusetts Institute of Technology (MIT)’s largest mathematics courses  and Columbia University’s Computational Linear Algebra. We solve questions from a MATH dataset , the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pretrained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8 to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work automatically solves university-level mathematics course questions at a human level and explains and generates university-level mathematics course questions at scale, a milestone for higher education. Until this work, it was widely believed that neural networks could not solve advanced mathematics problems . HoweverTransformers are deep-learning architectures based only on attention mechanisms  that do 4Pretraining a transformer is computationally expensive and often involves vast amounts of unlabeled data. The most common optimization objectives for pretraining language models are 1) masked word prediction, predicting a random deleted word in a sentence or predicting the next word, and 2) classifying whether two sentences follow each other. This computationally expensive step is usually done once, followed by a relatively fast fine-tuning step. In fine-tuning, the pretrained model is tuned using a specific dataset or task.This work demonstrates that OpenAI’s Codex , a transPrevious work has seen modest success on simpler or specialized mathematics problem benchmarks. Techniques based on cotraining output to verify , 10 or p11Our main contribution, as shown in This methodology increases the solution accuracy on the MATH benchmark  from 8.8The methods we propose are simple and broadly applicable. The first one uses a transformer model pretrained on text and fine-tuned on code so that it is adept at synthesizing programmatic solutions. The second one uses zero-shot learning of the questions as is or automatically added contextual information about the problem or program. The third one uses few-shot learning based on question–code pairs of similar questions that have been solved, found by using the cosine similarity of the question embeddings.We randomly sample 25 questions from each of the seven courses: MIT’s 18.01 Single Variable Calculus, 18.02 Multivariable Calculus, 18.03 Differential Equations, 18.05 Introduction to Probability and Statistics, 18.06 Linear Algebra, and 6.042 Mathematics for Computer Science and Columbia University’s COMS3251 Computational Linear Algebra. For the MATH dataset, we randomly sample 15 questions from six topics in the dataset . We validate that our results are not merely overfitting training data by solving questions from a new Computational Linear Algebra course COMS3251 that is unavailable online and was unseen by Codex when trained. We automatically obtain correct answers for 81% of the randomly sampled university math course questions and 81.1% of the MATH benchmark questions. Before this work, the previous state of the art on this benchmark was 8.8% , specifying that the program synthesized to solve the problem should use this package.Likewise, the best results are obtained when the Codex prompt specifies which programming package should be used. For instance, we may add the Python library SymPy as context  and require tidying to extract the essence of the question. Question tidying primarily involves removing redundant information, breaking down long sentence structures into smaller components, and converting prompts into a programming format.Another form of manual prompting occurs when an answer involves a plot and requires multiple steps to generate a visually pleasing and clear plot. These special cases, which are among the remaining 19% of the questions, require interactively prompting Codex until reaching the desired visualizations.Explanations are generated automatically using the question, the code generated by Codex when prompted with the question, and a prompt consisting of three quotes followed by the text “Here is what the above code is doing: 1.” This prompt is given after both the question and the generated code since the code may be a lossy representation of the question. The result is a step-by-step explanation of the solution code given to Codex.We also use Codex to generate new questions for each course. This is done by creating a numbered list of human-written questions from each class. This list is cut off after a random number of questions, and the result is used to prompt Codex to generate the next question. This process is repeated to create many new questions for each course.To evaluate the generated questions, we survey MIT students who have taken these courses or their equivalents to compare the quality and difficulty of machine-generated questions with human-written questions for each of the courses. The Institutional Review Board (IRB) that approved the survey is MIT IRB Exempt Id E-3792. The survey was optional and included informed consent, with the following description: “We are conducting a survey to assess the quality and difficulty of automatically generated questions for science, technology, engineering, and mathematics (STEM) courses. You will be presented with a series of blocks consisting of questions, either human-written  or generated with machine learning, but you will not be told the source of a given question. For each question, you will be asked (a) whether you think the question is human-written or machine-generated, (b) whether the question is appropriate for the given course, and finally, (c) how you would rate the difficulty of the question. Please carefully read each question and answer to the best of your ability.” We randomly sampled five original, human-written questions and five generated questions for each of the six MIT courses. Students are asked to read these 10 questions per course in the survey, mixed and presented randomly.For each of the 60 questions, the students are asked 3 survey questions: 1) “Is the question human-written or machine-generated?”, 2) “Is the question appropriate or not appropriate for the specific course?”, and 3) “What is the question’s difficulty level on a scale between 1 (easiest) and 5 (hardest)?”. An example of this survey format is given in SI Appendix. These 265 questions include 25 randomly sampled questions from each of the seven courses (18.01/18.02/18.03/18.05/18.06/6.042/COMS3251) and 15 randomly sampled questions for each of the six topics in the MATH dataset . The breakdown of automatic solve rate by zero-shot and few-shot learning using Codex compared with GPT-3 and GPT-3 with CoT is shown in We solve 265 questions, 213 of them automatically, as described in Top Right. In Left, we see a collection of the questions representing calculus from MIT’s 18.01 Single Variable Calculus, 18.02 Multivariable Calculus, and 18.03 Differential Equations. In Bottom Right, we see a cluster of the questions from MIT’s 18.05 Introduction to Probability and Statistics and 6.042 Mathematics for Computer Science, covering probability and statistics.We embed the 175 mathematics course questions onto a 2,048-dimensional space using OpenAI’s text-similarity-babbage-001 embedding engine, which captures semantic similarity between texts. We then use uniform manifold approximation and projection (UMAP) ,19 to reSI Appendix to demonstrate this capability. These include 10 new questions for each of the seven courses and each of the six MATH topics. We generate new questions for each course and topic by prompting Codex with numbered human-written questions to generate the next question automatically. Specifically, we create prompts of 25 randomly selected problems for which Codex generates correct answers, remove the questions after a randomly chosen question in the list, and have Codex complete the next new question. We present 130 new questions generated by Codex in Left) and the percentage of machine-generated questions rated as human written or machine generated (Right).Fifteen participants completed our survey, answering questions about all 60 questions, taking a median of 40 min. •Survey participants rated our machine-generated and human-written questions to be similar in difficulty within CIs.•Survey participants rated human-written questions slightly more appropriate for the courses than machine- generated ones.•Left. Survey participants rated machine-generated questions equally likely to be machine generated and human written as shown in Right.Survey participants rated human-written questions more likely to be human written as shown in The student survey results are summarized as follows:With our methodology, Codex reaches human performance levels in the contexts of both solving existing questions and generating new content. We achieve 81% automatic accuracy in solving mathematics course problems at MIT and Columbia, comparable to typical student performance on these problem sets in our MIT and Columbia University courses. Furthermore, we automatically generate new questions that are indistinguishable to students from human-written course questions.We make our data and code publicly available . We use Few-shot learning prompts are structured as follows: For each question–code example being used, we insert the question in a docstring on the following available line, have a line break, and then insert the code on the following lines. After all the examples, we insert the target question at the end in the same way as described above and prompt Codex.CoT prompts for GPT-3 are implemented by adding the text “Let’s think step by step”  after thThere are a few different types of problems the model is incapable of solving: 1) any problem for which the question is in the form of an image or other nontext modality; 2) questions with solutions that require proofs; and 3) problems that are computationally intractable, such as factoring very large primes. This last category is not expected in any math course assignment, as students themselves would also be unable to answer them. That being said, many questions that students can answer have generalizations that are computationally intractable.We demonstrate that few-shot learning and program synthesis using OpenAI Codex is able to solve, explain, and generate university-level mathematics problems at a human level. In contrast, previous methods using transformers pretrained only on text, such as GPT-3, fail on these tasks. We verify that our strong results are not overfitting the training data by solving a new course that is not available online. We also generate and analyze new problem sets. The success of this work confirms that programs serve as a good representation and computation environment for solving math problems. Since our approach requires no additional training, it is easily scalable. This work addresses significant pedagogical challenges, bringing substantial benefits to higher education like curriculum design and analysis tools and automatic content generation.We show that neural network synthesis with modern programming languages is more dynamic and widely applicable than expression trees and likely solves a broader range of problems. Although any finite computation could be expressed as a sufficiently large expression tree, one may see an arbitrarily large expansion in the size of the expression tree needed, as opposed to a Turing-complete language. This flexibility is bolstered by the massive corpus of existing programs, which eclipses the number of labeled expression trees available. Program outputs are also inherently more human readable, as the ability to use abstraction, modularity, and high-level logic leads to more explicit illustrations of the path to a solution. Furthermore, program synthesis can convey logical deductions directly through explanatory comments and function and variable names. In particular, we see such descriptive text and derivations in a number of the Codex outputs. The unification of such formal and informal language is an inherent advantage of our methodology. We emphasize that the results may be complex and multimodal. For example, by using packages such as Matplotlib, we can produce graphs of equations. This advanced and unique ability is time consuming for humans and offers a significant pedagogical benefit.In summary, we automatically solve, explain, and generate university-level mathematics course questions in real time at a human level . StudentSupplementary File


Herein, we report a Diels–Alder (DA) based crosslinked polyacrylonitrile/graphene nanocomposite (PAN-DA/GR), which has multiple-responsive properties of shape memory, self-healing, and reprocessing in addition to enhanced mechanical properties. The graphene sheets, which are well dispersed in the DA-based crosslinked PAN network, can act as intrinsic localized thermal sources by converting the absorbed external IR/microwave energies into heat, to trigger the glass transition for elasticity-based shape memory properties and retro-DA (rDA) reactions for healing. The incorporation of Diels–Alder bonds also gives the material solid state plasticity through topological network rearrangement, thus leading to versatile shape adaptability. Moreover, both regional shape control and targeted self-healing of the nanocomposites can be simply achieved by IR laser irradiation. Besides, the incorporation of a small amount of graphene can significantly improve the mechanical strength with respect to the DA-based crosslinked PAN. Both DSC and  A Diels–Alder covalent bond based crosslinked polyacrylonitrile/graphene nanocomposite is reported, which has the multiple-responsive properties of shape memory, self-healing, and reprocessing in addition to enhanced mechanical property. Inspired by the biological healing function in nature, self-healing polymers have been the focus of recent studies on stimuli-responsive polymer materials,15–24 due to their capability of self-healing after suffering from damage or fractures. In particular, reversible crosslinking using dynamic covalent bonds, such as the reversible Diels–Alder (DA) reaction,25,26 provides a new strategy to overcome the above difficulty in crosslinked SMPs.27–29 However, most of the DA-based SMPs can only be healed or reprocessed by heating-induced retro-DA reaction, which could severely limit their applications in a wide range of circumstances. Therefore, until now, it still remains a great challenge to develop crosslinked SMPs with superior mechanical properties and excellent capability of rapid self-healing and recycling via multiple approaches.Although significant advances have been achieved for the development and fabrication of high performance polymeric materials in recent decades, it still remains a great challenge to integrate superior material properties, such as shape memory, self-healing and recycling, multiple-responsiveness to external stimuli, into one structure by precise design of molecular architectures.30–34 Moreover, graphene can absorb IR and microwave energies and instantly converts them into heat, and thus enable the polymer materials with self-healing property by multiple approaches. Besides, the Diels–Alder bonds can also render the material solid state plasticity through topological network rearrangement at an elevated temperature, and thus leading to versatile shape adaptability. Therefore, it is expected that the combination of graphene and thermo-reversible Diels–Alder (DA) reaction can provide an attractive avenue to prepare novel multiple-responsive nanocomposites with shape memory, self-healing and recycling properties. Recently, we have demonstrated that rapid self-healing and recycling for the epoxy resin (ER) can achieved by simultaneously incorporating thermally reversible DA covalent bonds and graphene into the ER matrix.35 Herein, we further report a thermally reversible DA-crosslinked polyacrylonitrile/graphene nanocomposites (PAN-DA/GR) with outstanding mechanical strength as well as self-healing and shape memory properties triggered by multiple approaches. The well-dispersed graphene sheets in proximity to the DA crosslinkages can act as an intrinsic localized thermal source, by converting absorbed energies  into heat, to induce the polymer glass transition and trigger retro-DA (rDA) reactions. As a result, shape memory capability can be controlled by the glass transition at a temperature beyond Tg, whereas the self-healing/recycling properties can be achieved when the temperature is higher than rDA temperature (TrDA). Hence, the incorporation of graphene not only improves the mechanical properties with respect to the pristine crosslinked polymer, but also enables controlling the materials properties of self-healing, recycling and shape memory via multiple approaches including IR light, microwave and heating, as shown in Due to the outstanding mechanical properties of graphene, it has been widely used as a nanofiller for the fabrication of mechanical enhanced nanocomposites.Tg of the polymer nanocomposite from the rDA reaction temperature TrDA, methyl butylacrylate (BA) (∼15 wt%) and glycidyl methacrylate (GMA) with epoxy group (∼10 wt%) was co-polymerized with acrylonitrile (AN) monomers to obtain PAN-epoxy compounds. Subsequently, PAN-epoxy was dissolved in DMF solvents in together with furfurylmercaptan (2.8 g) and triethylamine to obtain linear PAN-furan for further DA reaction with bismaleimide (BM), i.e. PAN-DA compounds. For the PAN-DA/GR nanocomposites, PAN-furan, BM and reduced graphene oxide were both dissolved in NMP solvent for the DA reaction at 60 °C. Four samples, corresponding to a graphene weight fraction of 0, 0.2%, 0.4% and 0.6%, were prepared and named as PAN-DA/GR, PAN-DA/GR-0.2, PAN-DA/GR-0.4, PAN-DA/GR-0.6, respectively. More details about the chemical synthesis and the experimental details about the characterization methods can be found in the ESI.†The schematic procedures for the preparation of PAN-DA/GR nanocomposite is shown in via DA reaction between furan pendant groups in linear PAN-furan and the maleimide groups of cross-linker BM. In this way, thermal reversibility, related to recyclability and self-healing ability, can be achieved by the rDA reaction. (2) The monomers BA and GMA were incorporated into linear PAN to adjust the Tg of the nanocomposite that controls the shape memory property, so that the glass transition is not overlapped with the rDA reactions. In addition, it also greatly enhanced the mechanical toughness of the polymer. (3) The incorporation of a small amount of graphene not only improves the mechanical strength, but also remarkably enhances the efficiency of healing and recycling and enables controlling shape memory property via multiple approaches including IR light, microwave and heating due to the multiple-responsive nature of graphene. Besides, regional shape memory property and targeted self-healing can be achieved in response to local IR irradiation. Herein, a multiple-responsive crosslinked SMP with excellent mechanical properties and superior capability of rapid self-healing and reprocessing as well as shape-memory property is well demonstrated.Our key ideas of the molecular design shown in in situ variable temperature solid-state 13C NMR spectroscopy have been well explored and widely used for the investigation of reversible DA reactions. −1. In fact, complete separation of the enthalpy change induced by the glass transition and rDA reaction can be achieved by temperature modulated DSC (TOPEM) experiment, which is a new stochastic temperature-modulated DSC technique introduced by Mettler-Toledo in late 2005  solid-state 13C NMR experiments were further used to demonstrate the reversibility of DA reaction at the molecular level. Due to the enhanced segmental mobility at the high temperature, which will significantly decrease the cross polarization (CP) efficiency, a recently developed novel 13C CPNOE technique37 was utilized. Thus, the 13C signals of rigid components can be enhanced by CP, while that of mobile components can be enhanced by the NOE (nuclear Overhauser effect)-based polarization transfer. 13C CP spectra of PAN-AN/GR-0.4 nanocomposite at a thermal cycle of 25 °C (black), 135 °C (red) and 25 °C (blue), respectively. It is clearly shown that the peaks at 92 and 82 ppm associated with DA-bonds disappeared when temperature was increased from 25 °C to 135 °C; meanwhile, the intensities of small peaks associated with free furan groups  grow significantly. The above results unambiguously confirm the presence of unreacted furan moieties in the system due to the disassociation of DA adducts at the high temperature. When the sample temperature was decreased to 25 °C, the 13C spectrum is identical to that obtained before increasing the temperature, indicating that the DA-based crosslinked network was completely reconstructed after the thermal cycle. Because the IR light and microwaves irradiation can be absorbed and converted into heat, the above SSNMR results also indirectly confirm the reversible DA/rDA reactions under IR or microwave irradiation.Graphene is well known as a nanofiller for enhancing the mechanical strength. As shown in 38,39 In general, most shape memory behaviors origin from the elasticity of polymers, where the entropic energies can be stored and released via conformational changes of polymer chains. As a result, glass transition has been often used for controlling shape memory properties, where the crosslinkages act as the fixed phase whereas the glassy chains are used as the reversible phase. In contrast, polymer plasticity, where permanent polymer reshaping without melting can be achieved through dynamic bond exchange, has gain dramatic attention in recent years.40–43 Particularly, polymer plasticity through DA reaction has been recently examined in the crosslinked epoxy resin network.27 Herein, the elasticity and plasticity natures of PAN-DA/GR nanocomposites were well demonstrated by multiple approaches including heat, IR and microwaves, taking the PAN-DA/GR-0.4 as a typical example. TrDA. A fixed strain of 15% was initially loaded, and the stresses relaxed faster with increasing the temperature due to the shifted dynamic equilibrium towards rDA reactions. As is clearly seen, complete stress relaxation takes about 5 min at a temperature of 135 °C, which enables faster shape manipulation. Therefore, below we will explore the dynamic bond-based plasticity of PAN-DA/GR-0.4 sample at 135 °C. Quantitative demonstration of the shape-memory property of PAN-DA/GR-0.4 was measured under a stress-controlled mode with identical deformation and recovery temperatures of 75 °C in consecutive shape memory cycles shown in Tg and blow TrDA. The little deviation in these three cycles also means that the plasticity is suppressed under the temperature of 75 °C for the elastic shape memory experiment. As a result, the thermally distinct elasticity and plasticity can be probed in consecutive thermomechanical cycles as shown in Rret = ε/εload, where ε and εload corresponds to the strain amplitude at the specific plasticity temperature (135 °C) after and before load removal, respectively. Shape memory effect at highly deformation is still good  has greatly increased the Young's modulus and tensile strength at break with slight compromise at the elongation ratio at break. Furthermore, the elasticity and plasticity natures of such SMPs were well demonstrated by multiple approaches including heat, IR and microwave irradiation, in addition to rapid self-healing and recycling properties. Indeed, the incorporation of Diels–Alder bonds has rendered the material solid state plasticity through topological network rearrangement, and thus leading to versatile shape adaptability. The cycle-to-cycle DMA experiments showed quite good repetition of shapes, indicating excellent shape memory behaviours for this nanocomposite. In fact, the graphene in proximity to the DA crosslinkages can act as an intrinsic localized thermal source, by effectively converting the absorbed external energies into heat, to trigger the glass transition for shape memory property and rDA reactions for self-healing/recycling. Local shape memory property and targeted self-healing can be achieved by IR laser irradiation. Our experimental findings here well demonstrated that the PAN-DA/ER nanocomposites could be a promising self-healing and shape memory material and find wide applications in various fields. Overall, the current work could also provide guidance for the design and fabrication of high-performance shape-memory polymers with rapid self-healing, recyclability and multiple-responsibility.In summary, a multiple stimuli-responsive thermally reversible crosslinked PAN-DA/GR composites is reported here by simultaneously incorporating Diels–Alder (DA) covalent bonds and multiple-responsive graphene into the PAN-DA matrix. DSC and There are no conflicts to declare.RA-008-C7RA11484B-s001RA-008-C7RA11484B-s002