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Male Long–Evans rats were obtained from Charles River at 8–10 weeks old. Rats were pair housed in a colony maintained on a 12 h light/dark cycle, and were given food and water ad libitum outside of behavioural training. During training, rats were given food ad libitum but worked in a closed economy for water, obtaining 15 ml of 5% sucrose solution during the task. Experimental protocols were approved by Stanford University IACUC to meet guidelines of the National Institutes of Health guide for the Care and Use of Laboratory Animals. Sample sizes were chosen to meet or exceed those in previously published accounts of cognitive and decision-making tasks in rats31, 32. Post-hoc tests then verified adequate statistical power given the observed effect sizes (see ‘Power analyses’). All behaviour was assessed in operant chambers (Med Associates). One wall of the operant chamber was arranged such that the sucrose port (Med Associates ENV-200R3BM) was positioned in the bottom centre slot. The nosepoke (Med Associates ENV-114BM) used to initiate each trial was slotted immediately above the sucrose port. The retractable choice levers (Med Associates, ENV-112CM) were on either side of the sucrose port (Extended Data Fig. 1). In the first phase of training, both levers were extended into the chamber, and every press resulted in 50 μl sucrose reward. Rats were given two hours to earn and retrieve 150 total sucrose rewards. Most rats completed this phase in one day. In the second phase of training, a randomly-selected lever entered the chamber and retracted when pressed. Every press resulted in a 50-μl sucrose reward. Rats were given 2 h to earn and retrieve 200 sucrose rewards. In the third phase of training, rats were trained to initiate each trial with a one-second nosepoke. On the first trial, the rat was required to nosepoke for 250 ms, after which both levers would enter the chamber. The rat would then press a lever to obtain a 50-μl sucrose reward. In each subsequent trial, the length of the required nosepoke incremented by 5 ms. Rats were given 2 h to complete 200 lever presses. In the final phase of training, rats were exposed to the behavioural task described in Fig. 1a. Each trial was initiated with a 1-s nosepoke. If the rat failed to hold the nosepoke for 1 s, it could try again immediately without penalty, but the 1-s clock would start again from zero. One lever always delivered a 50-μl reward, while the other delivered a 10-μl reward with 75% probability and a 170-μl reward with 25% probability (expected value = 50 μl). These objective expected values were held constant throughout the task. For the first 50 ‘forced choice’ trials, one randomly chosen lever entered the chamber, and the rat pressed it to obtain its reward. For the remaining 200 ‘free choice’ trials, both levers entered the chamber and the rat was allowed to choose. Rats were trained until their fraction of risky choices across three consecutive days varied by less than 10%. On average, rats required approximately 5 sessions in the final phase of training before reaching a stable behavioural baseline (mean = 4.85, s.d. = 2.29). In total, 12 out of 132 rats failed to learn the task. Rats were excluded from experiments if they failed to learn the initial lever pressing task, lost a fibreoptic implant before the conclusion of testing, or failed to develop stable baseline behaviour; these criteria were established in advance of experimentation. All cell counting data collection in Extended Data Figs 5, 6, 7 was conducted blinded to condition; the behavioural experimenter was not blind to the risk preference of each animal, but instead all behaviour was conducted while the experimenter monitored the rats from a different room, so as not to influence the animals’ choices. To validate rat sensitivity to relative expected value across the two levers, rats were trained to a stable baseline, as described above. The expected value of the safe lever was then systematically increased across days, to map out behavioural response curves (Extended Data Fig. 1b). To validate that rats’ choices were due to preference for the safe or risky reward schedule, rather than simply to side bias or indifference, rats were trained to a stable baseline. The location of the risky lever was then alternated between left and right levers at an uncued time in blocks of 100–250 trials (Extended Data Fig. 1c). Trial lengths for these blocks were on the order of the number of trials used in the main gambling task (200 free choice trials). The loss-sensitive index is determined as shown in equation (1). PPX (Sigma-Aldrich, A1237) and A-77636 hydrochloride (Tocris Biosciences, 1701) were diluted in physiological saline and injected intraperitoneally 30 min before the start of the task at the doses described in Fig. 2. A large cohort of animals was trained to conduct this experiment, and separate animals within the cohort were used for each drug dose. Animals were trained to a stable baseline, as described above, before drug injections were initiated. Surgeries were performed on 8–10-week-old rats. Rats were anaesthetized with 2–3% isofluorane; scalps were shaved, and subjects were placed in a stereotactic head apparatus. Rats received a subcutaneous injection of buprenorphine (0.01 mg kg−1) and a subcutaneous injection of lactated ringer’s solution (3 ml). Ophthalmic ointment was applied to prevent eyes from drying. A midline scalp incision was made, and a craniotomy was drilled above each injection or fibre implantation site. For intracranial drug infusion, guide cannulas (PlasticsOne, C313G) were implanted bilaterally. OFC cannulas were implanted at (A/P 4.5, M/L ±1.4, D/V −4.2; all coordinates in mm and relative to bregma (here and below)). NAc cannulas were implanted at (A/P 1.5, M/L ±1.8, D/V −6.5). In both NAc and OFC, left cannulas were implanted vertically while right cannulas were implanted at a 20° angle. Dental adhesive (C&B metabond, Parkell) was applied and dental cement (Stoelting) was added to secure the cannulas to the skull. For photometry and optogenetics experiments, virus was injected with a 10-μl glass syringe and a 33-gauge beveled metal needle (World Precision Instruments). Importantly, virus should be injected at a titre no greater than 3 × 1012 viral particles per ml to avoid potential cytotoxicity and diluted in ice-cold PBS if necessary. The injection volume and flow rate (750 nl at 150 nl min−1) were controlled by an injection pump (Harvard Apparatus). Each NAc received two injections (A/P 1.5, M/L ±1.8 mm, D/V −7.6 and −7.0). After injection, the needle was left in place for 5 additional minutes and then slowly withdrawn. All rats were injected and implanted bilaterally. In each NAc, an 8-mm fibre stub, terminated with a 2.5-mm diameter ferrule was implanted at (A/P 1.5 mm, M/L ±1.8 mm, D/V −7.2 mm). Left cannulas were implanted vertically while right cannulas were implanted at a 20° angle. For stimulation, a 30-μm core diameter, 0.37 numerical aperture (NA) fibre was used; for photometry, a 400-μm core diameter, 0.48-NA low-autofluorescence fibre with low-fluorescence epoxy for photometry (implantable fibres assembled by Doric Lenses, using fibre manufactured by ThorLabs or CeramOptec). Dental adhesive (C&B metabond; Parkell) was applied and light-curing composite (Flow-It ALC, Pentron Clinical, N11VH) was added to secure the ferrules to the skull. All behavioural experiments occurred at least 3 weeks after virus injection. Rats’ innate behaviour determined their assignment to ‘risk-seeking’ or ‘risk-averse’ groups. For optogenetic manipulations, half of the rats were randomly assigned to ChR2 or YFP (control) groups. For photometry, each excitation source was set to an average power of 30 μW at the fibre tip. Light was delivered through a 400-μm core diameter, 0.48-NA low-fluorescence patch cord (Doric Lenses) and joined to the implanted fibre ferrules using zirconia sleeves (Thorlabs). Recording location (left or right NAc) was balanced across subjects. For optogenetic stimulation, light pulses were administered for 1 s at 20 Hz at a power of 15 mW per side (0.75 mW per side corrected for duty cycle). Decision period stimulation began when the rat initiated a nosepoke. Outcome period stimulation occurred in the 1 s after sucrose port entry. Light was delivered through a 300-μm core diameter, 0.37-NA fibre (Thorlabs), fed through a fibre optic rotary joint (Doric Lenses, FRJ_1x1_FC-FC), and split into two beams using a Doric minicube (Doric Lenses,DMC_1x2i_VIS_FC). At each output of the minicube a 0.5-m, 300-μm core diameter, 0.37-NA fibre, terminating in a 2.5-mm ferrule (Thorlabs) was attached. Each fibre was sheathed in a steel spring to protect from chewing (PlasticsOne) and joined to an implanted fibre ferrule using a zirconia sleeve (Thorlabs). Rats were anaesthetized with 1–2% isoflurane and were placed in a stereotactic head apparatus. PPX was dissolved in saline (10 μg μl−1, 0.9% NaCl). Thirty minutes before the behaviour, 0.5 μl of the PPX solution was infused in each side of OFC or each side of NAc via an internal infusion needle (PlasticsOne, C313I) inserted into the guide cannula. The internal needle was connected to a 10-μl Hamilton syringe (Nanofil; WPI). Flow rate (0.1 μl min−1) was regulated by a syringe pump (Harvard Apparatus). Cannula locations were verified in Nissl-stained sections. Infusions were conducted in an ABABA design, alternating infusions of saline or PPX across days. Rats were anaesthetized with Beuthanasia and perfused transcardially, first with ice-cold PBS (pH 7.4) and then with 4% paraformaldehyde (PFA) dissolved in PBS. The brains were removed and post-fixed in 4% PFA overnight at 4 °C, and then equilibrated in 30% sucrose in PBS. Forty-micrometre-thick coronal sections were prepared on a freezing microtome (Leica) and stored in cryoprotectant (25% glycerol and 30% ethylene glycol in PBS, pH 6.7) at 4 °C. Cell counts were conducted by blinded experimenters. For anti-D2R staining, (Millipore, AB1558) was used as described below. For anti-ChAT staining (Millipore, AB144P) was used as previously described33. For anti-GFP staining (Life Technologies, A-31852) was used as previously described28. For D2R staining, the following protocol was used: (1) rinse 40-μm sections in PBS (pH 7.4), 3 × 10 min. (2) Block in PBS plus 3% normal donkey serum and 0.3% Triton-X (PBS++) for 30 min. (3) Incubate in primary antibody (rabbit anti-D2R, Millipore ab1558) at 1:200 in PBS++ for 24 h at room temperature on a rotary shaker. (4) Wash slices for 4 × 15 min in PBS. (5) Incubate in secondary antibody (Alexa-fluor 647, goat anti-rabbit, Life Technologies, A-21245) at 1:200 in PBS++ overnight at room temperature on a rotary shaker. (6) Wash slices for 4 × 15 min in PBS. (7) Incubate in tertiary antibody (Alexa-fluor 647, donkey anti-goat, Life Technologies, A-21447) at 1:500 in PBS++ for 8 h at room temperature on a rotary shaker. (8) Wash for 15 min in PBS. (9) Wash for 15 min in 1:50,000 DAPI in PBS. (10) Wash for 15 min in PBS and mount with PVA-DABCO. We developed a novel dopamine D2R-specific promoter (D2SP) for expression of transgenes in rat D2R+ cells compatible with use in a single AAV vector (Extended Data Fig. 5). The new 1.5-kb D2SP fragment was taken from a region immediately upstream of the rat D2R (also known as Drd2) gene (full sequence: Extended Data Fig. 5), differing from a previously reported D2R promoter region34 by excluding exon 1 and including a Kozak sequence inserted between the promoter region and the gene that it controls. D2SP was amplified from rat genomic DNA using primers 5′-CGCACGCGTTTATCCTCGGTGCATCTCAGAG-3′ and 5′-GGCGGATCCCCCCGGCACTGAGGCTGGACAGCT-3′ digested with MluI and BamHI and ligated with pAAV-hSYN-eYFP or pAAV-hSYN-hChR2(H134R)-eYFP digested with the same two enzymes to yield pAAV-D2SP-eYFP or pAAV-D2SP-hChR2(H134R)-eYFP, respectively. pAAV-D2RE-eYFP was constructed using the D2R promoter sequence described previously34 to replace the hSYN promoter in pAAV-hSYN-eYFP. pAAV-D2SP-eChR2(H134R)-eYFP was constructed with the ER export motif and trafficking signal as described previously29. pGP-CMV-GCaMP6m (Addgene plasmid 40754) and pGP-CMV-GCaMP6f Kim (Addgene plasmid 40755) were a gift from D. Kim. The GCaMP DNA was amplified by PCR using 5′-CCGGATCCGCCACCATGGGTTCTCATCATCATCATC-3′ and 5′-CGATAAGCTTGTCACTTCGCTGTCATCATTTGTAC-3′, digested with BamH1 and HindIII and cloned under the CaMKIIa or D2SP promoters to yield pAAV-CaMKIIa-GCaMP6m, pAAV-CaMKIIa-GCaMP6f, pAAV-D2SP-GCaMP6m and pAAV-GCaMP6f. All constructs were fully sequenced to check for accuracy of the cloning procedure, and all AAV vectors were tested for in vitro expression before viral production as AAV8/Y733F serotype packaged by the Stanford Neuroscience Gene Vector and Virus Core. Updated maps are available at http://optogenetics.org/. Primary cultured striatal neurons were prepared from P0 Sprague-Dawley rat pups (Charles River). The striatum was isolated, digested with 0.4 mg ml−1 papain (Worthington), and plated onto glass coverslips precoated with 1:30 Matrigel (Beckton Dickinson Labware). Cultures were maintained in a 5% CO humid incubator with Neurobasal-A medium (Invitrogen Carlsbad) containing 1.25% FBS (Hyclone), 4% B-27 supplement (Gibco), 2 mM glutamax (Gibco), and FUDR (10 mg 5-fluoro-2′-deoxyuridine and 25 μg uridine) from Sigma, for 6–10 days in a 24-well plate at a density of 65,000 cells per well. For each coverslip, a DNA and CaCl mix was prepared with 1.5–3.0 μg DNA (Qiagen endotoxin-free preparation) and 1.875 μl 2 M CaCl (final Ca2+ concentration 250 mM) in 15 μl total H O. To the DNA and CaCl mix, 15 μl of 2× HEPES-buffered saline (pH 7.05) was added, and the final volume was mixed well by pipetting. After 20 min at room temperature, the 30 μl DNA–CaCl2 –HBS mix was added drop-wise into each well (from which the growth medium had been temporarily removed and replaced with 400 μl pre-warmed MEM) and transfection was allowed to proceed at 37 °C for 45–60 min. At the end of the incubation, each well was washed with 3× 1-ml warm MEM before the original growth medium was returned. Opsin expression was generally observed within 24 h. Coverslips of cultured neurons were transferred from the culture medium to a recording bath filled with Tyrode solution (containing in mM: 125 NaCl, 2 KCl, 2 CaCl , 2 MgCl , 30 glucose and 25 HEPES). The coverslip was scanned for GCaMP-expressing neurons and a glass monopolar stimulating electrode filled with Tyrode was placed nearby. A 10-s 50-Hz stimulation (pulse width 5-ms, intensity 5–6 mA) was used to obtain maximal responses. Wavelengths of either 475 nm or 400 nm, generated using a Spectra X LED light engine (Lumencor), were used to illuminate the cell. Video was recorded at 10 Hz using a CCD camera (RoleraXR, Q-Imaging). Coverslips of cultured neurons were transferred from the culture medium to a recording bath filled with Tyrode solution (containing in mM: 125 NaCl, 2 KCl, 2 CaCl , 2 MgCl , 30 glucose, 25 HEPES, 0.001 TTX, 0.005 NBQX, 0.05 APV and 0.05 picrotoxin). Whole-cell patch-clamp recordings were performed with glass electrodes (resistance 2.5–4.0 MΩ when filled with internal, which includes (in mM): 120 K-gluconate, 11 KCl, 1 CaCl , 1 MgCl , 10 EGTA, 10 HEPES, 2 Mg-ATP and 0.3 Na-GTP, adjusted to pH 7.3 with KOH). Signals were amplified with a Multiclamp 700B amplifier, acquired using a Digidata 1440A digitizer, sampled at 10 kHz, and filtered at 2 kHz. All data acquisition and analysis were performed using pCLAMP software (Molecular Devices). ChR2-expressing neurons were visually identified for patching using an upright microscope (Olympus BX51WI) equipped with DIC optics, a filter set for visualizing YFP, and a CCD camera (RoleraXR, Q-Imaging). To stimulate ChR2, 1 s of continuous blue light (~10 mW mm−2) was generated using a Spectra X LED light engine (Lumencor) and delivered to the slice via a ×40/0.8 water immersion objective focused onto the recorded neuron. Acute 300-μm coronal slices were prepared by transcardially perfusing the rat with room-temperature NMDG slicing solution (containing in mM: 92 N-methyl-d-glucamine, 2.5 KCl, 30 NaHCO , 1.2 NaH PO -H O, 20 HEPES, 25 glucose, 5 sodium ascorbate, 2 thiourea and 3 sodium pyruvate, adjusted to pH 7.4 with HCl) and slicing the brain tissue in the same solution using a vibratome (VT1200S, Leica). Slices were allowed to recover for 10 min at 33 °C in the NMDG solution, then another 20 min at 33 °C in a modified HEPES artificial cerebrospinal fluid (containing in mM: 92 NaCl, 2.5 KCl, 30 NaHCO , 1.2 NaH PO -H O, 20 HEPES, 25 glucose, 5 sodium ascorbate, 2 thiourea and 3 sodium pyruvate), then another 15 min at room temperature in the HEPES solution. Finally, slices were transferred to standard artificial cerebrospinal fluid (aCSF; containing in mM: 125 NaCl, 2.5 KCl, 2 CaCl , 1 MgCl , 26 NaHCO , 1.25 NaH PO -H O and 11 glucose) bubbled with 95%O /5%CO and stored at room temperature until recording. Whole-cell patch-clamp recordings were performed in aCSF at 30–32 °C. Synaptic blockers (5 μm NBQX, 50 μm d-AP5 (d(−)-2-amino-5-phosphonovaleric acid) and 50 μm picrotoxin; Tocris) were added to the aCSF to isolate direct ChR2 responses. Resistance of the patch pipettes was 2.5–4.0 MΩ when filled with intracellular solution containing the following (in mM): 120 K-gluconate, 11 KCl, 1 CaCl , 1 MgCl , 10 EGTA, 10 HEPES, 2 Mg-ATP and 0.3 Na-GTP, adjusted to pH 7.3 with KOH). Signals were amplified with a Multiclamp 700B amplifier, acquired using a Digidata 1440A digitizer, sampled at 10 kHz, and filtered at 2 kHz. All data acquisition and analysis were performed using pCLAMP software (Molecular Devices). ChR2-expressing neurons were visually identified for patching using an upright microscope (Olympus BX51WI) equipped with DIC optics, a filter set for visualizing YFP, and a CCD camera (RoleraXR, Q-Imaging). To stimulate ChR2, 1 s of 5-ms blue light pulses (~10 mW mm−2) were generated at 20 Hz using a Spectra X LED light engine (Lumencor) and delivered to the slice via a ×40/0.8 water immersion objective focused onto the recorded neuron. Ex-vivo and cell culture physiology data were analysed using Clampfit software (Axon Instruments Inc., Molecular Devices). Statistical analyses were performed using MATLAB (Mathworks Inc.) and GraphPad Prism (GraphPad Software). All custom-written MATLAB code is available on request. As described previously27, 28, we measured bulk fluorescence from deep brain regions using a single optical fibre for both delivery of excitation light to, and collection of emitted fluorescence from, the targeted brain region. The fluorescence output of the calcium sensor is modulated by varying the intensity of the excitation light, generating an amplitude-modulated fluorescence signal that can be demodulated to recover the original calcium sensor response. This ‘upconversion’ of the calcium signal to a frequency range of our choice allows us to avoid any contribution to the signal from changes in ambient light levels with behaviour (since these will not be modulated at the appropriate frequency), as well as avoiding drift or low-frequency ‘flicker noise’ in our photodetector. We have extended this method to the case of multiple excitation wavelengths delivered over the same fibre, each modulated at a distinct carrier frequency, to allow for ratiometric measurements. Fluorescence excitation was provided by two diode lasers at 488 nm and 405 nm with analogue modulation capabilities (Luxx, Omicron Laserage). A real-time signal processor (RP2.1, Tucker-Davis Technologies) running custom software sinusoidally modulated each laser’s output (average power at the fibre tip was set to 30 μW for each wavelength), and simultaneously demodulated the two output signals from the output of the single photodetector (Model 2151 Femtowatt Photoreceiver) as described below. Carrier frequencies (211 and 531 Hz for 488 and 405 nm excitation, respectively) were chosen to avoid contamination from overhead lights (120 Hz and harmonics) and cross-talk between channels (the bandwidth of GCaMP6M was observed to be <15 Hz), while remaining within the 30–750-Hz bandwidth of the photodetector. Excitation light from the two lasers was combined by a dichroic mirror (425-nm longpass, DMLP425), passed through a clean-up filter (Thorlabs, FES0500) and a dichroic mirror (505-nm long-pass, DMLP505), before being coupled into a large-core, high-NA, low-fluorescence optical fibre patch cord (400 μm diameter, 0.48 NA, Doric Lenses) using a fixed-focused coupler/collimator with a standard FC connector (F240FC-A, NA 0.51, f = 7.9 mm). The far end of the patch cord is butt-coupled to the chronically implanted fibre using standard 2.5 mm ferrules and a zirconia sleeve, allowing for easy connections and repeated measurements across days, as in standard optogenetics preparations. A small amount of the fluorescence emitted in the brain is captured at the tip of the implanted fibre and travels back to the rig, where it is collimated and passes through the last dichroic mirror and is focused onto the photodetector by a lens (NA 0.5, f = 12.7 mm, part 62-561, Edmund Optics). The photodetector signal was sampled at 6.1 kHz, and each of the two modulated signals was independently recovered using standard synchronous demodulation techniques: the detector output was routed to two product detectors, one using the selected channel’s modulation signal as a reference, and the other using a 90° phase-shifted copy of the same reference. These outputs were low-pass filtered (corner frequency of 15 Hz), and added in quadrature. This dual-phase detection approach makes the output insensitive to any phase delay between the reference and signal. The resulting fluorescence magnitude signals were then decimated to 382 Hz for recording to disk, and then further filtered using an ~2-Hz low-pass filter. The ratiometric fluorescence signal used throughout the paper was calculated for each behavioural session as follows. A linear least-squares fit between the two timeseries was calculated (that is, the 405-nm control signal values were the independent variable and the 488-nm signal was the dependent variable). Change in fluorescence (dF) was calculated as (488 nm signal−fitted 405 nm signal), adjusted so that a dF of 0 corresponded to the second percentile value of the signal. dF/F was calculated by dividing each point in dF by the 405-nm fit at that time, which scaled transients according to the degree of bleaching estimated at that time. Behavioural variables, such as lever presses and reward port entry times, were fed into the real-time processor as TTL signals from the operant chambers. For each figure, a statistical test matching the structure of the experiment and the structure of the data was employed. For simple comparisons between just two groups, t-tests were used. Where the structure of the data did not fit the assumptions of the test, the non-parametric Mann–Whitney (for unpaired tests) or Wilcoxon matched-pairs (for paired tests) was used instead. When comparing the magnitude of effects of a manipulation across two groups, a two-way ANOVA was used, and where significant interactions were detected, a Bonferroni post-hoc test was used to determine the nature of the differences. When quantifying repeated manipulations within a group, a repeated-measures ANOVA was used, and where significant interactions were detected, a Dunnet’s post-hoc test was used to determine whether the manipulation altered behaviour, while correcting for multiple comparisons. For linear correlation, the Pearson’s r test was used throughout. Variances within each group of data are displayed as s.e.m. throughout. To quantify the temporal stability of individual subjects’ risk preferences across days, we calculated the reliability of percentage risky choices in unmanipulated control animals’ behaviour across 7 days of testing. Odd-versus-even day split-half reliability estimates (as in ref. 35) indicated significant internal consistency in risk preferences for risk-seeking animals (ICC = 0.95, P = 0.0003), risk-averse animals (ICC = 0.99, P < 0.0001), and overall (ICC = 0.99, P < 0.0001). Bootstrap analysis of 10,000 randomly-assigned split halves of the data generates an average ICC = 0.987 (P < 0.0001; Extended Data Fig. 2). Across rats, the average standard deviation in percentage risky choices across the 7 days of testing was 6.1%. For each rat, we calculated the median neural activity during each nosepoke, in the 1 s after nosepoke entry, during successfully completed nosepokes, across all free choices, across all days of behaviour. We then sorted nosepoke periods based either on previous trial outcome (Fig. 3g, k) or on the upcoming choice (Fig. 3i, m). In the case of previous trial outcome, a t-test was used to compare a list of all nosepoke-period signals when the animal received a loss outcome (hundreds of individual trials) against a list of all the signals when the animal received a gain or safe outcome (also hundreds of individual trials). In the case of next decision, a t-test compared the list of all activity during nosepokes when the animal was about to choose safe to the list of all nosepoke activity when the rat was about to choose to take a risk. The signal was larger after loss outcomes than after gain or safe outcomes (Fig. 3e–g). This trend is individually significant in 5 out of 6 rats (t-test, P < 0.0001 in all cases). Decision-period activity was higher in D2R+ cells before safe choices versus risky choices (Fig. 3h, i). This trend held in all rats tested and was individually significant in 5 out of 6 rats (t-test, P < 0.02 in all cases). The logistic regression analysis displayed in Fig. 1b–e is supported by 17 animals and >9,800 individual data points. Post-hoc analyses revealed power of 0.9 and 0.84, respectively, for the subpanels in Fig. 1f and a power of 0.99 for Fig. 1g. The one-way ANOVA in Fig. 2a has a power of 0.96. The Mann–Whitney test in Fig. 2c has a power of 0.96. The repeated-measures ANOVA used in Fig. 2f has a power of 0.99. The data in Fig. 3 comprise 31 recording sessions across the 6 rats, totalling >7,500 trials. Post-hoc power tests on Fig. 3g, i, k, m reveal a power >0.84 for all significant results. Tests on the significant correlations reveal a power of 0.95 for Fig. 3n and a power of 0.86 for Fig. 3p. The optogenetics experiments in Fig. 4 contain a total of 62 animals across the 4 groups. Power analyses reveal that the two-way ANOVA used to evaluate Fig. 4d–i has a power of 0.99. The one-way ANOVA in Fig. 4j has a power of 0.89. The goal of this classification is to determine the probability that a rat will choose the risky lever on any given trial given recent outcome history. We used a soft-max decision function: where x is a vector representing the recent outcome history, is a dummy variable indicating whether the rat chose risky on a given trial, and θ is the set of weights learned by the model. In this scenario, we know the outcome history (x) and the choice outcomes (y). We seek to use these data to find a set of weights (θ) that minimizes the difference between the prediction (h (x)) and the rat’s actual behaviour (y). To accomplish this, we use the MATLAB gradient descent algorithm fminunc to generate a set of weights (θ) that minimize the cost function: over m training examples. We use the vectorized implementation: We then used the weights generated by running this optimization over the training data to determine how well the model generalized to test data from the same rats. To do this, we plugged the weights from the optimization over training data and the outcome histories from the test data into equation (2). The probabilities generated by equation (2) were then compared to actual choice outcomes on a trial-by-trial basis, such that [ when ] or [ when ] were considered correct predictions.


Takahashi A.,Instruments Company
International Journal of Automation Technology | Year: 2011

Length measurement was conducted for two years on glass ceramics, Zerodur ® and Clearceram ®, which have a low coefficient of thermal expansion, and on synthetic quartz. Commercially available glass ceramics were used for evaluating long-term stability, or secular change. Synthetic quartz ensured longterm length measurement stability. Two line scales of 300 mm length made of each material for a total of six line scales were simultaneously manufactured and measured to evaluate dimensional stability variation of the materials over time. Measurements were conducted with a line scale calibration system developed by Nikon. The calibration system is a one dimensional laser interferometer, featuring reduced Abbe's errors, laser interferometer paths in a vacuum and real-time wavelength calibration of laser frequency using a 633 nm iodine-stabilized He-Ne laser. Long-term quartz stability was 4.3 nm and 5.4 nm (2σ). The yearly stability coefficients of the two glassceramic scales were -0.22 and -0.23 parts per million per year (ppm/yr) for Zerodur and -0.16 and -0.16 ppm/yr for Clearceram. No significant difference in stability between the two scales was observed for Zerodur or Clearceram.


Takahashi A.,Instruments Company | Miwa N.,Nikon Corporation
Measurement Science and Technology | Year: 2010

Line scales are used as a working standard of length for the calibration of optical measuring instruments such as profile projectors, measuring microscopes and video measuring systems. The authors have developed a one-dimensional calibration system for line scales to obtain a lower uncertainty of measurement. The scale calibration system, named Standard Scale Calibrator SSC-05, employs a vacuum interferometer system for length measurement, a 633 nm iodine-stabilized He-Ne laser to calibrate the oscillating frequency of the interferometer laser light source and an Abbe's error compensation structure. To reduce the uncertainty of measurement, the uncertainty factors of the line scale and ambient conditions should not be neglected. Using the length calibration system, the expansion and contraction of a line scale due to changes in ambient air pressure were observed and the measured scale length was corrected into the length under standard atmospheric pressure, 1013.25 hPa. Utilizing a natural rapid change in the air pressure caused by a tropical storm (typhoon), we carried out an experiment on the length measurement of a 1000 mm long line scale made of glass ceramic with a low coefficient of thermal expansion. Using a compensation formula for the length change caused by changes in ambient air pressure, the length change of the 1000 mm long line scale was compensated with a standard deviation of less than 1 nm. © 2010 IOP Publishing Ltd.


Takahashi A.,Instruments Company
Measurement Science and Technology | Year: 2010

Line scales are commonly used as a working standard of length for the calibration of optical measuring instruments such as profile projectors, measuring microscopes and video measuring systems. For high-precision calibration, line scales with low thermal expansion are commonly used. Glass ceramics have a very low coefficient of thermal expansion (CTE) and are widely used for precision line scales. From a previous study, it is known that glass ceramics decrease in length from the time of production or heat treatment. The line scale measurement method can evaluate more than one section of the line scale and is capable of the evaluation of the longitudinal uniformity of the secular change of glass ceramics. In this paper, an arithmetic model of the secular change of a line scale and its longitudinal uniformity is proposed. Six line scales made of Zerodur®, Clearceram® and synthetic quartz were manufactured at the same time. The dimensional changes of the six line scales were experimentally evaluated over 2 years using a line scale calibration system. © 2010 IOP Publishing Ltd.


Choi S.,Texas A&M University | Akin B.,Instruments Incorporated | Rahimian M.M.,Texas A&M University | Toliyat H.A.,Texas A&M University
IEEE Transactions on Industrial Electronics | Year: 2011

In this paper, a complete cross-correlation-based fault-diagnostic method is proposed for real-time digital-signal-processor (DSP) applications that cover both the fault-monitoring and decision-making stages. In practice, a motor driven by an inverter or utility line is run at various operating points where the frequency, amplitude, and phase of the fault signatures vary unexpectedly. These changes are considered to be one of the common factors that yield erroneous fault tracking and unstable fault detection. In this paper, the proposed algorithms deal with the ambiguities of line-current noise or sensor-resolution errors and operating-point-dependent threshold issues. It is theoretically and experimentally verified that a motor fault can be continuously tracked when the sensor errors are within a limited range through the adaptively determined threshold definition of noise conditions. The offline experiments are performed via Matlab using actual line-current data obtained by a data-acquisition system. These results are verified on a DSP-based motor drive in real time where drive sensors and a digital signal processor are employed both for motor-control and fault-diagnostic purposes. © 2010 IEEE.


Takahashi A.,Instruments Company
Measurement Science and Technology | Year: 2012

Length measurement was carried out on line scales made of the ultralow-expansion ceramic NEXCERAand synthetic quartz for 13 months. 550 mm long precision line scales made of the two materials were manufactured and their changes in length were measured over the same period, using a high-precision laser-interferometric line scale calibration system. NEXCERA was used to evaluate its long-term dimensional stability. Synthetic quartz was used because of its long-term stability to ensure the stability of the long-term length measurement, including the line scale calibration system and measurement procedure. The long-term stabilities of relative length expressed in terms of 2 over 13 months were 1.1 1.1×10 8for NEXCERA and 4.2 6.3×10 8for synthetic quartz. The experimental results were within the estimated measurement error. No significant secular change in length was observed for the line scale made of NEXCERA. © 2012 IOP Publishing Ltd.


Takahashi A.,Instruments Company | Kokumai Y.,Nikon Corporation | Takigawa Y.,Nikon Corporation
International Journal of Automation Technology | Year: 2012

The measurement error resulting from graduation anomalies and the signal processing algorithm used for determining the positions of graduations on line scales was investigated by simulation and experiment. Optical image-forming simulations were carried out on models of 6-μm-wide graduations with three sizes of defects (0.5, 1.0 and 1.5 μm) at one edge. A digital filter was used in signal processing to obtain the first differential to determine the positions of the graduations. The minimum values of the lateral shift of the determined graduation positions were observed for the three defect sizes when using a 9-μm-wide differential filter. An experiment was also carried out on an ordinary line scale with 6-μm-wide graduations using a high-precision laser- interferometric line scale calibration system by measuring seven positions on the scale in the direction perpendicular to the measurementaxis. The root mean square of the standard deviations from the linear fitting lines constructed using the measured positions over a 300-mm-long line scale was 2.8 nmwhen the differential filter width was 9 μm. It was demonstrated that a differential filter was effective in reducing the lateral error due to graduation anomalies.


Fujimori Y.,Instruments Company | Tsuto T.,Nikon Corporation | Kudo Y.,Nikon Corporation | Inoue T.,Instruments Company | And 2 more authors.
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2011

A new methodology for inspection of TSV (Through Silicon Via) process wafers is developed by utilizing an optical diffraction signal from the wafers. The optical system uses telecentric illumination and has a two-dimensional sensor in order to capture the diffraction light from TSV arrays. The diffraction signal modulates the intensity of the wafer image. Furthermore, the optical configuration itself is optimized. The diffraction signal is sensitive to via-shape variations, and an abnormal via area is analyzed using the signal. Using the test wafers with deep hole patterns on silicon wafers, the performance is evaluated and the sensitivities for various pattern profile changes were confirmed. This new methodology is available for high-volume manufacturing of the future TSV-3D CMOS devices. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).


Some key points to consider when designing a system for continuous monitoring of the calorific value of mixed gaseous fuels: · Heating prevents errors from water vapor condensation. The sample stays intact during measurement. · Heating allows combustible gases with low vapor pressures (high boiling points) to be measured without losses in the sampling system. False low readings are avoided. · The aspirated system does not increase pressure above the process conditions. preventing condensation of water vapor or combustible gas that would otherwise condense. The sample is not affected. · Combustion calorimeter has good response factors, especially useful for unknown mixtures, practically anything that burns. · The use of hydrogen fuel stabilizes the flame and widens the measurement range, including zero. The flame is always ready to measure. · Its speed provides a continuous measurement that is useful when process conditions can change quickly. Speed can be as important as accuracy. Often, speed is crucial. PE.


Takahashi A.,Instruments Company | Takigawa Y.,Nikon Corporation | Miwa N.,Nikon Corporation
Measurement Science and Technology | Year: 2011

Measurement error resulting from the defocus and quadratic caustic of a line-detecting microscope in line scale measurement was investigated. The relationship between the lateral shift and defocus was clarified and a procedure for measuring the lateral shift without changing the tilt of the line scale under measurement was proposed. An experiment was performed on line scale measurement to demonstrate the proposed measurement procedure using a line scale calibration system. The calibration system used in this experiment was a one-dimensional, laser-interferometric length measurement system for line scales developed by Nikon. The calibration system features a reduced Abbe's error, laser interferometer paths installed in vacuum and real-time calibration of the wavelength of the Zeeman laser, which is used for length measurement, using a 633 nm iodine-stabilized He-Ne laser. The line scale used for the experiment was 300 mm in length, and made of glass ceramics. The experimental result of the lateral shift stemming from the defocus and quadratic caustic of the optics of the line-detecting microscope was approximately 4 nm for a defocus range of ±10 μm. The possibility of reducing this type of error was also discussed. © 2011 IOP Publishing Ltd.

Loading Instruments Inc. collaborators
Loading Instruments Inc. collaborators