PMC

G1(0), Group 1 without delay; G2(0), Group 2 without delay; G3(0), Group 3 without delay; G3 70, Group 3 with delay of 70 ms; G3 100, Group 3 with delay of 100 ms; G3 150, Group 3 with delay of 150 ms; G3 200, Group 3 with delay of 200 ms; and G3 300, Group 3 with delay of 300 ms.

The hatch delay situation after long-term Cr(VI) exposure in marine medaka offspring. (A,B) hatch delay rate; (A) the hatch delay rate of offspring under different Cr(VI) treatment, different letter means the significant differences among different treatment (upper letter: p ≤ 0.01, lower letter: p ≤ 0.05); (B) the daily hatch delay rate under different offspring Cr(VI) exposure after parental Cr(VI) exposure, X axis represents parental treatment, and Y axis represents daily hatch delay rate, the blank line represents offspring in control environment, the red line represents offspring in Cr(VI) environment; the function relationships between exposure time and hatch delay rate were y = 0.41767x + 75.92824, R² = 0.06479 (untreated offspring) and y = 0.60299x + 76.06081, R² = 0.2451 (treated offspring); (C–F) hatch delay time; (C) the hatch delay time of offspring under different Cr(VI) treatment, different upper case means the significant differences among different treatment (p ≤ 0.01); different letter means the significant differences among different treatment (upper letter: p ≤ 0.01, lower letter: p ≤ 0.05) (D) the interaction of parent and offspring Cr(VI) treatment for hatch delay time (p = 0.028); (C,D), daily hatch delay time under different offspring Cr(VI) exposure after parental Cr(VI) exposure; (E) parental Cr(VI) exposure for first month, the function relationships between exposure time and hatch delay time were y = 007303x + 6.60125, R² = −0.0685 (untreated offspring) and y = −0.27692x + 13.00838, R² = 0.04457 (treated offspring); (F) parental Cr(VI) exposure for 2nd month, the function relationships between exposure time and hatch rate were y = −0.81409x + 47.69364, R² = 0.92974 (untreated offspring) and y =−0.75x + 44.33333, R² = 0.92857 (treated offspring). The number of biological samples used for each group is as follow: con-con (N = 297), con-cr (N = 34), cr1-con (N = 70), cr1-cr (N = 70), cr2-con (N = 28), cr2-cr (N = 8).

Illustration of level-dependent group delay for normal and impaired ears. Left: Impulse responses of filters in the normal (top panel) and impaired (bottom panel) periphery. The impulse response of the filter depends on how sharply tuned the filter is (filter functions shown at the right). Broad filters have a short build-up time, whereas sharp filters have a long build-up time. The build-up time is proportional to the group delay; the vertical lines show the group-delay approximation for gammatone filters used in the SPC system. In the normal ear, the group delay constantly fluctuates between the low- and high-SPL group-delay values (see arrow labeled dynamic group delay). In the impaired ear, the group delay varies much less across SPLs (vertical lines are closer to each other). However, by adding a dynamic delay (SPC), the normal dynamic group delay can be approximated on the output of the impaired filter.

Experimental protocols. In all experiments, the participants’ hand (gray) was hidden from sight the entire time. a, Experiment 1: Delay versus Control, transfer to reaching. Sessions alternated between a pong game and a reaching task. During a reach trial, a target (gray square) appeared in one of three locations in space beyond a start location (black square), and participants were asked to reach and stop at the target. An experiment started with a Reach – Training session in which participants received full visual feedback of the hand location using a cursor on the screen (dark gray filled square). After training, participants were presented with a Pong game session (No Delay), in which the paddle moved instantaneously with their hand movement, followed by a Blind Reach session where no visual feedback was provided at any point during the trial (Post No Delay, blue frame). The second Pong game session (Delay) was introduced with a delay (Delay group) or without a delay (Control group) between hand and paddle movements, and was followed by another Blind Reach session (Post Delay, orange frame). b, Experiment 2: Abrupt versus Gradual delay, transfer to reaching. The experimental protocol was similar to experiment 1, but with the addition of a Blind Reach – Training session: the cursor was omitted during movement, but was displayed at the movement stop location. In the second Pong game session, we introduced either an abruptly (Abrupt group) or gradually (Gradual group) increasing delay. c, Experiment 3: Abrupt versus Gradual delay, transfer to tracking (figure-eight). Sessions alternated between a pong game and a tracking task. During a track trial, participants were asked to track a target that moved along a figure-eight path (dashed gray). The path was not presented to the participants in a direction illustrated by the dotted dark gray arrow. The experiment started with a Track – Training session in which participants received full visual feedback on their hand location (dark gray filled square). After training, participants were presented with a Pong game session with no delay (No Delay), followed by a Blind Track session (Post No Delay, purple frame). Next, a Pong game session was introduced with either an abruptly (Abrupt group) or gradually (Gradual group) increasing delay (Delay), and was followed by another Blind Track session (Post Delay, green frame). d, Experiment 4: Gradual delay, transfer to tracking (mixture of sinusoids). Sessions alternated between a pong game and a tracking task. During a track trial, participants were asked to track a target that moved along a sagittal path (dashed gray). The path was not presented to the participants. The target trajectory (left zooming window) was designed as a mixture of five sinusoids of different frequencies and phases. The experiment started with a Track – Training session in which participants received full visual feedback on their hand location (dark gray filled square), followed by a Blind Track – Training session. After training, participants were presented with a Pong game session with no delay (No Delay), followed by a Blind Track session (Post No Delay, magenta frame). Next, a Pong game session was introduced with a gradually increasing delay (Delay), and was followed by another Blind Track session (Post Delay, cyan frame).

Illustration of the relationship between group delay and phase properties of the cochlear filter. Left: Impulse responses of filters in the normal (top panel) and impaired (bottom panel) periphery. The duration of the build-up of the filter’s response depends upon how sharply tuned the filter is (filter functions shown at the right). Broad filters have short build-up times, whereas sharp filters have a long build-up time. The build-up time is proportional to the group delay; the vertical lines show the group delay approximation for gammatone filters used in the SPC system. In the normal ear, the actual group delay constantly fluctuates between the low- and high-SPL group-delay values (see arrow labeled dynamic group delay). In the impaired ear, the group delay varies much less across SPLs (vertical lines are closer to each other). However, by adding a dynamic delay (the correction), the normal dynamic group delay can be approximated on the output of the impaired filter.

Mean time (sec) + SEM spent in the saline-paired (white bars) and cocaine-paired (black bars) compartments for six groups of rats during baseline and on test day: a 0-min Delay group (top left, n=11) and 15-min delay group (top right, n=12) tested 1-day after place conditioning; two groups tested 1-week post conditioning, a 0-min Delay group (middle left, n=10) and a 15-min Delay group (middle right, n=15); two groups tested 3-weeks post conditioning, a 0-min Delay group (bottom left, n=11), and a 15-min Delay group (bottom right, n=14). *denotes significant differences in the time spent in the cocaine-paired versus saline-paired compartment on test day (p < .05).

a Schematic representation of the spontaneous object recognition (SOR) experiments. b Task performance with a 10-min sample and a 24-h delay during the 9th week of enrichment. The OC group demonstrated a significantly higher discrimination ratio (DR) compared to the SH group. OC, EH, and SH groups showed DRs above chance. c SOR task performance with a suboptimal sample time at two delay durations during the 10th week of enrichment. With a 20-min delay, all groups significantly discriminated above chance. With an increased delay to 24 h, the OC group DR was significantly higher compared to all other groups. (Delay x group interaction p < 0.001, delay main effect p < 0.001, and group main effect p = 0.003). Only the OC group showed a DR above chance. d Replication of c, but completed 1-month post-discontinuation of enrichment. With a 20-min delay, all groups significantly discriminated above chance, demonstrating intact object memory. With an increased delay to 24 h, the OC group demonstrated enhanced object memory, performing significantly better than the EH and CC groups (delay x group interaction p = 0.057, delay main effect p = 0.01, and group main effect p = 0.023). The OC group was the only group to discriminate the novel object significantly above chance. *p < 0.05, **p < 0.01, ***p < 0.001 indicate significant two-tailed paired-sample t-tests (choice DR vs. sample DR). ♦♦p < 0.01, ♦♦♦p < 0.001 indicate a significant difference between groups (two-tailed independent samples t-test, Bonferroni correction p = 0.0083). Error bars represent the standard error of the mean (s.e.m.) across animals.

a The reticular lamina (RL) 2f0 group delay is significantly larger than the f0 group delay at one-half of the best frequency, while there is no significant difference among the f0, 2f0, and 3f0 group delays at the best frequency. b The basilar membrane (BM) 2f0 group delay is also greater than the f0 group delay at one-half of the best frequency. c The RL 2f0 and 3f0 group delays are significantly smaller than the BM group delays, while the RL f0 group delay is larger than the BM f0 group delay. d The 2f0 and 3f0 group-delay differences between the RL and BM are significantly larger than the f0 group delay difference. e, f The phase differences between the RL and BM 2f0 and 3f0 as a function of frequency. The downward slopes of the phase-difference curves confirm that the RL 2f0 and 3f0 group delays are smaller than those of the BM. g The f0 phase difference between the RL and BM vibrations as a function of frequency. The upward phase slope of the f0 phase-difference curve indicates that the f0 arrives at the RL after the BM vibration. The solid and dotted lines in panels e–g represent the means and standard errors, and n=8.

Group means (normalized by subtracting the average responses of the no-delay Control Group) for ratings of perceived auditory feedback delay by the subject groups who experienced a delay throughout the Delay Exposure task (habituation groups, left panel), and the subject groups who experienced no delay during the Delay Exposure task (no-habituation groups right panel). Ratings at time points 1 through 6 were completed during the Delay Exposure task (each rating following a 5-minute block of speaking) whereas the rating at time point 7 was completed immediately following the Auditory-Motor Adaptation task. Shaded areas show +/− one standard error of the mean.

Experiment 1: reaching experimental results and representation model simulation results suggest a State-based rather than a Time-based Representation of delay. a, Single participant’s experimental results from each of the Delay (left, filled markers) and Control (right, hollow markers) groups. Movements start location is indicated by the black square and target locations are marked by the gray squares. Markers represent the end point locations of the hand at movement terminations during the Post No Delay (blue triangles) and Post Delay (orange circles) Blind Reach sessions. b, Experimental results group analysis. Colored bars represent the mean reaching movement amplitudes toward all targets of each participant, and for each of the Blind Reach sessions, averaged over all the participants in each group (Delay: left, n = 9, Control: right, n = 8) and after subtraction of each group’s average baseline amplitude (during the Blind Reach – Post No Delay session). Black bars (insets) represent the difference in mean amplitude between the Post Delay and the Post No Delay blind reaching sessions for each participant, averaged over all targets and over all the participants in each group. Dots represent differences of individual participants. Error bars represent the 95% confidence interval. c, Simulation results of reaching end points in the Delay group (Post No Delay – black outlined blue triangles, Post Delay – black outlined orange circles) for Time Representation (left) and State Representation (right) of the delay. **p < 0.01.

All x-axes are in the logarithmic scale. Each red dot is a single drawing, and each yellow dot is a drawing from the group of participants that returned 1–2 weeks after encoding. Although these yellow dots are visually included, they were not included in the analyses. (top panel) For location memory, delay time was only significantly predictive of location accuracy in the x-direction, but not the y-direction, meaning that increased delay time led to worse location memory in the x-direction. (bottom panel) Unlike location memory, size memory was unaffected by delay time, with neither width memory nor height memory influenced by how much time elapsed before recall.

The signal transmission format of Loran-C navigation chains. Abbreviations: group repetition interval (GRI); time delay for first secondary station (TDX); time delay for second secondary station (TDY).

In the left panel, the M-estimate of location of subjective anticipatory time was plotted against calendar time for each group and for each delay. In the right panel, subjective anticipatory time for each delay was estimated using the M-estimate of location of alpha and beta for each age group.

Volume of xenografted tumors formed by HCT116 cells in BALB/c-nu/nu mice following indicated treatment at indicated time points (n = 7/group; a), and the fold-change of tumor volumes at day 32 compared to those at the starting point of the treatment (day 12; b). Morphological appearance (c) and tumor weight (d) at day 32 are shown. e Tumor growth delay and enhancement factor of combinatorial treatment of nutlin-3 and p52-ZER6 knockdown. (A) Absolute growth delay was calculated by subtracting the doubling time of the tumor in the treated group from that of the shCon group; (B) normalized growth delay for shp52-ZER6 was calculated by subtracting the absolute growth delay of the shp52+nutlin-3 group from that of the shCon+nutlin group; (C) normalized growth delay for nutlin-3 was calculated by subtracting the absolute growth delay of the shp52+nutlin-3 group from that of the shp52 group; (D) enhancement factor for shp52-ZER6 was calculated by dividing the normalized growth delay for shp52-ZER6 (B) with the absolute growth delay of the shp52 group; (E) enhancement factor for nutlin-3 was calculated by dividing the normalized growth delay for nutlin-3 (C) with the absolute growth delay of the shCon+nutlin group. f p52-ZER6, p53, and p21 protein expression levels in xenografted tumors treated with indicated treatments, as determined using Western blotting. β-actin was used as a loading control. g Immunohistochemistry staining against p53, p21, and PCNA, as well as TUNEL assay in tissue sections of xenografted tumors treated with indicated treatments. Scale bars: 50 μm. Quantitative data are presented as mean ± SD. **P < 0.01.

Confocal microscopy of the MEPs in the gastrocnemius of mice with delayed repair after peripheral nerve injury.
(A–D) MEPs were stained with α-bungarotoxin (red, stained by Alexa Fluor647) and visualized in muscles in the immediate repair (A), 1-month delay (B), 3-month delay (C) and control (D) groups. Regenerated MEPs can be directly visualized after delayed repair. White arrows indicate perforation of MEPs. However, the shape of MEPs in the 1-month delay and 3-month delay groups was irregular compared with those in the immediate repair and control groups. Scale bars: 50 μm. (E) The superficial area of single MEPs in each group. The area is gradually reduced with longer denervation time. (F) The number of perforations of single MEPs in each group. MEP maturation is more severely perturbed in the 1-month delay and 3-month delay groups compared with the immediate repair and control groups. Data are expressed as mean ± SD (n= 6, 6, 7 and 6 in the immediate repair, 1-month delay, 3-month delay and control groups, respectively) *P< 0.05, vs. control group; #P< 0.05, vs. 3-month delay group; ^{^}P< 0.05, vs. 1-month delay group (one-way analysis of variance followed by the Student-Newman-Keuls test). MEP: Motor endplate.

Group delay profiles for order  and delay variations –. Constant group delay can be observed over 50% of the Nyquist interval. With temporal over-sampling of 3×, the usable range of the Thiran filter response is contained within the normalized −0.33 to 0.33 frequency band. The constant group delay establishes the role of Thiran filters in realizing fractional sample delays.

Group delay representation of a set of exponential with instantaneous rise time (simplest case of a synthetic Ca²⁺ signal)

Inter-trial group comparison for HC group of 32, SZ group of 49, during b epoch (Playback Tone). We again observe significantly higher DTW distance values in SZ (p < 0.0001) and also higher Delay in SZ (p = 0.046). DTW _SZ = 528.2 (CI = 507.7, 548.8, p < 0.0001). DTW _HC = 444.6 (CI = 413.4, 475.8, p < 0.0001). Delay _HC = 67 ms (CI = 57.5, 76.9, p = 0.046). Delay _SZ = 78 ms (CI = 73.5, 82.7, p = 0.046).

(a) Transient UV-visible absorption spectra obtained at 75 fs time delay (red curve) and 1 ps time delay (blue curve) for [Fe(bpy)₃]²⁺ in water. (b) Kβ transient difference spectra obtained at 50-fs time delay (red circles) and 1-ps time delay (blue square) for [Fe(bpy)₃]²⁺ in water. (c) UV-visible pump-probe difference spectrum at 75 fs (red curve) and 1 ps (blue curve) for [Fe(bpy)(CN)₄]^2- in dimethyl sulfoxide. (d) Kβ transient difference spectra obtained at 50 fs time delay (red circles) and 1 ps time delay (blue square) for [Fe(bpy)(CN)₄]^2- in dimethyl sulfoxide. (a) and (b) Adapted with permission from Zhang et al., Nature 509, 345 (2014). Copyright 2014 Nature Publishing Group. (c) and (d) Adapted with permission from Zhang et al., Chem. Sci. 8, 515 (2017). Copyright 2017 Royal Society of Chemistry.

Reaction times are defined by the time it took for the rat to exit the odor port after odor sampling. A, Reaction time as the delay became longer. B, Reaction time as the delay on the other side got longer. C, Reaction time as the reward size on the other side got bigger. D, Reaction time as the reward size got bigger. The p value reflects the significance level for a main effect of group (cocaine vs saline) in a two-factor ANOVA taking group and delay (or reward) as factors. Error bars indicate SE.