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(a) Time history of non-dimensional flame stand-off distance for a single oscillation cycle for non-responsive (unpulsed and 200Hz), responsive (80Hz, 100Hz and 120Hz) and transition (125Hz) frequencies. Yellow bands indicate the amplitude of Rf fluctuations (b) frequency spectra of Rf fluctuations at unpulsed and 100Hz excitation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... (a) Time-resolved dynamic flame behavior in a single oscillation cycle showing three distinct flame states at 100Hz pulsing and (b) 2D flame image sequences at the non-responsive 200Hz pulsing and 125Hz transition mode. ... Dimensionless RMS flame stand-off distance fluctuations as a function of forcing frequency (fP). Normalization parameter is the average Rf magnitude in unexcited case. ... Normalized rms velocity variation with forcing frequency at front stagnation point of the droplet under isothermal conditions. ... (a) Temporal variation of flame stand-off distance (Rf) (b) Time-dependent fluctuations in non-dimensional flame area (Af/Af avg, 0Hz) in a single 14Hz oscillation cycle.
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(A) Frame-by-frame analysis of the movements illustrated in Fig. 5 A. The curvature of the proximal 10μm of the flagellum is plotted using a mixture of open circles and crosses; the open circles represent video frames illustrated in Fig. 5 A. The curvature is seen to oscillate rapidly until the trailing edge of the antecedent full-sized R-bend (solid circles) has propagated off the tip. Downward deflection of curvature represents cryptic P-bends. (B) Another example of a hesitation cycle from the same headless sperm. (C) Frame-by-frame analysis, as in Fig. 6 A, of the intact specimen illustrated in Fig. 5 B. (D) Another example from a different intact sperm. In all four graphs, the velocity of propagation of the full-size R-bend shows irregularities that may possibly be related to the oscillatory movements on the proximal flagellum.... (A) Sequential images, from left to right, of a headless sperm in motion, during a beat cycle that showed “hesitation” in developing the reverse (R) bend. Bends P1 and R1 are identified in image 1. P1 reaches its greatest curvature proximally in image 3. Then in image 4, a slight proximal straightening indicates that the cryptic bend R2 has developed. Image 5 shows the cryptic bend P2. The rapid oscillation continues with cryptic R-bends in images 6, 8, and 10, and cryptic P-bends in images 7, 9, and 11. Only when bend R1 finally leaves the tip, in image 12, does the next full-size R-bend develop (images 13 and 14), followed without hesitation by (the first stages of) the next full-size P-bend (images 15 and 16). Duration of sequence 3.84s. Time intervals (left to right) were 0.23, 0.12, 0.07, 0.41, 0.12, 0.12, 0.07, 0.17, 0.36, 0.67, 0.36, 0.41, 0.43, 0.24, and 0.05s. (B) Sequential images, as in A but showing an intact sperm. P1 reaches its maximal angle in image 5. Cryptic R-bends are maximally developed in images 6, 8, 10, 12, and 14. Cryptic P-bends are seen in images 7, 9, 11, and 13. Bend R1 leaves the tip in image 15. Only then does the next full-size R-bend develop (images 16–19), followed immediately by the next full-size P-bend (beginning in image 20). Duration of sequence 3.54s. Time intervals (left to right) were 0.12, 0.24, 0.05, 0.72, 0.07, 0.17, 0.07, 0.14, 0.05, 0.12, 0.12, 0.19, 0.29, 0.12, 0.24, 0.19, 0.17, 0.24, and 0.24s. In both A and B, the individual frames have been selected to show the peaks of the oscillation, which is more obvious in B because of the tilting of the head. At this scale, the basal protrusions in A are difficult to see but are represented in Fig. 1. The sequence of frames has been spread from left to right to minimize confusing superimposition. Frame-by-frame quantitative analyses of these specimens is given in Fig. 6, A and C. Scale bar, 4μm. (Also see supplementary videos.) ... Measurements of the maximum angle reached by bend P1, taken from 21 beat cycles, from six spermatozoa. They are arranged in two columns according to whether or not bend P1 was followed by hesitations (i.e., rapid oscillations before the next full-size R-bend). The angle was measured just before the hesitations or normal propagations began. ... (A) Frame-by-frame analysis of the movements illustrated in Fig. 5 A. The curvature of the proximal 10μm of the flagellum is plotted using a mixture of open circles and crosses; the open circles represent video frames illustrated in Fig. 5 A. The curvature is seen to oscillate rapidly until the trailing edge of the antecedent full-sized R-bend (solid circles) has propagated off the tip. Downward deflection of curvature represents cryptic P-bends. (B) Another example of a hesitation cycle from the same headless sperm. (C) Frame-by-frame analysis, as in Fig. 6 A, of the intact specimen illustrated in Fig. 5 B. (D) Another example from a different intact sperm. In all four graphs, the velocity of propagation of the full-size R-bend shows irregularities that may possibly be related to the oscillatory movements on the proximal flagellum.
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Operating principle of the FO-TEEM generator. (a) Operating principle of the TENG component. The TENG component responds to the displacement of the floating oscillator. (b) Simulated charge density profile of the two Al electrodes and the floating oscillator with various positions (COMSOL Multiphysics). (c) Operating principle of the EMG component. The EMG component responds to the velocity of the floating oscillator. (d) Simulated current density profile of the two coils with the floating oscillator moving in various directions. ... Structure of the FO-TEEM generator. (a) Schematics of the floating oscillator-embedded triboelectric nanogenerator (TENG), electromagnetic generator (EMG), and hybrid FO-TEEM generator. (b) A photograph of the prototype FO-TEEM generator. Inset shows a magnified view of the magnetic rod surrounded by the PTFE coated PDMS sponge, which is used as the floating oscillator. (c) A photograph showing the inside of the tube. (d) SEM image of the Al electrode with the nano-grass structures. (e) SEM image of the PDMS sponge before coating with the PTFE layer. (f) SEM image of the PDMS sponge after the PTFE layer coating.
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Pressure oscillation with inlet pressure 2MPa. (a) Calculated pressure oscillation. (b) Power density of oscillation. ... Pressure oscillation at inlet pressure 3MPa. (a) Calculated pressure oscillation. (b) Power density of oscillation. ... Pressure oscillation
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Model of the Time Course of Motor Activation Prior to metaphase, the pool of motors that can be activated is established at the cortex via GPR-1/2. The size of the pool is indicated by the thickness of the green shaded areas: The pool is larger in the posterior half than in the anterior half but remains constant throughout metaphase and anaphase. Over time, the activity of the motors increases, indicated by the increasing opacity of the green shaded regions. The increasing motor activity accounts for the dynamics of both the oscillations and the posterior displacement. ... Phenotypes of Progressive Depletion of DLI-1 and GPR-1/2 Examples of the trajectories of the anterior (red) and posterior (blue) spindle poles are superimposed on the contour of the embryo. The circles represent the starting positions. Each panel shows a different embryo. (A–C) Depletion of dynein light intermediate chain in worms fed bacteria expressing inactivating RNA directed against dli-1. (A) An embryo 12 hr 40 min after transfer onto the feeding plates in which the oscillation is normal. (B) A different embryo 13 hr 30 min after transfer in which the oscillation was not present. (C) At 17 hr after transfer, the spindle was not aligned properly on the AP axis. (D–F) Depletion of GPR-1/2 after injection of dsRNA directed against gpr-1/2. (D) At short times after injection, the phenotype is almost normal. (E). At 11 hr 30 min, the oscillations are completely absent, although posterior displacement still occurs. (F) At 35 hr 12 min, there are no oscillations or posterior displacement, although spindles still elongate to 85% of their normal length. Interestingly, all the reduction of spindle elongation occurred over the first 13 hr, suggesting that spindle oscillations may be required to elongate the spindle to its full extent. ... Transverse Oscillations and Posterior Displacement of the Mitotic Spindle in an Unperturbed Embryo (A) Fluorescence image of the one-cell C. elegans embryo showing GFP-tagged γ-tubulin localizing preferentially to the centrosomes (spindle poles). The anterior spindle pole (left) is circled in red, the posterior (right) in blue. (B) The trajectories of the two poles during metaphase and anaphase measured every 0.5 s. The circles denote the initial positions. (C) The distances of the spindle poles from the anterior-posterior axis shows the buildup and die-down of the oscillations. The approximate onset of oscillations is indicated by the dashed line. (D) The position of the spindle (defined as the midpoint of the poles) along the AP axis (black). Zero is the center of the embryo. The slight oscillations are due to the arcing motion of the spindle apparent in the posterior trace in (B). The spindle length is shown in gray. All panels are from the same cell. ... The Antagonistic-Motors Model Accounts for the Buildup and Die-down of the Oscillations (A) The processivity of the motors is postulated to increase steadily during metaphase and anaphase (i.e., the off rate, k¯off, decreases). (B) As a consequence of the varying off rate, the mean attached probability, p¯, a measure of the activity of the motors, steadily increases. The probability is 0.5 when the off rate equals the on rate (kon) indicated by the vertical dashed line in (A). (C) As the probability increases, the coefficient of negative damping (Ξ) first increases and then decreases. When the coefficient of negative damping exceeds that of the positive damping (Γ), indicated by the horizontal dashed line, the system becomes unstable (shown as the hatched region), and spontaneous oscillations occur. When the coefficient of negative damping drops below the positive damping, the oscillations die out. (D) The instability occurs while the inertial coefficient (I) is increasing (solid curve). This leads to the observed decrease in the oscillation frequency over the course of the oscillations (Figure 4). The dashed curve shows the case if the on rate were decreasing. (E) Simulation of the oscillation. The gray region denotes the time when oscillations are resolved above the noise. (F) Because the probability increases monotonically, so too does the net posterior-directed force and the posterior displacement: Γ = 85.8 μN·s/m, K = 10 μN/m, N = 28, f¯ = 6 pN, fc = 1.5 pN, f′= 3 μN·s/m, kon = 0.6 s−1. ... Decrease in Frequency during the Oscillations The oscillation frequency decreased by about one-third over the duration of the oscillations. Four frequency measurements were made during each period of an oscillation by measuring the times in the cycle at which the position and velocity were at an extremum. The frequency was normalized to that at the peak amplitude and is plotted against time, measured in periods of oscillation, for 22 embryos. The slope is 0.0769 ± 0.0071 (mean ± SEM, p oscillation frequency and time for the average oscillation.
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Model for Nucleocytoplasmic Shuttling of Msn2 Coupled to Oscillations in the cAMP-PKA System Scheme of the model showing the different interactions between the components of the cAMP-PKA system and the coupling to Msn2 shuttling between cytosol and nucleus in yeast. The variables of the model are the following: the fractions GEFa and GAPa of active GEF (Cdc25) and GAP proteins (Ira1 and Ira2); the fraction Ras-GTP (RGTP) of Ras proteins (Ras1 and Ras2) bound to GTP; the fraction CYCLa of adenylate cyclase (Cyr1) in the active state; the concentration of cAMP; the fraction of active phosphodiesterase PDEa (Pde1 and Pde2); the fraction R2C2 of PKA in the form of a holoenzyme complex between the regulatory subunit Bcy1 (R) and the three catalytic subunits, free of cAMP (C). R2cAMP2 denotes the holoenzyme with a cAMP molecule bound to each of the two regulatory subunits. We assume that stress (of intensity Str) elicits the inactivation of GEF and the dephosphorylation of Msn2 both in the nucleus and in the cytosol. ... Dynamic Behavior Predicted by the Model (A) Time evolution of RGTP, cAMP, active PKA, and nuclear Msn2 predicted by the model for three different values of Str, the dimensionless parameter measuring stress intensity. At low value, Str = 0 (dotted blue curves), and at high value, Str = 2.5 (dotted red curves), a steady-state level is observed for the different components, whereas at intermediate value, Str = 1 (green curves), sustained oscillations occur. The curves show the oscillatory behavior after the elimination of transients. (B) Envelope of cAMP oscillations as a function of stress intensity showing the maximum (red curve) and the minimum (blue curve) values during sustained oscillations. The variation of periodicity (green dots) is also shown. (C) Envelope of oscillations in Msn2 subcellular localization. The curves show the maximum values (Max) and minimum values (Min) for cytoplasmic Msn2 (in blue) and nuclear Msn2 (in red). Outside of the oscillatory range, the system reaches a stable steady state. The curves have been obtained with the Berkeley Madonna program, by numerical integration of Equations S1–S4. Parameter values are given in Table S2. Initial conditions were as follows: GEFa 0.36, GAPa 0.5, RGTP 0.1, CYCLa 0.1, cAMP 1, R2C2 0.5, MC 0.25, MN 0.25, MCP 0.25, MNP 0.25, and PDEa 0.5. ... Lack of Oscillations in Mutants with Impaired Regulation of the cAMP-PKA Pathway (A) Dynamics of Msn2-GFP in a mutant tpk2w(E235Q). The Y3399 strain has been transformed with plasmid pJL42 coding for MSN2-GFP. Similar results were obtained with the strain Y2857 [tpk2w(V218G)], whereas in the strain Y3398 [tpk2w(Q138E)], Msn2-GFP was always in the nucleus, presumably because the residual activity of PKA was lower. The sequence of pictures (above) and the kinetic curve (below) are given as in Figure 1, except that pictures were taken every 20 s. (B) Dynamics of Msn2-GFP in a mutant ras1Δ, ras2Δ CRI4 (B). The F1D strain has been transformed with plasmid pGR213 coding for Msn2-GFP. The sequence of pictures (above) and the kinetic curve (below) are given as in Figure 1.
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Effects of the damping parameter ζs on the bifurcation curves given by Eq. (12a), depicted by a thick line and Eq. (12b), depicted by a thin line, defining the transition from one to three real solutions for the frequency-amplitude response of W, for ζ=0.03: ζs=0.005 (solid curve); ζs=0.03 (dash curve); and ζs=0.07 (dot curve). ... Effects of the damping parameter ζ on the bifurcation curves given by Eq. (12a), depicted by a thick line and Eq. (12b), depicted by a thin line, defining the transition from one to three real solutions for the frequency-amplitude response of W, for ζs=0.03: ζ=0 (solid curve); ζ=0.03 (dash curve); ζ=0.07 (dot curve); ζ=0.15 (dash-dot curve). ... FRCs of the normalized relative displacement W as a function of the normalized frequency Ω for ζs=0.046, ζ=0.015 and for different values of the nonlinear parameter γ: (a) γ=10‐5; (b) γ=10‐3; (c) γ=1.4×10‐3; (d) γ=10‐2; (e) γ=2.6×10‐2; and (f) γ=3×10‐2. Stable solution (blue solid line), unstable solution (red dashed line). Numerical solution by integrating Eqs. (5a,b) (black ‘○’). (For interpretation of the references to the colour in this figure legend, the reader is referred to the web version of this article.) ... FRCs of the normalized relative displacement W as a function of the normalized frequency Ω for ζs=0.046, ζ=0.026 and for different values of the nonlinear parameter γ: (a) γ=10‐5; (b) γ=10‐3; (c) γ=3.3×10‐3; (d) γ=10‐2; (e) γ=2.6×10‐2; and (f) γ=3×10‐2. Stable solution (blue solid line), unstable solution (red dashed line). Numerical solution by integrating Eqs. (5a, b) (black ‘○’). (For interpretation of the references to the colour in this figure legend, the reader is referred to the web version of this article.)
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Maximal power (means of normalized values ± SEM), and corresponding frequencies (means ± SEM) of the LFP oscillation recorded in the different groups at the period from the 10th to the 30th min after the injection. For the low-dose quinpirole + cocaine group the period is taken after the second injection. ... Scheme of the general experimental protocol and data analysis. Electrophysiological recordings were performed for 45 min in the baseline and for 60 min after the drug injections. Note that in the case of co-administration of quinpirole and cocaine, there were two injections with a 15 min interval. Upper area: For spectral power analysis of the LFPs we took 20 min periods starting from 10th min after the injection (see Fig. 2 for results). Lower area: To exclude the possible effect of the variations in locomotor velocity on the theta frequency, we extracted locomotor bouts, 10 s each, with similar patterns across groups, and took the corresponding LFP segments for frequency analysis and comparison (see Fig. 3 for results). Squared inset on the left side represents the scheme of the locomotor bout. ... Local field potential characteristics during the locomotor bouts in the different groups. Scatter plots depicting the frequency of the peak power (X axis) and the peak power normalized to the average power (Y axis), calculated for the 10 s LFP segments. In each panel, individual values during various drug regimens are compared to the values of the saline group (crosses, represented in each panel for comparative purposes). In addition, the area occupied by the saline values is outlined by the dashed line and filled in gray. Insets show the corresponding 10 s locomotor bouts. The number of segments used and the statistical values are indicated in Table 2. ... Maximal power (means of normalized values ± SEM), and corresponding frequencies (means ± SEM) of the LFP oscillation in the different groups, calculated for the LFP segments corresponding to the 10 s locomotor bouts. ... Electrophysiological effects of various drug regimens. A to D. Averaged power spectral densities of the LFPs recorded from the 10th to the 30th min after the injection in the different groups. Vertical dashed lines mark the peaks of frequency power in the saline and low-dose quinpirole + cocaine groups, respectively. Squared insets at the right side of each graph are schemes of the open-field arena with a corresponding example of the locomotor trajectories. The degree of significance versus the saline group is represented as °°p frequency).
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Language mapping in patient 2. (A) Neurostimulation: Stimulation of two electrode pairs of the posterior frontal lobe (Ch 37 and 45; 45 and 46; denoted by pink boxes) resulted in pure speech arrest with maintained comprehension. Language function was not satisfactorily assessed in the following electrode sites, where neurostimulation induced positive auditory or sensorimotor responses and stimulation had to be prematurely terminated before completion of a question-and-answer trial. Stimulation of an electrode pair of the posterior temporal lobe (Ch 33 and 41; denoted by a red box) induced subjective perception of an annoying high-pitch-sound. Since the patient stated that she did not want to hear such annoying sounds any longer, we decided not to stimulate a neighboring electrode pair (Ch 34 and 42) on the superior temporal gyrus. Stimulation of an electrode pair in the inferior post- and pre-central gyri (Ch 43 and 44; denoted by a blue box) resulted in movement of the throat, and stimulation of a pair (Ch 51 and 59; denoted by a blue box) resulted in movement of lip. Electrical stimulation of electrode pairs (Ch 11 and 12; 13 and 14; 15 and 16; 17 and 25; 18 and 26; 52 and 60) resulted in either motor (blue) or sensory-motor mixed (blue-green) responses involving the right upper extremity. Following the surgical resection of the superior frontal gyrus including the tumor, no postoperative language deficits were noted. (B) ECoG time–frequency analysis time-locked to patient's vocalization: This analytic method was designed to evaluate sequential brain activation associated with comprehension, word retrieval, and vocalization. A time–frequency plot matrix was placed on each subdural electrode. High-frequency gamma-augmentation began to involve the superior temporal gyrus (Ch 34) at 1580 ms prior to the onset of patient's vocalization, the medial part of superior frontal gyrus (Ch 8) and the cingulate gyrus (Ch 4) at 610 ms prior to the onset of patient's vocalization, the inferior frontal gyrus (Ch 46) at 570 ms prior to the onset of patient's vocalization, the inferior post-central gyrus (Ch 43) at 550 ms prior to the patient's vocalization, the medial temporal lobe structure (Ch 67) at 510 ms prior to the patient's vocalization, and the superior temporal gyrus (Ch 34) at 20 ms prior to the onset of patient's vocalization. Channels 48 and 49 were not assessed due to artifacts. (C) ECoG time–frequency analysis time-locked to auditory questions: This analytic method was designed to evaluate brain activation associated with the initiation of auditory question. High-frequency gamma-augmentation began to involve the superior temporal gyrus (Ch 34) at 90 ms after the onset of auditory questions, the cingulate gyrus (Ch 4) at 1000 ms after the onset of auditory questions, the inferior post-central gyrus (Ch 43) at 1410 ms after the onset of auditory questions, and the superior temporal gyrus (Ch 34) at 1510 ms after the onset of auditory questions. ... Language mapping in patient 1. (A) ECoG time–frequency analysis time-locked to patient's vocalization: This analytic method was designed to evaluate sequential brain activation associated with comprehension, word retrieval, and vocalization. A time–frequency plot matrix was placed on each subdural electrode. High-frequency gamma-augmentation began to involve the superior temporal gyrus (Ch 36) at 1750 ms prior to the onset of patient's vocalization, the middle temporal gyrus (Ch 25 and 33) at 740 ms prior to the onset of patient's vocalization, the medial part of superior frontal gyrus (Ch 7 and 8) and the cingulate gyrus (Ch 3) at 700 ms prior to the onset of patient's vocalization, the inferior frontal gyrus (Ch 56) at 510 ms prior to the onset of patient's vocalization, the inferior pre- and post-central gyri (most prominently seen in Ch 54 and 69) at 470 ms prior to the patient's vocalization, the medial temporal lobe structure (Ch 9) at 70 ms prior to the patient's vocalization, and the superior temporal gyrus (Ch 36) at 70 ms after the onset of patient's vocalization. (B) ECoG time–frequency analysis time-locked to auditory questions: This analytic method was designed to evaluate brain activation associated with the initiation of auditory question. High-frequency gamma-augmentation began to involve the superior temporal gyrus (Ch 36) at 30 ms after the onset of auditory questions, the medial part of superior frontal gyrus (Ch 7 and 8) at 1050 ms after the onset of auditory questions, the middle temporal gyrus (Ch 25) at 1260 ms after the onset of auditory questions, and the inferior pre- and post-central gyri (most prominently seen in Ch 54 and 69) at 990 ms after the onset of auditory questions. ... Language mapping in patient 3. (A) Neurostimulation: Stimulation of two electrodes pairs on the occipital lobe resulted in visual symptoms (Ch 1 and 2; 49 and 50; denoted by light-blue boxes). Stimulation of an electrode pair of the inferior pre-central gyrus (Ch 105 and 113; denoted by a pink–blue box) induced speech arrest associated with throat movement. Stimulation of an electrode pair of the inferior post-central gyrus (Ch 106 and 114; denoted by a green box) resulted in tingling of teeth. Language function was not satisfactorily assessed in the following electrode sites, where neurostimulation induced positive motor responses and stimulation had to be prematurely terminated before completion of a question-and-answer trial. Stimulation of an electrode pair of the pre- and post-central gyrus (Ch 121 and 129; denoted by a blue box) resulted in movement of mouth. Stimulation of an electrode pair of the post-central gyrus (Ch 122 and 129; denoted by a blue box) resulted in movement of the thumb. Stimulation of a pair of the medial frontal region (Ch 6 and 7; denoted by a blue box) resulted in tonic extension of the bilateral upper extremities. (B) ECoG time–frequency analysis time-locked to patient's vocalization: This analytic method was designed to evaluate sequential brain activation associated with comprehension, word retrieval, and vocalization. No cortical activation represented as gamma-augmentation was observed in the superior temporal gyrus (Ch 93) during auditory questions. High-frequency gamma-augmentation began to involve the posterior inferior temporal gyrus (Ch 55) at 1220-ms prior to the onset of patient's vocalization, the inferior frontal gyrus (Ch 103) at 590-ms prior to the onset of patient's vocalization, and the inferior pre-central gyrus (Ch 129) immediately prior to the patient's vocalization. (C) ECoG time–frequency analysis time-locked to auditory questions: This analytic method was designed to evaluate brain activation associated with the initiation of auditory question. High-frequency gamma-augmentation began to involve the left superior temporal gyrus (Ch 93) at 70-ms after the onset of auditory questions, the posterior inferior temporal gyrus (Ch 55) at 1020-ms after the onset of auditory questions, and the inferior frontal gyrus (Ch 103) at 910-ms after the onset of auditory questions. The time–frequency matrixes for the entire subdural electrode sites are presented as supplementary data on the website. ... Simultaneous recording of ECoG and vocal sound waves in patient 1. (A) An example of ECoG trace suitable for quantitative analysis is shown with a low-frequency filter of 53-Hz and a high-frequency filter of 300-Hz. Vocal sound waves were simultaneously recorded with intracranial ECoG. The time-lock trigger was placed at the onset of patient's vocalization. (B) Vocal sound wave on Cool Edit Pro Software is shown, and this was used to visually and audibly aid in the manual determination of the onset of the patient's vocalization. ... In vivo animation of auditory-language-induced gamma-oscillations in patient 1. Gamma-augmentation (50 to 150 Hz) initially involved the posterior part of the superior temporal gyrus. At 600 ms prior to the onset of patient's vocalization, gamma-augmentation in that area gradually subsided, and began to involve the most posterior part of middle temporal gyrus, the inferior frontal gyrus and the medial superior frontal gyrus. Immediately prior to the onset of vocalization, gamma-augmentation began to involve the pre- and post-central gyri. At 70 ms after the onset of vocalization, gamma-augmentation began to involve the posterior part of the superior temporal gyrus.
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Evolution of ξ(t)/π in the phase space difference for a CPG with N=4 oscillators and P=3 patterns ξ11=(π,0,0), ξ22=(0,π,0) and ξ43=(0,0,π). ... Schematic representation of the model. The model has three main blocks: the central pattern generator CPG, the CPG–robot interface and the virtual robot. The CPG has a pacemaker ψ, a number of P stored patterns ξk with phase instants τk, where k=1,…,P, and a retrieval network with N phase oscillators. We consider three external inputs from the environment to the system: I1(t) and I2(t) to the CPG, and, I3(t) to the interface CPG–robot. ... Phase oscillators
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