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Teaching Documents by Didier Depireux

We construct a new system of integrable non-linear differential equations associated with the ope... more We construct a new system of integrable non-linear differential equations associated with the operator algebra W (2) 3 of Polyakov. Its members are fractional generalizations of KdV type flows corresponding to an alternative set of constraints on the 2-dim SL(3) gauge connections. We obtain the first non-trivial examples by dimensional reduction from self-dual Yang-Mills and then generate recursively the entire hierarchy and its conserved quantities using a bi-Hamiltonian structure. Certain relations with the Boussinesq equation are also discussed together with possible generalizations of the formalism to SL(N ) gauge groups and W (l) N operator algebras with arbitrary N and l.

Papers by Didier Depireux

Running head: Predicting Responses to Dynamic Spectra J0856 5 (2 of 2) 2 functions were compared ... more Running head: Predicting Responses to Dynamic Spectra J0856 5 (2 of 2) 2 functions were compared to measured responses. The correlation between predicted and measured responses was found to be consistently high (84% with > 0:6). 5. The distribution of response parameters suggest that AI cells may encode the pro le of a dynamic spectrum by performing a multiscale spectro-temporal decomposition of the dynamic spectral pro le in a largely linear manner.

Journal of the Acoustical Society of America, Jun 1, 2019

Hearing loss is the most common form of sensory impairment in humans, with an anticipated rise in... more Hearing loss is the most common form of sensory impairment in humans, with an anticipated rise in incidence as the result of recreational noise exposures. Hearing loss is also the second most common health issue afflicting military veterans. Currently, there are no approved therapeutics to treat sensorineural hearing loss in humans. While hearing loss affects both men and women, sexual dimorphism is documented with respect to peripheral and central auditory physiology, as well as susceptibility to age-related and noise-induced hearing loss. Physiological differences between the sexes are often hormone-driven, and an increasing body of literature demonstrates that the hormone estrogen and its related signaling pathways may in part, modulate the aforementioned differences in hearing. From a mechanistic perspective, understanding the underpinnings of the hormonal modulation of hearing may lead to the development of therapeutics for age related and noise induced hearing loss. Here the authors review a number of studies that range from human populations to animal models, which have begun to provide a framework for understanding the functional role of estrogen signaling in hearing, particularly in normal and aberrant peripheral auditory physiology.

Journal of Neurophysiology, Nov 1, 1996

Journal of Neurophysiology, Nov 1, 1996

Cell Reports, Sep 1, 2021

Noise-induced hearing loss (NIHL) results from a complex interplay of damage to the sensory cells... more Noise-induced hearing loss (NIHL) results from a complex interplay of damage to the sensory cells of the inner ear, dysfunction of its lateral wall, axonal retraction of type 1C spiral ganglion neurons, and activation of the immune response. We use RiboTag and single-cell RNA sequencing to survey the cell-type-specific molecular landscape of the mouse inner ear before and after noise trauma. We identify induction of the transcription factors STAT3 and IRF7 and immune-related genes across all cell-types. Yet, cell-type-specific transcriptomic changes dominate the response. The ATF3/ATF4 stress-response pathway is robustly induced in the type 1A noise-resilient neurons, potassium transport genes are downregulated in the lateral wall, mRNA metabolism genes are downregulated in outer hair cells, and deafness-associated genes are downregulated in most cell types. This transcriptomic resource is available via the Gene Expression Analysis Resource (gEAR; https://umgear.org/NIHL) and provides a blueprint for the rational development of drugs to prevent and treat NIHL.

Journal of Magnetism and Magnetic Materials, 2018

Magnetic drug targeting envisions the use of external magnets to manipulate magnetic particles in... more Magnetic drug targeting envisions the use of external magnets to manipulate magnetic particles inside the human body, to direct them to disease targets such as tumors, infections, and ear and eye targets. A key question is how good are the particles? How well do they move in media under the action of applied magnetic gradients? To address this question, we designed and implemented a simple on-chip testing and image tracking system to quantitatively assess the motion of magnetic particles in response to an applied magnetic gradient. In this system, the magnetic particles are placed in on-chip wells and then a calibrated magnetic gradient is applied to the particles. The resulting motion of the particles is monitored and quantified by a microscope, camera, and by imaging software. The system measures both particle speed and chaining. We assessed the motion of seven different commercial magnetic particle ranging in size from 10 nm to 100 m in diameter. All seven particles displayed consistent trends: larger particles moved faster (according to a power law), particles at higher concentrations created longer chains or needle-like aggregates and moved faster, and both speed and chain or needle length increased with time yielding a final speed proportional to the square of particle diameter. The most striking finding was the consistency of all seven particles within these trends. There were no outliers. No particles performed above the trend lines (no high-performance outliers), nor were there any particles that performed below the trend line (no poor performance outliers). We hope the data collected can be used to better understand particle motion, including the physics of chaining and how it impacts the speed of particle transport in media, and will enable improved design of next-generation magnetic drug delivery systems.

The Hearing Journal, 2017

, where Dr. Shapiro is a professor while also serving as the president of Otomagnetics.

International Journal of Human Factors and Ergonomics, 2019

Pre-synaptic ribbons and active synapses at 16 kHz and 24 kHz. Representative fluorescence micros... more Pre-synaptic ribbons and active synapses at 16 kHz and 24 kHz. Representative fluorescence microscopy images of IHC stained for CtBP2 (red) and GluR2 (green) at 16 kHz (left) and 24 kHz (right) from control and noise-exposed mice. The dotted lines represent the approximate border of one IHC. The inset in the bottom left corner image represent a zoom in of active synapses where CtBP2 and GluR2 partially co-localize. Scale bar represents 10 μm. (PDF 1242 kb)

OHC loss does not account for the frequency-specific PTS at 16 and 24Â kHz or the sex differences... more OHC loss does not account for the frequency-specific PTS at 16 and 24Â kHz or the sex differences in NIHL. Line graph indicating the percentage of OHC loss from apex to base in vehicle-treated noise-exposed animals compared to control non-noise-exposed animals. The frequency range of noise exposure is shaded gray and a gray dotted line outlines the frequency range where significant PTS is seen. Error bars indicate S.E.M. (PDF 396Â kb)

OHC loss along the cochlear duct. Representative fluorescence microscopy images of the Organ of C... more OHC loss along the cochlear duct. Representative fluorescence microscopy images of the Organ of Corti at the level of the OHC (counter-stained with DAPI) at different frequency bands from controls and mice exposed at 101 dB SPL. There is little to no OHC loss in the control animals, whereas extensive OHC loss is seen above 32 kHz in animals exposed to noise. Scale bar represents 20 μm. (PDF 1120 kb)

Table S1.Comparison of average hearing thresholds at baseline in male and female mice (Sidak'... more Table S1.Comparison of average hearing thresholds at baseline in male and female mice (Sidak's multiple comparison test; ns: non-significant). Table S2. Average threshold shift values in dB at 24 h post-noise exposure (CTS) and 15 days post-noise exposure (PTS) in vehicle-treated males and females (Tukey's multiple comparisons test). Table S3. Statistical values for interactions between the two factors following a two-way ANOVA. The degrees of freedom for the numerator (DFn) and denominator (DFd) are shown in parenthesis before the F value. Significant results are shown in bold font. Table S4. Comparison of average ABR thresholds shifts at 24 h (CTS) and 15 days (PTS) post-noise exposure in male and female mice treated with vehicle only (Sidak's multiple comparison test; ns: non-significant). Table S5. Values for the percentage of OHC loss within 32–45.2 kHz, 45.2–51 kHz, and 51–55 kHz. Progressive OHC loss is seen up to 55 kHz which is the highest frequency counted. Bot...

We construct a new system of integrable non-linear differential equations associated with the ope... more We construct a new system of integrable non-linear differential equations associated with the operator algebra W (2) 3 of Polyakov. Its members are fractional generalizations of KdV type flows corresponding to an alternative set of constraints on the 2-dim SL(3) gauge connections. We obtain the first non-trivial examples by dimensional reduction from self-dual Yang-Mills and then generate recursively the entire hierarchy and its conserved quantities using a bi-Hamiltonian structure. Certain relations with the Boussinesq equation are also discussed together with possible generalizations of the formalism to SL(N ) gauge groups and W (l) N operator algebras with arbitrary N and l.

Running head: Predicting Responses to Dynamic Spectra J0856 5 (2 of 2) 2 functions were compared ... more Running head: Predicting Responses to Dynamic Spectra J0856 5 (2 of 2) 2 functions were compared to measured responses. The correlation between predicted and measured responses was found to be consistently high (84% with > 0:6). 5. The distribution of response parameters suggest that AI cells may encode the pro le of a dynamic spectrum by performing a multiscale spectro-temporal decomposition of the dynamic spectral pro le in a largely linear manner.

Journal of the Acoustical Society of America, Jun 1, 2019

Hearing loss is the most common form of sensory impairment in humans, with an anticipated rise in... more Hearing loss is the most common form of sensory impairment in humans, with an anticipated rise in incidence as the result of recreational noise exposures. Hearing loss is also the second most common health issue afflicting military veterans. Currently, there are no approved therapeutics to treat sensorineural hearing loss in humans. While hearing loss affects both men and women, sexual dimorphism is documented with respect to peripheral and central auditory physiology, as well as susceptibility to age-related and noise-induced hearing loss. Physiological differences between the sexes are often hormone-driven, and an increasing body of literature demonstrates that the hormone estrogen and its related signaling pathways may in part, modulate the aforementioned differences in hearing. From a mechanistic perspective, understanding the underpinnings of the hormonal modulation of hearing may lead to the development of therapeutics for age related and noise induced hearing loss. Here the authors review a number of studies that range from human populations to animal models, which have begun to provide a framework for understanding the functional role of estrogen signaling in hearing, particularly in normal and aberrant peripheral auditory physiology.

Journal of Neurophysiology, Nov 1, 1996

Journal of Neurophysiology, Nov 1, 1996

Cell Reports, Sep 1, 2021

Noise-induced hearing loss (NIHL) results from a complex interplay of damage to the sensory cells... more Noise-induced hearing loss (NIHL) results from a complex interplay of damage to the sensory cells of the inner ear, dysfunction of its lateral wall, axonal retraction of type 1C spiral ganglion neurons, and activation of the immune response. We use RiboTag and single-cell RNA sequencing to survey the cell-type-specific molecular landscape of the mouse inner ear before and after noise trauma. We identify induction of the transcription factors STAT3 and IRF7 and immune-related genes across all cell-types. Yet, cell-type-specific transcriptomic changes dominate the response. The ATF3/ATF4 stress-response pathway is robustly induced in the type 1A noise-resilient neurons, potassium transport genes are downregulated in the lateral wall, mRNA metabolism genes are downregulated in outer hair cells, and deafness-associated genes are downregulated in most cell types. This transcriptomic resource is available via the Gene Expression Analysis Resource (gEAR; https://umgear.org/NIHL) and provides a blueprint for the rational development of drugs to prevent and treat NIHL.

Journal of Magnetism and Magnetic Materials, 2018

Magnetic drug targeting envisions the use of external magnets to manipulate magnetic particles in... more Magnetic drug targeting envisions the use of external magnets to manipulate magnetic particles inside the human body, to direct them to disease targets such as tumors, infections, and ear and eye targets. A key question is how good are the particles? How well do they move in media under the action of applied magnetic gradients? To address this question, we designed and implemented a simple on-chip testing and image tracking system to quantitatively assess the motion of magnetic particles in response to an applied magnetic gradient. In this system, the magnetic particles are placed in on-chip wells and then a calibrated magnetic gradient is applied to the particles. The resulting motion of the particles is monitored and quantified by a microscope, camera, and by imaging software. The system measures both particle speed and chaining. We assessed the motion of seven different commercial magnetic particle ranging in size from 10 nm to 100 m in diameter. All seven particles displayed consistent trends: larger particles moved faster (according to a power law), particles at higher concentrations created longer chains or needle-like aggregates and moved faster, and both speed and chain or needle length increased with time yielding a final speed proportional to the square of particle diameter. The most striking finding was the consistency of all seven particles within these trends. There were no outliers. No particles performed above the trend lines (no high-performance outliers), nor were there any particles that performed below the trend line (no poor performance outliers). We hope the data collected can be used to better understand particle motion, including the physics of chaining and how it impacts the speed of particle transport in media, and will enable improved design of next-generation magnetic drug delivery systems.

The Hearing Journal, 2017

, where Dr. Shapiro is a professor while also serving as the president of Otomagnetics.

International Journal of Human Factors and Ergonomics, 2019

Pre-synaptic ribbons and active synapses at 16 kHz and 24 kHz. Representative fluorescence micros... more Pre-synaptic ribbons and active synapses at 16 kHz and 24 kHz. Representative fluorescence microscopy images of IHC stained for CtBP2 (red) and GluR2 (green) at 16 kHz (left) and 24 kHz (right) from control and noise-exposed mice. The dotted lines represent the approximate border of one IHC. The inset in the bottom left corner image represent a zoom in of active synapses where CtBP2 and GluR2 partially co-localize. Scale bar represents 10 μm. (PDF 1242 kb)

OHC loss does not account for the frequency-specific PTS at 16 and 24Â kHz or the sex differences... more OHC loss does not account for the frequency-specific PTS at 16 and 24Â kHz or the sex differences in NIHL. Line graph indicating the percentage of OHC loss from apex to base in vehicle-treated noise-exposed animals compared to control non-noise-exposed animals. The frequency range of noise exposure is shaded gray and a gray dotted line outlines the frequency range where significant PTS is seen. Error bars indicate S.E.M. (PDF 396Â kb)

OHC loss along the cochlear duct. Representative fluorescence microscopy images of the Organ of C... more OHC loss along the cochlear duct. Representative fluorescence microscopy images of the Organ of Corti at the level of the OHC (counter-stained with DAPI) at different frequency bands from controls and mice exposed at 101 dB SPL. There is little to no OHC loss in the control animals, whereas extensive OHC loss is seen above 32 kHz in animals exposed to noise. Scale bar represents 20 μm. (PDF 1120 kb)

Table S1.Comparison of average hearing thresholds at baseline in male and female mice (Sidak'... more Table S1.Comparison of average hearing thresholds at baseline in male and female mice (Sidak's multiple comparison test; ns: non-significant). Table S2. Average threshold shift values in dB at 24 h post-noise exposure (CTS) and 15 days post-noise exposure (PTS) in vehicle-treated males and females (Tukey's multiple comparisons test). Table S3. Statistical values for interactions between the two factors following a two-way ANOVA. The degrees of freedom for the numerator (DFn) and denominator (DFd) are shown in parenthesis before the F value. Significant results are shown in bold font. Table S4. Comparison of average ABR thresholds shifts at 24 h (CTS) and 15 days (PTS) post-noise exposure in male and female mice treated with vehicle only (Sidak's multiple comparison test; ns: non-significant). Table S5. Values for the percentage of OHC loss within 32–45.2 kHz, 45.2–51 kHz, and 51–55 kHz. Progressive OHC loss is seen up to 55 kHz which is the highest frequency counted. Bot...

Schematic showing ABR wave I extraction and analysis. Peak (P1) and trough (T1) values of wave I ... more Schematic showing ABR wave I extraction and analysis. Peak (P1) and trough (T1) values of wave I of the ABR traces (wave shaded in blue) were automatically extracted at stimuli levels from 55 to 85 dB SPL using a MatLab script. Wave I amplitudes were then plotted as a function of the stimuli levels. SigmaPlot was used to perform linear regression (dotted line) and calculate the slope (solid lines). Slopes were then compared between the different groups at 16 kHz. (PDF 471 kb)

Effect of noise on pre-synaptic ribbons and active synapses in IHC. Graphs representing the numbe... more Effect of noise on pre-synaptic ribbons and active synapses in IHC. Graphs representing the number of pre-synaptic ribbons (a) and active synapses (b) in IHC of control and vehicle-treated noise-exposed animals. A significant decrease in pre-synaptic ribbons and active synapses is observed at 24 and 32Â kHz in both males and females, but no difference is seen between sexes. Error bars indicate S.E.M. (PDF 418Â kb)

International Journal of Molecular Sciences, 2021

Recent studies have identified sex-differences in auditory physiology and in the susceptibility t... more Recent studies have identified sex-differences in auditory physiology and in the susceptibility to noise-induced hearing loss (NIHL). We hypothesize that 17β-estradiol (E2), a known modulator of auditory physiology, may underpin sex-differences in the response to noise trauma. Here, we gonadectomized B6CBAF1/J mice and used a combination of electrophysiological and histological techniques to study the effects of estrogen replacement on peripheral auditory physiology in the absence of noise exposure and on protection from NIHL. Functional analysis of auditory physiology in gonadectomized female mice revealed that E2-treatment modulated the peripheral response to sound in the absence of changes to the endocochlear potential compared to vehicle-treatment. E2-replacement in gonadectomized female mice protected against hearing loss following permanent threshold shift (PTS)- and temporary threshold shift (TTS)-inducing noise exposures. Histological analysis of the cochlear tissue revealed...

Journal of the Association for Research in Otolaryngology, 2010

IEEE Control Systems, 2012

Experimental Neurology, 2010

Disrupted ontogeny of forebrain inhibitory interneurons leads to neurological disorders, includin... more Disrupted ontogeny of forebrain inhibitory interneurons leads to neurological disorders, including epilepsy. Adult mice lacking the urokinase plasminogen activator receptor (Plaur) have decreased numbers of neocortical GABAergic interneurons and spontaneous seizures, attributed to a reduction of hepatocyte growth factor/scatter factor (HGF/SF). We report that by increasing endogenous HGF/ SF concentration in the postnatal Plaur null mouse brain maintains the interneuron populations in the adult, reverses the seizure behavior and stabilizes the spontaneous electroencephalogram activity. The perinatal intervention provides a pathway to reverse potential birth defects and ameliorate seizures in the adult.

The spectrotemporal receptive field (STRF) is a functional descriptor of the linear processing of... more The spectrotemporal receptive field (STRF) is a functional descriptor of the linear processing of timevarying acoustic spectra by the auditory system. By cross-correlating sustained neuronal activity with the dynamic spectrum of a spectrotemporally rich stimulus ensemble, one obtains an estimate of the STRF. In this article, the relationship between the spectrotemporal structure of any given stimulus and the quality of the STRF estimate is explored and exploited. Invoking the Fourier theorem, arbitrary dynamic spectra are described as sums of basic sinusoidal components---that is, moving ripples. Accurate estimation is found to be especially reliant on the prominence of components whose spectral and temporal characteristics are of relevance to the auditory locus under study and is sensitive to the phase relationships between components with identical temporal signatures. These and other observations have guided the development and use of stimuli with deterministic dynamic spectra co...