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Using both analytical and numerical methods, nonlinear dynamic behaviours including chaotic motions and subharmonic bifurcations of an inclined beam subjected to harmonic excitation in temperature field are investigated in this paper. Based on the Galerkin method, the mathematical model of motion is derived. Melnikov method is adopted to give an analytical expression of conditions for chaotic motions of the inclined beam. The chaotic feature on the inclined angle is studied in detail. It is presented that there exists a unique excitation frequency $\omega ^*$, such that the critical value of chaos is the monotone decreasing function of the inclination angle when the excitation frequency $\omega \omega ^*$, it is the monotone increasing function of the inclination angle. The subharmonic bifurcations are also studied. It is obtained that subharmonic bifurcations of even orders or odd orders may occur for this system. With the techniques of elliptic functions, it is proved rigorously that this system may undergo chaos through finite subharmonic bifurcations. Numerical simulations are given to verify the chaos threshold obtained by the analytical method.

Circular RNA (circRNA) plays a vital role in the occurrence and development of nasopharyngeal carcinoma (NPC). However, the role of certain specific circRNAs in NPC are still unknown. In this study, collect tumor samples and adjacent normal tissues from clinical NPC patients and detect the expression of circSOX9 by qRT-PCR. Use nucleoplasmic separation analysis, RNase R digestion assay and FISH to detect the characteristics of circSOX9. After knocking down circSOX9, clone formation experiment and transwell assay were used to detect the proliferation and invasion ability of nasopharyngeal carcinoma cells HONE1 and CNE2, and western blot was used to further detect the level of epithelial-mesenchymal transition (EMT). Use the database to screen for possible downstream target genes and verify them with dual-luciferase experiments. Bioinformatics analysis showed that circSOX9 was significantly up-regulated in NPC, and its expression level was positively correlated with the malignant progression of cancer. Data from function gain or loss studies showed that decrease of circSOX9 inhibited the invasion and proliferation of HONE1 and CNE2 cell lines. Further analysis proved that miR-485-3p was the downstream target of circSOX9. The luciferase test showed that by acting as a molecular sponge of miR-485-3p, circSOX9 promotes the proliferation and invasion of NPC cells, while miR-485-3p can target the expression of SOX9. In conclusion, circSOX9 acts as an oncogene in the progression of NPC through miR-485-3p/SOX9, indicating that circSOX9 can be used as a potential therapeutic target and predictive marker for nasopharyngeal carcinoma.

In this manuscript, multiple patterns of slow-fast motion in an accelerating viscoelastic beam model are analyzed from both analytic and numerical view. Based on the modified averaging method, the static solutions of amplitude response equations are obtained. The stability analysis about the zero solution of the averaged equations shows that the zero solution loses its stability through pitchfork bifurcation and the small eigenvalue indicates the existence of strong transient. The numerical bifurcation diagrams and time histories of the fast sub-system verify the results obtained from the averaging process, especially strong transient effects in the vicinity of small amplitude branch. Based on these, two cases of low frequency excitation are considered. When the period of the slow excitation is much larger than the critical time for the fast sub-system to converge to the intermediate branch, the transitions related to pitchfork bifurcation are always periodic. While, if the period of the slow excitation possesses the same magnitude as that of the critical time, transitions between the small amplitude branch and intermediate amplitude can present both regular and irregular manners, which results in complex dynamic buckling regimes. Thus, multiple patterns of slow-fast motion including “periodic bursts with quasi-periodic spiking”, “torus/short transient” mixed mode oscillations, periodic “pitchfork/long transient” mixed mode oscillations, amplitude-modulated oscillations, as well as irregular mixed mode oscillations, are analyzed from numerical view.

K+ cycling in the cochlea is critical to maintain hearing. Many sodium-potassium pumps are proved to participate in K+ cycling, such as Na/K-ATPase. The α2-Na/K-ATPase is an important isoform of Na/K-ATPase. The expression of α2-Na/K-ATPase in the cochlea is not clear. In this study, we used C57BL/6 mice as a model of presbycusis and implemented immunohistochemistry staining and quantitative real time-PCR, and the α2-Na/K-ATPase expression pattern was confirmed in the inner ear. It was found α2-Na/K-ATPase was expressed widely in cochlea and its mRNA and protein expression was gradually reduced with aging (4-, 14-, 26- and 48-weeks old mice). We suspected that, the down-regulation of α2-Na/K-ATPase expression might be associated with the remodeling of K+ cycling, degeneration of morphological structure and decrease of hearing function in aging C57 mice. In conclusion, we speculated that the reduction of α2-Na/K-ATPase might play an important role in the pathogenesis of age-related hearing loss.

In this manuscript, slow-fast motions in a two degrees of freedom model under slow parametric and fast external excitations are analyzed using analytical and numerical methods. By expressing the state variables as the sums of slowly varying average and fast oscillations, the averaged equations which govern the slow dynamics for different magnitudes of external amplitude are obtained. For the averaged equations, analyzation about the equilibria and the corresponding stability shows that, the averaged slow manifolds constitute a pitchfork structure. Meanwhile, the harmonic balancing method is used to compute the slowly varying envelopes of the fast oscillations. On the other hand, bifurcation diagrams of the fast sub-system show structures in accordance with the pitchfork obtained from averaged equations as well as the amplitude curves computed by harmonic balancing method. Two forms of relative location between the folds of cycle on the handle and pitchfork bifurcation point are presented. Based on these, concerning on the slow-fast flow, two patterns of transition behavior between the handle and the upper (lower) branch of pitchfork namely “pitchfork/pitchfork” and “fold/pitchfork” types are analyzed, which indicate the dynamic buckling behaviors. Particularly, discussion about the influence of external excitation shows that, for case of near-resonant external frequency, increasing the amplitude of external excitation will change the local structures as well as the quantitative properties of the pitchfork, but holistic form of pitchfork type is a topological invariant.

Chaotic dynamics and subharmonic bifurcations of a soft Duffing oscillator with a non-smooth periodic perturbation and a harmonic excitation are investigated analytically in this paper. With the Fourier series, the system is expanded to the equivalent smooth system, and chaos arising from heteroclinic intersections is studied with the Melnikov method. The chaotic feature on the system parameters is investigated in detail. Some new interesting dynamic phenomena, such as chaotic bands for some excitation frequencies, are presented. The relationship between the frequency range of chaotic bands and the amplitude of the excitation as well as the damping is obtained analytically. Particularly, for some system parameters satisfying a particular relationship, chaos cannot occur for any excitation amplitudes or frequencies. Subharmonic bifurcations are investigated with a subharmonic Melnikov method. It is analytically proved that the system may undergo chaotic motions through infinite or finite odd order subharmonic bifurcations. Numerical simulations are given to verify the chaos threshold and revolution from subharmonic bifurcations to chaos obtained by analytical methods.

OBJECTIVES/HYPOTHESIS To compare the efficacy and adverse effects of triamcinolone acetonide econazole cream and nystatin suspension in the treatment of otomycosis, and to determine the clinical features, predisposing factors, and etiology of otomycosis. STUDY DESIGN A prospective study. METHODS A prospective clinical trial was conducted on 786 patients diagnosed with otomycosis. The study population was randomly divided into two treatment groups of triamcinolone acetonide econazole cream (TAEC) and nystatin suspension in a 1:1 ratio. After clearing all fungal deposits in the external auditory canal, the antimycotic drugs were locally applied for at least 2 weeks. The efficacy and adverse effects were compared between the two antifungal reagents by statistical analysis. Meanwhile, patient clinical data were collected to find out the clinical features, predisposing factors, and etiology. RESULTS Pruritis was the most common symptom and Aspergillus niger was the leading fungal pathogen. There was high association (44.5%) of otomycosis with a history of unclean ear picking. The cure rate was 97.6% in the TAEC group and 73.5% in the nystatin group (P

To investigate predictive risk factors for complications associated with migrating fish bones in the surrounding tissue of upper gastrointestinal tract. A retrospective analysis over 12 years was conducted of 45 cases of buried fish bones in the surrounding tissue of upper gastrointestinal tract with complications. Meanwhile, a control group, including 39 cases of prolonged buried fish bones in the surrounding tissue of upper gastrointestinal tract without complications, was set. Patient clinical data were collected and analyzed to predict the risk factors for complications. The results of Chi-square test and univariate analysis both showed a significant difference in length of fish bone (> 2 cm), a history of concurrent medical illness (diabetes mellitus and renal hypofunction), symptoms (medium or heavy pain and dysphagia), and duration of significant symptoms (> 7 days) between the complication group and non-complication group. Multivariate analysis further identified length (> 2 cm), diabetes mellitus, medium or heavy pain, dysphagia, and duration of significant symptoms (> 7 days) as independent risk factors for complications. The consequences of fish bones migrating outside the upper gastrointestinal tract are various in different people. Awareness should be raised when encountering a patient ingesting a long fish bone, having a history of diabetes mellitus, presenting with significant discomforts, or these discomforts lasting for a long time. This study will help practitioners counsel their patients on the risks and `benefits of surgery versus observation of this condition.

In this brief communication, Melnikov’s method is adopted to investigate the chaotic behaviors of a nanoplate postulating nonlinear Winkler foundation. The critical curves separating the chaotic and non-chaotic regions are found. It is presented that the chaotic behaviors can occur when the parameters are chosen in the chaotic regions. Numerical simulations verify the theoretical analytical results. The results provide some inspiration and guidance for the analysis and dynamic design of this nanoplate.

Previous studies have demonstrated that elevated yes‑associated protein (YAP) expression is associated with tumor aggression and poor prognosis in various types of human cancer. However, the clinicopathological significance and the prognostic value of YAP in laryngeal squamous cell carcinoma (LSCC) is unknown. The aim of the present study was to identify the expression pattern and prognostic significance of YAP in patients with LSCC. YAP mRNA and protein expression levels were examined in fresh and archived LSCC samples using the reverse transcription‑quantitative polymerase chain reaction, immunohistochemistry (IHC) and western blotting. The association between YAP expression levels with the malignant status and prognosis of patients with LSCC was analyzed. Upregulated protein and mRNA expression levels of YAP were detected in LSCC tissues compared with paired healthy surgical margin tissues. Positive expression of YAP was identified in 84/121 (69.4%) LSCC tissues and in 4/30 (13.3%) healthy surgical margin tissues by IHC. Positive YAP protein expression was significantly associated with clinical stage, TNM classification, lymph node metastasis and differentiated degree. Patients with positive YAP expression exhibited a significantly decreased overall survival time compared with patients with negative YAP expression (P=0.0002). Multivariate analysis indicated that the level of YAP expression was an independent prognostic factor for poor survival in patients with LSCC (P=0.012). In conclusion, the expression level of YAP was significantly increased in LSCC and associated with the malignant status of LSCC. Therefore, YAP may represent a novel biomarker for predicting the prognosis of patients with LSCC.

Using both analytical and numerical methods, global dynamics including subharmonic bifurcations and chaotic motions for a class of inverted pendulum system are investigated in this paper. The expressions of the heteroclinic orbits and periodic orbits are obtained analytically. Chaos arising from heteroclinic intersections is studied with the Melnikov method. The critical curves separating the chaotic and non-chaotic regions are obtained. The conditions for subharmonic bifurcations are also obtained. It is proved that the system can be chaotically excited through finite subharmonic bifurcations. Some new dynamical phenomena are presented. Numerical simulations are given, which verify the analytical results.

In this paper, a dry friction oscillator with periodic excitation is investigated. Melnikov method is used to study chaos of this model. The parameter regions of chaos are obtained. Numerical simulations are also given, which verify the analytical results.

Objective: To investigate the clinical characteristics, etiology, treatment outcomes, and prognostic factors of sudden sensorineural hearing loss (SSNHL) in children to guide the clinical diagnosis and treatment of SSNHL in the pediatric population. Study Design: Retrospective case review. Setting: Tertiary referral center. Patients: Patients diagnosed with SSNHL from November 2011 to December 2017 with relatively complete clinical data. Intervention: Diagnosis and systemic treatment of SSNHL. Main Outcome Measures: Patients’ clinical characteristics, etiology, laboratory tests, imaging, pure-tone audiometry at admission, and discharge were analyzed. Results: A total of 25 children and 149 adults with SSNHL were included. Recent or previous viral infection rates (81.8%) and fasting blood glucose level (5.23 + 1.47 mmol/L) in children with SSNHL were lower than those in adult SSNHL patients (p = 0.033, p = 0.033). Autoimmune abnormalities (90.0%) and plasma fibrinogen abnormalities (27.3%) were higher in children with SSNHL than those in adult SSNHL patients (40.0%, 8.8%, respectively, p

With analytical and numerical methods, dynamic response of a composite laminated buckled beam with a lumped mass and an axial excitation is investigated in this paper. The dynamic equation of the first mode for this model, which is a perturbation of a Hamilton system with both quadratic and cubic nonlinearities as well as external and parametric excitations, is obtained with the Galerkin method. The distribution of the equilibriums, homoclinic orbits and periodic orbits for the unperturbed system under different system parameters are obtained analytically. Chaotic vibrations arising from homoclinic intersections are studied with Melnikov method. Chaotic feature on the location of the lumped mass is investigated in detail. It is presented that there exist controllable frequencies decreasing monotonously with the location of the lumped mass for this system. Subharmonic bifurcation is also studied with the subharmonic Melnikov method. It is numerically proved that the system may undergo chaotic motions through finite subharmonic bifurcations. Numerical simulations including the phase portraits, time histories, Poincar e ´ sections, Lyapunov spectrums and bifurcation diagram are given, which confirm the analytical results.

Based on the idea of slow-fast dynamics, two tapping modes are investigated in the Atomic Force Microscope (AFM) model with Lennard-Jones force and slow-fast base motion. According to the approximation derived from Taylor expansion in the vicinity of static equilibrium of the linearized system, we give a prediction about harmonic responses of the fast sub-system (FSS). Then a truncated version of harmonic balancing method (HBM) is combined with the Floquet theory to give the distribution and stability of the harmonic responses, which indicates the contact and non-contact modes dominated by cycle manifolds. By directly integrating the FSS, the numerical bifurcation diagrams and the frequency spectrums corresponding to the periodic solutions are obtained to verify the results given by the half-analytic process. Moreover, distribution of basins of attraction shows that, when the tri-stability is destroyed by fold bifurcation of cycle, due to the highly fragmented fractal structures in basins, transition between different mode manifolds may present an weak irregular way. On the other hand, when the slow excitation is introduced, the regular and irregular “cycle-cycle” type mixed mode oscillations (MMOs) triggered by “fold of cycle/fold of cycle” hysteresis can be observed, which results in two tapping mode, .i.e., the slow tapping mode and the “compound of contact/snap tapping” mode. Besides that, our results show that, for the AFM under slow and near-resonant excitation, the beneficial effects of constant contact mode and snap tapping mode can be utilized.

Age-related hearing loss (AHL) is one of the most common sensory disorders among elderly persons. The inwardly rectifying potassium channel 5.1 (Kir5.1) plays a vital role in regulating cochlear K(+) circulation which is necessary for normal hearing. The distribution of Kir5.1 in C57BL/6J mice cochleae, and the relationship between the expression of Kir5.1 and the etiology of AHL were investigated. Forty C57BL/6J mice were randomly divided into four groups at 4, 12, 24 and 52 weeks of age respectively. The location of Kir5.1 was detected by immunofluorescence technique. The mRNA and protein expression of Kir5.1 was evaluated in mice cochleae using real-time polymerase-chain reactions (RT-PCR) and Western blotting respectively. Kir5.1 was detected in the type II and IV fibrocytes of the spiral ligament in the cochlear lateral wall of C57BL/6J mice. The expression levels of Kir5.1 mRNA and protein in the cochleae of aging C57BL/6J mice were down-regulated. It was suggested that the age-related decreased expression of Kir5.1 in the lateral wall of C57BL/6J mice was associated with hearing loss. Our results indicated that Kir5.1 may play an important role in the pathogenesis of AHL.

The large conductance Ca(2+)-activated K(+ )channels (BK) expression is decreased in the cochleae of age-related hearing loss (AHL) mice. BK channel may be associated with AHL.AHL is the most common among elderly persons. BK channels act as sensors for membrane voltage and intracellular Ca(2+ )and are essential for hearing. To investigate the distribution of BK channel in the cochleae of C57BL/6J mice, and the relationship between the expression of BK channel and the etiology of AHL.BK expression was studied in the cochleae of C57BL/6J mice at various ages (4, 12, 26, 52 weeks). The expressions of BK at the protein and mRNA levels were detected by immunofluorescence technique, western blot and quantitative real time PCR.In comparison with 4-week-old mice, BK expressions in the cochleae at 12, 26 and 52 weeks of age were significantly and gradually decreased at both the protein and the mRNA levels. The immunofluorescence technique showed the BK channel was located in the hair cells and cells of the spiral ganglion, spiral ligament and stria vascularis and its expression also decreased with aging.

The size of cochlear nerve (CN) is atrophic in adult auditory neuropathy spectrum disorder (ANSD) patients compared with non-ANSD sensorineural hearing loss (SNHL) patients and normal hearing subjects, and CN deficiency is one of the lesions for ANSD patients.To evaluate the dimensions of CN in adult ANSD patients on magnetic resonance imaging (MRI) and confirm the hypothesis that CN deficiency is one of the lesions for ANSD patients.Medical records and MRI of 24 adult ANSD patients reviewed retrospectively and 20 non-ANSD SNHL and 24 volunteers with normal hearing were recruited as control groups. The long diameter (LD), short diameter (SD), and cross-sectional area (CSA) of CN and facial nerve (FN) were measured.Among the 24 ANSD patients, this study was able to reconstruct and measure the CN of 91.7% (22/24, total 43 ears) of patients and FN of 83.3% (20/24, total 38 ears) of patients. The mean values and standard deviations of LD, SD, and CSA of CN in ANSD patients were 0.65 ± 0.20 mm, 0.44 ± 0.15 mm, and 0.30 ± 0.19 mm(2), respectively. They were significantly smaller in ANSD patients than in control groups (p 0.001).

The dynamics equation of the compound pendulum system is studied with the Melnikov method. The critical condition of the chaotic motion is discussed and the critical curve of the parameter is drawn. With the Runge-Kutta method, Numerical simulations are given, which verified the analytical results. It is concluded that there exists Smale horseshoe chaos arising from transversal intersections of stable and unstable manifold of the homoclinic orbit. The critical values for chaos first increase and then decrease with the increasing of the driving torque.

LaminB1, a major component of the nuclear lamina, is a potent regulator of cellular proliferation and senescence and also known to be essential for neuronal migration and brain development. However, the expression patterns of LaminB1 in the rat cochleae are still not fully revealed. Utilizing immunofluorescence, Western blotting, and quantitative real-time PCR, we identified the distribution and expression of LaminB1 in the rat cochleae. Immunofluorescence staining indicated that LaminB1 was mainly localized in the auditory hair cells (HCs), spiral ganglion cells (SGC), stria vascularis (STV, including spiral ligament), Reissner's membrane (RM), and limbus laminae spiralis (LLS). Western blotting analysis illustrated that the distribution of LaminB1 in rat cochleae was characterized by tissue specificity. The LaminB1 protein was expressed more in SGC and basilar membrane (BM) than in STV. Meanwhile, the mRNA expression of LaminB1 displayed difference in cochlear tissues. These observations preliminarily revealed the expression patterns of LaminB1, providing a theoretical basis for further study on the role of LaminB1 in auditory function.

Subharmonic bifurcations and chaotic dynamics are investigated both analytically and numerically for a class of ship power system. Chaos arising from heteroclinic intersections is studied with the Melnikov method. The critical curves separating the chaotic and nonchaotic regions are obtained. The chaotic feature on the system parameters is discussed in detail. It is shown that there exist chaotic bands for this system. The conditions for subharmonic bifurcations with O type or R type are also obtained. It is proved that the system can be chaotically excited through finite subharmonic bifurcations with O type, and it also can be chaotically excited through infinite subharmonic bifurcations with R type. Some new dynamical phenomena are presented. Numerical simulations are given, which verify the analytical results.

International audience; To compare the degree and distribution of mineralization in femoral neck cortex from 23 women with hip fractures (age 65–96 years) and 17 female controls (age 72–103 years), we obtained 3D data by synchrotron radiation microtomography (SRμCT). Variables were degree of mineralization of bone (DMB) in total cortex (cDMBSRMEAN), osteons (oDMBSRMEAN), and pure interstitial tissue (intDMBSRMEAN). The cortex on SRμCT images was divided into nine to twelve 50-μm zones from the periosteum to the endosteum; cDMBSRMEAN, oDMBSRMEAN, and intDMBSRMEAN were measured in each zone. We used descriptive statistics and t tests, general linear model analyses to compare DMBSR values across zones and individuals, one-way analysis of variance for within-group comparisons of zones. In patients, the variance of mineral content value was not different than in controls, but mean values of degree of mineralization varied across zones. These cross-sectional data suggest that bone fragility may be related to a greater heterogeneity of the distribution of mineralization in femoral neck cortex.

Heat shock protein 70 (Hsp70) has been known to be able to play a protective role in the cochlea. The aim of this study was to investigate whether geldanamycin hydrosoluble derivative 17-(dimethylaminoethylamino)-17-demethoxygeldanamycin (17-DMAG) has the ability to induce Hsp70 up-regulation to protect hair cells from kanamycin-induced ototoxicity in vitro. The organ of Corti (OC) explants were isolated from mice at postnatal day 3–5. Then, the explants were exposed to kanamycin with or without pre-incubation with 17-DMAG. The expression of Hsp70 was assessed by reverse transcription-quantitative polymerase chain reaction, ELISA, and immunofluorescent staining. The surviving hair cells were examined by phalloidin labeling and were counted. We found that Hsp70 expression in the explants after pre-incubation with 17-DMAG was significantly increased at both mRNA and protein levels. Immunofluorescent staining showed that Hsp70 was mainly located in the auditory hair cells. Compared with kanamycin group, the loss of hair cells was inhibited significantly in 17-DMAG + kanamycin group. Our study demonstrated that 17-DMAG induces Hsp70 in the hair cells, and has a significant protective effect against kanamycin ototoxicity in vitro. 17-DMAG has the possibility to be a safe and effective anti-ototoxic drug.

The local dynamics including stability and Hopf bifurcation of autonomoius van der Pol-Duffing circuit system containing parallel resistor are investigated both analytically and numerically in this paper. All the equilibrium points and their stability conditions are presented. The parametric conditions for Hopf bifurcation are also obtained. Numerical simulations verify the analytical results.

The purpose of this study was to explore the central mechanism of transauricular vagus nerve stimulation (taVNS) to human by fMRI and to find a suitable taVNS site for potential tinnitus treatment. 24 healthy subjects aged between 28 and 38 years were enrolled in the experiment. 8 subjects were stimulated in the auricular acupoints Kindey (CO10), Yidan (CO11), Liver (CO12) and Shenmen (TF4) in the left ear, 8 subjects were stimulated at the anterior wall of the auditory canal and left lower limb as an anterior stimulation group; 8 persons who were arranged in a sham group received taVNS at the left ear lobe and tail of the helix. Functional magnetic resonance imaging (fMRI) data from the cortices was collected and an Alphasim analysis was performed. We found that taVNS at auricular acupoints CO10-12, TF4 can instantly and effectively generate blood oxygenation level dependent (BOLD) signal changes in the prefrontal, auditory and limbic cortices of healthy subjects by fMRI. When comparing the acupoints group and the sham group in the left brain, the signals from the prefrontal cortex, the auditory ascending pathway including superior temporal gyrus, middle temporal gyrus, thalamus and limbic system regions such as putamen, caudate, posterior cingulate cortex, amygdala and parahippocampal gyrus were increased under our stimulation. The difference of the BOLD signal in the left brain between acupoints group and anterior group was in the superior temporal gyrus. We could also find signal differences in several regions of right brain among the groups. In conclusion, taVNS at acupoints CO10-12, TF4 could activate the prefrontal, auditory and limbic cortices of healthy brain and this scheme could be a promising tool for tinnitus treatment.

Nonlinear dynamics including stability and Hopf bifurcation of the MR damper system are investigated in this paper. All the equilibriums of the system and their stability are studied in detail. Using the Hopf bifurcation theorem and the first Lyapunov coefficient, the conditions and the type of Hopf bifurcations for the system are obtained. With the Runge-Kutta method, numerical simulations are given, which verify the analytic results.

Employed both analytical and numerical methods, chaotic motions for the parametrically excited roll motion of a ship in regular longitudinal waves are investigated in this paper. It is presented that the mechanism for chaos is the intersection of the stable and unstable manifolds of the homoclinic orbits or heteroclinic cycle. The parameter conditions for chaos are obtained rigorously with the Melnikov method. The chaotic regions of the system parameters are illustrated. The chaotic feature on the system parameters is discussed in detail. It is obtained that the critical values of chaos for homoclinic orbits increase monotonously as the increasing of the nonlinear roll attenuation coefficient, while the critical values of chaos for the heteroclinic cycle decrease monotonously as the increasing of the nonlinear roll attenuation coefficient. On the other hand, critical values of chaos for both homoclinic orbits and heteroclinic cycle increase monotonously as the increasing of the excitation amplitude. It is also demonstrated that there exist chaotic bands for this model. Numerical simulations verify the analytical results.

In this paper, by employing both analytical and numerical methods, global dynamic responses including subharmonic bifurcations and chaos are investigated for a carbon nanotube supported by a Winkler and Pasternak foundation. The criteria of chaos arising from transverse intersections for stable and unstable manifolds of homoclinic orbits are proposed with the Melnikov method. The critical curves separating the chaotic and nonchaotic regions are plotted in the parameter plane. The parameter conditions for subharmonic bifurcations are also obtained by the subharmonic Melnikov method. It is proved rigorously that the route to chaos for this model is infinite subharmonic bifurcations. The stability of subharmonic bifurcations is also studied by the characteristic multipliers. Numerical simulations are given to confirm the analytical results.

Age-related hearing loss (ARHL) is the most common human morbidity. However, the molecular mechanisms underlying ARHL are little known. In the present study, the expression of Ca(v)1.3 calcium channels in the C57BL/6J ARHL mouse cochlea was investigated. The hearing threshold was assessed by auditory brainstem response and the expressions of Ca(v)1.3.3 calcium channels at the protein and mRNA levels were detected by immunohistochemistry, western blot, and real-time RT-PCR. Associated with the auditory brainstem response threshold increased with age, the Ca(v)1.3.3 expression was gradually decreased. In comparison with 4-week-old mice, Ca(v)1.3.3 expressions in the cochlea at 14, 24, and 48 weeks of age were significantly and gradually decreased at both the protein and the mRNA levels. Immunohistochemistry showed that the expression of Ca(v)1.3.3 was apparently reduced at the inner hair cells, outer hair cells, and stria vascularis in the cochlear lateral wall in the aged mice. Our findings indicate that Ca(v)1.3.3 calcium channel expression in the cochlea is reduced in the ARHL mice and is associated with ARHL. The data also support a view that Ca(v)1.3.3 calcium channel is a good target for prevention and therapy of ARHL.

Using a combination of analytical and numerical methods, the paper studies chaotic motions of a two-dimensional airfoil with cubic nonlinearity in supersonic flow. By using the undetermined coefficient method, the homoclinic orbit is found, and the uniform convergence of the homoclinic orbit series expansion is proved. It analytically demonstrates that there exists a homoclinic orbit joining the initial equilibrium point to itself, therefore Smale horseshoe chaos occurs for this system via Siʼlnikov criterion. The system evolves into chaotic motion through period-doubling bifurcation, and is periodic again as the dimensionless airflow speed increases. While the system is periodic and chaotic alternately as the wing mass static moment about the elastic axis increases. When the nonlinear stiffness coefficient crosses its critical value, the system is always chaotic. Numerical simulations are also given, which confirm the analytical results.

To investigate the location and distribution of plasma membrane Ca²⁺ -ATPase isoform 2(PMCA2) in the cochleas of C57BL/6J mice at various ages (4w, 14w, 22w, 45w), and to reveal the relationship of PMCA2 and age-related hearing loss (AHL).The distribution of PMCA2 in the cochleas of C57BL/6J mice was detected by immunohistochemistry at various ages (4w, 14w, 22w, 45w). Real-time polymerase chain reaction (Rt-PCR) was used to detect the level of PMCA2 mRNA in the cochleas of C57BL/6J mice at the ages of 4, 14, 22 and 45 weeks old respectively. Using SPSS17.0 software for statistical analysis.PMCA2 was mainly located in the hear cells, stria vascularis, and spiral ganglion cells. Faint labeling of PMCA2 was also observed in spiral ligament. Hair cells missed and the number of spiral ganglion cells reduced with age. Expression of PMCA2 in the cochleas of C57BL/6J mice also showed age-related decreasing. The results of Rt-PCR demonstrated the expression of mRNA of gene (Atp2b2) at 14 weeks age was significantly less than 4 week-old mice cochlears (P0.05). The expression of mRNA of gene (Atp2b2) at 22 weeks age was significantly less than 14 week-old mice cochlears (P0.05). The expression of mRNA of gene (Atp2b2) at 45 weeks age was significantly less than 14 week-old mice cochlears (P0.01).PMCA2 is mainly located in the hear cells, stria vascularis, and spiral ganglion cells. Faint labeling of PMCA2 is also observed in spiral ligament. The expression of PMCA2 demonstrates an age-related decrease with age. The mRNA expression level of PMCA2 gene(Atp2b2) in the cochleas of C57BL/6J mice displayed an age-related decrease. PMCA2 transporters may play a critical role in maintaining the normal morphology of the inner ear and it may be related to AHL.

Although Ca(V)1.3 channels are known to be essential for neuronal excitation and signal transduction in the auditory system, their expression patterns in the cochlea are still not fully understood, particularly in the regions where non-sensory cells are located. We performed immunohistochemistry, western blotting and reverse transcription-polymerase chain reaction (RT-PCR) to identify the expression and distribution of Ca(V)1.3 channels in the rat cochlea. Immunohistochemistry revealed that Ca(V)1.3 channels were localized in the outer hair cells (OHCs), inner hair cells (IHCs), limbus laminae spiralis, spiral ganglion cell, spiral ligament (SL), and stria vascularis (STV). The results of RT-PCR and western blotting demonstrated Ca(V)1.3 channels had a tissue-specific expression pattern. Ca(V)1.3 mRNA and protein were intensively expressed in the basilar membrane and spiral ganglion while moderate level of Ca(V)1.3 channels was observed in SL and STV. Our study preliminarily revealed the expression patterns of Ca(V)1.3 channels in the rat cochlea, providing a theoretical basis for further research on the role of Ca(V)1.3 channels in the periphery auditory system.

Using a combination of analytical and numerical methods, the paper studies bifurcations and chaotic motions of a two-dimensional airfoil with cubic nonlinearity in incompressible flow. One type of critical points (characterized by a negative eigenvalue, a simple zero eigenvalue and a pair of purely imaginary eigenvalues) for the bifurcation response equations is considered. With the aid of the normal form theory, the explicit expressions of the critical bifurcation lines leading to incipient and secondary bifurcations are obtained. The stability of the bifurcation solutions is also investigated. By using the undetermined coefficient method, the homoclinic orbit is found, and the uniform convergence of the homoclinic orbit series expansion is proved. It analytically demonstrates that there exists a homoclinic orbit joining the initial equilibrium point to itself, therefore Smale horseshoe chaos occurs for this system via Si’lnikov criterion. The system evolves into chaotic motion through period-doubling bifurcation, and is periodic again as the dimensionless airflow speed increases. Numerical simulations are also given, which confirm the analytical results.

Objective To study the expression of plasma membrane Ca2+-ATPase isoform 2 (PMCA2) and its alternative splicing at sites A (the first intracellular loop) and C (the C-terminal region) in the neonatal rat cochlea. Methods The cochleae from rats postnatal day 3 to postnatal day 4 (P3–P4) were dissected, fixed, embedded, and sectioned. Meanwhile, the cochlear coils from neonatal rats were isolated and fixed. Using immunofluorescence staining, the expression of PMCA2 was respectively examined in the cochlear sections and cochlear coils. In addition, the total RNAs of basilar membrane (BM, including the organ of corti, the same below), spiral ganglion (SG), spiral ligament (SL, including SV, the same below), and the whole cochlea from neonatal rats were respectively extracted and reverse transcribed to cDNAs, then subjected to primers flanking site A or C in the PMCA2 gene using reverse transcription polymerase chain reaction (RT-PCR). Western blot was also applied to detect the expression of PMCA2 isoforms in the cochlear tissues. Results We found that PMCA2 is strongly expressed in outer hair cell (OHC) bundles, SG, and stria vascularis (SV), weakly expressed in Reissner's membrane (RM), and occasionally expressed in inner hair cell (IHC) bundles. Moreover, w/a is the major splice form of PMCA2 present in hair cell bundles, z/b and z/c are the major splice forms of PMCA2 present in SG, and w/a and w/c are the major splice forms of PMCA2 present in SV. In the whole cochlea, variants w, y, and z were detected at site A, and variants a, b, and c were detected at site C. Using Western blot, variant a or b was also detectable in the same cochlear tissues mentioned above. Conclusions PMCA2 and its splice variants at sites A and C are differentially expressed in cochlear tissues of neonatal rat.

The global bifurcations and chaotic motions are investigated analytically for an arch structure with parametric and forced excitation. The critical curves separating the chaotic and non-chaotic regions are drawn, which show that the system in the case of 1:1 resonance is more easily chaotically excited than the case of 1:2 resonance. There exist “uncontrollable regions” or “chaotic bands” for the system as the natural frequency varies. There also exists a “controllable frequency” for the system with linear and cubic parametric excitation. The system can be chaotically excited through infinite subharmonic bifurcations of odd/even orders. Numerical results agree with the analytical ones.