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In this paper, we are concerned with the coefficients identification for the Helmholtz equation. This problem which consists of determining an unknown inner boundary of an annular domain and surface heat transfer coefficient from boundary Cauchy data. We propose two reconstruction algorithms to simultaneously recover the shape and the surface impedance of the obstacle within a body. This problem is ill-posed, thus we apply regularization techniques in order to improve the corresponding approximation. Numerical experiments are presented for the reconstruction algorithms, which show that both the shape and the surface impedance can be reconstructed accurately. AMS Mathematics Subject Classification 2010: 65N20,65N21.

In this paper, we consider an inverse conductive scattering problem for the Helmholtz equation from measurements on the outer boundary. We want to seek reconstruction algorithms to detect the numbe...

In this paper, we consider an inverse scattering problem of reconstructing the shape and impedance for a cavity from one point source and several measurements placed on a curve inside the cavity. T...

Aberrant increases in neuronal network excitability may contribute to cognitive deficits in Alzheimer's disease (AD). However, the mechanisms underlying hyperexcitability of neurons are not fully understood. Voltage-gated sodium channels (VGSC or Nav), which are involved in the formation of excitable cell's action potential and can directly influence the excitability of neural networks, have been implicated in AD-related abnormal neuronal hyperactivity and higher incidence of spontaneous non-convulsive seizures. Here, we have shown that the reduction of VGSC α-subunit Nav1.6 (by injecting adeno-associated virus (AAV) with short hairpin RNA (shRNA) into the hippocampus) rescues cognitive impairments and attenuates synaptic deficits in APP/PS1 transgenic mice. Concurrently, amyloid plaques in the hippocampus and levels of soluble Aβ are significantly reduced. Interfering with Nav1.6 reduces the transcription level of β-site APP-cleaving enzyme 1 (BACE1), which is Aβ-dependent. In the presence of Aβ oligomers, knockdown of Nav1.6 reduces intracellular calcium overload by suppressing reverse sodium-calcium exchange channel, consequently increasing inactive NFAT1 (the nuclear factor of activated T cells) levels and thus reducing BACE1 transcription. This mechanism leads to a reduction in the levels of Aβ in APP/PS1 transgenic mice, alleviates synaptic loss, improves learning and memory disorders in APP/PS1 mice after downregulating Nav1.6 in the hippocampus. Our study offers a new potential therapeutic strategy to counteract hippocampal hyperexcitability and subsequently rescue cognitive deficits in AD by selective blockade of Nav1.6 overexpression and/or hyperactivity.

In this paper, we study an inverse source problem for the Helmholtz equation from measurements. The purpose of this paper is to reconstruct the salient features of the hidden sources within a body. We propose three stable reconstruction algorithms to detect the number, the location, the size, and the shape of the hidden sources along with compact support from a single measurement of near-field Cauchy data on the external boundary. This problem is nonlinear and ill-posed; thus, we should consider regularization techniques in reconstruction algorithms. We give several numerical experiments to demonstrate the viability of our proposed reconstruction algorithms.

In this paper, we consider a two-dimensional inverse medium problem from noisy observation data. We propose effective reconstruction algorithms to detect the num-ber, the location and the size of the piecewise constant medium within a body, and then we try to recover the unknown shape of inhomogeneous media. This problem is nonlinear and ill-posed, thus we should consider stable and elegant approaches in order to improve the corresponding approximation. We give several examples to show the viability of our proposed algorithms.

In this paper, we consider an inverse geometric problem for the modified Helmholtz equation from measurements of the potential taken on the boundary of the geometrical domain. Our goal is to seek reconstruction algorithms to detect the number, the location, the size and the shape of unknown obstacles from Cauchy data on the external boundary. This problem is ill-posed and nonlinear, thus we should employ regularization techniques in our proposed algorithms. We give several numerical examples to demonstrate the stability of numerical algorithms.

Mammalian target of rapamycin (mTOR) signaling plays essential roles in brain development. Hyperactive mTOR is an essential pathological mechanism in autism spectrum disorder (ASD). Here, we show that tripartite motif protein 32 (TRIM32), as a maintainer of mTOR activity through promoting the proteasomal degradation of G protein signaling protein 10 (RGS10), regulates the proliferation of medial/lateral ganglionic eminence (M/LGE) progenitors. Deficiency of TRIM32 results in an impaired generation of GABAergic interneurons and autism-like behaviors in mice, concomitant with an elevated autophagy, which can be rescued by treatment embryonically with 3BDO, an mTOR activator. Transplantation of M/LGE progenitors or treatment postnatally with clonazepam, an agonist of the GABAA receptor, rescues the hyperexcitability and the autistic behaviors of TRIM32−/− mice, indicating a causal contribution of GABAergic disinhibition. Thus, the present study suggests a novel mechanism for ASD etiology in that TRIM32 deficiency-caused hypoactive mTOR, which is linked to an elevated autophagy, leads to autism-like behaviors via impairing generation of GABAergic interneurons. TRIM32−/− mouse is a novel autism model mouse.

In this paper, we consider the recovery of photon diffusion coefficient in the case of piecewise constant coefficients in optical tomography from boundary measurements of light propagation within a tissue. We propose an effective reconstruction algorithm to detect the number, the location, the size and the shape of piecewise constant coefficients. This problem is nonlinear and severely ill-posed, thus we should consider a regularisation technique in our approach in order to improve the corresponding approximation. We give several examples to show the viability of our proposed method.

In this paper, we study an inverse heat conduction problem without initial data in a bounded domain in which the Cauchy data at x=0 are given and the solution in 0

While many studies have compared Tibetans and low-altitude born Han living at high altitude, few have carefully controlled the chronological age at which lowlanders migrated, the length of time they had lived at high altitude, their nutrition, and their socio-economic status. This has produced an array of results that frequently do not support the hypothesis that Tibetans and Han show fundamental differences in their response to hypoxia. Unlike the situation in the Andes, only one study has tested the developmental adaptation hypothesis on the Qinghai-Tibetan plateau. This study shows that Tibetans and Han of the same age, who were born and raised in the same towns at the same altitudes, show considerable overlap in the individual distribution of [Hb], SaO2 and lung volumes. These results indicate that second-generation Han make substantial developmental adjustments to hypoxia that are not reflected in studies of first-generation migrants. Thus, there is a great need for further developmental studies to determine whether and/or how Han and Tibetan responses to hypoxia diverge, as well as for studies exploring whether Han and Tibetans who show similar responses also share genetic adaptations.

In this paper, we use a method of lines to determine a moving boundary from Cauchy data in a one-dimensional heat conduction problem. This problem is ill-posed; thus, a quasi-reversibility regularization method is applied to obtain a stable numerical solution. Numerical experiments for several examples show that the proposed method is effective and stable. © 2011 by Begell House, Inc.

In this paper, we consider a conductivity interface problem to recover the salient features of the inclusion within a body from noisy observation data on the boundary. Based on integral equations, we propose iterative algorithms to detect the location, the size and the shape of the conductivity inclusion. This problem is severely ill-posed and nonlinear, thus we should consider regularization techniques in order to improve the corresponding approximation. We give several examples to show the viability of our proposed reconstruction algorithms.

The method of lines is used to determine a moving boundary from Cauchy data in a one-dimensional heat-conduction problem in a multilayer domain. This problem is ill-posed and thus a quasi-reversibility method is applied to give a stable numerical solution. Numerical experiments for several examples show that the proposed method is feasible and stable.

In this article, we use the method of lines combined with a quasi-reversibility method to reconstruct a corrosion boundary for the Laplace equation. This problem is ill-posed, that is, the corrosion boundary does not depend continuously on the given Cauchy data. To restore the stability of approximate boundary on the noises in Cauchy data, we use a modified fourth-order partial differential equation to replace the original Laplace equation. Through the suitable choice of a regularization parameter, one can obtain a stable numerical approximation to the unknown boundary. Numerical examples show that the proposed method is feasible and stable.

Studies comparing the growth of indigenous high-altitude Aymara children and children of low-altitude European descent who have been born and raised at high altitude in the Andes have provided evidence for genetically-determined differences in thorax growth, as well as for population differences in height, weight and other measures of overall size. Comparable studies now can be undertaken in Asia because of the growing number of Han Chinese who have been born and raised at high altitude on the Qinghai-Tibetan Plateau.The study compares the growth of indigenous Tibetan children and children of Han descent who have been born and raised at the same high altitudes, and under similar socio-economic conditions.Measurements of stature, sitting height, weight, triceps and subscapular skinfolds, upper arm muscle area, transverse chest diameter, anterio-posterior chest diameter, and chest circumference were taken on 1439 Tibetan and Han males and females between the ages of 6 and 29 years who were born and raised 3200 m, 3800 m or at 4300 m in the high altitude province of Qinghai in western China.Han-Tibetan differences in body size do not occur systematically for any measurement, for any age group, or for either gender; nor is there a systematic pattern of body size differences between 3200 m and 4300 m. This indicates that there are no differences in general growth between the two groups at high altitude in Qinghai, although both groups grow more slowly than urban children at low altitude in China. On the other hand, Tibetan males possess significantly deeper chests than Han males, and Tibetan females possess significantly wider chests than Han females. Tibetans of both sexes possess significantly larger chest circumferences than Han males and females.Although genetic similarities cannot be ruled out, comparable dietary stress is a likely explanation for the similar and slow morphological growth of Han and Tibetans at high altitude. However, Han-Tibetan differences in thorax dimensions are likely a consequence of population (genetic) differences in the response to hypoxia during growth.

In this paper, we consider the inverse scattering problem of recovering the shape of a cavity or the surface impedance from one source and a knowledge of measurements placed on a curve inside the cavity. Based on a potential approach the inverse problem is equivalent to a system of nonlinear and ill-posed integral equations, a regularized Newton iterative approach is applied to reconstruct the boundary and the injectivity for the linearized system is established. Numerical examples are provided showing the viability of our method.

While many studies have compared Tibetans and low-altitude born Han living at high altitude, few have carefully controlled the chronological age at which lowlanders migrated, the length of time they had lived at high altitude, their nutrition, and their socio-economic status. This has produced an array of results that frequently do not support the hypothesis that Tibetans and Han show fundamental differences in their response to hypoxia. Unlike the situation in the Andes, only one study has tested the developmental adaptation hypothesis on the Qinghai-Tibetan plateau. This study shows that Tibetans and Han of the same age, who were born and raised in the same towns at the same altitudes, show considerable overlap in the individual distribution of [Hb], SaO2 and lung volumes. These results indicate that second-generation Han make substantial developmental adjustments to hypoxia that are not reflected in studies of first-generation migrants. Thus, there is a great need for further developmental studies to determine whether and/or how Han and Tibetan responses to hypoxia diverge, as well as for studies exploring whether Han and Tibetans who show similar responses also share genetic adaptations.

This study describes the hemoglobin concentration ([Hb]) and hematocrit (HCT) of over 1,000 Tibetan and Han children, adolescents, and young adults who were born and raised at 3,200 m, 3,800 m, or 4,300 m in Qinghai Province, western China. At 3,200 m, no altitude effect is evident in the hematological characteristics of either group. At 3,800 m and 4,300 m, both groups show [Hb] and HCT values that are above low-altitude norms. At both altitudes, Tibetan and Han children show no differences in the pattern of hematological response up to age 13. Among adolescents and young adults, however, the [Hb] and HCT of Han males and females are elevated compared to Tibetans. This indicates that the adolescent period may involve a divergence in the responses to hypoxia made by some individuals in these two groups. Also, many other adolescents and young adults in both groups show similar hematological characteristics, indicating that many Tibetans and Han share similar hematological responses to hypoxia.

Forced vital capacity (FVC), forced expiratory volume at 1 second (FEV(1)), and FEV(1)/FVC ratios were determined for 531 individuals of Han Chinese descent living at low altitude (250 m) near Beijing and for 592 individuals of Han descent who were born and raised at three high altitudes (3,200 m, 3,800 m, 4,300 m) in Qinghai Province, P.R.C. The study included males and females, ages 6-51 years. Thorax widths, depths, and circumferences of Han females and males born and raised at high altitude are similar to those of low-altitude Han. On the other hand, high-altitude children and adolescents have larger relative sitting heights, indicating greater thorax lengths. After adjusting for this variation in morphology, mean FVC values among 6-21 year-old Han at high altitude are only between 136 mL (for females) and 173 ml (for males) greater than those determined at low altitude but the differences are statistically significant and are maintained consistently throughout the growth period. These data indicate that growth at high altitude produces small-to-moderate increases in lung volumes (about 6%) relative to genetically similar groups growing up at low altitude. In addition, there is no evidence that lung volume growth is accelerated relative to morphological growth among Han children born and raised at high altitude. Adults, 22-51 years, also show greater FVC values at high altitude but the size of the increase relative to Han at low altitude is variable (3% in males and 11% in females). Greater lung function at high altitude is unlikely to result from increased activity or lower pollution, and thus appears to be primarily a result of development in a hypoxic environment. Differences in FVC and FEV(1) at 3,200 m, 3,800 m, and 4,300 m are generally not significant, so that living at altitudes between 3,200 m and 4,300 m appears to have little additional effect on volumetric growth.

This study compares the morphological characteristics of Han children, adolescents, and young adults who were born at 250 m near Beijing and at three high altitudes in Qinghai Province, Peoples Republic of China (3,200 m, 3,800 m, and 4,300 m). From ages 6 through 15, Han children growing up at high altitudes are significantly shorter, lighter, have less fat, and are less muscular than Han children growing up at low altitude. However, older adolescents and young adults show no such altitude differences. Younger adolescents and children in this study were all born after the government economic reforms of 1978. These reforms had a greater impact on the growth of children in and around large cities than on those in more remote areas. Therefore, the altitude differences in size among Han children ages 15 and younger may be a consequence of regional variation in health and nutrition, rather than due to the influence of hypoxia. There are no altitude-related differences in thorax dimensions among Han children, adolescents, or young adults. This suggests that hypoxia does not affect the thorax growth of Han children. Am. J. Hum. Biol. 12:665-681, 2000. Copyright 2000 Wiley-Liss, Inc.

In this paper, we consider the recovery problem of inclusions in three-dimensional and three-dimensional domains for Poisson’s equation from noisy observation data. We propose effective reconstruction algorithms to recover hidden inclusions within a body when one can only make measurements of voltage and current on the external boundary. Our motivation is to detect the number, the location, the size and the shape of inclusions. This problem is nonlinear and severely ill posed, thus we should apply regularization techniques in our approaches in order to improve the corresponding approximation. We give several examples to show the viability of our proposed methods.