Shape reconstructions by using plasmon resonances

We study the shape reconstruction of a dielectric inclusion from the faraway measurement of the associated electric field. This is an inverse problem of practical importance in biomedical imaging and is known to be notoriously ill-posed. By incorporating Drude's model of the dielectric parameter, we propose a novel reconstruction scheme by using the plasmon resonance with a significantly enhanced resonant field. We conduct a delicate sensitivity analysis to establish a sharp relationship between the sensitivity of the reconstruction and the plasmon resonance. It is shown that when plasmon resonance occurs, the sensitivity functional blows up and hence ensures a more robust and effective construction. Then we combine the Tikhonov regularization with the Laplace approximation to solve the inverse problem, which is an organic hybridization of the deterministic and stochastic methods and can quickly calculate the minimizer while capture the uncertainty of the solution. We conduct extensive numerical experiments to illustrate the promising features of the proposed reconstruction scheme

Determining a stationary mean field game system from full/partial boundary measurement

In this paper, we propose and study the utilization of the Dirichlet-to-Neumann (DN) map to uniquely identify the discount functions $r, k$ and cost function $F$ in a stationary mean field game (MFG) system. This study features several technical novelties that make it highly intriguing and challenging. Firstly, it involves a coupling of two nonlinear elliptic partial differential equations. Secondly, the simultaneous recovery of multiple parameters poses a significant implementation challenge. Thirdly, there is the probability measure constraint of the coupled equations to consider. Finally, the limited information available from partial boundary measurements adds another layer of complexity to the problem. Considering these challenges and problems, we present an enhanced higher-order linearization method to tackle the inverse problem related to the MFG system. Our proposed approach involves linearizing around a pair of zero solutions and fulfilling the probability measurement constraint by adjusting the positive input at the boundary. It is worth emphasizing that this technique is not only applicable for uniquely identifying multiple parameters using full-boundary measurements but also highly effective for utilizing partial-boundary measurements

NF-κB/p65 antagonizes Nrf2-ARE pathway by depriving CBP from Nrf2 and facilitating recruitment of HDAC3 to MafK

AbstractConstitutively activated NF-κB occurs in many inflammatory and tumor tissues. Does it interfere with anti-inflammatory or anti-tumor signaling pathway? Here, we report that NF-κB p65 subunit repressed the Nrf2-antioxidant response element (ARE) pathway at transcriptional level. In the cells where NF-κB and Nrf2 were simultaneously activated, p65 unidirectionally antagonized the transcriptional activity of Nrf2. In the p65-overexpressing cells, the ARE-dependent expression of heme oxygenase-1 was strongly suppressed. However, p65 inhibited the ARE-driven gene transcription in a way that was independent of its own transcriptional activity. Two mechanisms were found to coordinate the p65-mediated repression of ARE: (1) p65 selectively deprives CREB binding protein (CBP) from Nrf2 by competitive interaction with the CH1-KIX domain of CBP, which results in inactivation of Nrf2. The inactivation depends on PKA catalytic subunit-mediated phosphorylation of p65 at S276. (2) p65 promotes recruitment of histone deacetylase 3 (HDAC3), the corepressor, to ARE by facilitating the interaction of HDAC3 with either CBP or MafK, leading to local histone hypoacetylation. This investigation revealed the participation of NF-κB p65 in the negative regulation of Nrf2-ARE signaling, and might provide a new insight into a possible role of NF-κB in suppressing the expression of anti-inflammatory or anti-tumor genes

A mathematical theory of microscale hydrodynamic cloaking and shielding by electro-osmosis

In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first establish the representation formula of the solution of the coupled system using the layer potential techniques. Based on Fourier series, the perfect hydrodynamic cloaking and shielding conditions are derived for the control region with the cross-sectional shape being annulus or confocal ellipses. Then we further propose an optimization scheme for the design of approximate cloaks and shields within general geometries. The well-posedness of the optimization problem is proved. In particular, the condition that can ensure the occurrence of approximate cloaks and shields for general geometries are also established. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking and shielding

Enhanced Microscale Hydrodynamic Near-cloaking using Electro-osmosis

In this paper, we develop a general mathematical framework for enhanced hydrodynamic near-cloaking of electro-osmotic flow for more complex shapes, which is obtained by simultaneously perturbing the inner and outer boundaries of the perfect cloaking structure. We first derive the asymptotic expansions of perturbed fields and obtain a first-order coupled system. We then establish the representation formula of the solution to the first-order coupled system using the layer potential techniques. Based on the asymptotic analysis, the enhanced hydrodynamic near-cloaking conditions are derived for the control region with general cross-sectional shape. The conditions reveal the inner relationship between the shapes of the object and the control region. Especially, for the shape of a deformed annulus or confocal ellipses cylinder, the cloaking conditions and relationship of shapes are quantified more accurately. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking

ROR1, an embryonic protein with an emerging role in cancer biology

Receptor tyrosine kinase-like orphan receptor 1 (ROR1) is a member of the ROR family consisting of ROR1 and ROR2. RORs contain two distinct extracellular cysteine-rich domains and one transmembrane domain. Within the intracellular portion, ROR1 possesses a tyrosine kinase domain, two serine/threonine-rich domains and a proline-rich domain. RORs have been studied in the context of embryonic patterning and neurogenesis through a variety of homologs. These physiologic functions are dichotomous based on the requirement of the kinase domain. A growing literature has established ROR1 as a marker for cancer, such as in CLL and other blood malignancies. In addition, ROR1 is critically involved in progression of a number of blood and solid malignancies. ROR1 has been shown to inhibit apoptosis, potentiate EGFR signaling, and induce epithelial-mesenchymal transition (EMT). Importantly, ROR1 is only detectable in embryonic tissue and generally absent in adult tissue, making the protein an ideal drug target for cancer therapy

BCS-BEC crossover at finite temperature in spin-orbit coupled Fermi gases

By adopting a $T$-matrix-based method within the $G_0G$ approximation for the pair susceptibility, we study the effects of the pairing fluctuation on the three-dimensional spin-orbit coupled Fermi gases at finite temperature. The critical temperatures of the superfluid/normal phase transition are determined for three different types of spin-orbit coupling (SOC): (1) the extreme oblate (EO) or Rashba SOC, (2) the extreme prolate (EP) or equal Rashba-Dresselhaus SOC, and (3) the spherical (S) SOC. For EO- and S-type SOC, the SOC dependence of the critical temperature signals a crossover from BCS to BEC state; at strong SOC limit, the critical temperature recover those of ideal BEC of rashbons. The pairing fluctuation induces a pseudogap in the fermionic excitation spectrum in both superfluid and normal phases. We find that, for EO- and S-type SOC, even at weak coupling, sufficiently strong SOC can induce sizable pseudogap. Our research suggests that the spin-orbit coupled Fermi gases may open new means to the study of the pseudogap formation in fermionic systems.Comment: V2: 13 pages, 8 figures, more discussions added, matches published versio