Superconnection and family Bergman kernels

We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection as in the local family index theorem.Comment: C. R. Math. Acad. Sci. Pari

Bergman kernels and symplectic reduction

We generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic identification property. More precisely, we study the asymptotic expansion of the $G$-invariant Bergman kernel of the spin^c Dirac operator associated with high tensor powers of a positive line bundle on a symplectic manifold. We also develop a way to compute the coefficients of the expansion, and compute the first few of them, especially, we obtain the scalar curvature of the reduction space from the $G$-invariant Bergman kernel on the total space. These results generalize the corresponding results in the non-equivariant setting, which has played a crucial role in the recent work of Donaldson on stability of projective manifolds, to the geometric quantization setting. As another kind of application, we generalize some Toeplitz operator type properties in semi-classical analysis to the framework of geometric quantization. The method we use is inspired by Local Index Theory, especially by the analytic localization techniques developed by Bismut and Lebeau.Comment: 132 page

η\eta-invariant and flat vector bundles

We present an alternate definition of the mod {\bf Z} component of the Atiyah-Patodi-Singer $\eta$ invariant associated to (not necessary unitary) flat vector bundles, which identifies explicitly its real and imaginary parts. This is done by combining a deformation of flat connections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah, Patodi and Singer.Comment: 6 page

Development of therapeutic strategies for quiescent tumor cell populations

Phenotypic screening is an effective approach to the discovery of small-molecule drugs. In this thesis, I have used cancer cells grown as 3D microtissues (multicellular spheroids) to study the effect of anticancer drugs and as drug discovery tools. Most clinically used cytotoxic drugs have only modest efficacy on spheroids, possibly explaining their limited efficacy on many solid tumors. We therefore used spheroids as targets for screening campaigns aimed to discover novel anti-cancer drugs. This work resulted in the identification of compounds that showed preferential cytotoxicity to spheroids compared to monolayer cultures. We also used multicellular spheroids to study regrowth of cells after cytotoxic therapy. The compound VLX600 was identified in our spheroid screening work. This drug was found to induce autophagy and upregulation of glycolysis in tumor cells. Further work showed that VLX600 is an inhibitor of mitochondrial oxidative phosphorylation. The work has lead to the hypothesis that cells in the deep tumor parenchyme are sensitive to disturbances of energy metabolism due to lack of metabolic plasticity. Our studies demonstrated that VLX600 also decreased the levels of c-MYC. This phenomenon was also observed after treatment with other mitochondrial inhibitors. An additional screen was performed using glucose-deprived spheroids. This screen identified five molecules that showed selectivity to spheroids. All five drugs were found to inhibit mitochondrial respiration. The FDA-approved antiprotozoal drug nitazoxanide was chosen for further studies and may be a candidate for future clinical trials. Increased glycolysis in tumor cells leads to the generation of metabolic acids and a subsequent acidification of the microenvironment of solid tumors. We found that tumor acidosis leads to induction of autophagy and present evidence that autophagy is a mechanism for cancer cells to adapt to an acidic environment. We conclude from this work that multicellular spheroids can be used to screen for novel anticancer agents. Several drugs identified by this approach were found to be inhibitors of mitochondrial function. This finding suggests a therapeutic strategy to target quiescent tumor cells in metabolically compromised microenvironments

Enable Reliable and Secure Data Transmission in Resource-Constrained Emerging Networks

The increasing deployment of wireless devices has connected humans and objects all around the world, benefiting our daily life and the entire society in many aspects. Achieving those connectivity motivates the emergence of different types of paradigms, such as cellular networks, large-scale Internet of Things (IoT), cognitive networks, etc. Among these networks, enabling reliable and secure data transmission requires various resources including spectrum, energy, and computational capability. However, these resources are usually limited in many scenarios, especially when the number of devices is considerably large, bringing catastrophic consequences to data transmission. For example, given the fact that most of IoT devices have limited computational abilities and inadequate security protocols, data transmission is vulnerable to various attacks such as eavesdropping and replay attacks, for which traditional security approaches are unable to address. On the other hand, in the cellular network, the ever-increasing data traffic has exacerbated the depletion of spectrum along with the energy consumption. As a result, mobile users experience significant congestion and delays when they request data from the cellular service provider, especially in many crowded areas. In this dissertation, we target on reliable and secure data transmission in resource-constrained emerging networks. The first two works investigate new security challenges in the current heterogeneous IoT environment, and then provide certain countermeasures for reliable data communication. To be specific, we identify a new physical-layer attack, the signal emulation attack, in the heterogeneous environment, such as smart home IoT. To defend against the attack, we propose two defense strategies with the help of a commonly found wireless device. In addition, to enable secure data transmission in large-scale IoT network, e.g., the industrial IoT, we apply the amply-and-forward cooperative communication to increase the secrecy capacity by incentivizing relay IoT devices. Besides security concerns in IoT network, we seek data traffic alleviation approaches to achieve reliable and energy-efficient data transmission for a group of users in the cellular network. The concept of mobile participation is introduced to assist data offloading from the base station to users in the group by leveraging the mobility of users and the social features among a group of users. Following with that, we deploy device-to-device data offloading within the group to achieve the energy efficiency at the user side while adapting to their increasing traffic demands. In the end, we consider a perpendicular topic - dynamic spectrum access (DSA) - to alleviate the spectrum scarcity issue in cognitive radio network, where the spectrum resource is limited to users. Specifically, we focus on the security concerns and further propose two physical-layer schemes to prevent spectrum misuse in DSA in both additive white Gaussian noise and fading environments

Property Rights Restrictions on the Construction of Parking Spaces With Buildings

The construction of parking spaces is the main solution of parking spaces shortage in many cities. The government imposes requirements on the developers of land or housing and owners to ensure the availability of parking spaces. However, at the same time, parking space allocation has the possibility of restricting property rights. It is necessary to demonstrate the legitimacy of the government’s request for the construction of parking spaces for buildings through the control of private property by the government and the theoretical analysis of social obligations undertaken by private property rights, and to explain the rationality of the requirements of the construction of parking spaces with buildings through the realistic factors of management difficulties of large cities