This dissertation explores bridge n-sections of knotted surfaces in 4-manifolds by defining invariants that measure the complexity of their topology and by giving geometric constructions that determine Lagrangian surfaces in 4-manifolds under certain conditions. First, we present an elegant geometric construction that generates all triple grid…

Graph Signal Processing (GSP) plays a crucial role in addressing the growing need for information processing across networks, especially in tasks like supervised classification. However, the success of GSP in such tasks hinges on accurately identifying the underlying relational structures, which are often not readily available and must be inferred…

Online networks, as digital images reflecting every aspects of real world especially under the current context of information technology, have become the most massive and opulent data source these days, where vast amount of information keeps being produced and transmitted. Their rapid expansion in scale and data volume draws wide attention and…

The introduction to general topology represents a challenging transition for students of advanced mathematics. It requires the generalization of their previous understanding of ideas from fields like geometry, linear algebra, and real or complex analysis to fit within a more abstract conceptual system. Students must adopt a new lexicon of…

Social networks have received much attention these days. Researchers have developed different methods to study the structure and characteristics of the network topology. Our focus is on spectral analysis of the adjacency matrix of the underlying network. Recent work showed good properties in the adjacency spectral space but there are few…

Similar to mammalian brains, Artificial Neural Networks (ANN) are universal approximators, capable of yielding near-optimal solutions to a wide assortment of problems. ANNs are used in many fields including medicine, internet security, engineering, retail, robotics, warfare, intelligence control, and finance. "ANNs have a tendency to get…

Wireless Sensor Networks (WSNs) are now widely used for monitoring and controlling of systems where human intervention is not desirable or possible. Connected Dominating Sets (CDSs) based topology control in WSNs is one kind of hierarchical method to ensure sufficient coverage while reducing redundant connections in a relatively crowded network.…

Current "one disease, one target and one drug" drug development paradigm is under question as relatively few drugs have reached the market in the last two decades. Increasingly research focus is being placed on the study of drug action against biological systems as a whole rather than against a single component (called "Systems…

In this dissertation research, we argue that spatial alarms and activity-based social networks are two fundamentally new types of information and influence diffusion channels. Such new channels have the potential of enriching our professional experiences and our personal life quality in many unprecedented ways. First, we develop an activity driven…

The growing complexity of interactions between computers and networks makes the subject of network security a very interesting one. As our dependence on the services provided by computing networks grows, so does our investment in such technology. In this situation, there is a greater risk of occurrence of targeted malicious attacks on computers…

The recent evolution of wireless technology makes wireless devices ever more powerful and intelligent. One trend is that wireless devices are becoming more inexpensive and more diverse. As a result, new technologies make it possible to equip wireless nodes with several radio transmitters/receivers. Each radio may support multiple channels which…

The last decades have seen tremendous growth and transformation in the Internet's commercial landscape. Underneath this success, however, the underlying network architecture has shown a marked resistance to change; it is now described as stagnant and ossified. Numerous design proposals have been developed by researchers, implemented in code, and…

Virtual worlds provide useful platforms for social behavioral research, but impose stringent limitations on the rules of engagement, responsiveness, and data collection, along with other resource restrictions. The major challenge from a computer science standpoint in developing group behavior applications for such environments is accommodating the…

Many scholars have proposed concepts relevant to spatial reference. Herskovits (1982) proposed that the topological concepts support, contiguity and containment are basic in English, while Levinson et al.'s (2003) examination of nine unrelated languages revealed that the concept attachment is primary. Neither of these proposals is confirmed in…