On The Stability Problem of Quadratic Functional Equations in 2-Banach Spaces

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and Gavruta for the quadratic functional equation: f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 4f(x) - 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by the quadratic functional equation in normed spaces to 2-Banach spaces

Real-time analysis of aggregate network traffic for anomaly detection

The frequent and large-scale network attacks have led to an increased need for developing techniques for analyzing network traffic. If efficient analysis tools were available, it could become possible to detect the attacks, anomalies and to appropriately take action to contain the attacks before they have had time to propagate across the network. In this dissertation, we suggest a technique for traffic anomaly detection based on analyzing the correlation of destination IP addresses and distribution of image-based signal in postmortem and real-time, by passively monitoring packet headers of traffic. This address correlation data are transformed using discrete wavelet transform for effective detection of anomalies through statistical analysis. Results from trace-driven evaluation suggest that the proposed approach could provide an effective means of detecting anomalies close to the source. We present a multidimensional indicator using the correlation of port numbers as a means of detecting anomalies. We also present a network measurement approach that can simultaneously detect, identify and visualize attacks and anomalous traffic in real-time. We propose to represent samples of network packet header data as frames or images. With such a formulation, a series of samples can be seen as a sequence of frames or video. Thisenables techniques from image processing and video compression such as DCT to be applied to the packet header data to reveal interesting properties of traffic. We show that ??scene change analysis?? can reveal sudden changes in traffic behavior or anomalies. We show that ??motion prediction?? techniques can be employed to understand the patterns of some of the attacks. We show that it may be feasible to represent multiple pieces of data as different colors of an image enabling a uniform treatment of multidimensional packet header data. Measurement-based techniques for analyzing network traffic treat traffic volume and traffic header data as signals or images in order to make the analysis feasible. In this dissertation, we propose an approach based on the classical Neyman-Pearson Test employed in signal detection theory to evaluate these different strategies. We use both of analytical models and trace-driven experiments for comparing the performance of different strategies. Our evaluations on real traces reveal differences in the effectiveness of different traffic header data as potential signals for traffic analysis in terms of their detection rates and false alarm rates. Our results show that address distributions and number of flows are better signals than traffic volume for anomaly detection. Our results also show that sometimes statistical techniques can be more effective than the NP-test when the attack patterns change over time

Epidemic Response Coordination Networks in “Living Documents”

Response plans developed thoroughly are suggestive of a successful action, but there is a gap in the literature with respect to the way concerted efforts among organizations are planned and change during crises. Using organizational network data extracted from the South Korean government’s MERS response manuals, we examined the changes in the response coordination network planned during the epidemic’s distinct stages. The greatest difference in predicting tie formation was found in the networks planned before the event and revised during the outbreak. Local and governmental actors tend to form more ties consistently in the revised manuals. Two actors that are intended to transfer medical and/or personnel resources tend to form more ties across all stages. These findings suggest that transferring material and/or human resources are key activities in the epidemic response and planners tend to increase the connection of local and governmental actors over time

Homomorphisms and derivations on C*-ternary algebras assocoated with a generalized Cauchy-Jensen type additive functional equation

In this paper, we prove the generalized Hyers-Ulam stability of C∗-ternary homomorphisms and C∗-ternary derivations on C∗-ternary algebras associated with the generalized Cauchy-Jensen type additive functional equation for all xi; xj ∈ X where n ∈ Z+ is a fixed integer with n ≥ 3. &nbsp