Framework for cyber risk loss distribution of hospital infrastructure: Bond percolation on mixed random graphs approach.

Networks like those of healthcare infrastructure have been a primary target of cyberattacks for over a decade. From just a single cyberattack, a healthcare facility would expect to see millions of dollars in losses from legal fines, business interruption, and loss of revenue. As more medical devices become interconnected, more cyber vulnerabilities emerge, resulting in more potential exploitation that may disrupt patient care and give rise to catastrophic financial losses. In this paper, we propose a structural model of an aggregate loss distribution across multiple cyberattacks on a prototypical hospital network. Modeled as a mixed random graph, the hospital network consists of various patient-monitoring devices and medical imaging equipment as random nodes to account for the variable occupancy of patient rooms and availability of imaging equipment that are connected by bidirectional edges to fixed hospital and radiological information systems. Our framework accounts for the documented cyber vulnerabilities of a hospital's trusted internal network of its major medical assets. To our knowledge, there exist no other models of an aggregate loss distribution for cyber risk in this setting. We contextualize the problem in the probabilistic graph-theoretical framework using a percolation model and combinatorial techniques to compute the mean and variance of the loss distribution for a mixed random network with associated random costs that can be useful for healthcare administrators and cybersecurity professionals to improve cybersecurity management strategies. By characterizing this distribution, we allow for the further utility of pricing cyber risk.

Robustness of Interdependent Networks with Weak Dependency Based on Bond Percolation.

Real-world systems interact with one another via dependency connectivities. Dependency connectivities make systems less robust because failures may spread iteratively among systems via dependency links. Most previous studies have assumed that two nodes connected by a dependency link are strongly dependent on each other; that is, if one node fails, its dependent partner would also immediately fail. However, in many real scenarios, nodes from different networks may be weakly dependent, and links may fail instead of nodes. How interdependent networks with weak dependency react to link failures remains unknown. In this paper, we build a model of fully interdependent networks with weak dependency and define a parameter α in order to describe the node-coupling strength. If a node fails, its dependent partner has a probability of failing of 1−α. Then, we develop an analytical tool for analyzing the robustness of interdependent networks with weak dependency under link failures, with which we can accurately predict the system robustness when 1−p fractions of links are randomly removed. We find that as the node coupling strength increases, interdependent networks show a discontinuous phase transition when α<αc and a continuous phase transition when α>αc. Compared to site percolation with nodes being attacked, the crossover points αc are larger in the bond percolation with links being attacked. This finding can give us some suggestions for designing and protecting systems in which link failures can happen.

Mechanics of tablet formation: a comparative evaluation of percolation theory with classical concepts.

The present study is based on the fundamentals of percolation theory and its application in understanding compression and compaction of powder materials. Four materials, i.e. carbamazepine, microcrystalline cellulose, crospovidone and croscarmellose sodium, with dissimilar deformation and compaction behavior were selected to validate the hypotheses of percolation phenomenon. The values of two percolation thresholds, i.e. bond and site, corresponding to the lower and intermediate compression pressures, were determined using Heckel equation. The compactibility of powder materials was evaluated using classical models as well as the power law equation. The values of percolation thresholds were found to better assess the deformation behavior of powder materials compared to the values of mean yield pressure. The power law equation demonstrated better prediction of compactibility of powder materials compared to the classical models. The value of the critical exponent, q, determined using power law equation by plotting tensile strength vs. normalized relative density of powder compacts was found to be closer to the theoretical value of 2.70. Furthermore, the theoretical knowledge of percolation thresholds of individual powder components in the binary mixture was found to be helpful in improving compaction properties of the poorly compactible material, i.e. carbamazepine. Thus percolation theory can be helpful in predicting compression and compaction behavior of powder materials and serve as a potent tool for the successful design of tablet formulations.

High-Dimensional Contact Network Epidemiology.

Contact network models are recent alternatives to equation-based models in epidemiology. In this paper, the spread of disease is modeled on contact networks using bond percolation. The weight of the edges in the contact graphs is determined as a function of several variables in which case the weight is the product of the probabilities of independent events involving each of the variables. In the first experiment, the weight of the edges is computed from a single variable involving the number of passengers on flights between two cities within the United States, and in the second experiment, the weight of the edges is computed as a function of several variables using data from 2012 Kenyan household contact networks. In addition, the paper explored the dynamics and adaptive nature of contact networks. The results from the contact network model outperform the equation-based model in estimating the spread of the 1918 Influenza virus.