Optimal Security Protection Selection Strategy Based on Markov Model Attack Graph

Intrusion intent and path prediction are important for security administrators to gain insight into the possible threat behavior of attackers. Existing research has mainly focused on path prediction in ideal attack scenarios, yet the ideal attack path is not always the real path taken by an intruder. In order to accurately and comprehensively predict the path information of network intrusion, a multi-step attack path prediction method based on absorbing Markov chains is proposed. Firstly, the node state transfer probability normalization algorithm is designed by using the nil posteriority and absorption of state transfer in absorbing Markov chain, and it is proved that the complete attack graph can correspond to absorbing Markov chain, and the economic indexes of protection cost and attack benefit and the index quantification method are constructed, and the optimal security protection policy selection algorithm based on particle swarm algorithm is proposed, and finally the experimental verification of the model in protection Finally, we experimentally verify the feasibility and effectiveness of the model in protection policy decision-making, which can effectively reduce network security risks and provide more security protection guidance for timely response to network attack threats.

An Absorbing Markov Chain Model to Predict Dairy Cow Calving Time

Abnormal behavioral changes in the regular daily mobility routine of a pregnant dairy cow can be an indicator or early sign to recognize when a calving event is imminent. Image processing technology and statistical approaches can be effectively used to achieve a more accurate result in predicting the time of calving. We hypothesize that data collected using a 360-degree camera to monitor cows before and during calving can be used to establish the daily activities of individual pregnant cows and to detect changes in their routine. In this study, we develop an augmented Markov chain model to predict calving time and better understand associated behavior. The objective of this study is to determine the feasibility of this calving time prediction system by adapting a simple Markov model for use on a typical dairy cow dataset. This augmented absorbing Markov chain model is based on a behavior embedded transient Markov chain model for characterizing cow behavior patterns during the 48 h before calving and to predict the expected time of calving. In developing the model, we started with an embedded four-state Markov chain model, and then augmented that model by adding calving as both a transient state, and an absorbing state. Then, using this model, we derive (1) the probability of calving at 2 h intervals after a reference point, and (2) the expected time of calving, using their motions between the different transient states. Finally, we present some experimental results for the performance of this model on the dairy farm compared with other machine learning techniques, showing that the proposed method is promising.

Optimal Design of Photovoltaic Connected Energy Storage System Using Markov Chain Models

This study improves an approach for Markov chain-based photovoltaic-coupled energy storage model in order to serve a more reliable and sustainable power supply system. In this paper, two Markov chain models are proposed: Embedded Markov and Absorbing Markov chain. The equilibrium probabilities of the Embedded Markov chain completely characterize the system behavior at a certain point in time. Thus, the model can be used to calculate important measurements to evaluate the system such as the average availability or the probability when the battery is fully discharged. Also, Absorbing Markov chain is employed to calculate the expected duration until the system fails to serve the load demand, as well as the failure probability once a new battery is installed in the system. The results show that the optimal condition for satisfying the availability of 3 nines (0.999), with an average load usage of 1209.94 kWh, is the energy storage system capacity of 25 MW, and the number of photovoltaic modules is 67,510, which is considered for installation and operation cost. Also, when the initial state of charge is set to 80% or higher, the available time is stable for more than 20,000 h.

Saliency Detection with Bilateral Absorbing Markov Chain Guided by Depth Information

The effectiveness of depth information in saliency detection has been fully proved. However, it is still worth exploring how to utilize the depth information more efficiently. Erroneous depth information may cause detection failure, while non-salient objects may be closer to the camera which also leads to erroneously emphasis on non-salient regions. Moreover, most of the existing RGB-D saliency detection models have poor robustness when the salient object touches the image boundaries. To mitigate these problems, we propose a multi-stage saliency detection model with the bilateral absorbing Markov chain guided by depth information. The proposed model progressively extracts the saliency cues with three level (low-, mid-, and high-level) stages. First, we generate low-level saliency cues by explicitly combining color and depth information. Then, we design a bilateral absorbing Markov chain to calculate mid-level saliency maps. In mid-level, to suppress boundary touch problem, we present the background seed screening mechanism (BSSM) for improving the construction of the two-layer sparse graph and better selecting background-based absorbing nodes. Furthermore, the cross-modal multi-graph learning model (CMLM) is designed to fully explore the intrinsic complementary relationship between color and depth information. Finally, to obtain a more highlighted and homogeneous saliency map in high-level, we structure a depth-guided optimization module which combines cellular automata and suppression-enhancement function pair. This optimization module refines the saliency map in color space and depth space, respectively. Comprehensive experiments on three challenging benchmark datasets demonstrate the effectiveness of our proposed method both qualitatively and quantitatively.

Improving Graduation Rate Estimates Using Regularly Updating Multi-Level Absorbing Markov Chains

American universities use a procedure based on a rolling six-year graduation rate to calculate statistics regarding their students’ final educational outcomes (graduating or not graduating). As an alternative to the six-year graduation rate method, many studies have applied absorbing Markov chains for estimating graduation rates. In both cases, a frequentist approach is used. For the standard six-year graduation rate method, the frequentist approach corresponds to counting the number of students who finished their program within six years and dividing by the number of students who entered that year. In the case of absorbing Markov chains, the frequentist approach is used to compute the underlying transition matrix, which is then used to estimate the graduation rate. In this paper, we apply a sensitivity analysis to compare the performance of the standard six-year graduation rate method with that of absorbing Markov chains. Through the analysis, we highlight significant limitations with regards to the estimation accuracy of both approaches when applied to small sample sizes or cohorts at a university. Additionally, we note that the Absorbing Markov chain method introduces a significant bias, which leads to an underestimation of the true graduation rate. To overcome both these challenges, we propose and evaluate the use of a regularly updating multi-level absorbing Markov chain (RUML-AMC) in which the transition matrix is updated year to year. We empirically demonstrate that the proposed RUML-AMC approach nearly eliminates estimation bias while reducing the estimation variation by more than 40%, especially for populations with small sample sizes.

MARKOV CHAIN METHOD FOR COMPUTING THE RELIABILITY OF HAMMOCK NETWORKS

In this paper, we develop a new method for evaluating the reliability polynomial of a hammock network. The method is based on a homogeneous absorbing Markov chain and provides the exact reliability for networks of width less than 5 and arbitrary length. Moreover, it produces a lower bound for the reliability polynomial for networks of width greater than or equal to 5. To investigate how sharp this lower bound is, we compare our method with other approximation methods and it proves to be the most accurate in terms of absolute as well as relative error. Using the fundamental matrix, we also calculate the average time to absorption, which provides the mean length of a network that is expected to work.

Multimodal dynamics of nonhomogeneous absorbing Markov chains evolving at stochastic transition rates

The Tokuyama–Mori projection operator method for a reduced time-convolutionless description of a local temporal behavior of an open quantum system interacting with the weakly dissipative and fluctuating pervasive environment is applied to a Markov chain subject to random transition probabilities. The solution to the problem of the multimodal dynamics of a two-stage absorbing Markov chain with the fluctuating forward rate constant augmented by a symmetric dichotomous stochastic process is found exactly and compared with that of the problem for the same Markov chain with the fluctuating backward rate constant. It is shown that these two different tetramodal solutions cannot generally be reduced to but be complementary to each other. In the limit of very frequent fluctuations in forward/backward rate constants of a two-stage absorbing Markov chain, as well as in the case of a one-stage recurrent Markov chain, both solutions become bimodal and superimposed to one another. However, there is a distinction between using of those solutions for the dynamics of a two-stage absorbing Markov chain in the limit of very rare fluctuations at the critical point, in which the former solution shows the resonance effect exhibiting itself as the stochastic immobilization in an initial state, while the latter demonstrates the deterministic decay to the other state.

Modeling the Bimodal Behavior of Self-Repairing Optical Window Systems Prone to Brittle Failure

Using an exact solution for transient state population of a three-stage absorbing Markov chain the problem of modeling the bimodal behavior of three window materials represented as some self-repairing optical systems prone to brittle failure is considered quantitatively. It is shown that simulated maximum failure probability density distributions can well describe the experimental data of biaxial tests on OFG, CVD-ZnSe and a-plane sapphire ceramics. The conclusion is made that the competitive advantage of these materials grows in proportion to their distribution widths.