Travel Choice Behavior Model Based on Mental Accounting of Travel Time and Cost

This paper analyzes the utility calculation principle of travelers from the perspective of mental accounting and proposes a travel choice behavior model that considers travel time and cost (MA-TC model). Then, a questionnaire is designed to analyze the results of the travel choice under different decision-making scenarios. Model parameters are estimated using nonlinear regression, and the utility calculation principles are developed under different hypothetical scenarios. Then, new expressions for the utility function under deterministic and risky conditions are presented. For verification, the nonlinear correlation coefficient and hit rate are used to compare the proposed MA-TC model with the other two models: (1) the classical prospect theory with travel time and cost (PT-TC model) and (2) mental accounting based on the original hedonic editing criterion (MA-HE model). The results show that model parameters under deterministic and risky conditions are pretty different. In the deterministic case, travelers have similar sensitivity to the change in gain and loss of travel time and cost. The prediction accuracy of the MA-TC model is 3% lower than the PT-TC model and 6% higher than the MA-HE model. Under risky conditions, travelers are more sensitive to the change in loss than to the change in gain. Additionally, travelers tend to overestimate small probabilities and underestimate high probabilities when losing more than when gaining. The prediction accuracy of the MA-TC model is 2% higher than the PT-TC model and 6% higher than the MA-HE model.

Pattern Avoidance Over a Hypergraph

A classic result of Marcus and Tardos (previously known as the Stanley-Wilf conjecture) bounds from above the number of $n$-permutations ($\sigma \in S_n$) that do not contain a specific sub-permutation. In particular, it states that for any fixed permutation $\pi$, the number of $n$-permutations that avoid $\pi$ is at most exponential in $n$. In this paper, we generalize this result. We bound the number of avoidant $n$-permutations even if they only have to avoid $\pi$ at specific indices. We consider a $k$-uniform hypergraph $\Lambda$ on $n$ vertices and count the $n$-permutations that avoid $\pi$ at the indices corresponding to the edges of $\Lambda$. We analyze both the random and deterministic hypergraph cases. This problem was originally proposed by Asaf Ferber. When $\Lambda$ is a random hypergraph with edge density $\alpha$, we show that the expected number of $\Lambda$-avoiding $n$-permutations is bounded (both upper and lower) as $\exp(O(n))\alpha^{-\frac{n}{k-1}}$, using a supersaturation version of F\"{u}redi-Hajnal. In the deterministic case we show that, for $\Lambda$ containing many size $L$ cliques, the number of $\Lambda$-avoiding $n$-permutations is $O\left(\frac{n\log^{2+\epsilon}n}{L}\right)^n$, giving a nontrivial bound with $L$ polynomial in $n$. Our main tool in the analysis of this deterministic case is the new and revolutionary hypergraph containers method, developed in papers of Balogh-Morris-Samotij and Saxton-Thomason.

Dynamics of Tumor-Immune System with Random Noise

With deterministic differential equations, we can understand the dynamics of tumor-immune interactions. Cancer-immune interactions can, however, be greatly disrupted by random factors, such as physiological rhythms, environmental factors, and cell-to-cell communication. The present study introduces a stochastic differential model in infectious diseases and immunology of the dynamics of a tumor-immune system with random noise. Stationary ergodic distribution of positive solutions to the system is investigated in which the solution fluctuates around the equilibrium of the deterministic case and causes the disease to persist stochastically. In some conditions, it may be possible to attain infection-free status, where diseases die out exponentially with a probability of one. Some numerical simulations are conducted with the Euler–Maruyama scheme in order to verify the results. White noise intensity is a key factor in treating infectious diseases.

Introduction to matrix population models

Matrix population models (MPMs) are currently used in a range of fields, from basic research in ecology and evolutionary biology, to applied questions in conservation biology, management, and epidemiology. In MPMs individuals are classified into discrete stages, and the model projects the population over discrete time-steps. A rich analytical theory is available for these models, for both the linear deterministic case and for more complex dynamics including stochasticity and density dependence. This chapter provides a non comprehensive introduction to MPMs and some basic results on asymptotic dynamics, life history parameters, and sensitivities and elasticities of the long-term growth rate to projection matrix elements and to underlying parameters. We assume that readers are familiar with basic matrix calculations. Using examples with different kinds of demographic structure, we demonstrate how the general stage-structured model can be applied to each case.

The Role of Harvesting in Population Control in Presence of Multiple Stochastic Noise Sources

In this paper, we compare the role of constant and Michaelis-Menten type harvesting in single species population control in presence of stochastic noises sources. Steady state probability distributions and stationary potentials of the population for the two types of harvesting are determined by Fokker-Planck equations. Stochastic bifurcation analysis and mean first passage times have been computed. Noise induced critical transitions are observed depending on the strength of the noises. The extinction possibility of population in stochastic control with Michaelis-Menten type harvesting is higher than the constant rate of harvesting. One of the findings is the transition of the population from bistable to tristable for weak noise and Michaelis-Menten type harvesting. Another finding is noise enhanced stability phenomenon for negatively correlated noises. In case of population control, constant rate of harvesting is better in deterministic case whereas Michaelis-Menten type harvesting is better in stochastic case. The stochastic control is more efficient than deterministic control as average population size in stochastic case is lower than the deterministic case. The results obtained in this study can throw light on toxic phytoplankton blooms and its control in marine ecosystem. Moreover, the study can be useful to explain wild prey population outbreak and its control in deep forest.

On Uniform Stability with Growth Rates of Stochastic Skew-Evolution Semiflows in Banach Spaces

The main purpose of this paper is to study a more general concept of uniform stability in mean in which the uniform behavior in the classical sense is replaced by a weaker requirement with respect to some probability measure. This concept includes, as particular cases, the concepts of uniform exponential stability in mean and uniform polynomial stability in mean. Extending techniques employed in the deterministic case, we obtain variants of some results for the general cases of uniform stability in mean for stochastic skew-evolution semiflows in Banach spaces.

Reversible parallel communicating finite automata systems

We study the concept of reversibility in connection with parallel communicating systems of finite automata (PCFA in short). We define the notion of reversibility in the case of PCFA (also covering the non-deterministic case) and discuss the relationship of the reversibility of the systems and the reversibility of its components. We show that a system can be reversible with non-reversible components, and the other way around, the reversibility of the components does not necessarily imply the reversibility of the system as a whole. We also investigate the computational power of deterministic centralized reversible PCFA. We show that these very simple types of PCFA (returning or non-returning) can recognize regular languages which cannot be accepted by reversible (deterministic) finite automata, and that they can even accept languages that are not context-free. We also separate the deterministic and non-deterministic variants in the case of systems with non-returning communication. We show that there are languages accepted by non-deterministic centralized PCFA, which cannot be recognized by any deterministic variant of the same type.

Optimal Multi-port-based Teleportation Schemes

In this paper, we introduce optimal versions of a multi-port based teleportation scheme allowing to send a large amount of quantum information. We fully characterise probabilistic and deterministic case by presenting expressions for the average probability of success and entanglement fidelity. In the probabilistic case, the final expression depends only on global parameters describing the problem, such as the number of ports N, the number of teleported systems k, and local dimension d. It allows us to show square improvement in the number of ports with respect to the non-optimal case. We also show that the number of teleported systems can grow when the number N of ports increases as o(N) still giving high efficiency. In the deterministic case, we connect entanglement fidelity with the maximal eigenvalue of a generalised teleportation matrix. In both cases the optimal set of measurements and the optimal state shared between sender and receiver is presented. All the results are obtained by formulating and solving primal and dual SDP problems, which due to existing symmetries can be solved analytically. We use extensively tools from representation theory and formulate new results that could be of the separate interest for the potential readers.

Finite automata with undirected state graphs

We investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular, and in particular in the deterministic case, subreversible. In detail, we study the operational descriptional complexity of deterministic and nondeterministic undirected finite automata. To this end, the different types of automata on alphabets with few letters are characterized. Then, the operational state complexity of the Boolean operations as well as the operations concatenation and iteration is investigated, where tight upper and lower bounds are derived for unary as well as arbitrary alphabets under the condition that the corresponding language classes are closed under the operation considered.