We consider a one-dimensional stationary stochastic process $x(\tau)$ of duration $T$. study the probability density function (PDF) $P(t_{\rm m}|T)$ time $t_{\rm m}$ at which reaches its global maximum. By using path integral method, we compute for number equilibrium and nonequilibrium processes, including Ornstein-Uhlenbeck process, Brownian motion with resetting single confined run-and-tumble...

For a tree T $T$ , the mean subtree order of is average . In 1984, Jamison conjectured that decreases by at least 1/3 after contracting an edge in this article we prove conjecture special case contracted pendant edge. From result, have new proof established fact path P n ${P}_{n}$ has minimum among all trees $n$ Moreover, sharp lower bound derived for difference between orders and proper S $S$ ...

(V,A, c) be a directed network with node set V , arc set A = {e1, · · · , em}, and capacities on arcs c : A 7→ R+, where R+ is the set of non-negative rational numbers. Let s, t ∈ V be two distinct nodes, designated as the source and the destination. Let P = {p1, · · · , pk} be the set of s-t paths in G. Let aij = 1 if arc ei ∈ A lies on path pj ∈ P and aij = 0 otherwise. Let f : P 7→ R+ be a f...

[32] H. Yen, A polynomial time algorithm to decide pairwise concurrency of transitions for 1-bounded con BLOCKINict-free Petri nets, Inform. Some complexity bounds for problems concerning nite and 2-dimensional vector addition systems with states, Theoret. Comput. 1) _ (# 1 (t i) 1 ^ # 1 (t j) = 0))). As a result, B-fairness can be detected in P. Acknowledgements: The authors thank the anonymou...

A number of program-analysis problems can be tackled by transforming them into certain kinds of graph-reachability problems in labeled directed graphs. The edge labels can be used to filter out paths that are not of interest: A path P from vertex s to vertex t only counts as a “valid connection” between s and t if the word spelled out by P is in a certain language. Often the languages used for ...

Given a graph G = (V,E), two fixed vertices s, t ∈ V and a set F of pairs of vertices (called forbidden pairs), the problem of a path avoiding forbidden pairs is to find a path from s to t that contains at most one vertex from each pair in F . The problem is known to be NP-complete in general and a few restricted versions of the problem are known to be in P. We study the complexity of the probl...

1 The Branching Time Temporal Logics CTL and CTL + A transition system is a tuple T = (S, − →, L) where S is a set of states, − → ⊆ S × S a transition relation and L : P → 2 S a function that assigns to each q in some set P of atomic propositions the set of states L(q) in which q holds. Here we assume the transition relation to be total in the sense that for all s ∈ S there is a t ∈ S s.t. s − ...