Minimum Cost Homomorphisms to Locally Semicomplete and Quasi-Transitive Digraphs

For digraphs $G$ and $H$, a homomorphism of $G$ to $H$ is a mapping $f:\ V(G)\dom V(H)$such that$uv\in A(G)$implies$f(u)f(v)\in A(H)$. If, moreover, each vertex$u \in V(G)$is associated with costs$c_i(u), i \in V(H)$, then the cost of a homomorphism$f$is$\sum_{u\in V(G)}c_{f(u)}(u)$. For each fixed digraph$H$, the minimum cost homomorphism problem for$H$, denoted MinHOM($H$), can be formulated as follows: Given an input digraph$G$, together with costs$c_i(u)$,$u\in V(G)$,$i\in V(H)$, decide whether there exists a homomorphism of$G$to$H$ and, if one exists, to find one of minimum cost. Minimum cost homomorphism problems encompass (or are related to) many well studied optimization problems such as the minimum cost chromatic partition and repair analysis problems. We focus on the minimum cost homomorphism problem for locally semicomplete digraphs and quasi-transitive digraphs which are two well-known generalizations of tournaments. Using graph-theoretic characterization results for the two digraph classes, we obtain a full dichotomy classification of the complexity of minimum cost homomorphism problems for both classes

Algorithms for the workflow satisfiability problem engineered for counting constraints

The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorized users to the steps in a workflow specification that satisfies the constraints in the specification. The problem is NP-hard in general, but several subclasses of the problem are known to be fixed-parameter tractable (FPT) when parameterized by the number of steps in the specification. In this paper, we consider the WSP with user-independent counting constraints, a large class of constraints for which the WSP is known to be FPT. We describe an efficient implementation of an FPT algorithm for solving this subclass of the WSP and an experimental evaluation of this algorithm. The algorithm iteratively generates all equivalence classes of possible partial solutions until, whenever possible, it finds a complete solution to the problem. We also provide a reduction from a WSP instance to a pseudo-Boolean SAT instance. We apply this reduction to the instances used in our experiments and solve the resulting PB SAT problems using SAT4J, a PB SAT solver. We compare the performance of our algorithm with that of SAT4J and discuss which of the two approaches would be more effective in practice

Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes

Diffusion-limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure and particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in longwavelength fluctuations and is a universal function of the macroscopic decay rate

Comment on "Chain Length Scaling of Protein Folding Time", PRL 77, 5433 (1996)

In a recent Letter, Gutin, Abkevich, and Shakhnovich (GAS) reported on a series of dynamical Monte Carlo simulations on lattice models of proteins. Based on these highly simplified models, they found that four different potential energies lead to four different folding time scales tau_f, where tau_f scales with chain length as N^lambda (see, also, Refs. [2-4]), with lambda varying from 2.7 to 6.0. However, due to the lack of microscopic models of protein folding dynamics, the interpretation and origin of the data have remained somewhat speculative. It is the purpose of this Comment to point out that the application of a simple "mesoscopic" model (cond-mat/9512019, PRL 77, 2324, 1996) of protein folding provides a full account of the data presented in their paper. Moreover, we find a major qualitative disagreement with the argumentative interpretation of GAS. Including, the origin of the dynamics, and size of the critical folding nucleus.Comment: 1 page Revtex, 1 fig. upon request. Submitted to PR

The Persistent Southern Disadvantage in Us Early Life Mortality, 1965‒2014

Background: Recent studies of US adult mortality demonstrate a growing disadvantage among southern states. Few studies have examined long-term trends and geographic patterns in US early life (ages 1 to 24) mortality, ages at which key risk factors and causes of death are quite different than among adults. Objective: This article examines trends and variations in early life mortality rates across US states and census divisions. We assess whether those variations have changed over a 50-year time period and which causes of death contribute to contemporary geographic disparities. Methods: We calculate all-cause and cause-specific death rates using death certificate data from the Multiple Cause of Death files, combining public-use files from 1965‒2004 and restricted data with state geographic identifiers from 2005‒2014. State population (denominator) data come from US decennial censuses or intercensal estimates. Results: Results demonstrate a persistent mortality disadvantage for young people (ages 1 to 24) living in southern states over the last 50 years, particularly those located in the East South Central and West South Central divisions. Motor vehicle accidents and homicide by firearm account for most of the contemporary southern disadvantage in US early life mortality. Contribution: Our results illustrate that US children and youth living in the southern United States have long suffered from higher levels of mortality than children and youth living in other parts of the country. Our findings also suggest the contemporary southern disadvantage in US early life mortality could potentially be reduced with state-level policies designed to prevent deaths involving motor vehicles and firearms