The complexity of Free-Flood-It on 2xn boards

We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. Our main result is that computing the length of an optimal sequence is fixed parameter tractable (with the number of colours present as a parameter) when restricted to rectangular 2xn boards. We also show that, when the number of colours is unbounded, the problem remains NP-hard on such boards. This resolves a question of Clifford, Jalsenius, Montanaro and Sach (2010)

Archeological Investigations on the Weyerhaeuser Land Exchange Sites, McCurtain County, Oklahoma: An Update

This paper provides a brief overview of the testing work completed to date on sites within the Tiak Ranger District. Ouachita National Forest. McCurtain County, Oklahoma. This work was part of the requirements outlined in the Programmatic Agreement for the Ouachita National Forest/Weyerhaeuser Company Land Exchange. Nine prehistoric sites have been tested to determine their eligibility for inclusion on the National Register of Historic Places. Each site contains a Caddoan component. Six sites are believed to be eligible for listing

Credit market shocks: evidence from corporate spreads and defaults

Several recent papers have found that exogenous shocks to spreads paid in corporate credit markets are a substantial source of macroeconomic fluctuations. An alternative explanation of the data is that spreads respond endogenously to expectations of future default. We use a simple model of bond spreads to derive sign restrictions on the impulse-response functions of a VAR that identify credit shocks in the bond market, and compare them to results from a benchmark recursive VAR. We find that credit market shocks cause a persistent decline in output, prices and policy rates. Historical decompositions clearly show the negative effect of adverse credit market shocks on output in the recent recession. The identified credit shocks are unrelated to exogenous innovations to monetary policy and measures of bond market liquidity, but are related to measures of risk compensation. In contrast to results found using the benchmark restrictions, our identified credit shocks account for relatively little of the variance of output. Our results are consistent with a role for shocks in financial crises, but also with a lesser but non-zero role in normal business fluctuations.Bond market ; Vector autoregression ; Business cycles ; Interest rates ; Financial markets

Credit Shocks and Cycles: a Bayesian Calibration Approach

This paper asks how well a general equilibrium agency cost model describes the dynamic relationship between credit variables and the business cycle. A Bayesian VAR is used to obtain probability intervals for empirical correlations. The agency cost model is found to predict the leading, countercyclical correlation of spreads with output when shocks arising from the credit market contribute to output fluctuations. The contribution of technology shocks is held at conventional RBC levels. Sensitivity analysis shows that moderate prior calibration uncertainty leads to significant dispersion in predictedcorrelations. Most predictive uncertainty arises from a single parameter.agency costs, credit cycles, calibration, shocks.

The Parameterised Complexity of List Problems on Graphs of Bounded Treewidth

We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable, parameterised by treewidth, whereas List Hamilton Path is W[1]-hard, even parameterised by pathwidth. These results resolve two open questions of Fellows, Fomin, Lokshtanov, Rosamond, Saurabh, Szeider and Thomassen (2011).Comment: Author final version, to appear in Information and Computation. Changes from previous version include improved literature references and restructured proof in Section

Racial/Ethnic Disparities Related to Health Insurance Coverage, Access to Care and Ease in Health Care Services among Children in 2012 CCHAPS Data

nObjective:The aim of this study was to examine racial/ethnic disparities in unmet medical care, dental care and prescription medications and ease of using heath care services. Methods:This is a cross sectional study of households in a six-county service region in Texas (Tarrant, Johnson, Hood, Parker, Wise and Denton Counties). The participants included the parents/guardians of children aged 1-15 years. In 2012, a total of 8,439 parents completed the survey. In 2012, 4194 completed the version containing the health insurance type and unmet medical, prescription and dental health care and ease/difficulty in access to health care questions.The dependent variables in this study included perceived general health status; use of needed health care and ease/difficulty in access to health care services. Results/Discussion: . Disparities exist and a key area to address is the lack of insurance or inconsistency of insurance coverage especially in minorities. Almost 10% of the children in the study population had a lapse of health insurance coverage during the previous 12 months. There was no significant difference between the unmet health care of those with public or private insurance. In addition, racial/ethnic disparities were found in the ease of access to preventive and dental services as well as care for an illness

Solving Hard Stable Matching Problems Involving Groups of Similar Agents

Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to design efficient algorithms using elementary techniques. We focus on the setting in which all agents involved in some matching problem can be partitioned into k different types, where the type of an agent determines his or her preferences, and agents have preferences over types (which may be refined by more detailed preferences within a single type). This situation would arise in practice if agents form preferences solely based on some small collection of agents' attributes. We also consider a generalisation in which each agent may consider some small collection of other agents to be exceptional, and rank these in a way that is not consistent with their types; this could happen in practice if agents have prior contact with a small number of candidates. We show that (for the case without exceptions), several well-studied NP-hard stable matching problems including Max SMTI (that of finding the maximum cardinality stable matching in an instance of stable marriage with ties and incomplete lists) belong to the parameterised complexity class FPT when parameterised by the number of different types of agents needed to describe the instance. For Max SMTI this tractability result can be extended to the setting in which each agent promotes at most one `exceptional' candidate to the top of his/her list (when preferences within types are not refined), but the problem remains NP-hard if preference lists can contain two or more exceptions and the exceptional candidates can be placed anywhere in the preference lists, even if the number of types is bounded by a constant.Comment: Results on SMTI appear in proceedings of WINE 2018; Section 6 contains work in progres

Some hard families of parameterised counting problems

We consider parameterised subgraph-counting problems of the following form: given a graph G, how many k-tuples of its vertices have a given property? A number of such problems are known to be #W[1]-complete; here we substantially generalise some of these existing results by proving hardness for two large families of such problems. We demonstrate that it is #W[1]-hard to count the number of k-vertex subgraphs having any property where the number of distinct edge-densities of labelled subgraphs that satisfy the property is o(k^2). In the special case that the property in question depends only on the number of edges in the subgraph, we give a strengthening of this result which leads to our second family of hard problems.Comment: A few more minor changes. This version to appear in the ACM Transactions on Computation Theor

The parameterised complexity of counting even and odd induced subgraphs

We consider the problem of counting, in a given graph, the number of induced k-vertex subgraphs which have an even number of edges, and also the complementary problem of counting the k-vertex induced subgraphs having an odd number of edges. We demonstrate that both problems are #W[1]-hard when parameterised by k, in fact proving a somewhat stronger result about counting subgraphs with a property that only holds for some subset of k-vertex subgraphs which have an even (respectively odd) number of edges. On the other hand, we show that each of the problems admits an FPTRAS. These approximation schemes are based on a surprising structural result, which exploits ideas from Ramsey theory

On the complexity of finding and counting solution-free sets of integers

Given a linear equation $\mathcal{L}$, a set $A$ of integers is $\mathcal{L}$-free if $A$ does not contain any `non-trivial' solutions to $\mathcal{L}$. This notion incorporates many central topics in combinatorial number theory such as sum-free and progression-free sets. In this paper we initiate the study of (parameterised) complexity questions involving $\mathcal{L}$-free sets of integers. The main questions we consider involve deciding whether a finite set of integers $A$ has an $\mathcal{L}$-free subset of a given size, and counting all such $\mathcal{L}$-free subsets. We also raise a number of open problems.Comment: 27 page