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

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

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

Extremal properties of flood-filling games

The problem of determining the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It has been studied extensively from an algorithmic point of view, but basic questions about the maximum number of moves that might be required in the worst case remain unanswered. We begin a systematic investigation of such questions, with the goal of determining, for a given graph, the maximum number of moves that may be required, taken over all possible colourings. We give several upper and lower bounds on this quantity for arbitrary graphs and show that all of the bounds are tight for trees; we also investigate how much the upper bounds can be improved if we restrict our attention to graphs with higher edge-density.Comment: Final version, accepted to DMTC

Ulysses

The DSN (Deep Space Network) mission support requirements for Ulysses are summarized. The primary goal of the Ulysses mission is to explore the Sun, its environment, and possible links between solar variability and terrestrial weather and climate. The Ulysses spacecraft will be injected into an interplanetary orbit toward Jupiter after which the spacecraft travels in a heliocentric, out-of-ecliptic orbit with high heliographic inclination. The Ulysses mission objectives are outlined and the DSN support requirements are defined through the presentation of tables and narratives describing the spacecraft flight profile; DSN support coverage; frequency assignments; support parameters for telemetry, command and support systems; and tracking support responsibility

The rigidity of embedded constant mean curvature surfaces

We study the rigidity of complete, embedded constant mean curvature surfaces in R^3. Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R^3 or its isometry group contains an index two subgroup of isometries that extend.Comment: 10 page