Some Problems in Probabilistic Tomography

Given probability distributions F1 , F2 , . . ., Fk on R and distinct directions θ1, . . ., θk, one may ask whether there is a probability measure μ on R2 such that the marginal of μ in direction θj is Fj, j = 1, . . ., k. For example for k = 3 we ask what the marginal of μ at 45° can be if the x and y marginals are each say standard normal? In probabilistic language, if X and Y are each standard normal with an arbitrary joint distribution, what can the distribution of X + Y or X - Y be? This type of question is familiar to probabilists and is also familiar (except perhaps in that μ is positive) to tomographers, but is difficult to answer in special cases. The set of distributions for Z = X - Y is a convex and compact set, C, which contains the single point mass Z ≡ 0 since X ≡ Y, standard normal, is possible. We show that Z can be 3-valued, Z=0, ±a for any a, each with positive probability, but Z cannot have any (genuine) two-point distribution. Using numerical linear programming we present convincing evidence that Z can be uniform on the interval [-ε, ε] for ε small and give estimates for the largest such ε. The set of all extreme points of C seems impossible to determine explicitly. We also consider the more basic question of finding the extreme measures on the unit square with uniform marginals on both coordinates, and show that not every such measure has a support which has only one point on each horizontal or vertical line, which seems surprising

Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields in near-linear time solutions as well as upper bounds. Using various computational tools, we get solutions within considerably less than 1% of the optimum. An interesting feature of our approach is that, even though an FWP is hard to compute in theory and Edmonds' algorithm for maximum weighted matching yields a polynomial solution for the MWMP, the practical behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental Algorithms, 200

Factors influencing the frames and approaches of host organizations for collaborative catchment management in England

The frames and approaches adopted for collaborative catchment management (CCM) by 22 host organizations in England were examined. Hosts framed and approached CCM according to their particular funding arrangements, management priorities, actor networks, attitudes toward knowledge and uncertainty, and willingness to share power and take risks. The findings support the theory of path dependency, and indicate that the majority of hosts created CCM groups that were much narrower in scope, direction, and structure than had been envisaged by government policymakers. To address this, a new national policy framework for catchment management in England is recommended that defines guiding principles for collaboration and balances the needs for clear direction and discretion in policy implementation

Collaborative Delivery with Energy-Constrained Mobile Robots

We consider the problem of collectively delivering some message from a specified source to a designated target location in a graph, using multiple mobile agents. Each agent has a limited energy which constrains the distance it can move. Hence multiple agents need to collaborate to move the message, each agent handing over the message to the next agent to carry it forward. Given the positions of the agents in the graph and their respective budgets, the problem of finding a feasible movement schedule for the agents can be challenging. We consider two variants of the problem: in non-returning delivery, the agents can stop anywhere; whereas in returning delivery, each agent needs to return to its starting location, a variant which has not been studied before. We first provide a polynomial-time algorithm for returning delivery on trees, which is in contrast to the known (weak) NP-hardness of the non-returning version. In addition, we give resource-augmented algorithms for returning delivery in general graphs. Finally, we give tight lower bounds on the required resource augmentation for both variants of the problem. In this sense, our results close the gap left by previous research.Comment: 19 pages. An extended abstract of this paper was published at the 23rd International Colloquium on Structural Information and Communication Complexity 2016, SIROCCO'1

Peaks above the Harrison-Zel'dovich spectrum due to the Quark-Gluon to Hadron Transition

The quark-gluon to hadron transition affects the evolution of cosmological perturbations. If the phase transition is first order, the sound speed vanishes during the transition, and density perturbations fall freely. This distorts the primordial Harrison-Zel'dovich spectrum of density fluctuations below the Hubble scale at the transition. Peaks are produced, which grow at most linearly in wavenumber, both for the hadron-photon-lepton fluid and for cold dark matter. For cold dark matter which is kinetically decoupled well before the QCD transition clumps of masses below $10^{-10} M_\odot$ are produced.Comment: Extended version, including evolution of density perturbations for a bag model and for a lattice QCD fit (3 new figures). Spectrum for bag model (old figure) is available in astro-ph/9611186. 9 pages RevTeX, uses epsf.sty, 3 PS figure

New Services for Families in the DC Superior Court

Until recently, because of concerns about safety and parties’ abilities to make good decisions in cases with a history of high intimate partner violence or abuse (IPV/A), in the District of Columbia’s Superior Court such cases were screened out of mediation and sent back to the family court. But two big program additions — videoconferencing and shuttle mediation — have allowed parties in these cases to consider mediation. The Multi-Door Dispute Resolution Division of the DC Superior Court (Multi-Door) implemented this change after several years of preparation: its administrators added safety measures, provided in-depth training for staff and mediators, and consulted with experts to design a research study to compare videoconference, shuttle mediation, and the prior practice of returning these cases to court

Finite temperature effects on cosmological baryon diffusion and inhomogeneous Big-Bang nucleosynthesis

We have studied finite temperature corrections to the baryon transport cross sections and diffusion coefficients. These corrections are based upon the recently computed renormalized electron mass and the modified state density due to the background thermal bath in the early universe. It is found that the optimum nucleosynthesis yields computed using our diffusion coefficients shift to longer distance scales by a factor of about 3. We also find that the minimum value of $^4 He$ abundance decreases by $\Delta Y_p \simeq 0.01$ while $D$ and $^7 Li$ increase. Effects of these results on constraints from primordial nucleosynthesis are discussed. In particular, we find that a large baryonic contribution to the closure density (\Omega_b h_{50}^{2} \lsim 0.4) may be allowed in inhomogeneous models corrected for finite temperature.Comment: 7 pages, 6 figures, submitted to Phys. Rev.

Generalized Buneman pruning for inferring the most parsimonious multi-state phylogeny

Accurate reconstruction of phylogenies remains a key challenge in evolutionary biology. Most biologically plausible formulations of the problem are formally NP-hard, with no known efficient solution. The standard in practice are fast heuristic methods that are empirically known to work very well in general, but can yield results arbitrarily far from optimal. Practical exact methods, which yield exponential worst-case running times but generally much better times in practice, provide an important alternative. We report progress in this direction by introducing a provably optimal method for the weighted multi-state maximum parsimony phylogeny problem. The method is based on generalizing the notion of the Buneman graph, a construction key to efficient exact methods for binary sequences, so as to apply to sequences with arbitrary finite numbers of states with arbitrary state transition weights. We implement an integer linear programming (ILP) method for the multi-state problem using this generalized Buneman graph and demonstrate that the resulting method is able to solve data sets that are intractable by prior exact methods in run times comparable with popular heuristics. Our work provides the first method for provably optimal maximum parsimony phylogeny inference that is practical for multi-state data sets of more than a few characters.Comment: 15 page

One, two, or three stars? An investigation of an unusual eclipsing binary candidate undergoing dramatic period changes

We report our investigation of 1SWASP J234401.81-212229.1, a variable with a 18 461.6 s period. After identification in a 2011 search of the SuperWASP archive for main-sequence eclipsing binary candidates near the distribution's short-period limit of ~0.20 d, it was measured to be undergoing rapid period decrease in our earlier work, though later observations supported a cyclic variation in period length. Spectroscopic data obtained in 2012 with the Southern African Large Telescope did not, however, support the interpretation of the object as a normal eclipsing binary. Here, we consider three possible explanations consistent with the data: a single-star oblique rotator model in which variability results from stable cool spots on opposite magnetic poles; a two-star model in which the secondary is a brown dwarf; and a three-star model involving a low-mass eclipsing binary in a hierarchical triple system. We conclude that the latter is the most likely model