Guessing Games on Triangle-free Graphs

9 pages, submitted to Electronic Journal of Combinatoric9 pages, submitted to Electronic Journal of CombinatoricThe guessing game introduced by Riis is a variant of the "guessing your own hats" game and can be played on any simple directed graph G on n vertices. For each digraph G, it is proved that there exists a unique guessing number gn(G) associated to the guessing game played on G. When we consider the directed edge to be bidirected, in other words, the graph G is undirected, Christofides and Markstr om introduced a method to bound the value of the guessing number from below using the fractional clique number Kf(G). In particular they showed gn(G) >= |V(G)| - Kf(G). Moreover, it is pointed out that equality holds in this bound if the underlying undirected graph G falls into one of the following categories: perfect graphs, cycle graphs or their complement. In this paper, we show that there are triangle-free graphs that have guessing numbers which do not meet the fractional clique cover bound. In particular, the famous triangle-free Higman-Sims graph has guessing number at least 77 and at most 78, while the bound given by fractional clique cover is 50

Robust Estimation for Linear Panel Data Models

In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making meaningful statistical inferences. However, when the ordinary least squares (OLS) method is used to estimate the model parameters, presence of outliers may significantly alter the adequacy of such models by producing biased and inefficient estimates. In this work we propose a new, weighted likelihood based robust estimation procedure for linear panel data models with fixed and random effects. The finite sample performances of the proposed estimators have been illustrated through an extensive simulation study as well as with an application to blood pressure data set. Our thorough study demonstrates that the proposed estimators show significantly better performances over the traditional methods in the presence of outliers and produce competitive results to the OLS based estimates when no outliers are present in the data set

Electrochemically-triggered spatially and temporally resolved multi-component gels

Spatial control over gelation with low molecular weight gelators is possible using an electrochemically-driven pH triggering method. Gelation occurs at the electrode surface. We show here that composition control in multi-component low molecular weight hydrogels can also be achieved, allowing simultaneous spatial, temporal and compositional control

Divergent mathematical treatments in utility theory

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper

Protein Kinase C-beta Dictates B Cell Fate by Regulating Mitochondrial Remodeling, Metabolic Reprogramming, and Heme Biosynthesis

PKCβ-null (Prkcb−/−) mice are severely immunodeficient. Here we show that mice whose B cells lack PKCβ failed to form germinal centers and plasma cells, which undermined affinity maturation and antibody production in response to immunization. Moreover, these mice failed to develop plasma cells in response to viral infection. At the cellular level, we have shown that Prkcb−/−B cells exhibited defective antigen polarization and mTORC1 signaling. While altered antigen polarization impaired antigen presentation and likely restricted the potential of GC development, defective mTORC1 signaling impaired metabolic reprogramming, mitochondrial remodeling, and heme biosynthesis in these cells, which altogether overwhelmingly opposed plasma cell differentiation. Taken together, our study reveals mechanistic insights into the function of PKCβ as a key regulator of B cell polarity and metabolic reprogramming that instructs B cell fate. Lymphocyte activation is associated with major changes in metabolism. Tsui and colleagues demonstrate that PKCβ promotes metabolic reprogramming to drive effector fate decision in B cells

Transit Photometry as an Exoplanet Discovery Method

Photometry with the transit method has arguably been the most successful exoplanet discovery method to date. A short overview about the rise of that method to its present status is given. The method's strength is the rich set of parameters that can be obtained from transiting planets, in particular in combination with radial velocity observations; the basic principles of these parameters are given. The method has however also drawbacks, which are the low probability that transits appear in randomly oriented planet systems, and the presence of astrophysical phenomena that may mimic transits and give rise to false detection positives. In the second part we outline the main factors that determine the design of transit surveys, such as the size of the survey sample, the temporal coverage, the detection precision, the sample brightness and the methods to extract transit events from observed light curves. Lastly, an overview over past, current and future transit surveys is given. For these surveys we indicate their basic instrument configuration and their planet catch, including the ranges of planet sizes and stellar magnitudes that were encountered. Current and future transit detection experiments concentrate primarily on bright or special targets, and we expect that the transit method remains a principal driver of exoplanet science, through new discoveries to be made and through the development of new generations of instruments.Comment: Review chapte

Risk-Targeted Selection of Agricultural Holdings for Post-Epidemic Surveillance: Estimation of Efficiency Gains

Current post-epidemic sero-surveillance uses random selection of animal holdings. A better strategy may be to estimate the benefits gained by sampling each farm and use this to target selection. In this study we estimate the probability of undiscovered infection for sheep farms in Devon after the 2001 foot-and-mouth disease outbreak using the combination of a previously published model of daily infection risk and a simple model of probability of discovery of infection during the outbreak. This allows comparison of the system sensitivity (ability to detect infection in the area) of arbitrary, random sampling compared to risk-targeted selection across a full range of sampling budgets. We show that it is possible to achieve 95% system sensitivity by sampling, on average, 945 farms with random sampling and 184 farms with risk-targeted sampling. We also examine the effect of ordering samples by risk to expedite return to a disease-free status. Risk ordering the sampling process results in detection of positive farms, if present, 15.6 days sooner than with randomly ordered sampling, assuming 50 farms are tested per day

Can programme theory be used as a 'translational tool’ to optimise health service delivery in a national early years’ initiative in Scotland: a case study

Background Theory-based evaluation (TBE) approaches are heralded as supporting formative evaluation by facilitating increased use of evaluative findings to guide programme improvement. It is essential that learning from programme implementation is better used to improve delivery and to inform other initiatives, if interventions are to be as effective as they have the potential to be. Nonetheless, few studies describe formative feedback methods, or report direct instrumental use of findings resulting from TBE. This paper uses the case of Scotland’s, National Health Service, early years’, oral health improvement initiative (Childsmile) to describe the use of TBE as a framework for providing feedback on delivery to programme staff and to assess its impact on programmatic action.<p></p> Methods In-depth, semi-structured interviews and focus groups with key stakeholders explored perceived deviations between the Childsmile programme 'as delivered’ and its Programme Theory (PT). The data was thematically analysed using constant comparative methods. Findings were shared with key programme stakeholders and discussions around likely impact and necessary actions were facilitated by the authors. Documentary review and ongoing observations of programme meetings were undertaken to assess the extent to which learning was acted upon.<p></p> Results On the whole, the activities documented in Childsmile’s PT were implemented as intended. This paper purposefully focuses on those activities where variation in delivery was evident. Differences resulted from the stage of roll-out reached and the flexibility given to individual NHS boards to tailor local implementation. Some adaptations were thought to have diverged from the central features of Childsmile’s PT, to the extent that there was a risk to achieving outcomes. The methods employed prompted national service improvement action, and proposals for local action by individual NHS boards to address this.<p></p> Conclusions The TBE approach provided a platform, to direct attention to areas of risk within a national health initiative, and to agree which intervention components were 'core’ to its hypothesised success. The study demonstrates that PT can be used as a 'translational tool’ to facilitate instrumental use of evaluative findings to optimise implementation within a complex health improvement programme.<p></p&gt