Directed Random Markets: Connectivity determines Money

Boltzmann-Gibbs distribution arises as the statistical equilibrium probability distribution of money among the agents of a closed economic system where random and undirected exchanges are allowed. When considering a model with uniform savings in the exchanges, the final distribution is close to the gamma family. In this work, we implement these exchange rules on networks and we find that these stationary probability distributions are robust and they are not affected by the topology of the underlying network. We introduce a new family of interactions: random but directed ones. In this case, it is found the topology to be determinant and the mean money per economic agent is related to the degree of the node representing the agent in the network. The relation between the mean money per economic agent and its degree is shown to be linear.Comment: 14 pages, 6 figure

Supersymmetric particle mass measurement with invariant mass correlations

The kinematic end-point technique for measuring the masses of supersymmetric particles in R-Parity conserving models at hadron colliders is re-examined with a focus on exploiting additional constraints arising from correlations in invariant mass observables. The use of such correlations is shown to potentially resolve the ambiguity in the interpretation of quark+lepton end-points and enable discrimination between sequential two-body and three-body lepton-producing decays. The use of these techniques is shown to improve the SUSY particle mass measurement precision for the SPS1a benchmark model by at least 20-30% compared to the conventional end-point technique.Comment: 29 pages, 23 .eps figures, JHEP3 style; v2 adds some references and small clarifications to text; v3 adds some more clarifications to the tex

Scheduling Bidirectional Traffic on a Path

We study the fundamental problem of scheduling bidirectional traffic along a path composed of multiple segments. The main feature of the problem is that jobs traveling in the same direction can be scheduled in quick succession on a segment, while jobs in opposing directions cannot cross a segment at the same time. We show that this tradeoff makes the problem significantly harder than the related flow shop problem, by proving that it is NP-hard even for identical jobs. We complement this result with a PTAS for a single segment and non-identical jobs. If we allow some pairs of jobs traveling in different directions to cross a segment concurrently, the problem becomes APX-hard even on a single segment and with identical jobs. We give polynomial algorithms for the setting with restricted compatibilities between jobs on a single and any constant number of segments, respectively

On the stable degree of graphs

We define the stable degree s(G) of a graph G by s(G)∈=∈ min max d (v), where the minimum is taken over all maximal independent sets U of G. For this new parameter we prove the following. Deciding whether a graph has stable degree at most k is NP-complete for every fixed k∈≥∈3; and the stable degree is hard to approximate. For asteroidal triple-free graphs and graphs of bounded asteroidal number the stable degree can be computed in polynomial time. For graphs in these classes the treewidth is bounded from below and above in terms of the stable degree

Identifying Biomarkers to Pair with Targeting Treatments within Triple Negative Breast Cancer for Improved Patient Stratification.

The concept of precision medicine has been around for many years and recent advances in high-throughput sequencing techniques are enabling this to become reality. Within the field of breast cancer, a number of signatures have been developed to molecularly sub-classify tumours. Notable examples recently approved by National Institute for Health and Care Excellence in the UK to guide treatment decisions for oestrogen receptors (ER)+ human epidermal growth factor receptor 2 (HER2)- patients include Prosigna test, EndoPredict, and Oncotype DX. However, a population of still unmet need are those with triple negative breast cancer (TNBC). Accounting for 15-20% of patients, this population has comparatively poor prognosis and as yet no targeted treatment options. Studies have shown that some patients with TNBC respond favourably to DNA damaging drugs (carboplatin) or agents which inhibit DNA damage response (poly ADP ribose polymerase (PARP) inhibitors). Known to be a heterogeneous population, there is a need to identify further TNBC patients who may benefit from these treatments. A number of signatures have been identified based on association with treatment response or specific genetic features/pathways however many of these were not restricted to TNBC patients and as of yet are not common practice in the clinic

Processing Multi-Spectral Scanning Electron Microscopy Images for Quantitative Microfabric Analysis

Multi-spectral image analysis is a powerful method to characterise quantitatively the mineralogy and microfabric of soils, sediments, and other particulate materials. Backscattered scanning electron microscope (SEM) images of polished, resin-impregnated samples are grouped with the corresponding X-ray elemental maps using classification methods commonly used in remote sensing. However, the resulting mineral-segmented images require processing to render them suitable for quantification. In the past, this has been done subjectively and interactively, but the new objective methods described in this paper largely eliminate this subjectivity. An intensity gradient magnitude image of the original backscattered electron image is used as the basis of an interactive erosion and dilation sequence to generate skeleton outlines defining the edges of the mineral grains. The areas defined within the skeleton areas are then classified as a particular mineral according to the predominant feature in the corresponding mineral-segmented image. Subsequent processing tackles the problems of \u27holes\u27 defined by the skeleton outlines, and the over-segmentation associated with certain classes of mineral grain. Further methods to deal with particles made up of more than one mineral are considered. The matrix and porosity information is recombined to generate an image suitable for analysis using feature size statistics or general orientation analysis. The techniques described can be combined to permit batch processing of images. Applications of the techniques are illustrated on a soil from the East Anglian Breckland