On colouring point visibility graphs

In this paper we show that it can be decided in polynomial time whether or not the visibility graph of a given point set is 4-colourable, and such a 4-colouring, if it exists, can also be constructed in polynomial time. We show that the problem of deciding whether the visibility graph of a point set is 5-colourable, is NP-complete. We give an example of a point visibility graph that has chromatic number 6 while its clique number is only 4

Financial management 3B

Exam paper for second semester (Last Assessment Opportunity

Myosin-I nomenclature.

We suggest that the vertebrate myosin-I field adopt a common nomenclature system based on the names adopted by the Human Genome Organization (HUGO). At present, the myosin-I nomenclature is very confusing; not only are several systems in use, but several different genes have been given the same name. Despite their faults, we believe that the names adopted by the HUGO nomenclature group for genome annotation are the best compromise, and we recommend universal adoption

Flavour physics constraints in the BMSSM

We study the implications of the presence of the two leading-order, non-renormalizable operators in the Higgs sector of the MSSM to flavour physics observables. We identify the constraints of flavour physics on the parameters of the BMSSM when we: a) focus on a region of parameters for which electroweak baryogenesis is feasible, b) use a CMSSM-like parametrization, and c) consider the case of a generic NUHM-type model. We find significant differences as compared to the standard MSSM case.Comment: 22 pages, 7 figure

CP violation Beyond the MSSM: Baryogenesis and Electric Dipole Moments

We study electroweak baryogenesis and electric dipole moments in the presence of the two leading-order, non-renormalizable operators in the Higgs sector of the MSSM. Significant qualitative and quantitative differences from MSSM baryogenesis arise due to the presence of new CP-violating phases and to the relaxation of constraints on the supersymmetric spectrum (in particular, both stops can be light). We find: (1) spontaneous baryogenesis, driven by a change in the phase of the Higgs vevs across the bubble wall, becomes possible; (2) the top and stop CP-violating sources can become effective; (3) baryogenesis is viable in larger parts of parameter space, alleviating the well-known fine-tuning associated with MSSM baryogenesis. Nevertheless, electric dipole moments should be measured if experimental sensitivities are improved by about one order of magnitude.Comment: 33 pages, 6 figure

Sensory Electrical Stimulation Improves Foot Placement during Targeted Stepping Post-Stroke

Proper foot placement is vital for maintaining balance during walking, requiring the integration of multiple sensory signals with motor commands. Disruption of brain structures post-stroke likely alters the processing of sensory information by motor centers, interfering with precision control of foot placement and walking function for stroke survivors. In this study, we examined whether somatosensory stimulation, which improves functional movements of the paretic hand, could be used to improve foot placement of the paretic limb. Foot placement was evaluated before, during, and after application of somatosensory electrical stimulation to the paretic foot during a targeted stepping task. Starting from standing, twelve chronic stroke participants initiated movement with the non-paretic limb and stepped to one of five target locations projected onto the floor with distances normalized to the paretic stride length. Targeting error and lower extremity kinematics were used to assess changes in foot placement and limb control due to somatosensory stimulation. Significant reductions in placement error in the medial–lateral direction (p = 0.008) were observed during the stimulation and post-stimulation blocks. Seven participants, presenting with a hip circumduction walking pattern, had reductions (p = 0.008) in the magnitude and duration of hip abduction during swing with somatosensory stimulation. Reductions in circumduction correlated with both functional and clinical measures, with larger improvements observed in participants with greater impairment. The results of this study suggest that somatosensory stimulation of the paretic foot applied during movement can improve the precision control of foot placement

The a-theorem and conformal symmetry breaking in holographic RG flows

We study holographic models describing an RG flow between two fixed points driven by a relevant scalar operator. We show how to introduce a spurion field to restore Weyl invariance and compute the anomalous contribution to the generating functional in even dimensional theories. We find that the coefficient of the anomalous term is proportional to the difference of the conformal anomalies of the UV and IR fixed points, as expected from anomaly matching arguments in field theory. For any even dimensions the coefficient is positive as implied by the holographic a-theorem. For flows corresponding to spontaneous breaking of conformal invariance, we also compute the two-point functions of the energy-momentum tensor and the scalar operator and identify the dilaton mode. Surprisingly we find that in the simplest models with just one scalar field there is no dilaton pole in the two-point function of the scalar operator but a stronger singularity. We discuss the possible implications.Comment: 50 pages. v2: minor changes, added references, extended discussion. v3: we have clarified some of the calculations and assumptions, results unchanged. v4: published version in JHE

Preferential Paths of Air-water Two-phase Flow in Porous Structures with Special Consideration of Channel Thickness Effects.

Accurate understanding and predicting the flow paths of immiscible two-phase flow in rocky porous structures are of critical importance for the evaluation of oil or gas recovery and prediction of rock slides caused by gas-liquid flow. A 2D phase field model was established for compressible air-water two-phase flow in heterogenous porous structures. The dynamic characteristics of air-water two-phase interface and preferential paths in porous structures were simulated. The factors affecting the path selection of two-phase flow in porous structures were analyzed. Transparent physical models of complex porous structures were prepared using 3D printing technology. Tracer dye was used to visually observe the flow characteristics and path selection in air-water two-phase displacement experiments. The experimental observations agree with the numerical results used to validate the accuracy of phase field model. The effects of channel thickness on the air-water two-phase flow behavior and paths in porous structures were also analyzed. The results indicate that thick channels can induce secondary air flow paths due to the increase in flow resistance; consequently, the flow distribution is different from that in narrow channels. This study provides a new reference for quantitatively analyzing multi-phase flow and predicting the preferential paths of immiscible fluids in porous structures

Formation of regulatory modules by local sequence duplication

Turnover of regulatory sequence and function is an important part of molecular evolution. But what are the modes of sequence evolution leading to rapid formation and loss of regulatory sites? Here, we show that a large fraction of neighboring transcription factor binding sites in the fly genome have formed from a common sequence origin by local duplications. This mode of evolution is found to produce regulatory information: duplications can seed new sites in the neighborhood of existing sites. Duplicate seeds evolve subsequently by point mutations, often towards binding a different factor than their ancestral neighbor sites. These results are based on a statistical analysis of 346 cis-regulatory modules in the Drosophila melanogaster genome, and a comparison set of intergenic regulatory sequence in Saccharomyces cerevisiae. In fly regulatory modules, pairs of binding sites show significantly enhanced sequence similarity up to distances of about 50 bp. We analyze these data in terms of an evolutionary model with two distinct modes of site formation: (i) evolution from independent sequence origin and (ii) divergent evolution following duplication of a common ancestor sequence. Our results suggest that pervasive formation of binding sites by local sequence duplications distinguishes the complex regulatory architecture of higher eukaryotes from the simpler architecture of unicellular organisms

Locomotor hyperactivity in 14-3-3Zeta KO mice is associated with dopamine transporter dysfunction

Dopamine (DA) neurotransmission requires a complex series of enzymatic reactions that are tightly linked to catecholamine exocytosis and receptor interactions on pre- and postsynaptic neurons. Regulation of dopaminergic signalling is primarily achieved through reuptake of extracellular DA by the DA transporter (DAT) on presynaptic neurons. Aberrant regulation of DA signalling, and in particular hyperactivation, has been proposed as a key insult in the presentation of schizophrenia and related neuropsychiatric disorders. We recently identified 14-3-3ζ as an essential component of neurodevelopment and a central risk factor in the schizophrenia protein interaction network. Our analysis of 14-3-3ζ-deficient mice now shows that baseline hyperactivity of knockout (KO) mice is rescued by the antipsychotic drug clozapine. 14-3-3ζ KO mice displayed enhanced locomotor hyperactivity induced by the DA releaser amphetamine. Consistent with 14-3-3ζ having a role in DA signalling, we found increased levels of DA in the striatum of 14-3-3ζ KO mice. Although 14-3-3ζ is proposed to modulate activity of the rate-limiting DA biosynthesis enzyme, tyrosine hydroxylase (TH), we were unable to identify any differences in total TH levels, TH localization or TH activation in 14-3-3ζ KO mice. Rather, our analysis identified significantly reduced levels of DAT in the absence of notable differences in RNA or protein levels of DA receptors D1–D5. Providing insight into the mechanisms by which 14-3-3ζ controls DAT stability, we found a physical association between 14-3-3ζ and DAT by co-immunoprecipitation. Taken together, our results identify a novel role for 14-3-3ζ in DA neurotransmission and provide support to the hyperdopaminergic basis of pathologies associated with schizophrenia and related disorders.H Ramshaw, X Xu, EJ Jaehne, P McCarthy, Z Greenberg, E Saleh, B McClure, J Woodcock, S Kabbara, S Wiszniak, Ting-Yi Wang, C Parish, M van den Buuse, BT Baune, A Lopez and Q Schwar