An ultradiscrete matrix version of the fourth Painleve equation

We establish a matrix generalization of the ultradiscrete fourth Painlev\'e equation (ud-PIV). Well-defined multicomponent systems that permit ultradiscretization are obtained using an approach that relies on a group defined by constraints imposed by the requirement of a consistent evolution of the systems. The ultradiscrete limit of these systems yields coupled multicomponent ultradiscrete systems that generalize ud-PIV. The dynamics, irreducibility, and integrability of the matrix valued ultradiscrete systems are studied.Comment: 12 pages, 12 figures, Latex2e, Submitted to J. Phys. A, corrections mad

The processing of color preference in the brain

Decades of research has established that humans have preferences for some colors (e.g., blue) and a dislike of others (e.g., dark chartreuse), with preference varying systematically with variation in hue (e.g., Hurlbert & Owen, 2015). Here, we used functional MRI to investigate why humans have likes and dislikes for simple patches of color, and to understand the neural basis of preference, aesthetics and value judgements more generally. We looked for correlations of a behavioural measure of color preference with the blood oxygen level-dependent (BOLD) response when participants performed an irrelevant orientation judgement task on colored squares. A whole brain analysis found a significant correlation between BOLD activity and color preference in the posterior midline cortex (PMC), centred on the precuneus but extending into the adjacent posterior cingulate and cuneus. These results demonstrate that brain activity is modulated by color preference, even when such preferences are irrelevant to the ongoing task the participants are engaged. They also suggest that color preferences automatically influence our processing of the visual world. Interestingly, the effect in the PMC overlaps with regions identified in neuroimaging studies of preference and value judgements of other types of stimuli. Therefore, our findings extends this literature to show that the PMC is related to automatic encoding of subjective value even for basic visual features such as color

Modelling the robustness properties of HVAC plant under feedback control

Most existing building simulation programs fail to capture sufficient of the underlying dynamics of nonlinear HVAC plant and some have restricted room space modelling capabilities for low-time-horizon analyses. In this work, a simplified model of a room space with hot water heating and a chilled ceiling system is developed for the main purpose of analysing control system response. The room model is based on a new approach to lumped capacitance modelling and the heating and chilled ceiling emitters are modelled using third-order descriptions. Control system components are treated in detail and both controllers are ‘tuned’ at a nominal region of plant operation using a gradient-descent-based optimization procedure. Robustness qualities of the controllers are analysed with reference to extremes in plant operating conditions. A key feature of the work is the transparency of the modelling procedure, designed to have appeal to researchers as well as practitioners involved with HVAC control system design problems

Thermal comfort based fuzzy logic control

Most heating, ventilation and air conditioning (HVAC) control systems are considered as temperature control problems. In this work, the predicted mean vote (PMV) is used to control the indoor temperature of a space by setting it at a point where the PMV index becomes zero and the predicted percentage of persons dissatisfied (PPD) achieves a maximum threshold of 5%. This is achieved through the use of a fuzzy logic controller that takes into account a range of human comfort criteria in the formulation of the control action that should be applied to the heating system to bring the space to comfort conditions. The resulting controller is free of the set up and tuning problems that hinder conventional HVAC controllers. Simulation results show that the proposed control strategy makes it possible to maximize the indoor thermal comfort and, correspondingly, a reduction in energy use of 20% was obtained for a typical 7-day winter period when compared with conventional control

The Effects of Consumer Protection on Sales Signs, Consumer Search and Competition

Within a one-shot, duopoly game, we show that firms cannot use false in- store price comparisons to deter rational consumers from further beneficial price search in an effort to create market power. However, by introducing a consumer protection authority that monitors price comparisons, we formalise Nelson’s (1974) conjecture by showing that ‘middle-order’ monitoring can actually facilitate the deception of fully rational consumers, to deter them from otherwise optimal search. Despite this effect, we show that no increase in monitoring can ever harm consumers due to a second, larger effect that improves consumer information and increases the intensity of price competition.Comparative Price Advertising, Deception, Obfuscation, Cheap Talk

B→Dlν form factors at nonzero recoil and extraction of |Vcb|

We present a lattice QCD calculation of the B→Dlν semileptonic decay form factors f+(q2) and f0(q2) for the entire physical q2 range. Nonrelativistic QCD bottom quarks and highly improved staggered quark charm and light quarks are employed together with Nf=2+1 MILC gauge configurations. A joint fit to our lattice and BABAR experimental data allows an extraction of the Cabibbo-Kobayashi-Maskawa matrix element |Vcb|. We also determine the phenomenologically interesting ratio R(D)=B(B→Dτντ)/B(B→Dlνl) (l=e,μ). We find |Vcb|B→Dexcl=0.0402(17)(13), where the first error consists of the lattice simulation errors and the experimental statistical error and the second error is the experimental systematic error. For the branching fraction ratio we find R(D)=0.300(8)

Radial Stellar Pulsation and 3D Convection. I. Numerical Methods and Adiabatic Test Cases

We are developing a 3D radiation hydrodynamics code to simulate the interaction of convection and pulsation in classical variable stars. One key goal is the ability to carry these simulations to full amplitude in order to compare them with observed light and velocity curves. Previous 2D calculations were prevented from doing this because of drift in the radial coordinate system, due to the algorithm defining radial movement of the coordinate system during the pulsation cycle. We remove this difficulty by defining our coordinate system flow algorithm to require that the mass in a spherical shell remain constant throughout the pulsation cycle. We perform adiabatic test calculations to show that large amplitude solutions repeat over more than 150 pulsation periods. We also verify that the computational method conserves the peak kinetic energy per period, as must be true for adiabatic pulsation models