Inflow-Outflow Model with Conduction and Self-Consistent Feeding for Sgr A*

We propose a two-temperature radial inflow-outflow model near Sgr A* with self-consistent feeding and conduction. Stellar winds from individual stars are considered to find the rates of mass injection and energy injection. These source terms help to partially eliminate the boundary conditions on the inflow. Electron thermal conduction is crucial for inhibiting the accretion. Energy diffuses out from several gravitational radii, unbinding more gas at several arcseconds and limiting the accretion rate to <1% of Bondi rate. We successfully fit the X-Ray surface brightness profile found from the extensive Chandra observations and reveal the X-Ray point source in the center. The super-resolution technique allows us to infer the presence and estimate the unabsorbed luminosity $L\approx4\cdot10^{32}{\rm erg s^{-1}}$ of the point source. The employed relativistic heat capacity and direct heating of electrons naturally lead to low electron temperature $T_e\approx 4\cdot10^{10}$ K near the black hole. Within the same model we fit 86 GHz optically thick emission and obtain the order of magnitude agreement of Faraday rotation measure, thus achieving a single accretion model suitable at all radii.Comment: 6 pages, 5 figures, accepted by Ap

An algorithm for moment-matching scenario generation with application to financial portfolio optimization

We present an algorithm for moment-matching scenario generation. This method produces scenarios and corresponding probability weights that match exactly the given mean, the covariance matrix, the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector. Optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches. The algorithm is used for generating scenarios in a mean-CVaR portfolio optimisation model. For the chosen optimisation example, it is shown that desirable properties for a scenario generator are satisfied, including in-sample and out-of-sample stability. It is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example; thus, good solutions can apparently be obtained with a relatively small number of scenarios. The proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non-convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments (rather than average marginal moments)

Phase Transitions of the Typical Algorithmic Complexity of the Random Satisfiability Problem Studied with Linear Programming

Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in polynomial time for suitable ranges of the parameter. In fact, random $K$-SAT, with $\alpha=M/N$ as control parameter, can be solved quickly for small enough values of $\alpha$. It shows a phase transition between a satisfiable phase and an unsatisfiable phase. For branch and bound algorithms, which operate in the space of feasible Boolean configurations, the empirically hardest problems are located only close to this phase transition. Here we study $K$-SAT ($K=3,4$) and the related optimization problem MAX-SAT by a linear programming approach, which is widely used for practical problems and allows for polynomial run time. In contrast to branch and bound it operates outside the space of feasible configurations. On the other hand, finding a solution within polynomial time is not guaranteed. We investigated several variants like including artificial objective functions, so called cutting-plane approaches, and a mapping to the NP-complete vertex-cover problem. We observed several easy-hard transitions, from where the problems are typically solvable (in polynomial time) using the given algorithms, respectively, to where they are not solvable in polynomial time. For the related vertex-cover problem on random graphs these easy-hard transitions can be identified with structural properties of the graphs, like percolation transitions. For the present random $K$-SAT problem we have investigated numerous structural properties also exhibiting clear transitions, but they appear not be correlated to the here observed easy-hard transitions. This renders the behaviour of random $K$-SAT more complex than, e.g., the vertex-cover problem.Comment: 11 pages, 5 figure

Portfolio optimisation models and properties of return distributions

Mean-risk models have been widely used in portfolio optimisation. However, such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio which is nondominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties. The problem is multi-objective and is transformed into a single objective problem by using the reference point method, in which target levels, known as aspiration points, are specified for the objective function values. A model is proposed in which the aspiration points relate to ordered return outcomes of the portfolio return. The model is extended by additionally specifying reservation points, which act pre-emptively in the optimisation. The theoretical properties of the models are studied. The performance of the models on real data drawn from the Hang Seng index is also investigated

Behavioural and physiological adaptations to low-temperature environments in the common frog, Rana temporaria

&lt;b&gt;Background&lt;/b&gt;&lt;p&gt;&lt;/p&gt; Extreme environments can impose strong ecological and evolutionary pressures at a local level. Ectotherms are particularly sensitive to low-temperature environments, which can result in a reduced activity period, slowed physiological processes and increased exposure to sub-zero temperatures. The aim of this study was to assess the behavioural and physiological responses that facilitate survival in low-temperature environments. In particular, we asked: 1) do high-altitude common frog (Rana temporaria) adults extend the time available for larval growth by breeding at lower temperatures than low-altitude individuals?; and 2) do tadpoles sampled from high-altitude sites differ physiologically from those from low-altitude sites, in terms of routine metabolic rate (RMR) and freeze tolerance? Breeding date was assessed as the first day of spawn observation and local temperature recorded for five, paired high- and low-altitude R. temporaria breeding sites in Scotland. Spawn was collected and tadpoles raised in a common laboratory environment, where RMR was measured as oxygen consumed using a closed respiratory tube system. Freeze tolerance was measured as survival following slow cooling to the point when all container water had frozen.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Results&lt;/b&gt;&lt;p&gt;&lt;/p&gt; We found that breeding did not occur below 5°C at any site and there was no significant relationship between breeding temperature and altitude, leading to a delay in spawning of five days for every 100 m increase in altitude. The relationship between altitude and RMR varied by mountain but was lower for individuals sampled from high- than low-altitude sites within the three mountains with the highest high-altitude sites (≥900 m). In contrast, individuals sampled from low-altitudes survived freezing significantly better than those from high-altitudes, across all mountains.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Conclusions&lt;/b&gt;&lt;p&gt;&lt;/p&gt; Our results suggest that adults at high-altitude do not show behavioural adaptations in terms of breeding at lower temperatures. However, tadpoles appear to have the potential to adapt physiologically to surviving at high-altitude via reduced RMR but without an increase in freeze tolerance. Therefore, survival at high-altitude may be facilitated by physiological mechanisms that permit faster growth rates, allowing completion of larval development within a shorter time period, alleviating the need for adaptations that extend the time available for larval growth