The control network of Mars: April 1991

The modern geodetic control network of Mars was first established based on Mariner 9 images with 1-2 km/pixel resolutions and covered almost the entire Martian surface. The introduction of higher resolution (10-200 meter/pixel) Viking Orbiter images greatly improved the accuracy and density of points in the control network. Analysis of the Viking Lander radio tracking data led to more accurate measurements of Mars' rotation period, spin axis direction, and the lander coordinates relative to the inertial reference frame. The prime meridian on Mars was defined by the Geodesy/Cartography Group of the Mariner 9 Television Team as the crater Airy-0, located about 5 degrees south of the equator. The Viking 1 Lander site was identified on a high resolution Viking frame. The control point measurements form the basis of a least squares solution determined by analytical triangulation after the pixel measurements are corrected for geometric distortions and converted to millimeter coordinates in the camera focal plane. Photogrammetric strips encircling Mars at the equator and at 60 degree north south were used to strengthen the overall net and improve the accuracy of the coordinates of points. In addition, photogrammetric strips along 0, 90, 180, and 270 degrees longitude to the Viking 1 Lander site have all significantly strengthened the control network. Most recently, photogrammetric strips were added to the net along 30 degrees north latitude between 0 and 180 degrees, and along 30 degrees between 180 and 360 degrees. The Viking 1 Lander site and Airy-0 are linked through photogrammetric strips occurring along the 0 degree meridian from Airy-0 to 65 degrees north, from that point through the Viking 1 Lander site to the equator, and along the equator to 180 degrees longitude. The Viking 1 lander site is thus a well calibrated area with coordinates of points accurate to approximately 200 meters relative to the J2000 inertial coordinate system. This will be a useful calibration region for upcoming missions. The current status of the control network calculations is presented

Interview with Mert Henry by Andrea L’Hommedieu

Biographical NoteMerton G. “Mert” Henry was born on February 4, 1926, in Hampden, Maine. He lived there with his parents and helped out at his grandfather’s general store while growing up. He moved to South Portland just before starting high school. He deferred attending Bowdoin College until 1946 in order to serve in the Army, which sent him to the Philippines. He majored in history at Bowdoin and was graduated in the class of 1950. He also earned a law degree from Georgetown Law while working on a military history project at the Pentagon during the Korean War. A long-time leader in the Maine Republican Party, he worked for Senator Fredreick G. Payne of Maine and ran his unsuccessful 1958 reelection campaign, losing to Ed Muskie. Since then he has worked at the same law firm, currently under the name of Jensen Baird Gardner & Henry, in Portland, Maine, where he worked with George Mitchell for twelve years between 1965 and 1977. SummaryInterview includes discussion of: the Hampden, Maine community; Armed Services; Bowdoin College and law school in Washington D.C; involvement in Senator Frederick Payne’s campaigns, and Senator Margaret Chase Smith’s campaigns; meeting George Mitchell at Jenson Baird law firm; Mitchell’s campaign for governor in 1974; professional and personal relationship between Henry and Mitchell; advice to Mitchell about accepting his Senate appointment; U.S. Senate campaign (1982); Mitchell’s success as a senator; and changes in politics and campaigning

Nonuniversal power law scaling in the probability distribution of scientific citations

We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations ('classics') are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The 'tipping point' at which a paper becomes a classic is about 21 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 29 for Physical Review D papers published from 1975-1994, and 39 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited.Comment: 7 pages, 3 figures, 2 table

The control network of Mercury: April 1991

Features identified on Mariner 10 high resolution images of Mercury, acquired during three flybys between 1974 and 1975, form the basis of Mercury's planetwide control network. Although images from all three flybys are used in the net, the large amount of contiguous coverage from the second flyby, a southern bright-side pass, make these images the strongest contributors to the control net. Mercury is in synchronous rotation with a period of 58.6462 days and its spin axis is approximately normal to the equatorial plane. The 20 degree meridian is defined by the crater Hun Kal, located just south of the equator. The control network computations involve the photogrammetric determination of control point coordinates and an analytical triangulation solution. The current control network computations for Mercury are performed in the J2000 coordinate system according to the International Astronomical Union (IAU) convention. In recent years, updates to the control network have included improved trajectory solutions and modification of the standard radii (2439) at several points based on Earth-based radar altimetry data. The current status of the control network calculations is presented. Improvements were made to existing control points and new control points were added to the net to strengthen the overall network and improve the standard error of measurement

Financial rogue waves

The financial rogue waves are reported analytically in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These solutions may be used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.Comment: 4 papges, 2 figures, Final version accepted in Commun. Theor. Phys., 201

Role of Noise in a Market Model with Stochastic Volatility

We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES effect in our model with stochastic volatility. We investigate the role of the correlation between the two noise sources on the NES effect.Comment: 13 pages, 6 figures, Eur. Phys. J. B, in pres

Pricing Exotic Options in a Path Integral Approach

In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the cases of Asian, barrier knock out, reverse cliquet and basket call options, evaluating prices and Greeks. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at-the-money and out-of-the-money options, the path integral approach exhibits competitive performances.Comment: 21 pages, LaTeX, 3 figures, 6 table

The dynamics of financial stability in complex networks

We address the problem of banking system resilience by applying off-equilibrium statistical physics to a system of particles, representing the economic agents, modelled according to the theoretical foundation of the current banking regulation, the so called Merton-Vasicek model. Economic agents are attracted to each other to exchange `economic energy', forming a network of trades. When the capital level of one economic agent drops below a minimum, the economic agent becomes insolvent. The insolvency of one single economic agent affects the economic energy of all its neighbours which thus become susceptible to insolvency, being able to trigger a chain of insolvencies (avalanche). We show that the distribution of avalanche sizes follows a power-law whose exponent depends on the minimum capital level. Furthermore, we present evidence that under an increase in the minimum capital level, large crashes will be avoided only if one assumes that agents will accept a drop in business levels, while keeping their trading attitudes and policies unchanged. The alternative assumption, that agents will try to restore their business levels, may lead to the unexpected consequence that large crises occur with higher probability