John Maloney

Scalar equations for synchronous Boolean networks with biological applications

One way of coping with the complexity of biological systems is to use the simplest possible models which are able to reproduce at least some nontrivial features of reality. Although two value Boolean models have a long history in technology, it is perhaps a little bit surprising that they can also represent important features of living organizms. In this paper, the scalar equation approach to Boolean network models is further developed and then applied to two interesting biological models. In particular, a linear reduced scalar equation is derived from a more rudimentary nonlinear scalar equation. This simpler, but higher order, two term equation gives immediate information about both cycle and transient structure of the network.

Thermal network predictions of the daily temperature fluctuations in a direct gain room

Abstract This paper studies the daily temperature fluctuations in a direct gain room measuring 6.1 × 4.57 × 2.44 m3 (20 ft × 15 ft × 8 ft). The room is assumed to have losses on three faces and 8.36 m2 (90 ft2) of south glazing. Let r denote the ratio of the surface area of the mass wall to the area of the south facing glazing. The effect of r on mass walls 10.16, 20.32 and 30.48 cm (4, 8 and 12 in.) thick was determined for values of r equal to 1, 2, 4, 8 and 11.1. The temperature and solar insolation values for a typical January day in Nebraska were duplicated thirty consecutive times and were used for the weather data input to the modeling program. Using thirty consecutive like days has the advantage of damping out the transient solution to the point where it is negligible. It was found that for each thickness of wall, the temperature fluctuations over a day decrease as r increases, and it was also found that for a fixed value of r, the daily temperature fluctuations decrease as the wall thickness is increased. These results are consistent with those reported by Mazria. In addition cloudy day storage was considered for both the 10.16 and 20.32 cm (4 and 8 in.) walls, with r fixed at 4, runs were made with 20, 33, 50 and 100 per cent cloudy days. The results are presented in graphical form and indicate a rapid recovery of the system in most cases.

An analysis of a fractal Michaelis-Menten curve

Simple chemical reactions can be described by the Michaelis Menten response curve relating the velocity V of the reaction and the concentration [S] of the substrate S. To handle more complicated reactions without introducing general polynomial response curves, the rate constants can be considered to be scale dependent. This leads to a new response curve with characteristic sigmoidal shape. But not all sigmoidal curves can be accurately fit with three parameters. In order to get an accurate fit, the lower part of the ∫ shaped curve cannot be too shallow and the upper part can’t be too steep. This paper determines an exact mathematical expression for the steepness and shallowness allowed.

A reverse Hölder type inequality for the logarithmic mean and generalizations

An inequality involving the logarithmic mean is established. Specifically, we show that L(c, x) ln(c/x) ln(c/a) L(x, a) ln(x/a) ln(c/a) < L(c, a) (1) where 0 < a < x < c and L(x, y) = y−x ln y−ln x , 0 < x < y. Then several generalizations are given.

EVALUATION AND TESTING OF THE NEBRASKA MODIFIED ROOF POND FOR SEVERE HEATING AND COOLING ENVIRONMENTS

ABSTRACT The concept for the Nebraska modified roof pond was developed jointly by Richard C. Bourne of the Davis Energy Group and Bing Chen of the Passive Solar Research Group. As shown in Fig. 1 and Fig. 2, a fixed, rigid cement coated insulation made by Dow Chemical for roofing applications floats over the pond itself. At night, during summer operation (Fig 2), a submersible pump in the pond places water above the roof. Through the twin processes of evaporation and radiation by night sky, the water is cooled. This cooled water then migrates downward to the pond via seams and cracks in the floating insulation. During winter time, the roof pond water is heated by employing a thermosiphon passive solar heating drive system. (Fig. 1)

Discriminant analysis and linear programming

This paper discusses the linear programming approach to the discriminant analysis problem. Both the ‘separable’ and ‘non‐separable’ cases are considered. In the non‐separable case we develop a bicriteria linear programming model and based on this bicriteria linear program a linear discriminant function is determined.

An analysis of a fractal kinetics curve of Savageau

The fractal kinetics curve derived by Savageau is analysed to show that its parameters are not uniquely determined given four appropriately situated data points. Comparison is made with an alternate fractal Michaelis-Menten equation derived by Lopez-Quintela and Casado.

Using a simplified gradient method to solve a system or linear equations

The general gradient method of iterative solution to the system Ax == b is complicated. This paper presents a simplified iterative solution approach to the system. It utilizes the general gradient method; however, the method is simpler than the conjugate gradient method in concept as well as in its algorithm. Also, this proposed method is efficient in finding a solution.

PERFORMANCE COMPARISON OF SELECTIVE SURFACE TROMBE WALLS WITH TRADITIONAL THERMAL MASS WALLS

ABSTRACT Trombe walls have become one of the best known passive solar heating techniques. Known for their thermal performance and interior room temperature stability, Trombe walls or thermal mass walls have achieved widespread acceptance. In order to achieve a higher solar savings fraction value particularly in climates with cold winters the use of some form of insulation to cover external glazing at night is recommended. As an alternative, selective surface coatings applied directly to the Trombe wall surface are another means to improve thermal performance but without the need to apply cumbersome night shutters. The conclusions at Los Alamos Scientific Laboratories (LASL) suggest that the thermal performance of these selective surface coatings matches that of the more traditional Trombe wall with night insulation (Balcomb and colleagues, 1983). This paper reports on the results of similar testing performed over two winters at the passive Solar Research Test Facility in Omaha, Nebraska. The purpose of our studies was to validate LASL predictions (Chen and colleagues, 1983).