Six interesting works by Alston S. Householder, all found in The Bulletin of Mathematical Biophysics, 1939-19412. Offered in six individual issues of the journal, scarce in their original wrappers. Six issues, $850.00

Includes:

**Householder,** Alston. Mathematical biophysics of cellular forms and movements. The Bulletin of Mathematical Biophysics (1941) 3: 27-38, March 01, 1941. Rashevsky's equations for describing the joint variation of cell shape and concentration of a metabolite are discussed. Conditions for the existence of non-spherical equilibria and the location of these are obtained and involve only two parametersa andA. Sufficient (but not necessary) conditions for the stability of these equilibria can also be expressed in terms of these parameters alone. Necessary conditions involve in some cases a third parameterB. Quasi-periodic fluctuations about a stable nonspherical equilibrium may occur, but only in caseB lies on a certain finite range which can be defined in terms of a and A....

Householder, Alston S. A theory of steady-state activity in nerve-fiber networks II: The simple circuit. The Bulletin of Mathematical Biophysics (1941) 3: 105-112, September 01, 1941. It is found that for a simple circuit of neurons, if this contains an odd number of inhibitory fibers, or none at all, or if the product of the activity parameters is less than unity, then the stimulus pattern always determines uniquely the steady-state activity. For circuits not of one of these types, it is possible to classify exclusively and exhaustively all possible activity patterns into three types, here called “odd”, “even”, and “mixed”. For any pattern of odd type and any pattern of even type there always exists a stimulus pattern consistent with both, but in no other way can such an association of activity patterns be made.

Householder, Alston S. A theory of steady-state activity in nerve-fiber networks: I. Definitions and preliminary lemmas. The Bulletin of Mathematical Biophysics (1941) 3: 63-69, June 01, 1941. As an essay towards the determination of the effect of structural relations among nerve fibers upon the character of their activity, preliminary consideration is given to the steady-state activity of some simple neural structures. It is assumed as a first approximation that while acted upon by a constant stimulus, each fiber reaches a steady-state activity whose intensity is a linear function of the applied stimulus. It is shown by way of example that for a simple two-fiber circuit of inhibitory neurons knowledge of the stimuli applied to the separate fibers does not necessarily suffice to determine uniquely the activity that will result. On the other hand, there are deduced certain restrictions on the possible types of activity that may be consistent with a given pattern of applied stimulation.

Householder, Alston S. A note on the horopter. The Bulletin of Mathematical Biophysics (1940) 2: 135-140, September 01, 1940. By assuming the fixity (but not the symmetry) of corresponding points on the two retinae, it is possible to derive the equation of any horopter when one is known. In particular when, as experiment shows, one horopter is linear, then all horopters must be conics. These have the form given by Ogle, but whereas Ogle leaves one parameter undetermined at each fixation, on our assumption the only arbitrary parameter is determined by the position of the linear horopter.

Householder, A. S. A neural mechanism for discrimination: II. Discrimination of weights. The Bulletin of Mathematical Biophysics (1940) 2: 1-13, March 01, 1940. A theoretical central mechanism for the discrimination of intensities as previously developed, together with plausible assumptions concerning the receptors, are employed for the derivation of the discriminable difference between lifted weights as a function of the smaller of these weights. The function so derived depends upon three parameters, one parameter being the weight of the supporting member. Some empirical data are compared with the theoretical predictions, and a few remarks are added to describe the physiological significance of the parameters.

Householder, A. S. Studies in the mathematical theory of excitation. The Bulletin of Mathematical Biophysics (1939) 1: 129-141, September 01, 1939. The general linear two-factor nerve-excitation theory of the type of Rashevsky and Hill is discussed and normal forms are derived. It is shown that in some cases these equations are not reducible to the Rashevsky form.

Other contributors to these six journals include:

Rashevsky. Note on the mathematical biophysics of temporal sequences of stimuli. The Bulletin of Mathematical Biophysics (1941) 3: 89-92, September 01, 1941. By Rashevsky, N. Some general considerations are given regarding the effects of temporal sequences of stimuli in a neuronic network, which consists of a set of parallel chains of excitatory fibers with cross-connections made of inhibitory fibers. It is shown that, in general, the excitation produced by any individual stimulus of the series is a function of the order and duration of the previous stimuli, and that the effect of each stimulus thus depends on the whole temporal pattern considered.

Rashevsky, N. A note on the nature of correlations between different characteristics of organisms. The Bulletin of Mathematical Biophysics (1941) 3: 93-95, September 01, 1941. Different anatomical and physiological characteristics of organisms affect their interreaction with the inorganic world as well as their mutual interreactions. In this way they all may affect indirectly the total rate of reproduction of a species. It is shown that the requirement of a maximum rate of reproduction defines the distribution functions of the different characteristics and through those distribution functions determines statistical correlations between the characteristics.