In 1969 Barlow introduced the phrase "economy of impulses" to express the tendency for successive neural systems to use lower and lower levels of cell firings to produce equivalent encodings. From this viewpoint, the ultimate economy of impulses is a neural code of minimal redundancy. The hypothesis motivating our research is that energy expenditures, e.g., the metabolic cost of recovering from an action potential relative to the cost of inactivity, should also be factored into the economy of impulses. In fact, coding schemes with the largest representational capacity are not, in general, optimal when energy expenditures are taken into account. We show that for both binary and analog neurons, increased energy expenditure per neuron implies a decrease in average firing rate if energy efficient information transmission is to be maintained.

Organisms evolve as compromises, and many of these compromises can be expressed in terms of energy efficiency. For example, a compromise between rate of information processing and the energy consumed might explain certain neurophysiological and neuroanatomical observations (e.g., average firing frequency and number of neurons). Using this perspective reveals that the randomness injected into neural processing by the statistical uncertainty of synaptic transmission optimizes one kind of information processing relative to energy use. A critical hypothesis and insight is that neuronal information processing is appropriately measured, first, by considering dendrosomatic summation as a Shannon-type channel (1948) and, second, by considering such uncertain synaptic transmission as part of the dendrosomatic computation rather than as part of axonal information transmission. Using such a model of neural computation and matching the information gathered by dendritic summation to the axonal information transmitted, H(p*), conditions are defined that guarantee synaptic failures can improve the energetic efficiency of neurons. Further development provides a general expression relating optimal failure rate, f, to average firing rate, p*, and is consistent with physiologically observed values. The expression providing this relationship, f approximately 4(-H(p*)), generalizes across activity levels and is independent of the number of inputs to a neuron.

This paper investigates how noise affects a minimal computational model of the hippocampus and, in particular, region CA3. The architecture and physiology employed are consistent with the known anatomy and physiology of this region. Here, we use computer simulations to demonstrate and quantify the ability of this model to create context codes in sequential learning problems. These context codes are mediated by local context neurons which are analogous to hippocampal place-coding cells. These local context neurons endow the network with many of its problem-solving abilities. Our results show that the network encodes context on its own and then uses context to solve sequence prediction under ambiguous conditions. Noise during learning affects performance, and it also affects the development of context codes. The relationship between noise and performance in a sequence prediction is simple and corresponds to a disruption of local context neuron firing. As noise exceeds the signal, sequence completion and local context neuron firing are both lost. For the parameters investigated, extra learning trials and slower learning rates do not overcome either of the effects of noise. The results are consistent with the important role played, in this hippocampal model, by local context neurons in sequence prediction and for disambiguation across time.

The immediate object of a polarographic measurement is the precise determination of the currentvoltage curve for the "test" or "analytical" electrode. Various features of this curve can, in turn, be related to the concentration of the electroactive species, the number of electrons in the electrode reaction, the kinetics of the electrode reaction, the stability constant of a metal ion complex, or other information. The theories and equations relating the current-voltage curve (polarogram) to the desired information are almost always based on the assumption that the polarogram is a true measure of the test electrode current versus the test electrode potential. A true measure of electrode current is obtained by simply putting the current measuring device in series with the electrolytic cell. However, the potential across the cell includes the potential of the second (counter) electrode and the I R drop through the electrolyte solution as well as the test electrode potential. The traditional polarographic instrument produces a plot of cell current versus cell potential and relies upon proper cell design to reduce the IR drop and the variation in counter electrode potential to tolerable values ( I ) . Concentrated electrolyte solutions are required and a large "nonpolarizable" reference electrode with a low resistance salt bridge must be used for the counter electrode.Recently, a "controlled potential" polarographic instrument has been described in the literature (3). With controlled potential polarography, a reference electrode is used only to measure the test electrode potential; the necessary current is introduced into the cell through the counter electrode. (This is the socalled "three-electrode" system.) The measurement apparatus is designed to apply automatically to the cell the exact current required to maintain the test electrode potential a t the desired value. The advantages of the controlled potential instrument are: polarograms can he run in solutions with low electrolyte concentrations, e.g., nonaqueous solvents; a nonpolarizable counter electrode is not required (a piece of platinum will do very nicely); a convenient dip-type calomel reference electrode may be used in place of the large calomel and frit which require continuous maintenance and cannot he stored in a "ready" condition. The advantage of controlled potential polarography in cases of high cell resistance is shown in Figure 1. A Beckman fiber-type calomel reference electrode was used as the counter electrode in a two-electrode cell to obtain curve (a). The slope of the current-voltage curve shows the resistance of the electrode to be about 60 kilohms. The same reference electrode was used for curve (b) but with a platinum counter electrode in a three-electrode cell. and has the theoretical slope for a two-electron reduction. Although the ability to do nonaqueous polarography is the most widely claimed advantage of the controlled potential instrument, as yet very few articles using polarography in solutions of high specific resistance have appe...