Bertrand competition with intertemporal demand

In the text-book model of dynamic Bertrand competition, competing firms meet the same demand function every period. This is not a satisfactory model of the demand side if consumers can make intertemporal substitution between periods. Each period then leaves some residual demand to future periods, and consumers who observe price under-cutting may correctly anticipate an ensuing price war and therefore postpone their purchases. Accordingly, the interaction between the firms no longer constitutes a repeated game, and hence falls outside the domain of the usual Folk theorems. We analyze collusive pricing in such situations, and study cases when consumers have perfect and imperfect foresight and varying degrees of patience. It turns out that collusion against patient and forward-looking consumers is easier to sustain than collusion in the text-book model

Visual Neuroprosthetics: Functional Vision for the Blind

Journal ArticleResent progress in materials and microfabrication technologies have allowed researchers to reconsider the prospect of providing a useful visual sense to the profoundly blind. This will be accomplished by electrically stimulating their visual systems via an array of implanted microelectrodes. The techniques of the semiconductor industry have been employed to create electrode arrays with three dimensional architectures. These arrays are proving to be safely implantible into the visual parts of the brain of animals with little significant long term consequences. Thus, the tools of neuroprosthetics have been developed to the point that they will soon be used to validate some of the physiological foundations upon which artificial vision have been based. Validation of these foundations will accelerate the rapid pace of this research. If these physiological underpinnings can be shown to be solid, a demonstration of functionally useful vision in blind human volunteers may be possible within a five year time frame

Silicon-based, three-dimensional neural interface: manufacturing processes for an intracortical electrode array

Journal ArticleA method has been developed for the manufacture of a "three-dimensional" electrode array geometry for chronic intracortical stimulation. This silicon based array consists of a 4.2 x 4.2 x 0.12 mm thick monocrystalline substrate, from which project 100 conductive, silicon needles sharpened to facilitate cortical penetration. Each needle is electrically isolated from the other needles, and is about 0.09 mm thick at its base and 1.5 mm long. The sharpened end of each needle is coated with platinum to facilitate charge transfer into neural tissue. The following manufacturing processes were used to create this array. 1) Thermomigration of 100 aluminum pads through an n-type silicon block. This creates trails of highly conductive p+ silicon isolated from each other by opposing pn junctions. 2) A combination of mechanical and chemical micromachining which creates individual penetrating needles of the p+ silicon trails. 3) Metal deposition to create active electrode areas and electrical contact pads. 4) Array encapsulation with polyimide. The geometrical, mechanical, and electrical properties of these arrays should make them well suited as interfaces to cortical tissue

Mobility performance with a pixelized vision system

Journal ArticleA visual prosthesis, based on electrical stimulation of the visual cortex, has been suggested as a means for partially restoring functional vision in the blind. The prosthesis would create a pixelized visual sense consisting of punctate spots of light (phosphenes). The present study investigated the feasibility of achieving visually-guided mobility with such a visual sense. Psychophysical experiments were conducted on normally sighted human subjects, who were required to walk through a maze which included a series of obstacles, while their visual input was restricted to information from a pixelized vision simulator. Walking speed and number of body contacts with obstacles and walls were measured as a function of pixel number, pixel spacing, object minification, and field of view. The results indicate that a 25 x 25 array of pixels distributed within the foveal visual area could provide useful visually guided mobility in environments not requiring a high degree of pattern recognition

Signal integration at the pedicle of turtle cone photoreceptors: an anatomical and electrophysiological study

Journal ArticleThe morphology of the axon which connects the cell body and pedicle of turtle cone photoreceptors was studied by light and electron microscopy. The axon which contains numerous synaptic vesicles, some endoplasmic reticulum, and a few cisternae is basically filled with cytoplasm. The length of the axon is related to the class of cone and varies slightly with retinal location, with axons as short as 3-6 microns found in red cones, and as long as 60 microns in cones containing colorless oil droplets. By simultaneously voltage clamping the cell body and pedicle regions of single isolated cones, we measured the longitudinal axonal resistance and the cell body and pedicle membrane resistances. For each cell studied, the axonal resistance of cones with short axons was lower than the cell and pedicle membrane resistances. Thus, the cell can be considered to be an isopotential structure. However, in some cones with long axons, the axonal, cell body, and pedicle resistances were comparable. The pedicles of these cones, therefore, could act like summing points and may provide a locus for spatial signal integration. Electrical coupling between the principal and accessory members of double cones was also studied. Electron-microscopic observation of the membrane junction between the apposed inner segments of the double cones in the intact retina show narrow segments which resemble gap junctions. However, in every double cone studied in culture, passing currents into one member of the double cone did not result in measurable current flow in the adjacent cell. Thus, the two members of the double cone, isolated from the turtle retina, are not electrically coupled

Advanced demultiplexing system for physiological stimulation

Journal ArticleA CMOS very large scale integration (VLSI) chip has been designed and built to implement a scheme developed for multiplexing/demultiplexing the signals required to operate an intracortical stimulating electrode array. Because the use of radio telemetry in a proposed system utilizing this chip may impose limits upon the rate of data transmission to the chip, the scheme described herein was used to reduce the amount of digital information which must be sent to control a large quantity (up to several hundred) of stimulating electrodes. By incorporating multiple current sources on chip, many channels may be stimulated simultaneously. By incorporating on-chip timers, control over pulse timing is assigned to the chip, reducing by up to fourfold the amount of control data which must be sent. By incorporating on-chip RAM, information associated with the desired stimulus amplitude and pulse timing can be stored on chip. In this manner, it is necessary to send control information to the chip only when the information changes, rather than at the stimulus repeat rate for each channel. This further reduces the data rate by a factor of five to ten times or more. The architecture described here, implemented as an eight-channel stimulator, is scalable to a 625-channel stimulator while keeping data transmission rates under 2 Mbps

Selective motor unit recruitment via intrafascicular multielectrode stimulation

Journal ArticleRecruitment of force via independent asynchronous firing of large numbers of motor units produces the grace and endurance of physiological motion. We have investigated the possibility of reproducing this physiological recruitment strategy by determining the selectivity of access to large numbers of independent motor units through intrafascicular multielectrode stimulation (IFMS) of the peripheral nerve. A Utah Slanted Electrode Array containing 100, 0.5-1.5 mm-long penetrating electrodes was inserted into the sciatic nerve of a cat, and forces generated by the 3 heads of triceps surea in response to electrical stimulation of the nerve were monitored via force transducers attached to their tendons. We found a mean of 17.4 +/- 4.9 (mean +/- SEM) electrodes selectively excited maximal forces in medial gastrocnemius before exciting another muscle. Among electrodes demonstrating selectivity at threshold, a mean of 7.3 +/- 2.7 electrodes were shown to recruit independent populations of motor units innervating medial gastrocnemius (overlap < 20%). Corresponding numbers of electrodes were reported for lateral gastrocnemius and soleus, as well. We used these stimulation data to emulate physiological recruitment strategies, and found that independent motor unit pool recruitment approximates physiological activation more closely than does intensity-based recruitment or frequency-based recruitment

Silicon carbide enhanced thermomigration

Journal ArticleThe widespread acceptance of thermomigration technology to produce through-chip interconnects has been impaired by (i) a random walk of the Si-Al liquid eutectic inclusion as it traverses the wafer, and (ii) a ?surface barrier? which allows thermomigration of only relatively large inclusions. In this paper it is shown that these problems can be mitigated by thermomigrating at high wafer temperatures and with large temperature gradients through the wafer. It has been possible to achieve these high wafer temperatures and large gradients using a bank of infrared lamps and a bilaminar structure of silicon carbide powder compressed onto the top of a silicon wafer. This increases the delivery of energy to the wafer and reduces the random walk of the liquid inclusion. Further, the high wafer temperatures and enhanced temperature gradients created with this bilaminar silicon carbide structure allow relatively small, square aluminum pads (35 pm on a side) to thermomigrate through a l&nil-thick silicon wafer

100 electrode intracortical array: structural variability

Journal ArticleA technique has been developed for fabricating three dimensional "hair brush" electrode arrays from monocrystalline silicon blocks. Arrays consist of a square pattern of 100 penetrating electrodes, with 400 microns interelectrode spacing. Each electrode is 1.5mm in length and tapers from about 100 microns at its base to a sharp point at the tip. The tips of each electrode are coated with platinum and the entire structure, with the exception of the tips, is insulated with polyimide. Electrical connection to selected electrodes is made by wire bonding polyimide insulated 25 microns diameter gold lead wires to bonding pads on the rear surface of the array. As the geometrical characteristics of the electrodes in such an aray will influence their electrical properties (such as impedance, capacitance, spreading resistance in an electrolyte, etc.) it is desirable that such an array have minimal variability in geometry from electrode to electrode. A study was performed to determine the geometrical variability resulting from our micromachining techniques. Measurements of the diameter of each of the 100 electrodes were made at various planes above the silicon substrate of the array. For the array that was measured, the standard deviation of the diameters was approximately 9% of the mean diameter near the tip, 8% near the middle, and 6% near the base. We describe fabrication techniques which should further reduce these variabilities

Three-dimensional architecture for a parallel processing photosensing array

Journal ArticleA three-dimensional architecture for a photosensing array has been developed. This silicon based architecture consists of a 10 x 10 array of photosensors with 80 microns diameter, through chip interconnects to the back side of a 500 microns thick silicon wafer. Each photosensor consists of a 300 x 300 microns pn-junction photodiode. The following processes were used to create this photosensing architecture: 1) thermomigration of aluminum pads through an n-type silicon wafer; 2) creation of pn-junction photosensors on one side of the wafer; and 3) creation of aluminum pad ohmic contacts to the thermomigrated, through chip interconnects and the substrate on the back side of the wafer. The electrical and optical characteristics of the three-dimensional architecture indicates that it should be well suited as a photosensing framework around which a "silicon retina" could be built