Stability properties of slotted Aloha with multipacket receptioncapability

The stability of the Aloha random-access algorithm in an infinite-user slotted channel with multipacket-reception capability is considered. This channel is a generalization of the usual collision channel, in that it allows the correct reception of one or more packets involved in a collision. The number of successfully received packets in each slot is modeled as a random variable which depends exclusively on the number of simultaneously attempted transmissions. This general model includes as special cases channels with capture, noise, and code-division multiplexing. It is shown by drift analysis that the channel backlog Markov chain is ergodic if the packet-arrival rate is less than the expected number of packets successfully received in a collision of n as n goes to infinity. The properties of the backlog in the nonergodicity region are examined     

Discrete and continuous planning of hand movements and isometric force trajectories

We have previously demonstrated that, in preparing themselves to aim voluntary impulses of isometric elbow force to unpredictable targets, subjects selected default values for amplitude and direction according the range of targets that they expected. Once a specific target appeared, subjects specified amplitude and direction through parallel processes. Amplitude was specified continuously from an average or central default; direction was specified stochastically from one of the target directions. Using the same timed response paradigm, we now report three experiments to examine how the time available for processing target information influences trajectory characteristics in two-degree-of-freedom forces and multijoint movements. We first sought to determine whether the specification of force direction could also take the form of a discrete stochastic process in pulses of wrist muscle force, where direction can vary continuously. With four equiprobable targets (two force amplitudes in each of two directions separated by 22 degrees or 90 degrees), amplitude was specified from a central default value for both narrow and wide target separations as a continuous variable. Direction, however, remained specified as a discrete variable for wide target separations. For narrow target separations, the directional distribution of default responses suggested the presence of both discrete and central values. We next examined point-to-point movements in a multijoint planar hand movement task with targets at two distances and two directions but at five directional separations (from 30 degrees to 150 degrees separation). We found that extent was again specified continuously from a central default. Direction was specified discretely from alternative default directions when target separation was wide and continuously from a central default when separation was narrow. The specification of both extent and direction evolved over a 200-ms time period beginning about 100 ms after target presentation. As in elbow force pulses, extent was specified progressively in both correct and wrong direction responses through a progressive improvement in the scaling of acceleration and velocity peaks to the target. On the other hand, movement time and hand path straightness did not change significantly in the course of specification. Thus, the specification of movement time and linearity, global features of the trajectories, are given priority over the specific values of extent and direction. In a third experiment, we varied the distances between unidirectional target pairs and found that movement extent is specified discretely, like direction, when the disparity in distances is large. The implications of these findings for contextual effects on trajectory planning are discussed. The independence of extent and direction specification and the prior setting of response duration and straightness provide critical support for the hypothesis that point-to-point movements are planned vectorially.     

Expansions in time for the solution of one-dimensional stefan problems of crystal growth

A new method is presented for the solution of mass transport Stefan problems in one dimension and in semi-infinite regions. It relies on expansions of the concentration distribution and growth rate in powers of $\text{t}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. Field conditions at the moving boundary are not necessarily constant; they can be arbitrary. Such conditions often lead to non-similar solutions. Although these problems are nonlinear, the expansion coefficients satisfy linear recurrence relations. These coefficients result from simple algebraic manipulations of functions closely related to the iterated error functions. The method is applied to several examples of crystal growth from supersaturated solutions. The first two examples assume isothermal conditions; they illustrate the difference between surface equilibrium and finite surface kinetics. The third example demonstrates effects due to homogeneous cooling.     

The equilibrium constant for the reaction of ZnO + H2 and the chemical vapor transport of zno via the Zn + H2O reaction

Using a gas transpiration method, the equilibrium constant for the reaction ZnO(s) + H₂(v)⇄ Zn(v) + H₂O(v) was determined directly in the temperature interval 592–950°C. The data are described by the equation log₁₀K = [-11.794 × 10³/T] + 8.040 with ΔH° = 53.97 Kcal/mole and ΔS° = 36.79 e.u. Based on this Information, vapor-solid gas concentration curves useful for defining conditions for the chemical vapor transport of ZnO via the reverse of the above reaction have been computer calculated.     

Mass transport and surface reactions in lévêque's approximation

This paper addresses the general problem of multicomponent transport and heterogeneous reaction in Lévêque's approximation. The problem always admits an analytic solution when the surface reactions are first order in the concentrations. Here, explicit expressions for the concentration distributions are found for the case of a single reversible surface step, but the procedure equally applies to arbitrarily complex sequences of such steps. The behavior of the solution depends mainly on the value of a dimensionless axial parameter. Aside from axial distance and mean velocity, it involves all diffusion coefficients, reaction rate constants and stoichiometric coefficients. For small values of this parameter the solution behaves as if the surface were a source of constant flux; for large values, as if the surface were at constant concentration. Thus the solution exhibits a continuous change from a Neumann to a Dirichlet problem.     

Optimal decentralized control in the random access multipacketchannel

A decentralized control algorithm is sought that maximizes the stability region of the infinite-user slotted multipacket channel and is easily implementable. To this end, the perfect state information case in which the stations can use the instantaneous value of the backlog to compute the retransmission probability is studied first. The vest throughput possible for a decentralized control protocol is obtained, as well as an algorithm that achieves it. These results are then applied to derive a control scheme when the backlog is unknown, which is the case of practical relevance. This scheme, based on a binary feedback, is shown to be optimal, given some restrictions on the channel multipacket reception capability     

Differential impairments in reaching and grasping produced by local inactivation within the forelimb representation of the motor cortex in the cat

This study analyzed changes in the performance of a reaching task and its adaptive modification produced by reversible inactivation of three sites within the forelimb representation of the motor cortex (MCx, area 4 gamma) in five cats by microinjections of muscimol. Two sites were located in the lateral MCx, rostral (RL-MCx) and caudal (CL-MCx) to the end of the cruciate sulcus, where intracortical microstimulation (ICMS) produced contraction of the most distal muscles. The third site was located more medially, in the anterior sigmoid gyrus (RM-MCx) where ICMS primarily produced contraction of more proximal muscles. The task required the animals to reach into a horizontal target well, located in front of them at one of three possible heights, to grasp and retrieve a small piece of food. The height of the reach was primarily achieved by elbow flexion. Grasping consisted primarily of digit flexion, and food retrieval consisted of forearm supination and shoulder extension. In some blocks of trials, an obstacle was placed in the path of the limb to assess the animal's ability to adaptively adjust the kinematic characteristics of their response trajectory. In normal animals, contact with the bar on the first trial triggered a corrective response at short latency that allowed the paw to circumvent the bar. On all subsequent trials, the trajectory was adapted to prevent contact with the obstacle, with a safety margin of about 1 cm. Inactivation at all sites produced a slowing of movement, a protracted and extended forelimb posture, and increased variability of initial limb position. In addition, inactivation of RL-MCx immediately produced systematic reaching errors, consisting of hypermetric movements, as well as impaired grasping and food retrieval. The degree of hypermetria was similar for all target heights and was not associated with alterations in trajectory control. During inactivation, animals did not compensate for the hypermetria by reducing paw path elevation, suggesting a defect in kinematic planning or in adaptive control. This was confirmed by finding that trajectory adaptation to avoid bar contact was impaired during RL-MCx inactivation. The short latency corrective response, triggered by contact of the limb with the obstacle was, however, preserved. Inactivation of CL-MCx did not impair aiming, grasping, or adaptation immediately after injection. However, impairments occurred after about 1 h postinjection, and at that time mimicked the effects of RL-MCx inactivation.(ABSTRACT TRUNCATED AT 400 WORDS)