Poisson Counter Research Articles

Optimal control of sampled‐data systems based on an optimized stochastic sampling

This article addresses the optimal control problem of continuous-time sampled systems closed by a stochastically sampled controller. A model based on the Poisson Counter processes is proposed to describe the stochastic sampling, while another sampling frequency cost function is developed. As a results, more than one cost function will be considered and more difficult. In order to deal with the optimal control problem, the stability problem is first analyzed, while both the control gain and sampling sequence are given in advance and without optimized. Then, based on the optimized sampling sequence, both finite- and infinite-time nominally optimal controllers are designed respectively. Particularly, sufficient conditions for testing such optimal controllers existing or not are established by applying the above given results. Finally, some numerical examples are offered to verify the effectiveness and superiorities of the methods proposed in this study.

Suboptimal Filtering Over Sensor Networks With Random Communication

The problem of filter design is considered for continuous-time linear stochastic systems using distributed sensors. Each sensor unit, represented by a node in an undirected and connected graph, collects some information about the state and communicates its own estimate with the neighbors. It is stipulated that this communication between sensor nodes connected by an edge is time-sampled randomly and for each edge, the sampling process is an independent Poisson counter. Our proposed filtering algorithm for each sensor node is a stochastic hybrid system: It comprises a continuous-time differential equation, and at random time instants when communication takes place, each sensor node updates its state estimate based on the information received by its neighbors. In this setting, we compute the expectation of the error covariance matrix for each unit which is governed by a matrix differential equation. To study the asymptotic behavior of these covariance matrices, we show that if the gain matrices are appropriately chosen and the mean sampling rate is large enough, then the error covariances practically converge to a constant matrix.

Extending systems factorial technology to errored responses.

Systems factorial technology (SFT) is a theoretically derived methodology that allows for strong inferences to be made about underlying processing architectures (e.g., whether processing occurs in a pooled, coactive fashion or in serial or in parallel). Measures of mental architecture using SFT have been restricted to the use of error-free response times (RTs). In this article, through formal proofs and demonstrations, we extended the measure of architecture, the survivor interaction contrast (SIC), to RTs conditioned on whether they are correct or incorrect. We show that so long as an ordering relation (between stimulus conditions of different difficulty) is preserved, we learn that the canonical SIC predictions result when exhaustive processing is necessary and sufficient for a response. We further prove that this ordering relation holds for the popular Wiener diffusion model for both correct and error RTs but fails under some classes of a Poisson counter model, which affords a strong potential experimental test of the latter class versus the others. Our exploration also serves to point to the importance of detailed studies of how errors are made in perceptual and cognitive tasks. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Can the wrong horse win: The ability of race models to predict fast or slow errors

This report continues our probe of the fundamental properties of elementary psychological processes. In the present instance, we first distinguish between descriptive and state–space based parallel race models. Then we show, engaging previous results on stochastic dominance in Theorem 1, that descriptive race models can be designed that predict either faster ‘right’ channels or faster ‘wrong’ channels. Moving to state–space based models and in particular, to inhomogeneous Poisson counter models, we use Theorem 1 to prove Theorem 2 which offers sufficient conditions for such models to elicit faster ‘rights’ than ‘wrongs’. Then, constraining ourselves to models possessing proportional processing rates, we revisit an important finding by Smith and Van Zandt (2000) to the effect that in such models, mean processing times conditional on ‘right’ decisions are faster than those conditional on ‘wrong’ decisions. Theorem 3 expands that property to the much stronger level of ordered conditional distribution functions. The penultimate section constructs an example of an inhomogeneous Poisson race model that predicts faster ‘wrongs’ for fast processing times but faster ‘rights’ for slower processing times. We leave as an open problem the question of whether there exist inhomogeneous Poisson race models where ‘wrongs’ are stochastically faster than ‘rights’ for all durations of processing.

A physiologically based nonhomogeneous Poisson counter model of visual identification.

A physiologically based nonhomogeneous Poisson counter model of visual identification is presented. The model was developed in the framework of a Theory of Visual Attention (Bundesen, 1990; Kyllingsbæk, Markussen, & Bundesen, 2012) and meant for modeling visual identification of objects that are mutually confusable and hard to see. The model assumes that the visual system's initial sensory response consists in tentative visual categorizations, which are accumulated by leaky integration of both transient and sustained components comparable with those found in spike density patterns of early sensory neurons. The sensory response (tentative categorizations) feeds independent Poisson counters, each of which accumulates tentative object categorizations of a particular type to guide overt identification performance. We tested the model's ability to predict the effect of stimulus duration on observed distributions of responses in a nonspeeded (pure accuracy) identification task with eight response alternatives. The time courses of correct and erroneous categorizations were well accounted for when the event-rates of competing Poisson counters were allowed to vary independently over time in a way that mimicked the dynamics of receptive field selectivity as found in neurophysiological studies. Furthermore, the initial sensory response yielded theoretical hazard rate functions that closely resembled empirically estimated ones. Finally, supplied with a Naka-Rushton type contrast gain control, the model provided an explanation for Bloch's law. (PsycINFO Database Record

Gaussian counter models for visual identification of briefly presented, mutually confusable single stimuli in pure accuracy tasks

When identifying confusable visual stimuli, accumulation of information over time is an obvious strategy of the observer. However, the nature of the accumulation process is unresolved: for example it may be discrete or continuous in terms of the information encoded. Another unanswered question is whether or not stimulus sampling continues after the stimulus offset. In the present paper we propose various continuous Gaussian counter models of the time course of visual identification of briefly presented, mutually confusable single stimuli in a pure accuracy task. During stimulus analysis, tentative categorizations that stimulus i belongs to category j are made until a maximum time after the stimulus disappears. Two classes of models are proposed. First, the overt response is based on the categorization that had the highest value at the time the stimulus disappears (race models). Second, the overt response is based on the categorization that made the minimum first passage time through a constant boundary (first passage time models). Within this framework, multivariate Wiener and Ornstein–Uhlenbeck counter models are considered under different parameter regimes, assuming either that the stimulus sampling stops immediately or that it continues for some time after the stimulus offset. Each type of model was evaluated by Monte Carlo tests of goodness of fit against observed probability distributions of responses in two extensive experiments. A comparison of these continuous models with a simple discrete Poisson counter model proposed by Kyllingsbæk, Markussen, and Bundesen (2012) was carried out, together with model selection among the competing candidates. Both the Wiener and the Ornstein–Uhlenbeck race models provide a close fit to individual data on identification of both digits and Landolt rings, outperforming the first passage time model and the Poisson counter race model.

A Generalized Gossip Algorithm on Convex Metric Spaces

A consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest. This problem can be generalized in the context of convex metric spaces that extend the standard notion of convexity. In this paper we introduce and analyze a randomized gossip algorithm for solving the generalized consensus problem on convex metric spaces, where the communication between agents is controlled by a set of Poisson counters. We study the convergence properties of the algorithm using stochastic calculus. In particular, we show that the distances between the states of the agents converge to zero with probability one and in the r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> mean sense. In the special case of complete connectivity and uniform Poisson counters, we give upper bounds on the dynamics of the first and second moments of the distances between the states of the agents. In addition, we introduce instances of the generalized consensus algorithm for several examples of convex metric spaces together with numerical simulations.

Feedback Particle Filter for a Continuous-time Markov Chain

This technical note extends the feedback particle filter (FPF) methodology and algorithms to the problem of filtering a continuous-time Markov chain. The main contribution is the development of a feedback control-based transformation of the Wonham filter, where the control input is realized via a time-modulated Poisson counter process. A complete characterization of the feedback mechanism that defines the FPF is obtained, which leads to tractable algorithms for the nonlinear filtering problem even for large state spaces. Numerical examples are introduced to help illustrate the application of these techniques.

Optimal ensemble control of stochastic time-varying linear systems

We consider the optimal guidance of an ensemble of independent, structurally identical, finite-dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by applying a common control function without the use of feedback. Our exploration of such ensemble control systems is motivated by practical control design problems in which variation in system parameters and stochastic effects must be compensated for when state feedback is unavailable, such as in pulse design for nuclear magnetic resonance spectroscopy and imaging. In this paper, we extend the notion of ensemble control to stochastic linear systems with additive noise and jumps, which we model using white Gaussian noise and Poisson counters, respectively, and investigate the optimal steering problem. In our main result, we prove that the minimum norm solution to a Fredholm integral equation of the first kind provides the optimal control that simultaneously minimizes the mean square error (MSE) and the error in the mean of the terminal state. The optimal controls are generated numerically for several example ensemble control problems, and Monte Carlo simulations are used to illustrate their performance. This work has immediate applications to the control of dynamical systems with parameter dispersion or uncertainty that are subject to additive noise, which are of interest in quantum control, neuroscience, and sensorless robotic manipulation.

A Poisson counter model for visual identification of stimuli with varying contrast in pure accuracy tasks

Stimuli: Landolt rings with eight different orientations. Exposure duration was varied between 10 and 150 ms. A single stimulus appeared at one of eight possible locations and was postmasked. Independently, we also varied the negative Weber contrast of the stimuli between .033 and .13. Task: Participants identified the orientation of the Landolt ring, only responding when fairly certain to have seen the stimulus.

A Poisson Counter Model for Visual Identification of Stimuli with Varying Contrast in Pure Accuracy Tasks

We test a simple model of the time course of visual identification of briefly presented, mutually confusable single stimuli (Landolt's rings) with varying contrast in pure accuracy tasks. The model implies that during stimulus analysis, tentative categorizations that stimulus i belongs to category j are made at a constant Poisson rate, v(i,j). The analysis is continued until the stimulus disappears, and the overt response is based on the categorization made the greatest number of times. The model was evaluated by Monte Carlo tests of goodness of fit against observed probability distributions of responses in extensive experiments and also by quantifications of the information loss of the model compared with the observed data by use of information theoretic measures. The model provided a close fit to individual data on identification of Landolt's rings with varying contrast. Meeting abstract presented at VSS 2012

Testing a Poisson counter model for visual identification of briefly presented, mutually confusable single stimuli in pure accuracy tasks.

The authors propose and test a simple model of the time course of visual identification of briefly presented, mutually confusable single stimuli in pure accuracy tasks. The model implies that during stimulus analysis, tentative categorizations that stimulus i belongs to category j are made at a constant Poisson rate, v(i, j). The analysis is continued until the stimulus disappears, and the overt response is based on the categorization made the greatest number of times. The model was evaluated by Monte Carlo tests of goodness of fit against observed probability distributions of responses in two extensive experiments and also by quantifications of the information loss of the model compared with the observed data by use of information theoretic measures. The model provided a close fit to individual data on identification of digits and an apparently perfect fit to data on identification of Landolt rings.

Analysis of traffic correlation attacks on router queues

Traffic burstiness is known to be undesirable for a router as it increases the router’s queue length and hence the queueing delays of data flows. This poses a security problem in which an attacker intentionally introduces traffic burstiness into routers. We consider a correlation attack, whose fundamental characteristic is to correlate multiple attack flows to generate synchronized small attack bursts, in an attempt to aggregate the bursts into a large burst at a target router.In this paper, we develop an analytical, fluid-based framework that models how the correlation attack disrupts router queues and how it can be mitigated. Using Poisson Counter Stochastic Differential Equations (PCSDEs), our framework captures the dynamics of a router queue for special cases and gives the closed-form average router queue length as a function of the inter-flow correlation. To mitigate the correlation attack, we apply our analytical framework to model different pacing schemes including Markov ON–OFF pacing and rate limiting, which are respectively designed to break down the inter-flow correlation and suppress the peak rates of bursts. We verify that our fluid models conform to packet-level ns2 simulation results.

Analysis of networked estimation under contention-based medium access

We investigate the scalability of networked estimation under contention-based medium access. In our set-up, the state of a number of identical first-order linear plants are measured and transmitted over a shared medium. Each sensor transmits its readings to a supervisor node that maintains a continuous-time state estimate for the associated plant. When the medium access delay exceeds the sampling interval, measurements are discarded and replaced by more recent ones. Our analysis of the shared channel determines the probability of packet loss as a function of the sampling interval and the number of contending nodes. We compute the estimation distortion with periodically generated samples as a function of the packet loss rate and sampling interval, and derive a condition for stable estimator performance. We investigate the scalability limits of this stability as a function of the number of nodes. When stable estimation is possible, we provide a procedure that computes the sampling rate that minimizes the average estimation distortion. We reproduce the analysis of estimation performance when the sensors sample asynchronously according to independent Poisson counters.

A comparison of sequential sampling models for two-choice reaction time.

The authors evaluated 4 sequential sampling models for 2-choice decisions--the Wiener diffusion, Ornstein-Uhlenbeck (OU) diffusion, accumulator, and Poisson counter models--by fitting them to the response time (RT) distributions and accuracy data from 3 experiments. Each of the models was augmented with assumptions of variability across trials in the rate of accumulation of evidence from stimuli, the values of response criteria, and the value of base RT across trials. Although there was substantial model mimicry, empirical conditions were identified under which the models make discriminably different predictions. The best accounts of the data were provided by the Wiener diffusion model, the OU model with small-to-moderate decay, and the accumulator model with long-tailed (exponential) distributions of criteria, although the last was unable to produce error RTs shorter than correct RTs. The relationship between these models and 3 recent, neurally inspired models was also examined.

On fluid queueing systems with strict priority

We consider priority fluid queueing systems where high-priority class has strict priority access to service. Sample path analysis tools, such as Poisson counter driven stochastic differential equation, are employed to study system queueing behavior in steady state. We are able to obtain various analytical results for different fluid traffic models and system configurations. Those results can be used as a general rule of thumb in buffer dimensioning and other traffic engineering issues.

Analysis, simulation and implementation of wireless TCP flows with forward error correction

In this paper, we consider a communication link where the last hop is wireless, the congested router deploys RED queue management, and TCP is used as transport protocol over the end-to-end connection. The Poisson counter driven stochastic differential equation is employed to study the capacity of forward error correction (FEC) with link layer retransmission to hide losses over the wireless link to TCP in spite of the time-varying property of the wireless transmission channel. Both the analytical results of FEC with and without link layer retransmission show excellent agreement with those using NS-2 simulator. This method is proven to be effective in solving the problem of the wireless TCP with the congested RED router using link layer retransmission and FEC. Furthermore, we implement TCP with Reed–Solomon code in a test-bed. The experimental results are very close to the analytical results. The proposed analytical approach can be used to evaluate the performance and to choose the correct design parameters before deployment of wireless TCP with Reed–Solomon code.

Time‐dependent Poisson counter models of response latency in simple judgment

An important class of sequential-sampling models for response time (RT) assumes that evidence for competing response alternatives accrues in parallel and that a response is made when the evidence total for a particular response exceeds a criterion. One member of this class of models is the Poisson counter model, in which evidence accrues in unit increments and the waiting time between increments is exponentially distributed. This paper generalizes the counter model to allow the Poisson event rate to vary with time. General expressions are obtained for the RT distributions for the two- and the m-alternative cases. Closed-form expressions are obtained for response probabilities under a proportional-rates assumption and for mean RT under conditions in which the integrated event rate increases as an arbitrary power of time. An application in the area of early vision is described, in which the Poisson event rates are proportional to the outputs of sustained and transient channels.

Single-letter recognition as a function of exposure duration

The time course of visual letter recognition was investigated in a single-stimulus identification experiment. On each trial, a randomly chosen stimulus letter was presented at 1 of 12 equiprobable positions that were equally spaced around the circumference of an imaginary circle centered on fixation. Exposure duration was varied from 10 to 200 ms, and the letter was followed by a pattern mask. The subject's task was to report the identity of the stimulus letter but refrain from guessing. For the briefest exposures, correct reports never occurred. For longer exposures, the function relating the probability p of recognizing the letter to the duration t of the stimulus exposure was well approximated by an exponential distribution function: p(t) = 1 − exp[−v·(t−t0)], where v is the rate of processing and t0 is the minimum effective exposure duration. The generality of this finding may be limited to cases in which stimuli are highly discriminable and response criteria are conservative. Extensions to Poisson counter or random walk models are considered for cases in which stimuli are confusable.

Discrimination of Temporal Gaps

Ss were asked to discriminate between two time gaps, T and T+ΔT msec in duration. The gaps were silent intervals bounded by noise bursts. In the first of two experiments the duration of the noise bursts was 10 msec. The function relating the Weber fraction (ΔT/T for 75% discrimination) and the base gap T is nonmonotonic, showing a local minimum of 0.5 at approximately 4 msec and a local maximum of 0.6 at 10 msec. The function reaches a value of 0.2 after a slow decline from 10 to 640 msec. In the second experiment the noise bursts were 300 msec. The results are essentially similar to those of the first experiment, except that the local maximum at 10 msec is raised to 1.9. The data are compared with the results of Small and Campbell (1962), and with the predictions of Creelman's (1961) Poisson counter model. [This research was supported by the National Institutes of Health, Public Health Service, U. S. Department of Health, Education, and Welfare while the author was a National Research Council of Canada Postdoctorate Fellow.]