It is far from obvious that outside of highly specialized domains such as commercial agriculture, the methodology of biometrics—quantitative comparisons over groups of organisms—should be of any use in today’s bioinformatically informed biological sciences. The methods in our biometric textbooks, such as regressions and principal components analysis, make assumptions of homogeneity that are incompatible with current understandings of the origins of developmental or evolutionary data in historically contingent processes, processes that might have come out otherwise; the appropriate statistical methods are (...) those suited to random walks, not normal distributions. A valid methodology would further require that especially close attention be paid to the difference between aspects of processes that are plastic, those that encode their own histories or biographies, and the very small fraction of quantifications that can usefully and realistically be modeled as varying by colored noise around a central tendency that itself has some quantitative meaning. This point of view—that only a vanishingly small fraction of the quantitative information borne by any living organism is worth quantifying—is illustrated by some data on a human birth defect, namely, fetal alcohol syndrome. In a suggestive metaphor, the biometrician is like the pilgrim in Friedrich’s painting Der Wanderer über dem Nebelmeer, uncertain as to whether to measure the mountains or the clouds. The mountains stand for contingent history, the clouds for the subset of the data most closely matching controlled experiments suitable for quantitative biometric summary. Biometrics applies to the clouds, not the mountains. The success of statistical methods comes at the expense of all the theories that we simultaneously hold to be true about the biological materials to which they both pertain. Biometrics is thus complementary to all of the emerging reductionist sciences of biological structure. (shrink)

How realistic is it to adopt a quantum random walk model to account for decisions involving two choices? Here, we discuss the neural plausibility and the effect of initial state and boundary thresholds on such a model and contrast it with various features of the classical random walk model of decision making.

Vacuum radiation causes a particle to make a random walk about its dynamical trajectory. In this random walk the root mean square change in spatial coordinate is proportional to t 1/2, and the fractional changes in momentum and energy are proportional to t −1/2, where t is time. Thus the exchange of energy and momentum between a particle and the vacuum tends to zero over time. At the end of a mean free path the fractional change (...) in momentum of a particle in a gas is very small. However, at the end of the mean free path each particle undergoes an interaction that magnifies the preceding change, and the net result is that the momentum distribution of the particles in a gas is randomized in a few collision times. In this way the random action of vacuum radiation and its subsequent magnification by molecular interaction produces entropy increase. This process justifies the assumption of molecular chaos used in the Boltzmann transport equation. (shrink)

Free and weakly interacting particles are described by a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. They describe Gaussian random walks with collisions. By contrast, the fields of strongly interacting particles are governed by effective actions, whose extremum yields fractional field equations. Their particle orbits perform universal Lévy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong (...) windgusts, monster or rogue waves, earthquakes, and financial crashes. While earthquakes may destroy entire cities, the latter have the potential of devastating entire economies. (shrink)

Wavefunction collapse models modify Schrödinger's equation so that it describes the rapid evolution of a superposition of macroscopically distinguishable states to one of them. This provides a phenomenological basis for a physical resolution to the so-called “measurement problem.” Such models have experimentally testable differences from standard quantum theory. The most well developed such model at present is the Continuous Spontaneous Localization (CSL) model in which a universal fluctuating classical field interacts with particles to cause collapse. One “side effect” of this (...) interaction is that the field imparts energy to the particles: experimental evidence on this has led to restrictions on the parameters of the model, suggesting that the coupling of the classical field to the particles must be mass-proportional. Another “side effect” is that the field imparts momentum to particles, causing a small blob of matter to undergo random walk. Here we explore this in order to supply predictions which could be experimentally tested. We examine the translational diffusion of a sphere and a disc, and the rotational diffusion of a disc, according to CSL. For example, we find that the rms distance an isolated 10−5 cm radius sphere diffuses is ≈(its diameter, 5 cm) in (20 sec, a day), and that a disc of radius 2 ⋅ 10−5 cm and thickness 0.5 ⋅ 10−5 cm diffuses through 2πrad in about 70 sec (this assumes the “standard” CSL parameter values). The comparable rms diffusions of standard quantum theory are smaller than these by a factor 10−3±1. It is shown that the CSL diffusion in air at STP is much reduced and, indeed, is swamped by the ordinary Brownian motion. It is also shown that the sphere's diffusion in a thermal radiation bath at room temperature is comparable to the CSL diffusion, but is utterly negligible at liquid He temperature. Thus, in order to observe CSL diffusion, the pressure and temperature must be low. At the low reported pressure of 5 ⋅ 10−17 Torr, achieved at 4.2°K, the mean time between air molecule collisions with the (sphere, disc) is ≈(80, 45)min. This is ample time for observation of the putative CSL diffusion with the standard parameters and, it is pointed out, with any parameters in the range over which the theory may be considered viable. This encourages consideration of how such an experiment may actually be performed, and the paper closes with some thoughts on this subject. (shrink)

Though early ideas of evolution saw it as progressive, most modern theories see it as a random walk. The theories of Richard Dawkins, Stephen Jay Gould, Edward O. Wilson, Stuart Kauffman, Steven Rose, and Robert Wesson are surveyed, showing their agreement on the fact of evolution but not on the mechanism. Evolution is an incomplete theory. Any theology should therefore be based only on its broadest features. Generally, evolution is the development of complex forms from simple ancestors. Within a (...) Christian context, it can be seen as a journey toward the unification of all things in Christ, the ultimate complexity. (shrink)

Many NLP tasks rely on accurately estimating word dependency probabilities P(w1|w2), where the words w1 and w2 have a particular relationship (such as verb-object). Because of the sparseness of counts of such dependencies, smoothing and the ability to use multiple sources of knowledge are important challenges. For example, if the probability P(N |V ) of noun N being the subject of verb V is high, and V takes similar objects to V , and V is synonymous to V , then (...) we want to conclude that P(N |V ) should also be reasonably high—even when those words did not cooccur in the training data. (shrink)

Asymmetric Choquet random walks are defined, in the form of dynamically consistent random walks allowing for asymmetric conditional capacities. By revisiting Kast and Lapied and Kast et al. we show that some findings regarding the effects of ambiguity aversion are preserved in the more general framework, which is of interest in several applications to policy making, risk management, corporate decisions, real option valuation of investment/ disinvestment projects, etc. The effect of ambiguity on the higher moments is (...) investigated, as well, as they have an interpretation in terms of the psychological attitude of a decision-maker towards ambiguity. Finally, some financial applications are provided as an illustration. (shrink)

Algorithms have become a widespread trope for making sense of social life. Science, finance, journalism, warfare, and policing—there is hardly anything these days that has not been specified as “algorithmic.” Yet, although the trope has brought together a variety of audiences, it is not quite clear what kind of work it does. Often portrayed as powerful yet inscrutable entities, algorithms maintain an air of mystery that makes them both interesting and difficult to understand. This article takes on this problem and (...) examines the role of algorithms not as techno-scientific objects to be known, but as a figure that is used for making sense of observations. Following in the footsteps of Harold Garfinkel’s tutorial cases, I shall illustrate the implications of this view through an experiment with algorithmic navigation. Challenging participants to go on a walk, guided not by maps or GPS but by an algorithm developed on the spot, I highlight a number of dynamics typical of reasoning with running code, including the ongoing respecification of rules and observations, the stickiness of the procedure, and the selective invocation of the algorithm as an intelligible object. The materials thus provide an opportunity to rethink key issues at the intersection of the social sciences and the computational, including popular concerns with transparency, accountability, and ethics. (shrink)

By allowing one artificial neural network to govern the synaptic noise injected into another based upon its appraisal of patterns nucleating from such disturbances, a contemplative form of artifici...

Cognitive Science, Volume 46, Issue 1, January 2022.

Quantum walks exhibit different properties compared with classical random walks, most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as quantum-walk-replicating random walks, have been studied in the literature where the eventual properties of QWRW coincide with those of QWs. However, we consider that the unique attributes of QWRWs have not been fully utilized in the former studies to obtain deeper or (...) new insights into QWs. In this paper, we highlight the directivity of one-dimensional discrete quantum walks via QWRWs. By exploiting the fact that QWRW allows trajectories of individual walkers to be considered, we first discuss the determination of future directions of QWRWs, through which the effect of linear spreading and localization is manifested in another way. Furthermore, the transition probabilities of QWRWs can also be visualized and show a highly complex shape, representing QWs in a novel way. Moreover, we discuss the first return time to the origin between RWs and QWs, which is made possible via the notion of QWRWs. We observe that the first return time statistics of QWs are quite different from RWs, caused by both the linear spreading and localization properties of QWs. (shrink)

A simple model is presented in which the statevector evolves every ε seconds in one of two ways, according to a particular probability rule. It is shown that this random walk in Hilbert space results in reduction of the statevector. It is also shown how the continuous spontaneous localization (CSL) theory of statevector reduction is achieved as a limiting case of this model, exactly as Brownian motion is a limiting case of ordinary random walk. Finally, a slightly different (...) but completely equivalent form of the CSL equations suggested by the simple model given here is discussed. (shrink)

Chaos distributes with a covert method to condense the dynamic of complexity and satisfies the security requirements of a cryptographic system. This study gives an ability online/offline ID-based short signature scheme using conformable fractional chaotic maps. Furthermore, we establish its security under IBSS existential unforgeability of identity-based short signature under chosen message attack in the random oracle model. Some of the stimulating preparations of obtainable processes are that they give a multiperiod application of the offline storage, which licenses (...) the agent to recycle the offline pre-registered data in time series, rather than one-period usage in all past IBSS processes. (shrink)

The study of the chaotic dynamics in fractional-order discrete-time systems has received great attention over the last years. Some efforts have been also devoted to analyze fractional maps with special features. This paper makes a contribution to the topic by introducing a new fractional map that is characterized by both particular dynamic behaviors and specific properties related to the system equilibria. In particular, the conceived one dimensional map is algebraically simpler than all the proposed fractional maps (...) in the literature. Using numerical simulation, we investigate the dynamic and complexity of the fractional map. The results indicate that the new one-dimensional fractional map displays various types of coexisting attractors. The approximate entropy is used to observe the changes in the sequence sequence complexity when the fractional order and system parameter. Finally, the fractional map is applied to the problem of encrypting electrophysiological signals. For the encryption process, random numbers were generated using the values of the fractional map. Some statistical tests are given to show the performance of the encryption. (shrink)

Text classification involves deciding whether or not a document is about a given topic. It is an important problem in machine learning, because automated text classifiers have enormous potential for application in information retrieval systems. It is also an interesting problem for cognitive science, because it involves real world human decision making with complicated stimuli. This paper develops two models of human text document classification based on random walk and accumulator sequential sampling processes. The models are evaluated using data (...) from an experiment where participants classify text documents presented one word at a time under task instructions that emphasize either speed or accuracy, and rate their confidence in their decisions. Fitting the random walk and accumulator models to these data shows that the accumulator provides a better account of the decisions made, and a “balance of evidence” measure provides the best account of confidence. Both models are also evaluated in the applied information retrieval context, by comparing their performance to established machine learning techniques on the standard Reuters‐21578 corpus. It is found that they are almost as accurate as the benchmarks, and make decisions much more quickly because they only need to examine a small proportion of the words in the document. In addition, the ability of the accumulator model to produce useful confidence measures is shown to have application in prioritizing the results of classification decisions. (shrink)

Group contingency (GC) is an effective and cost-efficient strategy that can be successfully applied to technology-based interventions. This study examined the relative effectiveness and cost efficiency of three types of technology-based group contingencies on walking among adults. Seventy two students were divided into teams of three. Each team was randomly assigned to one of three GC conditions (independent, interdependent, or dependent) and underwent 66 days of technology-based group contingency intervention. Sixty five participants completed the intervention and 61 completed the follow-up (...) assessment 2 months later. Step counts and self-reported walking activity increased after the intervention under all three conditions. The proportion of participants that met the target step counts was significantly higher under the dependent group contingency condition. However, 2 months later, intervention effects were not maintained under any condition. For cost efficiency, the increase in step count per point was significantly higher under the interdependent group contingency condition. Group cohesion and social validity (point satisfaction and point utility) were significantly higher under the dependent group contingency condition. Finally, the clinical implications and limitations of this study are discussed. (shrink)

A person’s epistemic goals sometimes clash with pragmatic ones. At times, rational agents will degrade the quality of their epistemic process in order to satisfy a goal that is knowledge-independent (for example, to gain status or at least keep the peace with friends.) This is particularly so when the epistemic quest concerns an abstract political or economic theory, where evidence is likely to be softer and open to interpretation. Before wide-scale adoption of the Internet, people sought out or stumbled upon (...) evidence related to a proposition in a more random way. And it was difficult to aggregate the evidence of friends and other similar people to the exclusion of others, even if one had wanted to. Today, by contrast, the searchable Internet allows people to simultaneously pursue social and epistemic goals.This essay shows that the selection effect caused by a merging of social and epistemic activities will cause both polarization in beliefs and devaluation of expert testimony. This will occur even if agents are rational Bayesians and have moderate credences before talking to their peers. What appears to be rampant dogmatism could be just as well explained by the nonrandom walk in evidence-gathering. This explanation better matches the empirical evidence on how people behave on social media platforms. It also helps clarify why media outlets (not just the Internet platforms) might have their own pragmatic reasons to compromise their epistemic goals in today’s competitive and polarized information market. Yet, it also makes policy intervention much more difficult, since we are unlikely to neatly separate individuals’ epistemic goals from their social ones. (shrink)

The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex–valued Gaussian, looking for relevance to quantum mechanics. Here we show that the Gaussian, with all terms fully complex, acting as a propagator, leads to Schrödinger’s non-relativistic equation including scalar and vector potentials, assuming only that the norm is conserved. No physical laws need to be postulated a priori. It thereby presents as a process of (...) irregular motion analogous to the real random walk but executed under the rules of the complex number system. There is a standard view that Schrödinger’s equation is deterministic, whereas wavefunction “collapse” is probabilistic —we have now a demonstrated linkage to the central limit theorem, indicating a stochastic picture at the foundation of Schrödinger’s equation itself. It may be an example of Wheeler’s “It from bit” with “No underlying law”. Reasons for the primary role of \ are open to discussion. The present derivation is compared with recent reconstructions of the quantum formalism, which have the aim of rationalizing its obscurities. (shrink)

The phenomena, molecular path in a liquid or a gas, fluctuating price stoke, fission and fusion, quantum field theory, relativistic wave motion, etc., are modeled through the nonlinear time fractional clannish random Walker’s parabolic equation, nonlinear time fractional SharmaTassoOlver equation, and the nonlinear space-time fractional KleinGordon equation. The fractional derivative is described in the sense of conformable derivative. From there, the G ′ / G, 1 / G -expansion method is found to be ensuing, effective, (...) and capable to provide functional solutions to nonlinear models concerning physical and engineering problems. In this study, an extension of the G ′ / G, 1 / G -expansion method has been introduced. This enhancement establishes broad-ranging and adequate fresh solutions. In addition, some existing solutions attainable in the literature also confirm the validity of the suggested extension. We believe that the extension might be added to the literature as a reliable and efficient technique to examine a wide variety of nonlinear fractional systems with parameters including solitary and periodic wave solutions to nonlinear FDEs. (shrink)

The problem of generalizing the power option-pricing model to incorporate more empirical features becomes an urgent and necessary event. A new power option pricing method is designed for the financial market uncertainty that simultaneously involves randomness and fuzziness. The randomness in market uncertainty is modeled by a time-fractional diffusion model, which describes trend memory in underlying asset prices. The fuzziness in market uncertainty is characterized by a triangular interval type-2 fuzzy numbers, which better captures the fuzziness of underlying asset (...) prices. Considering the decision-maker’s subjective judgment, we show the price mean value with the possibility-necessity weight and pessimistic-optimistic index under the type-2 fuzzy environment. We develop the power option pricing model with the time-fractional diffusion model and the triangular interval type-2 fuzzy numbers. Furthermore, the analytic solutions of pricing call power option and put power option are obtained and verified by the variational iterative reconstruction method. Our study shows that power option pricing, which adopts the time-fractional model and the triangular interval type-2 fuzzy numbers, can better capture the trend memory and double fuzziness of the real market. In addition, a numerical example is provided to illustrate that the power option means the value is decreasing with respect to the pessimistic-optimistic index and is fluctuating with respect to the possibility-necessity weight index. (shrink)

The problem of missingness in observational data is ubiquitous. When the confounders are missing at random, multiple imputation is commonly used; however, the method requires congeniality conditions for valid inferences, which may not be satisfied when estimating average causal treatment effects. Alternatively, fractional imputation, proposed by Kim 2011, has been implemented to handling missing values in regression context. In this article, we develop fractional imputation methods for estimating the average treatment effects with confounders missing at random. (...) We show that the fractional imputation estimator of the average treatment effect is asymptotically normal, which permits a consistent variance estimate. Via simulation study, we compare fractional imputation’s accuracy and precision with that of multiple imputation. (shrink)

Common symptoms of multiple sclerosis (MS) include motor impairments of the lower extremities, particularly gait disturbances. Loss of balance and muscle weakness, representing some peripheral effects, have been shown to influence these symptoms, however, the individual role of cortical and subcortical structures in the central nervous system is still to be understood. Assessing [18F]fluorodeoxyglucose (FDG) uptake in the CNS can assess brain activity and is directly associated with regional neuronal activity. One potential modality to increase cortical excitability and improve motor (...) function in patients with MS (PwMS) is transcranial direct current stimulation (tDCS). However, tDCS group outcomes may not mirror individual subject responses, which impedes our knowledge of the pathophysiology and management of diseases like MS. Three PwMS randomly received both 3 mA tDCS and SHAM targeting the motor cortex (M1) that controls the more-affected leg for 20 min on separate days before walking on a treadmill. The radiotracer, FDG, was injected at minute two of the 20 min walk and the subjects underwent a Positron emission tomography (PET) scan immediately after the task. Differences in relative regional metabolism of areas under the tDCS anode and the basal ganglia were calculated and investigated. The results indicated diverse and individualized responses in regions under the anode and consistent increases in some basal ganglia areas (e.g., caudate nucleus). Thus, anodal tDCS targeting the M1 that controls the more-affected leg of PwMS might be capable of affecting remote subcortical regions and modulating the activity (motor, cognitive, and behavioral functions) of the circuitry connected to these regions. (shrink)

Stochastic dynamical reduction for the case of spin-z measurement of a spin-1/2 particle describes a random walk on the spin-z axis. The measurement’s result depends on which of the two points: spin-z=±ħ/2 is reached first. Born’s rule is recovered as long as the expected step size in spin-z is independent of proximity to endpoints. Here, we address the questions raised by this description: (1) When is collapse triggered, and what triggers it? (2) Why is the expected step size in (...) spin-z (as opposed to polar angle) independent of proximity to endpoints? (3) Why does spin “lock” in the vertical directions? The difficulties associated with (1) are rooted, as is Bell’s theorem, in the time-asymmetric assumption that the present distribution over hidden variables is independent of future settings. We believe, a priori of any of the experiments of modern physics, that such a time-asymmetric assumption is dubious when probing the microscopic scale. As for (2) and (3), they are simultaneously resolved by abandoning the fundamental distinction drawn between spin and spatial angular momentum, and by appealing to very tiny (in both magnitude and spatial extent) but numerous patches of magnetic noise in the Stern-Gerlach’s field. (shrink)

Introduction: Falls are the leading cause of fatal and nonfatal injuries among older adults. Studies showed that older adults can reduce the risk of falls after participation in an unexpected perturbation-based balance training, a relatively novel approach that challenged reactive balance control. This study aims to investigate the effect of the practice schedule on reactive balance function and its transfer to proactive balance function. Our primary hypothesis is that improvements in reactive balance control following block PBBT will be not inferior (...) to the improvements following random PBBT.Methods and Analysis: This is a double-blind randomized controlled trial. Fifty community-dwelling older adults will be recruited and randomly allocated to a random PBBT group or a block PBBT group. The random PBBT group will receive eight training sessions over 4 weeks that include unexpected machine-induced perturbations of balance during hands-free treadmill walking. The block PBBT group will be trained by the same perturbation treadmill system, but only one direction will be trained in each training session, and the direction of the external perturbations will be announced. Both PBBT groups will receive a similar perturbation intensity during training, the same training period, and the same concurrent cognitive tasks during training. The generalization and transfer of learning effects will be measured by assessing the reactive and proactive balance control during standing and walking before and after 1 month of PBBT, for example, step and multiple steps and fall thresholds, Berg balance test, and fear of falls. The dependent variable will be rank transformed prior to conducting the analysis of covariance to allow for nonparametric analysis.Discussion: This research will explore which of the balance retraining paradigms is more effective to improve reactive balance and proactive balance control in older adults over 1 month. The research will address key issues concerning balance retraining: older adults’ neuromotor capacities to optimize training responses and their applicability to real-life challenges.Clinical Trial Registration: Helsinki research ethics approval has been received. (shrink)

This study investigated the neuromodulatory effects of transspinal stimulation on soleus H-reflex excitability and electromyographic activity during stepping in humans with and without spinal cord injury. Thirteen able-bodied adults and 5 individuals with SCI participated in the study. EMG activity from both legs was determined for steps without, during, and after a single-pulse or pulse train transspinal stimulation delivered during stepping randomly at different phases of the step cycle. The soleus H-reflex was recorded in both subject groups under control conditions (...) and following single-pulse transspinal stimulation at an individualized exactly similar positive and negative conditioning-test interval. The EMG activity was decreased in both subject groups at the steps during transspinal stimulation, while intralimb and interlimb coordination were altered only in SCI subjects. At the steps immediately after transspinal stimulation, the physiological phase-dependent EMG modulation pattern remained unaffected in able-bodied subjects. The conditioned soleus H-reflex was depressed throughout the step cycle in both subject groups. Transspinal stimulation modulated depolarization of motoneurons over multiple segments, limb coordination, and soleus H-reflex excitability during assisted stepping. The soleus H-reflex depression may be the result of complex spinal inhibitory interneuronal circuits activated by transspinal stimulation and collision between orthodromic and antidromic volleys in the peripheral mixed nerve. The soleus H-reflex depression by transspinal stimulation suggests a potential application for normalization of spinal reflex excitability after SCI. (shrink)

A simple random walk model has been shown by Gaveauet al. to give rise to the Klein-Gordon equation under analytic continuation. This absolutely most probable path implies that the components of the Dirac wave function have a common phase; the influence of spin on the motion is neglected. There is a nonclassical path of relative maximum likelihood which satisfies the constraint that the probability density coincide with the quantum mechanical definition. In three space dimensions, and in the presence of (...) electromagnetic interaction, the Lagrangian for this optimal, nonclassical path coincides with the Lagrangian of the Dirac particle. The nonrelativistic, or diffusion, limit is shown to be a formal consequence of Einstein's dynamical equilibrium condition; the continuity equation reduces to the same diffusion equation derived from Schrödinger's equation. The relativistic, massless limit, which would describe a neutrino, is comparable (in the sense of analytic continuation) to a nonviscous liquid whose molecules possess internal degrees of freedom. (shrink)

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual particle trajectories are described as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they (...) visit during the walk. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, the Delta potential, particle on a ring, particle on a sphere and include quantization of energy levels and angular momentum, as well as momentum entanglement. (shrink)

When searching for concepts in memory—as in the verbal fluency task of naming all the animals one can think of—people appear to explore internal mental representations in much the same way that animals forage in physical space: searching locally within patches of information before transitioning globally between patches. However, the definition of the patches being searched in mental space is not well specified. Do we search by activating explicit predefined categories and recall items from within that category, or do we (...) activate and recall a connected sequence of individual items without using categorical information, with each item recalled leading to the retrieval of an associated item in a stream, or both? Using semantic representations in a search of associative memory framework and data from the animal fluency task, we tested competing hypotheses based on associative and categorical search models. Associative, but not categorical, patch transitions took longer to make than position-matched productions, suggesting that categorical transitions were not true transitions. There was also clear evidence of associative search even within categorical patch boundaries. Furthermore, most individuals' behavior was best explained by an associative search model without the addition of categorical information. Thus, our results support a search process that does not use categorical information, but for which patch boundaries shift with each recall and local search is well described by a random walk in semantic space, with switches to new regions of the semantic space when the current region is depleted. (shrink)

Following up on previous results by Falmagne, this paper investigates possible mechanisms explaining how preference relations are created and how they evolve over time. We postulate a preference relation which is initially empty and becomes increasingly intricate under the influence of a random environment delivering discrete tokens of information concerning the alternatives. The framework is that of a class of real-time stochastic processes having interlinked Markov and Poisson components. Specifically, the occurence of the tokens is governed by a Poisson (...) process, while the succession of preference relations is a Markov process. In an example case, the preference relations are the various possible semiorders on the set of alternatives. Asymptotic results are obtained in the form of the limit probabilities of any semiorder. The arguments extend to a much more general situation including interval orders, biorders and partial orders. The results provide (up to a small number of parameters) complete quantitative predictions for panel data of a standard type, in which the same sample of subjects has been asked to compare the alternatives a number of times. (shrink)

We interpret the modal µ-calculus over a new model [10], to give a temporal logic suitable for systems exhibiting both probabilistic and demonic nondeterminism. The logical formulae are real-valued, and the statements are not limited to properties that hold with probability 1. In achieving that conceptual step, our technical contribution is to determine the correct quantitative generalisation of the Boolean operators: one that allows many of the standard Boolean-based temporal laws to carry over the reals with little or no structural (...) alteration, even for properties that hold with probability strictly between 0 and 1. The generalisation is not obvious, but is dictated by our discovery elsewhere of the algebraic property that characterises the next-time operator over the new model: it is arithmetic 'sublinearity' [20, Fig. 4 p. 342], which replaces the Boolean conjunctivity that characterises next-time in a modal algebra.We confirm by example that the new modal laws can be used for quantitative reasoning about probabilistic/demonic behavior. The random walk is treated using only those laws and real-number arithmetic: arguing from precise numeric premises, more specific than simply 'with some non-zero probability', we reach numeric conclusions that are not simply 'with probability 1'. (shrink)