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.

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)

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)

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)

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)

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)

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)

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)

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)

Common symptoms of multiple sclerosis 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 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 is transcranial direct current stimulation. 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 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 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. 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 of the circuitry connected to these regions. (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)

We focus on a particular class of computably enumerable degrees, the array noncomputable degrees defined by Downey, Jockusch, and Stob, to answer questions related to lattice embeddings and definability in the partial ordering of c. e. degrees under Turing reducibility. We demonstrate that the latticeM5 cannot be embedded into the c. e. degrees below every array noncomputable degree, or even below every nonlow array noncomputable degree. As Downey and Shore have proved that M5 can be embedded below every nonlow2 degree, (...) our result is the best possible in terms of array noncomputable degrees and jump classes. Further, this result shows that the array noncomputable degrees are definably different from the nonlow2 degrees. We note also that there are embeddings of M5 in which all five degrees are array noncomputable, and in which the bottom degree is the computable degree 0 but the other four are array noncomputable. (shrink)

A mime presented on videotape Adler’s six great ideas of truth, goodness, beauty, liberty, equality, and justice; their opposites; and the transitions from the positive or “good” concepts to their opposites. Using Johansson’s (1973) technique, the performer’s 12 joints were marked with points of light. Overall, the viewers had marginal success in identifying the concepts, but females were much more successful than males in identifying the “bad” ones of evil, slavery, falsehood, and ugliness, averaging 62% correct to the males’ 23%. (...) The results agree with Hall’s (1984) discussion of sex differences in the interpretation of nonverbal behavior. (shrink)