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Is Fitts’ Law Continuous in Discrete Aiming?  [PDF]
Rita Sleimen-Malkoun, Jean-Jacques Temprado, Raoul Huys, Viktor Jirsa, Eric Berton
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0041190
Abstract: The lawful continuous linear relation between movement time and task difficulty (i.e., index of difficulty; ID) in a goal-directed rapid aiming task (Fitts’ law) has been recently challenged in reciprocal performance. Specifically, a discontinuity was observed at critical ID and was attributed to a transition between two distinct dynamic regimes that occurs with increasing difficulty. In the present paper, we show that such a discontinuity is also present in discrete aiming when ID is manipulated via target width (experiment 1) but not via target distance (experiment 2). Fitts’ law’s discontinuity appears, therefore, to be a suitable indicator of the underlying functional adaptations of the neuro-muscular-skeletal system to task properties/requirements, independently of reciprocal or discrete nature of the task. These findings open new perspectives to the study of dynamic regimes involved in discrete aiming and sensori-motor mechanisms underlying the speed-accuracy trade-off.
Cortical Correlates of Fitts’ Law  [PDF]
Peter J. Ifft,Mikhail A. Lebedev,Miguel A. L. Nicolelis
Frontiers in Integrative Neuroscience , 2011, DOI: 10.3389/fnint.2011.00085
Abstract: Fitts’ law describes the fundamental trade-off between movement accuracy and speed: it states that the duration of reaching movements is a function of target size (TS) and distance. While Fitts’ law has been extensively studied in ergonomics and has guided the design of human–computer interfaces, there have been few studies on its neuronal correlates. To elucidate sensorimotor cortical activity underlying Fitts’ law, we implanted two monkeys with multielectrode arrays in the primary motor (M1) and primary somatosensory (S1) cortices. The monkeys performed reaches with a joystick-controlled cursor toward targets of different size. The reaction time (RT), movement time, and movement velocity changed with TS, and M1 and S1 activity reflected these changes. Moreover, modifications of cortical activity could not be explained by changes of movement parameters alone, but required TS as an additional parameter. Neuronal representation of TS was especially prominent during the early RT period where it influenced the slope of the firing rate rise preceding movement initiation. During the movement period, cortical activity was correlated with movement velocity. Neural decoders were applied to simultaneously decode TS and motor parameters from cortical modulations. We suggest that sensorimotor cortex activity reflects the characteristics of both the movement and the target. Classifiers that extract these parameters from cortical ensembles could improve neuroprosthetic control.
A Note on the Validity of the Shannon Formulation for Fitts’ Index of Difficulty  [PDF]
Ian Scott MacKenzie
Open Journal of Applied Sciences (OJAppS) , 2013, DOI: 10.4236/ojapps.2013.36046
Abstract:

The three most common variations of Fitts’ index of difficulty are the Fitts formulation, the Welford formulation, and the Shannon formulation. A recent paper by Hoffmann [1] critiqued the three and concluded that the Fitts and Welford formulations are valid and that the Shannon formulation is invalid. In this paper, we challenge Hoffmann’s position regarding the Shannon formulation. It is argued that the issue of validity vs. invalidity is ill-conceived, given that Fitts’ law is a “model by analogy” with no basis in human motor control. The relevant questions are of utility: Does a model work? How well? Is it useful? Where alternative formulations exist, they may be critiqued and compared for strengths and weaknesses, but validity is an irrelevant construct. In a reanalysis of data from Fitts’ law experiments, models built using the Shannon formulation are (re)affirmed to be as good as, and generally better than, those built using the Fitts or Welford formulation.

Age-related dedifferentiation of cognitive and motor slowing: insight from the comparison of Hick–Hyman and Fitts’ laws  [PDF]
Rita Sleimen-Malkoun,Jean-Jacques Temprado,Eric Berton
Frontiers in Aging Neuroscience , 2013, DOI: 10.3389/fnagi.2013.00062
Abstract: The present study aimed to determine whether the general slowing hypothesis (GSH) could be extended to the motor domain by comparing cognitive and motor age-related slowing. To achieve this objective, we compared the slopes of Hick–Hyman’s law and Fitts’ law, in young and older adults. The general hypothesis was that, due to the dedifferentiation of cognitive and motor neural resources during aging, the slopes of Hick–Hyman’s law and Fitts’ law should become closer, if not similar, in older adults. Ten young adults (mean age = 26 ± 3 years) and 14 older adults (mean age = 78 ± 7 years) participated in the experiment. They had to perform a discrete rapid-aiming task and a reaction time (RT) task. In the aiming task, five index of difficulty (ID) levels were used (from three to seven bits by increments of 1.0 bit). Task difficulty was scaled via the manipulation of target distance from home position. In the RT task, five IDs were selected: 0, 1, 2, 3, and 4 bits, with incompatible S–R associations. RT and movement times were recorded. Efficiency and Brinley regression functions were calculated. Age-related slowing ratios were estimated. Response times increased in both tasks in older adults. The slopes of Hick–Hyman’s law and Fitts’ law were steeper in older adults than in young participants. In young participants, the slope of Hick–Hyman’s law was smaller than that of Fitts’ law. In older adults, no difference was found. Slowing ratios observed in both tasks were equivalent. The present results extended the GSH to the motor domain. They suggested that, due to dedifferentiation of cognitive and motor neural resources, decrease in processing speed acts as a common cause to behavioral slowing in both cognitive and motor tasks.
Performance is not Related to Perception of Target Width in Fitts’ Law  [cached]
Zelaznik Howard N.,Croxall Roxanne,Vanhooser Jake
BIO Web of Conferences , 2011, DOI: 10.1051/bioconf/20110100100
Abstract: We report a new experiment in a series of studies in which research participants perform a Fitts’ Law repetitive task, and then are required to judge the width of the target that was utilized. The first two experiments previously reported showed no relation between perception and performance. However in those two experiments subjects were never provided with feedback on their performance. In the current study, we provided participants with their performance score. Providing their performance score did not produce a relation between target width perception and performance. We posit that sports studies that have shown this relation are the results of intimate knowledge of what it means to perform well. Our inexperienced Fitts’ Law participants lacked such an understanding.
Validation of a mechanism to balance exercise difficulty in robot-assisted upper-extremity rehabilitation after stroke
Lukas Zimmerli, Carmen Krewer, Roger Gassert, Friedemann Müller, Robert Riener, Lars Lünenburger
Journal of NeuroEngineering and Rehabilitation , 2012, DOI: 10.1186/1743-0003-9-6
Abstract: We propose a computational mechanism based on Fitts' Law that balances i.e. adjusts the difficulty of an exercise for upper-extremity rehabilitation. The proposed mechanism was implemented into an augmented feedback application consisting of three difficulty conditions (easy, balanced, hard). The task of the exercise was to reach random targets on the screen from a starting point within a specified time window. The available time was decreased with increasing condition difficulty. Ten subacute stroke patients were recruited to validate the mechanism through a study. Cognitive and motor functions of patients were assessed using the upper extremity section of the Fugl-Meyer Assessment, the modified Ashworth scale as well as the Addenbrookes cognitive examination-revised. Handedness of patients was obtained using the Edinburgh handedness inventory. Patients' performance during the execution of the exercises was measured twice, once for the paretic and once for the non-paretic arm. Results were compared using a two-way ANOVA. Post hoc analysis was performed using a Tukey HSD with a significance level of p < 0.05.Results show that the mechanism was capable of balancing the difficulty of an exercise to the capabilities of the patients. Medians for both arms show a gradual decrease and significant difference of the number of successful trials with increasing condition difficulty (F2;60 = 44.623; p < 0.01; η2 = 0.623) but no significant difference between paretic and non-paretic arm (F1;60 = 3.768; p = 0.057; η2 = 0.065). Post hoc analysis revealed that, for both arms, the hard condition significantly differed from the easy condition (p < 0.01). In the non-paretic arm there was an additional significant difference between the balanced and the hard condition (p < 0.01). Reducing the time to reach the target, i.e., increasing the difficulty level, additionally revealed significant differences between conditions for movement speeds (F2;59 = 6.013; p < 0.01; η2 = 0.185), withou
Usage analysis for applying Fitts'' law in context of mobile/wearable computing
Fitts’ 模型在移动与可穿戴计算交互中的可用性研究*

SONG Hai-tao,LIU Huan-yu,
宋海涛
,刘桓宇

计算机应用研究 , 2011,
Abstract: Mobile and wearable computing have becoming bloom in these years.For which the interaction usually based on the restricted field of view devices,e.g.hand-held small display and head mounted display,as well as the multi-touch pointing device.However,the encountered various display field of view and small targets while interacting with those devices may significantly affect the interaction efficiency,and further influence the usability of traditional Fitts' law,the common tool to study it.This paper conducted...
Measurement of the Robot Motor Capability of a Robot Motor System: A Fitts’s-Law-Inspired Approach  [PDF]
Hsien-I Lin,C. S. George Lee
Sensors , 2013, DOI: 10.3390/s130708412
Abstract: Robot motor capability is a crucial factor for a robot, because it affects how accurately and rapidly a robot can perform a motion to accomplish a task constrained by spatial and temporal conditions. In this paper, we propose and derive a pseudo-index of motor performance ( pI p) to characterize robot motor capability with robot kinematics, dynamics and control taken into consideration. The proposed pI p provides a quantitative measure for a robot with revolute joints, which is inspired from an index of performance in Fitts’s law of human skills. Computer simulations and experiments on a PUMA 560 industrial robot were conducted to validate the proposed pI p for performing a motion accurately and rapidly.
Freedom of movement for persons in the European Union Law  [PDF]
Novi?i? ?aklina
Medjunarodni Problemi , 2003, DOI: 10.2298/medjp0301057n
Abstract: In this article the author analyses the evolution of complex corpus of legislation concerning the freedom of movement for persons in European Union Law. The article deals with the subject in two aspects: the first part of the analysis considers the conceptual development of free movement of persons by way of deliberation of building-up the authority of Union in that area, and the second part analyses the contents of the right of the Union citizens to move and reside freely within the territory of the Member State. The freedom of movement for people includes the right of Union citizens to enter, move and reside in another Member State and, in that context prohibition of any discrimination based on nationality. Conceived originally as primarily an economic phenomenon, the free movement of persons was closely linked to the pursuit of an occupation. It was the mobility of human resources as a factor of production, which inspired the chapters of the Treaty establishing the European Economic Community (1957) relating to the free movement of workers, freedom of establishment and the freedom to provide services. In that sense, freedom of movement is a part of a wider concept, that of the common/internal market. Since then, through the combined effect of secondary legislation and the case law of the Court of Justice, the concept has been broadened and it tends, from the Maastricht Treaty (1992), to form one of the fundamental and individual rights of Union citizens generally. Also, the amendments of EEC Treaty, which were made by the Single European Act (1985) and specially by the Treaty of Amsterdam (1997) and the Treaty of Nice (2001), have formalised the external aspect of freedom of movement. Namely, it was recognised that freedom of movement for persons could not take place at the expense of security, protection against crime and illegal immigration. The abolition of internal controls has generated the need of the transferring checks to the external frontiers of the Union and, in this connection, the gradual establishment of an area of freedom, security and justice. In the first part of the article the author presents and analyses the development of the Union power in the policies of freedom of movement: in facilitating of free movement of people as a principle of the common/internal/single market, in achievement of the right to free movement for Union citizens, and also in the fields related to the external aspect of freedom of movement, or, actually, the issues pertaining to visas, asylum and immigration. The second part presents the specific contents of
A Standard Law for the Equatorward Drift of the Sunspot Zones  [PDF]
D. H. Hathaway
Physics , 2011, DOI: 10.1007/s11207-011-9837-z
Abstract: The latitudinal location of the sunspot zones in each hemisphere is determined by calculating the centroid position of sunspot areas for each solar rotation from May 1874 to June 2011. When these centroid positions are plotted and analyzed as functions of time from each sunspot cycle maximum there appears to be systematic differences in the positions and equatorward drift rates as a function of sunspot cycle amplitude. If, instead, these centroid positions are plotted and analyzed as functions of time from each sunspot cycle minimum then most of the differences in the positions and equatorward drift rates disappear. The differences that remain disappear entirely if curve fitting is used to determine the starting times (which vary by as much as 8 months from the times of minima). The sunspot zone latitudes and equatorward drift measured relative to this starting time follow a standard path for all cycles with no dependence upon cycle strength or hemispheric dominance. Although Cycle 23 was peculiar in its length and the strength of the polar fields it produced, it too shows no significant variation from this standard. This standard law, and the lack of variation with sunspot cycle characteristics, is consistent with Dynamo Wave mechanisms but not consistent with current Flux Transport Dynamo models for the equatorward drift of the sunspot zones.
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