Random points associated with rectangles

Mathai, A. M.; Moschopoulos, P. G.; Pederzoli, Giorgio

doi:10.1007/bf02844387

Cited by 42 publications

(26 citation statements)

References 15 publications

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“…By analyzing many subsequent images, we found that switching events of opposite direction often occur close to each other, indicating a [26]). Green line: Distance distribution of uniformly distributed random points in a square [40,50]. (e) Distance distribution of nearest switching events of opposite direction [same movie as in (d)] shown in units of the nearest-neighbor distance.…”

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confidence: 99%

“…Their histogram (i.e., distances between red and blue spots, but not between spots of the same color) is shown in Fig. 3(d) in comparison with a curve for spatially uncorrelated events (i.e., the distance distribution of random points in a square [40]). Interestingly, there is a pronounced difference between the measured and the random distribution, with a clear preference for switching events of closely spaced molecules, indicating that switching of opposite direction preferentially occurs in close proximity, much closer than expected for random events.…”

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Observing single-atom diffusion at a molecule-metal interface

et al. 2016

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The dynamics at the interface between a close-packed porphyrin monolayer and Au(111) is investigated by time-dependent scanning tunneling microscopy, detecting the motion of single-interface adatoms in real space. Imaging sequences reveal predominant switching of the molecular appearance in adjacent molecules, pointing to a spatial correlation that is consistent with adatom diffusion from one molecule to the next. In some cases, the number of switching molecules is drastically increased, indicating collective switching events. In addition to the thermally induced motion of adatoms at the interface, also voltage pulses from the microscope tip can induce the process-revealing different yields in agreement with the model of adatom hopping. DOI: 10.1103/PhysRevB.94.035416 The interface between organic molecules and metal substrates plays a key role for many properties that are important, for instance, in catalytically driven reactions [1,2] and for charge transport [3]. The study of such systems gives detailed insight into fundamental processes that take place at an organic-inorganic interface. For an in-depth understanding, it is advantageous to use a scanning tunneling microscope (STM) for imaging because it provides information about the local environment of each individual molecule, which is important since the molecular properties might differ locallydue to defects, step edges, or different areas of a surface reconstruction [4,5]. For instance, individual C 60 molecules were found to change between dark and bright appearances in STM images, caused by the diffusion of surface [6] or bulk [7] vacancies, charge transfer between molecule and surface [8], or adsorption on small metal islands [9].Adatoms are known to diffuse on close-packed metal surfaces if the thermal energy is sufficient for their detachment from step edges [10]. When molecules are adsorbed on such a surface, the adatoms can interact with and even be trapped by molecules [11][12][13][14][15], leading to characteristic metallic nanostructures that reflect the molecular shape [16][17][18]. In addition to these self-organized structures, manipulation of single adatoms has been used to bring them in contact with molecules [19,20]. So far, real space studies of the molecule-surface interaction have been done mainly under static conditions [21,22] or focus on the lateral diffusion of molecules on surfaces [23][24][25]. Here, we report the dynamic behavior at the molecule-metal interface by observing the motion of individual gold adatoms underneath a molecular monolayer on Au(111) in time.As a molecular system we have chosen tetrabromophenylporphyrin [Br 4 TPP; Fig. 1(a) The appearance of our molecules strongly depends on the applied bias voltage: At −0.5 V all molecules appear at a similar height, while at around −1 V two dark and one bright molecular appearances can be found [ Fig. 1(b)]. The two dark molecules could be identified as two tautomers without a gold adatom, while bright molecules have a single gold adatom underneath, causing the shift i...

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Observing single-atom diffusion at a molecule-metal interface

et al. 2016

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“…The corresponding values of α, given by Eq. (27) and illustrated in Figure 4 for setting III, range between 0.71 and 1.917 for I < 0, between 0.007 and 0.017 for I > 0.…”

Section: Discussionmentioning

confidence: 96%

Information Integration from Distributed Threshold-Based Interactions

Barbosa

2017

Complexity

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We consider a collection of distributed units that interact with one another through the sending of messages. Each message carries a positive (+1) or negative (−1) tag and causes the receiving unit to send out messages as a function of the tags it has received and a threshold. This simple model abstracts some of the essential characteristics of several systems used in the field of artificial intelligence, and also of biological systems epitomized by the brain. We study the integration of information inside a temporal window as the model's dynamics unfolds. We quantify information integration by the total correlation, relative to the window's duration (w), of a set of random variables valued as a function of message arrival. Total correlation refers to the rise of information gain above and beyond that which the units already achieve individually, being therefore related to consciousness studies in some models. We report on extensive computational experiments that explore the interrelations of the model's parameters (two probabilities and the threshold), highlighting relevant scenarios of message traffic and how they impact the behavior of total correlation as a function of w. We find that total correlation can occur at significant fractions of the maximum possible value and provide semianalytical results on the message-traffic characteristics associated with values of w for which it peaks. We then reinterpret the model's parameters in terms of the current best estimates of some quantities pertaining to cortical structure and dynamics. We find the resulting possibilities for best values of w to be well aligned with the time frames within which percepts are thought to be processed and eventually rendered conscious.

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“…As all cells have the same size, P int ðdÞ is the same for all cells. In this work we use the closed form formula for P int provided in [30] for the distribution of the distance between two random points in a rectangle, and we focus on the analytical description of P c i c j ðdÞ, using the same approach as in [32].…”

Section: Distances Between Random Points In Different Cellsmentioning

confidence: 99%