Bisection

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Konstantinos Priftis - One of the best experts on this subject based on the ideXlab platform.

  • extra powerful on the visuo perceptual space but variable on the number space different effects of optokinetic stimulation in neglect patients
    Journal of Neuropsychology, 2015
    Co-Authors: Marco Pitteri, Ingo Keller, Francesca Meneghello, Georg Kerkhoff, Konstantinos Priftis
    Abstract:

    We studied the effects of optokinetic stimulation (OKS; leftward, rightward, control) on the visuo-perceptual and number space, in the same sample, during line Bisection and mental number interval Bisection tasks. To this end, we tested six patients with right-hemisphere damage and neglect, six patients with right-hemisphere damage but without neglect, and six neurologically healthy participants. In patients with neglect, we found a strong effect of leftward OKS on line Bisection, but not on mental number interval Bisection. We suggest that OKS influences the number space only under specific conditions.

  • processing of peripersonal and extrapersonal space using tools evidence from visual line Bisection in real and virtual environments
    Neuropsychologia, 2008
    Co-Authors: Luciano Gamberini, Bruno Seraglia, Konstantinos Priftis
    Abstract:

    Abstract The dissociation between peripersonal space (within reaching) and extrapersonal space (beyond reaching) has been reported in studies using the line Bisection task in left neglect patients and in healthy participants. Furthermore, this dissociation can be modulated by tool use. We conducted two experiments to compare line Bisection in peripersonal (i.e., 30, 60 cm) and extrapersonal space (i.e., 90, 120 cm). Healthy participants bisected visual lines using sticks and a laser pointer, according to the experimental paradigm of Longo and Lourenco [On the nature of near space: Effects of tool use and the transition to far space. Neuropsychologia , 44, 977–981, 2006]. In Experiment 1 participants performed line Bisection in a real environment, whereas in Experiment 2 participants performed line Bisection in a virtual environment. Results from both experiments revealed an abrupt midpoint shift from the peripersonal to the extrapersonal space but only when a laser pointer was used. In addition, we confirmed that peripersonal space can be extended to extrapersonal space when participants used a stick. Notably, virtual reality can be a useful technique for studying the dissociation between peripersonal and extrapersonal space and their interaction by means of tool use.

  • Explicit versus Implicit Processing of Representational Space in Neglect: Dissociations in Accessing the Mental Number Line
    Journal of cognitive neuroscience, 2006
    Co-Authors: Konstantinos Priftis, Francesca Meneghello, Marco Zorzi, Roberto Marenzi, Carlo Umiltà
    Abstract:

    The present study investigated the effects of left hemispatial neglect on two tasks activating the mental number line (MNL). Six patients with left neglect performed a mental number Bisection task and a modified version of the Spatial Numerical Association of Response Codes (SNARC) task. Effects of left neglect were observed in the number Bisection task, but not in the SNARC task. We argue that the dissociation between number Bisection and SNARC resembles, in the representational space of the MNL, previously reported dissociations on neglect between explicit knowledge (assessed by direct tasks) and implicit knowledge (assessed by indirect tasks).

  • The spatial representation of numerical and non-numerical sequences: evidence from neglect.
    Neuropsychologia, 2005
    Co-Authors: Marco Zorzi, Konstantinos Priftis, Francesca Meneghello, Roberto Marenzi, Carlo Umiltà
    Abstract:

    Psychophysical and neuropsychological studies have revealed that humans represent numbers along a continuous, left-to-right oriented mental line. However, it has been recently claimed that this format of representation is not special to numbers because non-numerical sequences would be spatially coded in the same way. To test this hypothesis, the present study investigated the effects of left neglect upon the Bisection of numerical and non-numerical intervals. Eight patients with left neglect performed a visual line Bisection task and three mental Bisection tasks with number, letter, and month intervals. The error pattern in the number Bisection task, indexed by the modulating effect of interval length, mirrored that of the visual task and confirmed the left-to-right spatial orientation of the mental number line. In contrast, the Bisection of non-numerical intervals showed a very different pattern. The results suggest that the spatial layout characterizing numerical representations constitutes a specific property of numbers rather than a general characteristic of ordered sequences.

Fabrizio Doricchi - One of the best experts on this subject based on the ideXlab platform.

  • dissociation between line Bisection and mental number line Bisection in healthy adults
    Neuropsychologia, 2015
    Co-Authors: Francesca Rotondaro, Marilena Aiello, Sheila Merola, Mario Pinto, Fabrizio Doricchi
    Abstract:

    Abstract Healthy adults bisect visual horizontal lines slightly to the left of their true center. This bias has been termed “pseudoneglect” and is considered to reflect right hemisphere dominance in the orienting of spatial attention. A previous investigation reported a positive correlation between pseudoneglect and a corresponding negative bias towards numbers lower than the true midpoint, i.e. supposedly to the left of the midpoint, during the mental Bisection of number intervals that were defined by two visual arabic digits presented one to the left and one to the right of a horizontal line (Longo and Lourenco, 2007, Neuropsychologia, 45, 7, 1400–1407). Here, studying a sample of 60 healthy participants we verified whether this correlation still holds when the endpoints of number intervals are defined verbally, i.e. with no visual-spatial cues suggesting their left-to-right arrangement. Participants bisected horizontal lines (2 cm, 10 cm and 20 cm), short number intervals (3-, 5-, 7- and 9-unit) and large number intervals (16-, 24-, 32-, 40-, 48-, 56-, and 64-unit). Pseudoneglect was observed both in line and number interval Bisection, confirming the results of Longo and Lourenco (2007). Nonetheless, the study of correlations between Bisection biases averaged across different line and number intervals lengths and between all possible pairings of line and number interval lengths revealed no significant or systematic pattern. During line Bisection pseudoneglect increased as a function of line length while with short number intervals pseudoneglect decreased and turned into an opposite positive bias as a function of interval length. With large number intervals no linear relationship was present between Bisection bias and interval length and, as in Longo and Lourenco (2007), the higher was the starting point of the number interval the larger was pseudoneglect. These results show that verbally defined number intervals are not mentally inspected with the same mechanisms that are engaged by the Bisection of horizontal visual lines. This suggests that number intervals are not inherently arranged along the mental equivalent of a left-to-right oriented horizontal line. This spatial representation seems rather adopted when, as in the case of the SNARC task, “left” vs. “right” codes must be used for the selection of responses associated with numbers or when, as in the case of Longo and Lourenco (2007), the numerical material to be processed is arranged in left-to-right order.

  • neglect around the clock dissociating number and spatial neglect in right brain damage
    Space Time and Number in the Brain#R##N#Searching for the Foundations of Mathematical Thought, 2011
    Co-Authors: Yves Rossetti, Marilena Aiello, S Jacquincourtois, Masami Ishihara, Claudio Brozzoli, Fabrizio Doricchi
    Abstract:

    Publisher Summary This chapter examines the link between number and the spatial biases observed in spatial neglect. Right-brain-damaged patients affected by left unilateral neglect are characterized by a pathological attentional bias to the right side of space. This left-sided deficit encompasses eye and head deviations, visual, somatosensory and auditory sensory processing, action initiation and realization, and mental representations. The spatial cueing effect arising in the external space coordinates was present irrespective of the emphasis in the instructions either concerning fingers or side of space. Neglect patient populations manifested a clear-cut double dissociation. Some of the patients displayed very severe neglect on the Bisection of visual lines and normal performance for the Bisection of number intervals. The increasing rightward error displayed by D participants in the Bisection of large 7-unit intervals located to the “left” side of decades offers another example of the apparent similarity between Bisection behavior in visual and number space. Another point that needs careful consideration when one discusses the associations and dissociations between numerical and spatial coding that can be observed in the healthy brain is whether the influence of numerical cues on spatial processing is as strong as the reciprocal influence of spatial cues on number processing.

  • Dissociation between physical and mental number line Bisection in right hemisphere brain damage
    Nature Neuroscience, 2005
    Co-Authors: Fabrizio Doricchi, Paola Guariglia, Marina Gasparini, Francesco Tomaiuolo
    Abstract:

    To compare numeric quantities, humans make use of a 'mental number line' with smaller quantities located to the left of larger ones; it is unclear, however, whether orienting along the number line is like orienting along a physical line. We found that in brain-damaged subjects with defective leftward orienting, rightward deviation in the Bisection of numeric and physical intervals is doubly dissociated. Deviation in numeric interval Bisection was associated with prefrontal damage and spatial working memory deficit.

Robert Krauthgamer - One of the best experts on this subject based on the ideXlab platform.

  • a polylogarithmic approximation of the minimum Bisection
    Siam Review, 2006
    Co-Authors: Uriel Feige, Robert Krauthgamer
    Abstract:

    A Bisection of a graph with $n$ vertices is a partition of its vertices into two sets, each of size $n/2$. The Bisection cost is the number of edges connecting the two sets. The problem of finding a Bisection of minimum cost is prototypical to graph partitioning problems, which arise in numerous contexts. This problem is NP-hard. We present an algorithm that finds a Bisection whose cost is within a factor of $O(\log^{1.5} n)$ from the minimum. For graphs excluding any fixed graph as a minor (e.g., planar graphs) we obtain an improved approximation ratio of $O(\log n)$. The previously known approximation ratio for Bisection was roughly $\sqrt{n}$.

  • a polylogarithmic approximation of the minimum Bisection
    SIAM Journal on Computing, 2002
    Co-Authors: Uriel Feige, Robert Krauthgamer
    Abstract:

    A Bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n/2. The Bisection cost is the number of edges connecting the two sets. It is known that finding a Bisection of minimum cost is NP-hard. We present an algorithm that finds a Bisection whose cost is within ratio of O(log2 n) from the minimum. For graphs excluding any fixed graph as a minor (e.g., planar graphs) we obtain an improved approximation ratio of O(log n). The previously known approximation ratio for Bisection was roughly $\sqrt{n}$.

  • a polylogarithmic approximation of the minimum Bisection
    Foundations of Computer Science, 2000
    Co-Authors: Uriel Feige, Robert Krauthgamer
    Abstract:

    A Bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n/2. The Bisection cost is the number of edges connecting the two sets. Finding the Bisection of minimum cost is NP-hard. We present an algorithm that finds a Bisection whose cost is within ratio of O(log/sup 2/ n) from the optimal. For graphs excluding any fixed graph as a minor (e.g. planar graphs) we obtain an improved approximation ratio of O(log n). The previously known approximation ratio for Bisection was roughly /spl radic/n.

Eike Seidel - One of the best experts on this subject based on the ideXlab platform.

  • polynomial time approximation schemes for max Bisection on planar and geometric graphs
    SIAM Journal on Computing, 2005
    Co-Authors: Klaus Jansen, Marek Karpinski, Andrzej Lingas, Eike Seidel
    Abstract:

    The max-Bisection and min-Bisection problems are to find a partition of the vertices of a graph into two equal size subsets that, respectively, maximizes or minimizes the number of edges with endpoints in both subsets. We design the first polynomial time approximation scheme for the max-Bisection problem on arbitrary planar graphs solving a long-standing open problem. The method of solution involves designing exact polynomial time algorithms for computing optimal partitions of bounded treewidth graphs, in particular max- and min-Bisection, which could be of independent interest. Using a similar method we design also the first polynomial time approximation scheme for max-Bisection on unit disk graphs (which could also be easily extended to other geometrically defined graphs).

  • polynomial time approximation schemes for max Bisection on planar and geometric graphs
    Lecture Notes in Computer Science, 2001
    Co-Authors: Klaus Jansen, Marek Karpinski, Andrzej Lingas, Eike Seidel
    Abstract:

    The Max-Bisection and Min-Bisection problems are to find a partition of the vertices of a graph into two equal size subsets that respectively maximizes or minimizes the number of edges with endpoints in both subsets. We design the first polynomial time approximation scheme for the Max-Bisection problem on arbitrary planar graphs solving a long time standing open problem. The method of solution involves designing exact polynomial time algorithms for computing optimal partitions of bounded treewidth graphs, in particular Max- and Min-Bisection, which could be of independent interest. Using similar method we design also the first polynomial time approximation scheme for Max-Bisection on unit disk graphs (which could be easily extended to other geometrically defined graphs).

Hans-otto Karnath - One of the best experts on this subject based on the ideXlab platform.

  • disturbed line Bisection is associated with posterior brain lesions
    Brain Research, 2006
    Co-Authors: Chris Rorden, Monika Fruhmann Berger, Hans-otto Karnath
    Abstract:

    Neglect patients classically fail to orient and respond to stimuli appearing on their contralesional side. Traditionally, the neglect syndrome has been associated with damage to the right inferior parietal lobule (IPL) and the right temporo-parietal junction (TPJ). Neglect is popularly assessed by two different tasks: line Bisection and cancellation. In a previous study (S. Ferber, H.-O. Karnath, How to assess spatial neglect-line Bisection or cancellation tasks. J. Clin. Exp. Neuropsychol. 23 (2001) 599-607), we observed that performance on the cancellation task correlates well with the characteristic behavioral disorders used to clinically diagnose spatial neglect, while line Bisection was a poor predictor. This might indicate that the disability to correctly bisect lines is a distinct disorder separable from spatial neglect. Here, we assess the anatomy of the patients investigated in that study, and reveal that damage to the temporo-occipital junction correlates with poor performance in the line Bisection task. This work extends previous work by Binder et al. (J. Binder, R. Marshall, R. Lazar, J. Benjamin, J.P. Mohr, Distinct syndromes of hemineglect. Arch. Neurol. 49 (1992) 1187-1194) suggesting that line Bisection and cancellation identify distinct syndromes. The data suggest that these two tasks dissociate both in terms of behavior and anatomy. This anatomical distinction may help reconcile our recent finding that spatial neglect is associated with damage to the superior temporal cortex and insula, while others have identified the IPL and TPJ. Specifically, we note that our previous anatomical studies did not use the line Bisection task to select neglect patients, while many others used this task. We suggest that anatomical studies that combine patients from both of these two distinct groups may result in misleading findings.

  • How to assess spatial neglect--line Bisection or cancellation tasks?
    Journal of clinical and experimental neuropsychology, 2001
    Co-Authors: Susanne Ferber, Hans-otto Karnath
    Abstract:

    Spatial neglect is usually assessed using cancellation tests or line Bisection. A recent comparison of these tests has revealed a double dissociation, in which one neglect patient was impaired in line Bisection but not in star cancellation whereas another showed the reverse deficit. This dissociation has prompted the question whether neglect is still a meaningful theoretical entity. We compared line Bisection and cancellation tasks regarding their accuracy in detecting spatial neglect. We tested 35 patients with well-defined spatial neglect using a line Bisection task and four different cancellation tasks. The line Bisection test missed 40% of our neglect patients. Far superior were the letter cancellation and bells tests, each of which missed only 6% of the cases. A deviation in line Bisection is not fundamentally related to spatial neglect, but may also arise from other causes (e.g., hemianopia, or which hand is used), and therefore, should be treated with caution in clinical diagnosis. Cancellation tes...