scholarly journals The neural dynamics associated with computational complexity

2022 ◽  
Author(s):  
Juan Pablo Franco ◽  
Peter Bossaerts ◽  
Carsten Murawski
Keyword(s):  
Computational Complexity ◽  
Complexity Theory ◽  
Brain Regions ◽  
Anterior Cingulate ◽  
Angular Gyrus ◽  
Dorsal Anterior Cingulate Cortex ◽  
Ultra High Field ◽  
Computational Complexity Theory ◽  
Neural Processes ◽  
Suitable Framework

Many everyday tasks require people to solve computationally complex problems. However, little is known about the effects of computational hardness on the neural processes associated with solving such problems. Here, we draw on computational complexity theory to address this issue. We performed an experiment in which participants solved several instances of the 0-1 knapsack problem, a combinatorial optimization problem, while undergoing ultra-high field (7T) functional magnetic resonance imaging (fMRI). Instances varied in two task-independent measures of intrinsic computational hardness: complexity and proof hardness. We characterise a network of brain regions whose activation was correlated with both measures but in distinct ways, including the anterior insula, dorsal anterior cingulate cortex and the intra-parietal sulcus/angular gyrus. Activation and connectivity changed dynamically as a function of complexity and proof hardness, in line with theoretical computational requirements. Overall, our results suggest that computational complexity theory provides a suitable framework to study the effects of computational hardness on the neural processes associated with solving complex cognitive tasks.

scholarly journals The trouble with the second quantifier

4OR ◽  
2021 ◽  
Author(s):  
Gerhard J. Woeginger
Keyword(s):  
Computational Complexity ◽  
Robust Optimization ◽  
Complexity Theory ◽  
Operational Research ◽  
Optimization Problems ◽  
Bilevel Optimization ◽  
Theoretical Background ◽  
Research Community ◽  
Universal Quantifier ◽  
Computational Complexity Theory

AbstractWe survey optimization problems that allow natural simple formulations with one existential and one universal quantifier. We summarize the theoretical background from computational complexity theory, and we present a multitude of illustrating examples. We discuss the connections to robust optimization and to bilevel optimization, and we explain the reasons why the operational research community should be interested in the theoretical aspects of this area.

Acetaminophen Reduces Social Pain

2010 ◽  
Vol 21 (7) ◽  
pp. 931-937 ◽  
Author(s):  
C. Nathan DeWall ◽  
Geoff MacDonald ◽  
Gregory D. Webster ◽  
Carrie L. Masten ◽  
Roy F. Baumeister ◽  
...  
Keyword(s):  
Brain Activity ◽  
Brain Regions ◽  
Daily Basis ◽  
Social Rejection ◽  
Neural Mechanisms ◽  
Anterior Cingulate ◽  
Neural Responses ◽  
Physical Pain ◽  
Social Pain ◽  
Dorsal Anterior Cingulate Cortex

Pain, whether caused by physical injury or social rejection, is an inevitable part of life. These two types of pain—physical and social—may rely on some of the same behavioral and neural mechanisms that register pain-related affect. To the extent that these pain processes overlap, acetaminophen, a physical pain suppressant that acts through central (rather than peripheral) neural mechanisms, may also reduce behavioral and neural responses to social rejection. In two experiments, participants took acetaminophen or placebo daily for 3 weeks. Doses of acetaminophen reduced reports of social pain on a daily basis (Experiment 1). We used functional magnetic resonance imaging to measure participants’ brain activity (Experiment 2), and found that acetaminophen reduced neural responses to social rejection in brain regions previously associated with distress caused by social pain and the affective component of physical pain (dorsal anterior cingulate cortex, anterior insula). Thus, acetaminophen reduces behavioral and neural responses associated with the pain of social rejection, demonstrating substantial overlap between social and physical pain.

The future of computational complexity theory: part II

1996 ◽  
Vol 27 (4) ◽  
pp. 3-7
Author(s):  
E. Allender ◽  
J. Feigenbaum ◽  
J. Goldsmith ◽  
T. Pitassi ◽  
S. Rudich
Keyword(s):  
Computational Complexity ◽  
Complexity Theory ◽  
Computational Complexity Theory ◽  
The Future

scholarly journals Computational Complexity Theory and the Philosophy of Mathematics†

2019 ◽  
Vol 27 (3) ◽  
pp. 381-439
Author(s):  
Walter Dean
Keyword(s):  
Computational Complexity ◽  
Computer Science ◽  
Complexity Theory ◽  
Philosophy Of Mathematics ◽  
Computability Theory ◽  
Computational Complexity Theory ◽  
Mathematical Problems ◽  
Np Problem

Abstract Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \mathbf{NP}$ problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof.

scholarly journals Incremental FPT Delay

Algorithms ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 122
Author(s):  
Arne Meier
Keyword(s):  
Computational Complexity ◽  
Complexity Theory ◽  
Complexity Classes ◽  
Computational Complexity Theory ◽  
Function Classes ◽  
Classical Setting ◽  
Classical Function ◽  
Multivalued Functions ◽  
Relationship Of ◽  
The Relationship

In this paper, we study the relationship of parameterized enumeration complexity classes defined by Creignou et al. (MFCS 2013). Specifically, we introduce two hierarchies (IncFPTa and CapIncFPTa) of enumeration complexity classes for incremental fpt-time in terms of exponent slices and show how they interleave. Furthermore, we define several parameterized function classes and, in particular, introduce the parameterized counterpart of the class of nondeterministic multivalued functions with values that are polynomially verifiable and guaranteed to exist, TFNP, known from Megiddo and Papadimitriou (TCS 1991). We show that this class TF(para-NP), the restriction of the function variant of NP to total functions, collapsing to F(FPT), the function variant of FPT, is equivalent to the result that OutputFPT coincides with IncFPT. In addition, these collapses are shown to be equivalent to TFNP = FP, and also equivalent to P equals NP intersected with coNP. Finally, we show that these two collapses are equivalent to the collapse of IncP and OutputP in the classical setting. These results are the first direct connections of collapses in parameterized enumeration complexity to collapses in classical enumeration complexity, parameterized function complexity, classical function complexity, and computational complexity theory.

Neural Dynamics of Rejection Sensitivity

2007 ◽  
Vol 19 (6) ◽  
pp. 945-956 ◽  
Author(s):  
Ethan Kross ◽  
Tobias Egner ◽  
Kevin Ochsner ◽  
Joy Hirsch ◽  
Geraldine Downey
Keyword(s):  
Cognitive Control ◽  
Emotional Processing ◽  
Rejection Sensitivity ◽  
Brain Regions ◽  
Anterior Cingulate ◽  
Self Report ◽  
Dorsal Anterior Cingulate Cortex ◽  
Affective Stimuli ◽  
Emotional Appraisal ◽  
Interest Level

Rejection sensitivity (RS) is the tendency to anxiously expect, readily perceive, and intensely react to rejection. This study used functional magnetic resonance imaging to explore whether individual differences in RS are mediated by differential recruitment of brain regions involved in emotional appraisal and/or cognitive control. High and low RS participants were scanned while viewing either representational paintings depicting themes of rejection and acceptance or nonrepresentational control paintings matched for positive or negative valence, arousal and interest level. Across all participants, rejection versus acceptance images activated regions of the brain involved in processing affective stimuli (posterior cingulate, insula), and cognitive control (dorsal anterior cingulate cortex; medial frontal cortex). Low and high RS individuals' responses to rejection versus acceptance images were not, however, identical. Low RS individuals displayed significantly more activity in left inferior and right dorsal frontal regions, and activity in these areas correlated negatively with participants' self-report distress ratings. In addition, control analyses revealed no effect of viewing negative versus positive images in any of the areas described above, suggesting that the aforementioned activations were involved in rejection-relevant processing rather than processing negatively valenced stimuli per se. Taken together, these findings suggest that responses in regions traditionally implicated in emotional processing and cognitive control are sensitive to rejection stimuli irrespective of RS, but that low RS individuals may activate prefrontal structures to regulate distress associated with viewing such images.

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