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1

Jukna, Stasys. Tropical Circuit Complexity. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-42354-3.

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2

Vollmer, Heribert. Introduction to Circuit Complexity. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03927-4.

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3

Håstad, Johan. Computational limitations of small-depth circuits. Cambridge, Mass: MIT Press, 1987.

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4

Vollmer, Heribert. Introduction to Circuit Complexity: A Uniform Approach. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999.

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5

Straubing, Howard. Finite Automata, Formal Logic, and Circuit Complexity. Boston, MA: Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-0289-9.

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6

Straubing, Howard. Finite automata, formal logic, and circuit complexity. Boston: Birkhäuser, 1994.

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7

Subramanian, Ashok. The computational complexity of the circuit value and network stability problems. Stanford, Calif: Dept. of Computer Science, Stanford University, 1990.

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8

Sridharan, K., B. Srinivasu, and Vikramkumar Pudi. Low-Complexity Arithmetic Circuit Design in Carbon Nanotube Field Effect Transistor Technology. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50699-5.

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9

IEEE, Conference on Computational Complexity (11th 1996 Philadelphia Penn ). Proceedings, Eleventh Annual IEEE Conference on Computational Complexity: May 24-27, 1996, Philadelphia, Pennsylvania. Los Alamitos, Calif: IEEE Computer Society Press, 1996.

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10

Myasnikov, Alexei G. Non-commutative cryptography and complexity of group-theoretic problems. Providence, R.I: American Mathematical Society, 2011.

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11

Haris, Skokos, ed. Complex Hamiltonian dynamics. Heidelberg: Springer, 2012.

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12

Sasao, Tsutomu. Representations of Discrete Functions. Boston, MA: Springer US, 1996.

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13

Deschamps, Jean-Pierre. Guide to FPGA Implementation of Arithmetic Functions. Dordrecht: Springer Netherlands, 2012.

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14

Keating, Michael. Simple art of SoC design: Closing the gap between RTL and ESL. New York: Springer, 2011.

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15

service), SpringerLink (Online, ed. Complex Time-Delay Systems: Theory and Applications. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2010.

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16

Braulio, García-Cámara, Prieto Manuel, Ruggiero Martino, Sicard Gilles, and SpringerLink (Online service), eds. Integrated Circuit and System Design. Power and Timing Modeling, Optimization, and Simulation: 21st International Workshop, PATMOS 2011, Madrid, Spain, September 26-29, 2011. Proceedings. Berlin, Heidelberg: Springer-Verlag GmbH Berlin Heidelberg, 2011.

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17

Järvisalo, Matti. Theory and Applications of Satisfiability Testing – SAT 2013: 16th International Conference, Helsinki, Finland, July 8-12, 2013. Proceedings. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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18

Rainer, Dahlhaus, ed. Mathematical methods in signal processing and digital image analysis. Berlin: Springer, 2008.

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19

International Conference Arithmetic, Geometry, Cryptography and Coding Theory (14th 2013 Marseille, France). Algorithmic arithmetic, geometry, and coding theory: 14th International Conference, Arithmetic, Geometry, Cryptography, and Coding Theory, June 3-7 2013, CIRM, Marseille, France. Edited by Ballet Stéphane 1971 editor, Perret, M. (Marc), 1963- editor, and Zaytsev, Alexey (Alexey I.), 1976- editor. Providence, Rhode Island: American Mathematical Society, 2015.

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20

Alta.) WIN (Conference) (2nd 2011 Banff. Women in Numbers 2: Research directions in number theory : BIRS Workshop, WIN2 - Women in Numbers 2, November 6-11, 2011, Banff International Research Station, Banff, Alberta, Canada. Edited by David Chantal 1964-, Lalín Matilde 1977-, and Manes Michelle 1970-. Providence, Rhode Island: American Mathematical Society, 2013.

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21

Leighton, Frank Thomson. Complexity Issues in VLSI. The MIT Press, 2003.

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22

Steele, Vaughn R., Vani Pariyadath, Rita Z. Goldstein, and Elliot A. Stein. Reward Circuitry and Drug Addiction. Edited by Dennis S. Charney, Eric J. Nestler, Pamela Sklar, and Joseph D. Buxbaum. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190681425.003.0044.

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Addiction is a complex neuropsychiatric syndrome related to dysregulation of brain systems including the mesocorticolimbic dopamine reward circuit. Dysregulation of reward circuitry is related to each of the three cyclical stages in the disease model of addiction: maintenance, abstinence, and relapse. Parsing reward circuitry is confounded due to the anatomical complexity of cortico-basal ganglia-thalamocortical loops, forward and backward projections within the circuit, and interactions between neurotransmitter systems. We begin by introducing the neurobiology of the reward system, specifically highlighting nodes of the circuit beyond the basal ganglia, followed by a review of the current literature on reward circuitry dysregulation in addiction. Finally, we discuss biomarkers of addiction identified with neuroimaging that could help guide neuroprediction models and development of targets for effective new interventions, such as noninvasive brain stimulation. The neurocircuitry of reward, especially non-prototypical nodes, may hold essential keys to understanding and treating addiction.
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23

Parberry, Ian. Circuit Complexity and Neural Networks. The MIT Press, 1994. http://dx.doi.org/10.7551/mitpress/1836.001.0001.

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24

Circuit complexity and neural networks. Cambridge, Mass: MIT Press, 1994.

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25

Parberry, Ian. Circuit Complexity and Neural Networks. MIT Press, 2018.

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26

Chaos and Complexity in Nonlinear Electronic Circuits. World Scientific Publishing Company, 1997.

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27

Ogorzalek, Maciej J. Chaos and Complexity in Nonlinear Electronic Circuits. World Scientific Publishing Co Pte Ltd, 1997.

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28

Chaos and Complexity in Nonlinear Electronic Circuits. World Scientific Publishing Co Pte Ltd, 1997.

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29

Kushilevitz, Eyal, and Noam Nisan. Communication Complexity. Cambridge University Press, 2011.

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30

Kushilevitz, Eyal, and Noam Nisan. Communication Complexity. Cambridge University Press, 2006.

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31

Kushilevitz, Eyal, and Noam Nisan. Communication Complexity. Cambridge University Press, 2009.

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32

Drechsler, Rolf, and Nabila Abdessaied. Reversible and Quantum Circuits: Optimization and Complexity Analysis. Springer International Publishing AG, 2016.

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33

Drechsler, Rolf, and Nabila Abdessaied. Reversible and Quantum Circuits: Optimization and Complexity Analysis. Springer London, Limited, 2016.

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34

Drechsler, Rolf, and Nabila Abdessaied. Reversible and Quantum Circuits: Optimization and Complexity Analysis. Springer, 2018.

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35

Straubing, Howard. Finite Automata, Formal Logic, and Circuit Complexity. Birkhauser Verlag, 2012.

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36

Finite Automata, Formal Logic, and Circuit Complexity. Birkhäuser Boston, 2012.

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37

Tropical Circuit Complexity: Limits of Pure Dynamic Programming. Springer International Publishing AG, 2023.

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38

Karchmer, Mauricio. Communication Complexity: A New Approach to Circuit Depth. The MIT Press, 1989.

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39

Communication complexity: A new approach to circuit depth. Cambridge, Mass: MIT Press, 1989.

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40

Lee, David. Contributions to information-based complexity, image understanding, and logic circuit design. 1986.

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41

Sridharan, K., Vikramkumar Pudi, and B. Srinivasu. Low-Complexity Arithmetic Circuit Design in Carbon Nanotube Field Effect Transistor Technology. Springer International Publishing AG, 2020.

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42

Sridharan, K., Vikramkumar Pudi, and B. Srinivasu. Low-Complexity Arithmetic Circuit Design in Carbon Nanotube Field Effect Transistor Technology. Springer International Publishing AG, 2021.

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43

Kuhn, Peter. Algorithms, complexity analysis and VLSI architectures for MPEG-4 motion estimation. 1999.

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44

Boolean Function Complexity Advances And Frontiers. Springer, 2012.

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45

Introduction to Circuit Complexity: A Uniform Approach (Texts in Theoretical Computer Science. An EATCS Series). Springer, 1999.

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46

Jukna, Stasys. Boolean Function Complexity: Advances and Frontiers (Algorithms and Combinatorics Book 27). Springer, 2012.

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47

Tee, Louis Y., and Guoping Feng. Mutant Mouse Models of OCD. Edited by Christopher Pittenger. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190228163.003.0033.

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Although mutant mouse models are unable to capture the subjective experiences and full complexity of psychiatric disorders, they have nonetheless provided important insights into the pathophysiology of various endophenotypes observed in neuropsychiatric illnesses. These mouse models enable the detailed dissection of cellular, molecular and circuit mechanisms that may underlie the abnormal behaviors observed in OCD, using methods that cannot be applied to human patients for ethical, practical and technical reasons. Mouse models exhibiting repetitive OCD-like behaviors, especially grooming, include the Sapap3-null (Sapap3-/-), Slitrk5-null (Slitrk5-/-), Hoxb8-null (Hoxb8-/-), and Shank3b-null (Shank3b-/-) mouse models. Evidence from these mice implicates a defect in cortico-striatal glutamatergic transmission in compulsive behavior. Moreover, studies using these mice have shown that this impaired cortico-striatal transmission is due to the aberrant expression of silent synapses. These mouse models support the hypothesis that defective glutamatergic neurotransmission in the cortico-striatal-thalamo-cortical circuit underlies OCD.
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48

Bountis, Tassos, and Haris Skokos. Complex Hamiltonian Dynamics. Springer Berlin / Heidelberg, 2014.

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49

Bountis, Tassos, and Haris Skokos. Complex Hamiltonian Dynamics. Springer, 2012.

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50

Paus, Tomáš. Combining brain imaging with brain stimulation: causality and connectivity. Edited by Charles M. Epstein, Eric M. Wassermann, and Ulf Ziemann. Oxford University Press, 2012. http://dx.doi.org/10.1093/oxfordhb/9780198568926.013.0034.

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This article establishes the concept of a methodological approach to combine brain imaging with brain stimulation. Transcranial magnetic stimulation (TMS) is a tool that allows perturbing neural activity, in time and space, in a noninvasive manner. This approach allows the study of the brain-behaviour relationship. Under certain circumstances, the influence of one region on other, called the effective connectivity, can be measured. Functional connectivity is the extent of correlation in brain activity measured across a number of spatially distinct brain regions. This tool of connectivity can be applied to any dataset acquired with brain-mapping tools. However, its interpretation is complex. Also, the technical complexity of the combined studies needs to be resolved. Future studies may benefit from focusing on neurochemical transmission in specific neural circuits and on temporal dynamics of cortico-cortical interactions.
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