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Artykuły w czasopismach na temat „Multilinear Depth 3 Circuits”

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Data publikacji: 6 września 2023

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1

Ghosal, Purnata, and B. V. Raghavendra Rao. "On Proving Parameterized Size Lower Bounds for Multilinear Algebraic Models." Fundamenta Informaticae 177, no. 1 (2020): 69–93. http://dx.doi.org/10.3233/fi-2020-1980.

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We consider the problem of obtaining parameterized lower bounds for the size of arithmetic circuits computing polynomials with the degree of the polynomial as the parameter. We consider the following special classes of multilinear algebraic branching programs: 1) Read Once Oblivious Branching Programs (ROABPs), 2) Strict interval branching programs, 3) Sum of read once formulas with restricted ordering. We obtain parameterized lower bounds (i.e., nΩ(t(k)) lower bound for some function t of k) on the size of the above models computing a multilinear polynomial that can be computed by a depth fou

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2

Saraf, Shubhangi, and Ilya Volkovich. "Black-Box Identity Testing of Depth-4 Multilinear Circuits." Combinatorica 38, no. 5 (2017): 1205–38. http://dx.doi.org/10.1007/s00493-016-3460-4.

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3

Raz, Ran, and Amir Yehudayoff. "Lower Bounds and Separations for Constant Depth Multilinear Circuits." computational complexity 18, no. 2 (2009): 171–207. http://dx.doi.org/10.1007/s00037-009-0270-8.

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4

Chillara, Suryajith. "On Computing Multilinear Polynomials Using Multi- r -ic Depth Four Circuits." ACM Transactions on Computation Theory 13, no. 3 (2021): 1–21. http://dx.doi.org/10.1145/3460952.

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In this article, we are interested in understanding the complexity of computing multilinear polynomials using depth four circuits in which the polynomial computed at every node has a bound on the individual degree of r ≥ 1 with respect to all its variables (referred to as multi- r -ic circuits). The goal of this study is to make progress towards proving superpolynomial lower bounds for general depth four circuits computing multilinear polynomials, by proving better bounds as the value of r increases. Recently, Kayal, Saha and Tavenas (Theory of Computing, 2018) showed that any depth four arith

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5

Karnin, Zohar S., Partha Mukhopadhyay, Amir Shpilka, and Ilya Volkovich. "Deterministic Identity Testing of Depth-4 Multilinear Circuits with Bounded Top Fan-in." SIAM Journal on Computing 42, no. 6 (2013): 2114–31. http://dx.doi.org/10.1137/110824516.

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6

Kayal, Neeraj, Vineet Nair, and Chandan Saha. "Separation Between Read-once Oblivious Algebraic Branching Programs (ROABPs) and Multilinear Depth-three Circuits." ACM Transactions on Computation Theory 12, no. 1 (2020): 1–27. http://dx.doi.org/10.1145/3369928.

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7

Gupta, Ankit, Pritish Kamath, Neeraj Kayal, and Ramprasad Saptharishi. "Arithmetic Circuits: A Chasm at Depth 3." SIAM Journal on Computing 45, no. 3 (2016): 1064–79. http://dx.doi.org/10.1137/140957123.

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8

Kayal, Neeraj, and Nitin Saxena. "Polynomial Identity Testing for Depth 3 Circuits." computational complexity 16, no. 2 (2007): 115–38. http://dx.doi.org/10.1007/s00037-007-0226-9.

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9

Fang, M., S. Fenner, F. Green, S. Homer, and Y. Zhang. "Quantum lower bounds for fanout." Quantum Information and Computation 6, no. 1 (2006): 46–57. http://dx.doi.org/10.26421/qic6.1-3.

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We consider the resource bounded quantum circuit model with circuits restricted by the number of qubits they act upon and by their depth. Focusing on natural universal sets of gates which are familiar from classical circuit theory, several new lower bounds for constant depth quantum circuits are proved. The main result is that parity (and hence fanout) requires log depth quantum circuits, when the circuits are composed of single qubit and arbitrary size Toffoli gates, and when they use only constantly many ancill\ae. Under this constraint, this bound is close to optimal. In the case of a non-c

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10

Lovett, Shachar, and Emanuele Viola. "Bounded-Depth Circuits Cannot Sample Good Codes." computational complexity 21, no. 2 (2012): 245–66. http://dx.doi.org/10.1007/s00037-012-0039-3.

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11

Boyar, Joan, Magnus Gausdal Find, and René Peralta. "Small low-depth circuits for cryptographic applications." Cryptography and Communications 11, no. 1 (2018): 109–27. http://dx.doi.org/10.1007/s12095-018-0296-3.

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12

Shpilka, A., and A. Wigderson. "Depth-3 arithmetic circuits over fields of characteristic zero." Computational Complexity 10, no. 1 (2001): 1–27. http://dx.doi.org/10.1007/pl00001609.

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13

Yan, P. Y., and I. Parberry. "Exponential Size Lower Bounds for Some Depth 3 Circuits." Information and Computation 112, no. 1 (1994): 117–30. http://dx.doi.org/10.1006/inco.1994.1054.

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14

Shpilka, Amir. "Interpolation of Depth-3 Arithmetic Circuits with Two Multiplication Gates." SIAM Journal on Computing 38, no. 6 (2009): 2130–61. http://dx.doi.org/10.1137/070694879.

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15

Kumar, Mrinal. "On the Power of Border of Depth-3 Arithmetic Circuits." ACM Transactions on Computation Theory 12, no. 1 (2020): 1–8. http://dx.doi.org/10.1145/3371506.

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16

Wolfovitz, Guy. "The complexity of depth-3 circuits computing symmetric Boolean functions." Information Processing Letters 100, no. 2 (2006): 41–46. http://dx.doi.org/10.1016/j.ipl.2006.06.008.

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17

Agrawal, Manindra, Chandan Saha, Ramprasad Saptharishi, and Nitin Saxena. "Jacobian Hits Circuits: Hitting Sets, Lower Bounds for Depth-$D$ Occur-$k$ Formulas and Depth-3 Transcendence Degree-$k$ Circuits." SIAM Journal on Computing 45, no. 4 (2016): 1533–62. http://dx.doi.org/10.1137/130910725.

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18

Albrecht, A., E. Hein, D. Melzer, K. Steinhöfel, M. Taupitz, and C. K. Wong. "Liver tissue classification by bounded-depth threshold circuits." International Congress Series 1230 (June 2001): 1156–57. http://dx.doi.org/10.1016/s0531-5131(01)00202-3.

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19

Fagin, Ronald, Maria M. Klawe, Nicholas J. Pippenger, and Larry Stockmeyer. "Bounded-depth, polynomial-size circuits for symmetric functions." Theoretical Computer Science 36 (1985): 239–50. http://dx.doi.org/10.1016/0304-3975(85)90045-3.

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20

Green, F., S. Homer, C. Moore, and C. Pollett. "Counting, fanout and the complexity of quantum ACC." Quantum Information and Computation 2, no. 1 (2002): 35–65. http://dx.doi.org/10.26421/qic2.1-3.

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We propose definitions of QAC^0, the quantum analog of the classical class AC^0 of constant-depth circuits with AND and OR gates of arbitrary fan-in, and QACC[q], the analog of the class ACC[q] where Mod_q gates are also allowed. We prove that parity or fanout allows us to construct quantum MOD_q gates in constant depth for any q, so QACC[2] = QACC. More generally, we show that for any q,p > 1, MOD_q is equivalent to MOD_p (up to constant depth and polynomial size). This implies that QAC^0 with unbounded fanout gates, denoted QACwf^0, is the same as QACC[q] and QACC for all q. Since \ACC[p]

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21

Brustmann, Bettina, and Ingo Wegener. "The complexity of symmetric functions in bounded-depth circuits." Information Processing Letters 25, no. 4 (1987): 217–19. http://dx.doi.org/10.1016/0020-0190(87)90163-3.

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22

Grolmusz, Vince. "A lower bound for depth-3 circuits with MOD m gates." Information Processing Letters 67, no. 2 (1998): 87–90. http://dx.doi.org/10.1016/s0020-0190(98)00093-3.

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23

Sergeev, Igor' S. "On the complexity of bounded-depth circuits and formulas over the basis of fan-in gates." Discrete Mathematics and Applications 29, no. 4 (2019): 241–54. http://dx.doi.org/10.1515/dma-2019-0022.

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Abstract We obtain estimates for the complexity of the implementation of n-place Boolean functions by circuits and formulas built of unbounded fan-in conjunction and disjunction gates and either negation gates or negations of variables as inputs. Restrictions on the depth of circuits and formulas are imposed. In a number of cases, the estimates obtained in the paper are shown to be asymptotically sharp. In particular, for the complexity of circuits with variables and their negations on inputs, the Shannon function is asymptotically estimated as $2\cdot {{2}^{n/2}};$this estimate is attained on

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24

Allender, Eric, V. Arvind, Rahul Santhanam, and Fengming Wang. "Uniform derandomization from pathetic lower bounds." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1971 (2012): 3512–35. http://dx.doi.org/10.1098/rsta.2011.0318.

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The notion of probabilistic computation dates back at least to Turing, who also wrestled with the practical problems of how to implement probabilistic algorithms on machines with, at best, very limited access to randomness. A more recent line of research, known as derandomization, studies the extent to which randomness is superfluous. A recurring theme in the literature on derandomization is that probabilistic algorithms can be simulated quickly by deterministic algorithms, if one can obtain impressive (i.e. superpolynomial, or even nearly exponential) circuit size lower bounds for certain pro

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25

Lai, Wenxing. "The Inapproximability of k-DominatingSet for Parameterized AC 0 Circuits †." Algorithms 12, no. 11 (2019): 230. http://dx.doi.org/10.3390/a12110230.

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Chen and Flum showed that any FPT-approximation of the k-Clique problem is not in para- AC 0 and the k-DominatingSet (k-DomSet) problem could not be computed by para- AC 0 circuits. It is natural to ask whether the f ( k ) -approximation of the k-DomSet problem is in para- AC 0 for some computable function f. Very recently it was proved that assuming W [ 1 ] ≠ FPT , the k-DomSet problem cannot be f ( k ) -approximated by FPT algorithms for any computable function f by S., Laekhanukit and Manurangsi and Lin, seperately. We observe that the constructions used in Lin’s work can be carried out usi

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26

Kulikov, Alexander S., and Vladimir V. Podolskii. "Computing Majority by Constant Depth Majority Circuits with Low Fan-in Gates." Theory of Computing Systems 63, no. 5 (2018): 956–86. http://dx.doi.org/10.1007/s00224-018-9900-3.

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27

Cai, Jin-yi. "Lower bounds for constant-depth circuits in the presence of help bits." Information Processing Letters 36, no. 2 (1990): 79–83. http://dx.doi.org/10.1016/0020-0190(90)90101-3.

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28

Dvir, Zeev, and Amir Shpilka. "Locally Decodable Codes with Two Queries and Polynomial Identity Testing for Depth 3 Circuits." SIAM Journal on Computing 36, no. 5 (2007): 1404–34. http://dx.doi.org/10.1137/05063605x.

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29

Jukna, Stasys. "Computing threshold functions by depth-3 threshold circuits with smaller thresholds of their gates." Information Processing Letters 56, no. 3 (1995): 147–50. http://dx.doi.org/10.1016/0020-0190(95)00137-2.

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30

Saxena, Nitin, and C. Seshadhri. "Blackbox Identity Testing for Bounded Top-Fanin Depth-3 Circuits: The Field Doesn't Matter." SIAM Journal on Computing 41, no. 5 (2012): 1285–98. http://dx.doi.org/10.1137/10848232.

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31

Ni, Xiaotong, and Maarten van den Nest. "Commuting quantum circuits: efficiently classical simulations versus hardness results." Quantum Information and Computation 13, no. 1&2 (2013): 54–72. http://dx.doi.org/10.26421/qic13.1-2-5.

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The study of quantum circuits composed of commuting gates is particularly useful to understand the delicate boundary between quantum and classical computation. Indeed, while being a restricted class, commuting circuits exhibit genuine quantum effects such as entanglement. In this paper we show that the computational power of commuting circuits exhibits a surprisingly rich structure. First we show that every 2-local commuting circuit acting on $d$-level systems and followed by single-qudit measurements can be efficiently simulated classically with high accuracy. In contrast, we prove that such

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32

Grigoriev, D., and A. Razborov. "Exponential Lower Bounds for Depth 3 Arithmetic Circuits in Algebras of Functions over Finite Fields." Applicable Algebra in Engineering, Communication and Computing 10, no. 6 (2000): 465–87. http://dx.doi.org/10.1007/s002009900021.

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33

Uchizawa, Kei, Rodney Douglas, and Wolfgang Maass. "On the Computational Power of Threshold Circuits with Sparse Activity." Neural Computation 18, no. 12 (2006): 2994–3008. http://dx.doi.org/10.1162/neco.2006.18.12.2994.

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Circuits composed of threshold gates (McCulloch-Pitts neurons, or perceptrons) are simplified models of neural circuits with the advantage that they are theoretically more tractable than their biological counterparts. However, when such threshold circuits are designed to perform a specific computational task, they usually differ in one important respect from computations in the brain: they require very high activity. On average every second threshold gate fires (sets a 1 as output) during a computation. By contrast, the activity of neurons in the brain is much sparser, with only about 1% of ne

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34

Dövencioğlu, Dicle, Hiroshi Ban, Andrew J. Schofield, and Andrew E. Welchman. "Perceptual Integration for Qualitatively Different 3-D Cues in the Human Brain." Journal of Cognitive Neuroscience 25, no. 9 (2013): 1527–41. http://dx.doi.org/10.1162/jocn_a_00417.

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The visual system's flexibility in estimating depth is remarkable: We readily perceive 3-D structure under diverse conditions from the seemingly random dots of a “magic eye” stereogram to the aesthetically beautiful, but obviously flat, canvasses of the Old Masters. Yet, 3-D perception is often enhanced when different cues specify the same depth. This perceptual process is understood as Bayesian inference that improves sensory estimates. Despite considerable behavioral support for this theory, insights into the cortical circuits involved are limited. Moreover, extant work tested quantitatively

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35

Karnin, Zohar S., and Amir Shpilka. "Black box polynomial identity testing of generalized depth-3 arithmetic circuits with bounded top fan-in." Combinatorica 31, no. 3 (2011): 333–64. http://dx.doi.org/10.1007/s00493-011-2537-3.

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36

Bun, Mark, Robin Kothari, and Justin Thaler. "Quantum algorithms and approximating polynomials for composed functions with shared inputs." Quantum 5 (September 16, 2021): 543. http://dx.doi.org/10.22331/q-2021-09-16-543.

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We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let f be an m-bit Boolean function and consider an n-bit function F obtained by applying f to conjunctions of possibly overlapping subsets of n variables. If f has quantum query complexity Q(f), we give an algorithm for evaluating F using O~(Q(f)⋅n) quantum queries. This improves on the bound of O(Q(f)⋅n) that follows by treating each conjunction independently, and our bound is tight for worst-case choices of f. Using completely different techniques, we prove a similar tight

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37

Amin, Kazi Rafsanjani, Carine Ladner, Guillaume Jourdan, Sébastien Hentz, Nicolas Roch, and Julien Renard. "Loss mechanisms in TiN high impedance superconducting microwave circuits." Applied Physics Letters 120, no. 16 (2022): 164001. http://dx.doi.org/10.1063/5.0086019.

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Aluminum-based platforms have allowed to reach major milestones for superconducting quantum circuits. For the next generation of devices, materials that are able to maintain low microwave losses while providing new functionalities, such as large kinetic inductance or compatibility with CMOS platform, are needed. Here, we report on a combined direct current and microwave investigation of titanium nitride films of different thicknesses grown using CMOS compatible methods. For microwave resonators made of 3 nm thick TiN, we measured large kinetic inductance [Formula: see text] pH/sq, high mode im

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38

Romano, A., J. Vanhellemont, A. De Keersgieter, W. Vandervorst, J. R. Morante, and J. Van Landuyt. "A novel TEM technique for junction delineation in integrated circuits." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 4 (1990): 748–49. http://dx.doi.org/10.1017/s0424820100176873.

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Ion implantation is a well established technique to dope selectively prespecified regions of silicon substrates. It has the drawback that a thermal treatment is required to activate the dopant and to reconstruct the crystal lattice. This leads to dopant diffusion in depth and also laterally, when the implantation has been preformed through a patterned mask.In this paper two different approaches to determine the doping profile using chemical etching and TEM are presented. Cross-section specimens are prepared using a technique described elsewhere, followed by preferential etching.The first appro

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39

Yetiş, Hasan, and Mehmet Karaköse. "A New Framework Containing Convolution and Pooling Circuits for Image Processing and Deep Learning Applications with Quantum Computing Implementation." Traitement du Signal 39, no. 2 (2022): 501–12. http://dx.doi.org/10.18280/ts.390212.

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The resource need for deep learning and quantum computers' high computing power potential encourage collaboration between the two fields. Today, variational quantum circuits are used to perform the convolution operation with quantum computing. However, the results produced by variational circuits do not show a direct resemblance to the classical convolution operation. Because classical data is encoded into quantum data with their exact values in value-encoded methods, in contrast to variational quantum circuits, arithmetical operations can be applied with high accuracy. In this study, value-en

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40

Asadpour, Ailin, Amir Sabbagh Molahosseini, and Azadeh Alsadat Emrani Zarandi. "The use of reversible logic gates in the design of residue number systems." International Journal of Electrical and Computer Engineering (IJECE) 13, no. 2 (2023): 2009. http://dx.doi.org/10.11591/ijece.v13i2.pp2009-2022.

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Reversible computing is an emerging technique to achieve ultra-low-power circuits. Reversible arithmetic circuits allow for achieving energy-efficient high-performance computational systems. Residue number systems (RNS) provide parallel and fault-tolerant additions and multiplications without carry propagation between residue digits. The parallelism and fault-tolerance features of RNS can be leveraged to achieve high-performance reversible computing. This paper proposed RNS full reversible circuits, including forward converters, modular adders and multipliers, and reverse converters used for a

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41

Kim and Choi. "Indirect Time-of-Flight Depth Sensor with Two-Step Comparison Scheme for Depth Frame Difference Detection." Sensors 19, no. 17 (2019): 3674. http://dx.doi.org/10.3390/s19173674.

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A depth sensor with integrated frame difference detection is proposed. Instead of frame difference detection using light intensity, which is vulnerable to ambient light, the difference in depth between successive frames can be acquired. Because the conventional time-of-flight depth sensor requires two frames of depth-image acquisition with four-phase modulation, it has large power consumption, as well as a large area for external frame memories. Therefore, we propose a simple two-step comparison scheme for generating the depth frame difference in a single frame. With the proposed scheme, only

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42

Prihozhy, Anatoly A. "Synthesis of quantum circuits based on incompletely specified functions and if-decision diagrams." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (December 14, 2021): 84–97. http://dx.doi.org/10.33581/2520-6508-2021-3-84-97.

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The problem of synthesis and optimisation of logical reversible and quantum circuits from functional descriptions represented as decision diagrams is considered. It is one of the key problems being solved with the aim of creating quantum computing technology and quantum computers. A new method of stepwise transformation of the initial functional specification to a quantum circuit is proposed, which provides for the following project states: reduced ordered binary decision diagram, if-decision diagram, functional if-decision diagram, reversible circuit and quantum circuit. The novelty of the me

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43

Emelyanov, V. V. "Passivation of a Conductive System of Integrated Circuits with a Layer of Aluminum Nitride." Doklady BGUIR 21, no. 3 (2023): 12–16. http://dx.doi.org/10.35596/1729-7648-2023-21-3-12-16.

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Passivation of the film conductive system of integrated circuits makes it more reliable by increasing the resistance to electromigration. The problem of manufacturing a passivating layer on the formed current-conducting system of an integrated circuit, obtained in a single technological cycle, including isotropic plasma-chemical etching of an aluminum alloy layer to a depth of 8–12 nm and isotropic plasma-chemical nitriding of the surface of the obtained current-carrying tracks until the aluminum nitride thickness from 10 to 50 nm, is considered. This task makes it possible to form a dielectri

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44

Yin, Yue-Xin, Xiao-Jie Yin, Xiao-Pei Zhang, et al. "High-Q-Factor Silica-Based Racetrack Microring Resonators." Photonics 8, no. 2 (2021): 43. http://dx.doi.org/10.3390/photonics8020043.

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In this paper, ultrahigh-Q factor racetrack microring resonators (MRRs) are demonstrated based on silica planar lightwave circuits (PLCs) platform. A loaded ultrahigh-Q factor Qload of 1.83 × 106 is obtained. The MRRs are packaged with fiber-to-fiber loss of ~5 dB. A notch depth of 3 dB and ~137 pm FSR are observed. These MRRs show great potential in optical communications as filters. Moreover, the devices are suitable used in monolithic integration and hybrid integration with other devices, especially in external cavity lasers (ECLs) to realize ultranarrow linewidths.

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45

Aslantas, Kubilay, Şükrü Ülker, Ömer Şahan, Danil Yu Pimenov, and Khaled Giasin. "Mechanistic modeling of cutting forces in high-speed microturning of titanium alloy with consideration of nose radius." International Journal of Advanced Manufacturing Technology 119, no. 3-4 (2021): 2393–408. http://dx.doi.org/10.1007/s00170-021-08437-w.

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AbstractMicroturning is a micromechanical machining process used to produce microcylindrical or axially symmetrical parts. Microcylindrical parts are mainly used in microfluidic systems, intravenous micromotors, microsurgical applications, optical lens applications, and microinjection systems. The workpiece diameter is very small in microturning and therefore is greatly affected by the cutting forces. For this reason, it is important to predict the cutting forces when machining miniature parts. In this study, an analytical mechanistic model of microturning is used to predict the cutting forces

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46

Simko, Steven J., and Richard A. Waldo. "Multitechnique problem solving using EDS/EPMA and surface analysis." Proceedings, annual meeting, Electron Microscopy Society of America 50, no. 2 (1992): 1782–83. http://dx.doi.org/10.1017/s0424820100133540.

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Thin films are used in a wide range of modern technologies. Examples include sensors, antiwear coatings, optical coatings, and integrated circuits. A variety of methods have evolved for characterizing thin films in the thickness range of 1 monolayer to several micrometers. Electron probe microanalysis (EPMA) or energy dispersive x-ray spectroscopy (EDS) are two methods for characterizing thicker films (>1 μm). In these techniques, the sampling depth depends on the penetration depth of the primary electron beam which can be controlled by changing the electron beam energy. Thin films can also

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47

Weisse, Julietta, Heinz Mitlehner, Lothar Frey, and Tobias Erlbacher. "Design of a 4H-SiC RESURF n-LDMOS Transistor for High Voltage Integrated Circuits." Materials Science Forum 963 (July 2019): 629–32. http://dx.doi.org/10.4028/www.scientific.net/msf.963.629.

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In this work, a lateral 4H-SiC n-LDMOS transistor, based on the principle of a reduced surface field due to charge compensation, is investigated by numerical simulations, in order to find adequate fabrication parameters for a lightly doped p-type epitaxy in combination with a higher doped channel region. The purpose of this work is the integration into an existing technology for a 10 V 4H-SiC-CMOS process. The simulations predict in a blocking voltage of 1.3 kV in combination with an On-resistance of 17 mΩcm2 for a device with a RESURF structure with a total implanted Al concentration of 6∙101

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TAYARI, MAHSHID, and MOHAMMAD ESHGHI. "DESIGN OF 3-INPUT REVERSIBLE PROGRAMMABLE LOGIC ARRAY." Journal of Circuits, Systems and Computers 20, no. 02 (2011): 283–97. http://dx.doi.org/10.1142/s0218126611007256.

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In this paper, for the first time a design for a Reversible Programmable Logic Array (RPLA) is introduced. This is the first RPLA design because the reversible PLA design, presented in previous research, is not a programmable circuit. In our presented RPLAs, four reversible AND array designs with different specifications are proposed. A reversible OR array, which can be programmed to generate any Boolean function, is also designed. This reversible and programmable OR array is also cascadable. That is, it produces a copy of inputted midterms at its outputs to be fed to another OR array in order

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Theys, Tom, Pierpaolo Pani, Johannes van Loon, Jan Goffin, and Peter Janssen. "Three-dimensional Shape Coding in Grasping Circuits: A Comparison between the Anterior Intraparietal Area and Ventral Premotor Area F5a." Journal of Cognitive Neuroscience 25, no. 3 (2013): 352–64. http://dx.doi.org/10.1162/jocn_a_00332.

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Depth information is necessary for adjusting the hand to the three-dimensional (3-D) shape of an object to grasp it. The transformation of visual information into appropriate distal motor commands is critically dependent on the anterior intraparietal area (AIP) and the ventral premotor cortex (area F5), particularly the F5p sector. Recent studies have demonstrated that both AIP and the F5a sector of the ventral premotor cortex contain neurons that respond selectively to disparity-defined 3-D shape. To investigate the neural coding of 3-D shape and the behavioral role of 3-D shape-selective neu

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Kim, Dongyung. "An Optimized Discrete Data Classification Method in N -Dimensional." Computational and Mathematical Methods 2022 (May 28, 2022): 1–8. http://dx.doi.org/10.1155/2022/8199872.

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We propose a discrete data classification method of scattered data in N -dimensional by solving the minimax problem for a set of points. The current research is extended from 2-dimensional and 3-dimensional to N -dimensional. The problem can be applied to artificial intelligence classification problems (machine learning, deep learning), point data analysis problems (data science problem), the optimized design of nanoscale circuits, and the location of facility problems, circle detection on 2D image, or sphere detection on depth image. We generalized the discrete data classification methodology

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