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Journal articles on the topic 'Discrete descent'

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Published: 30 May 2022
Last updated: 31 May 2022

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1

Sobral, Manuela. "Descent for Discrete (Co)fibrations." Applied Categorical Structures 12, no. 5/6 (October 2004): 527–35. http://dx.doi.org/10.1023/b:apcs.0000049316.87223.a4.

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2

CASTRO, CARLOS, FRANCISCO PALACIOS, and ENRIQUE ZUAZUA. "AN ALTERNATING DESCENT METHOD FOR THE OPTIMAL CONTROL OF THE INVISCID BURGERS EQUATION IN THE PRESENCE OF SHOCKS." Mathematical Models and Methods in Applied Sciences 18, no. 03 (March 2008): 369–416. http://dx.doi.org/10.1142/s0218202508002723.

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We introduce a new optimization strategy to compute numerical approximations of minimizers for optimal control problems governed by scalar conservation laws in the presence of shocks. We focus on the 1 - d inviscid Burgers equation. We first prove the existence of minimizers and, by a Γ-convergence argument, the convergence of discrete minima obtained by means of numerical approximation schemes satisfying the so-called one-sided Lipschitz condition (OSLC). Then we address the problem of developing efficient descent algorithms. We first consider and compare the existing two possible approaches: the so-called discrete approach, based on a direct computation of gradients in the discrete problem and the so-called continuous one, where the discrete descent direction is obtained as a discrete copy of the continuous one. When optimal solutions have shock discontinuities, both approaches produce highly oscillating minimizing sequences and the effective descent rate is very weak. As a solution we propose a new method, that we shall call alternating descent method, that uses the recent developments of generalized tangent vectors and the linearization around discontinuous solutions. This method distinguishes and alternates the descent directions that move the shock and those that perturb the profile of the solution away of it producing very efficient and fast descent algorithms.
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3

Carlson, David, Ya-Ping Hsieh, Edo Collins, Lawrence Carin, and Volkan Cevher. "Stochastic Spectral Descent for Discrete Graphical Models." IEEE Journal of Selected Topics in Signal Processing 10, no. 2 (March 2016): 296–311. http://dx.doi.org/10.1109/jstsp.2015.2505684.

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4

Diaz-Lopez, Alexander, Pamela E. Harris, Erik Insko, Mohamed Omar, and Bruce E. Sagan. "Descent polynomials." Discrete Mathematics 342, no. 6 (June 2019): 1674–86. http://dx.doi.org/10.1016/j.disc.2019.01.034.

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5

DAIDZIC, Nihad E. "An algebraic model of high-altitude aircraft decompression and emergency descent." Aviation 21, no. 3 (August 3, 2018): 92–101. http://dx.doi.org/10.3846/16487788.2017.1380081.

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An emergency descent maneuver initiated by pilots shortly after the onset of the decompression recognition was developed for subsonic, supersonic and hypersonic cruisers. Among other findings, the times when a passenger cabin is exposed to altitudes above 25,000 and 40,000 ft and the maximum cabin altitude reached are estimated. An airplane descent aerodynamic model was incorporated for high-speed and low-speed high-drag emergency descents. Airplane cabin atmosphere is assumed to be isothermal. The environmental atmosphere is simulated using the NLPAM nonlinear atmospheric model valid up to 47 geopotential kilometers. Rapid and slow decompressions at several discrete cruising altitudes ranging from 12 to 40 km and varying pilot reaction times in initiating the emergency descent were simulated. The main motivation for this work was to estimate times and altitudes a cabin reaches during depressurization for various flight conditions. This model can be utilized in optimizing the emergency-descent piloting techniques, calculating oxygen supplies, evaluating aeromedical factors, estimating harmful exposures to low pressures, and for other important high-altitude aircraft operations.
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6

Ehrenborg, Richard, and Swapneel Mahajan. "Maximizing the descent statistic." Annals of Combinatorics 2, no. 2 (June 1998): 111–29. http://dx.doi.org/10.1007/bf01608482.

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7

Mahavier, W. T. "A convergence result for discreet steepest decent in weighted sobolev spaces." Abstract and Applied Analysis 2, no. 1-2 (1997): 67–72. http://dx.doi.org/10.1155/s1085337597000274.

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A convergence result is given for discrete descent based on Sobolev gradients arising from differential equations which may be expressed as quadratic forms. The argument is an extension of the result of David G. Luenberger on Euclidean descent and compliments the work of John W. Neuberger on Sobolev descent.
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8

Ng, Chi-Kong, Duan Li, and Lian-Sheng Zhang. "Discrete global descent method for discrete global optimization and nonlinear integer programming." Journal of Global Optimization 37, no. 3 (August 17, 2006): 357–79. http://dx.doi.org/10.1007/s10898-006-9053-9.

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9

Murota, Kazuo. "On Steepest Descent Algorithms for Discrete Convex Functions." SIAM Journal on Optimization 14, no. 3 (January 2004): 699–707. http://dx.doi.org/10.1137/s1052623402419005.

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10

Yang, Yong-jian, and Lian-sheng Zhang. "A gradually descent method for discrete global optimization." Journal of Shanghai University (English Edition) 11, no. 1 (February 2007): 39–44. http://dx.doi.org/10.1007/s11741-007-0106-1.

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11

Ehrenborg, Richard, and N. Bradley Fox. "The descent set polynomial revisited." European Journal of Combinatorics 51 (January 2016): 47–68. http://dx.doi.org/10.1016/j.ejc.2015.03.027.

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12

Novelli, Jean-Christophe, and Jean-Yves Thibon. "Parking Functions and Descent Algebras." Annals of Combinatorics 11, no. 1 (April 2007): 59–68. http://dx.doi.org/10.1007/s00026-007-0305-2.

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13

Mehdi Fateh, Mohammad, Siamak Azargoshasb, and Saeed Khorashadizadeh. "Model-free discrete control for robot manipulators using a fuzzy estimator." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 33, no. 3 (April 29, 2014): 1051–67. http://dx.doi.org/10.1108/compel-05-2013-0185.

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Purpose – Discrete control of robot manipulators with uncertain model is the purpose of this paper. Design/methodology/approach – The proposed control design is model-free by employing an adaptive fuzzy estimator in the controller for the estimation of uncertainty as unknown function. An adaptive mechanism is proposed in order to overcome uncertainties. Parameters of the fuzzy estimator are adapted to minimize the estimation error using a gradient descent algorithm. Findings – The proposed model-free discrete control is robust against all uncertainties associated with the model of robotic system including the robot manipulator and actuators, and external disturbances. Stability analysis verifies the proposed control approach. Simulation results show its efficiency in the tracking control. Originality/value – A novel model-free discrete control approach for electrically driven robot manipulators is proposed. An adaptive fuzzy estimator is used in the controller to overcome uncertainties. The parameters of the estimator are regulated by a gradient descent algorithm. The most gradient descent algorithms have used a known cost function based on the tracking error for adaptation whereas the proposed gradient descent algorithm uses a cost function based on the uncertainty estimation error. Then, the uncertainty estimation error is calculated from the joint position error and its derivative using the closed-loop system.
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14

Galbraith, Steven D. "Weil Descent Of Jacobians." Electronic Notes in Discrete Mathematics 6 (April 2001): 459–68. http://dx.doi.org/10.1016/s1571-0653(04)00198-2.

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15

Galbraith, Steven D. "Weil descent of Jacobians." Discrete Applied Mathematics 128, no. 1 (May 2003): 165–80. http://dx.doi.org/10.1016/s0166-218x(02)00443-2.

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16

Ehrenborg, Richard, and Alex Happ. "The Boustrophedon Transform for Descent Polytopes." Annals of Combinatorics 23, no. 1 (February 12, 2019): 67–72. http://dx.doi.org/10.1007/s00026-019-00422-1.

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17

Weixiang Wang, Youlin Shang, and Shenhua Gui. "Application of Global Descent Function Method to Discrete Global Optimization." INTERNATIONAL JOURNAL ON Advances in Information Sciences and Service Sciences 5, no. 7 (April 15, 2013): 684–91. http://dx.doi.org/10.4156/aiss.vol5.issue7.80.

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18

Smorodin, A. "THE USE OF CONTROL THEORY METHODS IN TRAINING NEURAL NETWORKS ON THE EXAMPLE OF TEETH RECOGNITION ON PANORAMIC X-RAY IMAGES." Automation of technological and business processes 13, no. 2 (August 2, 2021): 36–40. http://dx.doi.org/10.15673/atbp.v13i2.2055.

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The article investigated a modification of stochastic gradient descent (SGD), based on the previously developed stabilization theory of discrete dynamical system cycles. Relation between stabilization of cycles in discrete dynamical systems and finding extremum points allowed us to apply new control methods to accelerate gradient descent when approaching local minima. Gradient descent is often used in training deep neural networks on a par with other iterative methods. Two gradient SGD and Adam were experimented, and we conducted comparative experiments. All experiments were conducted during solving a practical problem of teeth recognition on 2-D panoramic images. Network training showed that the new method outperforms the SGD in its capabilities and as for parameters chosen it approaches the capabilities of Adam, which is a “state of the art” method. Thus, practical utility of using control theory in the training of deep neural networks and possibility of expanding its applicability in the process of creating new algorithms in this important field are shown.
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19

Gadetsky, Artyom, Kirill Struminsky, Christopher Robinson, Novi Quadrianto, and Dmitry Vetrov. "Low-Variance Black-Box Gradient Estimates for the Plackett-Luce Distribution." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 06 (April 3, 2020): 10126–35. http://dx.doi.org/10.1609/aaai.v34i06.6572.

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Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradient estimates. Modern variance reduction techniques mostly consider categorical distributions and have limited applicability when the number of possible outcomes becomes large. In this work, we consider models with latent permutations and propose control variates for the Plackett-Luce distribution. In particular, the control variates allow us to optimize black-box functions over permutations using stochastic gradient descent. To illustrate the approach, we consider a variety of causal structure learning tasks for continuous and discrete data. We show that our method outperforms competitive relaxation-based optimization methods and is also applicable to non-differentiable score functions.
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20

Fu, Shishuo, Zhicong Lin, and Jiang Zeng. "On two unimodal descent polynomials." Discrete Mathematics 341, no. 9 (September 2018): 2616–26. http://dx.doi.org/10.1016/j.disc.2018.06.010.

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21

Sorokin, Stepan. "Feedback Optimality Condition for Nonconvex Discrete Linear-Quadratic Optimal Control Problem." System Analysis & Mathematical Modeling 3, no. 3 (December 16, 2021): 169–75. http://dx.doi.org/10.17150/2713-1734.2021.8(3).169-175.

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The paper analyzed a non-convex linear-quadratic optimization problem in a discrete dynamic system. We obtained necessary optimality condition with feedback controls which allow a descent of the functional cost. Such controls are generated by the quadratic majorant of the cost. In contrast to the discrete maximum principle, this condition does not require any convexity properties of the problem.
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22

Brändén, Petter. "Actions on permutations and unimodality of descent polynomials." European Journal of Combinatorics 29, no. 2 (February 2008): 514–31. http://dx.doi.org/10.1016/j.ejc.2006.12.010.

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23

Chung, Fan, Anders Claesson, Mark Dukes, and Ronald Graham. "Descent polynomials for permutations with bounded drop size." European Journal of Combinatorics 31, no. 7 (October 2010): 1853–67. http://dx.doi.org/10.1016/j.ejc.2010.01.011.

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24

Hyatt, Matthew. "Descent polynomials forkbubble-sortable permutations of type B." European Journal of Combinatorics 34, no. 7 (October 2013): 1177–91. http://dx.doi.org/10.1016/j.ejc.2013.04.006.

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25

Grady, Amy, and Svetlana Poznanović. "Tree Descent Polynomials: Unimodality and Central Limit Theorem." Annals of Combinatorics 24, no. 1 (January 16, 2020): 109–17. http://dx.doi.org/10.1007/s00026-019-00484-1.

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26

Gaetz, Christian, and Yibo Gao. "On q-analogs of descent and peak polynomials." European Journal of Combinatorics 97 (October 2021): 103397. http://dx.doi.org/10.1016/j.ejc.2021.103397.

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27

Bencs, Ferenc. "Some coefficient sequences related to the descent polynomial." European Journal of Combinatorics 98 (December 2021): 103396. http://dx.doi.org/10.1016/j.ejc.2021.103396.

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28

Renner, Lex E. "Descent systems for Bruhat posets." Journal of Algebraic Combinatorics 29, no. 4 (May 29, 2008): 413–35. http://dx.doi.org/10.1007/s10801-008-0141-4.

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29

Brown, David A., and Siva Nadarajah. "Inexactly constrained discrete adjoint approach for steepest descent-based optimization algorithms." Numerical Algorithms 78, no. 3 (September 7, 2017): 983–1000. http://dx.doi.org/10.1007/s11075-017-0409-7.

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30

Zhang, Cun-Hui. "Continuous Generalized Gradient Descent." Journal of Computational and Graphical Statistics 16, no. 4 (December 2007): 761–81. http://dx.doi.org/10.1198/106186007x238846.

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31

Kousidis, Stavros, and Andreas Wiemers. "On the first fall degree of summation polynomials." Journal of Mathematical Cryptology 13, no. 3-4 (October 1, 2019): 229–37. http://dx.doi.org/10.1515/jmc-2017-0022.

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Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.
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32

Ehrenborg, Richard, and N. Bradley Fox. "The signed descent set polynomial revisited." Discrete Mathematics 339, no. 9 (September 2016): 2263–66. http://dx.doi.org/10.1016/j.disc.2016.03.023.

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33

Baril, Jean-Luc, and Sergey Kirgizov. "The pure descent statistic on permutations." Discrete Mathematics 340, no. 10 (October 2017): 2550–58. http://dx.doi.org/10.1016/j.disc.2017.06.005.

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34

Barnabei, Marilena, Flavio Bonetti, and Matteo Silimbani. "The descent statistic on involutions is not log-concave." European Journal of Combinatorics 30, no. 1 (January 2009): 11–16. http://dx.doi.org/10.1016/j.ejc.2008.03.003.

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35

Novelli, Jean-Christophe, Christophe Reutenauer, and Jean-Yves Thibon. "Generalized descent patterns in permutations and associated Hopf algebras." European Journal of Combinatorics 32, no. 4 (May 2011): 618–27. http://dx.doi.org/10.1016/j.ejc.2011.01.004.

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36

Wei, Ming, Guan Long Deng, Zhen Hao Xu, and Xing Sheng Gu. "Parallel Machine Tardiness Scheduling Based on Improved Discrete Differential Evolution." Advanced Materials Research 459 (January 2012): 266–70. http://dx.doi.org/10.4028/www.scientific.net/amr.459.266.

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To study the identical parallel machine scheduling problem with total tardiness objective, an improved discrete differential evolution DDE_VND is presented. The proposed algorithm hybridizes discrete differential evolution (DDE) with variable neighborhood descent (VND) to enhance its local search ability. Moreover, a constructive heuristic MDD is employed to generate an initial solution in the algorithm to accelerate the convergence of the algorithm. At last, the experimental results based on 50 benchmark instances validate the effectiveness of the DDE_VND algorithm
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37

Randriamaro, Hery. "Spectral properties of descent algebra elements." Journal of Algebraic Combinatorics 39, no. 1 (April 11, 2013): 127–39. http://dx.doi.org/10.1007/s10801-013-0441-1.

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38

Jabr, Rabih A., and Izudin Dzafic. "Sensitivity-Based Discrete Coordinate-Descent for Volt/VAr Control in Distribution Networks." IEEE Transactions on Power Systems 31, no. 6 (November 2016): 4670–78. http://dx.doi.org/10.1109/tpwrs.2015.2512103.

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39

Leung, Ka Hin, and Bernhard Schmidt. "The anti-field-descent method." Journal of Combinatorial Theory, Series A 139 (April 2016): 87–131. http://dx.doi.org/10.1016/j.jcta.2015.11.005.

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40

Brenti, Francesco, and Angela Carnevale. "Odd length: Odd diagrams and descent classes." Discrete Mathematics 344, no. 5 (May 2021): 112308. http://dx.doi.org/10.1016/j.disc.2021.112308.

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41

Nikolić, Nebojša, Igor Grujičić, and Đorđe Dugošija. "Variable neighborhood descent heuristic for covering design problem." Electronic Notes in Discrete Mathematics 39 (December 2012): 193–200. http://dx.doi.org/10.1016/j.endm.2012.10.026.

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42

Fikl, Alexandru, Vincent Le Chenadec, and Taraneh Sayadi. "Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques." Fluids 5, no. 3 (September 10, 2020): 156. http://dx.doi.org/10.3390/fluids5030156.

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The applicability of adjoint-based gradient computation is investigated in the context of interfacial flows. Emphasis is set on the approximation of the transport of a characteristic function in a potential flow by means of an algebraic volume-of-fluid method. A class of optimisation problems with tracking-type functionals is proposed. Continuous (differentiate-then-discretize) and discrete (discretize-then-differentiate) adjoint-based gradient computations are formulated and compared in a one-dimensional configuration, the latter being ultimately used to perform optimisation in two dimensions. The gradient is used in truncated Newton and steepest descent optimisers, and the algorithms are shown to recover optimal solutions. These validations raise a number of open questions, which are finally discussed with directions for future work.
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43

Tan, Jiyuan, Xiangyun Shi, Zhiheng Li, Kaidi Yang, Na Xie, Haiyang Yu, Li Wang, and Zhengxi Li. "Continuous and Discrete-Time Optimal Controls for an Isolated Signalized Intersection." Journal of Sensors 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/6290248.

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A classical control problem for an isolated oversaturated intersection is revisited with a focus on the optimal control policy to minimize total delay. The difference and connection between existing continuous-time planning models and recently proposed discrete-time planning models are studied. A gradient descent algorithm is proposed to convert the optimal control plan of the continuous-time model to the plan of the discrete-time model in many cases. Analytic proof and numerical tests for the algorithm are also presented. The findings shed light on the links between two kinds of models.
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44

Karatapanis, Konstantinos. "One-dimensional system arising in stochastic gradient descent." Advances in Applied Probability 53, no. 2 (June 2021): 575–607. http://dx.doi.org/10.1017/apr.2020.10.

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AbstractWe consider stochastic differential equations of the form $dX_t = |f(X_t)|/t^{\gamma} dt+1/t^{\gamma} dB_t$, where f(x) behaves comparably to $|x|^k$ in a neighborhood of the origin, for $k\in [1,\infty)$. We show that there exists a threshold value $ \,{:}\,{\raise-1.5pt{=}}\, \tilde{\gamma}$ for $\gamma$, depending on k, such that if $\gamma \in (1/2, \tilde{\gamma})$, then $\mathbb{P}(X_t\rightarrow 0) = 0$, and for the rest of the permissible values of $\gamma$, $\mathbb{P}(X_t\rightarrow 0)>0$. These results extend to discrete processes that satisfy $X_{n+1}-X_n = f(X_n)/n^\gamma +Y_n/n^\gamma$. Here, $Y_{n+1}$ are martingale differences that are almost surely bounded.This result shows that for a function F whose second derivative at degenerate saddle points is of polynomial order, it is always possible to escape saddle points via the iteration $X_{n+1}-X_n =F'(X_n)/n^\gamma +Y_n/n^\gamma$ for a suitable choice of $\gamma$.
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45

Krcmar, Igor R., Milorad M. Bozic, and Petar S. Maric. "Data-Driven Gradient Descent Direct Adaptive Control for Discrete-Time Nonlinear SISO Systems." Electronics ETF 18, no. 1 (June 23, 2014): 39. http://dx.doi.org/10.7251/els1418039k.

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46

van Willigenburg, Stephanie. "Properties of the descent algebras of type D." Discrete Mathematics 269, no. 1-3 (July 2003): 325–32. http://dx.doi.org/10.1016/s0012-365x(03)00061-x.

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47

Wang, David G. L., and Tongyuan Zhao. "The peak and descent statistics over ballot permutations." Discrete Mathematics 345, no. 3 (March 2022): 112739. http://dx.doi.org/10.1016/j.disc.2021.112739.

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48

Liu, Yang, Xian De Zhu, and Chen Ye Wan. "Study on Sample Preparation Method of DEM." Advanced Materials Research 671-674 (March 2013): 333–36. http://dx.doi.org/10.4028/www.scientific.net/amr.671-674.333.

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Three numerical sample preparation methods, namely, radius expand method, hierarchical compaction method and gravity descent method, were studied using discrete element method (DEM) to simulate the actual sample. The processes of these three methods were described in details and the differences of these three methods were discussed. The impacts of mechanical parameters in DEM model on the numerical results were analyzed.
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49

Patras, Frédéric, and Manfred Schocker. "Trees, set compositions and the twisted descent algebra." Journal of Algebraic Combinatorics 28, no. 1 (July 22, 2006): 3–23. http://dx.doi.org/10.1007/s10801-006-0028-1.

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50

Bunge, Marta. "An application of descent to a classification theorem for toposes." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 1 (January 1990): 59–79. http://dx.doi.org/10.1017/s0305004100068365.

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The aim of this paper is to answer the following question. For a spatial groupoid G, i.e. for a groupoid in the category Sp of spaces (in the sense of [20]) in a topos , and continuous maps, the topos BG, of étale G-spaces, is called ‘the classifying topos of G’ by Moerdijk[22]. This terminology is suggested by the case of G a discrete group (in Sets), as then BG, the topos of G-sets, classifies principal G-bundles. This means that, for each topological space X, there is a bijection between isomorphism classes of principal G-bundles over X and isomorphism classes of geometric morphisms from Sh(X) to BG. The question is: what does BG classify, in terms of G, in the general case of a spatial groupoid G in a topos ?
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