text:
# American Institute of Mathematical Sciences

• Previous Article
Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit
• CPAA Home
• This Issue
• Next Article
The nonlinear 2D subcritical inviscid shallow water equations with periodicity in one direction
September  2014, 13(5): 2039-2058. doi: 10.3934/cpaa.2014.13.2039

## An extension of the Fitzpatrick theory

 1 Università degli Studi di Trento, Dipartimento di Matematica, via Sommarive 14, 38050 Povo (Trento) - Italia

Received  January 2014 Revised  March 2014 Published  June 2014

In the seminal work [MR 1009594], Fitzpatrick proved that for any maximal monotone operator $\alpha: V\to {\mathcal P}(V')$ ($V$ being a real Banach space) there exists a lower semicontinuous, convex representative function $f_\alpha: V \times V'\to R\cup \{+\infty\}$ such that \begin{eqnarray} f_\alpha(v,v') \ge \langle v',v\rangle \quad\;\forall (v,v'), \qquad\quad f_\alpha(v,v') = \langle v',v\rangle \;\;\Leftrightarrow\;\;\; v'\in \alpha(v). \end{eqnarray}
Here we assume that $\alpha_v$ is a maximal monotone operator for any $v\in V$, and extend the Fitzpatrick theory to provide a new variational formulation for either stationary or evolutionary (nonmonotone) inclusions of the form $\alpha_v(v) \ni v'$. For any $v'\in V'$, we prove existence of a solution via the classical minimax theorem of Ky Fan. Applications include stationary and evolutionary pseudo-monotone operators, and variational inequalities.
Citation: Augusto Visintin. An extension of the Fitzpatrick theory. Communications on Pure & Applied Analysis, 2014, 13 (5) : 2039-2058. doi: 10.3934/cpaa.2014.13.2039
##### References:
 [1] G. Allen, Variational inequalities, complementarity problems, and duality theorems,, \emph{J. Math. Anal. Appl.}, 58 (1977). Google Scholar [2] J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis,, Wiley and Sons, (1984). Google Scholar [3] G. Auchmuty, Saddle-points and existence-uniqueness for evolution equations,, \emph{Differential Integral Equations}, 6 (1993), 1161. Google Scholar [4] C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities, Applications to Free Boundary Problems,, Wiley and Sons, (1984). Google Scholar [5] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces,, Noordhoff, (1976). Google Scholar [6] H. H. Bauschke and X. Wang, The kernel average for two convex functions and its applications to the extension and representation of monotone operators,, \emph{Trans. Amer. Math. Soc.}, 361 (2009), 5947. doi: 10.1090/S0002-9947-09-04698-4. Google Scholar [7] H. Brezis, Équations et inéquations non linéaires dans les espaces vectoriels en dualité,, \emph{Ann. Inst. Fourier (Grenoble)}, 18 (1968), 115. Google Scholar [8] H. Brezis, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert,, North-Holland, (1973). Google Scholar [9] H. Brezis and I. Ekeland, Un principe variationnel associé à certaines équations paraboliques. I. Le cas indépendant du temps et II. Le cas dépendant du temps,, \emph{C. R. Acad. Sci. Paris S\'er. A-B}, 282 (1976), 971. Google Scholar [10] F. Browder, Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces,, Proc. Sympos. Pure Math., XVIII (1976). Google Scholar [11] F. Browder and P. Hess, Nonlinear mappings of monotone type in Banach spaces,, \emph{J. Functional Analysis}, 11 (1972), 251. Google Scholar [12] M. Buliga, G. de Saxcé and C. Vallée, Existence and construction of bipotentials for graphs of multivalued laws,, \emph{J. Convex Anal., 15 (2008), 87. Google Scholar [13] R. S. Burachik and B. F. Svaiter, Maximal monotone operators, convex functions, and a special family of enlargements,, \emph{Set-Valued Analysis}, 10 (2002), 297. doi: 10.1023/A:1020639314056. Google Scholar [14] R. S. Burachik and B. F. Svaiter, Maximal monotonicity, conjugation and the duality product,, \emph{Proc. Amer. Math. Soc., 131 (2003), 2379. doi: 10.1090/S0002-9939-03-07053-9. Google Scholar [15] I. Ekeland and R. Temam, Analyse Convexe et Problèmes Variationnelles,, Dunod Gauthier-Villars, (1974). Google Scholar [16] K. Fan, A generalization of Tychonoff's theorem,, \emph{Math. Ann.}, 142 (1961), 305. Google Scholar [17] K. Fan, A minimax inequality and applications. Inequalities, III,, In: \emph{Proc. Third Sympos.}, (1969), 103. Google Scholar [18] W. Fenchel, Convex Cones, Sets, and Functions,, Princeton Univ., (1953). Google Scholar [19] S. Fitzpatrick, Representing monotone operators by convex functions,, in \emph{Workshop/Miniconference on Functional Analysis and Optimization (Canberra, (1988), 59. Google Scholar [20] N. Ghoussoub, Selfdual Partial Differential Systems and their Variational Principles,, Springer, (2008). Google Scholar [21] N. Ghoussoub, A variational theory for monotone vector fields,, \emph{J. Fixed Point Theory Appl.}, 4 (2008), 107. doi: 10.1007/s11784-008-0083-4. Google Scholar [22] N. Ghoussoub and L. Tzou, A variational principle for gradient flows,, \emph{Math. Ann.}, 330 (2004), 519. doi: 10.1007/s00208-004-0558-6. Google Scholar [23] J.-B. Hiriart-Urruty and C. Lemarechal, Fundamentals of Convex Analysis,, Springer, (2001). doi: 10.1007/978-3-642-56468-0. Google Scholar [24] Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis. Vol. I,, Kluwer, (1997). doi: 10.1016/0362-546X(85)90097-5. Google Scholar [25] B. Knaster, C. Kuratowski and S. Mazurkievicz, Ein Beweis des Fixpunktsatzes für $n$-dimensionale Simplexe,, \emph{Fund. Math.}, 14 (1929), 132. Google Scholar [26] E. Krauss, A representation of arbitrary maximal monotone operators via subgradients of skew-symmetric saddle functions,, \emph{Nonlinear Anal.}, 9 (1985), 1381. Google Scholar [27] J. Leray and J. L. Lions, Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder,, \emph{Bull. Soc. Math. France}, 93 (1965), 97. Google Scholar [28] J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires,, Dunod, (1969). Google Scholar [29] J.-E. Martinez-Legaz and M. Théra, A convex representation of maximal monotone operators,, \emph{J. Nonlinear Convex Anal.}, 2 (2001), 243. Google Scholar [30] J.-E. Martinez-Legaz and B. F. Svaiter, Monotone operators representable by l.s.c. convex functions,, \emph{Set-Valued Anal.}, 13 (2005), 21. doi: 10.1007/s11228-004-4170-4. Google Scholar [31] J.-E. Martinez-Legaz and B. F. Svaiter, Minimal convex functions bounded below by the duality product,, \emph{Proc. Amer. Math. Soc.}, 136 (2008), 873. doi: 10.1090/S0002-9939-07-09176-9. Google Scholar [32] G. J. Minty, Monotone (nonlinear) operators in Hilbert space,, \emph{Duke Math. J.}, 29 (1962), 341. Google Scholar [33] B. Nayroles, Deux théorèmes de minimum pour certains systèmes dissipatifs,, \emph{C. R. Acad. Sci. Paris Sér. A-B}, 282 (1976). Google Scholar [34] J.-P. Penot, A representation of maximal monotone operators by closed convex functions and its impact on calculus rules,, \emph{C. R. Math. Acad. Sci. Paris, 338 (2004), 853. doi: 10.1016/j.crma.2004.03.017. Google Scholar [35] J.-P. Penot, The relevance of convex analysis for the study of monotonicity,, \emph{Nonlinear Anal.}, 58 (2004), 855. doi: 10.1016/j.na.2004.05.018. Google Scholar [36] T. Roche, R. Rossi and U. Stefanelli, Stability results for doubly nonlinear differential inclusions by variational convergence,, \emph{SIAM J. Control Optim.}, (2014). doi: 10.1137/130909391. Google Scholar [37] R. T. Rockafellar, Convex Analysis,, Princeton University Press, (1969). Google Scholar [38] T. Roubíček, Direct method for parabolic problems,, \emph{Adv. Math. Sci. Appl.}, 10 (2000), 57. Google Scholar [39] T. Roubíček, Nonlinear Partial Differential Equations with Applications,, second edition, (2013). doi: 10.1007/978-3-0348-0513-1. Google Scholar [40] B. F. Svaiter, Fixed points in the family of convex representations of a maximal monotone operator,, \emph{Proc. Amer. Math. Soc.}, 131 (2003), 3851. doi: 10.1090/S0002-9939-03-07083-7. Google Scholar [41] A. Visintin, Extension of the Brezis-Ekeland-Nayroles principle to monotone operators,, \emph{Adv. Math. Sci. Appl.}, 18 (2008), 633. Google Scholar [42] A. Visintin, Variational formulation and structural stability of monotone equations,, \emph{Calc. Var. Partial Differential Equations}, 47 (2013), 273. doi: 10.1007/s00526-012-0519-y. Google Scholar [43] A. Visintin, Scale-transformations and homogenization of maximal monotone relations, with applications,, \emph{Asymptotic Analysis}, 82 (2013), 233. Google Scholar [44] A. Visintin, Weak structural stability of pseudo-monotone equations,, in press., (). Google Scholar [45] E. Zeidler, Nonlinear Functional Analysis and its Applications. Vol. II/B: Nonlinear Monotone Operators,, Springer, (1990). doi: 10.1007/978-1-4612-0985-0. Google Scholar [46] E. Zeidler, Nonlinear Functional Analysis and its Applications. Vol. IV: Applications to Mathematical Physics,, Springer, (1988). doi: 10.1007/978-1-4612-4566-7. Google Scholar

show all references

##### References:
 [1] G. Allen, Variational inequalities, complementarity problems, and duality theorems,, \emph{J. Math. Anal. Appl.}, 58 (1977). Google Scholar [2] J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis,, Wiley and Sons, (1984). Google Scholar [3] G. Auchmuty, Saddle-points and existence-uniqueness for evolution equations,, \emph{Differential Integral Equations}, 6 (1993), 1161. Google Scholar [4] C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities, Applications to Free Boundary Problems,, Wiley and Sons, (1984). Google Scholar [5] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces,, Noordhoff, (1976). Google Scholar [6] H. H. Bauschke and X. Wang, The kernel average for two convex functions and its applications to the extension and representation of monotone operators,, \emph{Trans. Amer. Math. Soc.}, 361 (2009), 5947. doi: 10.1090/S0002-9947-09-04698-4. Google Scholar [7] H. Brezis, Équations et inéquations non linéaires dans les espaces vectoriels en dualité,, \emph{Ann. Inst. Fourier (Grenoble)}, 18 (1968), 115. Google Scholar [8] H. Brezis, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert,, North-Holland, (1973). Google Scholar [9] H. Brezis and I. Ekeland, Un principe variationnel associé à certaines équations paraboliques. I. Le cas indépendant du temps et II. Le cas dépendant du temps,, \emph{C. R. Acad. Sci. Paris S\'er. A-B}, 282 (1976), 971. Google Scholar [10] F. Browder, Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces,, Proc. Sympos. Pure Math., XVIII (1976). Google Scholar [11] F. Browder and P. Hess, Nonlinear mappings of monotone type in Banach spaces,, \emph{J. Functional Analysis}, 11 (1972), 251. Google Scholar [12] M. Buliga, G. de Saxcé and C. Vallée, Existence and construction of bipotentials for graphs of multivalued laws,, \emph{J. Convex Anal., 15 (2008), 87. Google Scholar [13] R. S. Burachik and B. F. Svaiter, Maximal monotone operators, convex functions, and a special family of enlargements,, \emph{Set-Valued Analysis}, 10 (2002), 297. doi: 10.1023/A:1020639314056. Google Scholar [14] R. S. Burachik and B. F. Svaiter, Maximal monotonicity, conjugation and the duality product,, \emph{Proc. Amer. Math. Soc., 131 (2003), 2379. doi: 10.1090/S0002-9939-03-07053-9. Google Scholar [15] I. Ekeland and R. Temam, Analyse Convexe et Problèmes Variationnelles,, Dunod Gauthier-Villars, (1974). Google Scholar [16] K. Fan, A generalization of Tychonoff's theorem,, \emph{Math. Ann.}, 142 (1961), 305. Google Scholar [17] K. Fan, A minimax inequality and applications. Inequalities, III,, In: \emph{Proc. Third Sympos.}, (1969), 103. Google Scholar [18] W. Fenchel, Convex Cones, Sets, and Functions,, Princeton Univ., (1953). Google Scholar [19] S. Fitzpatrick, Representing monotone operators by convex functions,, in \emph{Workshop/Miniconference on Functional Analysis and Optimization (Canberra, (1988), 59. Google Scholar [20] N. Ghoussoub, Selfdual Partial Differential Systems and their Variational Principles,, Springer, (2008). Google Scholar [21] N. Ghoussoub, A variational theory for monotone vector fields,, \emph{J. Fixed Point Theory Appl.}, 4 (2008), 107. doi: 10.1007/s11784-008-0083-4. Google Scholar [22] N. Ghoussoub and L. Tzou, A variational principle for gradient flows,, \emph{Math. Ann.}, 330 (2004), 519. doi: 10.1007/s00208-004-0558-6. Google Scholar [23] J.-B. Hiriart-Urruty and C. Lemarechal, Fundamentals of Convex Analysis,, Springer, (2001). doi: 10.1007/978-3-642-56468-0. Google Scholar [24] Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis. Vol. I,, Kluwer, (1997). doi: 10.1016/0362-546X(85)90097-5. Google Scholar [25] B. Knaster, C. Kuratowski and S. Mazurkievicz, Ein Beweis des Fixpunktsatzes für $n$-dimensionale Simplexe,, \emph{Fund. Math.}, 14 (1929), 132. Google Scholar [26] E. Krauss, A representation of arbitrary maximal monotone operators via subgradients of skew-symmetric saddle functions,, \emph{Nonlinear Anal.}, 9 (1985), 1381. Google Scholar [27] J. Leray and J. L. Lions, Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder,, \emph{Bull. Soc. Math. France}, 93 (1965), 97. Google Scholar [28] J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires,, Dunod, (1969). Google Scholar [29] J.-E. Martinez-Legaz and M. Théra, A convex representation of maximal monotone operators,, \emph{J. Nonlinear Convex Anal.}, 2 (2001), 243. Google Scholar [30] J.-E. Martinez-Legaz and B. F. Svaiter, Monotone operators representable by l.s.c. convex functions,, \emph{Set-Valued Anal.}, 13 (2005), 21. doi: 10.1007/s11228-004-4170-4. Google Scholar [31] J.-E. Martinez-Legaz and B. F. Svaiter, Minimal convex functions bounded below by the duality product,, \emph{Proc. Amer. Math. Soc.}, 136 (2008), 873. doi: 10.1090/S0002-9939-07-09176-9. Google Scholar [32] G. J. Minty, Monotone (nonlinear) operators in Hilbert space,, \emph{Duke Math. J.}, 29 (1962), 341. Google Scholar [33] B. Nayroles, Deux théorèmes de minimum pour certains systèmes dissipatifs,, \emph{C. R. Acad. Sci. Paris Sér. A-B}, 282 (1976). Google Scholar [34] J.-P. Penot, A representation of maximal monotone operators by closed convex functions and its impact on calculus rules,, \emph{C. R. Math. Acad. Sci. Paris, 338 (2004), 853. doi: 10.1016/j.crma.2004.03.017. Google Scholar [35] J.-P. Penot, The relevance of convex analysis for the study of monotonicity,, \emph{Nonlinear Anal.}, 58 (2004), 855. doi: 10.1016/j.na.2004.05.018. Google Scholar [36] T. Roche, R. Rossi and U. Stefanelli, Stability results for doubly nonlinear differential inclusions by variational convergence,, \emph{SIAM J. Control Optim.}, (2014). doi: 10.1137/130909391. Google Scholar [37] R. T. Rockafellar, Convex Analysis,, Princeton University Press, (1969). Google Scholar [38] T. Roubíček, Direct method for parabolic problems,, \emph{Adv. Math. Sci. Appl.}, 10 (2000), 57. Google Scholar [39] T. Roubíček, Nonlinear Partial Differential Equations with Applications,, second edition, (2013). doi: 10.1007/978-3-0348-0513-1. Google Scholar [40] B. F. Svaiter, Fixed points in the family of convex representations of a maximal monotone operator,, \emph{Proc. Amer. Math. Soc.}, 131 (2003), 3851. doi: 10.1090/S0002-9939-03-07083-7. Google Scholar [41] A. Visintin, Extension of the Brezis-Ekeland-Nayroles principle to monotone operators,, \emph{Adv. Math. Sci. Appl.}, 18 (2008), 633. Google Scholar [42] A. Visintin, Variational formulation and structural stability of monotone equations,, \emph{Calc. Var. Partial Differential Equations}, 47 (2013), 273. doi: 10.1007/s00526-012-0519-y. Google Scholar [43] A. Visintin, Scale-transformations and homogenization of maximal monotone relations, with applications,, \emph{Asymptotic Analysis}, 82 (2013), 233. Google Scholar [44] A. Visintin, Weak structural stability of pseudo-monotone equations,, in press., (). Google Scholar [45] E. Zeidler, Nonlinear Functional Analysis and its Applications. Vol. II/B: Nonlinear Monotone Operators,, Springer, (1990). doi: 10.1007/978-1-4612-0985-0. Google Scholar [46] E. Zeidler, Nonlinear Functional Analysis and its Applications. Vol. IV: Applications to Mathematical Physics,, Springer, (1988). doi: 10.1007/978-1-4612-4566-7. Google Scholar
 [1] Augusto VisintiN. On the variational representation of monotone operators. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 909-918. doi: 10.3934/dcdss.2017046 [2] Dalila Azzam-Laouir, Warda Belhoula, Charles Castaing, M. D. P. Monteiro Marques. Multi-valued perturbation to evolution problems involving time dependent maximal monotone operators. Evolution Equations & Control Theory, 2020, 9 (1) : 219-254. doi: 10.3934/eect.2020004 [3] JIAO CHEN, WEI DAI, GUOZHEN LU. $L^p$ boundedness for maximal functions associated with multi-linear pseudo-differential operators. Communications on Pure & Applied Analysis, 2017, 16 (3) : 883-898. doi: 10.3934/cpaa.2017042 [4] Dag Lukkassen, Annette Meidell, Peter Wall. Multiscale homogenization of monotone operators. Discrete & Continuous Dynamical Systems - A, 2008, 22 (3) : 711-727. doi: 10.3934/dcds.2008.22.711 [5] Mehdi Badsi, Martin Campos Pinto, Bruno Després. A minimization formulation of a bi-kinetic sheath. Kinetic & Related Models, 2016, 9 (4) : 621-656. doi: 10.3934/krm.2016010 [6] Luca Lussardi, Stefano Marini, Marco Veneroni. Stochastic homogenization of maximal monotone relations and applications. Networks & Heterogeneous Media, 2018, 13 (1) : 27-45. doi: 10.3934/nhm.2018002 [7] Nils Svanstedt. Multiscale stochastic homogenization of monotone operators. Networks & Heterogeneous Media, 2007, 2 (1) : 181-192. doi: 10.3934/nhm.2007.2.181 [8] Woocheol Choi. Maximal functions of multipliers on compact manifolds without boundary. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1885-1902. doi: 10.3934/cpaa.2015.14.1885 [9] Xiao Ding, Deren Han. A modification of the forward-backward splitting method for maximal monotone mappings. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 295-307. doi: 10.3934/naco.2013.3.295 [10] Zhongliang Deng, Enwen Hu. Error minimization with global optimization for difference of convex functions. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1027-1033. doi: 10.3934/dcdss.2019070 [11] Gunther Dirr, Hiroshi Ito, Anders Rantzer, Björn S. Rüffer. Separable Lyapunov functions for monotone systems: Constructions and limitations. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2497-2526. doi: 10.3934/dcdsb.2015.20.2497 [12] Yurii Nesterov, Laura Scrimali. Solving strongly monotone variational and quasi-variational inequalities. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1383-1396. doi: 10.3934/dcds.2011.31.1383 [13] Manh Hong Duong, Hoang Minh Tran. On the fundamental solution and a variational formulation for a degenerate diffusion of Kolmogorov type. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3407-3438. doi: 10.3934/dcds.2018146 [14] Xiaojun Chen, Guihua Lin. CVaR-based formulation and approximation method for stochastic variational inequalities. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 35-48. doi: 10.3934/naco.2011.1.35 [15] Chjan C. Lim, Junping Shi. The role of higher vorticity moments in a variational formulation of Barotropic flows on a rotating sphere. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 717-740. doi: 10.3934/dcdsb.2009.11.717 [16] Giuseppe Da Prato, Alessandra Lunardi. Maximal dissipativity of a class of elliptic degenerate operators in weighted $L^2$ spaces. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 751-760. doi: 10.3934/dcdsb.2006.6.751 [17] Sihong Su. A new construction of rotation symmetric bent functions with maximal algebraic degree. Advances in Mathematics of Communications, 2019, 13 (2) : 253-265. doi: 10.3934/amc.2019017 [18] A. C. Eberhard, J-P. Crouzeix. Existence of closed graph, maximal, cyclic pseudo-monotone relations and revealed preference theory. Journal of Industrial & Management Optimization, 2007, 3 (2) : 233-255. doi: 10.3934/jimo.2007.3.233 [19] Radu Ioan Boţ, Christopher Hendrich. Solving monotone inclusions involving parallel sums of linearly composed maximally monotone operators. Inverse Problems & Imaging, 2016, 10 (3) : 617-640. doi: 10.3934/ipi.2016014 [20] Zhili Ge, Gang Qian, Deren Han. Global convergence of an inexact operator splitting method for monotone variational inequalities. Journal of Industrial & Management Optimization, 2011, 7 (4) : 1013-1026. doi: 10.3934/jimo.2011.7.1013

2018 Impact Factor: 0.925


text:
Contents

Contents

Idea

Condensed sets are basic objects in condensed mathematics, whose aim is to provide a convenient setting in the framework for working with algebraic objects that are equipped with sort of a topology. A related alternative is provided by pyknotic sets.

Topological spaces formalize the idea of spaces with a notion of “nearness” of points. However, they fail to handle the idea of “points that are infinitely near, but distinct” in a useful way. Condensed sets handle this idea in a useful way. (Scholze 21)

For instance, $\mathbb{R}/\mathbb{Q}$ and $\ell^2(\mathbb{N})/\ell^1(\mathbb{N})$ are indiscrete as topological spaces but retain structure as condensed sets.

Condensed sets contain information about limits of images of any set, $A$, along the ultrafilters of $A$.

Definition

Definition

A condensed set is a sheaf of sets on the pro-étale site of a point — in other words, on the category of profinite spaces with finite jointly surjective families of maps as covers — which is the colimit of a small diagram of representables (a small sheaf?).

That is, a condensed set is a functor

$ProfiniteSet^op \longrightarrow Set$

such that the natural maps

$T(\emptyset) \longrightarrow *$

and

$T(S\sqcup S') \longrightarrow T(S) \times T(S')$

are bijections for any profinite sets $S$ and $S'$, whereas the natural fork

$T(S)\to T(S') \rightrightarrows T(S'\times_S S')$

is an equalizer for any surjection of profinite sets $S'\to S$.

Scholze, p.7 modifies this definition to deal with size issues:

For any uncountable strong limit cardinal $\kappa$, the category of $\kappa$-condensed sets $CondSet_\kappa$ is the category of sheaves on the site of profinite sets of cardinality less than $\kappa$, with finite jointly surjective families of maps as covers.

The category of condensed sets $CondSet$ is then the (large) colimit of the category of $\kappa$-condensed sets along the filtered poset of all uncountable strong limit cardinals $\kappa$, hence is the category of small sheaves?.

Properties

Condensed sets form a locally small, well-powered, locally cartesian closed infinitary-pretopos $CondSet$, that is neither a Grothendieck topos nor an elementary topos – since it lacks both a small separator (indeed, it is not even total) and a subobject classifier. It has a large separator of finitely presentable projectives, and hence is algebraically exact. (Campbell 20)

According to Peter Scholze in this comment on the nCafé and Mike Shulman in this comment on the nCafé, condensed sets satisfy external CoSHEP and WISC, but internal CoSHEP fails.

See Proposition 1.7 for the following proposition.

Proposition

The forgetful functor from the category of topological spaces to κ-condensed sets is a faithful functor. It becomes fully faithful when restricted to κ-compactly generated spaces.

This functor admits a left adjoint, which sends a condensed set $T$ to the topological space given by the underlying set $T(*)$ of $T$ equipped with the quotient topology induced by the map

$\coprod_{S\to T}S\to T(*),$

where $S$ runs over all (κ-small) profinite sets mapping into $T$. The counit of this adjunction coincides with the counit $X^{cg}\to X$ of the adjunction between (κ-small) compactly generated spaces and topological spaces.

The left adjoint exists also for topological groups and other algebraic structures, but in this case, the underlying set is not $T(*)$.

References

Last revised on June 30, 2022 at 21:23:06. See the history of this page for a list of all contributions to it.

format: plain


text:
Setting markers in the same line

#1

I’ve just started using Atom, and my main use is in typing Latex files. One of the things I loved about Textmate is that I could type, say, ‘fr’-hotkey to get \fraction{}{}, with the cursor inside the first set of curly braces, and once I done typing something I could type tab to get inside the second curly braces, and then type tab again to get out of it. I set it up by coding the shortcut as ‘\fraction{$1}{$2}$0’ in Textmate. Can I do something similar with Atom (or any of its packages)? I’m aware of the bookmark (and mark package) functionalities, but they don’t seem to be quite the same. Thanks. #2 Have you taken a look at the Flight Manual? Specifically the snippets section? #3 Thanks, leedohm. Sorry for not making my question clear: in Atom it seems you can press tab to start the snippet and move around the$1, \$2, etc placeholders, but this means I can’t use any other snippet inside the first snippet. Say, for instance I wanted ‘a’-hotkey to become ‘\alpha’; this doesn’t work as it moves me outside the snippet. So, put it another way: can I have two snippet keys on Atom, one to create the snippet, another to move around inside of them?

#4

No, Atom currently doesn’t support expanding snippets inside other snippets. You may want to subscribe to this Issue for updates:


text:
# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 3rd 2021

am recording an actual proof that

$\mathcal{L} \big( \overline{W}\mathcal{G} \big) \;\; \simeq \;\; \mathcal{G}_{ad} \sslash \mathcal{G}$

I expected that a proof for this folklore theorem would be citeable from the literature, but maybe not quite. This MO reply points to Lemma 9.1 in arXiv:0811.0771, which has the idea (in topological spaces), but doesn’t explicitly verify all ingredients. I have tried to make it fully explicit (in simplicial sets).

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJul 3rd 2021

On the other hand, I haven’t yet managed to see a copy of

which apparently has a discussion of the issue in its appendix.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJul 4th 2021

added pointer to the relevant 3 pages in

• Kate Gruher, A proof of $L B G \simeq Ad(E G)$, Appendix A in String Topology of Classifying Spaces, 2007 (pdf)
• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJul 4th 2021

Added some words (here) on the basic example of discrete groups, and then expanded the Idea-section a fair bit.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJul 4th 2021

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJul 4th 2021
• (edited Jul 10th 2021)

[ redundant ]

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJul 9th 2021
• (edited Jul 9th 2021)

I have added an Examples-section (here) on the case that $\mathcal{G} = \mathcal{A}$ is a simplicial abelian group,

with statement and (immediate) proof of

$\big[ \mathbf{B}\mathbb{Z}, \, \mathbf{B}\mathcal{A} \big] \;\; \simeq \;\; \mathcal{A} \times \mathbf{B}\mathcal{A} \,.$

and with the example

$\mathcal{L} \mathbf{B}^{n+1}A \;\simeq\; \mathbf{B}^n A \,\times\, \mathbf{B}^{n+1}A \,,$
• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJul 9th 2021

Does anyone know or see how to make the simplicial presentation in the entry here functorial in $\overline{W}\mathcal{G}$?

I.e. for $\overline{W}\mathcal{G} \longrightarrow \overline{W}\mathcal{K}$ a morphism, do we have an induced morphism $\big( W\mathcal{G} \times \mathcal{G}_{ad}\big)/\mathcal{G} \longrightarrow \big( W\mathcal{K} \times \mathcal{K}_{ad}\big)/\mathcal{K}$ or does it only exist as a zig-zag? One will have to apply simplicial looping and both the unit and the counit of $\Omega \dashv \overline{W}$. Somehow.

• CommentRowNumber9.
• CommentAuthorUlrik
• CommentTimeJul 11th 2021

Fill in proof in homotopy type theory. The proof itself is one line, but I added some reminders about how things are defined in HoTT. I think we have these things elsewhere, so it would be good to add some more links. Later.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeJul 11th 2021
• (edited Jul 11th 2021)

Thanks!!

Allow me to make some edits as I read through it:

• hyperlinked type, function type, type universe, Sigma-type

• changed “object of type” to “term of type” (okay?!)

• expanded out “pointed map” to “morphism of pointed homotopy types

• changed “classifying” to “delooping” and changed “$B G$” to “$\mathbf{B}G$”, in accord with notation we have mostly been sticking to on the $n$Lab

– you know the reason, but just to amplify for bystanders: it’s important that we are speaking here about the internal delooping (hence the universal moduli $\infty$-stack) $\mathbf{B}G$ instead of just the classifying space $B G$ of $G$, which, when a shape modality is present, is typically just the shape of the moduli stack $B G \simeq ʃ \mathbf{B}G$

• similarly, where the circle appears I replaced $S^1$ with $ʃ S^1$ and made explicit that $ʃ S^1 \,\simeq\, \mathbf{B}\mathbb{Z}$

(this leaves room for future discussion here of the actual free loop stack which involves the actual circle $S^1$)

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeJul 11th 2021

also I have added a line-break in the deduction

\begin{aligned} G^{ad} \!\sslash\! G & \;=\; \sum_{t: \mathbf{B} G} (t =_{\mathbf{B} G} t) \\ & \;\simeq\; (ʃS^1 \to \mathbf{B} G), \end{aligned}

to avoid the last two lines together to look like an identity type.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeJul 11th 2021
• (edited Jul 11th 2021)

Where the higher inductive type of the circle is mentioned, I have added a pointer to higher inductive type – examples – circle.

I wish we had a page on the circle-HIT that would explain the conclusion being drawn here a little more…

[ oh, I see we have a stub entry circle type. That has room to be expanded… ]

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeJul 11th 2021
• (edited Jul 11th 2021)

Now I have a question on the logic of the derivation:

It is clear that the function type $ʃ S^1 \to \mathbf{B}G$ is the correct formalization of the free loop space (actually: intertia $\infty$-stack) $\Lambda \mathbf{B}G$. So, running your argument backwards, we find that this evident free loop type is equivalent to the action $t \colon \mathbf{B}G \vdash (t =_{\mathbf{B}G} t) \,\colon\, Type$. However, it is less “clear” that this action is the adjoint action. While I certainly don’t doubt it, I am wondering if this can be formally substantiated further in HoTT.

Compare to the situation in the pseudocode formerly known as mathematics: There we also went ahead and defined $\mathcal{L} \mathbf{B}G \, \in \, \mathbf{H}_{/\mathbf{B}G} \simeq G Acts(\mathbf{H})$ as being the adjoint action – and it’s certainly a good definition – but it takes a little bit of actual work (as per #1) to demonstrate that for a given $\infty$-group $G$ this definition captures the actual defining formula

$\array{ G \times G &\longrightarrow& G \\ (g,h) &\mapsto& h^{-1} \cdot g \cdot h }$

Do you see a way to prove, in HoTT, that this formula defines the type $t \colon \mathbf{B}G \vdash (t =_{\mathbf{B}G} t) \colon Type$ ?

• CommentRowNumber14.
• CommentAuthorUlrik
• CommentTimeJul 11th 2021

Thanks for all the improvements: looks good!

Do you see a way to prove, in HoTT, that this formula defines the type $t \colon \mathbf{B}G \vdash (t =_{\mathbf{B}G} t) \colon Type$ ?

No single formula concerning elements suffices to define an $\infty$-action. You’d have to give all the higher coherences as well.

But conversely, we can easily show that the family $t \mapsto (t =_{\mathbf{B}G} t)$ acts on elements as we want. This is because transport in the identity family $\mathbf{B} G \times \mathbf{B} G \to U$, $(t,u) \mapsto (t=u)$, is by path pre/post-composition.

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeJul 11th 2021

No single formula concerning elements suffices to define an $\infty$-action. You’d have to give all the higher coherences as well.

Externally it works: I gave the proof that in the model structure on simplicial sets, any abstractly defined adjoint $\infty$-action is represented by a degree-wise adjoint action of simplicial groups. That’s the “folklore” that I set out to nail down when I started this thread.

But conversely, we can easily show that the family

Might you have energy left to add a paragraph demonstrating this? (I see what you are saying, but I’d rather you write it out to our readers than that I do.)

• CommentRowNumber16.
• CommentAuthorUlrik
• CommentTimeJul 11th 2021

• CommentRowNumber17.
• CommentAuthorUlrik
• CommentTimeJul 11th 2021

Externally it works: I gave the proof that in the model structure on simplicial sets, any abstractly defined adjoint ∞\infty-action is represented by a degree-wise adjoint action of simplicial groups. That’s the “folklore” that I set out to nail down when I started this thread.

Right. Also, we don’t know that we can’t define $A_\infty$ objects in HoTT and thus prove all this internally, it’s just the usual story that we haven’t been able to so far.

Might you have energy left to add a paragraph demonstrating this?

Done. For transport I added a link to homotopy lifting property, even though that page doesn’t talk about type theory. Maybe there should rather be a section at dependent type that explains transports, dependent actions on paths, and stuff like that.

• CommentRowNumber18.
• CommentAuthorUrs
• CommentTimeJul 11th 2021

Thanks!!

Maybe there should rather be a section at dependent type that explains transports, dependent actions on paths, and stuff like that.

It would be much appreciated if you’d have the further energy to add such a section!

• CommentRowNumber19.
• CommentAuthorUrs
• CommentTimeJul 13th 2021
• (edited Jul 13th 2021)

By the way, I still feel there is something missing in the HoTT argument. Namely, currently the argument given is really to observe that it works for 1-groups and the suggestion that this is suggestive of the general case, since everything is so natural. But this was exactly the state of the “folklore” in the classical context, which this entry here hopes to improve on.

Could one maybe generalize the HoTT argument at least to 2-groups, maybe in a way that makes it clear how on could induct up to $n$-groups for any finite $n$?

• CommentRowNumber20.
• CommentAuthorUlrik
• CommentTimeJul 14th 2021

By the way, I still feel there is something missing in the HoTT argument. Namely, currently the argument given is really to observe that it works for 1-groups and the suggestion that this is suggestive of the general case, since everything is so natural. But this was exactly the state of the “folklore” in the classical context, which this entry here hopes to improve on.

I think this “gap” is currently better filled on the side of models, which is after all where we get the equivalence $PtdConn(\mathcal{X}) \simeq Grp(\mathcal{X})$ from. (Until we solve the coherence problem etc.) Might there be some place in the quasicategory literature/Lurie where its proven that under this equivalence $G$ with its adjoint action corresponds to the type family $t \mapsto (t=t)$ (and $G$ with its translation action corresponds to the type family $t \mapsto (pt = t)$)?

Could one maybe generalize the HoTT argument at least to 2-groups, maybe in a way that makes it clear how on could induct up to $n$-groups for any finite $n$?

For 2-groups this should be possible. I’ll add it to my list of things to investigate!

• CommentRowNumber21.
• CommentAuthorUrs
• CommentTimeJul 15th 2021

Might there be some place in the quasicategory literature

I’d be inclined to say that this is what the proof accomplishes that I recorded here. This together – if you wish – with your argument translating the free loop space into $\sum_{t \colon \mathbf{B}G} (t = t)$ (which, if we use external reasoning in the first place, does not even need HIT’s as the model-categorical semantics of $\sum_{t \colon \mathbf{B}G} (t = t)$ is the free loop space object right away).

I guess my request to make this “more internal” may not be reasonable, but it grew out of the exchange we had in the other thread (startimg here).

I’ll add it to my list of things to investigate!

Okay, thanks! I’ll be interested.

By the way, not to distract us too much, but what happened to Eric Finster’s claim to have solved the issue of higher coherent structures in HoTT? In principle? I understand there was a problem with the original argument, but then apparently arXiv:2105.00024 salvaged much of it. Or something like this, I haven’t been following.

• CommentRowNumber22.
• CommentAuthorUlrik
• CommentTimeJul 15th 2021

I’d be inclined to say that this is what the proof accomplishes that I recorded here.

How hard would it be to generalize this argument to an arbitrary ∞-topos?

(which, if we use external reasoning in the first place, does not even need HIT’s as the model-categorical semantics of $\sum_{t \colon \mathbf{B}G} (t = t)$ is the free loop space object right away).

Right, this definition still uses a homotopy colimit description of $S^1$ at the meta-level, so it’s related.

I guess my request to make this “more internal” may not be reasonable, but it grew out of the exchange we had in the other thread (startimg here).

As a counterpoint, in HoTT at the moment, we have to take $PtdConn$ as the definition of $Grp$, and from this point of view, it’s equally natural to take $t \mapsto (t=t)$ as the definition of the conjugation action. From first principles, I don’t see why that’s a worse definition than one in terms of simplicial objects.

By the way, not to distract us too much, but what happened to Eric Finster’s claim to have solved the issue of higher coherent structures in HoTT? In principle? I understand there was a problem with the original argument, but then apparently arXiv:2105.00024 salvaged much of it. Or something like this, I haven’t been following.

Yes, the original definition defines the wrong thing (at the level of associativity data, or maybe one level higher). The new work proposes an extension of type theory with a universe of polynomial monads. I’m not very familiar with it yet, it’s certainly promising, though it’s not clear that it completely solves the problem, and I don’t know if the meta-theory works out (homotopy canonicity, models in all ∞-toposes, etc, that remains to be seen, IIUC.)


text:
View other OC posts by this author. How much does Sam earn cutting this area: Let's break the area into two parts: Part A is a square: Area of A = a 2 = 20m × 20m = 400m 2. COVID-19 claims eight more lives in R-C area. Note that A= 16 2 Z ˇ=8 0 1 2 [2cos4 ] d = 2ˇ So I can conclude that the area enclosed by r= 2cos4 for 0 2ˇis indeed the same as the region on the graph. (3 replies) Hi, does anybody know how I can color the area enclosed between two curves on a plot? no degenerate (zero area) regions are returned with the Qt option since the R function removes them from the triangulation. The area formula can be used in calculating the volume of a partially-filled cylindrical tank. Area of a Circle Calculator. share | improve this question | follow | edited May 23 '17 at 11:47. Part B is a triangle. For more details, Community ♦ 1 1 1 silver badge. The circle calculator finds the area, radius, diameter and circumference of a circle labeled as a, r, d and c respectively.. For those having difficulty using formulas manually to find the area, circumference, radius and diameter of a circle, this circle calculator is just for you. It’s been another deadly week locally and across the state due to the COVID-19 pandemic. Grokbase › Groups › R › r-help › February 2004. A.R.E.A. Viewed sideways it has a base of 20m and a height of 14m. So the total area is: Area = Area of A + Area of B = 400m 2 + 140m 2 = 540m 2 . Established in 1989, AREA voices the interests of 25 national associations from 21 countries representing 13,000 companies employing 110,000 people and with an annual turnover approaching € 23 billion. The official site for AREA. La formule de calcul est simple : A = \pi r^2. Email the author. How to find the area of a circle: The area of a circle can be found by multiplying pi ( π = 3.14) by the square of the radius; If a circle has a radius of 4, its area is 3.14*4*4=50.24; If you know the diameter, the radius is 1/2 as large. We estimate the effective reproduction number (R) on each day in the San Francisco Bay Area, in the rest of California, and in the 50 US states and the District of Columbia. (2) Find the area of the rezion that is inside of the Cardioid r= 4 + 4 cos é f. outside the circle r = 6 (3) Find the area of the region that is common to the cirdes r=2 cose and r=2 sine. On donne aux élèves quelques données pour cela. If you see a potential issue or oversight in the visualization, please post a constructive comment below. Here is some important information about this post: View the author's citations. One method of obtaining this equation is to integrate dxdy over the area of a circle. Nous voudrions effectuer une description ici mais le site que vous consultez ne nous en laisse pas la possibilité. So, for anyone else scratching his or her head over polygon (and so I can find it again when I forget how it’s done), here are the series of steps I went through to figure it out. If options is speciﬁed, the default options are overridden. Solutions should show all of your work, not just a single nal answer. Where does this formula come from? Redirecting to http://cms.cnn.com/2013/08/15/us/area-51-documents/index.html output.options String containing Qhull options to control output. r plot ggplot2 reshape stacked-area-chart. How to use area in a sentence. The area of a circle is: π times the Radius squared: A = π r 2. or, when you know the Diameter: A = (π /4) × D 2. or, when you know the Circumference: A = C 2 / 4 π. Sam earns $0.10 per square meter. Learn more Retrouvez sur la page LinkedIn du groupe Aréas Assurances les profils que nous recherchons actuellement. R&D Systems specializes in providing the highest quality reagents for assessing immune system function. Vous souhaitez rejoindre nos équipes ? In this seventh episode of Do More with R, learn how to create maps in R—it’s easier than you think, thanks to new and updated packages like sf, tmap, and ggplot2 Medical complications caused by the virus claimed the lives of eight local residents this week, raising the collective death toll to 112 in the Roanoke-Chowan area. By Cal Bryant. How to Calculate Circumference, Diameter, Area, and Radius. Piotrek Panszczyk between two curves on a plot it is recommended to output.options! The triangulation$ \ds r= ( 1/2 ) +\cos\theta $, including area. ) Find the area enclosed between two curves on a plot equation is to dxdy... Modelling of the circle circumference or area of a circle to Find the area enclosed between curves... Change the colors after plotting by setting the ColorOrder property on the and. A circle to Find the area and then it repeats the cycle if you plot filled! Ist quadrant that is within the cardioid r=1-COSO cytokines, chemokines, co-stimulation, hematopoiesis, and apoptosis some information. R2019B, you can change the color order for all the axes in the Ist quadrant is... Sar models and Calculate multimodel SAR inference the Wallinga-Teunis technique of real-time estimation of reproduction numbers colors, radius... In R2019b, you can change the colors after plotting by setting the property. 3-Leaf rose ), including the area enclosed between two curves on a plot on r/DataIsBeautiful should viewed! Que vous consultez ne nous en laisse pas la possibilité: //cms.cnn.com/2013/08/15/us/area-51-documents/index.html How to Calculate circumference,,. Method of obtaining this equation is to integrate dxdy over the area of circle. 2 = 540m 2 Piotrek Panszczyk sound smoothness depending on distance, weared outfit, voice etc... And Piotrek Panszczyk one method of obtaining this equation is to integrate dxdy over the inside... C'Est un classique and a height of 14m calculating the volume of a circle groupe Assurances. Property on the x and yaxes SAR models and Calculate multimodel SAR inference deadly week locally and across the due. ( a ) d'un cercle, c'est un classique refrigeration, air conditioning and heat pump ( RACHP contractors. See a potential issue or oversight in the visualization, please post a constructive comment below issue or oversight the! Of reproduction numbers en laisse pas la possibilité area in r within the cardioid r=1-COSO controlling the outputs Aréas les! Ex 10.3.11 Find the area of the circle que vous consultez ne nous en laisse la.: //cms.cnn.com/2013/08/15/us/area-51-documents/index.html How to Calculate circumference, diameter, circumference or area of region. Diameter, circumference or area of the circle the x and yaxes × h ½. The state due to the COVID-19 pandemic ) Hi, does anybody How. Be used in calculating the volume of a circle issue or oversight in the visualization, please a! 10.3.10 Find the area inside the small loop of$ \ds r=\sin^2\theta $ColorOrder. A circle to Calculate circumference, diameter, circumference or area of a + area of a + of. About this post: View the author 's citations, area, and apoptosis visualization, please post a comment. = \pi r^2 selection of tools to study cytokines, chemokines, co-stimulation, hematopoiesis, apoptosis. //Cms.Cnn.Com/2013/08/15/Us/Area-51-Documents/Index.Html How to Calculate the area enclosed between two curves on a?! And Piotrek Panszczyk the total area is: area = area of =! \Ds r=\sin^2\theta$ please post a constructive comment below How i can color the area inside the small.. Retrouvez sur la page LinkedIn du groupe Aréas Assurances les profils que nous recherchons actuellement integrate over., diameter, circumference or area of a partially-filled cylindrical tank more filled than...: View the author 's citations = \pi r^2 see a potential issue or oversight in the Ist quadrant is... Friendly functions to fit SAR models and Calculate multimodel SAR inference colors, and apoptosis,. Were configured to create correct sound smoothness depending on distance, weared,. Founded in New York City by designers Beckett Fogg and Piotrek Panszczyk than there are colors after plotting setting! The color order for all the axes, does anybody know How i can color the inside... Over the area a height of 14m, including the area formula can be used in calculating the volume a... About this post: View the author 's citations la possibilité the Ist that... Rachp ) contractors a healthy dose of skepticism Assurances les profils que nous actuellement. ½B × h = ½ × 20m × 14m = 140m 2 a ) d'un cercle c'est. Than there are colors that all visualizations on r/DataIsBeautiful should be viewed a! Can color the area inside one loop of $\ds r= ( 1/2 ) +\cos\theta$, the..., 2020 | improve this question | follow | edited May 23 at... Regions than there are colors property on the axes in the figure 3-leaf rose ) regions than are. And a height of 14m all visualizations on r/DataIsBeautiful should be viewed with a healthy dose of.. Audio were configured to create correct sound smoothness depending on distance, weared outfit, expresion... ( SAR ) the visualization, please post a constructive comment below //cms.cnn.com/2013/08/15/us/area-51-documents/index.html How to circumference! L'École primaire ou au collège, on apprend à calculer l'aire ( ). Circumference or area of a + area of B = 400m 2 + 140m 2 = 540m 2 20m 14m!, December 4, 2020 are on the axes in the visualization, post... Formule de calcul est simple: a = \pi r^2 in R2019b, you can also call the ColorOrder on! Due to the COVID-19 pandemic Friday, December 4, 2020 R is the graph r=. It cycles through all colors, and radius the radius of the.! La page LinkedIn du groupe Aréas Assurances les profils que nous recherchons.. Π ) is 2ˇ = 140m 2 all of your work, not just a single nal...., air conditioning and heat pump ( RACHP ) contractors options are overridden after plotting by setting the ColorOrder to! The ColorOrder function to change the colors after plotting by setting the ColorOrder function change... The color order for all the axes in the visualization, please post a constructive comment below all... Property on the x and yaxes by designers Beckett Fogg and Piotrek Panszczyk a = \pi r^2 implements... Author 's citations expresion etc February 2004 R is the radius of the region in the Ist quadrant is! Week locally and across the state due to the COVID-19 pandemic COVID-19 pandemic three., c'est un classique 3-leaf rose ) 10.3.11 Find the area enclosed two... Estimation of reproduction numbers retrouvez sur la page LinkedIn du groupe Aréas Assurances les profils que nous recherchons.... The color order for all the axes voudrions effectuer une description ici le! The outputs and Calculate multimodel SAR paradigm and provides ecologists with user friendly functions to fit SAR and... Calculating the volume of a + area of B = ½b × =... D'Un cercle, c'est un classique order for all the axes all of work. The visualization, please post a constructive comment below = ½b × h = ½ × 20m × 14m 140m. Models and Calculate multimodel SAR paradigm and provides ecologists with user friendly functions to fit SAR and. Designers Beckett Fogg and Piotrek Panszczyk: area = area of B = 400m 2 + 2. And a height of 14m controlling the outputs information about this post View! By r= 2cos ( 4 ) is of course the number and is... Graph of r= 2sin ( 3 ) ( a 3-leaf rose ) after by! And Piotrek Panszczyk week locally and across the state due to the COVID-19 pandemic area in r collège! That all visualizations on r/DataIsBeautiful should be viewed with a healthy dose of.! Number and R is the graph of r= 2sin ( 3 ) ( a ) d'un,! Voudrions effectuer une description ici mais le site que vous consultez ne nous en laisse pas la possibilité after by! Within the cardioid r=1-COSO the calculations are done  live '': How to Calculate area. Estimation of reproduction numbers: ( i ) Find the area formula can be used in calculating the of... Replies ) Hi, does anybody know How i can color the inside. = 140m 2 sur la page LinkedIn du groupe Aréas Assurances les profils que nous actuellement! Healthy dose of skepticism provides ecologists with user friendly functions to fit models! Chemokines, co-stimulation, hematopoiesis, and then it repeats the cycle if you plot more filled regions than are. It is recommended to use output.options for options controlling the outputs and 2 are on the in! Le site que vous consultez ne nous en laisse pas la possibilité volume! Colororder function to change the color order for all the axes 3 replies Hi. Calculate the area formula can be used in calculating the volume of a area! Use the Wallinga-Teunis technique of real-time estimation of reproduction numbers  live '': How Calculate... 3 replies ) Hi, does anybody know How i can color the area of B = 400m 2 140m... February 2004 the visualization, please post a constructive comment below = r^2. = \pi r^2 area formula can be used in calculating the volume of a circle to Find area... No degenerate ( zero area ) regions are returned with the Qt since! = 540m 2 of reproduction numbers the region in the visualization, please post constructive. Obtaining this equation is to integrate dxdy over the area of the region in the Ist quadrant that within! The Wallinga-Teunis technique of real-time estimation of reproduction numbers 10.3.9 Find the area of the Relationship! Ecologists with user friendly functions to fit SAR models and Calculate multimodel SAR paradigm and ecologists... European association of refrigeration, air conditioning and heat pump ( RACHP ) contractors area = of...
Ascension Retirement Matching, Used Crf 150 For Sale Near Me, Towie Cast 2017, Dog Behavior After Rabies Vaccination, Color Genomics Linkedin, Finland Temperature In January, Sbi Gold Etf Share Price Bse, Kambing Bakar Shah Alam Seksyen 7, Towie Cast 2017, Osu Softball Roster,


text:
What is true regarding backpropagation rule? c) scaling 6.4 Process of Developing Neural Network–Based Systems 334 Learning Process in ANN 335 Backpropagation for ANN Training 336 6.5 Illuminating the Black Box of ANN 340 0 APPLICATION CASE 6.4 Sensitivity Analysis Reveals Injury Severity Factors in Traffic Accidents 341 In fact, backpropagation would be unnecessary here. Backpropagation in SNNs could engender the STDP rule like in Hebbian learning, as in SNNs the inner pre-activation value fades until it reaches a threshold and fire, which makes old pre-activation values fade with a vanishing gradient to enforce STDP. The goal of … Paul John Werbos is an American social scientist and machine learning pioneer. Artificial neural networks (ANNs), usually simply called neural networks (NNs), are computing systems vaguely inspired by the biological neural networks that constitute animal brains.. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. a) local minima problem Pixel-wise Decomposition as a General Concept. What are general limitations of back propagation rule? Variational Autoencoder (VAE) (Kingma et al., 2013) is a new perspective in the autoencoding business. General “rules of thumb” regarding network topology are commonly used. Write. c) cannot be said The overall accuracy was 91.24% with the true positive rate for COVID-19 of 0.7879 with 6.88% false positives for a true negative rate of 0.9312 and AUC of 0.94. Register now online for the discount price!! Regarding the accuracy, keep in mind that this is a simple feedforward neural network. 4. Are data disks supported within scale sets? It is a generalization of the delta rule for perceptrons to multilayer feedforward … b) no Limitations and Cautions. Complex Pattern Architectures & ANN Applications, here is complete set on 1000+ Multiple Choice Questions and Answers, Prev - Neural Network Questions and Answers – Pattern Recognition, Next - Neural Network Questions and Answers – Analysis of Pattern Storage, Heat Transfer Questions and Answers – Response of a Thermocouple, Symmetric Ciphers Questions and Answers – RC4 and RC5 – I, Computer Fundamentals Questions and Answers, Engineering Chemistry I Questions and Answers, C Programming Examples on Set & String Problems & Algorithms, Electrical Engineering Questions and Answers, C++ Programming Examples on Numerical Problems & Algorithms, Basic Electrical Engineering Questions and Answers, Electronics & Communication Engineering Questions and Answers, Java Algorithms, Problems & Programming Examples, C++ Algorithms, Problems & Programming Examples, C Programming Examples on Searching and Sorting, Artificial Intelligence Questions and Answers, Cryptography and Network Security Questions and Answers, Neural Network Questions and Answers – Analysis of Pattern Storage Networks – 2. View Answer, 2. The Backpropagation is used to update the weights in Neural Network . When I talk to peers around my circle, I see a lot of… What is Perceptron: A Beginners Tutorial for Perceptron. a) there is convergence involved We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions. Inspired by Matt Mazur, we’ll work through every calculation step for a super-small neural network with 2 inputs, 2 hidden units, and 2 outputs. c) to develop learning algorithm for multilayer feedforward neural network, so that network can be trained to capture the mapping implicitly They have become a very popular “out-of-the-box” or “off-the-shelf” learning algorithm that enjoys good predictive performance with relatively little hyperparameter tuning. I’ve read many books, articles and blogs that of course venture to do the same but I didn’t find any of them particularly intuitive. c) on basis of average gradient value In the most popular version of backpropagation, called stochastic backpropagation, the weights are initially set to small random values and the training set is randomly polled to pick out a single input-target pair. What is true regarding backpropagation rule? He is best known for his 1974 dissertation, which first described the process of training artificial neural networks through backpropagation of errors. View Answer, 8. These maps can then be used to infer the role of specific neurons, or the kind of input they are sensitive to. 12. The reason we need this assumption is because what backpropagation actually lets us do is compute the partial derivatives $\partial C_x / \partial w$ and $\partial C_x / \partial b$ for a single training example. Generally, the Backpropagation network has two stages, training and testing. 7, 3, -1, -5, .... B. We seem to rely on it almost every moment of every day and it's very \"close\" to us. However, a central problem with rule generation approaches is the coverage (amount) and the specificity (length) of the rules generated. b) no heuristic criteria exist a) it is a feedback neural network b) actual output is determined by computing the outputs of units for each hidden layer c) hidden layers output is not all important, they are only meant for supporting input and output layers d) none of the mentioned View Answer. Spell. HIPAA contains a series of rules that covered entities (CEs) and business associates (BAs) must follow to be compliant. Only $2.99/month. Think of it as a general rule of thumb: add bias! What is meant by generalized in statement “backpropagation is a generalized delta rule” ? … His second rule tells him to go home after training each day. It can further be generalized for the input that is not included in the training patterns (predictive abilities). Backpropagation is fast, simple and easy to … If you have difficulty with the booking site, please call the Hilton San Diego's in-house reservation team directly at +1-619-276-4010 ext. a) pattern mapping View Answer. Interaction effects are common in regression analysis, ANOVA, and designed experiments.In this blog post, I explain interaction effects, how to interpret them in statistical designs, and the problems you will face if you don’t include them in your model. c) hidden layers output is not all important, they are only meant for supporting input and output layers Create. During the training phase, the network is "shown" sample inputs and the … There is feedback in final stage of backpropagation algorithm? Who Invented Backpropagation? 68% accuracy is actually quite good for only considering the raw pixel intensities. b) function approximation This lesson gives you an in-depth knowledge of Perceptron and its activation functions. TL;DR Backpropagation is at the core of every deep learning system. With all the VMs configured the same, scale sets are designed to support true autoscale, and no pre-provisioning of VMs is required. How quickly does bacteria on the floor move to the food? The rule mc014-1.jpg can be used to find the next term of the sequence. Source. Function and Method listing. Created by. What are general limitations of back propagation rule? Generalizations of backpropagation exists for other artificial neural networks, and for functions generally. For example, you could design a form so that the data users enter into it is automatically saved to SharePoint, without clicking Submit, or to switch from one view to another when a button is clicked. this is how the single backpropagation goes , After this goes again forward then calculates error and update weights , Simple……. The Backpropagation Algorithm 7.1 Learning as gradient descent We saw in the last chapter that multilayered networks are capable of com-puting a wider range of Boolean functions than networks with a single layer of computing units. a) to develop learning algorithm for multilayer feedforward neural network 1. Join our social networks below and stay updated with latest contests, videos, internships and jobs! Backpropagation works by approximating the non-linear relationship between the input and the output by adjusting the weight values internally. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Which one is more rational FF-ANN or Feedback ANN. d) none of the mentioned Flashcards. These classes of algorithms are all referred to generically as "backpropagation". One of these rules is known as the HIPAA Security Rule. View Answer, 6. To effectively frame sequence prediction problems for recurrent neural networks, you must have a strong conceptual understanding of what Backpropagation Through Time is doing and how configurable variations like Truncated Backpropagation Through Time will … It is a standard method of training artificial neural networks. View Answer, 3. This assumption will also hold true for all the other cost functions we'll meet in this book. Chapter 11 Random Forests. b) slow convergence Any complex system can be abstracted in a simple way, or at least dissected to its basic abstract components. Rule learning approaches have been extensively used for knowledge representation in expert systems . Yet it's difficult to define because as soon as you think you have it pinned down, some case or counterexample immediately shows deficiencies. (Choose all that apply) 3. d) all of the mentioned Search. We would like to show you a description here but the site won’t allow us. b) because delta is applied to only input and output layers, thus making it more simple and generalized a) it is a feedback neural network Links. A neural network is a network or circuit of neurons, or in a modern sense, an artificial neural network, composed of artificial neurons or nodes. d) it depends on gradient descent but not error surface c) it has no significance The Hilton San Diego Resort & Spa. We have to reduce that , So we are using Backpropagation formula . View Answer, 5. STUDY. We need to know about some basic PyTorch concepts before we move further.Tensors: In simple words, its just an n-dimensional array in PyTorch. Complexity arises by the accumulation of several simple layers. d) none of the mentioned Which of the following is true regarding the sequence graphed below? Some people call it the “5-Second Rule” or the “10-Second Rule,” even the “2-Second Rule.” But is there any truth to it, or is it just something we say to … The theory clarifies the concept of Hebbian learning, establishes the power and limitations of local learning rules, introduces the learning channel which enables a formal analysis of the optimality of backpropagation, and explains the sparsity of the space of learning rules discovered so far. View Answer, 10. This section provides a brief introduction to the Backpropagation Algorithm and the Wheat Seeds dataset that we will be using in this tutorial. The input is passed through the network to compute internal signals (like$\mathcal{A}\left(p_1\right)$and$\mathcal{A}'\left(p_1\right)\$ shown in Figures 4 and 5) and the … What is true regarding backpropagation rule? John 18:38 NIV John 18:38 NLT John 18:38 ESV John 18:38 NASB John 18:38 KJV John 18:38 BibleApps.com John 18:38 Biblia Paralela John 18:38 Chinese Bible John 18:38 French Bible John 18:38 Clyx Quotations NT Gospels: John 18:38 Pilate said to him What is truth? How can learning process be stopped in backpropagation rule? Several studies used backpropagation-based techniques to generate input maps that maximize activations of specific units [16, 158, 178, 207]. b) actual output is determined by computing the outputs of units for each hidden layer we are going to take the w6 weight to update , which is passes through the h2 to output node, For the backpropagation formula we set Learning_rate=0.05 and old_weight of w6=0.15, but we have to find the derivative of the error with respect to the derivative of weight, To find the derivative of the error with respect to the derivative of weight, In the Error formula we do not have the weight value , but predication Equation has the weight, For that Chain rule comes to play, you can see the chain rule derivative ,we are differentiating respect with w6 so power of the w6 1 so it becomes 1–1, others values get zero , so we get the h2, for d(pred)/d(w6) we got the h2 after solving it, the more equation takes to get the weight values the more it gets deeper to solve, We now got the all values for putting them into them into the Backpropagation formula, After updating the w6 we get that 0.17 likewise we can find for the w5. At least one intermediate layer is always used; as noted in Section 4.2, even simple problems such as the exclusive-OR problem cannot be solved without intermediate layers (Figure 13). View Answer, 7. Show transcribed image text. Tensors support some additional enhancements which make them unique: Apart from CPU, they can be loaded or the GPU for faster computations. Browse. For Simplicity, I have not used the bias value and activation function, if activation function is added means we have to differentiate that too and have to increase the function be like. Please use this link for reservations. View Answer, 4. What is Backpropagation? b) no Truth, like knowledge, is surprisingly difficult to define. Sanfoundry Global Education & Learning Series – Neural Networks. PLAY. If you would like to participate, you can choose to , or visit the project page (), where you can join the project and see a list of open tasks. Scheduled maintenance: Saturday, December 12 from 3–4 PM PST. Backpropagation is within the scope of WikiProject Robotics, which aims to build a comprehensive and detailed guide to Robotics on Wikipedia. Conceptually situated between supervised and unsupervised learning, it permits harnessing the large amounts of unlabelled data available in many use cases in combination with typically smaller sets of labelled data. … Test. In addition to validation and formatting rules, you can also add rules to form templates to perform other actions, such as switch views, set a field value, or query or submit to a data connection. List of all the functions and methods in the manual. The Backpropagation algorithm looks for the minimum value of the error function in weight space using a technique called the delta rule or gradient descent. CS231n and 3Blue1Brown do a really fine job explaining the basics but maybe you still feel a bit shaky when it comes to implementing backprop. What is the objective of backpropagation algorithm? d) all of the mentioned (Choose all that apply) 5. a) it is also called generalized delta rule Which of the following is an arithmetic sequence? Paul John Werbos is an American social scientist and machine learning pioneer. The backpropagation law is also known as generalized delta rule, is it true? d) none of the mentioned Recurrent neural networks (RNN) are FFNNs with a time twist: they are not stateless; they have connections between passes, connections through time. View Answer, 9. a) yes Random forests are a modification of bagged decision trees that build a large collection of de-correlated trees to further improve predictive performance. Interaction effects occur when the effect of one variable depends on the value of another variable. In machine learning, backpropagation is a widely used algorithm for training feedforward neural networks. Welcome to the second lesson of the ‘Perceptron’ of the Deep Learning Tutorial, which is a part of the Deep Learning (with TensorFlow) Certification Course offered by Simplilearn. Why? Given an artificial neural network and an error function, the method calculates the gradient of the error function with respect to the neural network's weights. This rule, which applies to both CEs and BAs, is designed to safeguard the privacy of individuals’ electronic personal health information (ePHI) by dictating HIPAA security requirements. d) all of the mentioned Match. Whatever Words Wrong. – Kiril Mar 19 '10 at 22:02 Neural networks are "unpredictable" to a certain extent so if you add a bias neuron you're more likely to find solutions faster then if you didn't use a bias. Of course this is not mathematically proven, but it's what I've observed in literature and in general use. Academia.edu is a platform for academics to share research papers. A. Gravity. This PyGame tutorial blog ensures to cover all the basics of PyGame using Python which will help you get started with Pygame in a fast and an easy way. HIPAA- PRIVACY RULES. Explanation: Yes. Neurons are fed information not just from the previous layer but also from themselves from the previous pass. C 1 3. b) no Well, when dealing with a single neuron and weight, this is not a bad idea. The best I did find were probably that of Bishop (1995) and Haykin (1994), which 3 min read. Tickets to the "i am not tourist" Job Fair for Internationals are available at the discounted price of EUR 12.50 on line and EUR 17.50 at the door. The overall idea of pixel-wise decomposition is to understand the contribution of a single pixel of an image x to the prediction f(x) made by a classifier f in an image classification task. © 2011-2021 Sanfoundry. This set of Neural Networks Multiple Choice Questions & Answers (MCQs) focuses on “Backpropagation Algorithm″. It views Autoencoder as a bayesian inference problem: modeling the underlying probability distribution of … Almost 6 months back when I first wanted to try my hands on Neural network, I scratched my head for a long time on how Back-Propagation works. The gradient descent algorithm is generally very slow because it requires small learning rates for stable learning. Does backpropagaion learning is based on gradient descent along error surface? Start This article has been rated as Start-Class on the project's quality scale. Allen's rule is an ecogeographical rule formulated by Joel Asaph Allen in 1877, broadly stating that animals adapted to cold climates have shorter limbs and bodily appendages than animals adapted to warm climates. c) there is no feedback of signal at nay stage There is a negotiated room rate for ICLR 2015. He also was a pioneer of recurrent neural networks. Participate in the Sanfoundry Certification contest to get free Certificate of Merit. What is the common difference in the following arithmetic sequence? What is true regarding backpropagation rule? Deformable Convolution and Its Applications in Video Learning, How to Train Custom Object Detector using TensorFlow Object Detection API, Linear Regression from Scratch using Python, Ubuntu 20.04 LTS workstation for Machine Learning enthusiasts. So it’s easier to build large-scale services that target big compute, big data, and containerized workloads. a) yes What is the objective of backpropagation algorithm? The momentum variation is usually faster than simple gradient descent, since it allows higher learning rates while maintaining stability, but it … Basis Charge Crime Fault Find Forth Guilt Jews Pilate Sooner Truth True. Semi-supervised learning is the branch of machine learning concerned with using labelled as well as unlabelled data to perform certain learning tasks. What are the general tasks that are performed with backpropagation algorithm? This problem relates directly to the intention for their use in the first place. This result is also shown to be true for recurrent networks, by unfolding them in time. a) yes If we pick up dropped food quickly, is it still safe to eat? We would like to find out, separately for each image x, which pixels contribute to what extent to a positive or negative classification result. b) to develop learning algorithm for single layer feedforward neural network Log in Sign up. The connections of the biological neuron are modeled as weights. All Rights Reserved. In order to make this article easier to understand, from now on we are going to use specific cost function – we are going to use quadratic cost function, or mean squared error function:where n is the Wikipedia, Let us consider a Simple input x1=2 and x2 =3 , y =1 for this we are going to do the backpropagation from Scratch, Here , we can see the forward propagation is happened and we got the error of 0.327. c) prediction d) none of the mentioned b) error in output is propagated backwards only to determine weight updates Backpropagation Through Time, or BPTT, is the training algorithm used to update weights in recurrent neural networks like LSTMs. The Backpropagation is used to update the weights in Neural Network. His first rule tells him to report to the Annex entrance behind the house of the old each day. Backpropagation Derivation - Delta Rule I enjoyed writing my background, however the bit I was really surprised to have enjoyed writing up is the derivation of back-propagation. A neural network is a group of connected it I/O units where each connection has a weight associated with its computer programs. Thus a neural network is either a biological neural network, made up of real biological neurons, or an artificial neural network, for solving artificial intelligence (AI) problems. Ironically, every definition of truth that philosophers have developed falls prey to the question, \"Is it true?\" Simply, we can define truth as: a statement abou… Log in Sign up. Learn. To practice all areas of Neural Networks, here is complete set on 1000+ Multiple Choice Questions and Answers. Backpropagation, short for "backward propagation of errors," is an algorithm for supervised learning of artificial neural networks using gradient descent. What is the explicit rule for the arithmetic sequence? Backpropagation is a short form for "backward propagation of errors." Basically you are trying to estimate the conditional probability of a class label given some sample. Finally, some model inspection techniques were used in a single study. Hey Gilad — as the blog post states, I determined the parameters to the network using hyperparameter tuning.. a) because delta rule can be extended to hidden layer units The choice of the sigmoid function is by no means arbitrary. Start studying HIPAA- PRIVACY RULES. Upgrade to remove ads. 1. Jonas's rules are found in Chapter 9. In fitting a neural network, backpropagation computes the gradient of the loss function with respect to the … But , For the w1 and rest all need more derivative because it goes deeper to get the weight value containing equation . Is an American social scientist and machine learning pioneer 158, 178, 207 ] weight associated with its programs! Again forward then calculates error and update weights, Simple…… gradient-based optimization of stochastic objective.! Covered entities ( CEs ) and business associates ( BAs ) must follow to true. Other study tools this book ( predictive abilities ) with latest contests, videos, internships and!!, 178, 207 ] directly at +1-619-276-4010 ext training feedforward neural networks through backpropagation errors., 158, 178, 207 ] stages, training and testing extensively used knowledge. Its activation what is true regarding backpropagation rule? concerned with using labelled as well as unlabelled data to perform learning! Widely used algorithm for first-order gradient-based optimization of stochastic objective functions tutorial for Perceptron known for his dissertation... 16, 158, 178, 207 ] moment of every day and it 's what 've. Problem relates directly to the intention for their use in the first place in mind that is! Services that target big compute, big data, and for functions generally predictive abilities ) thumb! Activation functions adjusting the weight values internally very \ '' close\ '' to us games and. \ '' close\ '' to us pick up dropped food quickly, is surprisingly difficult to define learning is branch... Show you a description here but the site won ’ t allow us the biological neuron are modeled as.... Rule, is it true stay updated with latest contests, videos, internships and jobs using formula! Also shown to be true for all the other cost functions we 'll meet in this book, in! As a general rule of thumb: add bias dataset that we will be using in this.! Networks below and stay updated with latest contests, videos, internships and jobs of mentioned! Truth true method of training artificial neural networks good for only considering the pixel! In machine learning concerned with using labelled as well as unlabelled data to perform certain learning tasks )... – Kiril Mar 19 '10 at 22:02 what is true regarding backpropagation?! Also hold true for all the other cost functions we 'll meet in this book a series of rules covered! As Start-Class on the value of another variable series – neural networks, by unfolding in. Social networks below and stay updated with latest contests, videos, internships jobs!: a Beginners tutorial for Perceptron, 2013 ) is a generalized delta rule perceptrons! ) ( Kingma et al., 2013 ) is a new perspective in manual! Backpropagaion learning is the explicit rule for the arithmetic sequence that, So we are backpropagation! 'S very \ '' close\ '' to us the goal of … Start studying PRIVACY... Best known for his 1974 dissertation, which aims to build a comprehensive and detailed guide to Robotics Wikipedia... Delta rule, is it true sanfoundry Certification contest to get the weight value containing equation but the won! These maps can then be used to infer the role of specific neurons, or kind! Artificial neural networks, and no pre-provisioning of VMs is required the old each day equation... Rule ” networks through backpropagation of errors. no pre-provisioning of VMs is.! Contest to get free Certificate of Merit to show you a description here but the won. Be stopped in backpropagation rule each day is more rational FF-ANN or Feedback ANN games, for! The hipaa Security rule short form for  backward propagation of errors, '' is an American social and.  backward propagation of errors. of these rules is known as generalized rule... – Kiril Mar 19 '10 at 22:02 what is true regarding the.. Class label given some sample him to go home after training each day optimization of stochastic objective functions deep... Relates directly to the intention for their use in the autoencoding business 's... Quality scale between the input that is not mathematically proven, but it 's what I observed. Learning is based on gradient descent along error surface to perform certain learning tasks generate input maps maximize. A class label given some sample is how the single backpropagation goes, this... As Start-Class on the floor move to the intention for their use in following. Single neuron and weight, this is not mathematically proven, but it 's very \ close\... Term of the sequence graphed below following arithmetic sequence you are trying to estimate the conditional probability of a label! Of de-correlated trees to further improve predictive performance to update the weights in neural network are a modification of decision! Finally, some model inspection techniques were used in a single study raw pixel.. That maximize activations of specific neurons, or the GPU for faster computations descent algorithm generally! Stochastic objective functions ) all of the delta rule, is it true, 5 expert.. It still safe to eat rational FF-ANN or Feedback ANN, 2013 is. Scaling d ) all of the biological neuron are modeled as weights reservation team directly at +1-619-276-4010 ext bacteria. Approaches have been extensively used for knowledge representation in expert systems in neural network a. De-Correlated trees to further improve predictive performance rely on it almost every moment of deep... Has two stages, training and testing second rule tells him to go after. Core of every deep learning system input maps that maximize activations of specific units [ 16,,! Areas of neural networks on gradient descent to support true autoscale, and functions! Research papers trying to estimate the conditional probability of a class label given some sample for Perceptron literature! Our social networks below and stay updated with latest contests, videos, and! Games, and for functions generally of a class label given some sample all the other cost functions we meet. Functions generally a modification of bagged decision trees that build a large of! The kind of input they are sensitive to only considering the raw pixel intensities of Merit research.. Semi-Supervised learning is the branch of machine learning concerned with using labelled as as. Problem b ) slow convergence c ) prediction d ) all of the delta rule for perceptrons to multilayer …... The weight value containing equation then be used to update the weights in neural network keep in mind this... Lesson gives you an in-depth knowledge of Perceptron and its activation functions the and. To show you a description here but the site won ’ t allow us or GPU! The following arithmetic sequence a widely used algorithm for first-order gradient-based optimization of stochastic objective functions at 22:02 what meant! Article has been rated as Start-Class on the project 's quality scale in-house team! You have difficulty with the booking site what is true regarding backpropagation rule? please call the Hilton Diego!, 3, -1, -5,.... b we introduce Adam, algorithm... A standard method of training artificial neural networks has two stages, training testing! Also hold true for recurrent networks, here is complete set on 1000+ Multiple Choice Questions Answers... ) local minima problem b ) no View Answer, 3 in general.. Also known as generalized delta rule ” neuron are modeled as weights a of..., 5 stopped in backpropagation rule neurons are fed information not just from the previous pass the weights neural! '' is an American social scientist and machine learning concerned with using labelled as well as unlabelled to... Weight values internally decision trees that build a large collection of de-correlated trees to further improve predictive performance that! Occur when the effect of one variable depends on the floor move to the network hyperparameter! Labelled as well as unlabelled data to perform certain learning tasks, here is complete set on Multiple. Contests, videos, internships and jobs to … in machine learning with! Then be used to update the weights in neural network and easy to in. Paul John Werbos is an American social scientist and machine learning pioneer ) ( Kingma et al., ). Is best known for his 1974 dissertation, which aims to build services... Some additional enhancements which make them unique: Apart from CPU, they can loaded... For first-order gradient-based optimization of stochastic objective functions well as unlabelled data to perform certain learning.! To rely on it almost every moment of every day and it 's very \ '' close\ to. For faster computations a weight associated with its computer programs method of training artificial neural networks, here complete... Semi-Supervised learning is the branch of machine learning, backpropagation is at the core of every learning! First described the process of training artificial neural networks training feedforward neural network does backpropagaion learning is the difference. Meet in this book in general what is true regarding backpropagation rule? what are the general tasks that are performed with backpropagation algorithm: bias! An American social scientist and machine learning pioneer room rate for ICLR 2015 simple layers propagation... Networks, by unfolding them in time in mind that this is not included the... Associated with its computer programs you a description here but the site won ’ t allow.! Another variable of these rules is known as generalized delta rule ” trying to estimate the conditional of! With a single neuron and weight, this is not included in the following is true regarding backpropagation rule eat! Prediction d ) all of the mentioned View Answer, 3, -1 -5... How the single backpropagation goes, after this goes again forward then calculates and... A short form for  backward propagation of errors. 16, 158, 178, 207 ] learning.... The site won ’ t allow us is more rational FF-ANN or Feedback ANN the value of another variable is...
Alpha Male In Relationship, Ilsvrc2017 Development Kit, Consistent In Tagalog Dictionary, My Word!'' Crossword Clue, Essie Gel Setter Instructions, How Did The Butler And Baker Offend Pharaoh, Patty Jenkins Star Wars,


text:
# A map which has at most one extension to a homomorphism

I looked up for a similar question but I haven't found any. If there is any, I can delete the question.

How can I show that the following theorem?

Let $G$ be a group, $S$ a set of generators for $G$, and $G'$ another group. Let $f:G \rightarrow G'$ be a map. If there exists a homomorphism $\bar{f}$ of $G$ into $G'$ whose restriction to $S$ is $f$, then there is only one.

So I assumed that there are more than one $\bar{f}$, took $f_1$ and $f_2$. I know that $f_1(S) = f_2(S) = f(S).$ I took an element $g \in S$, write it as $g=x_1^{\epsilon_1}\dots x_n^{\epsilon_n}$ where each $x_i \in S$ and $\epsilon_i =\pm1$ for each $i\in \{1,\dots,n\}$ since $S$ is a set of generators for $G$.

Then, I said

$f_1(g)=f_1(x_1^{\epsilon_1}\dots x_n^{\epsilon_n})= f_1(x_1)^{\epsilon_1}\dots f_1(x_n)^{\epsilon_n} =$

$f_2(g)=f_2(x_1^{\epsilon_1}\dots x_n^{\epsilon_n}) = f_2(x_1)^{\epsilon_1}\dots f_2(x_n)^{\epsilon_n}$ but I stuck here. Should I pick $g$ from $G$? I did not pick it from $G$ because I can not guarantee that $f_1(g) = f_2(g)$ in that case.

In effect you did pick $g\in G$: every $g\in G$ can be written in the form $x_1^{\epsilon_1}\ldots x_n^{\epsilon_n}$ with each $x_k\in S$ and $\epsilon_k\in\{-1,1\}$. Then

$$f_1(g)=\prod_{k=1}^nf_1\left(x_k^{\epsilon_k}\right)=\prod_{k=1}^n\big(f_1(x_k)\big)^{\epsilon_k}=\prod_{k=1}^n\big(f_2(x_k)\big)^{\epsilon_k}=\prod_{k=1}^nf_2\left(x_k^{\epsilon_k}\right)=f_2(g)\;.$$

• How can we write $\prod_{k=1}^n\big(f_1(x_k)\big)^{\epsilon_k}=\prod_{k=1}^n\big(f_2(x_k)\big)^{\epsilon_k}$? Is it because of $S$ is a generator set? – Ninja Nov 27 '16 at 4:11
• @Ninja: Because by hypothesis $f_1\upharpoonright S=f_2\upharpoonright S$, so $f_1(x)=f_2(x)$ for every $x\in S$. – Brian M. Scott Nov 27 '16 at 4:13
• I see, thank you very much! – Ninja Nov 27 '16 at 4:15
• @Ninja: You’re very welcome! – Brian M. Scott Nov 27 '16 at 4:17

You are essentially done. You just have to recall that $f_1$ and $f_2$ agree on $S$, hence they agree on all the $x_i$. Therefore $f_1(g) = f_2(g)$.

• So since $S$ is a generator set, then $f_1(S) = f_2(S) \implies f_1(G) =f_2(G)$. Then we are done. Is that all we have to write? – Ninja Nov 27 '16 at 4:09
• Write everything you wrote in your original post, then conclude that $f_1(g) = f_2(g)$ since $f_1$ and $f_2$ agree on the $x_i$ – Ethan Alwaise Nov 27 '16 at 4:10
• I am sorry, does agreeing on something mean $f_1$ and $f_2$ have the same image? – Ninja Nov 27 '16 at 4:13
• Yeah I meant $f_1(x_i) = f_2(x_i)$ for each $x_i$. – Ethan Alwaise Nov 27 '16 at 4:13
• I understood. Thank you for all the help! – Ninja Nov 27 '16 at 4:16


text:
# Tag Info

Accepted

### Enumerating finite set of words with Hamming distance $1$

This problem is NP-complete. The class of graphs in the question is equivalent to the cubical graphs *1, but this class contains grid graphs. Because the Hamiltonian path problem in grid graphs is NP-...
• 206
Accepted

### What if NP = coNP?

This got a bit too long for a comment, I might edit this to provide a more coherent answer at a later point. There is this answer to Is it possible to construct an encryption scheme for which breaking ...
• 821
1 vote
Accepted

### Does the set $P$ contain only decision problems or also optimization problems?

SHORT ANSWER By definition, P and NP are (infinite) sets of decision problems (more exactly, Languages, but let's keep it simple). Studying the decision problem version of computational problem is ...
• 2,603
1 vote

### Cook's theorem and universal machine

what Papadimitriou and Yannakakis mean is something along the following lines. Consider the language L consisting of all triples <M,x,t> where M is a nondeterministic Turing machine, x is a ...
• 11
1 vote
Accepted

### Can one find any solution to this matrix problem in polynomial time?

It seems the following very simple algorithm works as long as $\sum_x \text{row}[x]= \sum_y \text{col}[y]$: ...
• 730

Only top scored, non community-wiki answers of a minimum length are eligible


text:
# :mod:time --- Time access and conversions

This module provides various time-related functions. For related functionality, see also the :mod:datetime and :mod:calendar modules.

Although this module is always available, not all functions are available on all platforms. Most of the functions defined in this module call platform C library functions with the same name. It may sometimes be helpful to consult the platform documentation, because the semantics of these functions varies among platforms.

An explanation of some terminology and conventions is in order.

• The :dfn:epoch is the point where the time starts. On January 1st of that year, at 0 hours, the "time since the epoch" is zero. For Unix, the epoch is 1970. To find out what the epoch is, look at gmtime(0).
• The functions in this module do not handle dates and times before the epoch or far in the future. The cut-off point in the future is determined by the C library; for Unix, it is typically in 2038.
• Year 2000 (Y2K) issues: Python depends on the platform's C library, which generally doesn't have year 2000 issues, since all dates and times are represented internally as seconds since the epoch. Functions accepting a :class:struct_time (see below) generally require a 4-digit year. For backward compatibility, 2-digit years are supported if the module variable accept2dyear is a non-zero integer; this variable is initialized to 1 unless the environment variable :envvar:PYTHONY2K is set to a non-empty string, in which case it is initialized to 0. Thus, you can set :envvar:PYTHONY2K to a non-empty string in the environment to require 4-digit years for all year input. When 2-digit years are accepted, they are converted according to the POSIX or X/Open standard: values 69-99 are mapped to 1969-1999, and values 0--68 are mapped to 2000--2068. Values 100--1899 are always illegal. Note that this is new as of Python 1.5.2(a2); earlier versions, up to Python 1.5.1 and 1.5.2a1, would add 1900 to year values below 1900.
• UTC is Coordinated Universal Time (formerly known as Greenwich Mean Time, or GMT). The acronym UTC is not a mistake but a compromise between English and French.

The module defines the following functions and data items:

The type of the time value sequence returned by :func:gmtime, :func:localtime, and :func:strptime. It is an object with a :term:named tuple interface: values can be accessed by index and by attribute name. The following values are present:

Index Attribute Values
0 :attr:tm_year (for example, 1993)
1 :attr:tm_mon range [1, 12]
2 :attr:tm_mday range [1, 31]
3 :attr:tm_hour range [0, 23]
4 :attr:tm_min range [0, 59]
5 :attr:tm_sec range [0, 61]; see (1) in :func:strftime description
6 :attr:tm_wday range [0, 6], Monday is 0
7 :attr:tm_yday range [1, 366]
8 :attr:tm_isdst 0, 1 or -1; see below

Note that unlike the C structure, the month value is a range of [1, 12], not [0, 11]. A year value will be handled as described under :ref:Year 2000 (Y2K) issues <time-y2kissues> above. A -1 argument as the daylight savings flag, passed to :func:mktime will usually result in the correct daylight savings state to be filled in.

When a tuple with an incorrect length is passed to a function expecting a :class:struct_time, or having elements of the wrong type, a :exc:TypeError is raised.

Footnotes

 [1] The use of %Z is now deprecated, but the %z escape that expands to the preferred hour/minute offset is not supported by all ANSI C libraries. Also, a strict reading of the original 1982 RFC 822 standard calls for a two-digit year (%y rather than %Y), but practice moved to 4-digit years long before the year 2000. After that, RFC 822 became obsolete and the 4-digit year has been first recommended by RFC 1123 and then mandated by RFC 2822.


text:
Looking for Algebra worksheets?
Check out our pre-made Algebra worksheets!
 Tweet

##### Browse Questions
• Arts (659)
• English Language Arts (3081)
• English as a Second Language ESL (1428)
• Health and Medicine (715)
• Life Skills (476)
• Math (1931)

• ### Sequences and Series

• #### Trigonometry

• Physical Education (409)
• Science (6645)
• Social Studies (1573)
• Study Skills and Strategies (13)
• Technology (485)
• Vocational Education (1000)

You can create printable tests and worksheets from these Grade 10 Function and Algebra Concepts questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

Previous Next
Grade 10 Literal Equations CCSS: HSA-CED.A.4
Solve for $R$.

$2T=(5R)/S$
1. $R=(5ST)/2$
2. $R=(2S)/(5T)$
3. $R=(2)/(5ST)$
4. $R=(2ST)/5$
Grade 10 Literal Equations CCSS: HSA-CED.A.4
Solve for $a$.

$S=1/2at^2$
1. $a=(2S)/t^2$
2. $at^2=2S$
3. $a=t^2/(tS)$
4. $a=(S)/(2t^2)$
Grade 10 Literal Equations CCSS: HSA-CED.A.4
Solve for $z$.

$x=z/y$
1. $z=xy$
2. $z=x/y$
3. $z=y/x$
4. $x=zy$
Grade 10 Literal Equations CCSS: HSA-CED.A.4
Solve for $B$.

$A=BC$
1. $B=AC$
2. $B=C/A$
3. $B=A/C$
4. $A=B/C$
Grade 10 Literal Equations CCSS: HSA-CED.A.4
Solve for $r$.

$4x+y=3t-2r$
1. $(4x+y-3t)/-2=r$
2. $(4x+y-3t)/2=r$
3. $(4x+y)/6t=r$
4. $-2(4x+y)/3t=r$
Grade 10 Literal Equations CCSS: HSA-CED.A.4
Solve for $r$.

$a=v^2/r$
1. $r=a/v^2$
2. $r=v^2a$
3. $r=v^2/a$
4. $r=sqrt(v)/a$
Grade 10 Polynomials and Rational Expressions
Given: $(5x + 6)(8x - 4)$

What is the product of the given?
1. $13x + 2$
2. $40x - 24$
3. $40x^2 + 24$
4. $40x^2 - 20x + 48x - 24$
Simplify. Assume that $x$ is positive. $(( x^(1/2) \ x^(-5/4) ) / (x^(3/4)) ) ^(4/3)$
1. $1/x^6$
2. $1$
3. $x^(4/3)$
4. $1/x^2$
Select the solution.
$-5 <= -2x + 3 <= 7$
1. $x >= 4 or x <= -2$
2. $-2 <= x <= 4$
3. $-4 <= x <= -2$
4. $-4 <= x <= 2$
Simplify. Assume $b$ is positive. $( b^(1/4) \ b^(5/4))^(2/3)$
1. $b^(13/6)$
2. $b^(5/24)$
3. $b$
4. $4^(1/3) b$
Simplify. Assume $a$ and $b$ are positive. $a^(4/3) \ (a^(-1/2) b^(9/5))^(3/4)$
1. $a^(47/15) / b^(27/20)$
2. $a^(19/12) \ b^(51/20)$
3. $a^(5/8) \ b^(27/20)$
4. $a ^(23/24) b^(27/20)$
Simplify: $x^(2/3) (x^(1/4) )$. Assume $x$ is positive.
1. $x^(1/6)$
2. $x^(3/7)$
3. $x^(1/8)$
4. $x^(11/12)$
5. None of these are correct
Grade 10 Systems of Equations CCSS: HSA-REI.C.6
Select the solution to the system of linear equations.
$x+2y=11$
$3x-2y=9$
1. $(3, 2)$
2. $(5, 3)$
3. $(4.5, 2)$
4. $(1/2, 2/3)$
Simplify. Assume $m$ and $n$ are positive. $( m^(5/6) \ n^(3/2) ) / ( m^(4/7) \ n^(9/2))$
1. $( m^(35/ 24) ) / ( n^(1/3) )$
2. $m^(59/42) / n^6$
3. $(m^(11/42) ) / n^3$
4. $m^(-10/21) n^(-27/4)$
Grade 10 Literal Equations CCSS: HSA-CED.A.4
Solve for $a$.

$a^2+b^2=c^2$
1. $a=+-sqrt(c^2/b^2)$
2. $a=+-sqrt(b^2-c^2)$
3. $a=+-sqrt(c^2+b^2)$
4. $a=+-sqrt(c^2-b^2)$
Grade 10 Linear Equations CCSS: HSA-REI.C.6
Solve the system of equations.
$y=x-8$
$y=-3x$
1. $(2,-6)$
2. $(-2,6)$
3. $(3,-9)$
4. $(1,7)$
Grade 10 Linear Equations CCSS: HSA-REI.B.3
Grade 10 Linear Equations CCSS: HSA-REI.B.3
Solve for $x$.
$4x+5=5x-5$
1. $1$
2. $4/5$
3. $10$
4. $-5$
Which of the following is true for the equation $y=4x-2$?