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text:
\section{Introduction}

Nonlinear optics has been proven to be very useful for the investigation of
ferromagnetism at surfaces due to its enhanced sensitivity to
twodimensional {\em ferromagnetism} \cite {ref53}. The magnetic effects are
usually much stronger than in linear optics (rotations up to 90$^\circ$,
pronounced spin polarized quantum well state oscillations
\cite{ref64,ref65,vol1},
magnetic contrasts close to 100$\%$) \cite {vol1,ref22,pustu,vol2}. Recently,
Second Harmonic Generation (SHG) has been successfully applied to probe {\em
antiferromagnetism} (visualization of bulk AF domains \cite {ref18,ref4,ref12}).
The potential of SHG to study the surface antiferromagnetism has been announced
in Ref. \cite{dahn} extensively discussed in our previous paper \cite{ourpaper}.

The practical importance of studies in this field follows from the applications
of antiferromagnetic (AF) oxide layers in devices such as those based on TMR
(tunneling magnetoresistance), where a trilayer structure is commonly
used. The central layer
of TMR devices consists of an oxide sandwiched between a soft and a hard
magnetic layer. For these technological applications it is necessary
to develop a technique to study buried oxide interfaces. Such a technique can be
SHG. One of the promising materials for the mentioned devices is NiO.
However, to the best of our knowledge, the understanding of its detailed spin
structure is scarce - even the spin orientation on the ferromagnetically ordered
(111) surfaces is not known.

Our recent paper \cite{ourpaper} presented an extensive study of the nonlinear
electrical susceptibility tensor $\chi^{(2\omega)}_{el}$ (the source for SHG
within the electrical dipole approximation), mostly for monolayer structures. It
has been proven there that the spin structure of an antiferromagnetic monolayer
can be detected by means of SHG. Also the possibility of antiferromagnetic
surface domain imaging has been presented for the first time. As it was
mentioned in this previous work, bilayer spin structures are enough to account
for the symmetry of a surface of a cubic antiferromagnet. Here we present an
extention of that work to the (110) and (111) bilayer structures, thus
completing our group theoretical analysis of low Miller-index antiferromagnetic
surfaces.

\section{Results}
We follow exactly the group theoretical method described in Ref.
\cite{ourpaper}. At this point it is necessary to define the notions of
``phase'' and ``configuration'', used henceforth to classify our results.
``Phase'' describes the magnetic phase of the material, i.e. paramagnetic,
ferromagnetic, or AF. Secondly, the word ``configuration'' is reserved for the
description of the magnetic ordering
of the surface. It describes the various possibilities of the spin ordering,
which are different in the sense of topology. We describe AF
configurations, denoted by little letters a) to l), as well as several
ferromagnetic configurations, denoted as ``ferro1'', ``ferro2'', etc. The number
of possible configurations varies depending on the surface orientation. All the
analysis concerns collinear antiferromagnets, with one easy axis.

The tables show the allowed tensor elements for each configuration. The
tables also contain the information on the parity of the nonvanishing tensor
elements: the odd ones are printed in
boldface. In some situations an even tensor element (shown in lightface) is
equal to an odd element (shown in boldface), this means that this pair of tensor
elements is equal in the domain which is depicted on the corresponding figure,
but they are of opposite sign in the other domain. The parity of the elements
has been checked in the operations $2_z$, $4_z$, and in the operation connecting
mirror-domains to each other (for the definition of the mirror-domain structure
see Ref. \cite{ourpaper}). The domain operation(s) on which the parity depends
is (are),
if applicable, also displayed in the tables. If two or more domain operations
have the same effect, we display all of them together. To make the tables
shorter and more easily readable some domain operations (and the corresponding
parity information for the tensor elements) are not displayed, namely those that
can be created by a superposition of the displayed domain operations. We also do
not address the parity of tensor elements in the $6_z$ nor $3_z$ operations for
(111) surfaces nor any other operation that ``splits'' tensor elements, although
these operations also lead to a domain structure \cite{par111}. As has been
discussed in Ref. \cite{ourpaper} it is possible to define a parity of the
tensor elements for the $3_z$ and $6_z$ operations, however the tensor elements
then undergo more complicated changes. The situations where the parity of the
tensor elements is too complicated to be displayed in the tables are indicated
by a hyphen in the column ``domain operation''. For the paramagnetic phase,
where no domains exist, we display the hyphen as well. For some configurations,
none of the operations leads to a domain structure - in those configurations we
display the information ``one domain''. The reader is referred to Ref.
\cite{ourpaper} for the particularities of the parity check.

\subsection{(110) bilayer}
The previously described AF configurations of the (001) monolayer most commonly
get split into two different configurations when a bilayer structure is
considered. For the (110) bilayer it is not the case - only two of twelve AF
configurations get split in this way, thus one obtains 14 AF configurations of
the (110) bilayer. Describing the results of our analysis we use the
nomenclature of our previous article, i.e. the antiferromagnetic configurations
are labeled by small letters. Only the four configurations that result from
splitting of the two configurations of the monolayer structure are labeled by
small letters with subscripts that carry the information about how they have
been constructed from the (110) monolayer. For configurations with subscript
``a'' the lower layer is constructed by translation of the topmost layer by
vector (0.5a, 0.5b), where a and b are interatomic distances {\em within} the
(110) plane along $x$ and $y$ axes, respectively. For configurations with
subsript ``b'' the vector of translation is (-0.5a, 0.5b). This corresponds to
the way we constructed the (001) bilayers in \cite{ourpaper}.

The configurations of the (110) monolayer structure are depicted in Fig.
\ref{f110}, and the way the bilayer is constructed is depicted in Fig.
\ref{cons110}. The tensor elements are presented in Table \ref{t110}. In
general, we can observe five types of response. However, the possibility to
distinguish AF configurations is not much improved compared to the (110)
monolayer. Even the possibility to detect the magnetic phase of the surface is
not evident.

As for the (001) surface \cite{ourpaper}, there is no difference in SHG signal
between the monolayer and bilayer for the paramagnetic and ferromagnetic phases.
For most AF configurations, however (confs. a), b), c), e), f$_a$, f$_b$), g),
h), j), k), and l)) such a difference is present due to a lower symmetry of the
bilayer.

\subsection{(111) bilayer}

In order to be consistent with our previous work \cite{ourpaper} we keep the
same configuration names as in this earlier paper. That is why, for example,
conf. b) is not present here. The spin configurations of the (111) bilayer are
constructed from the configurations of the (111) surface of our previous work in
the way that the spin structure in the second atomic layer is the same as in the
topmost layer, but shifted accordingly to form a hcp structure. Taking into
account the spin structure of the second layer causes all the AF configurations
to split, thus one obtains 10 AF configurations of the (111) bilayer. The
configurations are labeled by small letters (indicating their ``parent''
configuration) with subscript ``a'' if the mentioned shifting is along the
positive $x$ axis, and ``b'' if the shifting is along the negative S$_{xy}$
axis.

The configurations of the (111) monolayer are depicted in Fig. \ref{f111} and
the construction of the bilayer is depicted in Fig. \ref{cons111}. The
corresponding tensor elements are displayed in Tab. \ref{t111}. The results are
identical to those of our previous work \cite{ourpaper}, where the second layer
of the (111) surface was treated as nonmagnetic.
This means that the spin spin structure of the second layer does not play any
role for SHG, however the presence of the atoms in the second layer does.

\section{Conclusion}
From our results follows that SHG can probe maximally two atomic layers of the
surface of cubic two sublattice antiferromagnets, and only one of the
paramagnetic or ferromagnetic surface. For the (111) surface, the {\em spin}
structure of the second layer does not have any influence on SHG, i.e. it does
not matter from the group-theoretical point of view if the investigated surface
is a termination of a bulk antiferromagnet or a monolayer grown on a nonmagnetic
substrate. However, these two situations can be very different from the
band-theoretical point of view.

redpajama_set_name: RedPajamaArXiv


Cape Town based company Alco Exotic, is a specialist in the procurement, warehousing, stockholding and supply of flooring products. The Company offers flooring accessories and flooring products like Bamboo and Oak. They are renowned for their attention to detail.


text:
function gX = ratquadKernDiagGradX(kern, X)

% RATQUADKERNDIAGGRADX Gradient of RATQUAD kernel's diagonal with respect to X.
%
%	Description:
%
%	GX = RATQUADKERNDIAGGRADX(KERN, X) computes the gradient of the
%	diagonal of the rational quadratic kernel matrix with respect to the
%	elements of the design matrix given in X.
%	 Returns:
%	  GX - the gradients of the diagonal with respect to each element of
%	   X. The returned matrix has the same dimensions as X.
%	 Arguments:
%	  KERN - the kernel structure for which gradients are being
%	   computed.
%	  X - the input data in the form of a design matrix.
%
%
%	See also
%	RATQUADKERNPARAMINIT, KERNDIAGGRADX, RATQUADKERNGRADX

%	Copyright (c) 2006 Neil D. Lawrence

gX = zeros(size(X));

redpajama_set_name: RedPajamaGithub


text:
var exec = require('mz/child_process').execFile;
var assert = require('assert');

module.exports = function (filename) {
  return exec('ffprobe', [
    '-v', 'error',
    '-of', 'flat=s=_',
    '-select_streams', 'v:0',
    '-show_entries', 'stream=height,width',
    filename
  ]).then(function (out) {
    var stdout = out[0].toString('utf8');
    var width = /width=(\d+)/.exec(stdout);
    var height = /height=(\d+)/.exec(stdout);
    assert(width && height, 'No dimensions found!');
    return {
      width: parseInt(width[1]),
      height: parseInt(height[1]),
    };
  });
}


Then I found out it was 2 players at a friend's house and awww yeah!!!
Another SNES RPG I completely loved and played to death. I had one game where I had leveled all spells and weapons to the max (never found all weapon orbs though).
My favorite game of all time!!
Best RPG and best Multiplayer Co-op experience ever.
The weird thing is that it was only this installment, as the next ones, PS and PS2 ones are rubbish.
Please Square, make a game with the exact SAME mechanic as this one, it was perfect, why change it?
I almost can't believe this only sold 2 million copies, I consider it the best 2D rpg ever.
This is the only game I consider on par with zelda, tough it's more complex.
It's relativly cheap on ebay, buy one if you can ;).


A good number of Gidding residents spent a delightful morning attending the joyous ceremony of Aarti at the Bharat Hindu Samaj in Peterborough. Following the ceremony – in which we were all invited to take part – our very knowledgeable guide for the morning, Gita, explained the Hindu philosophy and gave us a brief introduction to the role of Brahma and the nine, so far, reincarnations of Vishnu.
Following drinks the party then departed to Spicelands for lunch (unfortunately I can't report on that because we had to go back to work! But I bet it was lovely).


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Yes, with composites like Fibrex from Andersen you never have to worry about rotting or warping.
Yes, all installs are done by our own installers and subcontractors and all labor warranties are backed by Architect's Choice a division of Overhead Inc. of Toledo.
What is lead time on special order windows?
Typically special orders require 5-7 week lead time. Some lead times may vary based on size of order and more standardized options.
Does Andersen provide replacement windows or are they just for new construction? Both Architect's Choice and Andersen Windows have products for both the replacement and new construction applications.
Why are fiberglass entry doors better that steel?
Fiberglass has a lifetime warranty and will not rust or dent like a steel door, plus they are more energy efficient.
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No door is maintenance free. Fiberglass doors should be washed occasionally or when dirty much like you would do for your car. Wood grain stained doors may need refinishing or a coat of polyurethane as they are exposed to weather over the years, like a real wood door. Also like a real wood door the wood grain fiberglass can be stripped and re-stained to another color if desired.
Can I get a Lifestyle screen on any size garage door?
The smallest Lifestyle screen is 6' wide x 7' tall and the largest is 18' wide by 10' tall. Any size in between is no problem for the Lifestyle screen as they are customized for your project.


text:
Irreducibility and strong Feller property for stochastic evolution equations in Banach spaces
DCDS-B Home
June 2016, 21(4): 1027-1050. doi: 10.3934/dcdsb.2016.21.1027
Analysis of a reduced-order approximate deconvolution model and its interpretation as a Navier-Stokes-Voigt regularization
Luigi C. Berselli 1, , Tae-Yeon Kim 2, and Leo G. Rebholz 3,
Dipartimento di Matematica, Università di Pisa, I-56127 Pisa, Italy
Department of Civil Infrastructure and Environmental Engineering, Khalifa University of Science, Technology & Research (KUSTAR), Abu Dhabi, United Arab Emirates
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, United States
Received May 2015 Revised January 2016 Published March 2016
We study mathematical and physical properties of a family of recently introduced, reduced-order approximate deconvolution models. We first show a connection between these models and the Navier-Stokes-Voigt model, and also that Navier-Stokes-Voigt can be re-derived in the approximate deconvolution framework. We then study the energy balance and spectra of the model, and provide results of some turbulent-flow computations that backs up the theory. Analysis of global attractors for the model is also provided, as is a detailed analysis of the Voigt model's treatment of pulsatile flow.
Keywords: Voigt and NS-Voigt models, approximate deconvolution, numerical tests., Large eddy simulation, energy spectra.
Mathematics Subject Classification: Primary: 35Q35; Secondary: 76F65, 76D0.
Citation: Luigi C. Berselli, Tae-Yeon Kim, Leo G. Rebholz. Analysis of a reduced-order approximate deconvolution model and its interpretation as a Navier-Stokes-Voigt regularization. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1027-1050. doi: 10.3934/dcdsb.2016.21.1027
N. A. Adams and S. Stolz, Deconvolution Methods for Subgrid-Scale Approximation in Large Eddy Simulation, Modern Simulation Strategies for Turbulent Flow, R.T. Edwards, 2001. Google Scholar
N. A. Adams and S. Stolz, A subgrid-scale deconvolution approach for shock capturing, J. Comput. Phys., 178 (2002), 391-426. doi: 10.1006/jcph.2002.7034. Google Scholar
H. Beirão da Veiga, Time periodic solutions of the Navier-Stokes equations in unbounded cylindrical domains-Leray's problem for periodic flows, Arch. Ration. Mech. Anal., 178 (2005), 301-325. ibidem 198 (2010), 1095 doi: 10.1007/s00205-005-0376-3. Google Scholar
L. C. Berselli, Analysis of a Large Eddy Simulation model based on anisotropic filtering, J. Math. Anal. Appl., 386 (2012), 149-170. doi: 10.1016/j.jmaa.2011.07.044. Google Scholar
L. C. Berselli, Towards fluid equations by approximate deconvolution models, in Mathematical Aspects of Fluid Mechanics, vol. 402 of London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge, 2012, 1-22. Google Scholar
L. C. Berselli and L. Bisconti, On the structural stability of the Euler-Voigt and Navier-Stokes-Voigt models, Nonlinear Anal., 75 (2012), 117-130. doi: 10.1016/j.na.2011.08.011. Google Scholar
L. C. Berselli, F. Guerra, B. Mazzolai and E. Sinibaldi, Pulsatile viscous flows in elliptical vessels and annuli: solution to the inverse problem, with application to blood and cerebrospinal fluid flow, SIAM J. Appl. Math., 74 (2014), 40-59. doi: 10.1137/120903385. Google Scholar
L. C. Berselli, T. Iliescu and W. J. Layton, Mathematics of Large Eddy Simulation of Turbulent Flows, Scientific Computation, Springer-Verlag, Berlin, 2006. doi: 10.1007/b137408. Google Scholar
L. C. Berselli and R. Lewandowski, Convergence of approximate deconvolution models to the mean Navier-Stokes equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29 (2012), 171-198. doi: 10.1016/j.anihpc.2011.10.001. Google Scholar
L. C. Berselli and S. Spirito, On the Construction of Suitable Weak Solutions to the 3D Navier-Stokes Equations in a Bounded Domain by an Artificial Compressibility Method, Technical Report 1504.07800, arXiv, 2015, URL http://arxiv.org/abs/1504.07800. To appear in Commun. Contemp. Math. Google Scholar
A. L. Bowers, T.-Y. Kim, M. Neda, L. G. Rebholz and E. Fried, The Leray-$\alpha\beta$-deconvolution model: Energy analysis and numerical algorithms, Appl. Math. Model., 37 (2013), 1225-1241. doi: 10.1016/j.apm.2012.03.040. Google Scholar
Y. Cao, E. M. Lunasin and E. S. Titi, Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models, Commun. Math. Sci., 4 (2006), 823-848, \urlprefixhttp://projecteuclid.org/euclid.cms/1175797613. doi: 10.4310/CMS.2006.v4.n4.a8. Google Scholar
R. W. Carroll and R. E. Showalter, Singular and Degenerate Cauchy Problems, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976, Mathematics in Science and Engineering, Vol. 127. Google Scholar
T. Chacón Rebollo and R. Lewandowski, Mathematical and Numerical Foundations of Turbulence Models and Applications, Modeling and Simulation in Science, Engineering and Technology, Birkhäuser/Springer, New York, 2014. doi: 10.1007/978-1-4939-0455-6. Google Scholar
S. Chen, G. Doolen, R. Kraichnan and Z. She, On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence, Phys. Fluids A, 5 (1993), 458-463. doi: 10.1063/1.858897. Google Scholar
S. Chen, D. D. Holm, L. G. Margolin and R. Zhang, Direct numerical simulations of the Navier-Stokes alpha model, Phys. D, 133 (1999), 66-83, Predictability: quantifying uncertainty in models of complex phenomena (Los Alamos, NM, 1998). doi: 10.1016/S0167-2789(99)00099-8. Google Scholar
A. Cheskidov, D. D. Holm, E. Olson and E. S. Titi, On a Leray-$\alpha$ model of turbulence, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461 (2005), 629-649. doi: 10.1098/rspa.2004.1373. Google Scholar
A. Dunca and Y. Epshteyn, On the Stolz-Adams deconvolution model for the large-eddy simulation of turbulent flows, SIAM J. Math. Anal., 37 (2006), 1890-1902 (electronic). doi: 10.1137/S0036141003436302. Google Scholar
A. A. Dunca, A two-level multiscale deconvolution method for the large eddy simulation of turbulent flows, Math. Models Methods Appl. Sci., 22 (2012), 1250001, 30pp. doi: 10.1142/S0218202512500017. Google Scholar
C. Foias, D. D. Holm and E. S. Titi, The Navier-Stokes-alpha model of fluid turbulence, Phys. D, 152/153 (2001), 505-519, Advances in nonlinear mathematics and science. doi: 10.1016/S0167-2789(01)00191-9. Google Scholar
C. Foias, O. Manley, R. Rosa and R. Temam, Navier-Stokes Equations and Turbulence, vol. 83 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 2001. doi: 10.1017/CBO9780511546754. Google Scholar
U. Frisch, Turbulence, The Legacy of A.N. Kolmogorov, Cambridge University Press, Cambridge, 1995. Google Scholar
Y. C. Fung, Biomechanics. Circulation, Springer-Verlag, 1997. Google Scholar
K. J. Galvin, L. G. Rebholz and C. Trenchea, Efficient, unconditionally stable, and optimally accurate FE algorithms for approximate deconvolution models, SIAM J. Numer. Anal., 52 (2014), 678-707. doi: 10.1137/120887412. Google Scholar
D. F. Hinz, T.-Y. Kim and E. Fried, Statistics of the Navier-Stokes-alpha-beta regularization model for fluid turbulence, J. Phys. A, 47 (2014), 055501, 21pp. doi: 10.1088/1751-8113/47/5/055501. Google Scholar
K. J. K. Galvin, Advancements in Finite Element Methods for Newtonian and Non-Newtonian Flows, PhD thesis, Clemson University, 2013. Google Scholar
V. K. Kalantarov, B. Levant and E. S. Titi, Gevrey regularity for the attractor of the 3D Navier-Stokes-Voight equations, J. Nonlinear Sci., 19 (2009), 133-152. doi: 10.1007/s00332-008-9029-7. Google Scholar
V. K. Kalantarov and E. S. Titi, Global attractors and determining modes for the 3D Navier-Stokes-Voight equations, Chin. Ann. Math. Ser. B, 30 (2009), 697-714. doi: 10.1007/s11401-009-0205-3. Google Scholar
T.-Y. Kim, M. Cassiani, J. D. Albertson, J. E. Dolbow, E. Fried and M. E. Gurtin, Impact of the inherent separation of scales in the Navier-Stokes-$\alpha\beta$ equations, Phys. Rev. E (3), 79 (2009), 045307, 4pp. doi: 10.1103/PhysRevE.79.045307. Google Scholar
T.-Y. Kim, L. G. Rebholz and E. Fried, A deconvolution enhancement of the Navier-Stokes-$\alpha\beta$ model, J. Comput. Phys., 231 (2012), 4015-4027. doi: 10.1016/j.jcp.2011.12.003. Google Scholar
P. Kuberry, A. Larios, L. G. Rebholz and N. E. Wilson, Numerical approximation of the Voigt regularization for incompressible Navier-Stokes and magnetohydrodynamic flows, Comput. Math. Appl., 64 (2012), 2647-2662. doi: 10.1016/j.camwa.2012.07.010. Google Scholar
A. Larios, The Inviscid Voigt-Regularization for Hydrodynamic Models: Global Regularity, Boundary Conditions, and Blow-Up Phenomena, PhD thesis, Univ. California, Irvine, 2011. Google Scholar
A. Larios and E. S. Titi, On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models, Discrete Contin. Dyn. Syst. Ser. B, 14 (2010), 603-627. doi: 10.3934/dcdsb.2010.14.603. Google Scholar
W. J. Layton and R. Lewandowski, On a well-posed turbulence model, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 111-128 (electronic). doi: 10.3934/dcdsb.2006.6.111. Google Scholar
W. J. Layton and L. Rebholz, Approximate Deconvolution Models of Turbulence Approximate Deconvolution Models of Turbulence, vol. 2042 of Lecture Notes in Mathematics, Springer, Heidelberg, 2012. doi: 10.1007/978-3-642-24409-4. Google Scholar
B. Levant, F. Ramos and E. S. Titi, On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model, Commun. Math. Sci., 8 (2010), 277-293. doi: 10.4310/CMS.2010.v8.n1.a14. Google Scholar
A. P. Oskolkov, The uniqueness and solvability in the large of boundary value problems for the equations of motion of aqueous solutions of polymers, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 38 (1973), 98-136, Boundary value problems of mathematical physics and related questions in the theory of functions, 7. Google Scholar
A. P. Oskolkov, On the theory of unsteady flows of Kelvin-Voigt fluids, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 115 (1982), 191-202, 310, Boundary value problems of mathematical physics and related questions in the theory of functions, 14. Google Scholar
A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system, in Handbook of numerical analysis. Vol. XII, Handb. Numer. Anal., XII, North-Holland, Amsterdam, 2004, 3-127. doi: 10.1016/S1570-8659(03)12001-7. Google Scholar
L. G. Rebholz, Well-posedness of a reduced order approximate deconvolution turbulence model, J. Math. Anal. Appl., 405 (2013), 738-741. doi: 10.1016/j.jmaa.2013.04.036. Google Scholar
P. Sagaut, Large Eddy Simulation for Incompressible Flows, Scientific Computation, Springer-Verlag, Berlin, 2001, An introduction, With an introduction by Marcel Lesieur, Translated from the 1998 French original by the author. doi: 10.1007/978-3-662-04416-2. Google Scholar
Z. S. She, E. Jackson and S. A. Orszag, Statistical aspects of vortex dynamics in turbulence, in New perspectives in turbulence (Newport, RI, 1989), Springer, New York, 1991, 315-328. doi: 10.1007/978-1-4612-3156-1_12. Google Scholar
I. Stanculescu and C. C. Manica, Numerical analysis of Leray-Tikhonov deconvolution models of fluid motion, Comput. Math. Appl., 60 (2010), 1440-1456. doi: 10.1016/j.camwa.2010.06.026. Google Scholar
S. Stolz and N. A. Adams, An approximate deconvolution procedure for large-eddy simulation, Phys. Fluids, 11 (1999), 1699-1701. doi: 10.1063/1.869867. Google Scholar
S. Stolz, N. A. Adams and L. Kleiser, An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows, Phys. Fluids, 13 (2001), 997-1015. doi: 10.1063/1.1350896. Google Scholar
R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, vol. 68 of Applied Mathematical Sciences, 2nd edition, Springer-Verlag, New York, 1997. doi: 10.1007/978-1-4612-0645-3. Google Scholar
J. R. Womersley, Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, J. Physiol., 127 (1955), 553-563. doi: 10.1113/jphysiol.1955.sp005276. Google Scholar
Adam Larios, E. S. Titi. On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 603-627. doi: 10.3934/dcdsb.2010.14.603
Adam Larios, Yuan Pei. Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data. Evolution Equations & Control Theory, 2020, 9 (3) : 733-751. doi: 10.3934/eect.2020031
Andriy Sokolov, Robert Strehl, Stefan Turek. Numerical simulation of chemotaxis models on stationary surfaces. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2689-2704. doi: 10.3934/dcdsb.2013.18.2689
Mohammad Akil, Ibtissam Issa, Ali Wehbe. Energy decay of some boundary coupled systems involving wave\ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021059
Miroslav Bulíček, Josef Málek, K. R. Rajagopal. On Kelvin-Voigt model and its generalizations. Evolution Equations & Control Theory, 2012, 1 (1) : 17-42. doi: 10.3934/eect.2012.1.17
Victor Zvyagin, Vladimir Orlov. Weak solvability of fractional Voigt model of viscoelasticity. Discrete & Continuous Dynamical Systems, 2018, 38 (12) : 6327-6350. doi: 10.3934/dcds.2018270
Uwe Schäfer, Marco Schnurr. A comparison of simple tests for accuracy of approximate solutions to nonlinear systems with uncertain data. Journal of Industrial & Management Optimization, 2006, 2 (4) : 425-434. doi: 10.3934/jimo.2006.2.425
Louis Tebou. Stabilization of some elastodynamic systems with localized Kelvin-Voigt damping. Discrete & Continuous Dynamical Systems, 2016, 36 (12) : 7117-7136. doi: 10.3934/dcds.2016110
Hermes H. Ferreira, Artur O. Lopes, Silvia R. C. Lopes. Decision Theory and large deviations for dynamical hypotheses tests: The Neyman-Pearson Lemma, Min-Max and Bayesian tests. Journal of Dynamics & Games, 2022 doi: 10.3934/jdg.2021031
Marcel Lesieur. Two-point closure based large-eddy simulations in turbulence, Part 1: Isotropic turbulence. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 155-168. doi: 10.3934/dcdss.2011.4.155
Marcel Lesieur. Two-point closure based large-eddy simulations in turbulence. Part 2: Inhomogeneous cases. Discrete & Continuous Dynamical Systems, 2010, 28 (1) : 227-241. doi: 10.3934/dcds.2010.28.227
Manil T. Mohan. Global and exponential attractors for the 3D Kelvin-Voigt-Brinkman-Forchheimer equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3393-3436. doi: 10.3934/dcdsb.2020067
Fathi Hassine. Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1757-1774. doi: 10.3934/dcdsb.2016021
Cung The Anh, Dang Thi Phuong Thanh, Nguyen Duong Toan. Uniform attractors of 3D Navier-Stokes-Voigt equations with memory and singularly oscillating external forces. Evolution Equations & Control Theory, 2021, 10 (1) : 1-23. doi: 10.3934/eect.2020039
Aibin Zang. Kato's type theorems for the convergence of Euler-Voigt equations to Euler equations with Drichlet boundary conditions. Discrete & Continuous Dynamical Systems, 2019, 39 (9) : 4945-4953. doi: 10.3934/dcds.2019202
Xiaobin Yao, Qiaozhen Ma, Tingting Liu. Asymptotic behavior for stochastic plate equations with rotational inertia and Kelvin-Voigt dissipative term on unbounded domains. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1889-1917. doi: 10.3934/dcdsb.2018247
Serge Nicaise, Cristina Pignotti. Stability of the wave equation with localized Kelvin-Voigt damping and boundary delay feedback. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 791-813. doi: 10.3934/dcdss.2016029
Fabio Ramos, Edriss S. Titi. Invariant measures for the $3$D Navier-Stokes-Voigt equations and their Navier-Stokes limit. Discrete & Continuous Dynamical Systems, 2010, 28 (1) : 375-403. doi: 10.3934/dcds.2010.28.375
Robert E. Miller. Homogenization of time-dependent systems with Kelvin-Voigt damping by two-scale convergence. Discrete & Continuous Dynamical Systems, 1995, 1 (4) : 485-502. doi: 10.3934/dcds.1995.1.485
Manil T. Mohan. On the three dimensional Kelvin-Voigt fluids: global solvability, exponential stability and exact controllability of Galerkin approximations. Evolution Equations & Control Theory, 2020, 9 (2) : 301-339. doi: 10.3934/eect.2020007
Luigi C. Berselli Tae-Yeon Kim Leo G. Rebholz

redpajama_set_name: RedPajamaCommonCrawl


text:
Kira Kira: Top Ten Quotes
"Sometimes, for no reason that I could see, he would suddenly stand up and clap his hands together really loudly. After he got everyone's attention, he would just sit down again. He even made noise when he was thinking. When he was deep in thought, he had a way of turning his ears inside out so they looked kind of deformed. The ears would make a popping sound when they came undone."
pp. 8-9 This is Katie's amusing description of her Uncle Katsuhisa, a man who clearly has his eccentricities.
"Lynn took about two seconds to move a pawn. Uncle Katsuhisa took about fifteen minutes to move another pawn. Then Lynn moved a knight, and Uncle Katsuhisa looked stunned."
p. 32 Lynn is on her way to beating her uncle at chess, even though he considers himself an expert at the game.
"They talked like their mouths were full of rubber bands!"
p. 34 Katie finds a simile to describe the way people talk in the South. This is just after she and the family have moved to Georgia.
"It was funny how so many people ignored my mother, but they were all fascinated by this little Japanese baby. Then, when he grew up, they would probably ignore him and treat him like an ant!"
p. 56 Katie pinpoints a paradox in the attitude white people have to the Japanese people in Georgia. They think the babies and some of the children are "cute," but they are prejudiced against the adults. The reference to ants is to an earlier comment by Lynn, in which she complains that the white people treat them like ants.
"A union is when all the workers get together and fight the very people who have provided them with a job and the very people who pay the employees money to give them the means to buy a house someday."
p. 95 This is a comment by Katie's mother. The workers at the poultry processing plant are trying to create or join a labor union, but she does not approve of unions. She has a more traditional, conservative attitude that is deferential to the employer.
"He shouted out in his dream, 'Call me Mister Takeshima!'"
p. 118 Katie reports on what little Sammy says. He is only about four, but perhaps he has already at some level understood that the Japanese people in the town are not treated with the respect they deserve, and this is his unconscious protest.
"In my most humble opinion, Gregg was a little pukey. His hair looked like something you would brush a horse with."
p. 119 Gregg is Amber's boyfriend, and she has just told Katie that he is about to move away. Obviously, Katie thinks this is no great tragedy.
"She belonged to the sky, and the sky belonged to her."
p. 179 These are Katie's poetic words following the death of Lynn. Lynn and she used to love lying out gazing up at the night sky, and during her illness, Lynn would like to stare at the sky day or night.
Lynn could take a simple, everyday object like a box of Kleenex and use it to prove how amazing the world is."
p. 224 This is from the essay Katie writes as a tribute to Lynn after Lynn dies. It is a reference to the time when she and Katie climbed onto the roof with two boxes of Kleenex and threw the tissues one by one for the wind to catch them. Katie says that the tissues as they stretched over the cornfield looked like "giant butterflies."
"Here at the sea—especially at the sea—I could hear my sister's voice in the waves: 'Kira-kira! Kira-kira!'"
p. 244 These are Katie's words as she walks by the Pacific Ocean. This is after Lynn's death, when Katie's father takes the family to California for a vacation. Kira-kira is a Japanese word that means "glittering," and it is a word that Lynn taught to Katie when she was very young.
Kira Kira: Novel Summary:chapter 7-12
Kira Kira: Novel Summary:chapter 13-16
Kira Kira: Novel Summary:chapter 1
Kira Kira: Novel Summary:chapter 2-6
Kira Kira: Essay Q&A
Kira Kira: Biography
Kira Kira: Theme Analysis
Kira Kira: Metaphor Analysis
Kira Kira: Character Profiles


text:
41 Komenda Odcinka Nowy Targ – samodzielny pododdział Wojsk Ochrony Pogranicza.

Formowanie i zmiany organizacyjne
41 Komenda Odcinka sformowana została w 1945 roku, na bazie 16 pułku piechoty, w strukturze 9 Oddziału Ochrony Pogranicza. Służbę graniczną objęła 2 listopada 1945 roku. We wrześniu 1946 roku odcinek wszedł w skład Krakowskiego Oddziału WOP nr 9. W 1948 roku, na bazie 41 Komendy Odcinka sformowano Samodzielny Batalion Ochrony Pogranicza nr 53.

Działania bojowe
21 lutego 1947 roku żołnierze KBW i 41 komendy osaczyli w Ostrowsku oddział "Ognia". Zabito 4 osoby i wzięto do niewoli rannego dowódcę oddziału, który usiłował popełnić samobójstwo (zastrzelić się). "Ogień" zmarł w szpitalu w Nowym Targu. Zwłoki zabrała UB.

Struktura organizacyjna
Dyslokacja 41 Komendy Odcinka przedstawiała się następująco:
 komendantura odcinka i pododdziały sztabowe – Nowy Targ
 185 strażnica – Niedzica
 186 strażnica – Jurgów
 187 strażnica – Skała, Łysa Polana
 188 strażnica – Kuźnice, Kościelisko
 189 strażnica – Rostki Kiry

Uwagi

Przypisy

Bibliografia

Komendy odcinków Wojsk Ochrony Pogranicza
Historia Nowego Targu
Komendy odcinków WOP rozmieszczone na granicy polsko-czechosłowackiej

redpajama_set_name: RedPajamaWikipedia


بہیہ نام کا شمار لڑکیوں کے ناموں میں ہوتا ہے۔ بہیہ نام کی ابتدائی تاریخ عربی زبان سے نکلتی ہے۔ بہیہ نام کے افراد کے لیئے خوش قسمت نمر 4 مانا جاتا ہے . جبکہ خوش قسمت دنوں میں بدھ, جمعہ, ہفتہ شامل ہیں ۔ خوش قسمتی والی دھاتوں میں ہندسوں کے حساب ے چاندی, تانبا شامل ہیں بہیہ نام کے افراد کے لیئے موافق پتھروں میں ہیرا شامل ہیں .
Bahiyah is a Muslim Girl name which originates from the Arabic language. Lucky number for name Bahiyah is 4. Lucky days for name Bahiyah are Wednesday, Friday, Saturday and lucky metals are Silver, Copper for name Bahiyah. Lucky stones for name Bahiyah are Diamond.
Urdu names and meanings, Urdu name dictionary of Bahiyah, and other Girl names. Urdu names meaning dictionary for Muslim boys, and Muslim girls, Urdu baby name like Bahiyah and others. A complete Urdu names dictionary, a complete Arabic and Islamic name encyclopedia for new born babies. Bahiyah Urdu names English meaning. Check Bahiyah name English and Urdu spelling.
Islamic Name Bahiyah, Name Meaning in Urdu. Girl name Bahiyah and other Muslim Girl names dictionary. Bahiyah baby meaning in Urdu, Arabic and English. Find baby Girl names with easy translation. a complete Arabic and Islamic name encyclopedia for new born babies. Find Urdu name English meaning. Check name English and Urdu spelling and audio Pronunciation of the name!.


text:
import React from 'react';
import {
  View,
  StyleSheet,
} from 'react-native';

const propTypes = {
  ...View.propTypes,
};

class Invert extends React.Component {
  render() {
    return (
      <View {...this.props} style={[this.props.style, styles.invert]} />
    );
  }
}

Invert.propTypes = propTypes;

const styles = StyleSheet.create({
  invert: {
    transform: [{ scaleY: -1 }],
  },
});

export default Invert;


Mastertech's CVD (chemical vapor depostion diamond) tipped insert grades give you efficient production, ranging from high speed machining to heavy interrupted cutting.
CVD inserts offer a wide range of applications from low to high speed and finishing to roughing.
CVD inserts provide stable machining due to high toughness and crack resistance.
CVD inserts reduce machining time and provide good chip control with various molded-in chip breakers.


text:
\section{Introduction}
\label{sec_introduction}
Scene text recognition \cite{shi2016robust, shi2016end, cheng2017focusing, li2019show, lu2019master, chen2020text}, which aims at extracting text content from images, has attracted enormous attention from both the academy and industry due to its great commercial value in various real-world applications.

With the development of sequence modeling, many text recognition models \cite{liu2016star, cheng2018aon, liu2018char} have achieved remarkable results. Generally, most competitive text recognition models have an encoder-decoder architecture, which maps each input sequence into an output sequence of variable length. Connectionist Temporal Classification (CTC) is applied for text recognition \cite{shi2016end, liu2016star, he2015reading, wang2017gated} to obtain the sequence of characters corresponding to the text image without character-level segmentation. \cite{shi2016end} integrates Recurrent Neural Network (RNN) with CTC to extract rich contextual information and make the decoding parallel and fast. However, these CTC-based methods are insufficient to deal with irregular text.

\begin{figure}[t]
    \centering
    \includegraphics[scale=0.23]{hamming_codes.png}
    \caption{Hamming distances between characters. The vocabulary size is over $20,000$. Several characters are selected and their top $5$ nearest characters are shown. Note that the LSH code for each character contains $512$ bits.}
    \label{hamming_distance_fig}
\end{figure}

Recently, the attention mechanism, which is proposed to tackle machine translation in \cite{bahdanau2014neural}, is widely used to handle text recognition. For RNN-attention-based models \cite{lee2016recursive, cheng2017focusing, ghosh2017visual}, CNN and RNN are used as the encoder to extract contextual feature and another RNN combined with attention mechanism is employed as the decoder to align and decode character at each time step. A 2D attention mechanism, which can learn to select individual character features in the 2D space for decoding character, is proposed by \cite{li2019show}. \cite{wang2020decoupled} proposes a convolutional alignment module with UNet-style network architecture to address the misalignment issue. Inspired by the Transformer \cite{vaswani2017attention}, \cite{yang2020holistic, lu2019master} employ several transformer units to model the dependence among the sequence of output characters and align the visual features with the output character at each time-step.

Many state-of-the-art works adopt heavy models. For instance, Master \cite{lu2019master} uses ResNet31 \cite{he2016deep} and several transfomer units. It is over 220MB. Obviously, it's impractical to directly deploy these models on mobile system due to the immense storage overhead and computational cost. PaddleOCR\footnote{https://github.com/PaddlePaddle/PaddleOCR} provides a super lightweight CRNN \cite{shi2016end} using MobileNetV3 \cite{howard2019searching} to reduce model size from 31.8MB to 4.5MB.

The softmax regression layer used in these methods, contains a projection matrix $W$ with size $d\times L$, where $d$ is the dimension of the character-level feature and $L$ is the length of vocabulary list. To reduce the storage cost, we need a small $L$ and small $d$. However, small $d$ hurts the model performance and small $L$ limits its application in many scenarios, such as Chinese and multi-language character recognition. For example, the storage cost of matrix $W$ is $39.1$MB when the vocabulary size is $20,000$ and $d$ is $512$. More over, in \cite{li2019show, lu2019master}, a matrix with similar size is used in the embedding layer to encode the output character.

To address these issues, we propose a lightweight model, named Hamming OCR, to support scene text recognition with a large scale vocabulary. Hamming OCR is composed of four components: feature encoder, transformer decoder, Hamming embedding, and Hamming classifier, as shown in Figure \ref{fig:framework}.

In the Hamming classifier, we use LSH \cite{gionis1999similarity} to map the output of a pre-trained model's feature layer to Hamming space. A majority voting mechanism is used to generate the representation code for each character. Due to the natural of LSH code, visual similar characters will be mapped codes with small Hamming distance, as shown in Figure \ref{hamming_distance_fig}. In the training stage, we employ a Hinge-loss to learn the optimal projection matrix for the target code.

Compare with the traditional one-hot encoding used in softmax, LSH code is multi-hot and more efficient when the vocabulary size is large. For example, given a vocabulary with  $20,000$ characters and a feature layer of $512$-dimension, the storage cost of the Hamming classifier is $1.22$MB, which is $32$ times smaller than softmax regression. Moreover, the LSH code is directly used in the output embedding, and the number of model parameters is further reduced.

Like \cite{lu2019master, yang2020holistic, yu2020towards}, we solely use transformer units to align and decode characters. To reduce the number of parameters, we remove the feed-forward component of the transformer unit and propose cross-layer parameter sharing for different transformer units. To deploy the model on mobile devices, we balance performance and model size, MobileNetV2 \cite{sandler2018mobilenetv2} is chosen as the feature encoder.

In summary, our contributions are summarized as follows:
\begin{itemize}
    \item We present a method to generate the LSH code to map each character to Hamming space. In this space, visual similar characters will have small Hamming distance.
    \item We propose a novel Hamming classifier trained by Hinge-loss, which predicts output character using multi-hot LSH encoding instead of one-hot encoding. Using this strategy, the model's storage cost is significantly reduced when the vocabulary is large.
    \item The LSH code is directly used in the output embedding module. It further reduces the computational cost and model size.
    \item We also simplify the transformer decoder architecture by removing the feed-forward module and cross-layer parameter sharing.
    \item Hamming OCR delivers competitive results on several scene text datatsets, which is based on self-attention mechanism. More importantly, it can handle a large scale vocabulary and its size is very small.
\end{itemize}

\section{Related Work}
\label{sec_relatedwork}
Given an input image $I$, the goal of scene text recognition is to produce a sequence $(y_1,y_2,...,y_T)$, where $y_t\in\{1,2,...,L\}$ is the character indicator, $L$ is the length of a predefined vocabulary list $V$.

Generally, attention-based text recognition models \cite{li2019show, lu2019master, yu2020towards} have higher accuracy on irregular text datasets, which have an encoder-decoder architecture. Here, we mainly focus on attention-based models and divide a model into four basic components according to their role, including feature encoder, decoder, output embedding, and classifier.

The first component is feature encoder which maps the input text image to a representation. In order to extract high-level visual features, ResNet is regard as the most popular CNN. For instance, \cite{hu2020gtc, yu2020towards, baek2019wrong} adopt ResNet50 as the feature encoder's backbone, and \cite{lu2019master, ghosh2017visual} use ResNet31 as the feature encoder. Meanwhile, many other types of ResNet \cite{li2019show, shi2018aster} also are utilized. To enlarge the feature context, RNN over feature sequence is adopted \cite{shi2018aster, shi2016end}. However, ResNet is inconvenient to deploy on the mobile system due to its storage requirement.

Decoder is the second component, which is used for sequence modeling. \cite{li2019show} adopts a 2-layer RNN with a 2D attention mechanism to decode the holistic feature into a sequence of characters. With transformer achieving success in natural language processing, \cite{lu2019master, yang2020holistic, yu2020towards} utilize self-attention module as decoder to learn character dependencies. They directly use the Transformer decoder which is composed of a masked self-attention mechanism to model relations between different characters of the output sequence, an attention module aligning character-level features from encoder with the output characters, and a feed-forward layer. However, the storage consuming of transformer decoder cannot be ignored. For instance, a typical feed-forward layer contains two projection matrices with size $2048\times 512$.

Output embedding is widely used for sequence model. For text recognition, it encodes the output character of the previous time step as input for the decoder to decode the next character. Usually, learned embeddings \cite{lu2019master, vaswani2017attention} are employed to convert the input characters to vectors of dimension $d$. If we have $L$ characters for embedding, the size of the weight matrix of output embedding is $L\times d$. As the number of characters increases, the memory consumption of output embedding is unbearable for mobile devices.

One of the most common classification approaches is softmax regression. Most text recognition methods directly use softmax regression to map the character-level features into probabilities over the vocabulary $V$. In the following subsection, we introduce softmax regression.

\subsection{Softmax Regression for Classification}
Text recognition is a sequence prediction problem. At each time step, decoder extracts a character-level feature vector by use of attention mechanism. Then the character-level feature vector is mapped into the probability distribution over $V$ as
\begin{equation}
\label{distribution_eqn}
\begin{split}
\Pr(y|h, W) = \frac{\operatorname{exp}{(w_{y}^Th)}}{\sum_{j=1}^{L}\operatorname{exp}{(w_j^Th)}}, \\
\end{split}
\end{equation}
where $h\in\mathcal{F}$ denotes the character-level feature generated by decoder at each time step. $\mathcal{F}$ represents a $d$-dimensional character-level feature space.  $w_j\in\mathbb{R}^{d}$ denotes the $j$-th column of the weight $W\in\mathbb{R}^{d\times L}$. Then, classification decision is given by
\begin{equation}
\label{argmax_eqn}
\begin{split}
\hat{y} = \mathop{\arg\max}_{j\in\{1,2,...,L\}} \Pr(y=j|h, W).
\end{split}
\end{equation}
In the training process, to maximize the probability of the ground-truth sequence at each time step, hence, the cross-entropy loss $-\log(\Pr(y|h, W))$ is employed.

\begin{figure*}
     \centering
     \begin{subfigure}
         \centering
         \includegraphics[width=.4\textwidth, height=.5\textwidth]{framework_a.png}
     \end{subfigure}%
     \hfill
     \begin{subfigure}
         \centering
         \includegraphics[width=.4\textwidth, height=.5\textwidth]{framework_b.png}
     \end{subfigure}
        \caption{(a) The model architecture of the auxiliary model.  (b) The architecture of Hamming OCR model.}

        \label{fig:framework}
\end{figure*}

\section{Hamming OCR Model}
\label{sec_lightocr}
As shown in Figure \ref{fig:framework}(b), the Hamming OCR model contains four main components, feature encoder, transformer decoder, Hamming embedding, and Hamming classifier. In this section, we will first introduce the idea of LSH codebook for Hamming OCR model, then we will give the detail of each model components.

\subsection{LSH Codebook for Hamming OCR Model}
Different from the traditional OCR models, we use multi-hot codes as the training target, and the model output is also directly used in the output embedding layer. According to the experimental result, which will be shown later in Table \ref{tab:code}, the design of the multi-hot codebook isn't trivial. Randomly generated codebook will hurt the model performance significantly. Therefore the Hamming OCR model cannot be trained directly without the LSH codebook.

To address this issue, we use an auxiliary model which replace the Hamming classifier with softmax regression, and Hamming embedding with the traditional embedding technique, which is shown in Figure \ref{fig:framework} (a). This model can be trained end to end directly.

Using this model, any input text image is mapped into a sequence of character-level feature vectors $\{h_t\in\mathcal{F}\}_{t=1}^T$ for classification. Since the classifier isn't dependent on time-step $t$, we omit the time-step index and define $h_{i,j}\in\mathcal{F}$ to represent the $j$-th feature of $i$-th character class. Then we use LSH algorithm to project each feature vector $h_{i,j}$ to a $d'$-bits binary vector $b_{i,j}$ as follow
\begin{equation}
 \label{eqn:lsh}
     b_{i,j}^k = sgn(\psi_k^Th_{i,j}),
 \end{equation}
where $b_{i,j}^k$ is the $k$-th bit of the vector $b_{i,j}$, $\psi_k$ is the $k$-th vector of the random projection matrix $\Psi\in\mathbb{R}^{d\times d'}$.

Since the softmax loss has the tendency to force the feature vectors from the same class to be close in the feature space, after the LSH mapping, the codes from the same character class will be close in the Hamming space as well. Based on this assumption, a majority vote algorithm is used to generate representation code for each character class.
\begin{equation}
\label{eqn:hamming_code}
    \eta_i^k=I(\sum_j{b_{i,j}^k}>n_i/2),
\end{equation}

\noindent where $\eta_i^k$ is the $k$-th bit of the LSH code $\eta_i$ for the $i$-th character class, $n_i$ is the number of feature vectors in the $i$-th class, and $I(.)$ is the indicator function which has the value 1 when the input is true and has the value 0 when the input is false. Finally, we get the codebook $\eta=[\eta_1,\eta_2,...,\eta_L]$ corresponding to the vocabulary $V$.

Theoretically, there is a chance that two character class has the same representation vector. However, when $d>256$, the chance of such conflict is small. Actually, even for the similar characters, The Hamming distance between the corresponding codes is not small. For example, visually, the character ``0'' looks like ``o''. Their LSH codes generated by our method also are similar to each other. From Figure \ref{hamming_distance_fig}, the Hamming distance between ``0'' and ``o'' is much smaller than the others, which is $33$. It means that the edit distance between their LSH code is $33$.

\subsection{Hamming Classifier}

For each input vector $h_{i,j}$, the Hamming classifier will output a binary vector of $d'$ bits, using the equation:

\begin{equation}
    b_{i,j}^k=\mathop{sgn}(w_k^Th_{i,j}),
    \label{eq:inference}
\end{equation}

\noindent where $b_{i,j}^k$ is the $k$-th bit of the output binary vector $b_{i,j}$, $w_k$ is the $k$-th column of the projection matrix $W$ used in the Hamming classifier. We hope that the output code $b_{i,j}$ should be close to the target code $\eta_i$ in the Hamming space.

To achieve this goal, we propose to use the Hinge-loss \cite{cortes1995support} to train the whole model and find optimal $W$. The loss is defined as follow:
\begin{equation}
\label{loss_eqn}
\begin{split}
    \mathcal{L} = & \sum_{i,j,k}\{  \mathop{\max}\{0,\theta-w_k^Th_{i,j}\}\eta_i^k + \\
       & \mathop{\max}\{0,\theta+w_k^Th_{i,j}\}(1-\eta_i^k)\},
       \end{split}
\end{equation}

\noindent where $\theta$ is the margin, $w_k$ is the $k$-th project vector of $W$, $\eta_i^k$ is the $k$-th bit of the target code for the $i$-th class.

The Hamming classifier will map a feature vector into a point in a multi-dimension space. In each dimension of the space, the points from the same class will distribute in the same side of the axis. Due to the nature of Hinge-loss, these points are also be pushed away from the origin. It will reduce the chance of encoding error.

In the inference stage, we use the Equation (\ref{eq:inference}) to calculate the binary vector $b$ for each feature vector $h$. However, due to the possible classifier error, the binary code $b$ may not be exist in the codebook $\eta$. To address this issue, we use:
\begin{equation}
\label{argmax_eqn}
\begin{split}
\hat{y} = \mathop{\arg\min}_{j\in\{1,2,...,L\}} \mathop{HammingDistance(b, \eta_j)},
\end{split}
\end{equation}
to generate the prediction $\hat{y}$.

\subsection{Hamming Embedding}
This component is used to encode the output character. Traditional methods try to learn a $d$-dimensional vector as embedding for each character. As the number of characters increase, the memory consumption of output embedding also increases proportionally. When there is a large vocabulary, the storage cost of the output embedding is heavy. To address this issue, we use the output codes as embedding of output characters as shown in Figure \ref{fig:framework}.

\subsection{Feature Encoder}
We choose the backbone of Master \cite{lu2019master} as our network's backbone, which integrates ResNet31 with GCNet \cite{cao2019gcnet}. Considering the model size and time consuming, for mobile applications, a lightweight MobileNetV2, which is presented in Appendix A, is used as our feature encoder.

\subsection{Transformer Decoder}
Attention mechanism can align relevant visual features to the corresponding output character, which aggregates information from the entire input sequence. Inspired by Transformer, the decoder of Transformer is applied to model sequence prediction in text recognition. A standard decoder of Transformer is composed of a stack of $N$ identical layers, each of which has three sub-layers. The first sub-layer is a masked self-attention network, the second one is a self-attention network and the third one is a feed-forward network. $Y^{\ell}\in\mathbb{R}^{T\times d}$ that is embedding of the output sequence is denoted as the input tensor of the $\ell$-th layer, then, these three sub-modules can be written as the following equations:
\begin{subequations}
\begin{align}
        & Y^{\ell}=\cup_{k=1}^{H}{\operatorname{Att(Y^{\ell}_QW^Q_{k,\ell},Y^{\ell}_KW^K_{k,\ell},Y^{\ell}_VW^V_{k,\ell})}}\cdot W^O_{\ell} \label{transformera} \\
       & Y^{\ell}=\cup_{k=1}^{H}{\operatorname{Att(Y^{\ell}U^Q_{k,\ell},XU^K_{k.\ell},XU^V_{k,\ell})}}\cdot U^O_{\ell} \label{transformerb} \\
      &  Y^{\ell} = \operatorname{ReLU(Y^{\ell}W_1^{FF}+b_1^{FF})}W_2^{FF}+b_2^{FF} \label{transformerc}
\end{align}
\end{subequations}
where $\operatorname{Att}(\cdot)$ is scaled dot-product attention \cite{vaswani2017attention}, $H$ is the number of heads and $\cup_{k=1}^{H}$ denotes a concatenated operator. In Equation (\ref{transformera}), $Y^{\ell}_Q,Y^{\ell}_K,Y^{\ell}_V$ are masked $Y^{\ell}$ to prevent a given position from incorporating information about future output positions. $X$ in Equation (\ref{transformerb}) is extracted by the feature encoder. Note that residual connections and layer normalization are used for each sub-layer, which don't show in Equation (\ref{transformera}), (\ref{transformerb}) and (\ref{transformerc}).

For the $\ell$-th layer, $\{W_{k,\ell}^Q,W_{k,\ell}^K,W_{k,\ell}^V\}_{k=1}^{H}\in\mathbb{R}^{d\times \frac{d}{H}}$, and $W_{\ell}^{O}\in\mathbb{R}^{d\times d}$ are parameters corresponding to masked multi-head self-attention sub-layer. $\{U_{k,\ell}^Q,U_{k,\ell}^K,U_{k,\ell}^V\}_{k=1}^{H}\in\mathbb{R}^{d\times\frac{d}{H}}$, and $U_{\ell}^{O}\in\mathbb{R}^{d\times d}$ are parameters of multi-head self-attention modules. $W_1^{FF}\in\mathbb{R}^{d\times 2048}, W_2^{FF}\in\mathbb{R}^{2048\times d}$, and $b_1^{FF}\in\mathbb{R}^{2048},b_2^{FF}\in\mathbb{R}^{d}$ are parameters of feed-forward sub-layer. There are many parameters for one layer of transformer decoder.

\textit{Removing the feed-forward network and cross-layer parameter sharing} techniques are employed in our transformer decoder to reduce the storage requirement, which stacks three transformer decoder layers. From Equation (\ref{transformerc}), we find that the main function of a feed-forward network with two linear transformations is to learn a projection. However, in Equation (\ref{transformera}) and (\ref{transformerb}), each of them contains a projection matrix ($W_{\ell}^O,U_{\ell}^O)$ which has similar function with feed-forward network. More importantly, feed-forward network has many parameters. So, we remove the feed-forward network (Equation (\ref{transformerc})) in each layer of transformer decoder. For one layer of our transformer decoder, it contains two sub-layers. The first sub-layer is a masked self-attention network and another one is a self-attention network as is shown in Figure \ref{fig:framework}. Like \cite{lan2019albert}, cross-layer parameter sharing technique is used for all the three layers of our transformer decoder. That means, the parameters in Equation (\ref{transformera}) and (\ref{transformerb}) keep the same values for different layers.

\begin{table}[!h]
\centering
\caption{Model size of Hamming OCR under different settings.}
\resizebox{0.46\textwidth}{!}{%
\begin{tabular}{p{4.3cm}|p{1cm}<{\centering}p{1cm}<{\centering}p{1cm}<{\centering}p{1cm}<{\centering}p{1cm}<{\centering}p{1cm}<{\centering}p{1cm}<{\centering}}
\cmidrule[1.5pt]{1-8}
& \multicolumn{7}{c}{Hamming OCR}                                                \\
\hline
MobileNetV2        & $\times$ & \checkmark   & \checkmark   &  \checkmark   & \checkmark & \checkmark & \checkmark  \\
Hamming Classifier        & $\times$ &  & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\
Hamming Embedding             & $\times$ &                           &  & \checkmark & \checkmark & \checkmark & \checkmark \\
No Feed-Forward                   & $\times$ &                           &                           &   & \checkmark & \checkmark & \checkmark  \\
Cross-layer Parameter Sharing & $\times$ &                           &                           &                           &  & \checkmark & \checkmark \\
Half-Precision Float (FP16)        & $\times$ &                           &                           &                           &                           &     & \checkmark \\
\cmidrule[1.5pt]{1-8}
Model Size  & 305.8Mb   &55.6Mb &36.7Mb &16.6Mb &10.6Mb &6.6Mb  &3.9Mb                      \\
\cmidrule[1.5pt]{1-8}
\end{tabular}%
}
\label{memory_consumption_tab}
\end{table}

\subsection{Parameter Analysis}
In this subsection, we analyze the storage requirement of different models under different settings. Our baseline model has similar with \cite{lu2019master}, which uses a RestNet31 with GCNet as CNN's backbone and three-layer transformer decoder. We choose a vocabulary with $20,948$ characters. Then, we compute that the baseline model requires 305.8Mb storage resource. When MobileNetV2 is used to replace ResNet31, the model size sharply reduces to 55.6Mb. Different from the baseline model, Hamming OCR adopts many techniques to reduce the model size including Hamming Classifier, Hamming Embedding, removing feed-forward network of transformer decoder, and cross-layer parameter sharing. Table \ref{memory_consumption_tab} shows the model size for each model. Our MobileNetV2-based Hamming OCR only costs $6.6$Mb. Additionally, when we use 16-bit floating point to represent the weights of Hamming OCR, the most lightweight Hamming OCR is 3.9Mb.

\section{Experiments}
\label{tab:experiments}
We conduct extensive experiments to verify the effectiveness of our Hamming OCR. First, several public standard datasets are employed. However, these public datasets only contain English words and the number of characters to be recognized is relatively small. In order to further validate the capability of Hamming OCR, a dataset named as GBK21K is newly generated.

\subsection{Datasets}

\textbf{IIIT 5K-Words (IIIT5K)} \cite{mishra2012top} contains $3,000$ cropped scene text images for testing.

\noindent\textbf{Street View Text (SVT)} \cite{wang2011end} consists of $257$ training images and $647$ testing images, which is collected from Google Street Image.

\noindent\textbf{SVT-Perspective (SVTP)} \cite{quy2013recognizing} consists of $645$ cropped images. Many images have perspective distortions.

\noindent \textbf{CUTE80 (CUTE)} contains $288$ text patches cropped from natural scene images for curved text recognition.

\noindent \textbf{MJSynth (MJ)}  \cite{jaderberg2014synthetic} consists of $9$ millions image instances, which is randomly generated based on $90$k English words.

\noindent \textbf{GBK21K} is generated with the engine in \cite{gupta2016synthetic}, which includes $3$ million text patches for training and $30$k cropped images for testing. The text of each cropped image is generated by randomly selecting several characters from a vocabulary collected in advance. This vocabulary is a subset of the GBK Chinese characters \footnote{https://en.wikipedia.org/wiki/GBK\_(character\_encoding)} and contains $20,948$ characters including Chinese, English and numeric characters. The dataset is challenging due to low-resolution, clustered background, different fonts, and various illumination. Figure
\ref{fig:GBK21k} illustrates several cropped images and ground-truth texts.

\begin{figure}[!h]
    \centering
    \includegraphics[scale=0.5]{GBK21K.pdf}
    \caption{Examples of text in GBK21K. Several cropped images and corresponding ground truth texts are shown.}
    \label{fig:GBK21k}
\end{figure}

\subsection{Training Strategy}
The training of Hamming OCR includes two stages. In the first stage, we train a auxiliary model which uses ordinary output embedding and softmax regression. Cross entropy loss is used in this stage. With the trained model, we generate the codebook for all characters. In the second stage, we replace the output embedding with the Hamming embedding and the softmax regression with the Hamming classifier. The parameters of the backbone and transformer decoder are initially loaded from the model trained in the first stage.
We retrain the model using Hinge-loss.

We implement our Hamming OCR with PyTorch and run all experments on NVIDIA Tesla V100 GPUs with 16GB memory. The batch size on each GPU is $160$, with $8$ GPUs in total. All input images are padded and resized to $48\times 160$. For standard benchmarks, without any data augmentation, we directly use synthetic data MJSynth (7.2M) as our training data. There are $62$ characters to be recognized. For the GBK21K dataset, we generate $3$M cropped images for training and evaluate the performance on $30$K text images. GBK21k is used for Chinese text recognition and contains $20,948$ symbol classes. We adopt the Adam optimizer, and the following hyper-parameters are used: the initial learning rate of $0.001$ and the decay rate of $0.5$.

\begin{table*}[!t]
\centering
\caption{Performance and model size (Mb) comparison on several public benchmarks and a Chinese text dataset. Master\textsuperscript{*} represents the model trained on an union of MJSynth (MJ), SynthText \cite{gupta2016synthetic} (ST) and SynthAdd \cite{gupta2016synthetic} (SA). PaddleOCR$\ddagger$ and PaddleOCR$\dagger$ represent the officially supplied model and the model trained by ourselves with the official code respectively. ``HC'' and ``HE'' mean Hamming classifier and Hamming embedding are used respectively, ``NoFFN'' and ``PS'' are corresponding to removing feed-forward network and cross-layer parameter sharing techniques for transformer decoder. The
index ``Ratio (\%)'' represents the ratio of model size of Hamming classifier and output embedding in the whole model.}
\label{tab:performance}
\resizebox{\textwidth}{!}{%
\begin{tabular}{|m{5.4cm}||p{0.8cm}<{\centering}|m{1.3cm}|m{1cm}|m{1cm}|m{1cm}|m{1cm}||m{1.3cm}|m{1cm}|m{1cm}|}
\hline
\multicolumn{1}{|c||}{\multirow{2}{*}{\textbf{Methods}}} & \multicolumn{6}{c||}{\textbf{Public Benchmarks}} & \multicolumn{3}{c|}{\textbf{Chinese Text Recognition}}       \\ \cline{2-10}
\multicolumn{1}{|c||}{}                                  & \multicolumn{1}{c|}{Training Data} & \multicolumn{1}{c|}{Mode Size} & \multicolumn{1}{c|}{IIIT5K} & \multicolumn{1}{c|}{SVT} & \multicolumn{1}{c|}{SVTP} & \multicolumn{1}{c||}{CUTE} & \multicolumn{1}{c|}{Mode Size} & \multicolumn{1}{c|}{Ratio ($\%$)} & \multicolumn{1}{c|}{GBK21K} \\ \hline
\hline
RARE \cite{shi2016robust} & MJ &$-$ &$81.9$ &$81.9$ &$71.8$ &$59.2$ &$-$ &$-$ &$-$ \\
Yang et al. \cite{yang2017learning} & MJ &$-$ &$-$ &$-$ &$75.8$ &$69.3$ &$-$ &$-$  &$-$ \\
R\textsuperscript{2}AM \cite{lee2016recursive} &MJ &$-$ &$78.4$ &$80.7$ &$-$ &$-$ &$-$ &$-$  &$-$\\
CRNN \cite{shi2016end}&MJ &$31.8$ &$78.2$ &$80.8$ &$-$ &$-$ &$72.7$ &$56.3$ &$-$                            \\
CRNN (VGG) \cite{shi2018aster} &MJ &$-$ &$81.2$ &$82.7$ &$-$ &$-$ &$-$ &$-$  &$-$                \\

ASTER-A \cite{shi2018aster} &MJ &$-$ &$81.7$ &$80.2$ &$73.2$ &$63.9$ &$-$ &$-$ &$-$                         \\
ASTER-B \cite{shi2018aster} &MJ &$80.4$ &$83.2$&$81.6$&$75.4$&$67.4$&$161.9$& $49.7$ & $-$                       \\
PaddleOCR$\ddagger$ (MobileNetV3, large) &MJ+ST &$-$ &$83.7$ &$84.1$ &$71$ &$62.2$&$-$& $-$  & $-$                            \\
ASTER \cite{shi2018aster} & MJ+ST&$-$ &$93.4$&$89.5$&$78.5$&$79.5$&$-$& $-$ & $-$                      \\
SAR \cite{li2019show}  & MJ+ST+SA & $-$ & $91.5$ & $84.5$ & $76.4$ & $83.3$  & $-$&$-$ & $-$  \\
Master\textsuperscript{*} \cite{lu2019master}  & MJ+ST+SA & $223.9$ & $95.0$ & $91.8$ & $84.5$ & $87.5$  & $305.9$  &  $13.4$  & $-$  \\
\hline \hline
Master (ResNet31)  & MJ& $223.9$ & $85.4$ & $85.3$ & $74.1$ & $\textbf{69.8}$  &$305.9$  & $13.4$  &  $82.3$  \\
HC (ResNet31) & MJ &$224.7$ &$85.7$ &$\textbf{85.6}$ &$74.1$ &$69.1$ &$267.0$ &$16.3$ &$82.4$         \\
HC+HE (ResNet31) & MJ& $224.6$ &$\textbf{85.9}$ &$\textbf{85.6}$ &$\textbf{74.6}$ &$68.4$ &$226.9$ &$1.4$ &$82.5$ \\
NoFFN+PS (ResNet31)& MJ &$184.0$ &$84.8$ &$83.9$ &$73.2$ &$\textbf{69.8}$ &$266.1$ &$30.9$ &$82.1$ \\
Hamming OCR (ResNet31) & MJ &$184.8$ &$85.0$ &$84.5$ &$73.0$ &$69.1$ &$187.1$ &$1.2$ &$\textbf{82.8}$ \\
\hline \hline
PaddleOCR$\dagger$ (MobileNetV3, small) & MJ &$2.7$ &$79.5$& $79.8$&$63.7$&$52.4$&$9.4$ & $82.7$  & $48.3$  \\
PaddleOCR$\dagger$  (MobileNetV3, large) & MJ &$5.3$ &$81.6$& $80.7$&$68.2$&$58.7$&$11.7$ &$66.4$  & $66.5$  \\
Hamming OCR (MobileNetV2) &MJ &$4.6$ &$82.6$ &$83.3$ &$68.8$ &$61.1$ &$\textbf{6.6}$ &$27.1$ &$\textbf{71.2}$ \\
\hline
\end{tabular}
}
\end{table*}

\subsection{Recognition Performance Evaluation}
The recognition accuracies of different methods on five datasets, including regular (IIIT5K, SVT), irregular (SVTP, CUTE) and a Chinese text (GBK21K), are shown in Table \ref{tab:performance}. In Hamming OCR model, four techniques are used including Hamming classifier, Hamming embedding, removing feed-forward network and cross-layer parameter sharing. To compare the effect of different techniques, we design three models based on the Master model by: replacing the softmax regression with Hamming classifier, namely HC; replacing the softmax regression and output embedding with Hamming classifier and Hamming embedding respectively, namely HC+HE; and employing removing feed-forward network and cross-layer parameter sharing technique, namely NoFFN+PS.

Firstly, we analyze the performance of different methods on the four standard benchmarks. Compared with previous methods with the same training data (MJ), Hamming OCR achieves competitive results. Especially, HC+HE has the similar performance as Master in most situations, which verifies the effectiveness of the proposed Hamming classifier and Hamming embedding. When we use removing feed-forward network and cross-layer parameter sharing techniques in transformer decoder module, the results of NoFFN+PS are slightly lower than Master. Due to the lightweight CNN backbone, the results of Hamming OCR (MobileNetV2) significantly decrease. However, Hamming OCR (MobileNetV2) consistently outperforms PaddleOCR in comparison with the same training data. For instance, the accuracy of Hamming OCR model on IIIT5K is higher than the larger PaddleOCR model by one percentage, while its model size is smaller. Aster has outstanding results on irregular datasets due to its rectification module.

Secondly, On the GBK21K datatset, compared with Master, Hamming OCR not only obtains competitive performance but also sharply reduces the storage cost. The results show that Hamming OCR can handle such challenging Chinese recognition task. For the lightweight models, our Hamming OCR (MobileNetV2) outperforms PaddleOCR. Hamming OCR (MobileNetV2) includes a backbone of 2.3Mb, a simplified transformer decoder of 2.5Mb, a projection matrix of 0.5Mb and a codebook of 1.3Mb, while the PaddleOCR (MobileNetV3, large) includes a backbone of 3.0Mb, an LSTM decoder of 0.9Mb and a softmax classifier of 7.8Mb. It can been seen that softmax regression take a large portion of the storage cost of PaddleOCR.

In Hamming OCR, the projection matrix $\Psi$ used to generate the LSH codebook is randomly initialized. When we directly evaluate the performance of Hamming OCR with this initial projection matrix, its results are $50.9\%$ on IIIT5K, $48.5\%$ on SVT, $32.7\%$ on SVTP, $32.3\%$ on CUTE. Therefore, we confirm that retraining the model with the Hinge-loss is very vital.

\subsection{Ablation Study}

\subsubsection{Factorized Embedding Vs LSH Code.}
From a practical perspective, Chinese or multi-language text recognition usually require the length of the vocabulary list $L$ to be large, then increasing $L$ increases the size of the embedding matrix ($d\times L$) from output embedding and the projection matrix ($d\times L$) from softmax regression. As ALBERT \cite{lan2019albert}, we use a factorized embedding technique, which decomposes a matrix into two smaller matrices, to reduce the parameters. We take the linear transformation $W\in\mathbb{R}^{d\times L}$ of softmax regression as an example. It can be decomposed into $W_1\in\mathbb{R}^{d\times p}$ and $W_2\in\mathbb{R}^{p\times L}$. By using this decomposition, we reduce the parameters $W$ from $\mathcal{O}(d\times L)$ to $ \mathcal{O}(d\times p+p\times L)$. This parameter reduction is significant when $d>>p$.
 On the other hand, we present the LSH code can significantly reduce the parameters in classifier and output embedding modules. Thus, in this part, we take the experiments on GBK21K to evaluate the performance of factorized embedding technique and our Hamming classifier.

From Figure \ref{fig:embedding}, we can see that as the value of $p$ increases, the recognition accuracy of the model based on factorized embedding technique is also increasing. Compared with factorized embedding technique, Hamming OCR performs better and its size is smaller.

\begin{figure}[!h]
    \centering
    \includegraphics[scale=0.90]{HammingEmbedding.pdf}
    \caption{Performance comparison on GBK21K with different training steps. The performance of factorized embedding technique with $p=16,32,64,128$ are demonstrated.}
    \label{fig:embedding}
\end{figure}

\subsubsection{Random Code Vs LSH Code.}
In our Hamming OCR, we obtain LSH code by linear projection and thresholding. To verify the effectiveness of LSH code, we compare its performance with a random code, which is simply generated by a random method. To generate each element of the random code for a character, we randomly choose 0 or 1 with equal probability. To be fair, we adopt HC as the baseline model. Table \ref{tab:code} illustrates the recognition results on datasets. We can see that the performance of random code on the four standard benchmarks is competitive. For example, the recognition accuracy of LSH code is $85.6\%$ while random code can reach $84.5\%$ on the SVT dataset. However, for the GBK21K dataset, model with random code does not converge at all and can't recognize any text image correctly. As we know, the lexicon of SVT is very small, the random code can represent each character very well. However, there are over $20,000$ characters in GBK21K, it's possible that the representation ability of random code is insufficient. Different from random code, LSH code can reach $82.4\%$ recognition rate on GBK21K dataset.

\begin{table}[!h]
\centering
\caption{Performance comparison of baseline model with LSH code and random code on GBK21K. * means the model does not converge.}
\label{tab:code}
\resizebox{0.45\textwidth}{!}{%
\begin{tabular}{cccccc}
\toprule
 \textbf{Methods}        & \textbf{IIIT5K} & \textbf{SVT} & \textbf{SVTP} & \textbf{CUTE} & \textbf{GBK21K} \\ \midrule
Random Code                & $81.53$ &$84.54$ & $73.18$ & $68.06$ & $0.00^*$  \\
LSH Code              & $85.70$ &$85.63$ & $74.11$ & $69.10$ & $82.41$  \\
\bottomrule
\end{tabular}%
}
\end{table}

\subsubsection{Influence of The Length of LSH Code.}
Table \ref{tab:length} demonstrates the variation of recognition rate along with the length of LSH code. Obviously, LSH code with $512$-dimension performs very well. When the length of LSH code is less than $512$, the performance of Hamming OCR has declined. As the length of LSH code is larger than 512, the performance almost saturates. However, its negative impact is that the model size obviously becomes larger.

\begin{table}[!h]
\centering
\caption{Performance with different lengths of  LSH code on GBK21K.}
\label{tab:length}
\begin{tabular}{|c|c|c|c|c|}
\hline
Length (LSH Code) & $256$   & $512$   & $1024$  & $2048$  \\
\hline
GBK21K (accuracy)  & $81.86$ & $82.39$ & $82.26$ & $82.31$ \\
\hline
\end{tabular}%
\end{table}

\section{Conclusion}
\label{sec_conclusion}
In this paper, we present a lightweight and effective Hamming OCR method for scene text recognition. Most scene text recognition approaches adopt learnable output embedding and softmax regression for decoding the output characters and classification. Each of them has a parameter matrix, the size of which depends on the number of characters. when we need deploy a model with a large scale lexicon on mobile devices, these two matrices are encumbrances due to their massive storage requirements. Therefore, we present a method to generate a codebook for all characters and develop a Hamming classifier for classification. We further use the LSH code of each character as its embedding. As we know, this work is the first attempt to use LSH code as the representation vector of each class for classification and embedding. To reduce the parameters of a standard decoder of transformer, we introduce a simplified transformer decoder by removing the feed-forward network and using cross-layer parameter sharing technique. We combine Hamming classifier, Hamming embedding, and simplified transformer decoder into Hamming OCR. Hamming OCR achieve competitive results on on several standard benchmarks and one our own dataset.


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KENYA: ENFORCEMENT ALERT
Restrictive Practices
The Competition Authority of Kenya (CAK) recently announced that it had entered into a settlement agreement with local beer producer Kenya Breweries Limited (KBL), a subsidiary of UK Diageo's East African Breweries Ltd (EABL).
The settlement follows from an investigation by the CAK in terms of section 21 of the Competition Act (12 of 2010) wherein the CAK had found that KBL's distribution agreements with its downstream distributors – which provides for inter alia, territorial exclusivity – is anti-competitive and may lead to the lessening of intra-brand competition.
The settlement was reached in terms of section 38 of the Competition Act and requires that KBL establish an internal compliance policy and review and amend the problematic and restrictive clauses in its agreements with distributors.
Michael-James Currie, an African focused competition lawyer, says that the decision is particularly important for companies which use third parties to execute their distribution strategies as the majority of distribution agreements contain restrictions of some kind (often transported from international distribution agreements) which will need to be assessed against the standards of the Competition Act in Kenya as the CAK is actively focusing on these types of restrictive verticals arrangements.
Abuse of Dominance
Styles Industries (Darling Kenya)
Braids supplier, Styles Industries Ltd (Styles) has been found guilty by the CAK for abuse of dominance in contravention of Section 24 of the Competition Act.
The CAK launched an investigation into Styles on the basis of a complaint received by a competitor in the market, Solpia Kenya, claiming that Styles had abused its dominance by imposing unfair selling prices and conditions on suppliers who sell its products.
The CAK's investigation found that Styles had abused its dominance by imposing unfair trading conditions on its downstream suppliers which it sought to enforce through threatening its downstream suppliers with account closure, removal of discounts and refusal to supply products.
The CAK is currently in negotiations with the parties and have indicated that its finding could result in Styles paying the complainant an amount in damages and/or a fine Sh10 million. In terms of Section 54(3) of the Competition Act, the relevant individuals within Styles could further face imprisonment for a period of up to 5 years.
Kaluworks
The CAK dismissed an abuse of dominance case against cookware manufacturer, Kaluworks Limited (Kaluworks).
The case emanated from a complaint by rival company, Sufuria World (Sufuria) in which it was alleged that Kaluworks had refused to sell to them certain aluminum circles which it required for purposes of manufacturing its aluminum cooking ports. This, Sufuria claimed, amounted to an abuse of dominance in terms of section 23 and 24 of the Competition Act.
The CAK, however, found that the conduct did not amount to abuse of dominance under the Competition Act as Sufuria had other options available to it in that it had the ability to replicate the technologies used by Kaluworks to produce the aluminum circles (as other manufacturers have done) or it could increase its order volumes in order to make it economically feasible for Kaluworks to supply it with the aluminum circles.
This finding was based on the representations made by Kaluworks that:
it primarily produces aluminum circles for in-house production for a variety of its own cookware products intended for local and export markets; and
it could only manufacture the aluminum circles to third parties where such third parties placed an order which met certain minimum quantities that would guarantee optimal scale of production
In supporting its findings, the CAK stated that in assessing the conduct of a dominant firm and whether it amounts to a 'refusal to deal', "is necessary to prove indispensability of the facility to the operation of the complainant or other third parties as arbitrary intervention may hurt innovation."
Market Inquiries
Transport Inquiry
The CAK has recently announced that it has initiated a 'regional study' in the Shipping, Trucking and Haulage industry in Kenya, Uganda, Rwanda and Burundi.
According to the announcement, the objective of the inquiry is to identify and remedy features of the market and trade practices which are anti-competitive and which impedes the national and intra-regional trade which in terms slows the potential growth of the manufacturing sector in Kenya.
Leasing Sector
The CAK has further announced a market study into the leasing sector which it will be conducting in conjunction with the Financial Sector Deepening (FSD) Kenya.
The objective of the market study is to assess the level of competition in the sector and to identify areas of concern in order to enhance competition in the market by facilitating SME entrants into the market.
John Oxenham, director at African antitrust advisory firm Primerio, says that market inquiries can be used very effectively, however, they are resource intensive and in order to achieve there objectives must be concluded expeditiously. The CAK should be cognizant of the challenges and experiences of the South African Competition Commission (SACC) where the market inquiries are not being concluded timeously.
[The editor wishes to thank Charl van der Merwe for his contribution to this update]


The Tulsa Sports Commission presents the Tulsa Federal Credit Union Tulsa Run Expo at the Cox Business Center on Thursday, Oct. 25, from 4pm to 7pm and again on Friday, Oct. 26, from 10am to 7pm. Runners will receive their race packets, which includes timing chip, shirt and information.
There will be a dynamic bib assignment process this year. When you arrive at packet pick up, simply tell the volunteer at packet pick your name, show identification and they will verify your entry into the race and assign your race number. It's quick, easy and simple! If you're picking up for a friend, please bring written authorization.
Out of town runners will be allowed to pick up their packets from 6:30 to 8 a.m. on Race Day (Oct. 27) or can sign up for Bib Mailing during the registration process.
For more information on exhibiting or attending at the Tulsa Run Expo, and for information on the race, please visit https://runsignup.com/Race/OK/Tulsa/TulsaRun.


Communitarianism is a political philosophy and a social movement, which has been developing mostly in the United States since the 1980s. Locating itself between the traditional liberal and conservative approaches, communitarianism looks for a balance between what is individual, and what is communal; between individual freedom and social order.
One of the basic postulates of communitarianism is the revival of moral culture of communities. Communitarians advocate for a value-oriented organization of society, focused on the common good. Therefore, they strongly oppose the Kantian tradition of value-free, neutral perspective, as well as the vision of an unencumbered self freely deciding about his/her values.
In the paper, a critical analysis of the communitarian approach to moral culture will be presented. The following questions will be addressed: How to formulate and establish a moral culture within a community? Is it possible to reach an axiological consensus in a modern, pluralistic society? How to avoid community's oppressiveness with regard to people's values and behavior? What are the conflict-resolution procedures?


text:
Q: how to remove parents in firebase by its nested data? such data comes to the database
{
  "Markers" : {
    "brTRf3EfqzaWuaw0q42Ay8Jnj0F3" : {
      "-M5Tp8BZpUkJSbmV4Qya" : {
        "date" : "22, апр., 2020",
        "latitude" : "53.9150522051367",
        "longitude" : "27.440601512789726",
        "permission" : false,
        "time" : "01:21"
      },
      "-M5XhMon2UZiD6M_Zbp5" : {
        "date" : "22, апр., 2020",
        "latitude" : "53.914562076017575",
        "longitude" : "27.441855780780315",
        "permission" : false,
        "time" : "19:25"
      }
    }
  }
}

Take for example the first entry from the user: brTRf3EfqzaWuaw0q42Ay8Jnj0F3
He put a mark on the map with his parent:
 "-M5Tp8BZpUkJSbmV4Qya"
 and it contains a record with time data:
 "time": "01:21"
Actually the question:
 how to delete a parent record
 "-M5Tp8BZpUkJSbmV4Qya" by recording time in it ???

A: To delete the parent according to the query, do the following:
DatabaseReference markerRef = FirebaseDatabase.getInstance().getReference().child("Markers");
markerRef.child("brTRf3EfqzaWuaw0q42Ay8Jnj0F3").orderByChild("time").equalTo("01:21").addListenerForSingleValueEvent(new ValueEventListener() {
         @Override
      public void onDataChange(DataSnapshot dataSnapshot) {
          for(DataSnapshot data: dataSnapshot.getChildren()){
               data.getRef().removeValue();
                  }
            }

        @Override
       public void onCancelled(DatabaseError databaseError) {
                   throw databaseError.toException();
               }
          });

First add a reference to the node brTRf3EfqzaWuaw0q42Ay8Jnj0F3, then using orderByChild("time").equalTo("01:21") you can create a query to retrieve the node that contains the above time. Then iterate inside the snapshots and using getRef() you can obtain a reference to the source location for this snapshot.

redpajama_set_name: RedPajamaStackExchange


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