NLP Research Papers Dataset

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@kaggle.subhamjain_natural_language_processing_research_papers

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Researchppr

@kaggle.subhamjain_natural_language_processing_research_papers.researchppr

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article Article	abstract Abstract	section_names Section Names	unnamed_3 Unnamed: 3	unnamed_4 Unnamed: 4	unnamed_5 Unnamed: 5	unnamed_6 Unnamed: 6	unnamed_7 Unnamed: 7	unnamed_8 Unnamed: 8	unnamed_9 Unnamed: 9	unnamed_10 Unnamed: 10	unnamed_11 Unnamed: 11	unnamed_12 Unnamed: 12	unnamed_13 Unnamed: 13	unnamed_14 Unnamed: 14	unnamed_15 Unnamed: 15	unnamed_16 Unnamed: 16	unnamed_17 Unnamed: 17	unnamed_18 Unnamed: 18	unnamed_19 Unnamed: 19	unnamed_20 Unnamed: 20	unnamed_21 Unnamed: 21	unnamed_22 Unnamed: 22	unnamed_23 Unnamed: 23	unnamed_24 Unnamed: 24	unnamed_25 Unnamed: 25	unnamed_26 Unnamed: 26	unnamed_27 Unnamed: 27	unnamed_28 Unnamed: 28	unnamed_29 Unnamed: 29	unnamed_30 Unnamed: 30	unnamed_31 Unnamed: 31	unnamed_32 Unnamed: 32	unnamed_33 Unnamed: 33	unnamed_34 Unnamed: 34	unnamed_35 Unnamed: 35	unnamed_36 Unnamed: 36	unnamed_37 Unnamed: 37	unnamed_38 Unnamed: 38	unnamed_39 Unnamed: 39	unnamed_40 Unnamed: 40	unnamed_41 Unnamed: 41	unnamed_42 Unnamed: 42	unnamed_43 Unnamed: 43	unnamed_44 Unnamed: 44	unnamed_45 Unnamed: 45	unnamed_46 Unnamed: 46	unnamed_47 Unnamed: 47	unnamed_48 Unnamed: 48	unnamed_49 Unnamed: 49	unnamed_50 Unnamed: 50	unnamed_51 Unnamed: 51	unnamed_52 Unnamed: 52	unnamed_53 Unnamed: 53	unnamed_54 Unnamed: 54	unnamed_55 Unnamed: 55	unnamed_56 Unnamed: 56	unnamed_57 Unnamed: 57	unnamed_58 Unnamed: 58	unnamed_59 Unnamed: 59	unnamed_60 Unnamed: 60	unnamed_61 Unnamed: 61	unnamed_62 Unnamed: 62	unnamed_63 Unnamed: 63	unnamed_64 Unnamed: 64	unnamed_65 Unnamed: 65	unnamed_66 Unnamed: 66	unnamed_67 Unnamed: 67	unnamed_68 Unnamed: 68	unnamed_69 Unnamed: 69	unnamed_70 Unnamed: 70	unnamed_71 Unnamed: 71	unnamed_72 Unnamed: 72	unnamed_73 Unnamed: 73	unnamed_74 Unnamed: 74	unnamed_75 Unnamed: 75	unnamed_76 Unnamed: 76	unnamed_77 Unnamed: 77	unnamed_78 Unnamed: 78	unnamed_79 Unnamed: 79	unnamed_80 Unnamed: 80	unnamed_81 Unnamed: 81	unnamed_82 Unnamed: 82	unnamed_83 Unnamed: 83	unnamed_84 Unnamed: 84	unnamed_85 Unnamed: 85	unnamed_86 Unnamed: 86	unnamed_87 Unnamed: 87	unnamed_88 Unnamed: 88	unnamed_89 Unnamed: 89	unnamed_90 Unnamed: 90	unnamed_91 Unnamed: 91	unnamed_92 Unnamed: 92	unnamed_93 Unnamed: 93	unnamed_94 Unnamed: 94	unnamed_95 Unnamed: 95	unnamed_96 Unnamed: 96	unnamed_97 Unnamed: 97	unnamed_98 Unnamed: 98	unnamed_99 Unnamed: 99
additive models @xcite provide an important family of models for semiparametric regression or classification . some reasons for the success of additive models are their increased flexibility when compared to linear or generalized linear models and their increased interpretability when compared to fu…	additive models play an important role in semiparametric statistics . this paper gives learning rates for regularized kernel based methods for additive models . these learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonpara…	introduction main results on learning rates comparison of learning rates	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan
the leptonic decays of a charged pseudoscalar meson @xmath7 are processes of the type @xmath8 , where @xmath9 , @xmath10 , or @xmath11 . because no strong interactions are present in the leptonic final state @xmath12 , such decays provide a clean way to probe the complex , strong interactions that b…	we have studied the leptonic decay @xmath0 , via the decay channel @xmath1 , using a sample of tagged @xmath2 decays collected near the @xmath3 peak production energy in @xmath4 collisions with the cleo - c detector . we obtain @xmath5 and determine the decay constant @xmath6 mev , where the firs…	[sec:introduction]introduction [sec:detector]data and the cleo- detector [sec:analysys]analysis method [sec:conclusion]summary	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan
the transport properties of nonlinear non - equilibrium dynamical systems are far from well - understood@xcite . consider in particular so - called ratchet systems which are asymmetric periodic potentials where an ensemble of particles experience directed transport@xcite . the origins of the interes…	in 84 , 258 ( 2000 ) , mateos conjectured that current reversal in a classical deterministic ratchet is associated with bifurcations from chaotic to periodic regimes . this is based on the comparison of the current and the bifurcation diagram as a function of a given parameter for a periodic asymm…	introduction regularity and chaos in single-particle ratchet dynamics ensemble currents the relationship between bifurcation diagrams and ensemble currents acknowledgements	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan
studies of laser beams propagating through turbulent atmospheres are important for many applications such as remote sensing , tracking , and long - distance optical communications . howerver , fully coherent laser beams are very sensitive to fluctuations of the atmospheric refractive index . the ini…	the effect of a random phase diffuser on fluctuations of laser light ( scintillations ) is studied . not only spatial but also temporal phase variations introduced by the phase diffuser are analyzed . the explicit dependence of the scintillation index on finite - time phase variations is obtaine…	introduction the method of photon distribution function in the problem of scintillations. a phase diffuser with finite correlation time discussion conclusion acknowledgment	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan
the so - called `` nucleon spin crisis '' raised by the european muon collaboration ( emc ) measurement in 1988 is one of the most outstanding findings in the field of hadron physics @xcite,@xcite . the renaissance of the physics of high energy deep inelastic scatterings is greatly indebted to this …	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan
nd the lattice simulation reproduce the quark number sum rule @xmath212 with good prediction . turning to @xmath210	one observes that the prediction of the cqsm shows somewhat peculiar dependence on the pion mass . starting from a fairly small value in the chiral limit ( @xmath213 )	it first increases as @xmath183 increases	but as @xmath183 further increases it begins to decrease	thereby showing a tendency to match the lattice prediction in the heavy pion region . very interestingly	letting put aside the absolute value	a similar @xmath183 dependence is also observed in the chiral extrapolation of the lattice prediction for the momentum fraction @xmath214 shown in fig.25 of @xcite . physically	the quantity @xmath210 has a meaning of the difference of the momentum fractions carried by the @xmath69-quark and the @xmath70-quark . the empirical value for it is @xmath215 @xcite . one sees that the prediction of the cqsm in the chiral limit is not far from this empirical information	although more serious comparison must take account of the scale dependence of @xmath216 . and @xmath217 as functions of @xmath183	together with the corresponding lattice predictions @xcite	@xcite . the meaning of the symbols are the same as in fig.[fig : a1020is].	width=604	height=264 ] next	shown in fig.[fig : b1020is ] are the cqsm predictions for @xmath218 and @xmath217 . the former quantity is related to the isoscalar combination of the nucleon anomalous magnetic moment as @xmath219 . ( we recall that its empirical value is @xmath220 . ) we find that this quantity is very sensitive…	the difference is exaggerated too much in this comparison . in fact	if we carry out a comparison in the total isoscalar magnetic moment of the nucleon @xmath222	the cqsm in the chiral limit gives @xmath223 in comparison with the observed value @xmath224 . to our knowledge	no theoretical predictions are given for this quantity by either of the lhpc or qcdsf collaborations . the right panel of fig.4 shows the predictions for @xmath217	which is sometimes called the isoscalar part of the nucleon anomalous gravitomagnetic moment	or alternatively the _ net quark contribution to the nucleon anomalous gravitomagnetic moment_. as already pointed out	the prediction of the cqsm for this quantity is exactly zero : i.e. @xmath169 the explicit numerical calculation also confirms it . it should be recognized that the above result @xmath225 obtained in the cqsm is just a necessary consequence of the _ momentum sum rule _ and the _ total nucleon spin …	both of which are saturated by the quark field only in the cqsm as @xmath226 and @xmath227 \ = \ \langle j \rangle^{u + d } \ = \ \frac{1}{2 } .\ ] ] in real qcd	the gluon also contributes to these sum rules	thereby leading to more general identities : @xmath228 + [ a_{20}^g ( 0 ) + b_{20}^g ( 0 ) ] = 1	\end{aligned}\ ] ] which constrains that only the sum of @xmath217 and @xmath229 is forced to vanish as @xmath230 ( while we neglect here the contributions of other quarks than the @xmath69- and @xmath70-quarks	it loses no generality in our discussion below . in fact	to include them	we have only to replace the combination @xmath231 by @xmath232 . ) the above nontrivial identity claims that the net contributions of quark and gluon fields to the anomalous gravitomagnetic moment of the nucleon must be zero . an interesting question is whether the quark and gluon contribution to t…	a nonperturbative analysis within the framework of the lattice qcd indicates that the net quark contribution to the anomalous gravitomagnetic moment is small or nearly zero	@xmath233 @xcite	@xcite . ( to be more precise	we sees that the prediction of the lhpc collaboration for @xmath217 is slightly negative @xcite	while that of the qcdsf group is slightly positive @xcite . ) this strongly indicates a surprising possibility that the quark and gluon contribution to the anomalous gravitomagnetic moment of the nucleon may separately vanish . worthy of special mention here is an interesting argument given by tery…	claiming that the vanishing net quark contributions to the anomalous gravitomagnetic moment of the nucleon	violated in perturbation theory	is expected to be restored in full nonperturbative qcd due to the confinement @xcite	@xcite	@xcite . very interestingly	once it actually happens	it leads to a surprisingly simple result	i.e. the proportionality of the quark momentum and angular momentum fraction @xmath234 as advocated by teryaev @xcite	@xcite	@xcite . a far reaching physical consequence resulting from this observation was extensively discussed in our recent report @xcite . ( see also the discussion at the end of this section . ) and @xmath235 as functions of @xmath183	together with the corresponding lattice predictions @xcite	@xcite . the meaning of the symbols are the same as in fig.[fig : a1020is].	width=604	height=264 ] next	we show in fig.[fig : b1020iv ] the predictions for the isovector case	i.e. @xmath236 and @xmath235 . we recall first that the quantity @xmath236 represents the isovector combination of the nucleon anomalous magnetic moment @xmath237	the empirical value of which is known to be @xmath238 . one find that this quantity is extremely sensitive to the variation of the pion mass especially near @xmath239 . this is only natural if one remembers the important role of the pion cloud in the isovector magnetic moment of the nucleon . ( one…	however	that	within the framework of the cqsm	there is an important @xmath241 correction or the 1st order rotational correction to some kind of isovector quantities like the isovector magnetic moment of the nucleon in question or the axial - vector coupling constant of the nucleon @xcite@xcite . this next - to - leading correction in @xmath241…	the half of which can be interpreted as the difference of the total angular momentum carried by the @xmath69-quark and the @xmath70-quark fields according to ji s angular momentum sum rule @xcite . the cqsm predicts fairly small value for this quantity	in contrast to the lattice predictions of sizable magnitude . it seems that the pion mass dependence rescues this discrepancy only partially . here we argue that	the reason why the cqsm ( in the chiral limit ) gives rather small prediction for this quantity is intimately connected with the characteristic @xmath1 dependence of the quantity @xmath242	the forward limit of the isovector unpolarized spin - flip gpd of the nucleon . to show it	we first recall that	within the theoretical frame work of the cqsm	@xmath236 as well as @xmath243 are calculated as difference of @xmath244 and @xmath245 and of @xmath246 and @xmath247	respectively	as @xmath248 although the quantities of the rhs can be calculated directly without recourse to any distribution functions	they can also be evaluated as @xmath1-weighted integrals of the corresponding gpds as @xmath249 the distribution function @xmath242 has already been calculated within the cqsm in our recent paper @xcite . as shown there	the dirac sea contribution to this quantity has a sizably large peak around @xmath250 . since this significant peak due to the deformed dirac - sea quarks is approximately symmetric with respect to the reflection @xmath251	it hardly contributes to the second moment @xmath252	whereas it gives a sizable contribution to the first moment @xmath253 . the predicted significant peak of @xmath242 around @xmath250 can physically be interpreted as the effects of pion cloud . it can be convinced in several ways . first	we investigate how this behavior of @xmath242 changes as the pion mass is varied . obtained with @xmath182 and @xmath239.	width=340	height=264 ] dependence of @xmath254.	width=604	height=264 ] shown in fig.[fig : eiv_pi0 ] and in fig.[fig : eiv_pi24 ] are the cqsm predictions for @xmath242 with several values of @xmath183 . i.e. @xmath255	and @xmath256 . one clearly sees that the height of the peak around @xmath250	due to the deformed dirac - sea quarks	decreases rapidly as @xmath183 increases . this supports our interpretation of this peak as the effects of pion clouds . on the other hand	one also observes that the magnitude of the valence quark contribution	peaked around @xmath257	gradually increases as @xmath183 becomes large . this behavior of @xmath242 turns out to cause a somewhat unexpected @xmath183 dependence of @xmath253 and @xmath252 . as a function of @xmath183	the dirac sea contribution to @xmath253 decreases fast	whereas the valence quark contribution to it increases slowly	so that the total @xmath253 becomes a decreasing function of @xmath183 . on the other hand	owing to the approximate odd - function nature of the dirac sea contribution to @xmath258 with respect to @xmath1	it hardly contributes to @xmath259 independent of the pion mass	while the valence quark contribution to @xmath258 is an increasing function of @xmath183	thereby leading to the result that the net @xmath259 is a increasing function of @xmath183 . obtained with @xmath182 and @xmath239.	width=340	height=264 ] dependence of @xmath260.	width=604	height=264 ] we can give still another support to the above - mentioned interpretation of the contribution of the dirac - sea quarks . to see it	we first recall that the theoretical unpolarized distribution function @xmath261 appearing in the decomposition @xmath262 also has a sizable peak around @xmath250 due to the deformed dirac - sea quarks . as shown in fig.[fig : fiv_pi0 ] and in fig.[fig : fiv_pi24 ]	this peak is again a rapidly decreasing function of @xmath183	supporting our interpretation of it as the effects of pion clouds . here	we can say more . we point out that this small-@xmath1 behavior of @xmath261 is just what is required by the famous nmc measurement @xcite . to confirm it	first remember that the distribution @xmath263 in the negative @xmath1 region should actually be interpreted as the distribution of antiquarks . to be explicit	it holds that @xmath264 the large and positive value of @xmath261 in the negative @xmath1 region close to @xmath250 means that @xmath265 is negative	i.e. the dominance of the @xmath7-quark over the @xmath8-quark inside the proton	which has been established by the nmc measurement @xcite . evolved to @xmath266 and @xmath267 in comparison with the hermes and nutev data at the corresponding energy scales @xcite	@xcite.	width=340	height=283 ] shown in fig.[fig : dbdu ] are the predictions of the cqsm for @xmath268 evolved to the high energy scales corresponding to the experimental observation @xcite . ( the theoretical predictions here were obtained with @xmath182 and @xmath269 . ) the model reproduces well the observed b…
let @xmath1 . let @xmath2\longrightarrow [ 0,\pi_{p , q}/2]$ ] be the integral @xmath3 where @xmath4 . the @xmath0-_sine functions _ , @xmath5 , $ ] are defined to be the inverses of @xmath6 , @xmath7\ ] ] extended to @xmath8 by the rules @xmath9 which make them periodic , continuous , odd with resp…	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan
e piecewise linear interpolant of @xmath494 for the family of nodes @xmath497 has a graph below that of @xmath494 . the following computer codes written in the open source languages octave and python can be used to verify any of the numerical estimations presented in this paper . function for comput…	err	np]=apq(k	p	q ) # a is the kth fourier coefficient of the p	q sine function # err is the residual # np number of quadrature points # function [ a	err	np]=apq(k	p	q ) if mod(k	2)==0	disp('error : k should be odd ' ) ; return ; end [ i	err	np]=quadcc(@(y ) cos(kpibetainc(y.^q	1/q	(p-1)/p)/2)	0	1	1e-10 ) ; a = i2sqrt(2)/k / pi ; .... function for computing @xmath498 with 10-digits precision . .... # -- function file : [ s	err	np]=apqsum(k	p	q ) # s is the sum of the fourier coefficient of the p	q sine function # err is the residual # np number of quadrature points # function [ s	err	np]=apqsum(p	q ) [ i	err	np]=quadcc(@(y ) log(cot(pi*betainc(y.^q	1/q	(p-1)/p)/4))	0	1	1e-10 ) ; s = i*sqrt(2)/pi ; .... function for computing @xmath207 with variable precision . .... def a(k	p	q ) : "" "" "" computes the kth fourier coefficient of the p	q sine function . returns coefficient and residual . > > > from sympy.mpmath import * > > > mp.dps = 25 ; mp.pretty = true > > > a(1	mpf(12)/11	mpf(12)/11 ) > > > ( 0.8877665848468607372062737	1.0e-59 ) "" "" "" if isint(fraction(k	2 ) ) : apq=0 ; e=0 ; return apq	e f= lambda x : cos(kpibetainc(1/q	(p-1)/p	0	x**q	regularized = true)/2 ) ; ( i	e)=quad(f	[0	1]	error = true	maxdegree=10 ) ; apq = i2sqrt(2)/k / pi ; return apq	e .... function for computing @xmath498 with variable precision . .... def suma(p	q ) : "" "" "" computes the sum of the fourier coefficient of the p	q sine function . returns sum and residual . > > > from sympy.mpmath import * > > > mp.dps = 25 ; mp.pretty = true > > > suma(mpf(12)/11	mpf(12)/11 ) > > > ( 1.48634943002852603038783	1.0e-56 ) "" "" "" f= lambda x : log(cot(pi*betainc(1/q	(p-1)/p	0	x**q	regularized = true)/4 ) ) ; ( i	e)=quad(f	[0	1]	error = true	maxdegree=10 ) ; sumapq = i*sqrt(2)/pi ; return sumapq	e .... the authors wish to express their gratitude to paul binding who suggested this problem a few years back . they are also kindly grateful with stefania marcantognini for her insightful comments during the preparation of this manuscript . we acknowledge support by the british engineering and ph…	the research support fund of the edinburgh mathematical society and the instituto venezolano de investigaciones cientficas . -plane where theorem [ impro_implicit]-[aimplicit ] and [ bimplicit ]	as well as proposition [ beyond2 ] ( with different values of @xmath466 ) apply . in all graphs @xmath16 corresponds to the horizontal axis and @xmath260 to the vertical axis and the dotted line shows @xmath14 . [ th10ab]	title=""fig:""	height=226 ] -plane where theorem [ impro_implicit]-[aimplicit ] and [ bimplicit ]	as well as proposition [ beyond2 ] ( with different values of @xmath466 ) apply . in all graphs @xmath16 corresponds to the horizontal axis and @xmath260 to the vertical axis and the dotted line shows @xmath14 . [ th10ab]	title=""fig:""	height=226 ] -plane where theorem [ impro_implicit]-[aimplicit ] and [ bimplicit ]	as well as proposition [ beyond2 ] ( with different values of @xmath466 ) apply . in all graphs @xmath16 corresponds to the horizontal axis and @xmath260 to the vertical axis and the dotted line shows @xmath14 . [ th10ab]	title=""fig:""	height=226 ] -plane where theorem [ impro_implicit]-[aimplicit ] and [ bimplicit ]	as well as proposition [ beyond2 ] ( with different values of @xmath466 ) apply . in all graphs @xmath16 corresponds to the horizontal axis and @xmath260 to the vertical axis and the dotted line shows @xmath14 . [ th10ab]	title=""fig:""	height=226 ] -plane where theorem [ impro_implicit]-[aimplicit ] and [ bimplicit ]	as well as proposition [ beyond2 ] ( with different values of @xmath466 ) apply . in all graphs @xmath16 corresponds to the horizontal axis and @xmath260 to the vertical axis and the dotted line shows @xmath14 . [ th10ab]	title=""fig:""	height=226 ] -plane where theorem [ impro_implicit]-[aimplicit ] and [ bimplicit ]	as well as proposition [ beyond2 ] ( with different values of @xmath466 ) apply . in all graphs @xmath16 corresponds to the horizontal axis and @xmath260 to the vertical axis and the dotted line shows @xmath14 . [ th10ab]	title=""fig:""	height=226 ] -plane where theorem [ impro_implicit]-[cimplicit ] applies . even when we know @xmath43 is invertible in this region as a consequence of theorem [ impro_implicit]-[aimplicit ]	the upper bound on the riesz constant provided by improves upon that provided by ( case @xmath57 ) . in this graph @xmath16 corresponds to the horizontal axis and @xmath260 to the vertical axis and the dotted line shows @xmath14 . [ th10c]	title=""fig:""	height=226 ] -plane where theorem [ impro_implicit]-[cimplicit ] applies . even when we know @xmath43 is invertible in this region as a consequence of theorem [ impro_implicit]-[aimplicit ]	the upper bound on the riesz constant provided by improves upon that provided by ( case @xmath57 ) . in this graph @xmath16 corresponds to the horizontal axis and @xmath260 to the vertical axis and the dotted line shows @xmath14 . [ th10c]	title=""fig:""	height=226 ]"	we improve the currently known thresholds for basisness of the family of periodically dilated @xmath0-sine functions . our findings rely on a beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity . we also determine refined bounds …	introduction linear independence the different components of the change of coordinates map invertibility and bounds on the riesz constant riesz basis properties beyond the applicability of the case of equal indices the thresholds for invertibility and the regions of improvement the shape of @xmath46…	nan	nan	nan	nan	nan	nan	nan
the simulations we discuss here allowed us to obtain spectra of the shg response . we employed comsol multiphysics software ( www.comsol.com ) in order to perform simulations of the linear optical response as described in ref . @xcite . a unit cell containing a single sic pillar attached to the sic …	we report on strong enhancement of mid - infrared second harmonic generation ( shg ) from sic nanopillars due to the resonant excitation of localized surface phonon - polaritons within the reststrahlen band . the magnitude of the shg peak at the monopole mode experiences a strong dependence on the…	supplementary information: + numerical simulations	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan
with significant research efforts being directed to the development of neurocomputers based on the functionalities of the brain , a seismic shift is expected in the domain of computing based on the traditional von - neumann model . the @xmath0 @xcite , @xmath1 @xcite and the ibm @xmath2 @xcite are i…	synaptic memory is considered to be the main element responsible for learning and cognition in humans . although traditionally non - volatile long - term plasticity changes have been implemented in nanoelectronic synapses for neuromorphic applications , recent studies in neuroscience have revealed…	introduction formalism results and discussions conclusions acknowledgements	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan


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