Hi Petr, thank you for your reply regarding the scaling of loess curves. Our situation is the following : we do have 2 experiments, and for each experiment, the set of data is in the following format : "nodeA (chr, start, end) - node B (chr, start, end) - interaction intensity (between A and B)". We are trying to SCALE the LOESS curves ( for the graphs "distance between node A and node B" vs "intensity") for experiment1 vs experiment2, in order to make the experiments directly comparable. I have attached 2 figures with the LOESS curves for experiment1 and experiment2 to my email. Shall you have any suggestions, please let me know. Thanks a lot, -- bogdan On Mon, Sep 7, 2015 at 7:34 AM, PIKAL Petr <petr.pikal at precheza.cz> wrote:> Hi > > what about xlim or ylim? > > Cheers > Petr > > > > -----Original Message----- > > From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Bogdan > > Tanasa > > Sent: Monday, September 07, 2015 8:00 AM > > To: r-help > > Subject: [R] scaling loess curves > > > > Dear all, > > > > please could you advise about a method to scale 2 plots of LOESS > > curves. > > More specifically, we do have 2 sets of 5C data, and the loess plots > > reflect the relationship between INTENSITY and DISTANCE (please see the > > R code below). > > > > I am looking for a method/formula to scale these 2 LOESS plots and make > > them directly comparable. > > > > many thanks, > > > > -- bogdan > > > > > > > > -------------- the R code ------------------ > > > > > > > > a <- read.delim("a",header=T) > > qplot(data=a,distance,intensity)+geom_smooth(method = "loess", size > > 1, > > span=0.01)+xlab("distance")+ylab("intensity") > > > > > > > > b <- read.delim("b",header=T) > > qplot(data=b,distance,intensity)+geom_smooth(method = "loess", size > > 1, > > span=0.01)+xlab("distance")+ylab("intensity") > > > > [[alternative HTML version deleted]] > > > > ______________________________________________ > > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide http://www.R-project.org/posting- > > guide.html > > and provide commented, minimal, self-contained, reproducible code. > > ________________________________ > Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a jsou > ur?eny pouze jeho adres?t?m. > Jestli?e jste obdr?el(a) tento e-mail omylem, informujte laskav? > neprodlen? jeho odes?latele. Obsah tohoto emailu i s p??lohami a jeho kopie > vyma?te ze sv?ho syst?mu. > Nejste-li zam??len?m adres?tem tohoto emailu, nejste opr?vn?ni tento email > jakkoliv u??vat, roz?i?ovat, kop?rovat ?i zve?ej?ovat. > Odes?latel e-mailu neodpov?d? za eventu?ln? ?kodu zp?sobenou modifikacemi > ?i zpo?d?n?m p?enosu e-mailu. > > V p??pad?, ?e je tento e-mail sou??st? obchodn?ho jedn?n?: > - vyhrazuje si odes?latel pr?vo ukon?it kdykoliv jedn?n? o uzav?en? > smlouvy, a to z jak?hokoliv d?vodu i bez uveden? d?vodu. > - a obsahuje-li nab?dku, je adres?t opr?vn?n nab?dku bezodkladn? p?ijmout; > Odes?latel tohoto e-mailu (nab?dky) vylu?uje p?ijet? nab?dky ze strany > p??jemce s dodatkem ?i odchylkou. > - trv? odes?latel na tom, ?e p??slu?n? smlouva je uzav?ena teprve > v?slovn?m dosa?en?m shody na v?ech jej?ch n?le?itostech. > - odes?latel tohoto emailu informuje, ?e nen? opr?vn?n uzav?rat za > spole?nost ??dn? smlouvy s v?jimkou p??pad?, kdy k tomu byl p?semn? zmocn?n > nebo p?semn? pov??en a takov? pov??en? nebo pln? moc byly adres?tovi tohoto > emailu p??padn? osob?, kterou adres?t zastupuje, p?edlo?eny nebo jejich > existence je adres?tovi ?i osob? j?m zastoupen? zn?m?. > > This e-mail and any documents attached to it may be confidential and are > intended only for its intended recipients. > If you received this e-mail by mistake, please immediately inform its > sender. Delete the contents of this e-mail with all attachments and its > copies from your system. > If you are not the intended recipient of this e-mail, you are not > authorized to use, disseminate, copy or disclose this e-mail in any manner. > The sender of this e-mail shall not be liable for any possible damage > caused by modifications of the e-mail or by delay with transfer of the > email. > > In case that this e-mail forms part of business dealings: > - the sender reserves the right to end negotiations about entering into a > contract in any time, for any reason, and without stating any reasoning. > - if the e-mail contains an offer, the recipient is entitled to > immediately accept such offer; The sender of this e-mail (offer) excludes > any acceptance of the offer on the part of the recipient containing any > amendment or variation. > - the sender insists on that the respective contract is concluded only > upon an express mutual agreement on all its aspects. > - the sender of this e-mail informs that he/she is not authorized to enter > into any contracts on behalf of the company except for cases in which > he/she is expressly authorized to do so in writing, and such authorization > or power of attorney is submitted to the recipient or the person > represented by the recipient, or the existence of such authorization is > known to the recipient of the person represented by the recipient. >-------------- next part -------------- A non-text attachment was scrubbed... Name: example1-1.png Type: image/png Size: 16282 bytes Desc: not available URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20150911/3fa5e4ef/attachment.png> -------------- next part -------------- A non-text attachment was scrubbed... Name: example2-2.png Type: image/png Size: 15036 bytes Desc: not available URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20150911/3fa5e4ef/attachment-0001.png>
Hi based on your data maybe using logarithmic y scale shall give you desired result. http://stackoverflow.com/questions/4699493/transform-only-one-axis-to-log10-scale-with-ggplot2 Or you can recalculate intensity to scale 100-0 (or any other suitable scale). ?rescale Cheers Petr From: Bogdan Tanasa [mailto:tanasa at gmail.com] Sent: Friday, September 11, 2015 8:14 AM To: PIKAL Petr; r-help Subject: Re: [R] scaling loess curves Hi Petr, thank you for your reply regarding the scaling of loess curves. Our situation is the following : we do have 2 experiments, and for each experiment, the set of data is in the following format : "nodeA (chr, start, end) - node B (chr, start, end) - interaction intensity (between A and B)". We are trying to SCALE the LOESS curves ( for the graphs "distance between node A and node B" vs "intensity") for experiment1 vs experiment2, in order to make the experiments directly comparable. I have attached 2 figures with the LOESS curves for experiment1 and experiment2 to my email. Shall you have any suggestions, please let me know. Thanks a lot, -- bogdan On Mon, Sep 7, 2015 at 7:34 AM, PIKAL Petr <petr.pikal at precheza.cz<mailto:petr.pikal at precheza.cz>> wrote: Hi what about xlim or ylim? Cheers Petr> -----Original Message----- > From: R-help [mailto:r-help-bounces at r-project.org<mailto:r-help-bounces at r-project.org>] On Behalf Of Bogdan > Tanasa > Sent: Monday, September 07, 2015 8:00 AM > To: r-help > Subject: [R] scaling loess curves > > Dear all, > > please could you advise about a method to scale 2 plots of LOESS > curves. > More specifically, we do have 2 sets of 5C data, and the loess plots > reflect the relationship between INTENSITY and DISTANCE (please see the > R code below). > > I am looking for a method/formula to scale these 2 LOESS plots and make > them directly comparable. > > many thanks, > > -- bogdan > > > > -------------- the R code ------------------ > > > > a <- read.delim("a",header=T) > qplot(data=a,distance,intensity)+geom_smooth(method = "loess", size > 1, > span=0.01)+xlab("distance")+ylab("intensity") > > > > b <- read.delim("b",header=T) > qplot(data=b,distance,intensity)+geom_smooth(method = "loess", size > 1, > span=0.01)+xlab("distance")+ylab("intensity") > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org<mailto:R-help at r-project.org> mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting- > guide.html > and provide commented, minimal, self-contained, reproducible code.________________________________ Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a jsou ur?eny pouze jeho adres?t?m. Jestli?e jste obdr?el(a) tento e-mail omylem, informujte laskav? neprodlen? jeho odes?latele. Obsah tohoto emailu i s p??lohami a jeho kopie vyma?te ze sv?ho syst?mu. Nejste-li zam??len?m adres?tem tohoto emailu, nejste opr?vn?ni tento email jakkoliv u??vat, roz?i?ovat, kop?rovat ?i zve?ej?ovat. Odes?latel e-mailu neodpov?d? za eventu?ln? ?kodu zp?sobenou modifikacemi ?i zpo?d?n?m p?enosu e-mailu. V p??pad?, ?e je tento e-mail sou??st? obchodn?ho jedn?n?: - vyhrazuje si odes?latel pr?vo ukon?it kdykoliv jedn?n? o uzav?en? smlouvy, a to z jak?hokoliv d?vodu i bez uveden? d?vodu. - a obsahuje-li nab?dku, je adres?t opr?vn?n nab?dku bezodkladn? p?ijmout; Odes?latel tohoto e-mailu (nab?dky) vylu?uje p?ijet? nab?dky ze strany p??jemce s dodatkem ?i odchylkou. - trv? odes?latel na tom, ?e p??slu?n? smlouva je uzav?ena teprve v?slovn?m dosa?en?m shody na v?ech jej?ch n?le?itostech. - odes?latel tohoto emailu informuje, ?e nen? opr?vn?n uzav?rat za spole?nost ??dn? smlouvy s v?jimkou p??pad?, kdy k tomu byl p?semn? zmocn?n nebo p?semn? pov??en a takov? pov??en? nebo pln? moc byly adres?tovi tohoto emailu p??padn? osob?, kterou adres?t zastupuje, p?edlo?eny nebo jejich existence je adres?tovi ?i osob? j?m zastoupen? zn?m?. This e-mail and any documents attached to it may be confidential and are intended only for its intended recipients. If you received this e-mail by mistake, please immediately inform its sender. Delete the contents of this e-mail with all attachments and its copies from your system. If you are not the intended recipient of this e-mail, you are not authorized to use, disseminate, copy or disclose this e-mail in any manner. The sender of this e-mail shall not be liable for any possible damage caused by modifications of the e-mail or by delay with transfer of the email. In case that this e-mail forms part of business dealings: - the sender reserves the right to end negotiations about entering into a contract in any time, for any reason, and without stating any reasoning. - if the e-mail contains an offer, the recipient is entitled to immediately accept such offer; The sender of this e-mail (offer) excludes any acceptance of the offer on the part of the recipient containing any amendment or variation. - the sender insists on that the respective contract is concluded only upon an express mutual agreement on all its aspects. - the sender of this e-mail informs that he/she is not authorized to enter into any contracts on behalf of the company except for cases in which he/she is expressly authorized to do so in writing, and such authorization or power of attorney is submitted to the recipient or the person represented by the recipient, or the existence of such authorization is known to the recipient of the person represented by the recipient. ________________________________ Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a jsou ur?eny pouze jeho adres?t?m. Jestli?e jste obdr?el(a) tento e-mail omylem, informujte laskav? neprodlen? jeho odes?latele. Obsah tohoto emailu i s p??lohami a jeho kopie vyma?te ze sv?ho syst?mu. Nejste-li zam??len?m adres?tem tohoto emailu, nejste opr?vn?ni tento email jakkoliv u??vat, roz?i?ovat, kop?rovat ?i zve?ej?ovat. Odes?latel e-mailu neodpov?d? za eventu?ln? ?kodu zp?sobenou modifikacemi ?i zpo?d?n?m p?enosu e-mailu. V p??pad?, ?e je tento e-mail sou??st? obchodn?ho jedn?n?: - vyhrazuje si odes?latel pr?vo ukon?it kdykoliv jedn?n? o uzav?en? smlouvy, a to z jak?hokoliv d?vodu i bez uveden? d?vodu. - a obsahuje-li nab?dku, je adres?t opr?vn?n nab?dku bezodkladn? p?ijmout; Odes?latel tohoto e-mailu (nab?dky) vylu?uje p?ijet? nab?dky ze strany p??jemce s dodatkem ?i odchylkou. - trv? odes?latel na tom, ?e p??slu?n? smlouva je uzav?ena teprve v?slovn?m dosa?en?m shody na v?ech jej?ch n?le?itostech. - odes?latel tohoto emailu informuje, ?e nen? opr?vn?n uzav?rat za spole?nost ??dn? smlouvy s v?jimkou p??pad?, kdy k tomu byl p?semn? zmocn?n nebo p?semn? pov??en a takov? pov??en? nebo pln? moc byly adres?tovi tohoto emailu p??padn? osob?, kterou adres?t zastupuje, p?edlo?eny nebo jejich existence je adres?tovi ?i osob? j?m zastoupen? zn?m?. This e-mail and any documents attached to it may be confidential and are intended only for its intended recipients. If you received this e-mail by mistake, please immediately inform its sender. Delete the contents of this e-mail with all attachments and its copies from your system. If you are not the intended recipient of this e-mail, you are not authorized to use, disseminate, copy or disclose this e-mail in any manner. The sender of this e-mail shall not be liable for any possible damage caused by modifications of the e-mail or by delay with transfer of the email. In case that this e-mail forms part of business dealings: - the sender reserves the right to end negotiations about entering into a contract in any time, for any reason, and without stating any reasoning. - if the e-mail contains an offer, the recipient is entitled to immediately accept such offer; The sender of this e-mail (offer) excludes any acceptance of the offer on the part of the recipient containing any amendment or variation. - the sender insists on that the respective contract is concluded only upon an express mutual agreement on all its aspects. - the sender of this e-mail informs that he/she is not authorized to enter into any contracts on behalf of the company except for cases in which he/she is expressly authorized to do so in writing, and such authorization or power of attorney is submitted to the recipient or the person represented by the recipient, or the existence of such authorization is known to the recipient of the person represented by the recipient. [[alternative HTML version deleted]]
Dear Petr,
thank you very much, it helped. On a side note, shall I have 2 plots and 2
loess curves (as below), is there any way in ggplot2 to overlay these 2
graphs for "a" and "b" ? much thanks again !
qplot(data=a,distance,intensity)+geom_smooth(method = "loess", size =
1,
span=0.01)+xlab("distance")+ylab("intensity")
qplot(data=b,distance,intensity)+geom_smooth(method = "loess", size =
1,
span=0.01)+xlab("distance")+ylab("intensity")
-- bogdan
On Fri, Sep 11, 2015 at 3:06 AM, PIKAL Petr <petr.pikal at precheza.cz>
wrote:
> Hi
>
>
>
> based on your data maybe using logarithmic y scale shall give you desired
> result.
>
>
>
>
>
http://stackoverflow.com/questions/4699493/transform-only-one-axis-to-log10-scale-with-ggplot2
>
>
>
> Or you can recalculate intensity to scale 100-0 (or any other suitable
> scale).
>
>
>
> ?rescale
>
>
>
> Cheers
>
> Petr
>
>
>
> *From:* Bogdan Tanasa [mailto:tanasa at gmail.com]
> *Sent:* Friday, September 11, 2015 8:14 AM
> *To:* PIKAL Petr; r-help
> *Subject:* Re: [R] scaling loess curves
>
>
>
> Hi Petr,
>
> thank you for your reply regarding the scaling of loess curves. Our
> situation is the following :
>
> we do have 2 experiments, and for each experiment, the set of data is in
> the following format : "nodeA (chr, start, end) - node B (chr, start,
end)
> - interaction intensity (between A and B)".
>
> We are trying to SCALE the LOESS curves ( for the graphs "distance
between
> node A and node B" vs "intensity") for experiment1 vs
experiment2, in order
> to make the experiments directly comparable.
>
> I have attached 2 figures with the LOESS curves for experiment1 and
> experiment2 to my email. Shall you have any suggestions, please let me
> know. Thanks a lot,
>
>
>
> -- bogdan
>
>
>
> On Mon, Sep 7, 2015 at 7:34 AM, PIKAL Petr <petr.pikal at
precheza.cz> wrote:
>
> Hi
>
> what about xlim or ylim?
>
> Cheers
> Petr
>
>
>
> > -----Original Message-----
> > From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of
Bogdan
> > Tanasa
> > Sent: Monday, September 07, 2015 8:00 AM
> > To: r-help
> > Subject: [R] scaling loess curves
> >
> > Dear all,
> >
> > please could you advise about a method to scale 2 plots of LOESS
> > curves.
> > More specifically, we do have 2 sets of 5C data, and the loess plots
> > reflect the relationship between INTENSITY and DISTANCE (please see
the
> > R code below).
> >
> > I am looking for a method/formula to scale these 2 LOESS plots and
make
> > them directly comparable.
> >
> > many thanks,
> >
> > -- bogdan
> >
> >
> >
> > -------------- the R code ------------------
> >
> >
> >
> > a <- read.delim("a",header=T)
> > qplot(data=a,distance,intensity)+geom_smooth(method =
"loess", size > > 1,
> > span=0.01)+xlab("distance")+ylab("intensity")
> >
> >
> >
> > b <- read.delim("b",header=T)
> > qplot(data=b,distance,intensity)+geom_smooth(method =
"loess", size > > 1,
> > span=0.01)+xlab("distance")+ylab("intensity")
> >
>
> > [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide http://www.R-project.org/posting-
> > guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
> ________________________________
> Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a jsou
> ur?eny pouze jeho adres?t?m.
> Jestli?e jste obdr?el(a) tento e-mail omylem, informujte laskav?
> neprodlen? jeho odes?latele. Obsah tohoto emailu i s p??lohami a jeho kopie
> vyma?te ze sv?ho syst?mu.
> Nejste-li zam??len?m adres?tem tohoto emailu, nejste opr?vn?ni tento email
> jakkoliv u??vat, roz?i?ovat, kop?rovat ?i zve?ej?ovat.
> Odes?latel e-mailu neodpov?d? za eventu?ln? ?kodu zp?sobenou modifikacemi
> ?i zpo?d?n?m p?enosu e-mailu.
>
> V p??pad?, ?e je tento e-mail sou??st? obchodn?ho jedn?n?:
> - vyhrazuje si odes?latel pr?vo ukon?it kdykoliv jedn?n? o uzav?en?
> smlouvy, a to z jak?hokoliv d?vodu i bez uveden? d?vodu.
> - a obsahuje-li nab?dku, je adres?t opr?vn?n nab?dku bezodkladn? p?ijmout;
> Odes?latel tohoto e-mailu (nab?dky) vylu?uje p?ijet? nab?dky ze strany
> p??jemce s dodatkem ?i odchylkou.
> - trv? odes?latel na tom, ?e p??slu?n? smlouva je uzav?ena teprve
> v?slovn?m dosa?en?m shody na v?ech jej?ch n?le?itostech.
> - odes?latel tohoto emailu informuje, ?e nen? opr?vn?n uzav?rat za
> spole?nost ??dn? smlouvy s v?jimkou p??pad?, kdy k tomu byl p?semn? zmocn?n
> nebo p?semn? pov??en a takov? pov??en? nebo pln? moc byly adres?tovi tohoto
> emailu p??padn? osob?, kterou adres?t zastupuje, p?edlo?eny nebo jejich
> existence je adres?tovi ?i osob? j?m zastoupen? zn?m?.
>
> This e-mail and any documents attached to it may be confidential and are
> intended only for its intended recipients.
> If you received this e-mail by mistake, please immediately inform its
> sender. Delete the contents of this e-mail with all attachments and its
> copies from your system.
> If you are not the intended recipient of this e-mail, you are not
> authorized to use, disseminate, copy or disclose this e-mail in any manner.
> The sender of this e-mail shall not be liable for any possible damage
> caused by modifications of the e-mail or by delay with transfer of the
> email.
>
> In case that this e-mail forms part of business dealings:
> - the sender reserves the right to end negotiations about entering into a
> contract in any time, for any reason, and without stating any reasoning.
> - if the e-mail contains an offer, the recipient is entitled to
> immediately accept such offer; The sender of this e-mail (offer) excludes
> any acceptance of the offer on the part of the recipient containing any
> amendment or variation.
> - the sender insists on that the respective contract is concluded only
> upon an express mutual agreement on all its aspects.
> - the sender of this e-mail informs that he/she is not authorized to enter
> into any contracts on behalf of the company except for cases in which
> he/she is expressly authorized to do so in writing, and such authorization
> or power of attorney is submitted to the recipient or the person
> represented by the recipient, or the existence of such authorization is
> known to the recipient of the person represented by the recipient.
>
>
>
> ------------------------------
> Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a jsou
> ur?eny pouze jeho adres?t?m.
> Jestli?e jste obdr?el(a) tento e-mail omylem, informujte laskav?
> neprodlen? jeho odes?latele. Obsah tohoto emailu i s p??lohami a jeho kopie
> vyma?te ze sv?ho syst?mu.
> Nejste-li zam??len?m adres?tem tohoto emailu, nejste opr?vn?ni tento email
> jakkoliv u??vat, roz?i?ovat, kop?rovat ?i zve?ej?ovat.
> Odes?latel e-mailu neodpov?d? za eventu?ln? ?kodu zp?sobenou modifikacemi
> ?i zpo?d?n?m p?enosu e-mailu.
>
> V p??pad?, ?e je tento e-mail sou??st? obchodn?ho jedn?n?:
> - vyhrazuje si odes?latel pr?vo ukon?it kdykoliv jedn?n? o uzav?en?
> smlouvy, a to z jak?hokoliv d?vodu i bez uveden? d?vodu.
> - a obsahuje-li nab?dku, je adres?t opr?vn?n nab?dku bezodkladn? p?ijmout;
> Odes?latel tohoto e-mailu (nab?dky) vylu?uje p?ijet? nab?dky ze strany
> p??jemce s dodatkem ?i odchylkou.
> - trv? odes?latel na tom, ?e p??slu?n? smlouva je uzav?ena teprve
> v?slovn?m dosa?en?m shody na v?ech jej?ch n?le?itostech.
> - odes?latel tohoto emailu informuje, ?e nen? opr?vn?n uzav?rat za
> spole?nost ??dn? smlouvy s v?jimkou p??pad?, kdy k tomu byl p?semn? zmocn?n
> nebo p?semn? pov??en a takov? pov??en? nebo pln? moc byly adres?tovi tohoto
> emailu p??padn? osob?, kterou adres?t zastupuje, p?edlo?eny nebo jejich
> existence je adres?tovi ?i osob? j?m zastoupen? zn?m?.
>
> This e-mail and any documents attached to it may be confidential and are
> intended only for its intended recipients.
> If you received this e-mail by mistake, please immediately inform its
> sender. Delete the contents of this e-mail with all attachments and its
> copies from your system.
> If you are not the intended recipient of this e-mail, you are not
> authorized to use, disseminate, copy or disclose this e-mail in any manner.
> The sender of this e-mail shall not be liable for any possible damage
> caused by modifications of the e-mail or by delay with transfer of the
> email.
>
> In case that this e-mail forms part of business dealings:
> - the sender reserves the right to end negotiations about entering into a
> contract in any time, for any reason, and without stating any reasoning.
> - if the e-mail contains an offer, the recipient is entitled to
> immediately accept such offer; The sender of this e-mail (offer) excludes
> any acceptance of the offer on the part of the recipient containing any
> amendment or variation.
> - the sender insists on that the respective contract is concluded only
> upon an express mutual agreement on all its aspects.
> - the sender of this e-mail informs that he/she is not authorized to enter
> into any contracts on behalf of the company except for cases in which
> he/she is expressly authorized to do so in writing, and such authorization
> or power of attorney is submitted to the recipient or the person
> represented by the recipient, or the existence of such authorization is
> known to the recipient of the person represented by the recipient.
>
[[alternative HTML version deleted]]