{"id":105,"date":"2012-06-11T10:39:48","date_gmt":"2012-06-11T15:39:48","guid":{"rendered":"https:\/\/blogs.mathworks.com\/cleve\/?p=105"},"modified":"2013-05-02T10:06:14","modified_gmt":"2013-05-02T15:06:14","slug":"biorhythms-2","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/cleve\/2012\/06\/11\/biorhythms-2\/","title":{"rendered":"Biorhythms"},"content":{"rendered":"<!DOCTYPE html\r\n  PUBLIC \"-\/\/W3C\/\/DTD HTML 4.01 Transitional\/\/EN\">\r\n<style type=\"text\/css\">\r\n\r\nh1 { font-size:18pt; }\r\nh2.titlebg { font-size:13pt; }\r\nh3 { color:#4A4F55; padding:0px; margin:5px 0px 5px; font-family:Arial, Helvetica, sans-serif; font-size:11pt; font-weight:bold; line-height:140%; border-bottom:1px solid #d6d4d4; display:block; }\r\nh4 { color:#4A4F55; padding:0px; margin:0px 0px 5px; font-family:Arial, Helvetica, sans-serif; font-size:10pt; font-weight:bold; line-height:140%; border-bottom:1px solid #d6d4d4; display:block; }\r\n   \r\np { padding:0px; margin:0px 0px 20px; }\r\nimg { padding:0px; margin:0px 0px 20px; border:none; }\r\np img, pre img, tt img, li img { margin-bottom:0px; } \r\n\r\nul { padding:0px; margin:0px 0px 20px 23px; list-style:square; }\r\nul li { padding:0px; margin:0px 0px 7px 0px; background:none; }\r\nul li ul { padding:5px 0px 0px; margin:0px 0px 7px 23px; }\r\nul li ol li { list-style:decimal; }\r\nol { padding:0px; margin:0px 0px 20px 0px; list-style:decimal; }\r\nol li { padding:0px; margin:0px 0px 7px 23px; list-style-type:decimal; }\r\nol li ol { padding:5px 0px 0px; margin:0px 0px 7px 0px; }\r\nol li ol li { list-style-type:lower-alpha; }\r\nol li ul { padding-top:7px; }\r\nol li ul li { list-style:square; }\r\n\r\npre, tt, code { font-size:12px; }\r\npre { margin:0px 0px 20px; }\r\npre.error { color:red; }\r\npre.codeinput { padding:10px; border:1px solid #d3d3d3; background:#f7f7f7; }\r\npre.codeoutput { padding:10px 11px; margin:0px 0px 20px; color:#4c4c4c; }\r\n\r\n@media print { pre.codeinput, pre.codeoutput { word-wrap:break-word; width:100%; } }\r\n\r\nspan.keyword { color:#0000FF }\r\nspan.comment { color:#228B22 }\r\nspan.string { color:#A020F0 }\r\nspan.untermstring { color:#B20000 }\r\nspan.syscmd { color:#B28C00 }\r\n\r\n.footer { width:auto; padding:10px 0px; margin:25px 0px 0px; border-top:1px dotted #878787; font-size:0.8em; line-height:140%; font-style:italic; color:#878787; text-align:left; float:none; }\r\n.footer p { margin:0px; }\r\n\r\n  <\/style><div class=\"content\"><!--introduction--><p>Biorhythms were invented over 100 years ago and entered our popular culture in the 1960s. You can still find many Web sites today that offer to prepare personalized biorhythms, or that sell software to compute them. Biorhythms are based on the notion that three sinusoidal cycles influence our lives.  The physical cycle has a period of 23 days, the emotional cycle has a period of 28 days, and the intellectual cycle has a period of 33 days.  For any individual, the cycles are initialized at birth. All the people on earth born on one particular day share the biorhythm determined by that date.<\/p><!--\/introduction--><h3>Contents<\/h3><div><ul><li><a href=\"#177bbacf-8d35-4a04-b838-73a47c6f2386\">Personal biorhythm<\/a><\/li><li><a href=\"#49456cfe-4d3d-44fa-b61b-cf63015bba5e\">Vectorized plots<\/a><\/li><li><a href=\"#07f90852-cdea-4fc6-9cb6-2e49128e7ef7\">Date functions<\/a><\/li><li><a href=\"#f3f28c39-3235-45e7-a2d8-bed708a742bf\">Newborn<\/a><\/li><li><a href=\"#64f7d052-82e9-4101-a78d-5c42cef5f30f\">Twenty-first Birthday<\/a><\/li><li><a href=\"#823e5529-d53a-45e0-a942-96044e682169\">Rebirth<\/a><\/li><li><a href=\"#10eda8dd-3a73-4506-a50c-e1ed88a71e0d\">Nearly Perfect Day<\/a><\/li><li><a href=\"#3174f7a4-24fb-446c-9460-623dc725095d\">Detail<\/a><\/li><\/ul><\/div><h4>Personal biorhythm<a name=\"177bbacf-8d35-4a04-b838-73a47c6f2386\"><\/a><\/h4><p>I hope you can download the latest version of my <tt>biorhythm<\/tt> program from MATLAB Central at this <a href=\"https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/4405-biorhythm\">link<\/a>. If you already happen to have access to the programs from my <a href=\"https:\/\/www.mathworks.com\/moler\/exm\/index.html\">book<\/a> \"Experiments with MATLAB\", you will find an earlier version of <tt>biorhythm<\/tt> there.  Either of these programs will allow you to compute your own personal biorhythm.<\/p><h4>Vectorized plots<a name=\"49456cfe-4d3d-44fa-b61b-cf63015bba5e\"><\/a><\/h4><p>Biorhythms are an excellent way to illustrate MATLAB's vector plotting capabilities.  Let's start with a column vector of time measured in days.<\/p><pre class=\"codeinput\">t = (0:28)';\r\n<\/pre><p>The first way you might think of to compute the biorhythm for these days is create this array with three columns.<\/p><pre class=\"codeinput\">y = [sin(2*pi*t\/23) sin(2*pi*t\/28) sin(2*pi*t\/33)];\r\n<\/pre><p>Or, we can get fancy by moving the square brackets inside the <tt>sin(...)<\/tt> evaluation and, while we're at it, define an anonymous function. This vectorized calculation is the core of our <tt>biorhythm<\/tt> function.<\/p><pre class=\"codeinput\">bio = @(t) sin(2*pi*[t\/23 t\/28 t\/33]);\r\ny = bio(t);\r\n<\/pre><p>We're now ready for our first plot. Because <tt>t<\/tt> goes from 0 to 28, the 23-day blue curve covers more than its period, the 28-day green curve covers exactly one period, and the 33-day red curve covers less its period.<\/p><pre class=\"codeinput\">clf\r\nplot(t,y)\r\naxis <span class=\"string\">tight<\/span>\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/biorhythms_01.png\" alt=\"\"> <h4>Date functions<a name=\"07f90852-cdea-4fc6-9cb6-2e49128e7ef7\"><\/a><\/h4><p>MATLAB has several functions for computations involving calendars and dates. They are all based on a <i>date number<\/i>, which is the amount of time, in units of <i>days<\/i>, since an arbitrary origin in year zero.  The current <tt>datenum<\/tt> is provided by the function <tt>now<\/tt>.  I am writing this post on June 10, 2012, and every time I <tt>publish<\/tt> it, the value of <tt>now<\/tt> changes.  Here is the current value.<\/p><pre class=\"codeinput\">format <span class=\"string\">compact<\/span>\r\nformat <span class=\"string\">bank<\/span>\r\ndate = now\r\n<\/pre><pre class=\"codeoutput\">date =\r\n     735030.87\r\n<\/pre><p>A readable form of the current date is provided by <tt>datestr<\/tt>.<\/p><pre class=\"codeinput\">datestr(now)\r\n<\/pre><pre class=\"codeoutput\">ans =\r\n10-Jun-2012 20:45:47\r\n<\/pre><p>The integer part of <tt>now<\/tt> is a date number for the entire day. This value is used in <tt>biorhythm<\/tt>.<\/p><pre class=\"codeinput\">format <span class=\"string\">short<\/span>\r\ntoday = fix(now)\r\n<\/pre><pre class=\"codeoutput\">today =\r\n      735030\r\n<\/pre><h4>Newborn<a name=\"f3f28c39-3235-45e7-a2d8-bed708a742bf\"><\/a><\/h4><p>With no input arguments, my latest version of <tt>biorhythm<\/tt> plots the biorhythm for a baby born four weeks before <tt>today<\/tt>.  The plot covers the eight week period from the baby's birth until a date four weeks in the future. You can see the three curves all initialized at birth. The blue physical cycle has a 23-day period, so it passes through zero five days before <tt>today<\/tt>.  The green emotional cycle has a 28-day period, so it hits zero today.  And, the red intellectual cycle will be zero five days from today.<\/p><pre class=\"codeinput\">biorhythm\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/biorhythms_02.png\" alt=\"\"> <h4>Twenty-first Birthday<a name=\"64f7d052-82e9-4101-a78d-5c42cef5f30f\"><\/a><\/h4><p>Let's look at the biorhythm for someone whose 21st birthday is today. The <i>date vector<\/i> for such a birthday is obtained by subtracting 21 from the first component of today's <tt>datevec<\/tt>. This is a pretty unexciting, but typical, biorhythm. All three cycles are near their midpoints.  Blue and red peaked about a week ago and green will peak a little more than a week from now.<\/p><pre class=\"codeinput\">birthday = datevec(today) - [21 0 0 0 0 0];\r\nbiorhythm(birthday)\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/biorhythms_03.png\" alt=\"\"> <h4>Rebirth<a name=\"823e5529-d53a-45e0-a942-96044e682169\"><\/a><\/h4><p>Does your biorhythm ever start over?  Yes, it does, at a time <i>t<\/i> when <i>t<\/i>\/23, <i>t<\/i>\/28 and <i>t<\/i>\/33 are all integers.  Since the three periods are <i>relatively prime<\/i>, the first such value of <i>t<\/i> is their product.<\/p><pre class=\"codeinput\">tzero = 23*28*33\r\n<\/pre><pre class=\"codeoutput\">tzero =\r\n       21252\r\n<\/pre><p>How many years and days is this?<\/p><pre class=\"codeinput\">dpy = 365+97\/400         <span class=\"comment\">% 365 days\/year + 97\/400 for leap years.<\/span>\r\nyzero = fix(tzero\/dpy)\r\ndzero = dpy*mod(tzero\/dpy,1)\r\n<\/pre><pre class=\"codeoutput\">dpy =\r\n  365.2425\r\nyzero =\r\n    58\r\ndzero =\r\n   67.9350\r\n<\/pre><p>So, your biorhythm starts over when you are 58 years old, about 68 days after your birthday.<\/p><pre class=\"codeinput\">biorhythm(today-tzero)\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/biorhythms_04.png\" alt=\"\"> <h4>Nearly Perfect Day<a name=\"10eda8dd-3a73-4506-a50c-e1ed88a71e0d\"><\/a><\/h4><p>Is there ever a <i>perfect<\/i> day, one where all three cycles reach their maximum at the same time?  Well, not quite.  That would require a time <i>t<\/i> when, for <i>p<\/i> = 23, 28, 33, <i>t\/p<\/i> = <i>n<\/i>+1\/4, where <i>n<\/i> is an integer. Then <tt>sin(2*pi*t\/p)<\/tt> would equal <tt>sin(pi\/2)<\/tt>, which is the maximum. But, since the values of <i>p<\/i> are relatively prime, there is no such value of <i>t<\/i>.  But we can get close.  To find the nearly perfect day, look for the maximum value of the sum of the three cycles.<\/p><pre class=\"codeinput\">t = (1:tzero)';\r\ny = bio(t);\r\ns = sum(y,2);\r\ntop = find(s==max(s))\r\nbiorhythm(today-top)\r\n<\/pre><pre class=\"codeoutput\">top =\r\n       17003\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/biorhythms_05.png\" alt=\"\"> <p>How old are you on this nearly perfect day?<\/p><pre class=\"codeinput\">top\/dpy\r\n<\/pre><pre class=\"codeoutput\">ans =\r\n   46.5526\r\n<\/pre><p>So, half-way through your 46th year.<\/p><h4>Detail<a name=\"3174f7a4-24fb-446c-9460-623dc725095d\"><\/a><\/h4><p>But the nearly perfect day is not perfection.  The three cyles are not quite at their peaks.<\/p><pre class=\"codeinput\">bio(top)\r\n<\/pre><pre class=\"codeoutput\">ans =\r\n    0.9977    1.0000    0.9989\r\n<\/pre><p>Let's zoom in to a two day window around <tt>top<\/tt>, the location of the maximum sum.  Measure time in hours.<\/p><pre class=\"codeinput\">clf\r\nt = (-1:1\/24:1)';\r\ny = 100*bio(top+t);\r\nplot(24*t,y)\r\nset(gca,<span class=\"string\">'xaxislocation'<\/span>,<span class=\"string\">'top'<\/span>,<span class=\"string\">'xlim'<\/span>,[-24 24],<span class=\"string\">'xtick'<\/span>,-24:6:24,<span class=\"keyword\">...<\/span>\r\n   <span class=\"string\">'ylim'<\/span>,[96.0 100.4])\r\ntitle([<span class=\"string\">'biorhythms near day '<\/span> int2str(top) <span class=\"string\">', time in hours'<\/span>])\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/biorhythms_06.png\" alt=\"\"> <p>We can see that the three peaks occur six hours apart. This is the closest we get to perfection, and the only time in the entire 58-year cycle when we get even this close.<\/p><p>Have a good day.<\/p><script language=\"JavaScript\"> <!-- \r\n    function grabCode_360c4c470d8e44f7964197fa88acb484() {\r\n        \/\/ Remember the title so we can use it in the new page\r\n        title = document.title;\r\n\r\n        \/\/ Break up these strings so that their presence\r\n        \/\/ in the Javascript doesn't mess up the search for\r\n        \/\/ the MATLAB code.\r\n        t1='360c4c470d8e44f7964197fa88acb484 ' + '##### ' + 'SOURCE BEGIN' + ' #####';\r\n        t2='##### ' + 'SOURCE END' + ' #####' + ' 360c4c470d8e44f7964197fa88acb484';\r\n    \r\n        b=document.getElementsByTagName('body')[0];\r\n        i1=b.innerHTML.indexOf(t1)+t1.length;\r\n        i2=b.innerHTML.indexOf(t2);\r\n \r\n        code_string = b.innerHTML.substring(i1, i2);\r\n        code_string = code_string.replace(\/REPLACE_WITH_DASH_DASH\/g,'--');\r\n\r\n        \/\/ Use \/x3C\/g instead of the less-than character to avoid errors \r\n        \/\/ in the XML parser.\r\n        \/\/ Use '\\x26#60;' instead of '<' so that the XML parser\r\n        \/\/ doesn't go ahead and substitute the less-than character. \r\n        code_string = code_string.replace(\/\\x3C\/g, '\\x26#60;');\r\n\r\n        copyright = 'Copyright 2012 The MathWorks, Inc.';\r\n\r\n        w = window.open();\r\n        d = w.document;\r\n        d.write('<pre>\\n');\r\n        d.write(code_string);\r\n\r\n        \/\/ Add copyright line at the bottom if specified.\r\n        if (copyright.length > 0) {\r\n            d.writeln('');\r\n            d.writeln('%%');\r\n            if (copyright.length > 0) {\r\n                d.writeln('% _' + copyright + '_');\r\n            }\r\n        }\r\n\r\n        d.write('<\/pre>\\n');\r\n\r\n        d.title = title + ' (MATLAB code)';\r\n        d.close();\r\n    }   \r\n     --> <\/script><p style=\"text-align: right; font-size: xx-small; font-weight:lighter;   font-style: italic; color: gray\"><br><a href=\"javascript:grabCode_360c4c470d8e44f7964197fa88acb484()\"><span style=\"font-size: x-small;        font-style: italic;\">Get \r\n      the MATLAB code <noscript>(requires JavaScript)<\/noscript><\/span><\/a><br><br>\r\n      Published with MATLAB&reg; 7.14<br><\/p><p class=\"footer\"><br>\r\n      Published with MATLAB&reg; 7.14<br><\/p><\/div><!--\r\n360c4c470d8e44f7964197fa88acb484 ##### SOURCE BEGIN #####\r\n%% Biorhythms\r\n% Biorhythms were invented over 100 years ago and entered our popular\r\n% culture in the 1960s.\r\n% You can still find many Web sites today that offer to prepare personalized\r\n% biorhythms, or that sell software to compute them.\r\n% Biorhythms are based on the notion that three sinusoidal cycles influence\r\n% our lives.  The physical cycle has a period of 23 days, the emotional\r\n% cycle has a period of 28 days, and the intellectual cycle has a period\r\n% of 33 days.  For any individual, the cycles are initialized at birth.\r\n% All the people on earth born on one particular day share the biorhythm \r\n% determined by that date.\r\n\r\n%% Personal biorhythm\r\n% I hope you can download the latest version of my |biorhythm| program\r\n% from MATLAB Central at this\r\n% <https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/4405-biorhythm link>.\r\n% If you already happen to have access to the programs from my\r\n% <https:\/\/www.mathworks.com\/moler\/exm\/index.html book>\r\n% \"Experiments with MATLAB\", you will find an earlier version of |biorhythm|\r\n% there.  Either of these programs will allow you to compute your own\r\n% personal biorhythm.\r\n\r\n%% Vectorized plots\r\n% Biorhythms are an excellent way to illustrate MATLAB's vector plotting\r\n% capabilities.  Let's start with a column vector of time measured in days.\r\n\r\nt = (0:28)';\r\n\r\n%%\r\n% The first way you might think of to compute the biorhythm\r\n% for these days is create this array with three columns.\r\n\r\ny = [sin(2*pi*t\/23) sin(2*pi*t\/28) sin(2*pi*t\/33)]; \r\n\r\n%%\r\n% Or, we can get fancy by moving the square brackets inside the\r\n% |sin(...)| evaluation and, while we're at it, define an anonymous function.\r\n% This vectorized calculation is the core of our |biorhythm| function.\r\n\r\nbio = @(t) sin(2*pi*[t\/23 t\/28 t\/33]);\r\ny = bio(t);\r\n\r\n%%\r\n% We're now ready for our first plot.\r\n% Because |t| goes from 0 to 28, the 23-day blue curve covers\r\n% more than its period, the 28-day green curve covers exactly\r\n% one period, and the 33-day red curve covers less its period.\r\n\r\nclf\r\nplot(t,y)\r\naxis tight\r\n\r\n%% Date functions\r\n% MATLAB has several functions for computations involving calendars and dates.\r\n% They are all based on a _date number_, which is the amount of time,\r\n% in units of _days_, since an arbitrary origin in year zero.  The\r\n% current |datenum| is provided by the function |now|.  I am writing\r\n% this post on June 10, 2012, and every time I |publish| it, the value\r\n% of |now| changes.  Here is the current value.\r\n\r\nformat compact\r\nformat bank\r\ndate = now\r\n\r\n%%\r\n% A readable form of the current date is provided by |datestr|.\r\n\r\ndatestr(now) \r\n\r\n%%\r\n% The integer part of |now| is a date number for the entire day.\r\n% This value is used in |biorhythm|.\r\n\r\nformat short\r\ntoday = fix(now)\r\n\r\n%% Newborn\r\n% With no input arguments, my latest version of |biorhythm| plots\r\n% the biorhythm for a baby born four weeks before |today|.  The\r\n% plot covers the eight week period from the baby's birth until\r\n% a date four weeks in the future.\r\n% You can see the three curves all initialized at birth.\r\n% The blue physical cycle has a 23-day period, so it passes through zero\r\n% five days before |today|.  The green emotional cycle has a 28-day period,\r\n% so it hits zero today.  And, the red intellectual cycle will be zero\r\n% five days from today.\r\n\r\nbiorhythm\r\n\r\n%% Twenty-first Birthday\r\n% Let's look at the biorhythm for someone whose 21st birthday is today.\r\n% The _date vector_ for such a birthday is obtained by subtracting 21\r\n% from the first component of today's |datevec|.\r\n% This is a pretty unexciting, but typical, biorhythm.\r\n% All three cycles are near their midpoints.  Blue and red peaked\r\n% about a week ago and green will peak a little more than a week from now.\r\n\r\nbirthday = datevec(today) - [21 0 0 0 0 0];\r\nbiorhythm(birthday)\r\n\r\n%% Rebirth\r\n% Does your biorhythm ever start over?  Yes, it does, at a time _t_ when\r\n% _t_\/23, _t_\/28 and _t_\/33 are all integers.  Since the three periods\r\n% are _relatively prime_, the first such value of _t_ is their product.\r\n\r\ntzero = 23*28*33\r\n\r\n%%\r\n% How many years and days is this?\r\n\r\ndpy = 365+97\/400         % 365 days\/year + 97\/400 for leap years.\r\nyzero = fix(tzero\/dpy)\r\ndzero = dpy*mod(tzero\/dpy,1)\r\n\r\n%%\r\n% So, your biorhythm starts over when you are 58 years old, about 68\r\n% days after your birthday.\r\n\r\nbiorhythm(today-tzero)\r\n\r\n%% Nearly Perfect Day\r\n% Is there ever a _perfect_ day, one where all three cycles reach their\r\n% maximum at the same time?  Well, not quite.  That would require a time\r\n% _t_ when, for _p_ = 23, 28, 33, _t\/p_ = _n_+1\/4, where _n_ is an integer.\r\n% Then |sin(2*pi*t\/p)| would equal |sin(pi\/2)|, which is the maximum.\r\n% But, since the values of _p_ are relatively prime, there is no such\r\n% value of _t_.  But we can get close.  To find the nearly perfect day,\r\n% look for the maximum value of the sum of the three cycles.\r\n\r\nt = (1:tzero)';\r\ny = bio(t);\r\ns = sum(y,2);\r\ntop = find(s==max(s))\r\nbiorhythm(today-top)\r\n\r\n%%\r\n% How old are you on this nearly perfect day?\r\n\r\ntop\/dpy\r\n\r\n%%\r\n% So, half-way through your 46th year.\r\n\r\n%% Detail\r\n% But the nearly perfect day is not perfection.  The three cyles\r\n% are not quite at their peaks.\r\n\r\nbio(top)\r\n\r\n%%\r\n% Let's zoom in to a two day window around |top|, the location of the\r\n% maximum sum.  Measure time in hours.\r\n\r\nclf\r\nt = (-1:1\/24:1)';\r\ny = 100*bio(top+t);\r\nplot(24*t,y)\r\nset(gca,'xaxislocation','top','xlim',[-24 24],'xtick',-24:6:24,...\r\n   'ylim',[96.0 100.4])\r\ntitle(['biorhythms near day ' int2str(top) ', time in hours'])\r\n\r\n%%\r\n% We can see that the three peaks occur six hours apart.\r\n% This is the closest we get to perfection, and the only time\r\n% in the entire 58-year cycle when we get even this close.\r\n\r\n%%\r\n% Have a good day.\r\n\r\n##### SOURCE END ##### 360c4c470d8e44f7964197fa88acb484\r\n-->","protected":false},"excerpt":{"rendered":"<!--introduction--><p>Biorhythms were invented over 100 years ago and entered our popular culture in the 1960s. You can still find many Web sites today that offer to prepare personalized biorhythms, or that sell software to compute them. Biorhythms are based on the notion that three sinusoidal cycles influence our lives.  The physical cycle has a period of 23 days, the emotional cycle has a period of 28 days, and the intellectual cycle has a period of 33 days.  For any individual, the cycles are initialized at birth. All the people on earth born on one particular day share the biorhythm determined by that date.... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/cleve\/2012\/06\/11\/biorhythms-2\/\">read more >><\/a><\/p>","protected":false},"author":78,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[5],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/105"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/users\/78"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/comments?post=105"}],"version-history":[{"count":24,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/105\/revisions"}],"predecessor-version":[{"id":128,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/105\/revisions\/128"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media?parent=105"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/categories?post=105"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/tags?post=105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}