Andy's Brain Blog Advice Column: Should You Go to Graduate School?

Around this time of year legions of students will submit their graduate school applications; and, if I close my eyes, I can almost hear the click of the mouse buttons, the plastic staccato of keyboards filling in address information and reflective essays, the soft, almost inaudible squelching of eyeball saccades in their sockets as they gather information about potential laboratories to toil in and advisors to meet. So vivid is the imagination of these sounds, so powerful are the memories of my experience, that part of me can't help but feel a rill of nostalgia flutter down my spine, and possibly, somewhere, deep down, even a twinge of envy. I remember, as a young man, the heady experience of the application process: The shivers of expectation; the slow-burning, months-long buildup of excitement; the thrill of embarking upon an adventure of continuing to do work that you loved, but with new people to meet, new places to discover, and new worlds to conquer. For those about to undertake this journey, I say - Good fortune to you.

However, even in these times of expectation and excitement, I cannot refrain from advising caution; for I once knew a man in a similar situation, who, at the height of his powers, tried his hand at graduate studies; but, rather than augmenting his already considerable gifts, led to the most horrific of decays. So great a man was he, that to think of him is to think of an empire falling. This may smack of hyperbole; but the great promise of his early years, followed by the precipitous decline upon his entry to graduate school, do suggest the tragic dimensions of which I speak.

In his youth he was a hot-blooded hedonist, snatching at all pleasures as he could, carelessly, almost impulsively, like a shipwrecked sailor grasping at driftwood. During these years his life was one of wild debauch, filled with wagers and duels, wine-soaked bacchanalias and abducted women. Endowed with Herculean stamina and the unchained libido of a thousand-and-three Don Juans, every muscle, every sinew, every fiber of his being, was directed at vaulting his pleasure to its highest pinnacle and beyond. A dark aura of raw sexuality exuded from his being; the wellsprings were perennial which fueled his twisted desires. He wouldn't have known an excess if he saw one - his lusts were of such depravity they would have eclipsed even de Sade's darkest fantasies.

The nonstop orgies of his early years eventually petered out, however, and one morning he awoke to find himself in extreme want. Abandoned by his mistress, his fortune squandered, he eventually decided that applying to graduate school would be the best option; after all, styling himself a freethinker and an intellectual, the pursuits of business and politics seemed inadequate, even vulgar. A life of the mind, he concluded, was the only one for him, and thus did he eschew the red and the black in favor of the white labcoat of the researcher.

Among any other trade this man would have been happy, motivated and fulfilled, perfectly at home among the elegant rakes of any other era; but ambition denied withered him; his incessant studies dried up the springs of his energy; and melancholy marked him for her own. Instead of a life of health, vigor, and adventure, now he whittled away his days in a dreary, windowless room performing the most perfunctory and mind-numbing of tasks. Instead of using his masculine touch to awaken hundreds of young maidens into womanhood, now he could only practice a crippled eros that repeatedly failed to take wing. Poverty, alcoholism, and overwork became the staples of his life; his last years were clouded by religious mania; and, misunderstood and forgotten, he spent his final days in utter squalor, dying much as he foresaw - like a poisoned rat in a hole.

Limerick Intermezzo

There was a young man from Stamboul,

Who soliloquized thus to his tool:

"You took all my wealth

And you ruined my health,

And now you won't pee, you old fool."

My friend's story, though extreme, represents the experience of no small number of graduate students. It is not uncommon for the typical graduate to spend the prime of life in an environment he detests, doing work he abominates, with the energy that should go into the flower instead remaining in the leaves and stem. Frustration, disappointment, and monotony become his bywords. The great expectations he begins with, the intoxicating freedom of his new schedule, are all too quickly transformed into feelings of ennui and despair; the hot blood that once coursed through his veins gradually congeals into cold slime. He criticizes his program, his field, his advisors, all the while oblivious to the fact that he is a willing coauthor of his own misery. He manages to project a certain nonchalance, he gets along agreeably enough with his friends, but his most private moments - if not spent in a haze of wine or the arms of some debauched wench - are torture.

And yet - I have known a few individuals who persevere even under the most sordid of circumstances, who, even in the face of the most formidable of challenges, manage to live bravely, even joyfully. They are impervious to the most depressing of environments and the most hateful of colleagues. For these resilient few, their passion lifts them above the waves that would drown the merely indifferent; the iron in their souls allows them to withstand blows that would crush the weaker-willed. (I do not count myself among their number, but then again, I have never had the desire; I have been more than able to make up for any defects of personality or intelligence though flattery, intimidation, bribery, and blackmail.)

Let he who is considering graduate school, therefore, take stock of his weaknesses, and of his strengths; let him calculate the risks; let him understand that persisting in anything that leaves him feeling enervated and worthless is not the sign of some tragic hero, but the mark of a fool - it is the first step on the path to spiritual suicide.

If, by chance, he does have many years of happiness, let him rejoice in them all; yet let him remember the days of darkness, for they shall be many.

Mathematically Describing Neuronal Connections in the Brain

Students in my classes have started to catch on to the fact that I tend to dress up for lectures I am particularly excited about. For a topic I'm indifferent toward or lukewarm about, I wear my standard dress shirt, slacks, and dress shoes. To prepare for a subject I like a little bit more, that's when I throw on a sports jacket, and possibly a nice belt. But get me all hot and bothered, and that's when I break out...the ties.

Not surprisingly, then, I wear a three-piece suit when talking about neurons. These sexy little suckers act as the basic cells of communication throughout your brain and throughout your nervous system, relaying electrical transmissions all the way down your axons to the synaptic gap, those terminal buttons precariously poised on the precipice of a protoplasmic kiss, until finally, excruciatingly, those tiny vesicles of chemical bliss burst from their vile durance, recrudescent, crushing out the last throb of the last ecstasy man or monster has ever known.

...Let me catch my breath...Where was I? Oh yes - neurons. Besides their role in transmitting electrical and chemical signals throughout the brain, they also exist in astonishingly high numbers, with somewhere on the order of tens of billions of neurons packed into a single brain. On top of this, each one can share hundreds or thousands of connections with other neurons, leading to a staggering number of potential synaptic connections. The mind boggles.

To provide the full mathematical treatment of understanding neurons, we are joined again by Keith "The Rookie" Bartley, whose interest in synaptic connections was recently piqued by an introductory cognitive science course. Along the way Keith touches on mathematics, the Turing Test, Friends, oatmeal, the uncanny valley, and where genitals are represented in the brain, providing a theoretical basis for why foot massages can lead to greater chances for successful coitus.

==============

As a TA for an Introduction to Cognitive Science course, one of our instructors briefly discussed the concept of Block's "Aunt Bertha Machine" and how the Turing test alone required more bits of memory than there are atoms in the universe. (If you aren't familiar with Ned Block's work click here).  Below is a section of one of his slides:

Volume: (15*10^9 light-years)^3 = (15*10^9*10^16 meters)^3
Density: 1 bit per (10^-35 meters)^3
Total storage capacity: 10^184 bits < 10^200 bits < 2^670 bits
Critical Turing Test length: 670 bits < 670 characters < 140 words < 1 minute
 
Difficult as it is for some people to conceptualize and subsequently deal with such induced feelings of simultaneous intelligence, stupidity, and insignificance pervading recapitulations of their own life's meaning, I would like to warn those people that the following information about the capacity of the human brain is likely to do much worse. READ RESPONSIBLY.

For the human brain, the possible number of combinations and permutations of neural connections has been purported to vastly exceed the number of elementary particles in the Universe. Consider for a moment that the brain has 85,000,000,000 neurons, we'll round that up to the previously estimated 100,000,000,000 for hypothetical simplicity, each with a capacity for up to 10,000 synaptic "connections". 

1! = 1
10! = 3,628,800
100! = 9.33 x 10^157
1000! = 4.02 x 10^2,567
***This is where Google's calculator starts to report infinity***

For bigger factorials, we'll have to use Stirling's approximation.

Stirling MATLAB Code

So using Stirling's approximation....

10,000,000,000! ~ 2.33 x 10^95,657,055,186
100,000,000,000! ~ 3.75 x 10^1,056,570,551,815

But wait, each of the 100 billion neurons can have 10,000 synaptic connections, so…

10^11 * 10,000 = 1e26

So rather...

100,000,000,000,000,000,000,000,000! ~ REALLY BIG NUMBER

But Keith! Come on, this looks like a gross misrepresentation of the limits of human cognition?


Our theories about the brain are much more modular in scope, but at the same time, distributed enough to adapt. These two points function as a much better descriptor of the networked brain. It's reasonable to see, in our post-Scopes trial times, that humans' brains developed around how they are utilized in their day-to-day lives, and perhaps more importantly, the phenomenal ability to constantly adapt, even in the wake of extreme trauma. The development and existence of a single "grandmother neuron", is misrepresentative of our degree of sustainability in the brain. Neurons for your grandmother have to be very distributed, so that when some of your brains cells die off, as they often do, it's important you don't forget the old woman that squeezes your cheeks when she sees you, lest you punch her in the face for assault. Jennifer Aniston would no longer instill memories of how much time you wasted watching reruns of Friends on TBS every afternoon for 4 years, and Halle Berry would no longer remind you of how Hollywood reduced one of the greatest antiheroines in the history of DC Comics to a mannequin in spandex with a speech impediment. 

At the same time, however, that three pounds of oatmeal between your ears still retains a relative degree of modularity in regional function, which is a reason why your brain is compartmentalized in various folds (gyri) and crevices (sulci). When you have an itch from what is in fact a really small bug bite, your desired area to itch is very distributed across skin because the signals in the brain are themselves both distributed and modular. A diagram often used to demonstrate this modularity is the cortical homunculus.

Straight out of the backwoods of the uncanny valley, this diagram demonstrates the relative intensity and location that each section along your somatosensory cortex corresponds with on your body. As for the proximity of feet relative to your genitals, well that might just explain a lot about some guys now wouldn't it.

Introduction to Computational Modeling: Hodgkin-Huxley Model

Computational modeling can be a tough nut to crack. I'm not just talking pistachio-shell dense; I'm talking walnut-shell dense. I'm talking a nut so tough that not even a nutcracker who's cracked nearly every damn nut on the planet could crack this mother, even if this nutcracker is so badass that he wears a leather jacket, and that leather jacket owns a leather jacket, and that leather jacket smokes meth.

That being said, the best approach to eat this whale is with small bites. That way, you can digest the blubber over a period of several weeks before you reach the waxy, delicious ambergris and eventually the meaty whale guts of computational modeling and feel your consciousness expand a thousandfold. And the best way to begin is with a single neuron.


The Hodgkin-Huxley Model, and the Hunt for the Giant Squid

Way back in the 1950s - all the way back in the twentieth century - a team of notorious outlaws named Hodgkin and Huxley became obsessed and tormented by fevered dreams and hallucinations of the Giant Squid Neuron. (The neurons of a giant squid are, compared to every other creature on the planet, giant. That is why it is called the giant squid. Pay attention.)

After a series of appeals to Holy Roman Emperor Charles V and Pope Stephen II, Hodgkin and Huxley finally secured a commission to hunt the elusive giant squid and sailed to the middle of the Pacific Ocean in a skiff made out of the bones and fingernails and flayed skins of their enemies. Finally spotting the vast abhorrence of the giant squid, Hodgkin and Huxley gave chase over the fiercest seas and most violent winds of the Pacific, and after a tense, exhausting three-day hunt, finally cornered the giant squid in the darkest netherregions of the Marianas Trench. The giant squid sued for mercy, citing precedents and torts of bygone eras, quoting Blackstone and Coke, Anaxamander and Thales. But Huxley, his eyes shining with the cold light of purest hate, smashed his fist through the forehead of the dread beast which erupted in a bloody Vesuvius of brains and bits of bone both sphenoidal and ethmoidal intermixed and Hodgkin screamed and vomited simultaneously. And there stood Huxley triumphant, withdrawing his hand oversized with coagulate gore and clutching the prized Giant Squid Neuron. Hodgkin looked at him.

"Huxley, m'boy, that was cold-blooded!" he ejaculated.
"Yea, oy'm one mean cat, ain't I, guv?" said Huxley.
"'Dis here Pope Stephen II wanted this bloke alive, you twit!"
"Oy, not m'fault, guv," said Huxley, his grim smile twisting into a wicked sneer. "Things got outta hand."


Scene II

Drunk with victory, Hodgkin and Huxley took the Giant Squid Neuron back to their magical laboratory in the Ice Cream Forest and started sticking a bunch of wires and electrodes in it. To their surprise, there was a difference in voltage between the inside of the neuron and the bath surrounding it, suggesting that there were different quantities of electrical charge on both sides of the cell membrane. In fact, at a resting state the neuron appeared to stabilize around -70mV, suggesting that there was more of a negative electrical charge inside the membrane than outside.

Keep in mind that when our friends Hodgkin and Huxley began their quest, nobody knew exactly how the membrane of a neuron worked. Scientists had observed action potentials and understood that electrical forces were involved somehow, but until the experiments of the 1940s and '50s the exact mechanisms were still unknown. However, through a series of carefully controlled studies, the experimenters were able to measure how both current and voltage interacted in their model neuron. It turned out that three ions - sodium (Na+), potassium (K+), and chlorine (Cl-) - appeared to play the most important role in depolarizing the cell membrane and generating an action potential. Different concentrations of the ions, along with the negative charge inside the membrane, led to different pressures exerted on each of the ions.

For example, K+ was found to be much more concentrated inside of the neuron than outside, leading to a concentration gradient exerting pressure for the K+ ions to exit the cell; at the same time, however, the attractive negative force inside the membrane exerting a countering electrostatic pressure, as positively charged potassium ions would be drawn toward the inside of the cell. Similar characteristics of the sodium and chlorine ions were observed as well, as shown in the following figure:

Ned the Neuron, filled with Neuron Goo. Note that the gradient and electrostatic pressures, expressed in microvolts (mV) have arbitrary signs; the point is to show that for an ion like chlorine, the pressures cancel out, while for an ion like potassium, there is slightly more pressure to exit the cell than enter it. Also, if you noticed that these values aren't 100% accurate, then congratu-frickin-lations, you're smarter than I am, but there is no way in HECK that I am redoing this in Microsoft Paint.

In addition to these passive forces, Hodgkin and Huxley also observed an active, energy-consuming force in maintaining the resting potential - a mechanism which exchanged potassium for sodium ions, by kicking out roughly three sodium ions for each potassium ion. Even with this pump though, there is still a whopping 120mV of pressure for sodium ions to enter. What prevents them from rushing in there and trashing the place?

Hodgkin and Huxley hypothesized that certain channels in the neuron membrane were selectively permeable, meaning that only specific ions could pass through them. Furthermore, channels could be either open or closed; for example, there may be sodium channels dotting the membrane, but at a resting potential they are usually closed. In addition, Hodgkin and Huxley thought that within these channels were gates that regulated whether the channel was open or closed, and that these gates could be in either permissive or non-permissive states. The probability of a gate being in either state was dependent on the voltage difference between the inside and the outside of the membrane.

Although this all may seem conceptually straightforward, keep in mind that Hodgkin and Huxley were among the first to combine all of these properties into one unified model - something which could account for the conductances, voltage, and current, as well as how all of this affected the gates within each ion channel - and they were basically doing it from scratch. Also keep in mind that these crazy mofos didn't have stuff like Matlab or R to help them out; they did this the old-fashioned way, by changing one thing at a time and measuring that shit by hand. Insane. (Also think about how, in the good old days, people like Carthaginians and Romans and Greeks would march across entire continents for months, years sometimes, just to slaughter each other. Continents! These days, my idea of a taxing cardiovascular workout is operating a stapler.) To show how they did this for quantifying the relationship between voltage and conductance in potassium, for example, they simply applied a bunch of different currents, saw how it changed over time, and attempted to fit a mathematical function to it, which happens to fit quite nicely when you include n-gates and a fourth-power polynomial.

After a series of painstaking experiments and measurements, Hodgkin and Huxley calculated values for the conductances and equilibrium voltages for different ions. Quite a feat, when you couple that with the fact that they hunted down and killed their very own Giant Squid and then ripped a neuron out of its brain. Incredible. That is the very definition of alpha male behavior, and it's something I want all of my readers to emulate.

Table 3 from Hodgkin & Huxley (1952) showing empirical values for voltages and conductances, as well as the capacitance of the membrane.

The same procedure was used for the n, m, and h gates, which were also found to be functions of the membrane voltage. Once these were calculated, then the conductances and voltage potential could be found for any resting potential and any amount of injected current.

H & H's formulas for the n, m, and h gates as a function of voltage.

So where does that leave us? Since Hodgkin and Huxley have already done most of the heavy lifting for us, all we need to do is take their constants and equations they've already derived, and put it into a script that we can then run through Matlab. At some point, just to get some additional exercise, we may also operate a stapler.

But stay focused here. Most of the formulas and constants can simply be transcribed from their papers into a Matlab script, but we also need to think about the final output that we want, and how we are going to plot it. Note that the original Hodgkin and Huxley paper uses a differential formula for voltage to tie together the capacitance and conductance of the membrance, e.g.:

We can use a method like Euler first-order approximation to plot the voltages, in which each time step is based off of the previous one which is added to a function multiplied by a time step; in the sample code below, the time step can be extremely small, thus giving a better approximation to the true shape of the voltage timecourse. (See the "calculate the derivatives" section below.)

The following code runs a simulation of the Hodgkin Huxley model over 100 milliseconds with 50mA of current, although you are encouraged to try your own and see what happens. The sample plots below show the results of a typical simulation; namely, that the voltage depolarizes after receiving a large enough current and briefly becomes positive before returning to its previous resting potential. The conductances of sodium and potassium show that the sodium channels are quickly opened and quickly closed, while the potassium channels take relatively longer to open and longer to close.The point of the script is to show how equations from papers can be transcribed into code and then run to simulate what neural activity should look like under certain conditions. This can then be expanded into more complex areas such as memory, cognition, and learning.

The actual neuron, of course, is nowhere to be seen; and thank God for that, else we would run out of Giant Squids before you could say Jack Robinson.


Resources
Book of GENESIS, Chapter 4
Original Hodgkin & Huxley paper


%===simulation time===
simulationTime = 100; %in milliseconds
deltaT=.01;
t=0:deltaT:simulationTime;


%===specify the external current I===
changeTimes = [0]; %in milliseconds
currentLevels = [50]; %Change this to see effect of different currents on voltage (Suggested values: 3, 20, 50, 1000)

%Set externally applied current across time
%Here, first 500 timesteps are at current of 50, next 1500 timesteps at
%current of zero (resets resting potential of neuron), and the rest of
%timesteps are at constant current
I(1:500) = currentLevels; I(501:2000) = 0; I(2001:numel(t)) = currentLevels;
%Comment out the above line and uncomment the line below for constant current, and observe effects on voltage timecourse
%I(1:numel(t)) = currentLevels;


%===constant parameters===%
%All of these can be found in Table 3
gbar_K=36; gbar_Na=120; g_L=.3;
E_K = -12; E_Na=115; E_L=10.6;
C=1;


%===set the initial states===%
V=0; %Baseline voltage
alpha_n = .01 * ( (10-V) / (exp((10-V)/10)-1) ); %Equation 12
beta_n = .125*exp(-V/80); %Equation 13
alpha_m = .1*( (25-V) / (exp((25-V)/10)-1) ); %Equation 20
beta_m = 4*exp(-V/18); %Equation 21
alpha_h = .07*exp(-V/20); %Equation 23
beta_h = 1/(exp((30-V)/10)+1); %Equation 24

n(1) = alpha_n/(alpha_n+beta_n); %Equation 9
m(1) = alpha_m/(alpha_m+beta_m); %Equation 18
h(1) = alpha_h/(alpha_h+beta_h); %Equation 18


for i=1:numel(t)-1 %Compute coefficients, currents, and derivates at each time step
   
    %---calculate the coefficients---%
    %Equations here are same as above, just calculating at each time step
    alpha_n(i) = .01 * ( (10-V(i)) / (exp((10-V(i))/10)-1) );
    beta_n(i) = .125*exp(-V(i)/80);
    alpha_m(i) = .1*( (25-V(i)) / (exp((25-V(i))/10)-1) );
    beta_m(i) = 4*exp(-V(i)/18);
    alpha_h(i) = .07*exp(-V(i)/20);
    beta_h(i) = 1/(exp((30-V(i))/10)+1);
   
   
    %---calculate the currents---%
    I_Na = (m(i)^3) * gbar_Na * h(i) * (V(i)-E_Na); %Equations 3 and 14
    I_K = (n(i)^4) * gbar_K * (V(i)-E_K); %Equations 4 and 6
    I_L = g_L *(V(i)-E_L); %Equation 5
    I_ion = I(i) - I_K - I_Na - I_L;
   
   
    %---calculate the derivatives using Euler first order approximation---%
    V(i+1) = V(i) + deltaT*I_ion/C;
    n(i+1) = n(i) + deltaT*(alpha_n(i) *(1-n(i)) - beta_n(i) * n(i)); %Equation 7
    m(i+1) = m(i) + deltaT*(alpha_m(i) *(1-m(i)) - beta_m(i) * m(i)); %Equation 15
    h(i+1) = h(i) + deltaT*(alpha_h(i) *(1-h(i)) - beta_h(i) * h(i)); %Equation 16

end


V = V-70; %Set resting potential to -70mv

%===plot Voltage===%
plot(t,V,'LineWidth',3)
hold on
legend({'voltage'})
ylabel('Voltage (mv)')
xlabel('time (ms)')
title('Voltage over Time in Simulated Neuron')


%===plot Conductance===%
figure
p1 = plot(t,gbar_K*n.^4,'LineWidth',2);
hold on
p2 = plot(t,gbar_Na*(m.^3).*h,'r','LineWidth',2);
legend([p1, p2], 'Conductance for Potassium', 'Conductance for Sodium')
ylabel('Conductance')
xlabel('time (ms)')
title('Conductance for Potassium and Sodium Ions in Simulated Neuron')

What's in an SPM.mat File?

A while back I attempted to write up a document that summarized everything someone would need to know about using SPM. It was called, I believe, the SPM User's Ultimate Guide: For Alpha Males, By Alpha Males. The title was perhaps a little ambitious, since I stopped updating it after only a few dozen pages. In particular I remember a section where I attempted to tease apart everything contained within the SPM.mat files output after first- and second-level analyses. To me this was the most important section, since complex model setups could be executed fairly easily by someone with a good understanding of Matlab code, but I never completed it.

Fortunately, however, there is someone out there who already vivisected the SPM.mat file and publicly displayed its gruesome remains in the online piazza. Researcher Nikki Sullivan has written an excellent short summary of what each field means, broken down into neat, easily digestible categories. You can find it on her website here, and I have also copied and pasted the information below. It makes an excellent shorthand reference, especially if you've forgotten, for example, where contrast weights are stored in the structure, and don't want to go through the tedium of typing SPM, then SPM.xY, then SPM.xY.VY, and so on.

But if you've forgotten how to rock that body? Girl, ain't no remedy for that.

========================

details on experiment:

 

SPM.xY.RT - TR length (RT ="repeat time")
SPM.xY.P - matrix of file names
SPM.xY.VY - # of runs x 1 struct array of mapped image volumes (.img file info)
SPM.modality - the data you're using (PET, FMRI, EEG)
SPM.stats.[modality].UFp - critical F-threshold for selecting voxels over which the non-sphericity is estimated (if required) [default: 0.001]
SPM. stats.maxres - maximum number of residual images for smoothness estimation
SPM. stats.maxmem - maximum amount of data processed at a time (in bytes)
SPM.SPMid - version of SPM used
SPM.swd - directory for SPM.mat and img files. default is pwd

basis function:

 

SPM.xBF.name - name of basis function
SPM.xBF.length - length in seconds of basis
SPM.xBF.order - order of basis set
SPM.xBF.T - number of subdivisions of TR
SPM.xBF.T0 - first time bin (see slice timing)
SPM.xBF.UNITS - options: 'scans'|'secs' for onsets
SPM.xBF.Volterra - order of convolution
SPM.xBF.dt - length of time bin in seconds
SPM.xBF.bf - basis set matrix

Session Stucture:

 

user-specified covariates/regressors (e.g. motion)
SPM.Sess([sesssion]).C.C - [nxc double] regressor (c#covariates,n#sessions)
SPM.Sess([sesssion]).C.name - names of covariates
conditions & modulators specified - i.e. input structure array
SPM.Sess([sesssion]).U(condition).dt: - time bin length {seconds}
SPM.Sess([sesssion]).U(condition).name - names of conditions
SPM.Sess([sesssion]).U(condition).ons - onset for condition's trials
SPM.Sess([sesssion]).U(condition).dur - duration for condition's trials
SPM.Sess([sesssion]).U(condition).u - (t x j) inputs or stimulus function matrix
SPM.Sess([sesssion]).U(condition).pst - (1 x k) peri-stimulus times (seconds)
parameters/modulators specified
SPM.Sess([sesssion]).U(condition).P - parameter structure/matrix
SPM.Sess([sesssion]).U(condition).P.name - names of modulators/parameters
SPM.Sess([sesssion]).U(condition).P.h - polynomial order of modulating parameter (order of polynomial expansion where 0none)
SPM.Sess([sesssion]).U(condition).P.P - vector of modulating values
SPM.Sess([sesssion]).U(condition).P.P.i - sub-indices of U(i).u for plotting
scan indices for sessions
SPM.Sess([sesssion]).row
effect indices for sessions
SPM.Sess([sesssion]).col
F Contrast information for input-specific effects
SPM.Sess([sesssion]).Fc
SPM.Sess([sesssion]).Fc.i - F Contrast columns for input-specific effects
SPM.Sess([sesssion]).Fc.name - F Contrast names for input-specific effects
SPM.nscan([session]) - number of scans per session (or if e.g. a t-test, total number of con*.img files)

global variate/normalization details

 

SPM.xGX.iGXcalc - either "none" or "scaling." for fMRI usually is "none" (no global normalization). if global normalization is "Scaling", see spm_fmri_spm_ui for parameters that will then appear under SPM.xGX.

design matrix information:

 

SPM.xX.X - Design matrix (raw, not temporally smoothed)
SPM.xX.name - cellstr of parameter names corresponding to columns of design matrix
SPM.xX.I - nScan x 4 matrix of factor level indicators. first column is the replication number. other columns are the levels of each experimental factor. SPM.xX.iH - vector of H partition (indicator variables) indices
SPM.xX.iC - vector of C partition (covariates) indices
SPM.xX.iB - vector of B partition (block effects) indices
SPM.xX.iG - vector of G partition (nuisance variables) indices
SPM.xX.K - cell. low frequency confound: high-pass cutoff (secs)
SPM.xX.K.HParam - low frequency cutoff value
SPM.xX.K.X0 - cosines (high-pass filter)
SPM.xX.W - Optional whitening/weighting matrix used to give weighted least squares estimates (WLS).

• if not specified spm_spm will set this to whiten the data and render the OLS estimates maximum likelihood i.e. W*W' inv(xVi.V).

SPM.xX.xKXs - space structure for K*W*X, the 'filtered and whitened' design matrix
SPM.xX.xKXs.X - Mtx - matrix of trials and betas (columns) in each trial
SPM.xX.xKXs.tol - tolerance
SPM.xX.xKXs.ds - vectors of singular values
SPM.xX.xKXs.u - u as in X u*diag(ds)*v'
SPM.xX.xKXs.v - v as in X u*diag(ds)*v'
SPM.xX.xKXs.rk - rank
SPM.xX.xKXs.oP - orthogonal projector on X
SPM.xX.xKXs.oPp - orthogonal projector on X'
SPM.xX.xKXs.ups - space in which this one is embedded
SPM.xX.xKXs.sus - subspace
SPM.xX.pKX - pseudoinverse of K*W*X, computed by spm_sp
SPM.xX.Bcov - xX.pKX*xX.V*xX.pKX - variance-covariance matrix of parameter estimates (when multiplied by the voxel-specific hyperparameter ResMS of the parameter estimates (ResSS/xX.trRV ResMS) )
SPM.xX.trRV - trace of R*V
SPM.xX.trRVRV - trace of RVRV
SPM.xX.erdf - effective residual degrees of freedom (trRV^2/trRVRV)
SPM.xX.nKX - design matrix (xX.xKXs.X) scaled for display (see spm_DesMtx('sca',... for details) SPM.xX.sF - cellstr of factor names (columns in SPM.xX.I, i think) SPM.xX.D - struct, design definition SPM.xX.xVi - correlation constraints (see non-sphericity below) SPM.xC - struct. array of covariate info

header info

 

SPM.P - a matrix of filenames
SPM.V - a vector of structures containing image volume information.
SPM.V.fname - the filename of the image.
SPM.V.dim - the x, y and z dimensions of the volume
SPM.V.dt - A 1x2 array. First element is datatype (see spm_type). The second is 1 or 0 depending on the endian-ness.
SPM.V.mat- a 4x4 affine transformation matrix mapping from voxel coordinates to real world coordinates.
SPM.V.pinfo - plane info for each plane of the volume.
SPM.V.pinfo(1,:) - scale for each plane
SPM.V.pinfo(2,:) - offset for each plane The true voxel intensities of the jth image are given by: val*V.pinfo(1,j) + V.pinfo(2,j)
SPM.V.pinfo(3,:) - offset into image (in bytes).If the size of pinfo is 3x1, then the volume is assumed to be contiguous and each plane has the same scalefactor and offset.

structure describing intrinsic temporal non-sphericity

 

SPM.xVi.I - typically the same as SPM.xX.I SPM.xVi.h - hyperparameters
SPM.xVi.V xVi.h(1)*xVi.Vi{1} + ...
SPM.xVi.Cy - spatially whitened (used by ReML to estimate h)
SPM.xVi.CY - <(Y - )*(Y - )'>(used by spm_spm_Bayes)
SPM.xVi.Vi - array of non-sphericity components

• defaults to {speye(size(xX.X,1))} - i.ii.d.
• specifying a cell array of contraints ((Qi)
• These contraints invoke spm_reml to estimate hyperparameters assuming V is constant over voxels that provide a high precise estimate of xX.V

SPM.xVi.form - form of non-sphericity (either 'none' or 'AR(1)')
SPM.xX.V - Optional non-sphericity matrix. CCov(e)sigma^2*V.

• If not specified spm_spm will compute this using a 1st pass to identify signifcant voxels over which to estimate V. A 2nd pass is then used to re-estimate the parameters with WLS and save the ML estimates (unless xX.W is already specified)

 

filtering information

 

SPM.K - filter matrix or filtered structure:

• SPM.K(s) - struct array containing partition-specific specifications
• SPM.K(s).RT - observation interval in seconds
• SPM.K(s).row - row of Y constituting block/partitions
• SPM.K(s).HParam - cut-off period in seconds
• SPM.K(s).X0 - low frequencies to be removed (DCT)
• SPM.Y - filtered data matrix

 

masking information

 

SPM.xM - Structure containing masking information, or a simple column vector of thresholds corresponding to the images in VY.
SPM.xM.T - [n x 1 double] - Masking index
SPM.xM.TH - nVar x nScan matrix of analysis thresholds, one per image
SPM.xM.I - Implicit masking (0 --> none; 1 --> implicit zero/NaN mask)
SPM.xM.VM - struct array of mapped explicit mask image volumes
SPM.xM.xs - [1x1 struct] cellstr description

design information (self-explanatory names, for once) 

 

SPM.xsDes.Basis_functions - type of basis function
SPM.xsDes.Number_of_sessions
SPM.xsDes.Trials_per_session
SPM.xsDes.Interscan_interval
SPM.xsDes.High_pass_Filter
SPM.xsDes.Global_calculation
SPM.xsDes.Grand_mean_scaling
SPM.xsDes.Global_normalisation

details on scannerdata (e.g. smoothness) 

 

SPM.xVol - structure containing details of volume analyzed
SPM.xVol.M- 4x4 voxel --> mm transformation matrix
SPM.xVol.iM - 4x4 mm --> voxel transformation matrix
SPM.xVol.DIM - image dimensions - column vector (in voxels)
SPM.xVol.XYZ - 3 x S vector of in-mask voxel coordinates
SPM.xVol.S- Lebesgue measure or volume (in voxels)
SPM.xVol.R- vector of resel counts (in resels)
SPM.xVol.FWHM - Smoothness of components - FWHM, (in voxels)

info on beta files:

 

SPM.Vbeta - struct array of beta image handles
SPM.Vbeta.fname - beta img file names
SPM.Vbeta.descrip - names for each beta file

info on variance of the error

 

SPM.VResMS - file struct of ResMS image handle
SPM.VResMS.fname - variance of error file name

info on mask

 

SPM.VM - file struct of Mask image handle
SPM.VM.fname - name of mask img file

contrast details (added after running contrasts)

 

SPM.xCon - Contrast definitions structure array

• (see also spm_FcUtil.m for structure, rules &handling)

SPM.xCon.name - Contrast name
SPM.xCon.STAT - Statistic indicator character ('T', 'F' or 'P')
SPM.xCon.c - Contrast weights (column vector contrasts)
SPM.xCon.X0 - Reduced design matrix data (spans design space under Ho)

• Stored as coordinates in the orthogonal basis of xX.X from spm_sp
• (Matrix in SPM99b)
• Extract using X0 spm_FcUtil('X0',...
  

SPM.xCon.iX0 - Indicates how contrast was specified:

• If by columns for reduced design matrix then iX0 contains the column indices.
• Otherwise, it's a string containing the spm_FcUtil 'Set' action: Usually one of {'c','c+','X0'} defines the indices of the columns that will not be tested. Can be empty.

SPM.xCon.X1o - Remaining design space data (X1o is orthogonal to X0)

• Stored as coordinates in the orthogonal basis of xX.X from spm_sp (Matrix in SPM99b) Extract using X1o spm_FcUtil('X1o',...

SPM.xCon.eidf - Effective interest degrees of freedom (numerator df)

• Or effect-size threshold for Posterior probability

SPM.xCon.Vcon - Name of contrast (for 'T's) or ESS (for 'F's) image
SPM.xCon.Vspm - Name of SPM image

Multi-Variate Pattern Analysis (MVPA): An Introduction

Alert reader and fellow brain enthusiast Keith Bartley loves MVPA, and he's not ashamed to admit it. In fact, he loves MVPA so much that he was willing to share what he knows with all of us, as well as a couple of MVPA libraries he has ported from Matlab to Octave.

Why don't I write a post on MVPA, you ask? Maybe because I don't know doodley-squat about it, and maybe because I'm man enough to admit what I don't know. In my salad days when I was green in judgment I used to believe that I needed to know everything; nowadays, I get people to do that for me. This leaves me more time for gentlemanly activities, such as hunting, riding, shooting, fishing, and wenching.

So without further delay, here it is: An introduction to MVPA for those who are curious about it and maybe even want to do it themselves, but aren't exactly sure where to start. Be sure to check out the links at the end of the post for links to Keith's work, as well as Octave distributions he has been working on.

==================================

Well, it had to happen sometime. Time to call out the posers. Those who would bend neuroscience to their evil will. Where to start? How about the New York Times. Oh, New York Times. You've managed to play both sides of this coin equally well. Creating a neuroimaging fallout with bad reports, then throwing out neuroscience studies altogether ("The brain is not the mind" <- What? Stop. Wait, who are you again? Just stop). What's to be said for those few that rise above the absolutes of "newspaper neuroscience", and simply report findings, not headline grabbing inferences? Should we be opposed to gained knowledge, or seek to better understand the details? Boring you say? Pfft. Then you have yet to know the neuroscience I know.

As an example, a recent NYT article suggested that activation in both the primary auditory and visual cortices in response to an iPhone ring alone demonstrated that people were seeing the iPhone in their mind's eye.

...

This is a completely RIDICULOUS notion to suggest from univariate GLM BOLD response alone. But can we ever really know what a person sees in their mind's eye or hears in their mind's ear? Remember, good science happens in the setup, not the interpretation.

You may have heard of an increasingly implemented form of machine classification in brain-imaging dubbed Multi-Variate Pattern Analysis (MVPA). If you prefer the term "mind reading", sure go ahead, but remember to bring your scientific floaties, lest you drown from the lack of understanding as it escapes the proverbial lungs of your deoxygenated mind. Before you know it, you'll be believing things like this:

Verbose laughter ensues. Close, but no Vicodin. How does MVPA of BOLD responses really work?

Source: Kaplan & Meyer, 2011

By first training a program to recognize a pattern, in much the same way you might visually recognize a pattern, we can quantitatively measure the similarity or dissimilarity of patterns in response to differing conditions. But what does this have to do with knowing what a person might see in their mind? I recently compiled some soundless videos for a demonstration of just this. Watch them fullscreen for the greatest effect.

It's likely that the sound of coins clanking, a car crashing, or Captain Kirk screaming "KAHHHHN!!!" registered in your mind, and thus created distinct neural representations in your primary auditory cortex. If we train a machine classifier to recognize your brain's patterned neural response to the sound, we can then ask the classifier to guess which among all these stimuli your brain is distinctly representing in the absence of sound. If the machine classifier is successful statistically more than null permutations of chance, THEN we can MAYBE begin to suggest a top-down neural mechanism of alternate sensory modality stimulation. 

BUT, I promised you details, and details you shall have!

As a fan of Princeton's MVPA Matlab toolbox, opening it up for people without access to a Matlab license seemed like the next most logical step, prompting me to convert the toolbox, as well as its implementations of SPM and AFNI-for-MATLAB, to one unitary Octave distribution. Below is a link to my website and Github page. There you will find setup instructions as well as tutorial data and a script that Dr. Marc Coutanche (See his rigorously awesome research in MVPA here) and I implemented in a recent workshop. Coded are step-by-step instructions to complete what is a research caliber implementation of pattern analysis. Learn it, live it, repeat it, and finally bask in your ability to understand something that would make your grandma's head explode (See the Flynn Effect for possible explanation there). As with anything I post, if you have questions, comments, or criticisms, feel free to message me through any medium of communication ...unless you are a psychic. I'd like to keep my mind's ear to myself. 

BartleyNeuro.org

github.com/bartleyneuro/OctaveMVPA

De Profundis

Since school started back up a little over a month ago, I've been teaching my own introductory psychology course - the first one I've ever taught. It's been great; when I do it, I feel happy, energized, useful. Not only do I get to teach a couple of hundred persons, some of whom really like the class, but I even get to write my own test questions. If ten years ago you told me I would be lecturing in front of college students and creating exams, I would've told you to go kick rocks. But oddly enough, I enjoy it. For instance, I get to come up with test questions like this:

Sigmund Freud was:

A) correct
B) completely insane
C) a cocaine abuser
D) all of the above


Understandably, the writing here took a hit, as I left the mistress of my youth, blogging, for the wife of mine age, teaching. I figured that whatever basics someone needed to know they could find somewhere in the archives. I thought that I probably was spending too much time on it anyway, feeling a distinct negative correlation between the amount of material that was posted on here and my actual productivity as a researcher. Maybe once in while, I thought, I would post about relationship advice, or books I was reading, or possibly a sequel to my post about erotic neuroimaging journal titles. In any case, though, I thought that I written most of what I had wanted to. Quod scripsi, scripsi.

However, I got a jolt a couple of days ago when the government shut down. Normally this wouldn't affect me all that much, except for the AFNI developers sending out a warning that the entire website would be shut down and the message boards closed until further notice. Apparently it's illegal for federal employees to use government emails for correspondence during a shutdown. No more AFNI support; no more new AFNI materials; no more infamous Bob Cox insults, put-downs, and slams. All gone.

Which made me realize, God forbid, that AFNI won't be around forever. I doubt that even fMRI will be all that popular twenty, thirty years from now, as technology progresses and we find some new way to image the brain yet still get significant results no matter how badly we screw up. But the need for understanding the processes will still be there; people will always want easy, accessible introductions for learning new tools and new methods. So I will continue to do that, no matter how incomplete my understanding, no matter how many miles I run, no matter how many jars of Nutella I devour. And that's a campaign promise.

At least one researcher out there has offered to write about topics that I am either entirely ignorant of, or only have a limited grasp. Starting soon, I will begin to interleave some of those posts with what I write to make the blog more centralized for information relating to fMRI. In the meantime, if anyone reading wants to contribute, just let me know. We'll see how it works out.