Creating Functional Connectivity Maps in AFNI (Second Step on the Road Towards Glory)

Having used 3dSynthesize to create a dataset with the effects of no interest, we are now ready to subtract those effects from the dataset that went into 3dDeconvolve; for you players using the AFNI_data6 tutorial data, this is the all_runs.FT+orig dataset. We can use 3dcalc for this operation:

3dcalc -a all_runs.FT+orig -b effectsNoInterest+orig -expr 'a-b' -prefix cleanData+orig

This will create a time series with all the drift correction and motion parameter schmutz subtracted out and cast into the pit. What is left over will be signal untainted by motion or drift effects, which we can then use to generate a seed time series.

Before that, however, there is the additional step of warping our data to a template space (such as MNI or Talairach). Assuming you have already warped your anatomical dataset to a template space either manually or using @auto_tlrc, and assuming that there is already good alignment between your anatomical and functional data, you can use the command adwarp:

adwarp -apar anat_final.FT+tlrc -dpar cleanData+orig -dxyz 3 -prefix EPI_subj_01

(Note: There are better ways to do warping, such as the warping option built into align_epi_anat.py (which calls upon @auto_tlrc), but for pedagogical purposes we will stick with adwarp.)

Once this is done, all we need to do is select a seed region for our functional connectivity analysis. This could be a single voxel, a region of interest that averages over an entire area of voxels, or a region selected based on a contrast or an anatomical landmark; it depends on your research question, or whether you want to mess around and do some exploratory analyses. For now, we will use a single voxel using XYZ coordinates centered on the left motor cortex (note that, in this coordinate system, left is positive and posterior is positive):

3dmaskdump -noijk -dbox 20 19 53 EPI_subj_01+tlrc > ideal_ts.1D

Because 3dmaskdump outputs a single row, we will need to transpose this into a column:

1dtranspose ideal_ts.1D LeftMotorIdeal.1D

After you have output your ideal timeseries, open up the AFNI viewer and make sure that what was output matches up with the actual timeseries. In this example, set EPI_subj_01+tlrc as an underlay and right click in the slices viewer to jump to XYZ coordinates of 20, 19, 53; open up the timeseries graph as well, and scroll to the first time point. Does the value there match up with the first entry of your ideal time file? If not, you may have mis-specified the voxel you wanted, or you are using a different XYZ grid than is displayed in the upper left corner of the AFNI viewer. If you run into this situation, consult your local AFNI guru; if you don't have one of those, well...

In any case, we now have all the ingredients for the functional connectivity analysis, and we're ready to pull the trigger. Assemble your materials using 3dfim+ (which, as far as I can understand, stands for "functional intensity map," or something like that):

3dfim+ -polort 3 -input EPI_subj_01+tlrc -ideal_file LeftMotorIdeal.1D -out Correlation -bucket Corr_subj01

You will now have a dataset, Corr_subj_01+tlrc, which is a functional connectivity map between your seed region and the rest of the brain. Note that the threshold slider will now be in R values, instead of beta coefficients or t-statistics; therefore, make sure the order of magnitude button (next to the '**' below the slider) is 0, to restrict the range between +1 and -1.

The last step is to convert these correlation values into z-scores, to reduce skewness and make the distribution more normal. This is done through Fisher's R-to-Z transformation, given by the formula z =  (1/2) * ln((1+r)/(1-r)). Using 3dcalc, we can apply this transformation:

3dcalc -a Corr_subj01+tlrc -expr 'log((1+a)/(1-a))/2' -prefix Corr_subj01_Z+tlrc

Those Z-maps can then be entered into a second-level design just like any other, using 3dttest+ or some other variation.

Sanity check: When viewing the correlation maps, jump to your seed region and observe the r-value. It should be 1, which makes sense given that this was the region we were correlating with every other part of the brain, and correlating it with itself should be perfect.

Like me.

Debussy: La Fille Aux Cheveux De Lin

FMRI analysis can be stressful; graduate school can be stressful; life and relationships can be stressful. Therefore, it can be salutary to take stock of everything once in a while, just to keep things in perspective; because all of those things listed above can, sometimes, if you pay attention - be very, very good.

Just kidding; you're probably going to have an extremely stressful week anyway. Regardless, here's some relaxing music to help you out.

AFNI Command: 3dSynthesize (First Step on the Road Towards Glory)

Before we get into full-blown functional connectivity mode, we need to get acquainted with a command called 3dSynthesize. This will create a fitted time series based on selected regressors from your model, and will be used for subtracting out effects of no interest - that is, things like drift correction and motion regressors - so that the correlation we observe is protected from systematic differences in things like head motion, which can be particularly problematic in patient populations and children.

3dSynthesize requires a bucket dataset only containing coefficients from your model; therefore, you may need to go back and rerun 3dDeconvolve with the -cbucket option to make that magic happen. Once done, feed 3dSynthesize the coefficient bucket, the X matrix from 3dDeconvolve, and a selection of columns that you want for a fitted time series, e.g.:

3dSynthesize -prefix effectsNoInterest -cbucket CStats.FT+orig -matrix X.xmat.1D -select 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 19

The columns I've selected here are based on the dataset in AFNI_data6; obviously, yours will probably differ. The columns can be selected based on number, as above, or the actual label names, which can be retrieved from the X matrix with the grep command:

grep ColumnLabels X.xmat.1D

In any case, check the X matrix with either aiv or 1dplot to make sure that the columns you are extracting are indeed the effects that you want.

Hit the video for a brief demonstration, as well as a 30-second monologue to get you pumped up to use 3dSynthesize.

Andy's Brain Blog Book Club: Blood Meridian

When I was a child, I remember reading a story about a single soldier who executed several thousand of prisoners of war using only a service-issued pistol. Every night for a month he would don his military cap and leather gloves and a leather butcher's apron and lead the prisoners one after another into an antechamber draped in the crimson of the Rodina and tell them why they were to be killed and then shoot them in the head. At night he would share vodka with his men and the next day it would begin again. Over ten hours a day he worked over a period of four weeks, at the incredible rate of one execution every three minutes. At the end of his own personal holocaust he would have some seven thousand souls to his credit.

I am told that he died years later, insane and in utter wretchedness. What right man would have it any other way?

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Cormac McCarthy is a difficult writer to pin down. His works deal with the grisly and the grotesque, and although it is unfair to label McCarthy as a pessimist or a misanthrope, his books can hardly be considered an argument for optimism. The characters haunting his books are the violent, the dispossessed, and the desperate - men thrown into situations of extreme violence and deprivation faced with horrifying scenes of murder, infanticide, necrophilia, psychopaths, irate wildlife, and a God that can only be understood after journeying through universes of pain and suffering. On the whole, not the most comfortable material to read.

One small part of it, however, is an unadulterated masterpiece. When Blood Meridian was first published in 1985, it was not unnoticed, it is true, but it was not necessarily understood; some thought it an interesting, but minor, failure. Fifteen years later, McCarthy's stock had risen considerably. Nearly another fifteen years later, the change in the book's reputation is greater still; it is now hailed as one of the most important American novels of the twentieth century, and as one of the finest pieces of fiction written by a currently living author. After having read my way through his entire oeuvre, I cannot help but see the books from the beginning of his career as forming a sort of prelude, in which he tested and experimented and honed his craft; and in everything he wrote after its publication, he never quite sounded that magical, eerie note again. It is the apex of his career; Blood Meridian is his reception piece.

Before starting the book, however, there are a few points to keep in mind. First, it is not merely a brutal geek show where McCarthy is daring the reader to look away. (Although, if it were, it would surely outrank all others.) Second, it is not simply a book about the West, a piece of interesting historical fiction based on the scalphunting operation of the real-life Glanton gang; it is, rather, an investigation into McCarthy's central obsession - the nature of violence and death - and he is exploiting material he has studied intimately. Just as Conrad's works are not, expect superficially, mere sea-stories, so this is not just a Western, but an uncompromising exploration into the darker regions of the soul.

Third, there is a very real possibility, even for the most jaded, that you will not finish the book on the first try; and afterward, you may decide not to return to it. With Blood Meridian, even some of our finest critics have had false starts.

Even knowing all of this, Blood Meridian is tough going. McCarthy's style is paradoxically both sparse and dense; and his odd punctuation, lack of quotation marks, technically detailed language, and pockets of untranslated Spanish can be difficult to adjust oneself to. Finally, there is the issue of the violence itself, which is extremely - some would say virtuosically - graphic. Random killings, decapitations, dismemberments, scalpings, bizarre tortures, spectacular scenes of mass infanticide, crucifixions, immolations, flamboyant acts of sadism, and wholesale slaughters of humans and animals alike are only the beginning of what the book has to offer on its grisly bill of fare, building in a vicious crescendo to the final, unnameable atrocity. It is well for the reader to know this. To read Blood Meridian is to descend into an inferno.

A passage from the scalphunters' slaughter of the Gileños both highlights the cold precision of McCarthy's prose and the horror suffused throughout the whole novel:

Within that first minute the slaughter had become general. Women were screaming and naked children and one old man tottered forth waving a pair of white pantaloons. The horsemen moved among then and slew them with clubs or knives. A hundred tethered dogs were howling and others were racing crazed among the huts ripping at one another and at the tied dogs nor would this bedlam and clamor cease or diminish from the first moment the riders entered the village. Already a number of the huts were afire and a whole enfilade of refugees had begun streaming north along the shore wailing crazily with the riders among them like herdsmen clubbing down the laggards first.

When Glanton and his chiefs swung back through the village people were running out under the horses' hooves and the horses were plunging and some of the men were moving on foot among the huts with torches and dragging the victims out, slathered and dripping with blood, hacking at the dying and decapitating those who knelt for mercy. There were in the camp a number of Mexican slaves and these ran forth calling out in spanish and were brained or shot and one of the Delawares emerged from the smoke with a naked infant dangling in each hand and squatted at a ring of midden stones and swung them by the heels each in turn and bashed their heads against the stones so that the brains burst forth through the fontanel in a bloody spew and humans on fire came shrieking forth like berserkers and the riders hacked them down with their enormous knives and a young woman ran up and embraced the bloodied forefeet of Glanton's warhorse.

McCarthy allows us to witness this nightmarish world through a character known only as the kid. We never know his name, we know virtually nothing about him, and we know little about what he thinks. Furthermore, there are long stretches of the book where he disappears completely from view; all we know is that he is young, desperate, and that within him "...broods a taste for mindless violence." He is less an actual person than an avatar for the reader - a representation of our race's dark, powerful, deep-seated fascination with violence that, for better or for worse, can be managed and suppressed but never entirely rooted out of our souls; that troubled, darkened corner of our psyche which always finds some part of itself both appalled and enticed by the carnage of the battlefield, both horrified and inflamed by the screams of the tortured victim.

This same mindless incitement to violence is embodied in the Glanton gang as a whole, a grim reflection of the more sordid aspects of the human condition. Nearly always caked with the dried gore of their enemies and adorned with grisly trophies hacked or cut away from the corpses of their victims, the scalphunters are described in words mythological; they are "ogres," a "heliotropic plague spreading westward," and more than once they are referred to as "argonauts." They carry shotguns and revolvers with bores big enough to stick ones thumbs in, and wield Bowie knives as big as claymores; one of their Indian enemies, flamboyantly attired, is described as a "wild thaumaturge out of an atavistic drama." Thus the feeling that they are not really representing themselves - actual individuals from an actual scalphunting operation that massacred their way across the plains and deserts of western Mexico - but rather timeless embodiments of the violence and warfare weaved throughout the history of our species.

The Gang's gradual descent into madness leads to murdering out of sheer compulsion, as illustrated in one self-contained paragraph which, bookended by larger, more complex scenes, appears to be a throwaway - but upon closer inspection becomes one of the most chilling:

The next town they entered was two days deeper into the sierras. They never knew what it was called. A collection of mud huts pitched on the naked plateau. As they rode in the people ran before them like harried game. Their cries to one another or perhaps the visible frailty of them seemed to incite something in Glanton...He nudged forth his horse and drew his pistol and this somnolent pueblo was forthwith dragooned into a weltering shambles. Many of the people had been running toward the church where they knelt clutching the altar and from this refuge they were dragged howling one by one and one by one they were slain and scalped in the chancel floor. When the riders passed through this same village four days later the dead were still in the streets and buzzards and pigs were feeding on them. The scavengers watched in silence while the company picked their way past like supernumeraries in a dream. When the last of them was gone they commenced to feed again.

Blood Meridian echoes several other works, including Paradise Lost (compare the Judge's creation of gunpowder to that of Satan's), Moby-Dick (Toadvine contemplating whether to kill the Judge, as compared to Starbuck contemplating whether to kill Ahab), and the Bible (those acquainted with the bloodier bits of the Book of Judges and the Book of Samuel will find much here that is familiar). The allusions are calculated and deliberate; McCarthy draws upon references to books and rituals that, even if one has never directly read them or heard of them, are so thoroughly ingrained in our heritage that we cannot help but resonate to them. There is the scene of the fortune-telling around the campfire (which, if paid attention to, reveals much more about the architecture of the book than at first glance); the story within the story about the son whose father is murdered and who himself becomes a killer of men; the burning tree in the middle of the desert, struck by lightning; and, in the shortest chapter of the novel, the baptism of the lunatic, a rare but bizarre moment of tenderness whose meaning is completely lost upon the insane.

In addition to his literary references, McCarthy devotes considerable time to describing the land itself; that indifferent, often terrifying aspect of nature from which we, if we are sensitive enough, always feel ourselves somehow estranged. In a way, the landscape becomes one of the book's primary characters. Everywhere and at all times are felt the dangers of unpredictable weather, of exposure, of infection or blood poisoning from an unfortunate encounter with any of the innumerable beasts hiding within the forests or crawling upon the sands of the deserts. A wrong step, a delayed reaction, can mean the difference between life and death; and given the utter isolation and desolation of the landscape, one's death is greeted not with grief or mourning, but with terrible silence:

The following evening as they rode up onto the western rim they lost one of the mules. It went skittering off down the canyon wall with the contents of the panniers exploding soundlessly in the hot dry air and it fell through sunlight and through shade, turning in that lonely void until it fell from sight into a sink of cold blue space that absolved it forever of memory in the mind of any living thing that ever was.

Counterbalancing the stark reality of the book is the Judge, an enormous, completely hairless man resembling a gigantic infant. In a novel surfeited with atrocities and depravity, the Judge stands apart. Explorer, orator, gunslinger, murderer, pedophile, childkiller, Judge Holden is a quasi-supernatural being, the horrifying spiritual emblem of the Glanton gang. Seemingly all-knowing, all-present, and nearly invincible, the Judge assumes the role of a demigod, appearing to know all tongues, all arts, all sciences, all histories, and desiring to record every thing upon the earth, living or inanimate, into his depthless logs - and then obliterate it.

More compelling than his fantastical appearance and ghoulish predilections is his oratory; as with Satan in Paradise Lost, even though we know his rhetoric is riddled with nihilism and casuistry, we want to hear the Judge speak. Our first experience of the Judge is his inciting a mob to murder a preacher, based on false accusations of sodomy and bestiality; immediately we are aware of his demonic charisma, his methods, and his association with violence. His utterances are those of a supremely intelligent maniac, in full control of his rhetorical powers but seemingly not in control of his mind, pontificating in Biblical periods and declaiming in the epic mode. His speeches throughout the novel - which, read together, form a sort of loose progression charting the spiritual decay of the Gang - seem to be only so much eloquent gibberish, but contain a seed of truth that we somehow cannot simply wave away.

One example will suffice. As one night the men discuss whether there is any life elsewhere in the universe, the Judge says that there is not. The rest of his answer verges on insanity; and through him we possibly are allowed a glimpse into the author's own mind:

The truth about the world, he said, is that anything is possible. Had you not seen it all from birth and thereby bled it of its strangeness it would appear to you for what it is, a hat trick in a medicine show, a fevered dream, a trance bepopulate with chimeras having neither analogue nor precedent, an itinerant carnival, a migratory tentshow whose ultimate destination after many a pitch in many a mudded field is unspeakable and calamitous beyond reckoning.

The universe is no narrow thing and the order within it is not constrained by any latitude in its conception to repeat what exists in one part in any other part. Even in this world more things exist without our knowledge than with it and the order in creation which you see is that which you have put there, like a string in a maze, so that you shall not lose your way. For existence has its own order and that no man’s mind can compass, that mind itself being but a fact among others.

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Blood Meridian is that rarest and most precious of works, a book which speaks directly to the human condition. McCarthy deals with the most profound, the most horrifying, the most powerful drives and instincts embedded within the human spirit, and uses depictions of extreme violence to enumerate its contents. It is a refreshing contrast to the relentless flood of books concerned with the glands, but not the heart; it is a much-needed tonic of the epic and the grandiose, in an age that jeers at grandeur. Most importantly, it is the work of an uncompromising artist and a ferocious intelligence, terrifically enjoyable to read even when dealing with subjects at their most wretched. With McCarthy, every sentence, every word, is weighted for effect; when he chooses to, he strikes like a thunderbolt. Once you reach the end of a sentence, a phrase, a paragraph, the images he conjures up will bloom in your mind like blood in water.

Above all is his supreme achievement, the creation of Judge Holden. Enormous, terrible, bewitching, irresistible, he is less a man, a character, a fictional being, than a force of nature. He is the animating spirit, the driving force, the engine of absolute war and violence for its own sake; he is reality itself in its most depraved and sanguinary aspect. His dance is the Totentanz, never-ending, all-consuming, dancing to the strains of the fiddles sawing up a hellish roundelay and the sound of jackboots slamming on the floorboards, keeping time to the tattoo of the wardrums and the beating of the human heart. He says he never sleeps, we are told. He says he will never die.

In any case, a book to haunt one's dreams.

Introduction to Functional Connectivity

It seems as though everyone these days wants to do something more than just the same old standard mass univariate analyses. And why not? Given the embarrassment of riches we have with any FMRI dataset - literally thousands upon thousands of voxels in just a single image, like some gargantuan godsized Rubik's Cube with as many interlocking blocks as there are grains of sand on the beach - it is too tempting not to. In each dataset - hundreds of thousands of voxels. In each experiment - millions. In a lab - tens of millions. In a university - billions. And on and on. As Jeeves would say: The mind boggles, sir.

With so much data at our disposal, one naturally wants to do more sophisticated analyses and test for more interesting types of interactions; and this impulse becomes even stronger among the neurotic academic who has to make things much more complex then they really have to be. To see whether there are any special affinities between different regions of the brain, as it were. Due to the incredibly high number of connections within it, more complex analysis of the interactions between the signals of the voxels themselves becomes compelling - and one of the ways to do this is through a technique called functional connectivity.

All functional connectivity is, in its most basic form, is calculating the correlation between the timeseries of different voxels. The reference timecourse is determined entirely by the investigator; it can be a single peak voxel within a cluster defined by a contrast, it can be an average timecourse across an entire blob of contiguous voxels, or it can be a voxel chosen on the basis of its anatomical location. However it is chosen, this reference timecourse is compared against every other voxel in the brain, and a correlation coefficient computed to measure the similarity between the timecourses. In other words, does this voxel's timeseries, picked from an arbitrary point on the left side of the brain:

Match up well with another voxel picked from the right side of the brain?

Reference timecourse overlaid in red, above the comparison voxel's timecourse in black.

And this same procedure is applied for every other voxel as well.

However, it is worth noting that the name "Functional Connectivity" is misleading at best. Really what it is is a simple correlation analysis, often more appropriately called a bivariate correlation analysis. There is no connectivity to speak of in this kind of analysis; we merely operate under the assumption voxels showing similar timecourses might - might - be connected somehow. But even this is a somewhat laughable assumption to make. No temporal delay is really considered, and no directionality can be inferred.

With this I come to a conclusion and pronounce my judgment. I condemn the name functional connectivity; I raise against this wretched misnomer the most terrible of all the accusations that an accuser ever uttered. It is, to me, the highest of all conceivable corruptions; it seeks to work the ultimate corruption, the worst possible corruption. The name "functional connectivity" has left nothing untouched by its depravity; it has turned every value into worthlessness, and every truth into a lie, and every integrity into vileness of soul. Let any one dare to speak to me of its "scientific" blessings!

Parasitism is the only practice of those who call it so; with its anemic and "connectivity" ideals, sucking all the blood, all the love, all the hope out of life; the will to negate all reality; the word "connectivity" as the mark of recognition for most subterranean conspiracy ever heard of - against health, beauty, well-being, intellect, graciousness of soul - against life itself. This eternal indictment against the name functional connectivity I shall write upon all walls, wherever walls are to be found - I have letters that even the blind will be able to see.

I call that name the one great curse, the one great intrinsic depravity, for which no means are venomous enough, or secret, subterranean and small enough; I call it the one immortal blemish upon the human race.



Of course, if you do want to do a real connectivity analysis, that requires some more steps. We will get to all of that later; but first things first. Here are some of the basics.

AFNI Start to Finish Playlist

Although the title may sound a little risqué, what it actually refers to is a compilation of tutorials - twenty-one in all - that cover the analysis of a single subject from data import to viewing the results and making publication-quality pictures. I closely follow a script already up on the AFNI website written by Rick Reynolds, and I've included links to the relevant step of the script. The idea here was to actually show what each step looks like, and to provide some additional commentary. Half of the commentary is wrong, though; the only problem is, I'm not sure which half.

A link to the script can be found here; a link to the tutorials can be found here. Particularly important is understanding the design matrix, and gaining an intuition for how it is applied at each voxel; I will be going into more detail about that in the future.

If I Forget Thee, Bloomington

By the Genesee River, there I sat down, yea, I wept, when I remembered Bloomington.

If I forget thee, Bloomington, let my right hand forget her cunning; if I do not remember thee, let my tongue cleave to the roof of my mouth, if I prefer not Bloomington above my chief joy.

O daughter of Rochester, who art to be destroyed; happy shall he be, that rewardeth thee as thou hast served us.

Happy shall he be, that taketh and dasheth thy little ones against the stones.



Get the car, Sydney; I'm coming back.

Social Psychology Blog: SociallyMindful.com

For those of you who are curious, I actually do have a few friends, and one of them specializes in social psychology. Her name is Elizabeth Bendycki, and, jealous of my success and popularity, she decided to start a blog of her own focusing on her research: SociallyMindful.com. The stated purpose of the blog is to "[Explore] issues at the intersection of brain sciences and human social behavior," to "Raise awareness of the societal and ethical implications of psychological and neuroscience research," to "Further the cause of Marxism, Lysenkoism, and the hasten the inevitable victory of the proletariat," and "Crush AndysBrainBlog in number of hits per day." In your dreams, Lizzie!

I encourage you all to check out her blog to support her and learn more about what she does. And then, I encourage you to realize how good you had it, and come crawling back here to beg forgiveness for ever leaving me.

Comprehensive Computational Model of ACC: Expected Value of Control

Figure 1: Example of cognitive control failure

A new comprehensive computational model of dorsal anterior cingulate cortex function (dACC) was published in last week's issue of Neuron, sending shockwaves throughout the computational modeling community and sending computational modelers running to neuroscience magazinestands in droves. (That's right, I used the word droves - and you know I reserve that word only for special cases.)

The new model, published by Shenhav, Botvinick, and Cohen, attempts to unify existing models and empirical data of dACC function by modifying the traditional monitoring role usually ascribed to the dACC. In previous models of dACC function, such as error detection and conflict monitoring, the primary role of the dACC was that of a monitor involved in detecting errors, or monitoring for mutually exclusive responses and signaling the need to override prepotent but potentially wrong responses. The current model, on the other hand, suggests that the dACC monitors the expected value associated with certain responses, and weighs the potential cost of recruiting more cognitive control against the potential value (e.g., reward or other positive outcome) for implementing cognitive control.

This kind of tradeoff is best illustrated with a basic task like the Stroop task, where a color word - such as "green" - is presented in an incongruent ink, such as red. The instructions in this task are to respond to the color, and not the word; however, this is difficult since reading a word is an automatic process. Overriding this automatic tendency to respond to the word itself requires cognitive control, or strengthening task-relevant associations - in this case, focusing more on the color and not the word itself.

However, there is a drawback: using cognitive control requires effort, and effort isn't always pleasant. Therefore, it stands to reason that the positives for expending this mental effort should outweigh the negatives of using cognitive control. The following figure shows this as a series of meters with greater cognitive control going from left to right:

Figure 1B from Shenhav et al, 2013

As the meters for control signal intensity increase, so does the probability of choosing the correct option that will lead to positive feedback, as shown by the increasing thickness of the arrows from left to right. The role of the dACC, according to the model, is to make sure that the amount of cognitive control implemented is optimal: if someone always goes balls-to-the-wall with the amount of cognitive control they bring to the table, they will probably expend far more energy then would be necessary, even though they would have a much higher probability of being correct every time. (Study question: Do you know anybody like this?) Thus, the dACC attempts to reach a balance between the cognitive control needed and the value of the outcome, as shown in the middle column of the above figure.

This balance is referred to as the expected value of control (EVC): the difference between control costs and outcome values you can expect for a range of control signal intensities. The expected value can be plotted as a curve integrating both the costs and benefits of increased control, with a clear peak at the level of intensity that maximizes the difference between the expected payoff and control cost (Figure 2):

EVC curves (in blue) integrating costs and payoffs for control intensity. (Reproduced from Figure 4 from Shenhav et al, 2013)

That, in very broad strokes, is the essence of the EVC model. There are, of course, other aspects to it, including a role for the dACC in choosing the control identity which orients toward the appropriate behavior and response-outcome associations (for example, actually paying attention to the color of the stroop stimulus in the first place), which can be read about in further detail in the paper. Overall, the model seems to strike a good balance between complexity and conciseness, and the equations are relatively straightforward and should be easy to implement for anyone looking to run their own simulations.

So, the next time you see a supermodel in a bathtub full of Nutella inviting you to join her, be aware that there are several different, conflicting impulses being processed in your dorsal anterior cingulate. To wit, 1) How did this chick get in my bathtub? 2) How did she fill it up with Nutella? Do they sell that stuff wholesale at CostCo or something? and 3) What is the tradeoff between exerting enough control to just say no, given that eating that much chocolate hazelnut spread will cause me to be unable to move for the next three days, and giving in to temptation? It is a question that speaks directly to the human condition; between abjuring gluttony and the million ailments that follow on vice, and simply giving in, dragging that broad out of your bathtub and toweling the chocolate off her so you don't waste any of it, showing her the door, and then returning to the tub and plunging your insatiable maw into that chocolatey reservoir of bliss, that muddy fountain of pleasure, and inhaling pure ecstasy.

Rochester Updates

I've only been in Rochester for about ten days now, but so far it's been a good experience. After arriving in the middle of a heatwave and sleeping in a room with no air conditioning - similar to Alec Guinness and the corrugated shed in The Bridge on the River Kwai - the heat spell broke and cooler air came in, making the weather for the past week some of the most pleasant I have ever breathed into my lungs and felt upon my skin. In addition, the trail system here is fantastic, with several miles of smooth, uninterrupted pavement running along the Genesee River and the Erie Canal. Every morning I wake up a little after six, run eight or ten or twelve miles on the sunwarmed trails, go to work, come home later in the evening, eat at the Mt. Hope Diner across the street, and sometimes get in another run before going to bed. I love it.

My lab hosts here have also provided me with everything that I wanted to learn and get done during my trip, including hashing out some ideas for a joint project, getting some hands-on experience and a soup-to-nuts tutorial on setting up a monkey and guiding electrodes into their brains and recording action potentials from their neurons, and presenting my research and going to lab meetings and journal clubs. I didn't know what to expect going in, but the days have been productive and I've met some great people.

Having recently finished teaching the FMRI workshop, I am also putting together a playlist of tutorial videos covering the analysis of a single subject from start to finish, following the text files on the AFNI website. There are about twenty steps in all, and they cover the fundamentals of FMRI acquisition and analysis, as well as the technical details of how to operate AFNI. I hope this will provide a good starting point for AFNI newcomers, and in the future I will be putting together more coherent playlists to cover certain topics in depth.

The playlist