Nosimpler

To busy readers: Skip to the tl;dr summary at the end of this post.

A psychology researcher sent me an email with subject line, “There’s a hell of a paper coming out in PPNAS today.” He sent me a copy of the paper, “Physical and situational inequality on airplanes predicts air rage,” by Katherine DeCelles and Michael Norton, edited by Susan Fiske, and it did not disappoint. By which I mean it exhibited the mix of forking paths and open-ended storytelling characteristic of these sorts of PPNAS or Psychological Science papers on himmicanes, power pose, ovulation and clothing, and all the rest.

There’s so much to love (by which I mean, hate) here, I hardly know where to start.

– Coefficient estimate and standard errors such as “1.0031** (0.0014)” (yes, that’s statistically significantly different from the baseline value of 1.0000).

– Another coefficient of “11.8594” (dig that precision) with a standard error of “11.8367” which is still declared statistically significant at the 5% level. Whoops!

– The ridiculous hyper-precision of “Flights with first class present are ∼46.1% of the population of flights” (good thing they assured us that it wasn’t exactly 46.1%).

– The interpretation of zillions of regression coefficients, each one controlling for all the others. For example, “As predicted, front boarding of planes predicted 2.18-times greater odds of an economy cabin incident than middle boarding (P = 0.005; model 2), an effect equivalent to an additional 5-h and 58-min flight delay (0.7772 front boarding/0.1305 delay hours).” What does it all mean? Who cares!

– No raw data. Sorry, proprietary restrictions so nobody can reproduce this analysis! (Don’t get me wrong, I have no problem with researchers learning from proprietary information, I do it all the time. What the National Academy of Sciences is doing publishing this sort of thing, I have no idea. Or, yes, I do have an idea, but I don’t like it.)

– Story time: “We argue that exposure to both physical and situational inequality can result in antisocial behavior. . . . even temporary exposure to physical inequality—being literally placed in one’s “class” (economy class) for the duration of a flight—relates to antisocial behavior . . .”

– A charming reference in the abstract to testing of predictions, even though no predictions were supplied before the data were analyzed.

– Dovetailing!

The data

The authors don’t share any of their data, but they do say that there were between 1500 and 4500 incidents in their database, out of between 1 and 5 million flights. So that’s about 1 incident per thousand flights.

They report a rate of incidents of 1.58 per thousand flights in economy seats on flights with first class, .14 per thousand flights in economy seats with no first class, and .31 per thousand flights in first class.

It seems like these numbers are per flight, not per passenger, but that can’t be right: lots more people are in economy class than in first class, and flights with first class seats tend to be in bigger planes than flights with no first class seats. This isn’t as bad as the himmicanes analysis but it displays a similar incoherence.

There’s no reason we should take this sort of tea-leaf-reading exercise seriously. Or, to put it another way—and I’m talking to you, journalists—just pretend this was published in some obscure outlet such as the Journal of Airline Safety. Subtract the hype, subtract the claims of general relevance, just treat it as data (which we don’t get to see).

I should perhaps clarify that I can only assume these researchers were trying their best. They were playing by the rules. Not their fault that the rules were wrong. Statistics is hard, like basketball or knitting. As I wrote a few months ago, I think we have to accept statistical incompetence not as an aberration but as the norm. Doing poor statistical analysis doesn’t make Katherine DeCelles and Michael Norton bad people, any more than I’m a bad person just cos I can’t sink a layup.

tl;dr summary

NPR will love this paper. It directly targets their demographic of people who are rich enough to fly a lot but not rich enough to fly first class, and who think that inequality is the cause of the world’s ills.

P.S. I was unfair to NPR. See here.

The post Ahhhh, PPNAS! appeared first on Statistical Modeling, Causal Inference, and Social Science.

I included this footnote in a paper in which I mentioned that the number of partitions of the empty set is 1 (every member of any partition is a non-empty set, and of course every member of the empty set is a non-empty set):

"Perhaps as a result of studying set theory, I was surprised when I learned that some respectable combinatorialists consider such things as this to be mere convention. One of them even said a case could be made for setting the number of partitions to 0 when $n=0$. By stark contrast, Gian-Carlo Rota wrote in [Rota2], p.~15, that 'the kind of mathematical reasoning that physicists find unbearably pedantic' leads not only to the conclusion that the elementary symmetric function in no variables is 1, but straight from there to the theory of the Euler characteristic, so that 'such reasoning does pay off.' The only other really sexy example I know is from applied statistics: the non-central chi-square distribution with zero degrees of freedom, unlike its 'central' counterpart, is non-trivial."

The cited paper was: G-C. Rota, Geometric Probability, Mathematical Intelligencer, 20 (4), 1998, pp. 11–16. The paper in which my footnote appears is the first one you see here, doi: 10.37236/1027.

Question: What other really gaudy examples are there?

Some remarks:

• From one point of view, the whole concept of vacuous truth is silly. It is a counterintuitive but true proposition that Minneapolis is at a higher latitude than Toronto. "Ex falso quodlibet" (or whatever the Latin phrase is) and so if you believe Toronto is a more northerly locale than Minneapolis, it will lead you into all sorts of mistakes like $2 + 2 = 5$, etc. But that is nonsense.

• From another point of view, in its proper mathematical context, it makes perfect sense.

• People use examples like propositions about all volcanoes made of pure gold, etc. That's bad pedagogy and bad in other ways. What if I ask whether all cell phones in the classroom have been shut off? If there are no cell phones in the room (that is more realistic than volcanoes made of gold, isn't it??) then the correct answer is "yes". That's a good example, showing, if only in a small way, the utility of the concept when used properly.

• I don't think it's mere convention that the number of partitions of the empty set is 1; it follows logically from some basic things in logic. Those don't make sense in some contexts (see "Minneapolis", "Toronto", etc., above) but in fact the only truth value that can be assigned to "$F\Longrightarrow F$" or "$F\Longrightarrow T$" that makes it possible to fill in the truth table without knowing the content of the false proposition (and satisfies the other desiderata?) is $T$. That's a fact whose truth doesn't depend on conventions.

The processing of interoceptive signals in the insular cortex is thought to underlie self-awareness. However, the influence of interoception on visual awareness and the role of the insular cortex in this process remain unclear. Here, we show in a series of experiments that the relative timing of visual stimuli with respect to the heartbeat modulates visual awareness. We used two masking techniques and show that conscious access for visual stimuli synchronous to participants' heartbeat is suppressed compared with the same stimuli presented asynchronously to their heartbeat. Two independent brain imaging experiments using high-resolution fMRI revealed that the insular cortex was sensitive to both visible and invisible cardio–visual stimulation, showing reduced activation for visual stimuli presented synchronously to the heartbeat. Our results show that interoceptive insular processing affects visual awareness, demonstrating the role of the insula in integrating interoceptive and exteroceptive signals and in the processing of conscious signals beyond self-awareness.

SIGNIFICANCE STATEMENT There is growing evidence that interoceptive signals conveying information regarding the internal state of the body influence perception and self-awareness. The insular cortex, which receives sensory inputs from both interoceptive and exteroceptive sources, is thought to integrate these multimodal signals. This study shows that cardiac interoceptive signals modulate awareness for visual stimuli such that visual stimuli occurring at the cardiac frequency take longer to access visual awareness and are more difficult to discriminate. Two fMRI experiments show that the insular region is sensitive to this cardio–visual synchrony even when the visual stimuli are rendered invisible through interocular masking. The results indicate a perceptual and neural suppression for visual events coinciding with cardiac interoceptive signals.

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Author(s): T. Zhang, Duanduan Wan, J. M. Schwarz, and M. J. Bowick

Sheets of liquid droplets can spontaneously and reversibly change their shape.

[Phys. Rev. Lett. 116, 108301] Published Wed Mar 09, 2016

We see so few popular science books on computer science, particularly outside of crypto and theory. Pedro Domingos' The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake the World, despite the hyped title and prologue, does a nice job giving the landscape of machine learning algorithms and putting them in a common text from their philosophical underpinnings to the models that they build on, all in a mostly non-technical way. I love the diagram he creates:

Working out from the inner ring are the representations of the models, how we measure goodness, the main tool to optimize the model and the philosophies that drove that model. The book hits on other major ML topics including unsupervised and reinforcement learning.

In the bullseye you can see the "Master Equation" or the Master Algorithm, one learning algorithm to rule them all. The quest for such an algorithm drives the book, and Domingos describes his own, admittedly limited attempts, towards reaching that goal.

I diverge from Domingos in whether we can truly have a single Master Algorithm. What model captures all the inner-ring models above: circuits. A Master Algorithm would find a minimum-sized circuit relative to some measure of goodness. You can do that if P = NP and while we don't think circuit-minimization is NP-hard, it would break cryptography and factor numbers. One of Domingos' arguments states "If we invent an algorithm that can learn to solve satisfiability, it would have a good claim to being the Master Algorithm". Good luck with that.

A multidimensional financial system could provide benefits for individuals, companies, and states. Instead of top-down control, which is destined to eventually fail in a hyperconnected world, a bottom-up creation of value can unleash creative potential and drive innovations. Multiple currency dimensions can represent different externalities and thus enable the design of incentives and feedback mechanisms that foster the ability of complex dynamical systems to self-organize and lead to a more resilient society and sustainable economy. Modern information and communication technologies play a crucial role in this process, as Web 2.0 and online social networks promote cooperation and collaboration on unprecedented scales. Within this contribution, we discuss how one dimension of a multidimensional currency system could represent socio-digital capital (Social Bitcoins) that can be generated in a bottom-up way by individuals who perform search and navigation tasks in a future version of the digital world. The incentive to mine Social Bitcoins could sustain digital diversity, which mitigates the risk of totalitarian control by powerful monopolies of information and can create new business opportunities needed in times where a large fraction of current jobs is estimated to disappear due to computerisation.

Group discussions are essential for organizing every aspect of modern life, from faculty meetings to senate debates, from grant review panels to papal conclaves. While costly in terms of time and organization effort, group discussions are commonly seen as a way of reaching better decisions compared to solutions that do not require coordination between the individuals (e.g. voting)---through discussion, the sum becomes greater than the parts. However, this assumption is not irrefutable: anecdotal evidence of wasteful discussions abounds, and in our own experiments we find that over 30% of discussions are unproductive.

We propose a framework for analyzing conversational dynamics in order to determine whether a given task-oriented discussion is worth having or not. We exploit conversational patterns reflecting the flow of ideas and the balance between the participants, as well as their linguistic choices. We apply this framework to conversations naturally occurring in an online collaborative world exploration game developed and deployed to support this research. Using this setting, we show that linguistic cues and conversational patterns extracted from the first 20 seconds of a team discussion are predictive of whether it will be a wasteful or a productive one.

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Criminal convictions shouldn't follow anyone around for the rest of their lives, in any way.

RICHMOND, Va. (AP) — More than 200,000 convicted felons will be eligible to vote and run for public office in Virginia under a sweeping executive order announced Friday by Democratic Gov. Terry McAuliffe.

McAuliffe said his actions would help undo Virginia's long history of trying to suppress the black vote.

And kudos for acknowledging the explicitly racial (racist) element of this.

The post The Number of Publicy Traded Firms Has Halved appeared first on Marginal REVOLUTION.

The Intercept’s Lee Fang discusses his recent exposé on how In-Q-Tel, the venture capital arm of the Central Intelligence Agency, is funding the manufacturer of Clearista, a popular beauty product. Clearista’s parent company, Skincential Sciences, has developed a patented technology that removes a thin outer layer of the skin, revealing unique biomarkers that can be used for a variety of diagnostic tests, including DNA collection.

Der and Martius suggest that a novel plasticity rule can explain the development of sensorimotor intelligence, without having to postulate higher-level constructs such as intrinsic motivation, curiosity, or a specific reward system.  This seems to me to be groundbreaking and fascinating work. I pass on their overview video, and then some context from their introduction, which I recommend that you read.  Here is their abstract. (I don't even begin to understand the description of their feed-forward controller network and humanoid robot, which follows a “chaining together what changes together” rule. I can send motivated readers a PDF of the whole article with technical details and equations.)

 

Research in neuroscience produces an understanding of the brain on many different levels. At the smallest scale, there is enormous progress in understanding mechanisms of neural signal transmission and processing. At the other end, neuroimaging and related techniques enable the creation of a global understanding of the brain’s functional organization. However, a gap remains in binding these results together, which leaves open the question of how all these complex mechanisms interact. This paper advocates for the role of self-organization in bridging this gap. We focus on the functionality of neural circuits acquired during individual development by processes of self-organization—making complex global behavior emerge from simple local rules.

Donald Hebb’s formula “cells that fire together wire together” may be seen as an early example of such a simple local rule which has proven successful in building associative memories and perceptual functions. However, Hebb’s law and its successors...are restricted to scenarios where the learning is driven passively by an externally generated data stream. However, from the perspective of an autonomous agent, sensory input is mainly determined by its own actions. The challenge of behavioral self-organization requires a new kind of learning that bootstraps novel behavior out of the self-generated past experiences.

This paper introduces a rule which may be expressed as “chaining together what changes together.” This rule takes into account temporal structure and establishes contact to the external world by directly relating the behavioral level to the synaptic dynamics. These features together provide a mechanism for bootstrapping behavioral patterns from scratch.

This synaptic mechanism is neurobiologically plausible and raises the question of whether it is present in living beings. This paper aims to encourage such initiatives by using bioinspired robots as a methodological tool. Admittedly, there is a large gap between biological beings and such robots. However, in the last decade, robotics has seen a change of paradigm from classical AI thinking to embodied AI which recognizes the role of embedding the specific body in its environment. This has moved robotics closer to biological systems and supports their use as a testbed for neuroscientific hypotheses.

We deepen this argument by presenting concrete results showing that the proposed synaptic plasticity rule generates a large number of phenomena which are important for neuroscience. We show that up to the level of sensorimotor contingencies, self-determined behavioral development can be grounded in synaptic dynamics, without having to postulate higher-level constructs such as intrinsic motivation, curiosity, or a specific reward system. This is achieved with a very simple neuronal control structure by outsourcing much of the complexity to the embodiment [the idea of morphological computation].

After all, if a character isn’t written as gay, then that character can’t possibly be gay, right? We all agree on that? Good, then we can move on to more important matters, and…

… Sorry? Was there a comment in the back?

… Yes, you, Grant Morrison, writer of several Batman comics (Arkham Asylum, JLA, Batman, Batman Inc.) over the course of the past three decades? You had something you wish to add? Something you said to Playboy magazine in 2012?

Gayness is built into Batman.

… Um.

Batman is VERY, very gay.  

OK great super helpful thanks for that—

Obviously as a fictional character he’s intended to be heterosexual…

Yes! My point! THANK you. Now—

… but the whole basis of the concept is utterly gay.

You can read more at a very interesting article at Slate.

Even if a Democrat wins the presidency -

Why not put another beloved, big story in play and consider whether the House might flip? There is one very good reason: It is not going to happen.

One hesitates to call anything impossible during a campaign season that has upended so much historical wisdom. Nevertheless, this is impossible. But if we’re going to have seven more months of debating whether the Democrats have even the tiniest chance of capturing the House, it is important to understand all the politics and recent history which explains why it’s off the table, even if Trump leads the GOP into an epic rout at the presidential level...

...how sophisticated the GOP redistricting operation was in 2010 and 2011 — and how it has made our politics more extreme both in the House and in many state legislatures. It was different, perhaps historically so, thanks to driven GOP strategists determined to take full advantage of redistricting, new mapping and demographic technologies that made it easier than ever to craft unbeatable GOP majorities, and the wave of post-Citizens United dark money which helped fund it. They called it REDMAP, for Redistricting Majority Project, and did it ever live up to its name...

This Pennsylvania district, the 7th [inset at right], explains a lot if you want to understand just how precisely mapmakers did their work after 2010. Every one of these lines — described by some as Donald Duck kicking Goofy — exists to draw specific Republicans into this district, and to make as many surrounding districts as Republican as possible. Then, mapmakers packed so many Democrats into Chaka Fattah’s Philadelphia district that he won with more votes than any congressman in the country in 2012...

Let’s keep all of these numbers and the reality of these maps in mind when talking about the prospect of Democratic control over the next few months. Any piece or cable news discussion on this topic that does not include REDMAP or understand how the 2011 redistricting was different and more advanced than any that came before isn’t just missing part of the story. It’s missing the entire story, and engaging in punditry as fantasy.

A remarkable (and counterintuitive) graph -

The US economy keeps expanding and the population keeps growing. But we actually use less water now for all purposes than we did back in 1970. That includes freshwater for our showers and toilets. It includes farm irrigation. It also includes withdrawals of both fresh and saline water to cool our fossil fuel and nuclear power plants.

The underlying data comes from a new report by the US Geological Survey, which notes that water for power plants (45 percent) and irrigation (33 percent) still made up most water withdrawals in the US as of 2010. But use in both of those areas has been declining over time.

More at Vox, including an explanation of "withdrawal" vs. "consumption."

Twin primes are much beloved. But a computer search has shown that among numbers less than a trillion, most common distance between successive primes is 6. It seems this goes on for quite a while longer…

… but Andrew Odlyzko, Michael Rubinstein and Marek Wolf have persuaded most experts that somewhere around x=1.7427×10 35x = 1.7427 \times 10^{35}, the most common gap between consecutive primes less than xx switches from 6 to 30:

• Andrew Odlyzko, Michael Rubinstein, and Marek Wolf, Jumping champions, Experimental Mathematics 8 (1999), 107–118.

This is a nice example of how you may need to explore very large numbers to understand the true behavior of primes.

They give a sophisticated heuristic argument for their claim—not a rigorous proof. But they also checked the basic idea using Maple’s ‘probable prime’ function. It takes work to check if a number is prime, but there’s a much faster way to check if it’s probably prime in a certain sense. Using this, they worked out the gaps between probable primes from 10 3010^{30} and 10 30+10 710^{30}+10^7. They found that there are 5278 gaps of size 6 and just 5060 of size 30. They also worked out the gaps between probable primes from 10 4010^{40} and 10 40+10 710^{40}+10^7. There were 3120 of size 6 and 3209 of size 30.

So, it seems that somewhere between 10 3010^{30} and 10 4010^{40}, the number 30 replaces 6 as the most probable gap between successive primes!

Using the same heuristic argument, they argue that somewhere around 10 45010^{450}, the number 30 ceases to be the most probable gap. The number 210 replaces 30 as the champion—and reigns for an even longer time.

Furthermore, they argue that this pattern continues forever, with the main champions being the ‘primorials’:

2 2

2⋅3=6 2 \cdot 3 = 6

2⋅3⋅5=30 2 \cdot 3 \cdot 5 = 30

2⋅3⋅5⋅7=210 2 \cdot 3 \cdot 5 \cdot 7 = 210

2⋅3⋅5⋅7⋅11=2310 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 = 2310

etc.

There will come soft rains and the smell of the ground,
And swallows circling with their shimmering sound;

And frogs in the pools, singing at night,
And wild plum trees in tremulous white,

Robins will wear their feathery fire,
Whistling their whims on a low fence-wire;

And not one will know of the war, not one
Will care at last when it is done.

Not one would mind, neither bird nor tree,
If mankind perished utterly;

And Spring herself, when she woke at dawn,
Would scarcely know that we were gone.

Found while re-reading Ray Bradbury's The Martian Chronicles.  I find it interesting that Sara Teasdale gave voice to this postapocalyptic scenario twenty-five years before the invention of nuclear weapons.

Both the Donald and Bernie get shit for supposedly not having appropriate "foreign policy teams." The Foreign Policy Community in DC is really where the Very Serious People live. They're the deep state, and if you say the wrong thing Fred Hiatt will let them plant an op-ed about how unserious you are. They're the nexus of the security state, the military industrial complex, and international oligarchs. Big War, Big Finance, Big Exploitation, Big Tax Avoidance, Big Assholes.

Not saying that one should be ignorant about foreign affairs, just that one should not take advice from the Very Serious People who for some reason are in charge of dispensing it. Not clear they know anything about anything anyway.

The brain routinely discovers sensory clues that predict opportunities or dangers. However, it is unclear how neural learning processes can bridge the typically long delays between sensory clues and behavioral outcomes. Here, I introduce a learning concept, aggregate-label learning, that enables biologically plausible model neurons to solve this temporal credit assignment problem. Aggregate-label learning matches a neuron’s number of output spikes to a feedback signal that is proportional to the number of clues but carries no information about their timing. Aggregate-label learning outperforms stochastic reinforcement learning at identifying predictive clues and is able to solve unsegmented speech-recognition tasks. Furthermore, it allows unsupervised neural networks to discover reoccurring constellations of sensory features even when they are widely dispersed across space and time. Author: Robert Gütig

As you may remember from an earlier post on this blog, Discrete Analysis is a new mathematics journal that runs just like any other journal except in one respect: the articles we publish live on the arXiv. This is supposed to highlight the fact that in the internet age, and in particular in an age when it is becoming routine for mathematicians to deposit their articles on the arXiv before they submit them to journals, the only important function left for journals is organizing peer review. Since this is done through the voluntary work of academics, it should in principle be possible to run a journal for almost nothing. The legacy publishers (as they are sometimes called) frequently call people naive for suggesting this, so it is important to have actual examples to prove it, and Discrete Analysis is set up to be one such example. Its website goes live today.

We have decided to splash out and use a publishing platform called Scholastica. Scholastica was founded in 2011 by some University of Chicago graduates who wanted to disrupt the current state of affairs in academic publishing by making it very easy to create electronic journals. I say “splash out” because they charge $10 per submission, whereas there are other ways of creating electronic journals that are free. But we have got a lot for that $10, as I shall explain later in this post, and the charge compares favourably, to put it mildly, with the article processing charges levied by more traditional publishers. (An example: if you have had an article accepted by the Elsevier journal Advances in Mathematics, the price you need to pay to make that article open access is $1500; the same amount of money would cover 100 submissions to Discrete Analysis. I didn’t say 150 because there are some small further costs we incur, such as a subscription to CrossRef, which enables us to issue DOIs to our articles.) Most importantly, we do not pass on even this $10 charge to authors, as we have a small fund that covers it.

Now that we have been handling submissions for almost six months, we have been forced to make decisions that leave us with a rather clearer idea about what the scope and standards of the journal are. As far as the scope is concerned, we want to be reasonably broad. For example, the analysis in the paper by Tuomas Hytönen, Sean Li and Assaf Naor is not really discrete in any useful sense, but we judged it to have a similar spirit to the kind of papers that fit the title of the journal more obviously by treating discrete structures using analytic tools. Our rough policy is that if a paper is good enough, then we will not be too worried about whether it has the right sort of subject matter, as long as it isn’t in an area that is completely foreign to the editorial board.

As for the quality, we have been surprised and gratified by the high standard of submissions we have received, which has allowed us to set a high bar, turn away some perfectly respectable papers, and establish Discrete Analysis as a distinctly good journal.

That is an important part of our mission, because we want to show that the cheapness of running the journal is completely compatible with high quality. And that does not just mean mathematical quality. One thing I hope you will notice is that the journal’s website is far better designed than almost any other website of a mathematics journal. This design was done by the Scholastica team for no charge (I think they see it as an investment, since they would like to attract more journals to their platform), and it satisfies various requirements I felt strongly about: for example, that it should be attractive to look at, that one should be able to explore the content of the journal without undue clicking and loading of new pages, and that it would be able to handle basic LaTeX. But it has other features that I did not think of, such as having an image associated with each article (which seems pointless until you actually look at the site and see how the image makes it easier to browse and more tempting to find out about the article) and making the site work well on your phone as well as your laptop. If you compare it with, say, the website of Forum of Mathematics, Sigma, it’s like comparing a Rolls Royce with a Trabant, except that someone has mischievously exchanged the price tags. (Let me add here that there are many good things about Forum of Mathematics. In particular, its editorial practices have been a strong influence on those of Discrete Analysis. And it is far from alone in having an unimaginative and inconvenient website.)

Since I am keen to promote the arXiv overlay model, I was also particularly concerned that Discrete Analysis should not be perceived as “just like a normal journal, but without X, Y and Z”. Rather, I wanted it to be better than a normal journal in important respects (and at least equal to a normal journal in all respects that anyone actually cares about). If you visit the website, you will notice that each article gives you an option to click on the words “Editorial introduction”. If you do so, then up comes a description of the article (not on a new webpage, I hasten to add), which sets it in some kind of context and helps you to judge whether you might want to go ahead and read it on the arXiv.

There are at least two reasons for doing this. One is that if the website were nothing but a list of links, then there would be a danger that it would seem a bit pointless: about the only reason to visit it would be to check that when an author claims to have been published by us, then that is actually true. But with article descriptions and a well-designed website, one can actually browse the journal. Browsing is something I used to enjoy doing back when print journals were all that there were, but it is quite a lot harder when everything is electronic. (Some websites try to interest you in related content, but it seems to be chosen by rather unsophisticated algorithms, and in any case is not what I am talking about — I mean the less focused kind of browsing where you stumble on an interesting paper that neither you nor an algorithm based on your browsing history would ever have thought of looking at.)

A second reason is that having these introductions goes a small way towards dealing with a serious objection to the current system of peer review, which is that a great deal of valuable information never gets made public. As an editor, I sometimes get to read very interesting information that puts a submitted article into a context that I didn’t know about. All the reader of the journal gets is one bit of information: that the article was accepted rather than rejected. (One could argue that it isn’t even one bit, since we do not learn which articles have been rejected.) Of course, under cover of privacy and anonymity, referees can also make remarks that one would not want to make public, but with article descriptions we don’t have to. We can simply write the descriptions using information from the article itself, prior knowledge, remarks made by the referees, remarks made by editors, relevant facts discovered from the internet, and so on. And how this information is selected and combined can vary from article to article, so the reader won’t know whether any particular piece of information was part of a referee’s report.

Thus, Discrete Analysis is offering services that other journals do not offer. Here’s another one. Suppose you submit an article to Discrete Analysis and we accept it. The next stage is for you to submit a revision to arXiv, taking account of the referee’s comments. Once that’s done, we make sure we have an editorial introduction and appropriate metadata in place, and publish it. But what if at some later date you suddenly realize that there is a shorter and more informative proof of Lemma 2.3? With the conventional publishing system, that’s basically just too bad: you’re stuck with the accepted version.

In a way that’s true for us too. The version that’s accepted becomes what people like to call the version of record, so that when people refer to your paper there won’t be any confusion about what exactly they are referring to. (This is important of course, though in my view the legacy publishers massively exaggerate its importance.) However, being an arXiv overlay journal allows us to reach a much more satisfactory compromise between having a fixed version of record and allowing updates. If you follow the link from the journal webpage to the article and the article has subsequently been updated, the arXiv page you link to will inform you that the version you are looking at is not the latest one. So without our having to do anything, since it happens automatically with the arXiv, readers get the best of both worlds. As an example, here is the arXiv page for a version of a preprint by Bourgain and Demeter (not submitted to Discrete Analysis). As you’ll see, the information that it is not the latest version is clearly highlighted in red.

Another feature of Discrete Analysis, but this one it shares with other purely electronic journals, is that we are not artificially constrained by the need to fill a certain number of pages per year. So you will not hear from us that we receive many more good articles than we can accept, or that your article, though excellent, is too long — we just have a standard we are aiming for and will accept all articles that we judge to reach it.

So if you have a good paper that could conceivably be within our scope, then why not submit it to us? Your paper will have some very good company (just look at the website if you don’t believe me). It will be properly promoted on a website that embraces what the internet has to offer rather than merely being a pale shadow of a paper journal. And you will be helping, in a small way, to bring about a change to the absurdly expensive and anachronistic system of academic publishing that we still have to put up with.

We develop a general duality between neural networks and compositional kernels, striving towards a better understanding of deep learning. We show that initial representations generated by common random initializations are sufficiently rich to express all functions in the dual kernel space. Hence, though the training objective is hard to optimize in the worst case, the initial weights form a good starting point for optimization. Our dual view also reveals a pragmatic and aesthetic perspective of neural networks and underscores their expressive power.

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