Aside from the issues that I had with my adviser, graduate school was a really great place. When I first started out, however, I was overwhelmed, because I was placed on a very, very large grant project and given a very complex, open-ended mathematical task to complete with little direction. To make matters worse, no one on the project told me what they expected of me, where I should pick up relevant information, what journals I should be reading, who I could possibly collaborate with, how long I had to complete certain objectives, and so on. As well, they assumed I joined the project with a deep knowledge of probability and statistics, which I didn't have (and they should have known, considering that I mentioned it to them several times during the interview process), since all of my undergraduate coursework was on the hardware side of electrical and computer engineering.

In any event after a few months of floundering, banging my head against the wall, bringing myself up to speed, slogging through classes, and just trying to find the time to go out and meet people, I heard that I was accepted into medical school and also was set to receive a fellowship. As if by magic, all of my worries melted away with that news, since I wouldn't have to rely on my position on the grant to pay for tuition or my shoebox-sized apartment, I could afford to go out to eat, and would ultimately have much more freedom with regards to how many classes I took or how much free time I could allot myself. In fact, looking back, I really made the most of those 5 years of funding, as I had enough time off to meet a lot of new friends (something I didn't do when I was an undergraduate, since I spent all of 2 years, after high school, on my S.B. EE), was able to travel the world, see new places, experience new foods and cultures, could afford to take whatever classes I wanted without question (I loaded up on math, biology, neuroscience, and statistics courses during my off-years of medical school), could work on any research projects, and, overall, just enjoy life.

While I did relish all of that freedom, one of the biggest hurdles I ran into was publishing on my own, as I had no collaborators and was fairly isolated due to my fellowship. Instead of sticking it out and spending 2-4 months per journal paper, I decided that it would nice if I could offload some of the work, give up some credit, and churn out journal papers every 3-4 weeks (under a light class load). Initially, I tried doing this with one of my publishing-inclined peers, but I ended up having a huge argument with him, as he tried to usurp ownership of an idea (despite contributing only a small proof that turned out to be wrong and unmendable) and publish it on his own at some conference. Eventually, I thought that it would be good try collaborating on a grant project again, as there would be a bit more oversight and I could avoid having someone trying to claim ownership of my work. Unfortunately, I made a big mistake when I mentioned this desire to my adviser (who had the authority to cut the strings on my fellowship after 4 years) and he effectively strong-armed me into working on his grants if I wanted to keep my fellowship. (The only upshot to that arrangement with him was that he had to pay me by the hour, to get around the fellowship restrictions, so I ended up making almost as much as the assistant professors in the electrical engineering department my final year there.)

In any event, after my entire ordeal with him and the justice system, I had the option of going back, getting another adviser, and paying to finish a Ph.D./M.D. Instead, I opted to head back to my alma mater for a bit, to build up my network of contacts and find people to write letters of recommendation, before transferring to a better school. Fortunately, with my body of coursework and publications, I was able to test out of the classes that were similar to ones I had taken before or was able to write a journal paper with the professor to "demonstrate" my knowledge of the subject matter. As well, I was able to find a younger, MUCH better adviser that time around, who recognized that I was a paper-writing fiend (which helped with building up his case for tenure) and just threw a bunch of money and support at me so that I would keep publishing.

Since graduating, I've had a fair number of opportunities ranging from becoming a tenure-track professor or a research professor to taking a job out in industry doing biostatistics work or designing hardware. However, despite all of my problems I had with academia, I truly enjoy the environment, let alone publishing, researching, and sometimes teaching.

A good majority of the mathematical work that I do is relatively simple compared to the stuff you'd find in some of the higher-end SIAM journals, Journal of Differential Geometry, Geometry and Topology, Journal of Algebraic Geometry, etc. For instance, in a typical paper that I send to engineering journals, e.g., various IEEE/ACM Transactions, the most I'll end up doing is: (i) constructing a Gibbs, reversible-jump Markov chain Monte Carlo, or variational Bayes sampler for a generative model (the latter of which just involves taking some derivatives), (ii) proving some simple properties about a statistical model (such as its mean and variance, that one can obtain a predictive formula through marginalization, or that it behaves a certain way, which basically amount to taking some anti-derivatives and recalling basic probability assumptions), or (iii) possibly giving a convergence proof of a method to show that the iterates tend to a local optimum (which relies on modifications of standard nonlinear programming results like from Zangwill, transforming the method into a contractive fixed-point algorithm, etc.). All-in-all, the amount of work usually takes a day or two to complete on my own.

Now, there will be times where I break out of this mold and actually flex my mathematical muscles. A recent example of this is a paper that I just submitted that provided a means of simplifying the algorithmic complexity of a method by casting the underlying computational problem on a very special kind of manifold (which, unfortunately, resisted simple analysis). In order to finish the paper (which was a relatively short 30 pages) I ended up having to translate and rework the concepts in several differential geometry books and papers (which made for a 150 page appendix) to ensure that all of the derivations my work relied on were correct. While I can't remember exactly when I began on the project, I believe it took approximately a year to complete, along with the input and help of a few mathematicians.

If you don't mind waiting about 12-ish hours for me to respond, I'll be happy to do so then!

I also happened to omit lots of details about my adviser and painted a rather one-sided story above.

Touching on what you said, though, my adviser got to where he was at through hard work and perseverance during the first 25 years of his career. In fact, he was one of the top five researchers in a rather large field, which is why I went to work with him in the first place.

In any event, the problem wasn't that he was desperate, that the environment was too competitive, that he was a cheater, or that the school wasn't selective enough in choosing him so many years ago for a faculty position. The problem was that once he became famous, and hence was tenured with a named professorship, had offers to transfer to places like Dartmouth, etc., there was no need for him to produce anything of substance. That is, he was finally able, after 25 years, to finally sit back and let his well-oiled machine run its course without much hands-on involvement. For example, he had his pick of the top students and didn't need to spend much time grooming them and could instead turn them loose on problems and expect to them to write up and publish their papers in his pet conferences and journals. He also was able to join some of the upper level scientific committees that would spend an inordinate amount of money to fly him, and other members out, to various high-profile spots so they could recount stories, get free food, and do only the minimal amount of work necessary at the meetings to justify the need for a face-to-face trip. As well, he had joint departmental appointments out the wazoo, had tons of perks through the university, was insulated from politics, and really had nothing to worry about once he became an emeritus professor and eventually retired, as he would be making around $110k/yr at that point just for showing up every so often and wandering the halls.

Of course, with all of this, my adviser slowly started to distance himself from doing actual research, i.e., proving theorems, writing papers, and possibly designing and running experiments. From what I can tell, I think he actually forgot how to do any of it and pushed himself back into the fray when I showed up and started publishing like crazy. Further, I'm sure it was incredibly disconcerting, from his point of view, to have some young 20 outdoing him, ignoring his input (since he was incredibly out of touch with the state of the art), and so forth. (Had there had been safeguards in place to ensure that he was forced to do a certain amount of original, top-quality work on his own, though, I'm certain that our contention could have been avoided.)

It was rather bad.

To preface everything, my adviser was around 65 years old and nearing retirement, whereas I came into the Ph.D. program way too early (at 19) and was treated very differently from the rest of his students (who were 29-35 years old) almost at the get-go, but definitely after being there for four years. For instance, he would talk down to me, saying that I was a kid and wouldn't be able to understand something, or would belittle my work, despite not having authored a paper on his own or done anything but managerial tasks in over 10 years. Heaven forbid if I made a mistake when proving a theorem or in not exhaustively completing a task: he would never let me forget about it and would bring it up at any moment it suited him, especially to call into question the validity of heavy mathematical work that I was going to publish on my own or to question why I had time for pursuing other endeavors beyond those he paid me to do for 20 hours per week. The only reason I put up with his bullshit for so long was that he was paying me incredibly well for a research assistant ($35000/yr) and basically gave me a fellowship that waived both my grad. tuition and my M.D. tuition (which would have saved me something like $400k overall).

Ultimately, from what I've corroborated from other sources, this guy was rather jealous of my ability to work, without supervision, on whatever suited my interests, have my papers accepted in better venues (not because I was smarter, just that I knew the value of presentation, getting 3d artists to make my graphics and figures, etc.), live in a relatively care-free environment, be able to travel on a whim to conferences, regard him as a manager/peer and not as someone who was a "better" researcher, and so forth. Since he was nearing retirement age, these issues were even more poignant, and he took on more responsibilities to prove to himself that he still "had it." Unfortunately for him, the more duties he picked up, the less time he had for actually doing anything remotely research-oriented and the more he became jealous of my infinite free time and the 50 hours per week that I'd spend on my research.

Eventually, due to all of these bottled-up feelings, he exploded into a profanity-laden tirade and lashed out at me during one seemingly routine one-on-one sit down where I was presenting my work for one of his grant projects. Needless to say, I wasn't keen to stick around after all of that and sought to move up to a much better school. However, I was fairly distraught to find that I was rejected from all of the schools I had applied to, despite being sole or lead author on every paper and only publishing in top-tier journals and having a better overall profile than students already in the Ph.D. programs at those schools; later, I found out that he had a hand in unduly blocking my admission, as he basically wrote the letter of recommendation, if you could even call it that, for a junior professor I had tapped, which precipitated my legal action against him.

With regards to your situation, if you want to go back to graduate school, I would recommend taking some time out to publish on your own, depending upon your field, even if you can't target the top-tier journals. For example, if you're in computer science or engineering, there are plenty of topics that you can work on that only require access to literature (which you can often get through friends at a university or by signing up for a 0 credit hour class for a semester), a decent computer, MATLAB/C/C++ programming knowledge, and some creativity.

It's definitely not a problem! I only wish someone had done the same for me, or, rather, that I had the foresight, to uncover some of these points early on, as it would have saved me 3 or so years of time.

In any event, there are a few things I forgot to add:

- As a student, you are basically free to go up to famous people at conferences and talk to them (I don't know how prevalent conferences are in physics, but they're very common in engineering/computer science). Use this to your advantage to network, ask about lab openings, about going to the school, etc., as, once you graduate and become a postdoc or faculty member, this becomes harder to do (at least from what I've been seen or told) unless you're already in their social group by proxy or are famous too. (As an anecdote, when I was at a biologically-themed conference a few years ago, I had the chance to talk with one of the former editors in chief of a top neuroscience journal, told him how cool his research was, and wished that I had time to break away from my area to dabble in his, even if it was just analyzing data or doing a bunch of grunt work,which I normally hate to do outside of a bio-laboratory setting. Rather surprisingly, he offered me a paid summer position in his lab, on the spot, and even paid for me to visit, tour the lab, and meet his students to get a handle on what I could do to help out before I settled in that summer.)

- From what I've seen, students with dual technical Bachelors degrees, especially in areas that don't heavily overlap, e.g., Computer Science and Mathematics or Electrical Engineering and Bioengineering, tend to have a better chance of being accepted to high-ranking schools when coming from non-high-ranking ones; my conjecture is that it shows the admissions committee that you have the capacity to successfully learn two very different sets of skills and hence are more likely to do well in the future. As such, if you have the opportunity/funding to pursue another undergraduate degree, it would definitely be prudent to do so, as I mentioned above, especially because it gives you more time to secure internships and will allow you to get your feet wet with research. For example, since your S.B. is in Physics, you could pursue an A.B. Mathematics, an S.B. Electrical/Computer/Bio/etc. Engineering, or an S.B. Computer Science.
If you do the dual Bachelors route, since you want to go into physics, it would be best to ask your physics professors about undergraduate research opportunities while pursuing the other degree. Be sure and mention to them that they don't necessarily need to pay you, but that you're wanting to explore the possibility of a research career and publish. If you do this, there will likely be a line of professors waiting to snatch you up and will be willing to write you a very strong letter of recommendation once you graduate.

- Another thing worth noting is that you should make friends with either English majors or people with strong technical writing skills and a very strong grasp of grammar: these individuals will be ultimately invaluable for helping you scan over your publications, before they're submitted, and making any corrections that improve clarity. At the same time, it won't hurt to take a technical writing class, provided you haven't already.

Anything related to math, e.g., applied maths, theoretical maths, and statistics, is in high demand in finance, let alone other sectors, especially if you've got a base degree or focus that matches, e.g., an S.B./S.M. Bioengineering/Biology or an M.D. if you want to do principled biomedical work. In fact, with the right position, you could easily spend all day publishing biostatistics papers in Biometrika, Biometrics, the Journal of the American Statistical Association, and the Journal of the Royal Statistical Society on, say, models that analyze the effects of some treatment or drug under development, yet get paid more than someone doing the same thing in academia.

Touching on your overall concerns and questions, here are a laundry list of things that I found useful during my graduate years, with respect to a career in academia:

- Take some time to really figure out what you want to study and, ultimately, do in the future while you're in graduate school. If you don't have a firm plan, it's not a bad idea to stay in graduate school longer, provided you have grant funding from your adviser or a fellowship, to pursue other options or investigate other disciplines.

- If you are committed to being a researcher, figure out why the top scientists are where they're at today and maneuver yourself accordingly. For example, within machine learning, people like Michael Jordan, David Blei, Zoubin Ghahramani, Bill Freeman, etc. are successful because they have a somewhat strong statistical background and statistics makes up a large portion of prominent pattern recognition schemes; if you were in, say, computer science or electrical engineering and wanted to be a prominent contributor to the field, it would probably be wise to pursue an S.M./Ph.D. Statistics or an S.M./Ph.D. Applied Math to ensure that your skill set is highly developed. With respect to condensed particle physics, on the theoretical side, you'd probably be well-served by pursuing an S.M. Mathematics, with a focus in differential geometry, topology, and algebra, while, on the practical side, having some programming knowledge wouldn't hurt.

- If you're wanting to do research within academia, determine, as early as possible, where you would ultimately like to obtain a faculty position. This will dictate where you should complete your terminal degree, since, once you graduate, unless you do some incredibly amazing work in your early years, happen to work with someone very famous, or are nearing retirement with a large body of work, you will mostly be constrained to moving laterally, slightly up, or down compared to your alma mater's ranking. As an example, if you want to work at Stanford, it'd likely be good to do your Ph.D. at either Stanford, UIUC, MIT, Harvard, Cornell, or UC-Berkeley.

- If you're unable to get into a really good school during your first round of graduate applications, and you know that you'd like to teach at one, either settle for a somewhat mediocre school to start out with, especially if they offer you a research assistantship, or pursue a second undergraduate degree at your alma mater. During this time, you should ascertain how the current crop of graduate students at the good schools got admitted. If it was based upon publications, find out what journals the "best" publications are in your field are being sent to and start targeting those venues, if possible, before you reapply. If it was based upon internships, try to do more of those at better institutions/labs. If it was based upon the "old boys network" and recommendations from a trusted source, surreptitiously determine, e.g., by looking at publication records, if anyone you're either working with or that knows you well happens to have either collaborated with someone at or graduated from a better university and if they can put you in touch. (I say surreptitiously because, if you chose the mediocre graduate school route, blatantly asking someone like your committee adviser about moving to better university, especially when that move is still a bit in the future, can cause them to basically yank your assistantship funding away and give it to someone who is going to stay there much longer.)

- It's a good idea to apply for as many graduate fellowships, like from the National Science Foundation, as early as possible, as you may get lucky and have four years of tuition paid for along with a generous living stipend. (Unfortunately, the NSF's process for handing out these fellowships is still a mystery to me, as they'll give one to a non-minority, male EE student at MIT with one publication at a mid-/top-tier conference and skip over the non-minority, male EE student with 20 top-tier journal publications at someplace like Texas A&M or the University of Florida.) Since you won't likely have the chance to apply for fellowships until you start graduate school, be sure and pester departmental faculty, once you're accepted, about a research assistantship. (However, don't ask them for such a position before you are accepted, though, unless you happen to be introduced to them from a known third party, as they get tons of emails from foreign nationals about such matters on a daily basis and those emails go straight into the trash can.)

- Most importantly: never piss off your adviser, as you can quickly find your education sidetracked, your reputation unduly slandered, especially if they are petty and vindictive,, and your chances of easily switching to another school dashed. I ended up inadvertently making that mistake and it derailed my Ph.D. EE and M.D. for two years, forced me to basically redo my both degrees, albeit at a much better institution, and cost a pretty penny to sue him for assault and libel before eventually settling.

I think you meant to reply to the grandparent poster, not my comment.

However, in case you gathered something different from my statements than what I intended, let me clearly state that I am in favor of protecting the speech and expression freedoms of teachers, both in, to a certain degree, and out of the classroom; for example, I don't agree with the ruling of Mayer v. Monroe County Community School Corporation et al., as it set a bad precedent due to, what was, a rather innocuous statement made by an instructor concerning seeking a peaceful solution to the war in Iraq. At the same time, it is difficult to determine what limits should be imposed, if there should even be any at all, given the gamut of views and beliefs held by others and the chances for offending those individuals or their parents.

How could you even begin to assume that I am a liberal and a union supporter (when, in fact, I am not and do not, respectively) merely on the basis of my desire to see that freedom of speech and expression are upheld for public employees?

The fact that you can't spot thinly veiled raillery is adorable. Have a great day!

Hosts files are terrible.

Here's a link to the pre-published manuscript: http://web.mit.edu/~velten/www/corner/corner-prep.pdf, a related manuscript: http://web.mit.edu/~velten/www/corner/arxivoe.pdf, and a technical report: http://dspace.mit.edu/handle/1721.1/67888

Yes, I could imagine playing Gears of War 3, or any other similar, graphically-intensive game, on a tablet. However, I wouldn't expect to physically interact the tablet whilst doing so.

To elaborate on the first part, as smart phones and tablets become more complex and powerful, they will begin to encroach and eventually overlap with the processing and graphical capabilities of consoles. (The PowerVR G6200/G6400, let alone NVIDIA's Tegra offerings and the state-of-the-art devices in the research literature, are a testament to this, from a GPU standpoint. From a CPU one, the quad-core ARMv7 Cortex-A15 handily beats out the triple-core IBM Xenon in the Xbox 360 and the Cell processor in the PS3, in terms of MIPS.) As this happens, there will only be a handful of relatively minor reasons, most of which concern how to handle older, potentially out-dated devices, as to why we could not expect to see quality games ported over to these mobile platforms, let alone have studios change focus and solely push their titles for them.

Now, as for actually playing the games, it's easy to imagine a few scenarios for how this could be done for a variety of titles. One that would work well, in general, would be to interface the tablet or phone with a TV, either through an HDMI connection or perhaps wirelessly through something like the Apple TV, and rely on one or more Bluetooth controllers for input. In this instance, the device is functioning like a console; however, once you're done playing, you can just grab it, take it with you, and revert back to using it for a multitude of other purposes.

What is needed is an architectural paradigm shift, not necessarily a more beefy, faster (single-instruction, multiple-threaded-based) GPU.

To elaborate, with a naive implementation where independent kernels are run in parallel, one of the major bottlenecks for ray/path tracing via GPGPU processing is that every warp, a set of 32 threads, essentially executes the same instruction, with branching realizing by transparently masking out threads; as such, if branching often leads to divergent threads, then there will be low hardware utilization and performance will degrade. With a more robust implementation, you can improve hardware utilization by appropriately partitioning sub-kernels, but you'll run into issues when you start handling secondary rays.

For ray/path tracing to be carried out in an expeditious manner, it would be prudent to move to a programmable multiple-instruction, multiple-threaded (MIMT) architecture with many small cores that can handle many threads. In fact, researchers have been moving in this direction for quite some time now and the results are rather promising: while an NVIDIA GTX 285, which has a die area of around 300mm^2, can handle around 100M primary rays/sec and 60M diffuse rays/sec, with a thread issue rate of ~70% and ~50%, respectively, a custom MIMT ASIC solution, with an area of 200mm^2 at the same fabrication level, can reach around 400M primary and diffuse rays/sec, with a thread issue rate of ~70-80% for both. (As an aside, I have a paper, that's being submitted to either the ACM Trans. Graphics or IEEE Trans. Comp. Graphics and Vis., on an FPGA and theorized ASIC solution that blows these numbers away.)

On top of everything else you have reading comprehension issues. To help make things clear for you, I never said that I owned a hackintosh.

However, I will mention that I assembled my workstation, if you can even classify it as such, and it is far more powerful than a Mac Pro: it has 8 Xeon E7-8870s, for a total of 80 cores and 160 threads @ 2.4/2.8 GHz, a Supermicro X8OBN-F motherboard, 512 GB (16x 32 GB DIMMs) DDR3 RAM, and 4 NVIDIA M2070s. (As an aside, a single Xeon E7-8870 costs more than the entry-level, dual-socket Mac Pro and the entire computer is a few thousand dollars short of the price of a new Porsche 911 Carrera.) Oh, and yes, I routinely develop software or run simulations that actually require that much, or far more, computing power: try running lattice-Boltzmann/finite element or Stokesian particulate flows, for modeling thousands to hundreds of million red blood cells, on a Mac Pro.

Continuing the above remark, it's laughable that you take what I've written and automatically default to assuming that I'm "unemployed," let alone a baby boomer. Just so you know, I'm not even 30.

What a humorous, yet snide, response to my merely pointing out and verifying that you can have a workstation with the same quality as a Mac Pro, at least where the components are concerned, not necessarily functionality and aesthetics, for much, much less than what you could get through Apple; clearly, you have some serious issues that you need to address.

Oh, and to answer your question, yes I do have a job: I work as an applied maths researcher and pay for my salary, research endeavors, and travel arrangements to present papers at conferences like NIPS, ICCV, CVPR, and ECCV through the annual interest made on my investments and healthcare patent royalties from GE, Intel, Honeywell, etc. so I don't have to bother with writing grant proposals or department politics.