## Tuesday, October 10, 2017

### Review: Don't buy the JBL Link 10 or the JBL Link 20! Junk speakers have unavoidable ugly popping noises.

 TL;DR The JBL LINK 10 and LINK 20 should have been amazing products. Unfortunately, all three units purchased from two different Best Buy stores have the same major audio problem. The audio cracks and pops even at medium volume of the most delicate content. I cannot get through Clair de Lune (at medium volume) or even streaming of voice content from NPR without very noticeable popping at random instants – the kind of popping you might expect if you had a loose connection within a speaker amplifier that generates discontinuous movements of a speaker every time it vibrates loose for a moment. We have returned all three speakers. I do not recommend you waste your time or money with these things.

I was originally very excited by the announcement of the JBL LINK Series, with the JBL LINK 10 (below, left) and the JBL LINK 20 (below, right) models being particularly interesting to me.

On the day the JBL LINK 20 was released, we purchased a $199 JBL LINK 20 from a local Best Buy. Setting it up was identical to setting up a Google Home. The unit came with a JBL's characteristic orange 10W USB charger and micro-USB cable; however, the unit had plenty of charge and could be used off the charger out of the box. Once I set it up, I asked Google Assistant to stream from our local NPR station. I was surprised to hear subtle but very noticeable popping at random times during the stream. I thought this could be a problem with the stream (although I did not notice these popping noises when I streamed on true Google Home or Amazon Echo devices in our home), and so I played a nice song called "Tennessee Whiskey" by Chris Stapleton, and I noticed the same problem. Finally, I played the gentle, all-piano "Clair de Lune" by Claude Debussy at medium volume (2 or 3 dots on the front of the unit) and heard the same random popping. The popping is unrelated to whether the speaker is plugged into the charger or not; it is consistent in all operating conditions. Being an optimist, I assumed I must have received a dud. Trying to minimize the chances of getting another from a batch of duds, I returned the unit back to a different Best Buy and purchased BOTH a$149 JBL LINK 10 and a brand new $199 JBL LINK 20 to try them out. I was surprised to find out that the$50 difference between the two not only paid for the larger speaker and battery but also paid for the USB charger! Although the LINK 20 comes with a 10W charger, the LINK 10 only comes with the cable. Regardless of that, they BOTH had the exact same problem as the first LINK 20 we purchased – they couldn't pass the "Clair de Lune" test at medium volume! So I have to conclude that there is something fundamentally wrong with the JBL LINK series (at least in the LINK 10 and LINK 20 varieties).

I tried my "4X" DSC (or Dorco USA) razor for the first time this weekend. It was an OK razor. It had a nice heavy handle, but the angle of the pivoting head was not as steep as I'd like, and the moisturizing strip was far too thick. Consequently, it was very awkward to get into small nooks -- like under the nose. The "4X" razor doesn't have a trimming edge either (the more expensive 6-blade "Executive" model does), which would really improve matters. But after the shave, my face felt pretty good. It just took a lot longer to get through a full shave. So I'm not sure I can fully recommend these razors over, say, Schick Quattro Titanium disposable razors, which actually have a trimming edge and are pretty cheap from local stores or from Amazon (around $7/3 razors). DSC also sent me a tester of their "Dr. Carver's Easy Shave Butter," which actually burned my face a bit as it went on (but I have sensitive skin). My face was fine afterward. But using Nivea For Men Active3 Body Wash for Body, Hair & Shave worked just as well without the sting. So I'm not sure I can recommend the Shave Butter either. So I'm torn. It's possible that the 6-blade+edging "Executive" unit will be better. Either way, in the long run, it's cheaper to buy from Dorco USA directly, and I like the idea of dropping the subscription service. Dorco USA also sells other razor models and even disposable models. They also sell razors designed for women, whereas DSC just tells women to buy the 4X. The 4X has a handle which is somewhere between what you'd want for the face and the leg, but I think it's biased toward face shaving. So the lady's models at Dorco USA are definitely recommended if you need to shave legs. So that's my brief review. tl;dr -- Check out DORCO if you like DSC's blades but don't like the subscription service. References: ## Monday, December 29, 2014 ### Looking for a cheap Bluetooth-capable portable MP3 player? Buy a no-contract smartphone and don't activate it! My father needed a portable Bluetooth-capable MP3 player with large or expandable memory. Portable MP3 players with such features typically sell for$80+ (Trio mini), with the nicest units being at least $150 (iPod nano) or much more. The cheap models have terrible battery life (3 hours for Trio mini). Creative solution? He bought a no-contract LG Optimus Exceed 2 from Verizon Wireless for less than$50 at Best Buy and used a 16GB microSD card that he already owned.
 LG Optimus Exceed 2, Prepaid (no-contract) Phone from Verizon Wireless
This particular no-contract phone is fast, runs Android 4.4.2, and can be used without activating. In fact, it is very easy to bypass the initial activation screen with a special key sequence – volume up, volume down, back, home – pressed after restart at the language selection screen. After bypassing that screen just once, the phone is happy to run unactivated indefinitely after that – it will never present that activate screen again. Use airplane mode to prevent phone from looking for a network to save battery, and flip on WiFi and Bluetooth. It's like a $50 iPod touch. Nice deal. You can get this phone from a number of places, as shown in links below. Of course, there are other no-contract phone choices you could make (check all no-contract carriers – Boost Mobile, Virgin Mobile USA, T-Mobile, etc.). If you're willing to compromise on the phone software or other capabilities, you can get decent "MP3 player phones" for$30 or even $20. For example, you can get essentially the same phone from Boost Mobile packaged as the LG Realm for only$35 on Amazon right now. It's $40 from other retailers.  LG Realm, Prepaid (no-contract) Phone from Boost Mobile So that's like a$35 iPod touch. Even nicer deal!

## Monday, February 04, 2013

### LaTeX template for NSF-style Biographical Sketch

On large multi-university NSF grant proposals, NSF requires that senior personnel submit a 2-page biographical sketch ("biosketch") that is formatting according to certain rules in their Grant Proposal Guide (GPG). The format is pretty simple, and so there does not seem to be much demand for a solid LaTeX template for one. Nevertheless, I thought some people might find one helpful. I've posted a PDF of my NSF-style biosketch below along with the TeX source used to generate it. On a related note, you can also find my curriculum vitae (CV) tailored for faculty searches (PDF, TeX) as well as for industry searches (PDF, TeX).

## Thursday, January 24, 2013

### Discrete-time Phase Portraits?

I was contacted recently by e-mail asking how to produce a phase portrait of a discrete-time system. In my initial response, I explained that a true "phase portrait" wasn't defined for discrete-time systems because the technical notion of a phase portrait depends on a special structure that comes along with ordinary differential equations. The original poster needed some additional clarification, and so I sent a second e-mail that I have posted below. It touches a little bit on the original poster's question, it comments on differences between discrete-time and continuous-time systems, it talks a bit about chaos, and it gives a brief description of Poincaré/return maps that are often used in the study of approximately periodic systems.

My point is that a discrete-time system really cannot be interpreted within a field-theoretic framework. A "phase portrait" captures both position and momentum of a continuous-time system described by an ordinary differential equation. These momentum variables setup the "field" that gives structure to the phase portrait. In a discrete-time system, we don't have the same kind of momentum.

For a continuous-time system, I can plot a point at an individual position, and I can also then draw a vector pointing away from that point representing the velocity at that instant of time. It is these velocity vectors that are put together to make a phase portrait of the system.

For a discrete-time system, there is no point-based velocity. In order for me to calculate the approximate "velocity" at a point, I need to know the position at the next point. Then I can draw a line between those two points and approximate the "velocity" of the system as going from the first point to the second point. However, if I have to know the next point in future anyway, it's more useful to just draw the second point.

Now, some discrete-time systems have a more predictable structure. For example, if you have a linear time-invariant discrete-time system like:

x[k+1] = M*x[k]

then the algebraic structure of the "M" matrix gives us insight into how trajectories will evolve. So for these special cases, it is possible to draw a kind of "phase portrait" for the discrete-time system. However, this is primarily because such a discrete-time system can be viewed as a sampled version of a continuous-time linear time-invariant system which does have a phase portrait.

So, for an arbitrary discrete-time system, the best thing you can do is explore trajectories from different initial conditions. Gradually, as you explore the space more and more, you may find boundaries of attractors (possibly strange attractors). A complication with discrete-time systems is that the "next" point may be very far from the "previous" point. Take, for example:

x[k+1] = -1.1*x[k]

If you start at x[0]=1, the trajectory will bounce from point clustered above 1 to points clustered below -1. In a continuous-time system, you might expect to see initial conditions above 1 stay near 1 and initial conditions below -1 stay near -1. That is, in a continuous-time system, you wouldn't imagine trajectories could cross x=0 (which is an equilibrium/fixed-point of this system). However, the discrete-time system can jump wildly from point to point.

Take, for example, the Henon map you mention. Wolfram's Mathworld has some nice plots:

http://mathworld.wolfram.com/HenonMap.html

The first pair of side-by-side plots are colored "according to the number of iterations required to escape". That is, the plots were generated by starting at several initial conditions and recording the resulting trajectories. Each "iteration" gives the next point from the previous point. For a while, a trajectory will stay around its initial condition. Eventually, it will escape and move away from the region. The regions are colored based on how many iterations (i.e., how many calculations after the initial condition) it took for the trajectory to leave the region.

The second pair of side-by-side plots show a SINGLE trajectory started at x[0]=0 and y[0]=0. Each point was recorded and gradually a pattern emerged. Notice how in the left plot the two regions appear to be disconnected. If you saw a phase portrait that looked like this in a continuous-time system, you would conclude that initial conditions within one region would not be able to join the other region for this set of parameters. However, this plot was generated from a SINGLE initial condition. So the plot jumps from points in the top left to points in the bottom right and back.

So that's how you can explore something like the "phase space" for discrete-time systems. You can probe it with different initial conditions. For chaotic systems, you have to be very careful you don't accidentally jump over an interesting region of initial conditions that may have qualitatively different trajectories that follow from them.

As an aside, I guess it's also worth mentioning that many popular discrete-time chaotic maps are actually Poincaré maps of continuous-time dynamical systems. Poincaré maps have other names, including "return maps." Consider, for example, the planets as they orbit the sun. The actual orbits of the planets in three dimensions looks like a tangled mess when you consider their histories over several cycles around the sun because each orbit is slightly different than the previous orbit (i.e., they aren't entirely planar). However, if you insert a plane perpendicular to their orbits at a single location, each planet pierces the plane at one point every cycle. The resulting shapes that are poked out of that cross section reveal structure in the orbits.

I hope that helps! --
Ted

## Tuesday, October 09, 2012

### natbib-like frontend for chicago-style macros

For some reason, the ACM has baked in chicago-like citation macros into the ACM SIG proceedings LaTeX templates instead of using the far superior natbib that literally everyone else on the planet uses. I'm much more accustomed to typing \citet as opposed to \shortciteN, \citeauthor as opposed to \shortciteANP, etc. So I decided to add this little translation table to my preamble:
\def\citet{\shortciteN}
\def\Citet{\shortciteN}
\def\citeauthor{\shortciteANP}
\def\Citeauthor{\shortciteANP}

\let\chicagociteyear\citeyear
\def\citeyearpar{\chicagociteyear}
\def\citeyear{\citeyearNP}

\def\citep{\shortcite}
Unfortunately, that means I can't use any of the optional arguments to \citep or \citet. If you are just looking for a translation table so you can use the chicago-style macros directly, try this:
natbibchicago
\citet or \Citet\shortciteN
\citeauthor or \Citeauthor\shortciteANP
\citeyear\citeyearNP
\citeyearpar\citeyear
\citep\shortcite
It's crazy how chicago-style macros sometimes use "N" to mean "noun" and other times to be the first half of "NP" being "no parentheses."

## Thursday, August 09, 2012

### CTAN search engine definition for Firefox

If you're looking for search engine definitions for CTAN that are compatible with Firefox's search toolbar, then visit:While on that page, click on the down arrow in the icon in your your Firefox search toolbar. You should see several "Add" options at the bottom. That lets you add several different types of CTAN search to your toolbar. You can then "Manage Search Engines" and add a keyword to some of them. I use the keyword "ctan" to search package ID's and the keyword "ctanp" to search over package ID's and descriptions. The keyword lets me search directly from the awesome bar without having to use the search bar. [ These definitions were inspired by firefox_ctan_plugins by Martin Engler, but those don't work with CTAN anymore. ]