At TEDGlobal 2010, author Matt Ridley shows how, throughout history, the engine of human progress has been the meeting and mating of ideas to make new ideas. It's not important how clever individuals are, he says; what really matters is how smart the collective brain is.
This is essentially the mathematician’s equivalent of the adage “Fake it ’til you make it.”
Q: When did Nicholas Bourbaki quit writing books about mathematics?
A: When (t)he(y) realized that Serge Lang was only one person!
In the last two years, at least 10 law schools have made their grading systems more lenient to give their students a better chance in a soft job market.
Is GPA tampering and grade inflation going too far with changes like this?
He really has a great sense of humor, doesn’t he?
For the first time in the United States, stem cells have been directly injected into the spinal cord of a patient, researchers announced Thursday.
As a separate note, who really wants to waste the time building thousands and thousands of followers when none of them are really going to ever pay attention to you? Yes, it’s great to have a high number, but really what is your ultimate reach? How many people are you engaging?
Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the structure of degradable quantum channels, including a number of new results as well as alternate proofs of some known results. In the case of qubits, we provide a complete characterization of all degradable channels with two dimensional output, give a new proof that a qubit channel with two Kraus operators is either degradable or anti-degradable, and present a complete description of anti-degradable unital qubit channels with a new proof. For higher output dimensions we explore the relationship between the output and environment dimensions (dB and dE, respectively) of degradable channels. For several broad classes of channels we show that they can be modeled with an environment that is “small” in the sense of ΦC. Such channels include all those with qubit or qutrit output, those that map some pure state to an output with full rank, and all those which can be represented using simultaneously diagonal Kraus operators, even in a non-orthogonal basis. Perhaps surprisingly, we also present examples of degradable channels with “large” environments, in the sense that the minimal dimension dE>dB. Indeed, one can have dE>14d2B. These examples can also be used to give a negative answer to the question of whether additivity of the coherent information is helpful for establishing additivity for the Holevo capacity of a pair of channels. In the case of channels with diagonal Kraus operators, we describe the subclasses that are complements of entanglement breaking channels. We also obtain a number of results for channels in the convex hull of conjugations with generalized Pauli matrices. However, a number of open questions remain about these channels and the more general case of random unitary channels.
Dates: September 13-14, 2008; 10am - 6pm, both days Los Angeles Convention Center, 1201 South Figueroa Street Los Angeles, California 90015 Still FREE Registration is Open until September 10th, 2008. Please visit our official site for more details and to sign up!
Microscopy, phenotyping and visual screens are frequently applied to model organisms in combination with genetics. Although widely used, these techniques for multicellular organisms have mostly remained manual and low-throughput. Here we report the complete automation of sample handling, high-resolution microscopy, phenotyping and sorting of Caenorhabditis elegans. The engineered microfluidic system, coupled with customized software, has enabled high-throughput, high-resolution microscopy and sorting with no human intervention and may be combined with any microscopy setup. The microchip is capable of robust local temperature control, self-regulated sample-loading and automatic sample-positioning, while the integrated software performs imaging and classification of worms based on morphological and intensity features. We demonstrate the ability to perform sensitive and quantitative screens based on cellular and subcellular phenotypes with over 95% accuracy per round and a rate of several hundred worms per hour. Screening time can be reduced by orders of magnitude; moreover, screening is completely automated.