Here are my
;-)
Friday, December 31, 2010
Thursday, December 9, 2010
Latex Incorporated :)
I have finally been successful at incorporating Latex and we can now type any equation!
$ R_{ \mu \nu } - \frac{1}{2}g_{\mu \nu} R + g_{\mu \nu} \Lambda = \frac{8\piG}{C^4}T_{ \mu \nu} $
See :)
And this is one of my favourite equations.
Using latex is very easy, you just need to know the commands.
Usha ma'am, satyajit, and Raghu are already experts at it :).
Here are a few examples:
$ s = \int L ( q, \dot{q} , t ) dt $
To type this equation, one has to type & s = \int L ( q, \dot{q} , t ) dt &
You just have to replace & with $$.
Any latex commands can be used by enclosing them between $$ .
Similarly
$ \frac{\partial u}{\partial t} = h^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2} \right) $
is & \frac{\partial u}{\partial t} = h^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2} \right) &
( again just replace & with $$ )
For those who want to use latex and want to know all the commands, here are some links that will help you:
http://web.ift.uib.no/Teori/KURS/WRK/TeX/symALL.html
http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/Calculus.html
Have fun :)
$ R_{ \mu \nu } - \frac{1}{2}g_{\mu \nu} R + g_{\mu \nu} \Lambda = \frac{8\piG}{C^4}T_{ \mu \nu} $
See :)
And this is one of my favourite equations.
Using latex is very easy, you just need to know the commands.
Usha ma'am, satyajit, and Raghu are already experts at it :).
Here are a few examples:
$ s = \int L ( q, \dot{q} , t ) dt $
To type this equation, one has to type & s = \int L ( q, \dot{q} , t ) dt &
You just have to replace & with $$.
Any latex commands can be used by enclosing them between $$ .
Similarly
$ \frac{\partial u}{\partial t} = h^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2} \right) $
is & \frac{\partial u}{\partial t} = h^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2} \right) &
( again just replace & with $$ )
For those who want to use latex and want to know all the commands, here are some links that will help you:
http://web.ift.uib.no/Teori/KURS/WRK/TeX/symALL.html
http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/Calculus.html
Have fun :)
Wednesday, December 8, 2010
Waking Life - Part 1
" There are two kinds of sufferers in this world: those who suffer from a lack of life and those who suffer from an over-abundance of life. I've always found myself in the second category.
When you come to think of it,almost all human behaviour and activity...is not essentially any different from animal behaviour.The most advanced technologies and craftsmanship... bring us, at best, up to the super-chimpanzee level. Actually, the gap between,say, Plato or Nietzsche and the average human...is greater than the gap between that chimpanzee and the average human.The realm of the real spirit, the true artist, the saint, the philosopher, is rarely achieved.
Why so few? Why is world history and evolution not stories of progress...but rather this endless and futile addition of zeroes? No greater values have developed. Hell, the Greeks years ago were just as advanced as we are. So what are these barriers that keep people... from reaching anywhere near their real potential? The answer to that can be found in another question, and that's this:
Which is the most universal human characteristic--
fear or laziness?"
-From the movie "Waking Life"
When you come to think of it,almost all human behaviour and activity...is not essentially any different from animal behaviour.The most advanced technologies and craftsmanship... bring us, at best, up to the super-chimpanzee level. Actually, the gap between,say, Plato or Nietzsche and the average human...is greater than the gap between that chimpanzee and the average human.The realm of the real spirit, the true artist, the saint, the philosopher, is rarely achieved.
Why so few? Why is world history and evolution not stories of progress...but rather this endless and futile addition of zeroes? No greater values have developed. Hell, the Greeks years ago were just as advanced as we are. So what are these barriers that keep people... from reaching anywhere near their real potential? The answer to that can be found in another question, and that's this:
Which is the most universal human characteristic--
fear or laziness?"
-From the movie "Waking Life"
Tuesday, December 7, 2010
Latex?
I was thinking of making the blog more technical and this will require us to be able to type equations. So does anyone know if Latex can be incorporated on the blog? Is there any html script or something using which this can be done?
Please let me know thanks.
Please let me know thanks.
Sunday, December 5, 2010
Mathematical structure of nature
For a while now, the correspondence between a mathematical structure and the way nature behaves has puzzled and amazed me. In other words, Why is it that I can write down equations on a sheets of paper and predict something about a natural object?
Newtonian Mechanics had a certain mathematical structure and Maxwell's Electrodynamics had a certain mathematical structure, and these two structures couldn't co-exist. Just by trying make the equations co-variant, we were able to get great insights into the way nature worked. We could get testable predictions which we were ofcourse verified by experiment.
Quantum Mechanics brought in another mathematical structure which takes into account the relationship between the observer and the observed, and gives us the nature of a measurement.
There may be domains where experimental physics cannot yet reach. There may be some underlying physical phenomena which cannot yet be detected by experiments. To probe into those domains, as of now, we may only have mathematical tools at our disposal.
Here is a paragraph from a book on Quantum Mechanics by Bohm ( Ref 3) that I think is worth mentioning:
" Physicists believe that there is something in nature, or in each restricted domain of it, that may be "understood"; that there is a structure in nature. To "understand" means to bring this structure into congruence with some structure in our mind, with a structure of thought objects, with a structure that has been created by our minds. For physics, this structure of thought objects is a mathematical structure. So to understand part of physical nature means to map its structure on a mathematical structure. To obtain a physical theory, then, means to obtain a mathematical image of a physical system.
For the domains of quantum physics the mathematical structures are algebras of linear operators in linear spaces. The discovery of this, the fundamental properties of the algebra, and the other basic assumptions of quantum mechanics was a very difficult process. "
I just hope we have the capability to recognise the true underlying structure of nature( however naive this may sound).
P.s. The references are given in the column on the right.
Newtonian Mechanics had a certain mathematical structure and Maxwell's Electrodynamics had a certain mathematical structure, and these two structures couldn't co-exist. Just by trying make the equations co-variant, we were able to get great insights into the way nature worked. We could get testable predictions which we were ofcourse verified by experiment.
Quantum Mechanics brought in another mathematical structure which takes into account the relationship between the observer and the observed, and gives us the nature of a measurement.
There may be domains where experimental physics cannot yet reach. There may be some underlying physical phenomena which cannot yet be detected by experiments. To probe into those domains, as of now, we may only have mathematical tools at our disposal.
Here is a paragraph from a book on Quantum Mechanics by Bohm ( Ref 3) that I think is worth mentioning:
" Physicists believe that there is something in nature, or in each restricted domain of it, that may be "understood"; that there is a structure in nature. To "understand" means to bring this structure into congruence with some structure in our mind, with a structure of thought objects, with a structure that has been created by our minds. For physics, this structure of thought objects is a mathematical structure. So to understand part of physical nature means to map its structure on a mathematical structure. To obtain a physical theory, then, means to obtain a mathematical image of a physical system.
For the domains of quantum physics the mathematical structures are algebras of linear operators in linear spaces. The discovery of this, the fundamental properties of the algebra, and the other basic assumptions of quantum mechanics was a very difficult process. "
I just hope we have the capability to recognise the true underlying structure of nature( however naive this may sound).
P.s. The references are given in the column on the right.
Thursday, December 2, 2010
Academy Lecture
Indian Academy of Sciences
Bangalore
"Chandra: Gentleman, Scholar and Telescope"
Academy Public Lecture by
Professor Roger Blandford
Kavli Institute for Particle Astrophysics and Cosmology
Stanford
Date : Wednesday, 8th December 2010
Time: 6.00 p.m.
Venue: Faculty Hall, Indian Institute of Science, Bangalore
Abstract: Professor Subrahmanyan Chandrasekhar, or "Chandra" as he was widely known, was a singular scientist and intellectual. Blessed with formidable mathematical ability and legendary powers of concentration, he was a scientific leader over an unequalled suite of the most challenging astrophysical disciplines. Although he may be most famous for his youthful discovery of a mass limit for white dwarfs and its famous corollary that black holes must exist, for which he was awarded the 1983 Nobel Prize, his lifetime contributions to mathematical physics, astrophysics and even the humanities, are even greater. The range and durability of his scholarship was memorialised in the naming of the finest imaging X-ray telescope ever launched. Vignettes from his life will be interspersed with a description of some of the amazing discoveries made by Chandra X-ray Observatory.
About the speaker: Roger Blandford is director of the Kavli Institute for Particle Astrophysics and Cosmology. He oversees research that seeks to answer some of our great cosmic questions: What powered the Big Bang? What are dark matter and dark energy? What is happening around black holes?. He is a Fellow of The Royal Society and the American Academy of Arts and Sciences, and a Member of the National Academy of Sciences.
All are welcome
Bangalore
"Chandra: Gentleman, Scholar and Telescope"
Academy Public Lecture by
Professor Roger Blandford
Kavli Institute for Particle Astrophysics and Cosmology
Stanford
Date : Wednesday, 8th December 2010
Time: 6.00 p.m.
Venue: Faculty Hall, Indian Institute of Science, Bangalore
Abstract: Professor Subrahmanyan Chandrasekhar, or "Chandra" as he was widely known, was a singular scientist and intellectual. Blessed with formidable mathematical ability and legendary powers of concentration, he was a scientific leader over an unequalled suite of the most challenging astrophysical disciplines. Although he may be most famous for his youthful discovery of a mass limit for white dwarfs and its famous corollary that black holes must exist, for which he was awarded the 1983 Nobel Prize, his lifetime contributions to mathematical physics, astrophysics and even the humanities, are even greater. The range and durability of his scholarship was memorialised in the naming of the finest imaging X-ray telescope ever launched. Vignettes from his life will be interspersed with a description of some of the amazing discoveries made by Chandra X-ray Observatory.
About the speaker: Roger Blandford is director of the Kavli Institute for Particle Astrophysics and Cosmology. He oversees research that seeks to answer some of our great cosmic questions: What powered the Big Bang? What are dark matter and dark energy? What is happening around black holes?. He is a Fellow of The Royal Society and the American Academy of Arts and Sciences, and a Member of the National Academy of Sciences.
All are welcome
Coffee/tea will be served at 5.30 p.m.
Quantum Cryptography Lecture
Centre for Quantum Information and Quantum Computing
Indian Institute of Science
Bangalore
Announces its lecture
By
Dr. Prabha Mandayam
Institute for Quantum Information
California Institute of Technology, Pasadena, USA
Title:
" Uncertainty and Complementarity in Quantum Cryptography: Security in the Noisy Storage model"
On Wednesday the 8th December, 2010 at 4.00 pm
Venue: Lecture Hall - I, Department of Physics, Indian Institute of Science.
Abstract
Historically, uncertainty relations have played an important role in our understanding of quantum mechanics. Recently, entropic uncertainty relations have gained prominence in the field of quantum information. In particular, they play a crucial role in analyzing the security of quantum cryptographic protocols such as quantum key-distribution and information locking. While optimal entropic uncertainty relations have been obtained for two measurements, not much is known in a general setting with more than two outcomes. We outline a novel construction of symmetric mutually unbiased bases (MUBs), using the 2n generators of the Clifford algebra in dimension d = 2^n. These bases satisfy the symmetry property that they are cyclically permuted under a unitary transformation. We prove a lower bound for entropic uncertainty relations for any set of MUBs and show that symmetry plays a central role in obtaining tight bounds. Finally, we describe a two-party protocol based on recent cryptographic models -- the "bounded-storage model" and the "noisy-storage model" -- whose security is directly related to a lower bound on the average entropy of complementary bases. While the security of most cryptographic systems in use today is based on the premise that certain computational problems are hard to solve for the adversary, these models are based on the physical assumption that no large-scale reliable quantum storage is available to the cheating party. Our protocol achieves security in the bounded-storage model even if the cheating party can store all but a constant fraction of the transmitted information, thus resolving an open question on the achievable physical limits of this model. In the general setting of the noisy-storage model, our protocol extends the range of storage devices for which security can be achieved.
Indian Institute of Science
Bangalore
Announces its lecture
By
Dr. Prabha Mandayam
Institute for Quantum Information
California Institute of Technology, Pasadena, USA
Title:
" Uncertainty and Complementarity in Quantum Cryptography: Security in the Noisy Storage model"
On Wednesday the 8th December, 2010 at 4.00 pm
Venue: Lecture Hall - I, Department of Physics, Indian Institute of Science.
Abstract
Historically, uncertainty relations have played an important role in our understanding of quantum mechanics. Recently, entropic uncertainty relations have gained prominence in the field of quantum information. In particular, they play a crucial role in analyzing the security of quantum cryptographic protocols such as quantum key-distribution and information locking. While optimal entropic uncertainty relations have been obtained for two measurements, not much is known in a general setting with more than two outcomes. We outline a novel construction of symmetric mutually unbiased bases (MUBs), using the 2n generators of the Clifford algebra in dimension d = 2^n. These bases satisfy the symmetry property that they are cyclically permuted under a unitary transformation. We prove a lower bound for entropic uncertainty relations for any set of MUBs and show that symmetry plays a central role in obtaining tight bounds. Finally, we describe a two-party protocol based on recent cryptographic models -- the "bounded-storage model" and the "noisy-storage model" -- whose security is directly related to a lower bound on the average entropy of complementary bases. While the security of most cryptographic systems in use today is based on the premise that certain computational problems are hard to solve for the adversary, these models are based on the physical assumption that no large-scale reliable quantum storage is available to the cheating party. Our protocol achieves security in the bounded-storage model even if the cheating party can store all but a constant fraction of the transmitted information, thus resolving an open question on the achievable physical limits of this model. In the general setting of the noisy-storage model, our protocol extends the range of storage devices for which security can be achieved.
All are Welcome
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