The key assumptions made
in deriving the error bounds were:
bounded loss function
finite collection of candidate functions
The bounds are valid for every
${P}_{XY}$ and are called
distribution-free.
Deriving bounds for countably infinite spaces
In this lecture we will generalize the previous results in a
powerful way by developing bounds applicable to possibly infinitecollections of candidates. To start let us suppose that
$\mathcal{F}$ is a
countable, possibly infinite, collection of candidate functions.Assign a positive number c(
$f$ ) to each
$f\in \mathcal{F}$ , such that
However, it may be difficult to design a probability distribution
over an infinite class of candidates. The coding perspectiveprovides a very practical means to this end.
Assume that we have assigned a uniquely decodable binary code to
each
$f\in \mathcal{F}$ , and let c(
$f$ ) denote the codelength for
$f$ . That
is, the code for
$f$ is c(
$f$ ) bits long. A very useful class of
uniquely decodable codes are called prefix codes.
Prefix Code
A code is called a prefix codeif no codeword is a
prefix of any other codeword.
The kraft inequality
For any binary prefix code, the codeword lengths
${c}_{1}$ ,
${c}_{2}$ , ...
satisfy
$$\sum _{i=1}^{\infty}{2}^{-{c}_{i}}\le 1.$$
Conversely, given any
${c}_{1}$ ,
${c}_{2}$ , ... satisfying the inequality
above we can construct a prefix code with these codeword lengths.We will prove this result a bit later, but now let's see how this
is useful in our learning problem.
Assume that we have assigned a binary prefix codeword to each
$f\in \mathcal{F}$ , and let c(
$f$ ) denote the bit-length of the codeword for
$f$ . Set
$\delta \left(f\right)={2}^{-c\left(f\right)}\delta $ . Then
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.