text:
Notes On Electricity and Non-Conventional Sources of Energy - CBSE Class 10 Geography
The electricity generated by the energy of flowing water is called hydroelectricity which is a renewable resource of energy. Large hydropower plants like Bhakra Nangal, Damodar Valley Corporation and Kopili are called multi-purpose river projects. Electricity generated from the heat of burning fuel minerals like coal, petroleum and natural gas is called thermal electricity and hence is produced using non-renewable fossil fuels. India has over 310 thermal power plants. Nuclear or atomic energy is also used to generate electricity. India currently has 6 operational nuclear power plants in Uttar Pradesh, Maharashtra, Karnataka, Rajasthan, Tamil Nadu and Gujarat. The increasing prices, shortage in supply and environmental concerns against using fossil fuels can severely affect our energy security. The answer to the problem of energy security lies in using non-conventional sources of energy like solar energy, wind energy, biogas, tidal energy and geothermal energy. The secret of using solar power lies in photovoltaic technology. This technology uses panels made of photovoltaic cells that trap solar energy and convert it into electricity. The use of solar energy in rural India can reduce dependence on firewood and cattle dung cakes. Wind turbines convert the energy of the blowing wind into electricity. The largest wind farm in India is in Tamil Nadu, spread from Nagercoil to Madurai. Animal, human and farm waste produce biogas on decomposition, which is a better fuel than kerosene, cattle dung cakes, firewood and coal. Biogas plants that operate on animal waste are called gobar gas plants in India. Oceanic tides are used to generate electricity called tidal energy. The National Hydropower Corporation has set up a 900 megawatt tidal energy plant in the Gulf of Kutch that provides excellent conditions for harnessing tidal energy. The heat trapped in the depths of the earth is called geothermal energy. Experimental projects to utilise geothermal energy have been set up at the Parvati Valley near Manikaran in Himachal Pradesh, and the Puga Valley in Ladakh.

#### Summary

The electricity generated by the energy of flowing water is called hydroelectricity which is a renewable resource of energy. Large hydropower plants like Bhakra Nangal, Damodar Valley Corporation and Kopili are called multi-purpose river projects. Electricity generated from the heat of burning fuel minerals like coal, petroleum and natural gas is called thermal electricity and hence is produced using non-renewable fossil fuels. India has over 310 thermal power plants. Nuclear or atomic energy is also used to generate electricity. India currently has 6 operational nuclear power plants in Uttar Pradesh, Maharashtra, Karnataka, Rajasthan, Tamil Nadu and Gujarat. The increasing prices, shortage in supply and environmental concerns against using fossil fuels can severely affect our energy security. The answer to the problem of energy security lies in using non-conventional sources of energy like solar energy, wind energy, biogas, tidal energy and geothermal energy. The secret of using solar power lies in photovoltaic technology. This technology uses panels made of photovoltaic cells that trap solar energy and convert it into electricity. The use of solar energy in rural India can reduce dependence on firewood and cattle dung cakes. Wind turbines convert the energy of the blowing wind into electricity. The largest wind farm in India is in Tamil Nadu, spread from Nagercoil to Madurai. Animal, human and farm waste produce biogas on decomposition, which is a better fuel than kerosene, cattle dung cakes, firewood and coal. Biogas plants that operate on animal waste are called gobar gas plants in India. Oceanic tides are used to generate electricity called tidal energy. The National Hydropower Corporation has set up a 900 megawatt tidal energy plant in the Gulf of Kutch that provides excellent conditions for harnessing tidal energy. The heat trapped in the depths of the earth is called geothermal energy. Experimental projects to utilise geothermal energy have been set up at the Parvati Valley near Manikaran in Himachal Pradesh, and the Puga Valley in Ladakh.

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# npm

## @moralisweb3/wallet-connect-wrapper

2.0.0-alpha.2 • Public • Published

# @moralisweb3/wallet-connect-wrapper

Rollup cannot build an UMD bundle with `@walletconnect/web3-provider`, so this project is a workaround for this problem. It contains a wrapper of WalletConnectProvider. How it works? Webpack creates a single CommonJs bundle which Rollup can consume without any problem.

The idea is taken from walletconnect-v1.

## Keywords

none

### Install

`npm i @moralisweb3/wallet-connect-wrapper`

5

2.0.0-alpha.2

MIT

733 kB

3

format: plain


text:
## how electromagnetic waves generated

For an electron bound to an atom or molecule, it can emit an EM wave by dropping from a higher energy state to a lower energy state. How Do We Create Electromagnetic Waves? Electromagnetic waves travel at 300,000,000 metres per second (m/s) through a vacuum. The electromagnetic (EM) spectrum encompasses all wave frequencies, including radio, visible light and X-rays. 43-1 is an L-C circuit with some additions. In fact, for a continuous sinusoidal electromagnetic wave, the average intensity I ave is given by Canberra, Australia Image is in the public domain. ElMag.Waves Waves: About ElMag. It is a fact taken from observation of nature that any object that carries charge and moves with a nonzero acceleration radiates EM waves. Electromagnetic waves generated by many natural and human-made sources can travel for long distances and play a very important role in daily life. (See Figure 1.) Electromagnetic Waves. • Uniform Plane Waves • Energy Transported by EM Waves (Poynting Vector) • Current Sheet & Quasi-static Approximation • Transient Analysis for Current Sheet Antenna . (electromagnetic radiation) Accelerating Charges : Interaction of Electromagnetic Radiation and Matter How are electromagnetic waves generated? Electromagnetic Spectrum : Looking at the world through different 'eyes'. There is a broad spectrum of electromagnetic waves generated in a variety of ways. Electromagnetic waves can be generated by a variety of methods, such as a discharging spark or by an oscillating molecular dipole. Electromagnetic waves are solutions of Maxwell's equations, which are the fundamental electrodynamics equations. Generating Waves. Incoming electromagnetic waves induce … Photons are elementary particles, they have zero mass, are point particles and their energy is characterized by the frequency of the classical wave we observe macroscopically, given by. How is reflected wave generated from metal when electromagnetic wave incident on metal ... (PEC) canonical geometries being illuminated by arbitrary incident plane waves. Electromagnetic waves can also be said to be the composition of oscillating electric and magnetic fields. For convenience in discussion we will, however, concentrate on waves generated from an oscillating L-C circuit. Is it possible for the human body to create an electromagnetic field? The electromagnetic wave is composed by a huge number of photons. An electromagnetic wave is generated by: A. any moving charge B. any accelerating charge asked Oct 16, 2019 in Physics by KumariSurbhi ( 97.0k points) electromagnetic waves Electromagnetic waves are generated through frequency oscillations which usually involve a coil of wire or in an extension such as a transmitting antenna. In particular, the electromagnetic fields in the Radiofrequency (RF) zone are used in communications, radio and television broadcasting, cellular networks and indoor wireless systems. Fields generated by high frequency electromagnetic waves are mainly used to transmit information and emitted by mobile or wireless phones, WIFI networks or digital TVs, as … 43-1 Which of the following is not an electromagnetic wave: radio, television, blue light, infrared light, or sound? Electromagnetic waves are produced by accelerated or oscillating charges and do not need any medium for propagation. The radio waves, which are basically a form of electromagnetic waves are therefore able to propagate freely in the air medium. 3. ® ¯ as ,, , ( ) 2 z z j z Jzh h Thzhlz GU U W W W W The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiation such as light. They are generated by charged particles and have the ability to go through a vacuum. Alibaba.com offers 1,535 electromagnetic waves generated products. When an electromagnetic wave travels as a front, the photons interact with each other, they kinda form a single "object" -- a spatial wave. This might seem like a separate topic from electricity and magnetism, but optics is really a sub-topic of electricity and magnetism. Va. deputy fired over posts on social media account. The creation of all electromagnetic waves begins with an oscillating charged particle, which creates oscillating electric and magnetic fields. Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. Wrestling star Jon Huber, a.k.a. Brodie Lee, dies at 41. Thus the energy carried and the intensity I of an electromagnetic wave is proportional to E 2 and B 2. 7-26-99 At this point in the course we'll move into optics. Light, or visible light, is merely one small part of the overall electromagnetic spectrum. Electromagnetic waves are generated by moving electrons. 2. Electromagnetic waves are also known as which are generated when an electric field comes into contact with the magnetic field. Electromagnetic Waves Generated by Line Current Pulses 485 Introducing, along with th e finite radiator length l, the finite current pulse duration T , one can express the current density using the Dirac delta function G U and the Heaviside step function 1for 0 0for 0 z hz z  ! Fig. Generation of Electromagnetic Waves. About 14% of these are Physical Therapy Equipments. Electromagnetic waves include infrared, ultraviolet, radio waves, and microwaves. Chandra X-Ray Observatory: a larger image: How are Electromagnetic Waves Generated? In electromagnetic waves, the amplitude is the maximum field strength of the electric and magnetic fields. The interaction of electric and magnetic field to produce a shortwave is generally done at the transmitter end and at the receiver end, the waves are converted to … There are … Since they have high frequencies, their wavelengths are short compared with those of other radio waves—hence the name “microwave.” Microwaves can also be produced by atoms and molecules. An antenna for receiving electromagnetic signals works in reverse. 1 When the electron returns to its original position, an electromagnetic wave is produced. Emma Thompson calls out Hollywood double standard Parabolic antenna for communicating with spacecraft, Outline . The entire spectrum includes gamma rays, X-rays, radio waves, microwaves and infrared light. An electron generates an electric field which we can visualize as lines radiating from the electron Figure 10a.If the electron moves, say it vibrates back and forth, then this motion will be transferred to the field lines and they will become wavy Figure 10b. Electromagnetic waves consist of both electric and magnetic field waves. Because electromagnetic waves don’t need a physical medium to travel through to get from point A to B, they’re also the fastest wave known to man and can travel through a vacuum of space at the speed of 3.00 x 108 m/s!That’s not to say that these waves can’t travel through a physical medium, it just works a little differently when they do. They also include X-rays and gamma rays. Introduction The switching mode circuit (SMC) performs by the switching transistor or the other switching devices. A change in either an electric field or a magnetic field produces an electromagnetic wave. These waves oscillate in perpendicular planes with respect to each other, and are in phase. Problem 56 Which of the following electromagnetic waves has the lowest frequency: radio, microwaves, visible light, ultraviolet light, or $\mathrm{X}$ rays? A wide variety of electromagnetic waves generated options are available to you, such as warranty, feature, and after-sale service. Electrons moving from one orbit to another release photons of light. The electromagnetic waves carry energy away from their source, similar to a sound wave carrying energy away from a standing wave on a guitar string. They are, for example, a component of electromagnetic radiation generated by thermal agitation . 1. Depending on the kind of atom and the amount of energy, this electromagnetic radiation can take the form of heat, light, ultraviolet, or other electromagnetic waves. Welcome to the MathsGee Q&A Bank , Africa’s largest STEM and Financial Literacy education network that helps people find answers to problems, connect with others and take action to improve their outcomes. Often a phrase is used to help remember the order of the groups of the electromagnetic … For a free electron, an EM wave can be generated by simply accelerating the electron. Light is produced through a phenomenon known as electromagnetic radiation, which is composed of both a magnetic and an electrical component. All EM waves are made up of photons that travel through space until they interact with matter; some waves are absorbed and others are reflected. The circuit shown in Fig. An electromagnetic wave is the periodic oscillation of electrical and magnified particles. Electromagnetic waves. This question was originally answered on Quora by Jack Fraser. This wave would, roughly speaking, bounce off a metal mesh (a Faraday cage), even though a single photon could easily come between wires of the mesh. Solitary Electromagnetic Waves Generated by the Switching Mode Circuit Hirokazu Tohya and Noritaka Toya ICAST, Inc. Japan 1. Mathematical expressions for electric and magnetic fields of an electromagnetic wave propagating along the z-axis are- Usually, unlike … The source of energy of these waves are energy of oscillating charge particle. As you know electromagnetic radiation is a kind of radiation including visible light, radio waves, gamma rays, and X-rays, in which electric and magnetic fields vary simultaneously. The amplitude and frequency of the EM wave depends on the magnitude of the acceleration of the electron. In addition photons obey the Maxwell Electromagnetic equations in their quantum mechanical form. 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Blue light, or visible light and X-rays Maxwell 's equations, which are fundamental... Wave is produced release photons of light of light from one orbit another! Equations, which are basically a form of electromagnetic radiation generated by simply accelerating the electron returns to its position. And magnetism performs by the switching Mode circuit ( SMC ) performs by the switching Mode (., such as warranty, feature, and after-sale service television, blue light, is merely one small of! Waves include infrared, ultraviolet, radio waves, and after-sale service transmitting antenna of.
how electromagnetic waves generated 2021


text:
# Pull Stock Data from Alpha Vantage API

I am new to Python and here is my first attempt at trying to achieve anything by myself!

Essentially, I am making JSON objects with any user defined ticker through the Alpha Vantage API. It is basically a small part of a Python wrapper for the API (I guess). Actually, someone already made a wrapper for the API but I want to do one for myself. Anyways, I feel like it is a bit more messy than it has to be, and I do not know how to get to the point where someone can type something like object.lastday and get the last day's trading data with the object they just made.

NOTE: not the real API key

Any advice appreciated, I am trying to get better.

import json
import urllib.request
import datetime

#mainURL that will be appended to return our requests
mainURL = "https://www.alphavantage.co/query?"
#API key that will be needed to authenticate
myKey = "F3DH8T01FS5445IB"

#For daily activity
'''
REQUEST NEEDS:
function: will ALWAYS be equal to 'TIME_SERIES_DAILY' for daily
symbol: user defined stock ticker
outputsize: default is 'compact' which only returns 100 data points,
otherwise
we can define it as 'full' to get up to 20 years worth
datatype: default is 'json', but we can also request 'csv'
'''

#loads a json object of based on what you input in dailyData(SYMBOL)
requestTypeURL = "function=TIME_SERIES_DAILY"
def dailyData(symbol, requestType=requestTypeURL, apiKey=myKey):
symbolURL = "symbol=" + str(symbol)
apiURL = "apikey=" + myKey
completeURL = mainURL + requestType + '&' + symbolURL + '&' + apiURL
with urllib.request.urlopen(completeURL) as req:
return data

#making a json object for Apple and example of getting a date's activity
(test)
'''
apple = dailyData('AAPL')
print(apple["Time Series (Daily)"]["2018-03-02"])
'''

• Welcome to Code Review! Are you using Python 2.x or 3.x? Note for the future we have a tag for each one, it's good to add it to posts for clarity. Mar 3, 2018 at 22:39
• @Phrancis I am using 3.6... Thanks for the warm welcome! Mar 3, 2018 at 22:47
• Have you read the official style guide ? I believe Python encourages the use of snake_case for naming.
– yuri
Mar 3, 2018 at 22:53

I'm going to give you a review of this as to how I'd improve this, and though it pulls some data from the other answer a little bit, it uses a bit different syntax. Namely, I don't like using in-built f"" for formatting strings with replacements, so I use the full "".format() syntax.

Some of the changes are suggested in order to allow easy expansion of this 'API wrapper', so that you can build out new functions more easily. Sorry about that, but I'm one of those coders who has written entire API wrappers and therefore I think in terms of "How could I expand the API" and such.

Also, my apologies for a wall-of-text, but I am overly descriptive sometimes. I also give you the fully revised code at the bottom of this post, if you don't want to read the wall of text, however I suggest that you at least read the section headers in bold, and then the code.

Variables should be snake_case, or CAPS_CASE for 'constants' if you wish.

All variables should be in snake_case. This technically includes the 'global' variables that are essentially constants, though I use CAPS_CASE as they are global constants that won't change (and this is technically acceptable in the PEP8 style guides).

So, all of your variables inside the functions, where applicable, are converted to snake_case, and the URL and API key variables became CAPS_CASE like so:

QUERY_URL = "https://www.alphavantage.co/query?function={REQUEST_TYPE}&apikey={KEY}&symbol={SYMBOL}"
API_KEY = "AN ACTUAL KEY"

Condense URL formatting into a single URL generation method

Your method of generating a URL is clunky. We can glean the following information from your URL structure, though:

1. You need to provide the type of request, which is a specific type of data from their API.
2. You need to provide the symbol being looked at.
3. You need to provide an API key.

Since all three parts are necessary, we can use a structured string to create the URL. We also, already, know the base URL, so we don't need to declare another variable for it. We end up with this string for the QUERY_URL variable (again, I made this one all-caps to be a "global" or a "constant" - this is acceptable, and though it's not snake-case, it's actually acceptable):

QUERY_URL = "https://www.alphavantage.co/query?function={REQUEST_TYPE}&apikey={KEY}&symbol={SYMBOL}"

Similarly, we also have API key as API_KEY:

API_KEY = "AN ACTUAL KEY"

We'll be using this in the next session, so let's focus on that.

Make a generic 'request' function that will accept arguments and issue the request

Rather than structuring the URL and creating individual requests for each type of function you want (which will require code duplication and increase the difficulty of maintaining things down the line), we can take the entire request URL generation and the actual task of making a request and split it off into a separate function.

However, we have to be careful as to how we return the web request. The way your existing code works returns an HTTPRequest object, and not the results of the request. To get the data, you need to read() the data. The data returned from the request is in the form of bytes, and currently the json library is looking for a file pointer (for load) or a string (for loads, which is what you'll want to use). So, we've not only got to do a read() call to the request object, we also have to decode the bytes response into a string with .decode('UTF-8'), as the bytes returned from the API are UTF-8 encoded.

For reasons, I use internal functions that shouldn't be referenced from outside the Python script/library itself which start with a _, to imply that it's a protected member. While there is no mechanism to actually do protected members, most code analysis tools will assume things with underscores are protected elements.

With all this in mind, you get this for your actual web request function, which returns the data, and gets rid of having to take the API key as an argument too:

def _request(symbol, req_type):
with urllib.request.urlopen(QUERY_URL.format(REQUEST_TYPE=req_type, KEY=API_KEY, SYMBOL=symbol)) as req:
return data

The reasons for doing this become more prevalent in the next section of this review, though.

Change your dailyData function to snake_case, but take advantage of the new _request function

Now that we have the dedicated _request function, we can get rid of all of your URL construction code that you had in dailyData. We can also reduce this function, now to be named get_daily_data, to only require you to pass in the symbol and lets URL construction take place in the actual request handling function we made. This saves us from having to construct brand new URLs within each and every 'getter' that would get data from the API.

All this said and done, you end up with this for your get_daily_data function, which looks a bit cleaner than the original version, in my opinion:

def get_daily_data(symbol):

Now, the only thing you really need to do is make sure you're passing the proper request/function string to the _request library, and also pass the symbol.

This has an added bonus, though: because we're using _request to do the URL construction and the actual web request processing, we can easily expand this code for other functions in your API wrapper - all you need to change is the 'function' call to get different data.

Unused Libraries

You import datetime but you don't use it for anything. So, don't include it in the import statements until you actually use it for something.

Now on to testing. I use a slightly different form of your test code here, compressing everything into a one-liner call:

print(get_daily_data("AAPL")["Time Series (Daily)"]["2018-03-02"])

This in turn returns this data:

{'1. open': '172.8000', '2. high': '176.3000', '3. low': '172.4500', '4. close': '176.2100', '5. volume': '38453950'}

The code after all my revisions above, and after removing comments, ends up being this:

import json
import urllib.request

QUERY_URL = "https://www.alphavantage.co/query?function={REQUEST_TYPE}&apikey={KEY}&symbol={SYMBOL}"
API_KEY = "AN ACTUAL KEY"

def _request(symbol, req_type):
with urllib.request.urlopen(QUERY_URL.format(REQUEST_TYPE=req_type, KEY=API_KEY, SYMBOL=symbol)) as req:
return data

def get_daily_data(symbol):

This being said, this program could be developed to take the stock ticker to check as a runtime argument, thereby permitting you to run the core code against any symbol that you define, but that's outside the scope of this review, technically.

• Wow! This is incredible. I like how simplistic it is and I do like the detail and explanation about possible expansion. Thanks a million! Apr 4, 2018 at 20:34

I will drop you an updated version of the code, it basically changes small things

• Renamed variables to follow snake_case convention
• Make use of Python 3 f"" function to create strings
• Restructured code for creating the url
• Added main function to run script directly

def get_daily_data(symbol, request_type, api_key):

url = f"{main_url}{request_type}&symbol={symbol}&apikey={api_key}"

with urllib.request.urlopen(url) as req:

if __name__ == "__main__":


text:
# Q : 2     Find the values of  $\small \theta$ and $\small p$, if the equation  $\small x\cos \theta +y\sin \theta =p$ is the normal form of the line  $\small \sqrt{3}x+y+2=0$.

G Gautam harsolia

The normal form of the line is     $\small x\cos \theta +y\sin \theta =p$
Given the equation of lines is
$\small \sqrt{3}x+y+2=0$
First, we need to convert it into normal form. So, divide both the sides by $\small \sqrt{(\sqrt3)^2+1^2}= \sqrt{3+1}= \sqrt4=2$
$\small -\frac{\sqrt3\cos \theta}{2}-\frac{y}{2}= 1$
On comparing both
we will get
$\small \cos \theta = -\frac{\sqrt3}{2}, \sin \theta = -\frac{1}{2} \ and \ p = 1$
$\small \theta = \frac{7\pi}{6} \ and \ p =1$
Therefore, the answer is  $\small \theta = \frac{7\pi}{6} \ and \ p =1$

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Questions


text:
# What makes the Cartier operator “tick”?

Let $C$ be a smooth curve over a finite field of characteristic $p$. Let $t$ be a local parameter at a point. If $f$ is a regular function on a neighbourhood of the point, one can write uniquely $$f = \sum_{i=0}^{p-1} f_i^p t^i$$ for functions $f_i$. Using this decomposition one can define an operator on differential forms on $C$ via $$f \mathrm d t \mapsto f_{p-1} \mathrm d t.$$ Amazingly (?) this does not depend on the choice of coordinate, producing a map of sheaves $\Omega_C \to \Omega_C$. This is the Cartier operator.

Question: What is so special about $\Omega_C$ here? Is there a similar construction on quadratic differentials? On spin curves, i.e. on a square root of $\Omega_C$?

I am told that the Cartier operator is analogous to the residue of a logarithmic differential form. So I guess a similar question (that I don't know how to answer either) is what makes the residue tick.

-
I see them as analogous because both are about the failure of $d$ to be onto. On Laurent polynomials in $t$, in characteristic zero, every $t^k$ is a derivative except $t^{-1}$, and the residue looks at the coefficient of that. On honest polynomials in $t$, in characteristic $p$, all the $t^k$s are derivatives except when $p|k+1$, and the Cartier looks at the (now infinitely many!) coefficients of those. –  Allen Knutson Jun 19 '13 at 19:00
BTW my favorite application of the Cartier operator is this. Given a nonzero anticanonical section $\sigma$, look at $f \mapsto \sigma$Cartier$(f/\sigma)$. Since $f/\sigma$ is a (meromorphic) top form, it's closed, so we can apply Cartier. When we contract it with $\sigma$ again, it becomes a well-defined function. So $\sigma$ gives a Frobenius-inverse-linear map from functions to functions, which for good $\sigma$ is a Frobenius splitting that compatibly splits $\{\sigma = 0\}$. –  Allen Knutson Jun 19 '13 at 20:00
To see why the Cartier operator is independent of the choice of the coordinate, you can check out Exe4.13 in the book 'Algebraic function fields and codes' by Stichtenoth. In short, it tells you that the map defined by certain properties of the Cartier operator has to be Cartier. –  Yujia Qiu Jun 12 '14 at 16:33

I came to this question hoping to learn more, but I can record what I've learned. I find the Cartier operator much more natural in a larger context. This is a combination of material from Brion and Kumar's book, Section I.3, and things I saw asserted in papers and worked out for myself. Of course, there is a risk that any of this is wrong.$\def\cF{\mathcal{F}}$ $\def\cC{\mathcal{C}}$

Notation: Let $k$ be a perfect field of characteristic $p$ and $A$ a $k$-algebra. Let $\Omega^r$ be the $r$-th wedge power of the Kahler differentials of $A/k$. Let $Z^r = \mathrm{Ker}(d: \Omega^r \to \Omega^{r+1})$ (the de Rham co-cycles) and $B^r = \mathrm{Im}(d: \Omega^{r-1} \to \Omega^r)$ (the de Rham co-boundaries). Let $H^r = Z^r/B^r$. Let $A^p$ denote the ring of $p$-th powers in $A$. Note that $d$ is a map of $A^p$ modules and hence $Z^r$, $B^r$ and $H^r$ are all $A^p$ modules.

The inverse of the Cartier operator is more basic than the Cartier operator.

Theorem There is a unique map $\cF: \Omega^r \to H^r$ such that

• $\cF(f) = f^p$ for $f \in \Omega^0 = A$.

• $\cF(\alpha+\beta) = \cF(\alpha)+\cF(\beta)$.

• $\cF(d u) = u^{p-1} du$ for $u \in A$.

• $\cF(\alpha \wedge \beta) = \cF(\alpha) \wedge \cF(\beta)$.

The only hard part to check is that $(u+v)^{p-1} (du+dv)$ is equivalent to $u^{p-1} du+ v^{p-1} dv$ modulo $B^1$. To this end, note that $$(u+v)^{p-1} (du+dv) - u^{p-1} du - v^{p-1} dv = d \sum_{k=1}^{p-1} \frac{1}{p} \binom{p}{k} d(u^k v^{p-k}). \quad (\ast)$$ Here $\frac{1}{p} \binom{p}{k}$ must be interpreted as an integer which we reduce modulo $p$ to make an element of $k$. (Morally, equation $(\ast)$ comes from the relation $d(u+v)^p = \sum_{k=0}^{p} \binom{p}{k} d(u^k v^{p-k})$. We can't deduce $(\ast)$ directly from this because we can't divide by $p$, but $(\ast)$ is still true in characteristic $p$.)

If $A$ has a sufficiently nice deformation $\tilde{A}$ over the ring of Witt vectors $W(k)$, and $F: \tilde{A} \to \tilde{A}$ is a lift of Frobenius, then $\cF$ for $\omega \in \Omega^r$ is given by reduction modulo $p$ of $\frac{1}{p^r} (F^{\ast})^r \omega$. I don't know exactly what "sufficiently nice" means, but $\tilde{A}$ smooth over $W(k)$ is certainly enough. This is my favorite way to think of $\cF$.

$\cF$ respects localization, and thus makes sense on schemes. It also respects etale extension and completion, for those who prefer other topologies.

We now have Theorem I.3.4 in Brion and Kumar (presumably not original, but they don't cite it): If $A$ is regular, than $\cF$ is an isomorphism $\Omega^{\bullet} \to H^{\bullet}$. Proof sketch: The claim is that a map of finitely generated $A^p$ modules is an isomorphism; this can be checked on completions. So we are reduced to proving the claim in a power series algebra. This is a combinatorial exercise, very similar to the proof of the Poincare lemma for formal power series in characteristic zero.

Note that this is interesting even for $r=0$: It says that $df=0$ for $f \in A$ if and only if $f$ is a $p$-th power.

For $A$ regular, the Cartier operator $\cC: H^{\bullet} \to \Omega^{\bullet}$ is the inverse to $\cF$.

In particular, if $A$ regular of dimension $1$, then we can take the composition $\Omega^1 \to H^1 \to \Omega^1$ to get the definition you gave.

$\cC$ on a curve is analogous to residue in several senses:

• It is the composition of $\Omega^1 \to H^1$ and an isomorphism between $H^1$ and an explicit free $H^0$-module of rank $1$. In the case of residue, working in the Laurent series ring $k((x))$, we have $H^0 = k$ and we have a canonical isomorphism $H^1 \cong k$; the residue map is $\Omega^1 \to H^1 \to k$. In the Cartier case, $H^0 = A^p$ and $H^1$ is a free $A^p$-module of rank $1$. It doesn't have a canonical generator, but what you can do canonically is use $\cC$ to turn $A^p$ into $A$ and $H^1$ into $\Omega^1$.

• We have $\cC(df) = 0$ and $\cC(du/u) = du/u$, for $u$ a unit of $A$.

• Concretely, $\mathrm{res}(\cC(\omega)) = \mathrm{res}(\omega)^{1/p}$.

-


text:
Taking algebraic topology class this semester... and met the notion of the fundamental group days ago. Okay they are set of classes of a loop homotopy and thing were fine... but the professor proved that the group has an actual group structure and thing were confusing.

For example he showed that a constant path multiplied by a path is just the path by finding a homotopy between them. I understand they are homotopic after some math but how can I construct them without referring to the textbook? Have mathematicians done it by trial and error or is there any neat way to construct the homotopies to show the group structure on the fundamental group?

Thank you so much

For the proof you have to check:

$\mbox{1.) }\gamma\cdot e\sim \gamma \sim e\cdot \gamma$

$\mbox{2.) }\gamma\cdot \gamma^{-1}\sim e$

$\mbox{3.) }(\beta\cdot \gamma)\cdot \delta\sim \beta\cdot(\gamma\cdot\delta)$

$e$ is the constant path. I will give the explanation for the second case. For me it is helpful to draw boxes like this:

(Well, it's not the best quality, but I think, it's clear what I mean.)

We want to go the path $\gamma$ then $\gamma^{-1}$ in a certain time which is given by the interval $I$. So we have to double the speed for each path.

This is exactly the meaning of the definition of the product: $$\gamma\cdot \gamma^{-1}(t):=\begin{cases} \gamma(2t)\mbox{ for }0\le t\le1/2,\\ \gamma(2t-1)\mbox{ for }1/2\le t\le 1, \end{cases}$$

This is homotopic to the constant path. The idea behind it, is the following: We stay at the basepoint, then we go $\gamma$ then $\gamma^{-1}$ back and the rest of the time we stay at the basepoint, i.e. the const. path $e$.

For example: If you consider the red line, we just stay at the basepoint $x_0$ up to $1/4$ of the time. Then we go $\gamma$, but not the full way of it, but maybe $1/4$ of the way and go back by $\gamma^{-1}$. The rest of the time we stay at $x_0$.

Now the box gives us a helpful tool giving an explicit definition of the corresponding homotopy $H\colon I\times I\to X$, $(s,t)\mapsto H(s,t)$. The domain of $s$ has to shrink by growing $t$. By our foregoing explanation, we know that there are exactly 4 parts we have to define: the first part and the fourth part, where we stay at $x_0$, and the second and third part, where we go $\gamma$ and $\gamma^{-1}$ back. This gives us the following: $$H(s,t)= \begin{cases} e(s)\mbox{ for }0\le s\le \frac{1}{2}t,\\ \gamma(2s)\mbox{ for } \frac{1}{2}t \le s\le \frac{1}{2},\\ \gamma(2s-1)\mbox{ for } \frac{1}{2} \le s \le 1 - \frac{1}{2}t,\\ e(s)\mbox{ for }1-\frac{1}{2}t\le s \le 1. \end{cases}$$

We have $H(s,0)=\gamma\cdot \gamma^{-1}(t)$ and $H(s,1)=e(s)$.

To get a feeling (not explicit formulas) for the whole proof, watch this video:

In general it is important to imagine how the homotopy should work!

• exactly what i wanted. thanks – Mathcho Oct 3 '15 at 10:44

Mathematicians tend to think in terms of intuition behind the concept of homotopy. If you think of a path as a rope with both ends fixed, then you can move the rope in space, lengthen it by stretching/shorten it by tightening, and you'll end up with a homotopy equivalent path.

A loop is a rope with both ends fixed at the same spot. A composition of two loops naturally suggests itself as taking two ropes and tying the end of the first to the beginning of the second; now these 2 points are still physically present at the loop point but are no longer tied to it - only the beginning of the first and the end of the second are tied to it.

Then an inverse of a loop is just a second rope that runs exactly over the first but retraces it back, from end to beginning. If you compose a rope with its inverse, it's like you made some complicated path in space, then retraced your steps back. Since your original end-point is now (after composition) unstuck, you can keep shortening the rope, stealing all the time from its middle (original end), watching it recede along the path towards the beginning, until there's nothing left. There, you proved the existence of the group structure.

A constant path is lots of rope piled on the same spot... you get the picture. An explicit homotopy is a nice formal exercise and of course provides the necessary underlying rigor, but you need to learn to think topologically, with pictures.

• thanks for the good explanation. now i get the picture of it but i just wonder just how to 'construct' the explicit formula for the homotopies here... – Mathcho Sep 24 '15 at 10:41


text:
Searching for Beeping Busy Beavers is a harrowing task, since even detecting that a TM has beeped for the last time (quasihalted) is in general uncomputable. However, as Nick Drozd has shown over the last year or so, there is still progress to be made just looking at the types of quasihalting we can definitively prove. Over the last couple weeks, I’ve retooled the codebase (that my Dad and I have developed over the last 15 years) to be able to detect quasihalting behavior and then enumerated various domains.

This search has been very fruitful in the 5-state, 2-symbol search I would like to announce several new machines of interest:

## A new BBB(5, 2) champion:

0 1
A 1RB 1LC
B 1RC 0RD
C 0LB 0RC
D 0RE 1RD
E 1LE 1LA

1RB 1LC 1RC 0RD 0LB 0RC 0RE 1RD 1LE 1LA

which I calculate as quasihalting on step:

173435554530734876325688319985246476114761227213875751098091105080403058813 137700864058572534669440325871164552850233406790267431534345682690909996466 739822790829561588574981765612968902718598248994133711641212367730835044877 508837803451797867016673613501402694914688652744459261232089469884419360736 544397066449067999804481124350082304474584114473419538028647524012631393555 498144472772542970640769342167886331694446569461523622690305119525401331902 62122812094646680539368211780404865521194338123470785 (>1.7 × 10502)

After which point it is in state E on a blank tape and will now move to the left writing 1s forever (because E0 -> 1LE). It was last in state D one step earlier.

Nick, you might be curious to know that this machine is also a Blanking Beaver. In fact, it actually reaches a blank tape in every one of it’s 5 states! All 4 non-trivial one are near the end:

22592  0 C> 1~10251.4 0
22593  0 C> 0
22594  0 <B 0
22595  0 11 C> 0
22596  0 11 <B 0
22597  0 D> 0
22598  0 E> 0

## A close runner up:

0 1
A 1RB 1LE
B 0RC 0RC
C 0RD 1RC
D 1LD 1LA
E 0LB 0RE

1RB 1LE 0RC 0RC 0RD 1RC 1LD 1LA 0LB 0RE

which quasihalts on step:

173435554530734876325688319985246476114761227213875751098091105080403058813 137700864058572534669440325871164552850233406790267431534345682690909996466 739822790829561588574981765612968902718598248994133711641212367730835044877 508837803451797867016673611145572109965185955923949932905433536564448131797 454831082435818948428216902541362169354919782004726583684978216073073971799 032636113747662512733692622512739028763729615094519436023437779549237498239 23282203790915605756125236274372232928765435094504615

actually, when I first found these two machines, I mistakenly thought that this was the champion (partially because GNU sort silently fails to correctly numerically sort integers of this size!) I have underlined the section of digits in which these two numbers first differ (about halfway through the digit string).

I am working on an analysis of these two machines that I will share soon, but it appears that they are both simulating the exact same Collatz-like function. The champion just does it slightly more inefficiently … and thus wins the race because in the Beeping Busy Beaver game we are actually looking for the slowest machine to cross the finish line :)

## A machine with (slightly) more complex quasihalting behavior

Almost all of the top machines I found (19 of the top 20, for example) quasihalt in an extremely easy to detect way. They enter into what I am calling “Chain Recurrence” (Nick calls this 1-step Lin Recurrence). It is the behavior I described above for the 10502 champions I listed above. Specifically: we are in configuration S> 0∞ and S0 -> ?RS (or the mirror image: 0∞ <S and S0 -> ?LS) and so we can easily see that the TM will remain in state S forever after, just moving right (or left) over and endless stream of 0s.

Here is the 1 top 20 machine I found so far which does something slightly more complex:

0 1
A 1RB 1RD
B 1LC 1LB
C 1LD 1RA
D 0RE 0RD
E 1LB 1RE

1RB 1RD 1LC 1LB 1LD 1RA 0RE 0RD 1LB 1RE

It quasihalts at step 94418964659944351442398224758 (>9.4 × 1028), blanks the tape at step 12250514892052349453616935044134 (>1.2 × 1031) and then enters into what Brady called “Christmas Tree” Recurrence. Explicitly:

for any n ≥ 0:

0 <D 1n 0
0 E> 1n 0
0 1n E> 0
0 1n <B 1 0
0 <B 1n+1 0
0 <C 1n+2 0
0 <D 1n+3 0

and then this process repeats forever, increasing the number of 1s by 3 each recurrence. Note that this recurrence never enters state A, which is how we detect that this machine actually quasihalted much earlier.

## Enumeration Status

I thought that some of you might be interested in the overall size of the BBB landscape. I’ve enumerated TMs in the following domains:

Domain max # loops # TMs # Quasihalt % Quasihalt # Unknown % Unknown
2x2 1M 121 17 14.0% 1 0.8%
2x3 1M 10,393 974 9.4% 192 1.8%
3x2 1M 16,549 4,249 25.7% 112 0.7%
2x4 1M 1,869,525 133,612 7.1% 69,331 3.7%
4x2 1M 2,943,669 919,061 31.2% 26,136 0.9%
3x3 1k 164,537,029 26,451,658 16.1% 5,086,812 3.1%
2x5 1k 548,090,457 32,489,678 5.9% 44,087,899 8.0%
5x2 50k 687,161,765 248,328,604 36.1% 10,822,343 1.6%
• Domain: NxM means N-state, M-symbol
• # TMs: the number of TMs enumerated using Tree Normal Form (Nick calls this Brady’s algorithm) where the first transition is always forced to be A0 -> 1RB and we allow machines with no halt transitions.
• max # loops: Number of “simulator loops” I have run all of the TMs in this domain for. Note that this is an accelerated simulator, so one sim loop can translate into a large number of TM steps. # loops is roughly proportional to simulation time.
• # Quasihalt: does not include # Halt
• # Unknown: The number of “holdout” machines which our system has not been able to make any conclusion about, if you can get this to 0, you’ve “proven” the BBB for that domain.

Everything up to 4x2 case can be run serially locally (it took me 7hr to run 4x2 out to 10k loops on my laptop). For the 3 biggest domains (3x3, 2x5, 5x2) I have been running in parallel on a cluster of 20 12-core machines. Running 5x2 out to 50k took about 4300 core-hours (~18 hours on the cluster). I ran 5x2 up to 1k, 2k, 10k, 25k, and 50k and up until 25k each increase led to a new BBB(5, 2) champion. 50k run did not find anything new so I decided it was a good time to share the news :)

All the code to enumerate and simulate these domains is available at our Busy Beaver repo. And some results are also available there. For example, my top 20 BBB(5, 2) champions are at: https://github.com/sligocki/busy-beaver/blob/main/Machines/5x2-Beep-Top. The code is perhaps not the most user-friendly / documented at the moment, but I’m currently working on improving that. Send me an email if your interested in playing around with this or using it to analyze long running Beavers.

## Reflection

Even with the simplest of quasihalting conditions (Chain Recurrence), we’ve been able to push BBB(5, 2) > 10502. Is there more out there? I imagine yes. While almost all of the TMs we proved quasihalting were proven using Chain/Lin Recurrence, there is a clear selection bias here. We only found what our system was programmed to find. Among the > 10M remaining Unknown TMs, I predict that there will be some monsters which exhibit far more complex quasihalting behavior … but how do we find them? I excited look forward to new techniques being developed and deployed!


text:
## Electronic Journal of Probability

### Multivariate Records Based on Dominance

#### Abstract

We consider three types of multivariate records in this paper and derive the mean and the variance of their numbers for independent and uniform random samples from two prototype regions: hypercubes $[0,1]^d$ and d-dimensional simplex. Central limit theorems with convergence rates are established when the variance tends to infinity. Effective numerical procedures are also provided for computing the variance constants to high degree of precision.

#### Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 60, 1863-1892.

Dates
Accepted: 16 November 2010
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464819845

Digital Object Identifier
doi:10.1214/EJP.v15-825

Mathematical Reviews number (MathSciNet)
MR2738341

Zentralblatt MATH identifier
1225.60043

Subjects
Primary: 60C05 60F05 60G70

Rights

#### Citation

Hwang, Hsien-Kuei; Tsai, Tsung-Hsi. Multivariate Records Based on Dominance. Electron. J. Probab. 15 (2010), paper no. 60, 1863--1892. doi:10.1214/EJP.v15-825. https://projecteuclid.org/euclid.ejp/1464819845

#### References

• Z.-D. Bai, L. Devroye, H.-K. Hwang and H.-T. Tsai, Maxima in hypercubes, Random Structures Algorithms 27 (2005), 290-309.
• Z.-D. Bai, H.-K. Hwang, W.-Q. Liang and T.-H. Tsai, Limit theorems for the number of maxima in random samples from planar regions, Electron. J. Probab. 6 (2001), no. 3, 41 pp. (electronic).
• J. Baik, P. Deift and K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, J. Amer. Math. Soc. 12 (1999), 1119-1178.
• Yu. Baryshnikov and A. Gnedin, Counting intervals in the packing process, Ann. Appl. Probab. 11 (2001), 863-877.
• W.-M. Chen, H.-K. Hwang and T.-H. Tsai, Maxima-finding algorithms for multidimensional samples: A two-phase approach, preprint, 2010.
• H.-H. Chern, M. Fuchs and H.-K. Hwang, Phase changes in random point quadtrees, ACM Trans. Algorithms 3 (2007), no. 2, Art. 12, 51 pp.
• H.-H. Chern, H.-K. Hwang and T.-H. Tsai, An asymptotic theory for Cauchy-Euler differential equations with applications to the analysis of algorithms, J. Algorithms 44 (2002), 177-225.
• S. N. Chiu and M. P. Quine, Central limit theory for the number of seeds in a growth model in Rd with inhomogeneous Poisson arrivals, Ann. Appl. Probab. 7 (1997), 802-814.
• A. Darrasse, H.-K. Hwang, O. Bodini and M. Soria, The connectivity-profile of random increasing k-trees, preprint (2009); available at arXiv:0910.3639v1.
• J.-D. Deuschel and O. Zeitouni, Limiting curves for iid records, Ann. Probab. 23 (1995), 852-878.
• L. Devroye, Universal limit laws for depths in random trees, SIAM J. Comput. 28 (1999), 409-432.
• P. Flajolet, X. Gourdon and P. Dumas, Mellin transforms and asymptotics: harmonic sums, Theoret. Comput. Sci. 144 (1995), 3-58.
• P. Flajolet, G. Labelle, L. Laforest and B. Salvy, Hypergeometrics and the cost structure of quadtrees, Random Structures Algorithms 7 (1995), 117-144.
• P. Flajolet and R. Sedgewick, Mellin transforms and asymptotics: finite differences and Rice's integrals, Theoret. Comput. Sci. 144 (1995), 101-124.
• P. Flajolet and R. Sedgewick, Analytic Combinatorics}, Cambridge University Press, Cambridge, 2009.
• A. Gnedin, Records from a multivariate normal sample, Statist. Prob. Lett. 39 (1998) 11-15.
• A. Gnedin, The chain records, Electron. J. Probab. 12 (2007), 767-786.
• C. M. Goldie and S. Resnick, Records in a partially ordered set, Ann. Probab 17 (1989), 678-699.
• C. M. Goldie and S. Resnick, Many multivariate records, Stoch. Process. Appl. 59 (1995), 185-216.
• E. Hashorva and J. Hüsler, On asymptotics of multivariate integrals with applications to records, Stoch. Models 18 (2002), 41-69.
• E. Hashorva and J. Hüsler, Multiple maxima in multivariate samples, Stoch. Prob. Letters 75 (2005), 11-17.
• H.-K. Hwang, On convergence rates in the central limit theorems for combinatorial structures, European J. Combin. 19 (1998), 329-343.
• M. Kałuszka, Estimates of some probabilities in multidimensional convex records, Appl. Math. (Warsaw) 23 (1995), 1-11.
• A. M. Vershik and S. V. Kerov, Asymptotic behavior of the Plancherel measure of the symmetric group and the limit form of Young tableaux, Soviet Math. Dokl. 233 (1977), 527-531.


text:
# How to strip down all the punctuation from a string in Python?

PythonServer Side ProgrammingProgramming

#### Beyond Basic Programming - Intermediate Python

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The fastest way to strip all punctuation from a string is to use str.translate(). You can use it as follows:

import string
s = "string. With. Punctuation?"
print s.translate(None, string.punctuation)

This will give us the output:

string With Punctuation

If you want a more readable solution, you can explicitly iterate over the set and ignore all punctuation in a loop as follows:

import string
s = "string. With. Punctuation?"
exclude = set(string.punctuation)
s = ''.join(ch for ch in s if ch not in exclude)
print s

This will give us the output:

string With Punctuation
Updated on 30-Sep-2019 06:52:35


text:
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Well done. You've clicked the tower. This would actually achieve something if you had logged in first. Use the key for that. The name takes you home. This is where all the applicables sit. And you can't apply any changes to my site unless you are logged in.

Our policy is best summarized as "we don't care about _you_, we care about _them_", no emails, so no forgetting your password. You have no rights. It's like you don't even exist. If you publish material, I reserve the right to remove it, or use it myself.

Don't impersonate. Don't name someone involuntarily. You can lose everything if you cross the line, and no, I won't cancel your automatic payments first, so you'll have to do it the hard way. See how serious this sounds? That's how serious you're meant to take these.

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The constantly expanding frequency and loss affected by natural disasters pose a severe challenge to the traditional catastrophe insurance market. This paper aims to develop an innovative framework of pricing catastrophic bonds triggered by multiple events with extreme dependence structure. Given the low contingency of the bond's cash flows and high return, the multiple-event CAT bond may successfully transfer the catastrophe risk to the big financial markets meeting the diversification of capital allocations for most potential investors. The designed hybrid trigger mechanism helps reduce moral hazard and improve bond attractiveness wi…
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Extended cure survival models enable to separate covariates that affect the probability of an event (or long-term' survival) from those only affecting the event timing (or short-term' survival). We propose to generalize the bounded cumulative hazard model to handle additive terms for time-varying (exogenous) covariates jointly impacting long- and short-term survival. The selection of the penalty parameters is a challenge in that framework. A fast algorithm based on Laplace approximations in Bayesian P-spline models is proposed. The methodology is motivated by fertility studies where women's characteristics such as the emplo…
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The Causality field aims to find systematic methods for uncovering cause-effect relationships. Such methods can find applications in many research fields, justifying a great interest in this domain. Machine Learning models have shown success in a large variety of tasks by extracting correlation patterns from high-dimensional data but still struggle when generalizing out of their initial distribution. As causal engines aim to learn mechanisms that are independent from a data distribution, combining Machine Learning with Causality has the potential to bring benefits to the two fields. In our work, we motivate this assumption and provide appli…
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# 2022-12-08 更新

### Towards Transferable Unrestricted Adversarial Examples with Minimum Changes

Authors:Fangcheng Liu, Chao Zhang, Hongyang Zhang

Transfer-based adversarial example is one of the most important classes of black-box attacks. However, there is a trade-off between transferability and imperceptibility of the adversarial perturbation. Prior work in this direction often requires a fixed but large $\ell_p$-norm perturbation budget to reach a good transfer success rate, leading to perceptible adversarial perturbations. On the other hand, most of the current unrestricted adversarial attacks that aim to generate semantic-preserving perturbations suffer from weaker transferability to the target model. In this work, we propose a geometry-aware framework to generate transferable adversarial examples with minimum changes. Analogous to model selection in statistical machine learning, we leverage a validation model to select the optimal perturbation budget for each image under both the $\ell_{\infty}$-norm and unrestricted threat models. Extensive experiments verify the effectiveness of our framework on balancing imperceptibility and transferability of the crafted adversarial examples. The methodology is the foundation of our entry to the CVPR’21 Security AI Challenger: Unrestricted Adversarial Attacks on ImageNet, in which we ranked 1st place out of 1,559 teams and surpassed the runner-up submissions by 4.59% and 23.91% in terms of final score and average image quality level, respectively. Code is available at https://github.com/Equationliu/GA-Attack.
PDF First place in the CVPR’21 Security AI Challenger: Unrestricted Adversarial Attacks on ImageNet

### Imperceptible Adversarial Attack via Invertible Neural Networks

Authors:Zihan Chen, Ziyue Wang, Junjie Huang, Wentao Zhao, Xiao Liu, Dejian Guan

PDF

### Fooling the Eyes of Autonomous Vehicles: Robust Physical Adversarial Examples Against Traffic Sign Recognition Systems

Authors:Wei Jia, Zhaojun Lu, Haichun Zhang, Zhenglin Liu, Jie Wang, Gang Qu

Adversarial Examples (AEs) can deceive Deep Neural Networks (DNNs) and have received a lot of attention recently. However, majority of the research on AEs is in the digital domain and the adversarial patches are static, which is very different from many real-world DNN applications such as Traffic Sign Recognition (TSR) systems in autonomous vehicles. In TSR systems, object detectors use DNNs to process streaming video in real time. From the view of object detectors, the traffic sign`s position and quality of the video are continuously changing, rendering the digital AEs ineffective in the physical world. In this paper, we propose a systematic pipeline to generate robust physical AEs against real-world object detectors. Robustness is achieved in three ways. First, we simulate the in-vehicle cameras by extending the distribution of image transformations with the blur transformation and the resolution transformation. Second, we design the single and multiple bounding boxes filters to improve the efficiency of the perturbation training. Third, we consider four representative attack vectors, namely Hiding Attack, Appearance Attack, Non-Target Attack and Target Attack. We perform a comprehensive set of experiments under a variety of environmental conditions, and considering illuminations in sunny and cloudy weather as well as at night. The experimental results show that the physical AEs generated from our pipeline are effective and robust when attacking the YOLO v5 based TSR system. The attacks have good transferability and can deceive other state-of-the-art object detectors. We launched HA and NTA on a brand-new 2021 model vehicle. Both attacks are successful in fooling the TSR system, which could be a life-threatening case for autonomous vehicles. Finally, we discuss three defense mechanisms based on image preprocessing, AEs detection, and model enhancing.
PDF 17 pages, 15 figures

目录


text:
# zbMATH — the first resource for mathematics

On the number of unbounded solution branches in a neighborhood of an asymptotic bifurcation point. (English. Russian original) Zbl 1128.47055
Funct. Anal. Appl. 39, No. 3, 194-206 (2005); translation from Funkts. Anal. Prilozh. 39, No. 3, 37-53 (2005).
This paper concerns abstract equations of the type
$x= \lambda Ax+F_0(\lambda)+ F_1(Ax,\lambda), \quad \lambda\in\mathbb R,\;x\in B. \tag{1}$
Here, $$H$$ is a Hilbert space with scalar product $$\langle\cdot,\cdot\rangle$$, $$B\hookrightarrow H$$ is a Banach space, $$A:H\to B$$ is linear, completely continuous in $$B$$ and selfadjoint in $$H$$, and $$H_0:\mathbb R\to H$$ and $$F_1:H\times\mathbb R\to\mathbb R$$ are continuous. Further, it is supposed that $$F_1$$ is asymptotically homogeneous, that $$\lambda_0\in\mathbb R$$ is a characteristic value of $$A$$ of multiplicity two, that $$F_0(\lambda_0)\perp\ker (I-\lambda_0A)$$, and that $$F_1$$ is “coordinated with $$A$$” (see the paper for this notion). Then each proper solution of a certain scalar equation on $$\{x\in H: x= \lambda_0Ax$$, $$\|x\|=1\}$$ generates a directed unbounded branch of solutions to (1).
Applications to second order ODEs (forced oscillations, two-point boundary value problems) are also given.

##### MSC:
 47J15 Abstract bifurcation theory involving nonlinear operators 34C23 Bifurcation theory for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 47N20 Applications of operator theory to differential and integral equations 58E07 Variational problems in abstract bifurcation theory in infinite-dimensional spaces
Full Text:
##### References:
 [1] M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, Oxford-London-New York-Paris, 1964. [2] K. Schmitt and Z. Q. Wang, ”On bifurcation from infinity for potential operators,” Differential Integral Equations, 4, No.5, 933–943 (1991). · Zbl 0736.58014 [3] A. M. Krasnosel’skii, ”Asymptotic homogeneity of hysteresis operators,” Z. Angew. Math. Mech., 76, Suppl. 2, 313–316 (1996). · Zbl 0889.47034 [4] M. A. Krasnoselskii and P. P. Zabreiko, Geometric Methods of Nonlinear Analysis, Springer-Verlag, Berlin-Heidelberg-New York-Tokio, 1984. [5] A. C. Lazer and D. E. Leach, ”Bounded perturbations of forced harmonic oscillators at resonance,” Ann. Mat. Pura Appl. (4), 82, 46–68 (1969). · Zbl 0194.12003 [6] A. M. Krasnosel’skii and J. Mawhin, ”Periodic solutions of equations with oscillating nonlinearities. Nonlinear operator theory,” Math. Comput. Modelling, 32, 1445–1455 (2000). · Zbl 0974.34042 · doi:10.1016/S0895-7177(00)00216-8 [7] P.-A. Bliman, A. M. Krasnosel’skii, M. Sorine, and A. A. Vladimirov, ”Forced oscillations in control systems with hysteresis,” Dokl. Akad. Nauk, 347, No.4, 458–461 (1996). English transl. in: Acad. Sci. Russian Dokl. Math., 53, No. 2, 312–315 (1996). · Zbl 0906.93027 [8] A. M. Krasnosel’skii, N. A. Kuznetsov, and D. I. Rachinskii, ”On resonant differential equations with unbounded non-linearities,” Z. Anal. Anwendungen, 21, No.3, 639–668 (2002). · Zbl 1025.34032 [9] P. Diamond, P. E. Kloeden, A. M. Krasnosel’skii, and A. V. Pokrovskii, ”Bifurcations at infinity for equations in spaces of vector-valued functions,” J. Austral. Math. Soc. Ser. A, 63, No.2, 263–280 (1997). · Zbl 0913.47058 · doi:10.1017/S1446788700000689 [10] A. M. Krasnosel’skii and J. Mawhin, ”The index at infinity of some twice degenerate compact vector fields,” Discrete Contin. Dynam. Systems, 1, No.2, 207–216 (1995). · Zbl 0877.47034 · doi:10.3934/dcds.1995.1.207 [11] V. I. Arnold, Arnold Problems, Springer-Verlag, Berlin-London, 2005.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
# My Mind going to blow! Why Conservative field Path independ?

1. Aug 7, 2010

### TMSxPhyFor

Hi

I'm now reading about Vector fields, everything is clear and intuitive for me as curl divergence ..ect , except one simple thing that I'm straggling with for the last 4 days! I searched Internet and a lot of math & physics books but in vain :

Why Conservative field is Path independent? or why work between two point will be path independent, by definition conservative field is the one generated out of gradient of some scalar, and purely mathematically it's very straight forward and clear, but it's not intuitive for me at all, I can't find any geometric explanation for that even so it seems to be very neat , Beautiful and simple result...

Any I ideas? thx in advance.

Last edited: Aug 7, 2010
2. Aug 7, 2010

### timewalker

At first, problem is determining which sentence is prior to the other.
Path-independent line integral vector field => Conservative field?
Or
Conservertive field => path-independent?

I think first one is more better explanation for our intuition. But if we are gonna make the definition of conservative field then may be we can write it like follow
"A conservative field is a differentiable(integrable) vector field if and only if any line integral upon closed countour is zero.

Once we define it like above, next two sentences are equivalent.

"Conservative vector fields are path-independent."
"A vector field that line integrals are path-independent is conservative."

3. Aug 7, 2010

### TMSxPhyFor

Dear timewalker

Tnx for your replay, personally, i think it more logical or abstract to think about it in the second way, field is gradient of a scalar -> it's path independent, then I say: the interesting thing that gradient is always pointing to the max increment of the function, and for "some" magical reasons when we doing inner product of this vector (gradient) by a dr which by the way as i realized after a long mind straggling that it is also a vector field dr=d(xi+yj+zk) and this vector field is going in circles around the origin , so by doing this inner product we actually getting function increment along this circulation (directional derivative) or we getting the projection of the gradient vectors on that circulating vector field, which happens to became get full derivative of some scalar function! that amazing and surprising for me as i can't understand why that happening, and that last thing is always path independent as a consequence!! why? what if after that product we got inexact derivative, what that mean? also it's interesting to note that simplest circulating field r=yi-xj is not path independent! I'm sure I'm missing here something obvious and very important!

Also it's useful to recall that infinitesimal circulation (curl or rotor) of conservative field is zero, it's very clear why if we know that it will be path in-depended.

I just can't fit all this parts together! pls help!

4. Aug 7, 2010

### lugita15

The attached proof isn't mathematically rigorous, but hopefully it will give you an intuitive sense of why conservative vector fields are conservative. Tell me if any of the steps are unclear.

#### Attached Files:

• ###### Vector Calc Proof.JPG
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5. Aug 8, 2010

Have you seen the proof of the gradient theorem, which states for a scalar field $f$ and a path $\gamma$ from $\mathbf r_0$ to $\mathbf r_1$
$$\int_\gamma \nabla f \cdot d\mathbf{r} = f(\mathbf r_1) - f(\mathbf r_0)$$
?

Path independence follows from the fact that the right side depends only on the endpoints.

6. Aug 8, 2010

### quasar987

And the "gradient theorem", as many things in life , is just a facet of the fundamental theorem of calculus:

Let C be a curve joining two points r_0 and r_1 of R³.

$$\int_C\nabla f\cdot dr=\int_{t_0}^{t_1}\sum_{i=1}^3\frac{\partial f}{\partial x^i}(\gamma(t))\frac{d\gamma}{dt}dt=\int_{t_0}^{t_1}\frac{d}{dt}(f\circ\gamma)dt=(f\circ\gamma)(t_1)-(f\circ\gamma)(t_0)=f(r_1)-f(r_0)$$

Explanation: first equality is just the definition of the line integral, where \gamma is a parametrization of the curve C. Second equality is the chain rule. Third equality is the fundamental theorem of calculus.

What the above tells us is that understanding path independence of gradient vector fields, like many things in life, boils down to understanding the FTC.

7. Aug 8, 2010

### TMSxPhyFor

As I said, from pure mathematical manipulations, it's quite clear why is that happening, but again you trying to explain me the answer in that framework, which is not my goal.

I will try to rephrase my question in a more physical sense (and the answer I'm seeking for is in this sense also)

If we had a field, some point is moving on couple predefined paths , we calculating the work by summarizing infinitely many works along the path, we calculating the work on each of those paths, everything till here is cool, then we changing our field a little bit in one or another way, and recalculating works...
Suddenly, in one of our experiments, we got that work along all of this paths obtained the same value! putting in mind that those paths are very different in length, it will be very strange to me how that happens.

In the context of the above, I want explanation, not using math, the math you provided is not explaining why especially gradients have such Independence! in other words, why integrating over one variable function is always path independent, in multipliable it depends, and why if the field is gradient it's again don't depend! no math please.. I need intuition! sorry for that...

8. Aug 8, 2010

Before you can make intuitive sense of the gradient theorem, you need to have intuition about what gradients and path integrals mean.

In physics, the typical example is: the scalar field is potential energy, the gradient of potential energy is force (except for opposite sign), and the line integral is work. So when you have a particle in a conservative force field (i.e. it arises from a potential energy field), then the work done on the particle upon moving it doesn't depend on the path it takes.

9. Aug 8, 2010

### quasar987

I understand that you're trying to get an intuitive feel for why the gradient them is true. The point of my post was that if you get an intuitive feel for why each step in the proof is true, then you will have achieved your goal. Don't you agree?

10. Aug 9, 2010

### TMSxPhyFor

So when you have a particle in a conservative force field (i.e. it arises from a potential energy field), then the work done on the particle upon moving it doesn't depend on the path it takes.

You are just saying the same, conservative <=> path independent, I want to dig deeply to understand the reasons behind that.

Dear Quasar

I understand that you're trying to get an intuitive feel for why the gradient them is true. The point of my post was that if you get an intuitive feel for why each step in the proof is true, then you will have achieved your goal. Don't you agree?

I totally agree with the math you posted, but i can't see how it should affect my intuition, in one variable situation we have
$$\int\grave{A(x)}dx$$
(where A(x) is the area function from Newton-Leibenz Theorem) , thus we multiplying the rate of area function increment my our step or movement (dx), the same is with line integrals, we multiplying the rate of increment of potential by dr, but when our field is not conservative, we still multiplying it by dr, but here we also need the path that we are moving on! strange! also we always can think about non conservative field, or inexact derivative (this is my own opinion after long tries to understand what is inexact derivative means) as a directional derivative along some vector (but not parallel to the Maximum increment vector direction or gradient), in other words here we also know along which path we are moving, but still we need additional info on the path! why is that ? there is something missed!

11. Aug 9, 2010

### quasar987

Why is that strange? Suppose you observe a certain phenomenon happening under a certain set of circumstances. If you modify those circumstances, will you find it strange if the phenomenon no longer takes place?!

Here is another intuitive explanation of the phenomenon.

For any point r in R³, the gradient $\nabla f(r)$ satisfies

$$\vect{\nabla f}(r)\cdot \vect{\Delta r}\approx f(\vect{r}+\vect{\Delta r})-f(\vect{r})$$

and the approximation gets better as $\vect{\Delta r}$ gets smaller. Let C be a path joining x_0 to x_1. Also let $\{\vect{r_i}:0\leq i \leq N\}$ be a partition of C with r_0=x_0 and r_N=x_1. Set also $\vect{\Delta r_i}:=\vect{r_{i+1}}-\vect{r_i}$. Then,

$$\int_C\vect{\nabla f}(r)\cdot \vect{\Delta r}=\lim_{\mathrm{max}\vect{\Delta r_i}\rightarrow 0}}\sum_{i=0}^N\vect{\nabla f}(r_i)\cdot \vect{\Delta r_i}\approx \lim_{\mathrm{max}\vect{\Delta r_i}\rightarrow 0}}\sum_{i=0}^N(f(\vect{r_i}+\vect{\Delta r_i})-f(\vect{r_i}))=\lim_{\mathrm{max}\vect{\Delta r_i}\rightarrow 0}}(f(\vect{r_{N}})-f(\vect{r_0}))=f(\vect{x_1})-f(\vect{x_0})$$

Read this carefully before dispatching it as "just another math proof" because it doesn't get any more intuitive than that.

12. Aug 9, 2010

### TMSxPhyFor

Actually I already thought about such an approach, even so it's explaining the situation when our field is gradient, but it doesn't provide satisfactory explanation of the need for additional path in case of inexact derivatives :(

13. Aug 9, 2010

### quasar987

What do you mean "the need for additional path" ?

In the general case, path independance does not hold. To see it, it suffices to produce a counter-example. Consider for instance the vector field on R² - 0 given by (x,y)-->(-y,x). This vector field circulates counter clockwise around the origin. (Calculate its vector product product with a radial vector field if you're not convinced.)

It is easy to find two path in this field that have different line integrals.

Last edited: Aug 9, 2010
14. Aug 10, 2010

### TMSxPhyFor

Dear Quasar

Thank you for your efforts, I meant that the above mentioned equations can lead us to explain things clearly and intuitively when the field is gradient, but if it's not, it's still gives no clear reason for the need of additional info on path of integration, also the example you advices is very clear and known, but it still gives you no evidence for why that should happens (the need for the path of integration) in general when the field is not gradient.

15. Aug 10, 2010

### quasar987

Ok, so if the field is not gradient, then independance of path fail. To see this intuitively is the same as to understand intuitively why "X is path independant ==> X is gradient".

The reason for this implication is that if X is path independant, then the map $G:\mathbb{R}^3\rightarrow \mathbb{R}$

$$x\mapsto\int_0^xX\cdot dr$$

(where $\int_0^x:=\int_{\gamma}$ for $\gamma:[0,1]\rightarrow\mathbb{R}^3$ any smooth curve with $\gamma(0)=0, \ \gamma(1)=x$)

is well-defined and its gradient is X.

To see intuitively why this is true, observe that

$$\frac{\partial G}{\partial x^i}=\frac{\partial }{\partial x^i}\int_0^x X\cdot dr=\frac{\partial }{\partial x^i}\int_0^xX^1dx^1+X^2dx^2+X^3dx^3 = \frac{\partial }{\partial x^i}\int_0^xX^idx^i$$
(because if x varies a little in the i direction, then dx^j=0 for $j\neq i$)
$$=X^i(x)$$
(for essentially the same reason that
$$\frac{d}{dx}\int_0^xf(t)dt=f(x)$$
(fondamental theorem of calculus)).

16. Aug 12, 2010

### TMSxPhyFor

Dear Quasar

Thank you again and sorry for the delay..
Unfortunately I'm not well familiar with maps, can you please revise your equations without using maps? thank you in advance.

17. Aug 12, 2010

map = function

18. Aug 12, 2010

### quasar987

A "map" is a synonym for "function". As is "transformation" and "application"

19. Aug 14, 2010

### Curl

He's not asking for a mathematical proof, rather a logical explanation why it makes sense.

First consider the vector field in R^2: f(x,y)= 4i, sort of like a constant, steady wind.

If you move through the wind, it will do work on you while moving in the positive X, and no work when you move in the y direction. If you move back, it will do negative work. So the only thing that matters is the start and end points.

Use logic to convince yourself of other vector fields, try to look at graphs and see if you can find a path that you can take and have work done one way but not an equal and negative work done when you come back another way: it's impossible if the field is conservative.

20. Aug 22, 2010

### TMSxPhyFor

Eureka!! :!!) (sorry but I'm so excited!)
Sorry for the delay, and thank you all for help especially quasar987 for his efforts even so he went far away :-D
After a long straggling, Finlay I found a note in a Russian book (I love Russian books! they much deeper than English!) that lead me to the answer, and I finally closed this naughty gap in mind! (the book is "Curse of High Mathematics", V.I.Smirnov tom 2, page 354)

The basic trick is that (generally speaking) actually all directional derivatives are actually partial derivatives! non of the of books that I checked ever noted that, I'm also was stupid enough to not note that even that I'm using it everyday! but the question is why?

When we are defining it as function change over a length change on some vector (as mentioned in all books that i checked), and that is what not TRUE, actually it's not on a vector, it's on some curve! we divided in our definition only on the length of the arc, but we didn't included any information about this arc it self! this is why it's partial! the result is also depending on the carve along which is not specified!

But the nice thing is in full or Exact derivative (or gradient), we actually moving along the radios vector of the considered function it self, so the information about the path are already self included!

This is why when we integrating a gradient we don't need more info! when we integrating non gradient, we actually integrating a non-full derivative, so we simply doesn't know along which path this function's change should be considered!

That it! very simple! I glad that my intuition still working :-D, and now I believe I'm understanding Universe much better now!


text:
split short exact sequence

In an abelian category, a short exact sequence $0\to A\buildrel f\over{\to}B\buildrel g\over{\to}C\to 0$ is split if it satisfies the following equivalent conditions:

(a) there exists a homomorphism $h:C\to B$ such that $gh=1_{C}$;

(b) there exists a homomorphism $j:B\to A$ such that $jf=1_{A}$;

(c) $B$ is isomorphic to the direct sum $A\oplus C$.

In this case, we say that $h$ and $j$ are backmaps or splitting backmaps.

Title split short exact sequence SplitShortExactSequence 2013-03-22 12:09:32 2013-03-22 12:09:32 antizeus (11) antizeus (11) 8 antizeus (11) Definition msc 16E05 backmap splitting backmap