 Unfortunately, there’s nothing like the tantalizing lure of speed and power to blind even the most cautious of web surfers, especially if your Internet connection is agonizingly sluggish.
It’s not surprising then, that this tubetorial on speeding up the Internet with Firefox caught my attention. I did briefly try it out before turning it off in horror.
The hack involves turning on ‘pipelining’ in Firefox, which basically means it starts sending out multiple requests for web pages and speeds up loading times. Well, as one suspicious user pointed out in the comments, pipelining is not a great idea. MozillaZine recommends the following about its usage: “Users who want better page loading speed can try setting this preference to true, keeping in mind _this may break some websites.” (_emphasis mine). More broken websites? Doesn’t sound too good to me. I think I’ll just stick to taking it nice and slow.


Theorem Proving:
Enumeration, Computation, Deduction
Goals
Computer-Assisted proof components
Automated Deduction
Limits of Set theory and First-order Logic
Goals
- Goal: Use computers to greatly increase our ability to discover and prove
mathematical results across areas of mathematics.
- Why?
- How?
Learn to search for, construct and recognize useful mathematical objects.
What?
- There are infinitely many prime numbers.
- There are arbitrarily long arithmetic progressions all of whose elements are prime numbers.
- There are infinitely many natural numbers $n$ such $n$ and $n+2$ are both primes.
Computer-Assisted proof components
- Computers have been used in various ways to provide a component of a proof:
- Enumeration,
- Symbolic algebra,
- Exact real number arithmetic,
- Linear programming,
- SAT solvers.
- Some examples:
- Four colour theorem,
- Kepler conjecture,
- Boolean Pythagorean triples problem.
First-order logic: languages
- A first-order language, which describes a domain of discourse (e.g. $\mathbb{N}$) has vocabulary consisting of
- Variables - can be taken to be a fixed countable set.
- Constants (e.g. $0$, $1$).
- Functions (e.g. $+$).
- Predicates (e.g. $<$, $=$).
- Special symbols $\Rightarrow$, $\iff$, $\wedge$, $\vee$, $\forall$, $\exists$, ...
- We form two kinds of expressions from these, terms (e.g. $1+1$, $n + 3$)
and formulas (e.g. $n + 1 < 2$, $4 < 3$).
- Terms and formulas may depend on variables.
- Terms represent objects in the domain of discourse.
- Formulas are either true or false.
Deduction and theories
- We can deduce formulas from other formulas using the rules of deduction.
- The main deduction rule is Modus Ponens : given $P$ and $P\Rightarrow Q$ we deduce $Q$.
- A theory is a language together with a collection of formulas, called axioms in the language.
- A formula is deducible in a theory if it can be
obtained from the axioms by the rules of deduction.
Universal deducer?
- A universal deducer is a computable function (algorithm) which, given a proposition (formula),
returns a proof if it is deducible and otherwise returns failure.
- By results of Turing, there is no such algorithm.
- We can enumerate proofs and check if they prove either the given proposition or its negation.
This does not always work as there are statements that are true but not provable.
- Practically, we can conclude that there is no best deducer,
as any given proof can be found by some deducer but no deducer can find all proofs.
Resolution theorem proving: Conjunctive normal form
- To prove a proposition $P$ from axioms, we can derive a contradiction from $\neg P$ and the axioms.
- We can rewrite $\implies$, $\wedge$ etc in terms of $\vee$ and $\neg$.
- Suppose a variable is existentially quantified,
- e.g. $\delta$ in $\forall \epsilon \exists \delta\ |x| < \delta \implies |x|^2 < \epsilon$,
- we can regard the variable $\delta$ as a function $\delta(\epsilon)$,
- we extend the language with additional functions (or constants)
for existentially quantified variables.
- In the extended language we no longer need $\exists$,
$\forall \epsilon\ |x| < \delta(\epsilon) \implies |x|^2 < \epsilon$.
- Variables without explicit quanitification are regarded as universally quantified.
Resolution theorem proving
- By the above process, we reduce to
- A list of statements all of which are true, i.e., a conjunction of clauses.
- Each clause consists of atomic formulas and their negations combined by $\vee$,
i.e., a disjunction of literals.
- From these we seek a contradiction - an empty clause.
- Resolution is the rule by which if two clauses are of the form
$P\vee Q_1\vee\dots\vee Q_n$ and $\neg P \vee R_1\vee \dots\vee R_m$, we deduce
$Q_1\vee\dots\vee Q_n\vee R_1\vee \dots\vee R_m$.
- Combined with unification - substituting expressions for variables to make literals equal, this is refutation complete.
- To handle equality efficiently, paramodulation is used.
First-order logic deducers; machine learning
- Theorem proving is thus reduced to a search for the empty clause,
starting with a given collection of clauses and using moves such as resolution and paramodulation.
- Various search heuristics can be used.
- We can also add premises corresponding to theorems in a formal library
(Mizar has been used for this).
- Machine learning has been used to select both strategies and premises.
Robbins conjecture
- Robbins conjecture was a conjectural characterization of Boolean algebras in terms of
associativity and commutativity of $\vee$ and the Robbins equation
$\neg(\neg(a\vee b)\vee \neg(a \vee \neg b)) = a$.
- This was conjectured in the 1930s, and finally proved in 1996 using the
automated theorem prover EQP.
- So far, this seems to be the only major success of deductive theorem provers.
- First-order logic theorem provers are, however, used in interactive proof systems
(hammer tactics).
Real-life mathematics
- A proof in real-life mathematics consists of:
- definitions, axioms, assumptions, notation;
- assertions;
- hints about which assertions, definitions etc. are used in the proof of a given assertion.
- The reader is expected to deduce all assertions based on the hints
(or at least believe that he/she can do so).
- In particular, there is no objective sense in which a proof is complete or correct.
- Interactive proof systems modelled on human proofs, such as Mizar and Naproche,
follow a similar approach.
“ Since the first half of the 20th century mathematics has been presented as a science based on
ZFC and ZFC was introduced as a particular theory in Predicate Logic.
“ Therefore someone who wanted to get to the bottom of things in mathematics had a simple
road to follow - learn what Predicate Logic is, then learn a particular theory called ZFC, then
learn how to translate propositions about a few basic mathematical concepts into formulas of
ZFC, and then learn to believe, through examples, that the rest of mathematics can be reduced
to these few basic concepts.”
Vladimir Voevodsky
Why new foundations?
- In the usual foundations of mathematics, $sin(3)$ and $3(sin)$ are syntactically equally valid.
- We need additional (run-time) conditions for being well-defined.
- We do have types, i.e., syntactic restrictions, in Category theory and Higher-order logic.
- However, proofs are still not first class, so not composable.
- We instead have patterns of proof (such as induction) in mathematics,
and tactical meta-language in formal proof systems (which are then implicitly part of the foundations).
“ The roadblock that prevented generations of interested mathematicians and computer scientists
from solving the problem of computer verification of mathematical reasoning was the
unpreparedness of foundations of mathematics for the requirements of this task.”
“ Formulating mathematical reasoning in a language precise enough for a computer to follow
meant using a foundational system of mathematics not as a standard of consistency applied only
to establish a few fundamental theorems, but as a tool that can be employed in everyday
mathematical work. ”
Vladimir Voevodsky


_PyPI link: https://pypi.org/project/setuptools .. image:: https://dev.azure.com/jaraco/setuptools/_apis/build/status/jaraco.setuptools?branchName=master :target: https://dev.azure.com/jaraco/setuptools/_build/latest?definitionId=1&branchName=master .. image:: https://img.shields.io/travis/pypa/setuptools/master.svg?label=Linux%20CI&logo=travis&logoColor=white :target: https://travis-ci.org/pypa/setuptools .. image:: https://img.shields.io/appveyor/ci/pypa/setuptools/master.svg?label=Windows%20CI&logo=appveyor&logoColor=white :target: https://ci.appveyor.com/project/pypa/setuptools/branch/master .. image:: https://img.shields.io/readthedocs/setuptools/latest.svg :target: https://setuptools.readthedocs.io .. image:: https://img.shields.io/codecov/c/github/pypa/setuptools/master.svg?logo=codecov&logoColor=white :target: https://codecov.io/gh/pypa/setuptools .. image:: https://tidelift.com/badges/github/pypa/setuptools?style=flat :target: https://tidelift.com/subscription/pkg/pypi-setuptools?utm_source=pypi-setuptools&utm_medium=readme See the `Installation Instructions <https://packaging.python.org/installing/>`_ in the Python Packaging User's Guide for instructions on installing, upgrading, and uninstalling Setuptools. Questions and comments should be directed to the `distutils-sig mailing list <http://mail.python.org/pipermail/distutils-sig/>`_. Bug reports and especially tested patches may be submitted directly to the `bug tracker <https://github.com/pypa/setuptools/issues>`_. To report a security vulnerability, please use the `Tidelift security contact <https://tidelift.com/security>`_. Tidelift will coordinate the fix and disclosure. For Enterprise ============== Available as part of the Tidelift Subscription. Setuptools and the maintainers of thousands of other packages are working with Tidelift to deliver one enterprise subscription that covers all of the open source you use. `Learn more <https://tidelift.com/subscription/pkg/pypi-setuptools?utm_source=pypi-setuptools&utm_medium=referral&utm_campaign=github>`_. Code of Conduct =============== Everyone interacting in the setuptools project's codebases, issue trackers, chat rooms, and mailing lists is expected to follow the `PyPA Code of Conduct <https://www.pypa.io/en/latest/code-of-conduct/>`_.


The Career Center sponsors two general on-campus career fairs—one during the fall and the other during the spring semester. Our events are open to current and former Spinoza students. As a research institution, we host employers seeking to hire candidates at the undergraduate and graduate levels.
View EventA hackathon (also known as a hack day, hackfest or codefest) is a design sprint-like event in which computer programmers and others involved in software development, including graphic designers, interface designers, project managers, and others, often including subject-matter-experts, collaborate intensively on software projects.
View EventThese extraordinarily tough economic times call for extraordinary solutions…for challenging assumptions and thinking out of the box. These powerful critical thinking skills and business innovation courses help you unleash the power of your thinking potential. You’ll gain the critical thinking skills you need to become a more effective problem solver, decision maker, communicator and manager.
View EventThis convention provides the singular opportunity for thousands from around the city to come together to shape the future of volunteerism. As the state's largest service-related convening, it brings more than 350 nonprofit, government, business and civic leaders together to gain and share knowledge, resources and connections needed to galvanize the power of people to create change.
View EventThose new to the job hunt have a unique opportunity to join together on an incredible outdoor adventure. Learn about teamwork, perseverance, and setting personal goals on this annual retreat.
View Event


Puberty Plot Pro Web Application
Step 1: Upload your data (SPSS, CSV or Tab Delimited)
Data should be formatted like this:
demo.sav
or
demo.csv
or
demo.txt
Input
Loading...
Datafile:
Buttons:
File was successfully uploaded!
Puberty Plot S-plus package by Stef van Buuren, TNO Quality of Life. (c) 2008 TNO.
Web application written by Jeroen Ooms, Utrecht University, 2008.
Email: stef.vanbuuren[at]tno[dot]nl || jeroenooms[at]gmail[dot]com.


Brook's Sandwich House
2710 N Brevard St
Charlotte
Mecklenburg
4
Only Burger
3710 Shannon Rd #118
Durham
Durham
9
Hops Burger Bar
2419 Spring Garden St
Greensboro
Guilford
3
Duke's Grill
1114 Concord Ave
Monroe
Union
5
El's Drive-in
3706 Arendell Street
Morehead City
Carteret
8
The Loaded Goat
247 City Hall St
Mount Airy
Surry
2
Johnson's Drive-in
1520 E 11th Street
Siler City
Chatham
6
P T's Olde Fashioned Grille
8116 Market St
Wilmington
New Hanover
7


Preparation time
overnight
Cooking time
10 to 30 mins
Serves
Serves 4-6
This belly pork takes no time to cook on the barbecue, but an overnight preparation gets you an aromatic marinated flavour and lots of perfect crackling.
Make sure you or your butcher score the pork skin well (using a small, sharp kitchen knife or a clean DIY knife) - nice fine scores make better crackling. Mix the salt, ground star anise and the orange zest together and rub well into the skin, making sure the salt goes into all the cuts of the pork rind.
Using a mini-blender or a pestle and mortar, add the bay leaves, garlic, Szechuan peppercorns, five spice and blend to a paste, then slowly add the olive oil while mixing.
Leave the pork to dry overnight in the fridge; do not cover as you want it to dry.
Heat a barbecue or griddle and slice the pork into thin slices. Place the pork slices onto the hot griddle or barbeque and brush with the marinade. Cook each side for a few minutes, or until cooked through and the skin is crisp.


BHMC Event Signup Confirmation
You have been signed up for a Bunker Hills Golf Event by Stuart Finley.
| Event: |
Major 2-Man Best Ball |
| Date: |
Saturday, May 14, 2016 |
| Start Time: |
Tee Times |
| Course Name: |
TBD |
| Starting Hole: |
1 |
Event Fees
| Required Event Fees: |
$20.00 |
| Optional Fees: |
$0.00 |
| Transaction Fees: |
$0.90 |
| Total Event Cost: |
$20.90 |
Payment Confirmation #: xxxx
Members that have been signed up
Stuart Finley<EMAIL_ADDRESS>Event Fee: $10.00
Bill Giesie<EMAIL_ADDRESS>Event Fee: $10.00
Please pay for your green fees in the Pro Shop prior to the event unless you have
already paid online. Bunker Hills GC reserves the right to check at random for payment
receipts. Failure to pay for green fees prior to an event will result in
disqualification from the event and may result in expulsion from BHMC pending a Board of
Directors inquiry.
|


The increased regulation of coins deemed securities (which essentially leads to a ban) may increase demand for coins that are epitomes of non-securities such as XMR, LTC, BCH, and DOGE. These coins were (i) fairly started, (ii) fairly mined, (iii) did not perform an ICO/IEO, and (iv) are not backed by a company and are therefore not at risk of being classified as a security. These coins will also remain available to U.S. based investors and are therefore arguably more attractive. For example, Monero is listed on the following U.S. based exchanges:
- Poloniex
- Kraken
- Bittrex
- Beaxy
- Huobi US
And the following U.S. based OTC firms:
- DVchain
- Cumberland Mining
- Kraken's OTC desk
- Circle's OTC desk
- Galaxy Digital's OTC desk
As well as the following crypto asset brokers:
- Abra (according to their CEO, Monero will soon be added as a native asset)
- Circle Invest
- Voyager Invest
I think it is fair to say Monero is well positioned to attract U.S. based investors, especially given that they cannot access a lot of other altcoins anymore.
Lastly, it is naive to expect that only the U.S. will increase regulation on coins deemed securities. Each country effectively has security laws that are fairly similar.