The Trizor XV employs a three-stage sharpening and honing process using diamond-impregnated cutting wheels. The first time you sharpen a blade, you use the coarsest setting first to establish a completely new bevel. The fine wheels then form a secondary bevel, and finally the honing wheels polish the secondary bevel. The result is an arch-shaped edge that Chef’sChoice claims is more durable than a standard triangular edge. Thereafter, use of the honing wheels and an occasional pass on the fine wheels will keep the edge sharp for months or years before you need to cut an entirely new edge with the coarse wheels.
Your Cutlery – Before taking a look at your sharpener options, you should take the time to check out your knives! Each individual type of sharpener is better suited for particular knives! Make sure that you take this into consideration. Still, some sharpeners are very well rounded and can be used for various types of knives. This is definitely another thing to take into account.

This tool can be used for quick sharpening while maintaining the safety of the user. Very easy to use as it is a basic design sharpener. For the long blade, you can use a wider wooden base to keep the tool in a fix position. This stone is perfect for your daily maintenance by removing very little material away from your blade in a very short time. Before starting to use, first soak the stone for five minutes in the water and then place it on a firm platform.
Both Belgian Blue and Vielsalm Coticule are ancient stone layers found in the Belgian Ardenne Mountains with characteristics similar to both Novaculite and Siliciclastic sedimentary stone in that it is a metamorphic stone consisting of both gray and yellow volcanic ash mixed with tiny Spessartite Garnet crystals suspended in a clay matrix. However, due to its geology, both types of stone occur only in vertical seams sandwiched between two thick layers of bluish-purple slate and thus, they must be meticulously extracted mostly by hand. However, this type of extraction process is both very time-consuming and very labor-intensive and, quarrymen can only extract the stone for a few months each year due to inclement weather conditions. Consequently, both Belgium Blue and Coticule whetstones tend to be somewhat expensive.
Edges lose their sharpness for the very purpose they cater to. Cutting acidic fruits and vegetables like lemon, tomato causes corrosion in the blades. Knives are often used to accomplish tasks they’re not meant to perform, like scraping or opening tin cans. Blade buckling is also a very common kind of damage your knife faces every now and then. It happens due to slicing items heavier than the knife itself or crushing ice. Keeping the knife in high temperature or washing it with harsh chemical based detergents also has havocking effects on the sharpness. Taking proper care of your cooking combat hunting knife is the only way to prevent it from fraying. Always select a suitable knife for the task, avoid heavy wooden cut boards and wash it immediately with cold water right after using.


So, are you planning on donating to a non-profit organization? Do you want to know more about a non-profit organization before you donate? Then, you have come to the right place. This post will help you understand what a non-profit organization is.

A non-profit organization is quite similar to any business, but it enjoys tax-exempt status by the IRS (Internal Revenue Service) because it is established for furthering a social cause and benefiting the public. Donations that are made to non-profit organizations tend to be tax-deductible for both businesses and individuals.

The non-profit organization does not have to pay tax on the donations it receives and nor does it have to pay tax on the money that is generated through fundraising activities. It is often called an NPO.

Qualifications for NPO Status

Not just every organization can become an NPO. There are certain qualifications that the organization has to meet to benefit from the tax-exempt status. Normally, NPOs are established to further public safety, literary, education, charitable, scientific and religious purposes. Some examples of non-profit organizations include mosques, churches, synagogues, temples, foundations, charities, universities and hospitals. The Salvation Army Houston is an NPO that strives to serve humanity based on the Gospel.

The NPO has to serve the public in some way. It could either be by offering the public services, good or a combination of them both. Moreover, it is also required to make operating and financial public so that donors can stay informed regarding how and where their contributions are used. NPOs might also exist to collect income for dispensing donations to different charities.

In the United States, NPOs need to request for NPO status from the IRS under 501 (C) (3). Once an organization is registered as an NPO, it has to maintain compliance. Organizations need to explicitly state that they would not engage in any political campaign or make expenditures for political purposes.

Operating Rules for NPO Status

Although some non-profit organizations use only volunteer labor, most large NPOs hire paid, full-time staff. Despite benefiting from exempt-tax, NPOs need to pay employment tax and abide by federal and state workplace rules just like for-profit organizations.

NPOs are allowed to provide income or assets to individuals as fair compensation. The organization has to explicitly state that it would not use the donations for personal benefit or gain in the organizing papers.

Non-Profit Vs. Not-For-profit

Most of the time, the terms not-for-profit organizations and non-profit organizations are used interchangeably. However, there are certain distinctions between these two. The main difference is their purpose. Non-profits need to offer some goods or services and some social benefits. On the other hand, not-for-profits do not require a similar orientation and can exist simply to serve membership to certain members of society, rather than the society as a whole. NFPOs tend to sports clubs or recreational centers. While on the other hand, NPOs are solely operated for educational, literary, scientific, charitable and religious purposes.


Being a Surrogate Mother: Be Careful What You Eat!

There are certain requirements that applicants need to meet to become a surrogate mother. One of them is BMI, which is calculated from an individual’s height and weight. Surrogacy agencies usually use this number to accurately screen applicants for weight-related health issues, like diabetes, that can lead to complications during pregnancy. But how much of

Questions to Ask Before Becoming a Surrogate for a Friend or Family

Becoming a surrogate for a friend or a family member is a wonderful and selfless thing to do. You might have seen your friend or family member struggle to become pregnant for months or years. All you really want is for them to have a child. They also may have asked you to become a


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witness_intimidation [2017/05/09 21:03] (current)
barnaby2015 created
Line 1: Line 1:
 +Witness intimidation is when an attempt is made to threaten or persuade a witness not to give evidence to the police or courts, or to give evidence in a way that is favourable to the defendant. In most cases, the offender will be the defendant or the defendant’s family or friends.
 +A further form of intimidation may be thought of as 'cultural intimidation'. This occurs where family or friends of the victim or witness try to dissuade him or her from assisting in an investigation or an inquiry. There may be a variety of reasons for this including bringing shame on the victim's family. In addition, there may be norms of behaviour within a culture for dealing with criminal matters that do not involve the formal agencies of the criminal justice system.
 +Section 51 Criminal Justice and Public Order Act 1994 creates two offences:
 +s.51(1) creates an offence directed at acts against a person assisting in the investigation of an offence or is a witness or potential witness or juror or potential juror whilst an investigation or trial is in progress; and
 +s.51(2) creates an offence directed at acts against a person who assisted in an investigation of an offence or who was a witness or juror after an investigation or trial has been concluded.
 +The offences are triable either way. In the magistrates' court, the maximum penalty is six months' imprisonment and/or a fine to the statutory maximum. In the Crown Court, the maximum penalty is five years' imprisonment and/or a fine.
witness_intimidation.txt · Last modified: 2017/05/09 21:03 by barnaby2015


Good american history research paper topics

The collection contains extensive and diverse resources including primary and secondary texts, site plans, digital images, and maps. Is it possible for North and South Korea to become a united country again? The Christiana Riot Incident demonstrated the growing conflict between states rights and the federal legislature on the issue of slavery.

This paper would have three sections: United States Historical Census Data Browser Provides data from census records and other government sources for How might we preserve endangered species?

Four or More Authors Spiller, Robert, et al. How were ziggurats used in ancient Mesopotamia? Double space in between entries. Use this structure for ANY political or historical figure.

Because slaves were property, not people, by this ruling they could not sue in court. What is the best way to help people who have lost a limb? Suggest alternative strategies, or reinforce the rationale of the actions. What is the organization of the Hindu gods?

Most of these were in the North, but Revolutionary sentiments also motivated Southern slaveholders. What are the most efficient means that can be used to reduce global warming? Blacks established their own churches, towns and businesses.

These owners considered whites to be more reliable and educable. Should a law be imposed to prevent cyber bullying? Your target audience should always know where your argument is coming from, currently where it is now and where it going Analyze Break your content into parts that study the interrelations of the parts.

The Metropolitan Museum of Art: They removed language from the Declaration of Independence that included the promotion of slavery amongst the offenses of King George III. Is achieving a higher education in American worth the large amount of debt it will incur?

The most famous artistic feature of the culture is the Totem pole, with carvings of animals and other characters to commemorate cultural beliefs, legends, and notable events. Stories link to organized primary and secondary source materials found principally at U.

If you are doing a Position, Argument, or a Cause paperyou will need to know the different perspectives, but you will use your answer to the question as your thesis statement. Tells of new evidence that Gastric Bypass surgery can cure diabetes. Some cities had independent black seamstresses, cooks, basketmakers, confectioners and more.

The owners were never compensated.

Welcome to the Purdue OWL

Research and analyze the emergence of the Catholic Church as a political force following the collapse of the Roman Empire. Trace the path leading to the convocation of the Estates in France in the late 18th century, leading to the Revolution.

Sandford Peter [63] aka Gordona former slave displays the telltale criss-cross, keloid scars from being bullwhipped How a bill becomes law. Each conflict contains a brief video clip, statistical information, and a set of artifacts.

To what extent is the development of new technologies having a negative effect? What are some of the best strategies to combat social anxiety? What was that of Plekhanov? When there are two book by the same author designate one as book one and the other as book two.

She is a highly acclaimed educational technology guru and her articles, web sites, and books have helped countless teachers, students, and educators.

While the information may seem limited at times, it provides a good layout for students to begin formulating a general idea of what they want to focus on. They sometimes sued to gain their freedom or purchased it.

Proofread Your readers will thank you for not submitting the first draft.Hire a highly qualified essay writer to cater for all your content needs. Whether you struggle to write an essay, coursework, research paper, annotated bibliography or dissertation, we’ll connect you with a screened academic.

AMERICAN HISTORY RESEARCH TOPICS Constitutional Issues 1. First Amendment: What have been the issues surrounding freedom of speech, press, and/or religion? Center for History and New Media: Reference Desk The Center for History and New Media produces historical works in new media, tests their effectiveness in the classroom, and reflects critically on the success of new media in historical practice.

Writing a term paper for your U.S History class can be a pretty difficult task if you don’t have a clue about what you want to write about. Before you start any of your planning, research or writing, you want to choose a term paper topic that gets you as excited as you want your reader to be.

A good research question defines the focus of your research project. Your research question helps readers to know the specific subject matter you will be addressing within the broad topic of environmental history.

200 Research Paper Topics For Students + Writing Tips from Our Expert

History/English Research Paper Topic List The following is a list of possible research paper topics. A research paper is not a report. Instead, it must deal with a .

Good american history research paper topics
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Reaction Journal to American Civil War - Book Report/Review Example

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The turn of the century tended to be full of promise to numerous people. Several people viewed commerce and industry as future waves as agriculture also boomed in the…
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Reaction Journal to American Civil War Introduction It is during the turn of the century period that there were many changes witnessed in the American’s lives. The turn of the century tended to be full of promise to numerous people. Several people viewed commerce and industry as future waves as agriculture also boomed in the US. There were witnessed sexual revolution, women’s liberation movements, as well as the enhancement of large corporations, and extensive labor, which immensely transformed people’s lives. People had freedoms to participate in agriculture and employed technology and heavy irrigation methods and fertilization in regions such as California, which were essential in factory farms1. People also enjoyed the freedom to buy new products, stored in better stores as well as new modes of transportation that tended to change life hastily. However, the class definition also persisted, as it was a rigid one there were the wealthiest and poorest in society. These definitions created a foundation for progressivism2. Education was provided to both male and female in the same schools while the young generations dated openly in public as they interacted in amusement parks such as Coney Island.
Evidently the changes from the reconstruction era were minimal, although there were witnessed alterations in the American race relations; the equal rights among the races were not fully resolved3. The wealth distribution was another issue that did not change as although the slaves were granted freedom, the whites exploited them, as land was left in the hands of the whites. However, there were improved political and economical advancements.
Freedom entailed the young women, although with restrictions managed to secure jobs. Moist young women were single mothers who managed to tend for their families for working in factories such as cotton and sewing industries. In addition, laws that provided for minimum wage, maximum hour or child labor were enacted to protect workers4.
According to Kathy Peiss, The young women, who were mostly industry employees, socialized in places like dance halls, film theaters, amusement parks and beaches in the turn of the century. They were able to share public space with other young people even in various states of undress.
She thinks that these activities were significant in their social lives as there were many excitements involved. They were more of recreation activities for them. These things were able to allow women to live more free and make their own life choices and decisions.
Riis’ photographs depict the challenging and difficult lifestyles of the immigrants. They lived in shanties that were crowded with poor living conditions that were undesirable. He wanted those in the middle class to understand the poor living condition of the immigrant workers and offer them better places to live.
During the progressive era period, there was witnessed unprecedented number of entertainments that emerged in the American social environment. The people began to follow organized sports avidly more so boxing and baseball among others. These posed social problem in relation to work reformers established controls and regulations. The Americans were transformed in this era from farm dwellers to a diverse, urban, affluent, leisure obsessed, and teeming multitude. The reformers of this period, embarked in enacting regulations, to control social life.
According to Florence Kelly,5 the rapid industrialization has negative effects on the working urban class concerning their families, health, and education of the working people as well as the economic morality concerning the control of production means. She suggests changing this, through probable legislation to mitigate the difficulties that were at end passed as federal laws. This is because she wants the modern industrialization in America, which is expanding rapidly to contribute constructively to the nation. Furthermore, the speeches of Theodore Roosevelt6 and William Jennings Bryan, promoted labor liberalism and money regulation in a period when inflation was escalating and heavily affecting the economy.
List of references
Anderson, L. William. 2006. The Progressive Era, Part 2: Progressives and the Economy.
Freedom daily. Accessed at,
<> Barton, Rebekah. 2009. Progressive Era Leisure and Capitalism: Freedom, License,
Reform. Pp 1-25.
< > Edwards, Rebecca. 2006. New Spirits, 1865 -1905. New York: Oxford University
Kelley, Florence. 2011. Modern industry in relation to the family, health, education, morality.
New York: Longmans, Green, and Co.
McGerr, Michael E. 2003. A fierce discontent: the rise and fall of the Progressive movement in
America, 1870-1920. New York: Oxford University Press.
Tomlins, Christopher L. 2010. Freedom bound law, labor, and civic identity in colonizing
English America, 1580-1865. New York: Cambridge University Press. Read More
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Unwanted letters next to tickboxes in Excel

Michael Wright
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Office 365 - Excel 0n Windows 10.  I have a questionnaire with multiple tickboxes.  Just re-opened my document - ALL of the tickboxes have gained the letter 'C' next to them.  I didn't put them there.  Why are they there and how to I get rid of them?

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A pipeline critic’s perspective: CEPA speaks with the Pipeline Safety Trust

Carl Weimer, executive director of Pipeline Safety Trust and member of CEPA's External Advisory Panel (EAP)

Carl Weimer, executive director of Pipeline Safety Trust and member of CEPA’s External Advisory Panel (EAP)

Carl Weimer is a member of CEPA’s External Advisory Panel (EAP) and the executive director of Pipeline Safety Trust, a U.S. based advocacy group formed after three people were killed in a pipeline explosion in Bellingham, Washington, in 1999. As a pipeline critic and a member of the EAP, Weimer is working with CEPA to share his perspectives and concerns about the pipeline industry. To read more about how CEPA is listening to pipeline critics through the EAP, read this week’s blog.

Here is the full text of Weimer’s interview:

1. Why have you chosen to become a member of CEPA’s External Advisory Panel (EAP)?

There are really four reasons I chose to join the CEPA EAP. Mainly, I wanted to ensure that the voice of concerned citizens was well represented on the EAP and that lessons hard learned in the United States are shared with those on the panel and within CEPA. I also believe membership will provide me with new insights to the way the top leadership of pipeline companies think about safety and then implement those beliefs in their companies. It also provides a great opportunity to access the executives of major pipeline companies without being filtered through various layers of public or governmental relations employees. And finally I hope it will allow me to learn more about the way pipelines are operated and regulated in Canada that may be better than in the United States, so I can use those best practices in the future.

2. What do you hope your participation in the panel will achieve in terms of pipeline safety in both Canada and the U.S.?

I believe that only when citizens, industry and regulators are willing to embrace the conflicts that currently keep us apart, and discuss and deal with those conflicts in a constructive way, can true trust in pipeline safety be achieved. To achieve such success around the various conflicts currently in play depends on a good deal more information being available to citizens and local governments. The Pipeline Safety Trust has had a good deal of success in the United States gaining greater transparency of information on pipelines, and it appears this is an area where Canada has some catching up to do. If my participation on the EAP achieves nothing else, I hope I can move greater transparency of information forward in Canada.

3. What has your experience with the Canadian industry been like thus far?

My personal experience with the Canadian industry has been positive, with both CEPA and individual companies saying they are willing to work toward fine sounding commitments to safety, openness and transparency. While I have no direct conflicts with Canadian companies, there are numerous conflicting stories on a nearly daily basis in the news media where companies’ actions seem to be at odds with the commitments portrayed in CEPA’s Integrity First principles. The apparent discrepancy between the commitments made in the Integrity First policy and what is reported in the media and by local citizens is one area ripe for constructive conflict resolution discussions that could help build real trust.

4. Why do you choose to work directly with the pipeline industry to achieve your goal of improving pipeline safety?

The Pipeline Safety Trust works with any of the various stakeholder groups that we believe want to move pipeline safety forward. The pipeline industry is the most direct route for meaningful change since the industry owns, maintains and operates the pipelines. If the industry chooses to make changes they can do so much faster than trying to achieve those same changes through governmental regulations or public pressure.


Migraine Causes and Treatments

Learn more about causes, treatment and prevention of migraines.

What Causes Migraines?

The exact cause of migraines is unknown, but there are a number of factors that are associated with them. Migraines tend to run in families, although no specific gene has been linked to the disorder. Age and gender may also play a role in determining who will get migraines. Although migraines can appear at any age, they often begin in adolescence, are most frequent when people are in their 30s, and then decrease over the following decades. During childhood, boys are more likely to get migraines than girls, but that trend reverses during puberty, and women are three times more likely than men to have migraines.

Migraines have also been linked to smoking and depression. Stress, oversleeping, normal hormonal changes related to the menstrual cycle and some oral contraceptives, and fluctuations in barometric pressure can also bring on a migraine. Some common foods and food additives can also trigger migraines, including: Cheeses, Chocolate, Alcoholic beverages, dairy products, sweeteners, MSG (monosodium glutamate) and nitrates (preservatives used in smoked meats).

Treating and Preventing Migraines

The aims of treatment are to prevent them, if possible, and ease the symptoms when they do occur.

Once you've got a migraine, the only thing you want is for the pain to stop. The key to managing a migraine is to start treatment as soon as you feel the migraine pain –whether its over-the-counter medication like Advil Liqui-Gels® or something your doctor prescribes. Treatment is more effective when the pain is still mild.

You may be able to reduce your chances of suffering from a migraine attack by knowing your potential migraine triggers. A good place to begin is by keeping a headache diary Recording lifestyle factors such as what you eat, how much sleep you get, exercise routines, and stress levels along with when your headaches start and the type of pain you experience can help you monitor these patterns. That way you will be able to make lifestyle changes to reduce the number of migraines you get.

Be sure this product is right for you. Always read and follow the directions on the label. This information is provided for educational purposes only and should not be used as a substitute for professional medical advice, diagnosis, or treatment. Speak to your healthcare professional before making any changes to your lifestyle or before beginning or discontinuing any course of treatment. Never disregard professional medical advice or delay in seeking it because of something you have read on this site.


Creative Artist: A Journal of Theatre and Media Studies

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Embedded marketing and the quality-quantity dichotomy in Nollywood

CU Ihentuge

Filmmaking is a marriage of art and business. Hence, in successful and relevant films, art and business embrace each other for the consumer’s delight. The Nigerian video film industry was born out of business necessities and not artistic concerns. Right from its inception, the industry is manned and driven by petty traders. The films are shot and produced on the video format with the most possible minimal budget and production time in order to minimize cost and maximize profit. Based on this, decisions are usually based on commercial considerations. Nollywood’s world acclaim is based on quantity, and not quality, of films produced. Again, some Nollywood filmmakers make their monies by further tainting the image of the country by the pictures they paint of the country in their films. This paper discusses how embedded marketing can be harnessed to yield additional sources of funding to Nollywood filmmakers so that they can focus on quality in their productions and not cut corners to minimize production costs. It also x-rays how the sociological functions of Nollywood in image laundering can be engendered through embedded marketing. The work relies on data gathered through both primary and secondary research methods. Nollywood filmmakers, government and her agencies, public, private and multi-national companies, and institutions that offer products and services as well as international organisations that have stakes in Nigeria are encouraged to look towards embedded marketing in Nollywood. This has the potential of enhancing quality control in the industry and engendering its continued and better contributions to nation building.

AJOL African Journals Online


The Azimuth Project
Blog - Petri net programming (part 1) (Rev #9)

Petri nets are a simple model of computation, which have a diverse range of applications to modelling processes such as chemical reaction networks and population biology dynamics. They are a kind of dataflow graph through which entities called tokens percolate and have their types transformed. They also intriguing mathematical properties, which are the subject of an extensive literature. See the Network Theory series on the Azimuth Blog for an exciting and in-depth treatment of the applications and the theory. Those articles are also recommended for the good pictures they contain, showing the Petri net diagrams and the way the tokens flow through them.

In this series of articles, we will study the concepts in order to write programs that put them to work. We aim for a readership that includes anyone who is interested in using software to think about problems and solve them. That would include coding enthusiasts, programmers, software engineers, computer scientists, and scientists interested in programming. The articles will (1) present tutorial material, in a semi-rigorous format, (2) give working programs that exercise the concepts, and (3) perform a concept-based dissection of the code. These will be “toy” programs that actually work. Hopefully, they will give the reader some clay to work with.

In this first article we introduce Petri nets and give a small program to simulate them. The simulation will be applied to a simplistic yet interesting model of a chemical reaction network that involves the synthesis of water molecules from hydrogen and oxygen, along with the opposite reaction that dissociates water molecules. We will see that it doesn’t take that much to build a Petri net with substantive content.

Definition of Petri nets

A Petri net is a diagram with two kinds of nodes: passive container nodes, called species (aka “places” or “states”), which can hold zero or more tokens, and active process nodes, called transitions. Each transition is “wired” to some containers called its inputs, and others called its outputs. A transition can have multiple input connections to a single container, and multiple output connections as well.

Note: there are several names that are used for the containers (species, places, states), each of which makes sense in its own application context. We will be calling them “species,” but in this section we continue with the neutral term “container.”

When a transition fires, it removes one token from each of its input container, and adds one token to each of its output containers. If there are multiple inputs from the same container, then that many tokens get removed from the container. If there are multiple connections to an output container, then that many tokens are added to the output container.

The total state of the Petri net is characterized by a labelling function that maps each container to the number of tokens that it holds. Given a labelling, we say that a transition is enabled to fire if there are a sufficient number of tokens at each of its input containers. If no transitions are enabled in a labelling, then its evolution has reached a dead-end, and we say that it is halted.

This model of computation is non-deterministic. Given a labelling, which gives the token count at each of the containers, there may be multiple transitions which are enabled. Therefore, there is not a unique execution sequence that is determined.

Dataflow arises when one transition outputs tokens to a container that is input to another transition.

Using Petri nets to model “entity reaction networks”

Petri nets can describe reaction networks that consist of entities belonging to different species, with “reactions” that convert entities from the input species to the output species. Each entity is symbolized by a token in the net, and all the tokens for a species are grouped into a container. The conversion of entities is symbolized by the transition that operates on their tokens.

One area of application is to modeling population dynamics. Tokens represent organisms, and the species are biological species. A pedagogical example is given on the Network Theory page, where there are two species, Wolf and Rabbit, and three transitions: Birth, which takes one Rabbit in and outputs two Rabbits (think of asexual reproduction), Predation, which converts Rabbit + Wolf to Wolf + Wolf, and Death, which takes one Wolf in and outputs nothing.

The application we will take up is to chemical reaction networks. The entities are chemical units: molecules, isolated atoms, or ions. Each chemical unit is represented by a token, and a container holds all of the tokens for a chemical species. The transitions that transform the tokens symbolize the reactions that transform the chemical units.

We will be using, from the Network Theory page, the following model for water formation and dissociation:

  • The species are H, O, and H2O. (Note that the model is only intended to show the idea of chemical reaction Petri nets. The actual reactions involves H2 and O2.)

  • Transition combine inputs two H atoms and one O atom, and outputs an H2O molecule.

  • Transition split is the reverse process.

A Petri net simulator

We now give a program that builds a model of a Petri net, given parameters that define the species and transitions. The rule for sequencing the transitions is to choose a random enabled transition. The simulation runs for a specified number of steps, starting from an initial labelling. At each stage of the process, the labelling is printed on the console.

Running the script

The code is HERE. It is a self-contained Python script. See the APPENDIX for notes on obtaining the interpeter. The parameters for the model are already coded into the script. So let’s give it whirl:

This produced the output:

H, O, H2O, Transition
5, 3, 4, split
7, 4, 3, split
9, 5, 2, combine
7, 4, 3, combine
5, 3, 4, split
7, 4, 3, split
9, 5, 2, split
11, 6, 1, combine
9, 5, 2, split
11, 6, 1, split
13, 7, 0, ...

In words, we started out in a state with 5 H’s, 3 O’s, and 2 H2O’s, then a split took place, which increased H by 2, increased O by 1, and decreased H2O by one, then…

Running it again gives a different execution sequence. See the APPENDIX for notes on the language runtime environment.

Top-level structure of the script

The job of the script is to construct a Petri net instance, given parameters that define the species and transitions, and then to execute it.

Here is the statement that builds it:

petriNet = PetriNet(
    ["H", "O", "H2O"],    # states
    ["combine", "split"], # transitions
    [("combine",2,"H"), ("combine",1,"O"), ("split",1,"H2O")], # inputs
    [("combine",1,"H2O"), ("split",2,"H"), ("split",1,"O")],   # outputs
    # combine has 2 H inputs, 1 O input, and 1 H2O output
    # split has 1 H20 input, 2 H outputs, and 1 O output

Then we setup the initial condition of the net:

initialLabelling = {"H":5, "O":3, "H2O":4}

And run it for twenty steps:

steps = 20
petriNet.RunSimulation(steps, initialLabelling)

Exercise: Improve the script to accept the model parameters from the command-line. Hints: Use “import sys,” and sys.argv[i]. Then you can pass strings like “[H, O, H20]” from the command line, and use the eval function on them.

Anatomy of the program

We represent species by their names (strings), and use classes for Transition and Petri net.

The Transition class contains a map that describes the input connections. It maps each species name to the number of times that it is taken as input. The transition class contains a similar map to describe the output connections.

A Petri net object has a member that holds the current labelling, which is a map (dictionary) from stateName to the token count.

The chief data in the Petri net classes are the Transition objects, and the labeling, which describes the current configuration of the net.

The Transition object contains two maps… Transition exposes two key methods, both of which operate on labellings: isEnabled takes a labeling as parameter, and returns a boolean saying whether it is enabled to fire. This is determined by comparing the input map for the transition with the token counts in the labeling, to see if there is sufficient tokens for it to fire.

The constructor for the Petri net class takes the transition specifications, and “digests” them into the initial data structures used in the simulation. This involves constructing Transition objects for each of the transitions.

Each transition object contains a map (dictionary) from input species name to the number of times that the species is input to the transition, and an output map with the same structure.

The PetriNet class contains the list of species names, the list of transition names, the current labelling, which maps species names to integers, and a map from transition names to Transition objects.

The top-level method in PetriNet is RunSimulation, which makes repeated calls to a method called FireOneRule. FireOneRule constructs the list of enabled transitions, chooses one randomly, and fires it. This is facilitated by the methods IsEnabled and Fire on the Transition class.

The fire method takes a labeling in, and performs the action indicated by the transition: it removes tokens from the input, and adds tokens to the output. It modifies the labelling, decreasing the values for the inputs, and increasing the values for the outputs.

Here is the Transition class:

Now that our Petri net is equipped with a labelling and a list of Transitions, each with an isEnabled and fire method, it has everything that it needs to fire a rule: pick a transition, check if it is enabled in the current labelling, and if so, call the Fire method on the transition, to update the labelling to the new state. All that is left for running a simulation is to specify a rule for choosing which enabled transition to fire: For this, our first program, we will just choose a random transition.

The top-level entry point is the method runSimulation, which takes the initial labelling, and a number of states to iterate.

Here is the main Petri net class:

Note that the PetriNet inherits from a base class PetriNetDataStructures. This base class was separated for clarity, and contains the “housekeeping” methods needed to support PetriNet: printHeader, printLabelling, and, not to be forgotten, the constructor, which converts the specifications ‘[combine,2,H etc. into the actual transition objects. Here is the code for it:]

# Author line
# for Windows without cygwin, use this form for the top line:

import string
from random import random,randrange

def selectRandom(list):
    return list[randrange(len(list))]

# States are represented just by their names, no class is needed

class Transition:
    # Fields used in this class:
    # name -- transitionName
    # inputs: stateName -> inputCount
    # outputs: stateName -> outputCount

    def __init__(this, transitionName):
       this.transitionName = transitionName
       this.inputs = {}
       this.outputs = {}

    def isEnabled(this, labelling):
       for inputState in this.inputs.keys():
          if labelling[inputState] < this.inputs[inputState]:
              return False  # not enough tokens to fire

       return True # good to go

    def fire(this, labelling):

       print this.transitionName

       for inputName in this.inputs.keys():
          labelling[inputName] = labelling[inputName] - this.inputs[inputName]

       for outputName in this.outputs.keys():
          labelling[outputName] = labelling[outputName] + this.outputs[outputName]

class PetriNetDataStructures:
    # Fields:
    # transitionNames
    # stateNames
    # transitionMap: transitionName -> TransitionObject
    # labelling -- mapping (dict) from state name to count

    def buildTransitions(this, inputSpecs, outputSpecs):
        this.transitionMap = {}

        for (transitionName, degree, stateName) in inputSpecs:
           this.getTransition(transitionName).inputs[stateName] = degree

        for (transitionName, degree, stateName) in outputSpecs:
           this.getTransition(transitionName).outputs[stateName] = degree
    def getTransition(this, transitionName):
        if not(this.transitionMap.has_key(transitionName)):
            this.transitionMap[transitionName] = Transition(transitionName)
        return this.transitionMap[transitionName]

    def printHeader(this):
        print string.join(this.stateNames, ", ") + ", Transition"
    def printLabelling(this):
        for stateName in this.stateNames:
            print str(this.labelling[stateName]) + ",",

class PetriNet(PetriNetDataStructures):

    def __init__(this, stateNames, transitionNames, inputMap, outputMap):
        this.stateNames = stateNames
        this.transitionNames = transitionNames
        this.buildTransitions(inputMap, outputMap)

    def runSimulation(this, iterations, initialLabelling):

        this.labelling = initialLabelling

        i = 0
        while not(this.isHalted()):

           i = i + 1
           if i == iterations:
               print "done"

        print "halted"

    def enabledTransitions(this):
        return filter(
            lambda transition: transition.isEnabled(this.labelling),

    def isHalted(this):
        return len(this.enabledTransitions()) == 0

    def fireOneRule(this):

# now build a net for two opposite transitions:
# combine: formation of water molecule
# split: dissociation of water molecule

net = PetriNet(
    ["combine", "split"], # transitions

steps = 20

net.runSimulation(steps, initialLabelling)

We’ve learned a cool new idea, and how to do something cool with it. This is only the beginning, in terms of the applications and the theory.

There is an important limitation to our current program: it just randomly picks a rule. In our example, the system just made a kind of random walk (back and forth) between the states of full dissociation – all H and O atoms, no H2O molecules – and all H2O molecules. But in a real system, the rates at which the transitions fires are probabilistically determined, and depend, among other things, on the temperature of the system. With a high probability for formation, and a low probability for dissociation, we would expect the system to reach an equilibrium state in which H2O is the predominant “token” in the system. [The relative concentration of H20 would depend on the relative probabilities of the transitions.]

This gives motivation for the topic of our next article, which is stochastic Petri nets.

Appendix: Notes on the software environment

The sample programs here are in Python, which is a good language for simple proof-of-concept programs.

You have a few options to choose from, in terms of distributions:

  • If you are on a Linux/unix type of system, it may already be installed, or use the package manager to install it.

  • In Windows, you can use the version from the web site. Alternatively, install cygwin, and choose Python on the setup menu, and then you can try to pretend that you are working in a nix system.

  • Another interesting distribution is [from] Enthought, which comes pre-built with an open-source scientific and numeric computing environment, scipy, numpy, matplotlib, …

The program is distributed as a self-contained script, so from Linux and cygwin, you can just execute ./ You just have to adjust the first line to point to the interpreter. Even from cygwin, you can refer to the native python executable, or the enthought distribution.

  • Network Theory

  • Petri Nets – Wikipedia

  • python

  • cygwin

  • enthought

Stochastic Petri nets

A nice elaboration of the basic model is the stochastic Petri net, which consists of a Petri net, along with data that gives a rate coefficient for each transition. The firing rate for a transition will equal its rate coefficient times the product of the number of tokens at each input state (using multiple factors if a state occurs multiple times as an input).

This definition is motivated by the model of chemical reaction networks where the reaction rates are proportional to the product of the concentrations of the input constituents. We can think of the rate coefficient for a transition as a magnitude that takes into account both the “temperature” of the system of tokens and the “ease” with which the input tokens will combine to trigger the reaction, once they are brought into proximity.


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Premarin is also used to replace estrogen in women with ovarian failure or other conditions that cause a lack of natural estrogen in the body. Premarin is also used as part of breast cancer treatment in both women and men.

How should I use this medicine?

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Menopause occurs naturally in women, typically between the ages of 45 and 55. During menopause, your body produces less estrogen than it did beforehand. This can cause symptoms such as "hot flushes".

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Ancient Greek History

About the Helladic Period of Ancient Greece

Written by in Comments Off on About the Helladic Period of Ancient Greece

How did mainland Greece develop during ancient times during the Greek Bronze Age? There were a lot of advancements and changes that took place during this time period and it can be hard to track them. Historians and archaeologists have made an effort to categorize this time period, and their efforts are referred to as the Helladic Period, or Helladic Chronology, which contains three distinct periods: Early, Middle, and Late Helladic.

The different periods are largely determined by changes in pottery, since the Aegean culture lacked a writing system. The period overall is distinguished by advances in fortification, as demonstrated by large fortified settlements like Manika and Lerna. The making of tools and art saw more metallurgy, and societies became more cohesive. Here’s more information about it:

Early Helladic

The Early Helladic period occurred at roughly the same time as the Old Kingdom in Egypt: 3200-2000 BCE. It is divided into three chronological-cultural phases – EH I, EH II, and EH III – plus a transition phase between EH II and EH III. The Early Helladic period demonstrated an increase in the use of metals, particularly bronze and copper, and settlements became larger and more organized.

EH I was primarily a transitional period from the Final Neolithic period and demonstrates considerable continuity. Metal objects were uncommon. In EH II, communities began to use a “longhouse” building called a megaron. This period also saw the first oxen-driven plows, and societies became more hierarchical. During EH III, culture shifted as a result of importations from across mainland Greece and other nearby regions. Climate change may also have instigated cultural changes.

Middle Helladic

The Middle Helladic period (2000-1550 BCE) saw a retrogression that has led to it being considered a dark period. The quantity of metals and imported products decreased, and social stratification also leveled, resulting in burial practices characterized by widespread equality.

MH art, however, saw a number of technological advances. Minyan pottery was widespread during the MH period, and matt-painted pottery was another new style. Settlements were tightly packed and usually situated on top of hills. Most information about the MH period comes from the community of Lerna, which has been carefully excavated.

Late Helladic

The Late Helladic period was a flourishing era that is often called the Mycenaean Age. During this time (1550-1050 BCE), Mycenae was the most powerful state in Greece. The LH period is divided into LH I, LH II, and LH III.

The volcanic eruption of Thera occurred during LH I, devastating several islands and settlements in the Aegean peninsula. After the eruption, a style of pottery called Peloponnesian LHI developed into the LH II period. During LH III, Mycenaean art expanded across the Eastern Mediterranean.

Many well-known figures from Greek mythology were from the end of the MH period and the LH period, such as Heracles and Oedipus. The Trojan War also occurred in about 1250 BCE during the Mycenaean Age.

Toward the end of the this period, many Mycenaean palaces were destroyed by invasions from the Doric and Sea Peoples. Greece sank into another decline that was caused by invasion and war, a time that coincides with the end of the Bronze Age. Afterwards, the culture and society of Aegean civilization had shifted.

Helladic chronology – Wikipedia

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