Think Twice before You Disparage Capitalism

Capitalism serves miraculously if free from the fetters of limitless state intervention.

"Everybody for himself, said the elephant as he danced around among the chickens." This lampoon of capitalism came from a Canadian politician. The word "capitalism" has fallen into disrepute. It is associated with other pejorative terms such as "fat cat," "big business," "military-industrial complex," "greedy industrialists," "stand patters," "reactionaries," and "property values without regard to human values." Many serious scholars look on capitalism as a transitional system between late feudalism and inevitable socialism.

Adam Smith has been associated with the word "capitalism" even though he did not use the term. He did not so much as refer to capital by that name, but used the word "stock" to describe what we call capital. Karl Marx wrote in response to Adam Smith’s Wealth of Nations and called his great work Das Kapital. There was disparagement and scorn—even hate—for the ideas of the free market economy. The term capitalism has been less than appealing to many people since that time even though they know little about the contents of the Marx benchmark in political economy.

Some political economists who cherish individual liberty and the free market have suggested that a new name be found to describe economic liberty and individual responsibility. Until a new name appears, however, the thoughtful person does well to think twice before he disparages the market economy with all of its implications implied by the term capitalism since there is now no ready alternative available for reasonable discourse.

Is the System Outmoded?

Many thoughtful citizens of America think of capitalism as a quaint and vanishing vestige of our Yankee industrial beginnings. With burgeoning population, urbanization and industrialization, they argue, capitalism disappears. They are not quite ready to embrace socialism, but they heartily approve government planning and intervention. John Kenneth Galbraith, articulate spokesman for the liberal establishment, calls for the open acclaim of a new socialism which he believes to be both imminent and necessary. "The new socialism allows of no acceptable alternatives; it cannot be escaped except at the price of grave discomfort, considerable social disorder and, on occasion, lethal damage to health and well-being. The new socialism is not ideological; it is compelled by circumstance." 1

At first blush, the Marxian assumption of economic determinism is quite plausible, but I do not believe it can stand up to the scrutiny of experience. My study of history leads me to assume with many of my thoughtful colleagues that free people can, within certain limits, choose their own systems of political economy. This is precisely what happened in West Germany at the time of Ludwig Erhard. The Germans chose capitalism rather than the socialism recommended by many American, British, and Continental economists and politicians. It is my opinion that Americans can and should call for a renewal of capitalism rather than a new socialism.

Capitalism has been neither understood nor sympathetically considered by most contemporary Americans. Capitalism is a radical and appealing system of political economy which needs a new and favorable review. The new socialism has never been tried. The old socialism is not very inviting. Consider Russia, China, Cuba, Chile, and now Britain. Capitalism has been tried with the most amazing success in all history. What is the nature of a political and economic system which has made the poor people of America more prosperous than the rich of many countries operating under state control? Here are my paragraphs in praise of capitalism. They are somewhat lyrical but grounded in fact and open to review.

An Enviable Record

Capitalism is the one system of political economy which works, has worked and, given a chance, will continue to work. The alternative system is socialism. Socialism is seductive in theory, but tends toward tyranny and serfdom in practice.

Capitalism was not born with The Wealth of Nations, nor will it die with Das Kapital. It is as old as history and as new as a paper route for a small boy. Capitalism is a point of view and a way of life. Its principles apply whether or not they are understood, approved and cherished.

Capitalism is no relic of Colonial America. It has the genius of freedom to change with the times and to meet the challenges of big industries, big unions, and big government if it can free itself from the restraints of interest-group intervention which eventuates in needless government expansion and spending. Let the market work, and the ambition of each individual will serve the common good of society.

Capitalism is an economic system which believes with Locke and Jefferson that life, liberty, and property are among the inalienable rights of man.

Capitalism denies the banal dichotomy between property values and human values. Property values are human values. Imagine the disjunction when it is applied to a person with a mechanical limb or a cardiac pacemaker. The workman with his tools and the farmer with his land are almost as dramatic in the exemplification of the identity between a person and his property.

Capitalism is belief in man—an assumption that prosperity and happiness are best achieved when each person lives by his own will and his own intelligence. Each person is a responsible citizen.

Limited Government

Capitalism recognizes the potential tyranny of any government. The government is made for man; not man for the government. Therefore, government should be limited in size and function, lest free individuals lose their identity, become wards of the State. Frédéric Bastiat has called the State a "great fiction wherein everybody tries to live at the expense of everybody else."

Capitalism denies the naïve and mystic faith in the State to control wages and prices. A fair price is the amount agreed upon by the buyer and seller. Competition in a free market is far more trustworthy than any government administrator. The government is a worthy defense against force and fraud, but the market is much better at protecting against monopoly, inflation, soaring prices, depressed wages and the problems of scarcity. Capitalism works to the advantage of consumer and worker alike.

Capitalism denies the right of government to take the property of a private citizen at will, or to tax away his livelihood at will, or to tell him when and where he must work or how and where he must live. Capitalism is built on the firm foundation of individual liberty.

Capitalism believes that every person deserves an opportunity. "All men are created equal" in terms of opportunity, but people are not equal—nor should they be. How dull a world in which nobody could outrun anybody! Competition is a good thing no matter how much people try to avoid it. Equality and liberty are contradictory. Capitalism chooses liberty!

Equality of Opportunity

Capitalism gives a poor person an opportunity to become rich. It does not lock people into the condition of poverty. It calls on every individual to help his neighbor, but not to pauperize him with making him dependent. Independence for every person is the capitalist ideal.

When a person contracts to work for a day, a week, or a month before he is paid, he is practicing capitalism. It is a series of contracts for transactions to be completed in the future. Capitalism is promise and fulfillment.

Capitalism offers full employment to those who wish to work. The worker is free to accept a job at any wage he can get. He can join with his fellows in voluntary association to improve his salary and working conditions. He can change jobs or start his own business. He relies on his ability to perform rather than on the coercive power of the State to force his employment.

Capitalism is color-blind. Black, brown, yellow, red, and white are alike in the market place. A person is regarded for his ability rather than his race. Economic rewards in the market place, like honor and acclaim on the playing field, are proportionate to performance. The person who has the most skill, ability and ingenuity to produce is paid accordingly by the people who value and need his goods and services.

Trust in the Market

Capitalism is a belief that nobody is wise enough and knows enough to control the lives of other people. When each person buys, sells, consumes, produces, saves, and spends at will, what Leonard Read calls "the miracle of the market" enables everyone to benefit.

Capitalism respects the market as the only effective and fair means of allocating scarce goods. A free market responds to shortages and spurs production by rising prices.

Arbitrary controls merely accept and keep the shortages. When rising prices inspire human ingenuity to invent and produce, the goods return and prices fall. Nobody knows enough to build an airplane or a computer, but hundreds of people working together perform these amazing acts of creation. This is the notable human achievement which Adam Smith called "The Division of Labor."

Capitalism derives its name from the fact that capital is essential to the success of any venture whether it involves an individual, a corporation, or a nation-state. Capital is formed by thrift. The person who accumulates capital is personally rewarded and, at the same time, a public benefactor.

Capitalism makes every person a trustee of what he has. It appoints him general manager of his own life and property, and it holds him responsible for that trusteeship.

Church and Family Ties

Capitalism is a natural ally of religion. The Judeo-Christian doctrines of stewardship and vocation are reflected in a free market economy. Churches and synagogues can be free and thriving with capitalism. When the churches falter, the moral strength of capitalism is diminished.

Capitalism depends on the family for much of its social and moral strength. When the family disintegrates, the capitalist order falls into confusion and disarray. The motive power for the pursuit of life, liberty, and property is in the filial and parental love of a home with its dimensions of ancestry and posterity.

Capitalism enables entrepreneurs to be free people, taking their own risks and collecting their own rewards.

Work is a privilege and a virtue under capitalism. Leisure is honored, but idleness is suspect. The idea that work is a scourge and a curse has no place in the climate of capitalism.

Capitalism holds profits derived from risk and investment to be as honorable as wages or rent. Dividends paid to those who invest capital in an enterprise are as worthy as interest paid to a depositor in a savings bank. The idea abroad that risk capital is unproductive is patently false.

The Voluntary Way

Capitalism honors and promotes charity and virtue. True charity cannot be compelled. Universities, hospitals, social agencies, are more satisfactory and more fun when they derive from voluntary support. Money taken by force and bestowed by formula is no gift.

The consumer is sovereign under capitalism. No bureaucrat, marketing expert, advertiser, politician, or self-appointed protector can tell him what to buy, sell, or make.

Capitalism encourages invention, innovation and technological advance. Creativity cannot be legislated. Only free people can bring significant discovery to society. Thomas A. Edison was not commissioned by the government.

The concept of free and private enterprise applies to learning and living as well as to the production of goods and services. When a student learns anything it is his own. Nobody, let alone a state, ever taught anybody anything. The State can compel conformity of a sort, but genuine learning is an individual matter—an act of free enterprise and discovery.

Respect for the Individual

Capitalism honors the liberty and dignity of every person. The private citizen is not regarded as a stupid dupe to every crook and con man. He is regarded as a free citizen under God and under the law—able to make his own choices; not a ward of the State who must be protected by his self-appointed superiors who administer government offices.

Capitalism is a system which distributes power to the worker, the young, the consumer and the disadvantaged by offering freedom for voluntary organization, dissent, change, choice and political preference, without hindrance from the police power of government. The renewal of capitalism could be the renewal of America. Nothing could be more radical, more timely, or more beneficial to the responsible and trustworthy common people who are now beguiled by the soft and seductive promises of the new socialism.

No political and economic system is perfect. Plato’s Republic was in heaven—not on earth. If people were all generous and good, any system would work. Since people are self-centered, they are more free and happy in a system which allows the avarice and aggressiveness of each to serve the best interest of all. Capitalism is such a system. It is modestly effective even in chains. The time has come for daring people to release it and let us once more startle the world with the initiative and productivity of free people!

Some of my academic colleagues will deny, dispute, or scorn the foregoing laudatory comments about capitalism. They will say that socialism benefits the poor, the young, the consumer, the minorities, and that capitalism protects the rich and the powerful. When discussion is joined, however, they will argue in terms of politics rather than economics, ideology rather than empirical evidence, and they will accuse me of doing the same. When the most persuasive case is produced, it will not convince. Political opinions are not changed by rational argument.

A Call for Renewal

Those who have socialist ideological preferences are merely annoyed to arrogance and disdain by such honest appreciation of capitalism as I have presented. Those scholars, however, who like Ludwig von Mises, Friedrich Hayek, and Milton Friedman have explored the relevance of capitalism to our present predicament, will join in the call for renewal of a system that works. Those who, like the late Joseph Schumpeter, have watched the apparently relentless disintegration of capitalism, and have concluded that socialism will work, albeit with painful disadvantages, will heave a long sad sigh of regret at the passing of the happy and prosperous capitalist way of life. They will, as people must, accept what appears from their perspective inevitable, and try to make the best of the gray and level life of socialism.

Schumpeter, however, was no defeatist. He was a perceptive analyst of human affairs. In the preface to the second edition of his magnum opus he wrote, "This, finally, leads to the charge of 'defeatism.' I deny entirely that this term is applicable to a piece of analysis. Defeatism denotes a certain psychic state that has meaning only in reference to action. Facts in themselves and inferences from them can never be defeatist or the opposite whatever that might be. The report that a given ship is sinking is not defeatist. Only the spirit in which this report is received can be defeatist: The crew can sit down and drink. But it can also rush to the pumps.”2

Friends of liberty, to the pumps!

Those who love liberty more than equality, those who are uneasy with unlimited government, those who have faith in man’s ability to shape his own destiny, those who have marveled at the miracle of the market will join me in this call for renewal of this simple, reasonable, versatile and open system of capitalism which has worked, is working, and will work if freed from the fetters of limitless state intervention. The choice, I believe, is ours. The alternative is the stifling sovereign state.

1Galbraith, John Kenneth, Economics and the Public Purpose (Boston: Houghton Mifflin Company, 1973), p. 277.

2Schumpeter, Joseph, Capitalism, Socialism and Democracy (New York: Harper and Row, 1950, p. xi.)


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Summary. The Mayor’s Chest Key can be found inside the infirmary on the table. The infirmary is located on the island with Mudhogs.

Can you catch pigs in raft?

Livestock Animals are non-hostile, but if not tamed, they will try to escape and run away when the player approaches it. … The player can use the Net Launcher to capture Livestock Animals. They have to be put on the Raft and fed with Grass Plots.

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To obtain it, you need to first kill a Poison-Puffer which has a 100% chance of dropping a single Explosive Goo and a 33% chance of dropping a second. Put one Explosive Goo in a Smelter to obtain one Explosive Powder.

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Note: The launch code is 4813.

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Summary. Eggs are laid by Cluckers after being caught and tamed with the Net Launcher. Once caught, eggs are laid by the Cluckers within an interval of 240–360 seconds (4–6 minutes).

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Uses. Used in the Recipes for Head Broth and Fish Stew. If consumed, quenches a little Thirst and adds a bonus to the Hunger bar. Four Buckets of Milk fill up the Biofuel Refiner completely.

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Late Lunch Wednesday August 10th 2022

In the context of unprecedented and astronomic rises in the cost of running his business, local bakery owner Patrick McCloskey explained why he has had to increase his prices. Dr Kate McCann told us why Obesity must be recognised as a disease, Geordan Richardson is a young man with an entrepreneurial spirit and did you know our Virtuoso of Vino, Rick Cronje, is also King of the Barbeque!!

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THE purpose of this case report is to alert anesthesiologists and other medical and surgical staff as to the potential for increased postoperative bleeding in patients undergoing heart surgery after having received the recently introduced low-molecular-weight heparin (LMWH) preparations (e.g. , enoxaparin) and new platelet inhibitors (e.g. , tirofiban) in the setting of acute coronary syndromes or coronary interventional procedures.

Four days after acute anterolateral myocardial infarction, a 75-yr-old, 56-kg man was scheduled for coronary arterial revascularization. His preoperative medications were 60 mg enoxaparin subcutaneously two times a day, aspirin and metoprolol orally, and intravenous infusion of the platelet glycoprotein (GP) IIb/IIIa receptor inhibitor tirofiban (Aggrastat, Merck, West Point, PA). The tirofiban infusion was discontinued at midnight before the day of operation.

Normal electrolyte and hematologic panels were obtained preoperatively: prothrombin and activated partial thromboplastin times (aPTT) of 13.9 (1.1 × control, international standardized index [ISI] 2) and 34.9 s (1.1 × control), respectively, a hematocrit of 48.1%, and a platelet count of 152,000/μl. Creatinine and blood urea nitrogen levels were normal as well (1.2 mg/dl and 10 mg/dl, respectively). During 90 min of extracorporeal support, with an ischemic time of 51 min, the surgical procedure involved anastomosis of the left internal thoracic artery to the left anterior descending coronary artery and a free reversed saphenous vein graft to the left circumflex coronary artery. During cardiopulmonary bypass (CPB), the triggers for additional heparin administration were an activated clotting time of less than 480 s and a whole blood heparin concentration less than the patients’ pre-CPB reference level (4.2 U/ml) using an automated protamine titration method (Hepcon, Medtronic Blood Management, Parker, CO). After discontinuation of CPB, the total dose (23,000 IU) of heparin was neutralized with a total of 350 mg protamine sulphate, as guided by the automated protamine titration method. Nevertheless, the surgical wound appeared diffusely “wet,” and the subjective diagnosis of microvascular bleeding was made by the staff surgeon. Based on immediately available whole blood tests, which revealed a normal activated clotting time (> 120 s); no detectable heparin (automated protamine titration heparin concentration method); a hematocrit of 22%; a platelet count of 55,000/μl; and a whole blood prothrombin/PTT of 17.8 s (1.48 × control, ISI 2)/40.9 s (1.32 × control), respectively; 2 U of packed erythrocytes and one single donor pack (apheresis) of platelets were transfused. The patient remained normothermic (36.9°C) after discontinuation of bypass. While in the cardiothoracic intensive care unit, routine hematologic assays (prothrombin/aPTT, hematocrit, and platelet count) were performed to guide transfusion therapy in the setting of excessive chest tube drainage (CTD;fig. 1) During the first 8 h, one six-pack of random donor platelets was administered for excessive bleeding (CTD: 960 ml) in the presence of a platelet count of 64,000/μl. During the next 8-h period, 4 U fresh frozen plasma were given for ongoing bleeding (CTD: 740 ml) in the setting of prothrombin/aPTT values of 15.2 s (1.2 × control)/61.7 s (1.9 × control), as well as a single donor apheresis platelet unit (six-pack equivalent) for a platelet count of 82,000/μl. Persistent excessive CTD (660 ml) during the third 8-h period necessitated the administration of an additional six-pack of random donor platelets. Despite excessive CTD (3,750 ml over 2 days), necessitating the transfusion of 7 U erythrocytes, the patient was hemodynamically stable, did not require vasopressor therapy, and was extubated the morning after surgery (15 h postoperatively). No additional hematologic assays were performed. Neither thromboelastography nor anti-Xa assay are available in our institution, and a point-of-care platelet function test, although available, was not performed by the managing physicians, who were not aware of the potential for excessive postbypass bleeding in the setting of concurrent use of LMWH and tirofiban. The patient was discharged from the intensive care unit 2 days later and from the hospital after 5 days.

Fig. 1. Graphic description of the relation between chest tube drainage (milliliters), displayed as bars; platelet count (× 1,000/μl), displayed as circles; activated partial thromboplastin time (seconds), displayed as triangles; and administration of hemostatic blood products: platelet concentrates (  white arrows ) and fresh frozen plasma (  thin black arrows ) perioperatively. P = preoperatively; OR = intraoperatively.

Close modal

Based on results of the ESSENCE trial, 1the combination of LMWH and aspirin is increasingly being used for patients with acute coronary syndromes. LMWHs, such as enoxaparin, are derived from unfractionated heparin (UFH) and produce their major anticoagulant effect by accelerating the binding of antithrombin III (AT III) to predominantly factor Xa (enoxaparin has an anti-Xa:anti-IIa activity ratio of 3.8:1.0). 2LMWHs generally have enhanced bioavailability, a longer half-life (two to four times as long as that of UFH), a dose-independent renal clearance, and a slightly decreased incidence of heparin-induced thrombocytopenia. 3LMWHs exhibit an antithrombotic effect that is assessed most accurately by measuring anti-Xa activity (which is often unavailable). The inability of routine doses of protamine to completely reverse the anti-Xa activity represents a significant limitation. 2In an animal study, the dose of protamine sulfate necessary to fully minimize bleeding was 10-fold greater for LMWH than for UFH. 4In addition, excessive CTD was observed, 5,6when enoxaparin was used as an alternative to UFH in patients with heparin-induced thrombocytopenia undergoing CPB.

Platelet aggregation has been implicated as one of the major causes in the development of unstable angina and acute myocardial infarction. Activation of the platelet IIb/IIIa GP receptor represents a crucial step in platelet aggregation, and 80–100% blockade of this receptor should completely suppress platelet aggregation. Therefore, potent platelet inhibitors, such as the intravenous GP IIb/IIIa inhibitors have been developed, and their clinical effectiveness is supported by several studies. 7

Recent data showed that substantially increased blood usage was associated with use of the GP IIb/IIIa inhibitor abciximab, especially if surgery was performed within 24 h after receiving the medication. 8However, these findings have not been universal. 9Platelet transfusions, which will reduce the drug's receptor occupancy on platelet surfaces to less than the critical 50% threshold associated with prolongation of the bleeding time, 10is the most appropriate therapy.

Although postbypass bleeding can have a multifactorial cause, several important factors, such as prolonged duration of CPB and type of procedure, are associated with transfusion of hemostatic blood products and increased CTD. 11The postoperative CTD of our patient, 2,360 ml over the first 24 h and 1,380 during the second 24 h, far exceeded the previously reported mean 24-h cumulative chest tube output of 986 ± 581 ml. 11In the case presented, the CPB duration was rather short, bleeding from the two distal anastomoses should have been easily detected, and normothermia was maintained after CPB. The role of tirofiban with respect to excessive bleeding is uncertain based on its short half-life time of about 90 min, 12and the infusion was discontinued the night before. Use of this agent may be important because the patient also received enoxaparin on the day of the surgery. The peak anti-Xa activity after subcutaneous LMWH administration occurs within 3–4 h, and the anti-Xa levels are approximately 50% of peak levels 12 h later. 13

When patients who are receiving a LMWH preparation are scheduled to undergo a surgical procedure, such as coronary revascularization, it would be prudent to discontinue the LMWH at least 24 h before surgery or to replace the LMWH with an intravenous infusion of UFH. This approach may be even more important in the setting of concurrent administration of a potent platelet inhibitor, such as tirofiban. In the setting of concurrent use of LMWH and platelet inhibitors, routine coagulation results (prothrombin, aPTT, activated clotting time, platelet count) will most likely not be helpful in guiding appropriate therapy. Further studies are needed to evaluate the relation between concomitant use of these new antithrombotic agents and perioperative bleeding, as well as the use of new monitoring systems and heparin reversal agents. Future advances in coagulation monitoring may help in the evaluation of patients with residual anti-Xa activity, such as the HepTest anti-Xa (Haemachem, St. Louis, MO), a test that directly measures the inhibition of factors Xa and IIa. 14Point-of-care tests of platelet function, such as platelet activating factor–mediated acceleration of coagulation (hemoSTATUS 15; Medtronic Blood Management, Parker, CO), thromboelastography (Haemoscope, Skokie, IL), 16agglutination of fibrinogen-coated beads (Ultegra; Accumetrics, San Diego, CA), and platelet-force development (Hemodyne, Richmond, VA), may facilitate evaluation of the degree of residual platelet inhibition as well as the degree of CPB-related platelet dysfunction. Novel reversal agents, such as the [+18RGD] protamine variant, which reverses conventional UFH and enoxaparin, may be clinically useful in reversing the anticoagulant effects of LMWH. 17

Cohen M, Demers C, Gurfinkel EP, Turpie AGG, Fromell GJ, Goodman S, Langer A, Califf RM, Fox KAA, Premmereur J, Bigonzi F: A comparison of low-molecular-weight heparin with unfractionated heparin for unstable coronary disease. N Engl J Med 1997; 337: 447–52
Weitz JI: Low-molecular-weight-heparins. N Engl J Med 1997; 337: 688–98
Warkentin TE, Levine MN, Hirsh J, Horsewood P, Roberts RS, Gent M, Kelton JG: Heparin-induced thrombocytopenia in patients treated with low-molecular-weight heparin or unfractionated heparin. N Engl J Med 1995; 332: 1330–5
Van Ryn-McKenna JV, Cai L, Ofusu FA, Hirsh J, Buchanan MR: Neutralization of enoxaparin-induced bleeding by protamine sulfate. Thromb Haemost 1990; 63: 271–4
Ganjoo AK, Harloff MG, Johnson WD: Cardiopulmonary bypass for heparin-induced thrombcytopenia: Management with a heparin-bonded circuit and enoxaparin. J Thorac Cardiovasc Surg 1996; 112: 1390–2
Robitaille D, Leclerc JR, Laberg R, Sahab P, Atkinson S, Cartier R: Cardiopulmonary bypass with a low-molecular-weight heparin fraction (enoxaparin) in a patient with a history of heparin-induced thrombocytopenia. J Thorac Cardiovasc Surg 1992; 103: 597–8
Braunwald E, Maserit A, Armstrong PW, Califf RM, Gibler WB, Hamm CW, Simmons ML, Van de Werf F: Rationale and clinical evidence for the use of GP IIb/IIIa inhibitors in acute coronary syndromes. Eur Heart J 1998; 19:(suppl D): D22–30
Bracey A, Radovancevic R, Vaughn W, Ferguson J, Livesay J: Blood use in emergency coronary artery bypass after receipt of abciximab during angioplasty (abstract). Transfusion 1998; 38: S250
Booth JE, Patel VB, Balog C, Miller DP, Juran NB, LeNarz L, Lincoff AM: Is bleeding risk increased in patients undergoing urgent coronary bypass surgery following abciximab? (abstract). Circulation 1998; 98:I-845
Ferguson JJ, Kereiakes DJ, Adgey AAJ, Fox KAA, Hillegass WB, Pfisterer M, Vassanelli C: Safe use of platelet GP IIb/IIIa inhibitors. Eur Heart J 1998; 19:(suppl D): D40–51
Despotis GJ, Filos KS, Zoys TN, Hogue CW, Spitznagel E, Lappas DG: Factors associated with excessive postoperative blood loss and hemostatic transfusion requirements: A multivariate analysis in cardiac surgical patients. Anest Analg 1996; 82: 13–21
Barrett JS, Murphy G, Peerlinck K, De Lapeleire I, Gould RJ, Panebianco D, Hand E, Deckmyn H, Vermylen J: Pharmacokinetics and pharmacodynamics of MK-383, a selective non-peptide platelet glycoprotein-IIb-IIIa receptor antagonist, in healthy men. Clin Pharm Ther 1994; 56: 377–88
Hirsh J, Levine MN: Low molecular weight heparin: Laboratory properties and clinical evaluation. Eur J Surg 1994; 571(suppl): 9–22
Yin E: Appraisal of clot-based and amidolytic anti-Xa methods for the monitoring of heparin and its derivatives. Sem Thromb Hemostas 1985; 11: 243–4
Despotis GJ, Ikonomakou S, Levine V, Joiner-Maier D, Santoro SA, Joist JH: Effects of platelets and white blood cells and antiplatelet agent c7E3 (Reopro™) on a new test of PAF procoagulant activity of whole blood. Thromb Res 1997; 86: 205–19
Greilich PE, Alving BM, O'Neill KL, Chang AS, Reid TJ: A modified thromboelastographic method for monitoring c7E3 Fab in heparinized patients. Anesth Analg 1997; 84: 31–8
Wakefield TW, Andrews PC, Wrobleski SK, Kadell AM, Tejwani S, Hulin MS, Stanley JC: A [+18RGD] protamine variant for nontoxic and effective reversal of conventional heparin and low-molecular-weight heparin anticoagulation. J Surg Res 1996; 63: 280–6


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What does a circular flow model of a market economy show?

The circular flow model shows the interaction between two groups of economic decision-makers―households and businesses―and two types of economic markets―the market for resources and the market for goods and services.

Where are factors of production exchanged in the circular flow model?

-market for factors of production (such as labour or capital), where firms purchase factors of production from households in exchange for money. The market for goods and services is the place where households spend their money buying goods and services produced by firms.

What are the types of circular flow?

The two types of circular flows are: (i) Real flow (ii) money flow.

Which are the two markets represented in the simplest circular flow diagram?

What two markets are represented in the circular-flow diagram? The market for goods and services and the market for factors.

What are the elements of the circular flow diagram?

In economics, the circular flow diagram represents the organization of an economy in a simple economic model. This diagram contains, households, firms, markets for factors of production, and markets for goods and services.

What is the use of circular flow diagram?

The basic purpose of the circular flow model is to understand how money moves within an economy. It breaks the economy down into two primary players: households and corporations. It separates the markets that these participants operate in as markets for goods and services and the markets for the factors of production.

What is circular flow of income explain with diagram?

What are the types of circular flow of income?

Circular flow of income can be depicted in two sectors (Households and Firm), three sectors (Households, Firm and Government) and four sectors (Households, Firm, Government and Rest of the World) models.

How many types of circular flow of income are there?

How many types of circular flow are there? Answer: There are two types of circular flow. Real flow: The term real flow means the flow of factor services from households to firms.

What are the two basic principles of circular flow of income?

The circular flow of income involves two basic principles: (ii) Goods and services flow in one direction and the money payment to acquire them, flow in the return direction giving rise to a circular flow.

What are the three phases of circular flow?

What Is Circular Flow of Income? It can be described as the flow of products, services, income and expenses in an economy. Typically, there are 3 phases inflow of income – Production phase, income phase and expenditure phase.

What are the key elements of circular economy?

Core elements

  • Stretch The lifetime.

What is circular flow of income in four sector model?

The circular flow model in four sector economy provides a realistic picture of the circular flow in an economy. Four sector model studies the circular flow in an open economy which comprises of the household sector, business sector, government sector, and foreign sector.

What are the circular economy strategies?

Section 3 will focus on five circular economy strategies that can be used to mitigate supply issues due to critical materials: 1) recycling, remanufacturing, and reuse, 2) collection (e.g. reverse channels, product take-back, extended producer responsibility), 3) lean principles (e.g. Kaizen, six sigma, yield increases …

What is circular economy strategy?

A circular economy (also referred to as “circularity”) is an economic system aimed at eliminating waste and the continual use of resources. This regenerative approach is in contrast to the traditional linear economy, which has a “take, make, dispose” model of production.

How do you promote circular economy?

More sustainable manufacturing and consumption through market incentives. The government can use targeted price incentives (market incentives) to guide the country towards a circular economy. This can encourage manufacturers to opt for recycled or bio-based materials, and consumers to choose sustainable products.

What are three phases of circular flow?

What is difference between stock and flow?

A stock is measured at one specific time, and represents a quantity existing at that point in time (say, December 31, 2004), which may have accumulated in the past. A flow variable is measured over an interval of time. Therefore, a flow would be measured per unit of time (say a year).

What is the five sector circular flow model?

The Five Sector Circular Flow Model of an Economy. It’s called a “five sector model” because it focuses on these five sectors: households, firms, the financial sector, the government sector, and the overseas sector. Note that both households and firms save money.

Why is the circular flow model important?

The circular flow of payments is important within an economy because it 1) measures the national income, 2) provides knowledge of interdependence, 3) illustrates the unending nature of economic activities, and 4) shows injections and leakages.

What is the two sector circular flow model?

The circular flow model in the two-sector economy is a hypothetical concept which states that there are only two sectors in the economy, household sector and business sector (business firms). The household sector is the source of factors of production who earn by providing factor services to the business sector.

What is the formula used under 2 sector of circular flow of money?

Since the value of output sold in a simple two sector economy is equal to the sum of consumption expenditure and investment expenditure we have y= C+ I where Y = Value of aggregate output, C = Consumption expenditure and I = Investment expenditure.

What is the two sector model?

Broadly speaking, the two-sector model is an analytical framework that embodies stylized dynamic economies with two production processes. Each sector is devoted to the production of a unique good, and there are usually two factors of production that can freely move across sectors.

What are the four factors of productions?

What is flow variable?

A flow variable is a variable that is measured over a specific period of time. A stock variable is a variable that is independent of time. Income is an example of a flow variable. The balance in a checking account is an example of a stock variable.

What are examples of flow variables?

National income, investment in the economy and aggregate supply- all are flow variables since they relate to a period of time.


There have always been concerns about the security of cloud computing environments, but recent news regarding the so-called VENOM flaw may send some organizations into full-blown panic mode.

An acronym for “virtualized environment neglected operations manipulation,” the VENOM flaw was first discovered by researchers at a firm called CrowdStrike based in Irvine, California. The issue stems from a problem in the code for virtual floppy disk controllers in an open-source technology called QUEMU, which serves as a sort of window or hypervisor in virtual machine environments. While floppy drives are ancient history to many IT administrators, hackers could still use the exploit to penetrate systems that use common tools to virtualize their IT infrastructure, provided they have root or admin permissions.

ZDNet reported that major open source organizations have been quick to offer patches, including Red Hat Software, Xen and those behind the QUEMU project itself. In some cases, making the necessary changes will involve executing a series of commands and even powering-off virtual machine guests, which could have an operational impact in some organizations. Of course, that’s still preferable to a cybercriminal taking advantage of the VENOM flaw, which could threaten an enormous number of data centers.

The nature of the VENOM flaw quickly drew comparisons with last year’s Heartbleed, but in some respects it may be even worse. That’s because, as Fortune explained, there has long been a sense that virtualization technology allowed companies to isolate virtual machines in a way that would make them safer. If hackers know what they’re doing, they could use a bug like this to overwrite parts of a machine’s memory, execute code and do other damage.

Given that virtual machines allow companies to host compute resources on behalf of other firms, the VENOM flaw could also tarnish the reputations of major cloud computing firms. VentureBeat noted that Amazon, Rackspace and Google were all quick to reassure customers and prospects that their data centers are not at risk or that they had already addressed the vulnerability. Still, there may be questions about how they stay on top of potential bugs like this and how quickly they can plug any holes.

On the other hand, it’s important to stress that there have been no reports of the VENOM flaw leading to any actual data theft, and CSO Online suggested the hype and “marketing” around the potential danger has already gotten out of hand. For most organizations, however, it only takes being bitten once by a major security problem to become twice shy.

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Reliability SIRO’s 100% fibre-to-the-premise network is delivered using ESB existing infrastructure, with no copper connection at any point in the network. For example, the signal on a copper wire drops massively over just two kilometres, whereas fibre-optic cable over the same distance is extremely reliable.

Gigabit Speed: SIRO’s 100% fibre broadband offers speeds of 1 Gigabit per second, while a copper-based network generally delivers speeds of up to 100 Megabits per second. A 25GB HD movie would take 3 minutes to download on a FTTH 1Gbps connection, but more than 30 minutes on a FTTC 100Mbps connection.

Multiple Devices: Our homes are full of devices as we continue to work remotely – multiple laptops, tablets, consoles and mobiles are usually connected to the internet at once. With SIRO 100% fibre broadband, you can connect as many devices to your broadband as you like and not slow down your connection.

Future Proof: Unlike copper network, fibre-optic cables are extremely resilient to heat, humidity and extreme weather conditions, making this the last broadband connection you’ll ever need. Our Gigabit network is capable of supporting much faster speeds in the future, enabling homes and businesses to cater to evolving technologies and meet future data needs.


HR for Health and Henry Schein, Inc. Announce Exclusive Business Relationship to Provide Doctors with New Solutions to Simplify Human Resources & Payroll

Henry Schein, Inc., a solutions company for health care professionals, and HR for Health, a SaaS human resources software for private health care practices, announced an exclusive business relationship to assist doctors with reducing their employment compliance risk while simplifying human resources management.

Together, Henry Schein Business Solutions, which offers dentists resources for business operations, finance, marketing, education, training and more, and HR for Health’s human resources and compliance software will provide doctors with a comprehensive portfolio of solutions to help address the challenges of practice ownership, including team performance management, new patient flow, operations, payroll processing, and complying with ever-changing employment laws.

This new business relationship with Henry Schein will expand HR for Health’s ability to provide health care professionals with access to a high-quality HR solution that will help guide them through the ever-changing human resources landscape, reducing their compliance risk.

“For health care professionals, patient care is the number one priority, but the intricacies of operating a business can be hard to manage,” said AJ Caffentzis, President, North American Dental Group, Henry Schein, Inc. “Together with HR for Health, practitioners can rely on us to provide access to a quality HR solution, so they can focus on patient care.”

“Ignoring HR, both from a compliance and also from a practice management perspective, can be a costly mistake for practices,” said Ali Oromchian, CEO of HR for Health. “Thanks to our newly formed relationship with Henry Schein, we can help more practices achieve HR compliance and find peace of mind.”


Monkeypox: What to know

Dreyma Beronja/NW

HEALTHY CAMPUS — NMU’s Health Center offers various services to the campus community, including monkeypox testing.

Ayanna Allen, Assistant News Editor

COVID-19 was the largest collective trauma event that has happened in this lifetime. Many people have reported that their lives have been permanently changed because of the ongoing pandemic. With monkeypox contributing to the United States’ constant state of “survival mode” seen in its people, a significant amount of misinformation and myths have circulated.

As of Sept. 6, the current reported number of cases of monkeypox, or MPV, in the United States is a little under 20,000. In Michigan, that number is 190. There have only been 15 reported fatalities globally, with one of those cases being in Texas.

Dr. Christopher Kirkpatrick, NMU’s medical director, said, “The last time we spoke with the health department they had not seen any confirmed cases in the Upper Peninsula which is good. And, I have not heard that it has changed.”

MPV was originally observed in 1958 by a group of researchers observing monkeys. Therefore, it was named monkeypox. However, the first human case was not recorded until the 70s and had not circulated much outside of central and western Africa.

According to the CDC, MPV is a disease that causes a rash that often looks like pimples or blisters on the skin and mucous membranes.

“This one usually causes fatigue and a little bit of a headache when it first starts, and then you are looking for these characteristic lesions on the skin’s surface,” Kirkpatrick said.

Some other common side effects include flu-like symptoms such as respiratory issues, muscle aches, fever, etc. Those who catch MPV are contagious until the scabs fall off and new skin has grown over.

“Some of the initial media reports you have to be careful about that because it is not an accurate representation [of MPV],” Kirkpatrick said. “It is just [transmitted through] skin to skin contact and that can affect any person on any particular group.”

A popular misconception about MPV is that it is a disease that is only impacting queer populations, specifically those who participate in anal sex. While MPV does disproportionately hurt minority communities, as did COVID, it is not exclusively found in them.

However, according to NPR, the World Health Organization presented a study that found out of 3,900 people that contracted monkeypox, 90% of them acquired the disease through sexual interaction.

“It was first found in people that were having sexual contact, but it is not technically a sexual transmitted disease,” said Kirkpatrick.

Regardless, catching MPV is incredibly rare in a public setting. The chances of touching a contaminated surface or contracting it from a face-to-face interaction are low.

In order to protect oneself, there are a few steps that need to be taken. As a primarily sexually transmitted disease, it is important to practice safe sex and to get vaccinated.

Kirkpatrick stated that students who are concerned about having monkeypox are encouraged to reach out to their primary care provider or contact NMU’s health center as they do have the equipment to test for MPV if necessary.

For those seeking vaccination resources, the Marquette County Health Department is offering MPV vaccinations to those who meet the criteria


Studless vs. Studdable Tires: The Main Differences

Last Updated September 9, 2022 is reader-supported. When you buy through links on our site, we may earn an affiliate commission at no added cost to you

Whenever I talk about all-season tires, I mainly mention that for the best possible winter performance, you need proper winter tires, which is what I’ll be talking about today. Some people think that there’s only one type of those and to get the model that fits their needs, but that’s not the case here.

Studless vs. Studdable Tires

Whenever we say winter tires, we usually mean those “traditional” models we get for when the snow gets deeper, or there are some icy roads we need to drive on. Generally, they get the job done, but their performance has some limitations.

With that said, if a winter tire cannot get the job done, what kind of tire can? A studdable one, of course. In this comparison, I’ll be looking at the standard winter tires or studless ones and comparing them with the studdable ones to see which would be a better option.

Studless vs. Studdable Tires

Studless tires are regular winter tires that most people get for their cars. They are designed to deliver excellent performance in those conditions and are a suitable option for many conditions. With that said, they cannot be fitted with studs, so there are some limitations, especially on deeper snow or ice.

Studdable tires, on the other hand, are like regular winter tires, but manufacturers design the tread with small holes to fit the studs. Without them, the tire performs like a regular winter tire, but for situations where you want better performance, you can fit the studs and improve performance on ice.

What are Studless Tires?

A studless tire is the “regular” winter tire that most people are getting from manufacturers. These are tires designed specifically for winter conditions, and they’re not designed to be fitted with studs. They’re so common because, in most cases, they get the job done, and car owners don’t have to worry about a lack of performance or safety.

There are two things that make a good winter tire – the rubber compound and the tread design. Manufacturers use a rubber compound that strikes an excellent balance between its capability to remain pliable at freezing temperatures and not melting like ice cream once it starts rolling. Generally speaking, studless tires are “softer” as they should be, considering that their compound is designed to deliver performance at temperatures lower than what your typical summer tire can handle.

The second crucial part of a studless tire is the tread design, which delivers traction in various conditions. Most manufacturers go for the zig-zag pattern with biting edges around the blocks with the main task of delivering traction on snowy surfaces.

When you start comparing designs between multiple models, you’ll notice differences, meaning that, in some cases, you’ll have different performances. Some tires may be able to bite in snow better than others, while in some cases, you may find studless tires that can offer some ice performance.

What are Studdable Tires?

The simplest definition is that studdable tires are regular winter tires to which you can fit studs. This is a fairly broad explanation, so let’s dive into some of the specifics.

Studdable tires are primarily winter tires, so there’s a big similarity with the studless ones. The rubber compound’s basics are similar; manufacturers aim to have a tire capable of delivering the advertised performance in winter conditions, regardless of whether we’re talking about dry roads or several inches of snow.

The tread pattern also plays a huge role here, but there is a slight difference. When you look at a studdable winter tire, you’ll notice that it features sipes or a zig-zag pattern which help it with traction on snow or slush. This is for when you don’t have the studs on, and you’re driving it as a regular winter tire.

One thing that sets studdable winter tires from the studless is the ability to insert metal studs in the small holes on the blocks. These aren’t just random places where a technician drilled holes. They are specially designed so that once you install the studs, the tire’s performance in the harshest conditions improves. The biggest benefit of going for these types of tires can be seen on icy surfaces, something that some studless tires will struggle with.

Differences Between Studless and Studdable Tires

Based on the definition, you’ve probably figured out that the main difference between studless and studdable tires is the ability to fit studs. This is where the most significant difference lies, but first, let’s take a look at the differences without the tiny metal helpers.

A more precise comparison can be made between two specific models, but I’m giving you the broad one. A studless tire will perform similarly to a studdable one without the studs. Both types are focused on delivering performance in wintery conditions, so low temperatures, snow, and sometimes ice is something that should be an issue. Naturally, there are some bad apples in both categories, so you’ll need to check out our reviews or comparisons for a specific model.

I mentioned that some studless tires could offer acceptable performance in icy conditions, and that is true, up to a point. As good as some studless tires can be on ice, the performance is limited and barely passes as usable, something you should consider only in a pinch. This is where the metal studs of the studdable tires come into play, as without them, these tires are not too different from the studless ones on ice.

The idea behind the studs is like with chains, so you should be getting improved performance in very harsh conditions like packed snow and ice. With the studs, these tires can dig in even on hard surfaces and deliver traction that the studless tires cannot.

In terms of the rest of the performance, without studs, both types of tires are more or less on a similar level. There are individual cases where a tire can be more responsive while others can be softer, but at the end of the day, they are comparable.

When Should you Get Studless Tires?

Anytime the winter is harsh-enough so that an all-season tire cannot get the job done, you should consider studless tires. Since they’re designed to be used only in winter conditions, you will be getting better performance compared to other types of tires on the market.

While a studless tire does an excellent job at keeping things under control in the winter, it has some limitations. With this type of tire, you’re looking at excellent performance on unpacked snow and pretty good on packed one. The area where a studless tire won’t impress anyone is performance on ice. You may get some acceptable performance with a handful of models, but that’s as much as you can expect.

Overall, people should look at studless tires if they don’t drive in too harsh conditions, something that I do. The winters here are not too mild, but we don’t see some overly harsh conditions, so studless tires do an excellent job for me. All my driving “adventures” are on either clean roads or with an inch or two of snow, so these tires perfectly satisfy my needs.

If by any chance I get in a situation where I need more performance, I have a set of chains in the trunk, which have come in handy once or twice.

When Should you Get Studdable Tires?

Studdable tires are like regular ones, but you can fit metal studs throughout the tread, so you should consider these if the performance of the studless ones won’t fit your needs.

The great thing about studdable tires is that the studs can be removed or added depending on what you need. If the performance explained in the studless tires is what works for you in every winter situation, then you probably won’t benefit too much from studdable tires. Sure, if you have them, you may use them, but this is where it gets tricky. If you haven’t used studdable tires in the past and haven’t felt the need for them, then you probably don’t need them.

Here’s an example from my history book. In my years spent driving, I’ve only needed to fit chains on my tires once, meaning that I’ve only thought about studdable tires only once. My driving habits don’t include driving on too much ice or too packed snow, so it would be pointless for me to get studdable tires. It would be nice to have them, but not necessary.

This leads me to “when should you get studdable tires,” and the answer is in the previous paragraph. Ice and packed snow are something that studless tires can do, but not very well. If you find yourself in those situations too often, studdable tires are a much better option. You’ll get better performance and, most importantly – safer performance.

Where do Studded Tires Come Into Play?

If you know a thing or two about tires, you’re probably wondering why I didn’t mention studded tires, and there’s a good reason for that.

For those confused, here’s a quick intro: Studded tires are winter tires with permanently fitted studs, unlike the studdable ones where you can remove them. These were the golden standard for driving in the harshest winter conditions for a long time, but there was a problem with them.

Studded tires may still exist, but only a very limited amount of people would be after them. As good as they are on snow or ice, they won’t be your first choice on dry and wet roads. The studs don’t have the gripping power as rubber, so you’re getting a bit of limited performance. Next is the noise, which, as you can guess, isn’t on the low side. Metal on concrete isn’t a pleasant sound, especially from your tires.

Finally, we have the law. In some areas and states, studded tires are considered illegal due to their “poor” performance on the road. While I’m on the subject, I should mention that the same thing goes for studdable tires if you drive them with the studs on.

As always, get the tires that fit your needs the best. For most people, myself included, a set of studless tires is more than enough to get through the winter. They provide excellent performance in most winter conditions ranging from dry and wet roads to snow, slush, and in some rare cases, a bit of ice performance.

If you feel that this won’t be enough and want more, then the studdable tires are the ones you should be looking at. They can do pretty much everything the studless can, but with the added benefit of the studs. With those, the performance on ice increases drastically, and you will also notice traction and grip improvements over hard-packed snow.

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Renata Centurión

My mission is to find what bothers customers and help them understand that their processes can be more productive and interesting. I’ve been working with B2B sales for more than 20 years, in multinational companies like Bayer, Merial, Groupon others.

I believe that sales is about caring for people and each other problems, listening, to help them solve issues in a better way. Knowing and meeting different people, building trust and delivering value. That’s why I love this environment.

About me: Can you figure out a big Italian family? If you do, you know me. I’m the second oldest of twenty cousins, but the first baby girl. I was always given lots of attention and always had some responsibility helping others, even since I was little. I come from a family of teachers, mixed with sales. I think that’s why I’m always caring for people’s problems, trying to understand and help.

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Kuwait eyes food investment abroad

This post has been read 12843 times!

KUWAIT CITY, Aug 10: The Ministry of Commerce and Industry has completed its recommendations to address the effects of high food prices and the food security file in Kuwait, reports Al- Qabas daily. The document submitted to the Council of Ministers states the food security file submitted by the Ministry of Commerce and Industry, includes several recommendations that require quick measures that may limit the effects of high food prices in the short term, which requires speedy implementation and seriousness without any delay that may result in adverse consequences and affect the stability of the domestic market.

The Ministry of Commerce and Industry stressed the need to develop a food security strategy in the country through a comprehensive system based on enabling sustainable food production. The study demands increase in financial support for government food companies such as the Kuwait Catering Company, the Kuwait Flour Mills and Bakeries Company, and the Kuwait Livestock Transport and Trading Company, with the state bearing the price difference for its products in case of high prices while selling it to citizens and consumers at the acceptable fixed price.

The ministry suggested the state’s expansion of international agricultural investment by owning agricultural lands outside Kuwait, specifically in the fertile regions. The Ministry of Commerce stressed the need for Kuwait to adopt an integrated strategy for food and water security that includes the following dimensions — Strengthening the national food basket by expanding regional and international agricultural investments, and owning agricultural land, livestock and fisheries in the countries of the fertile regions; working on diversifying import sources and developing the country’s supply chains; reconsidering the distribution of land, agricultural holdings, livestock breeding and fodder support on the basis of achieving self-sufficiency in the state and connecting agricultural holdings with a network of factories for food products through small and medium enterprises to achieve an integrated agricultural economic cycle that ensures stability in the medium and long term in the face of fluctuations in global markets.

This is in addition to paying attention to the water resources management system in the country and ways to diversify its sources to ensure local water security by using advanced technologies and technological applications, which constitute a major requirement to achieve agricultural production and sustain food security and expanding the role of private sector companies, investment companies, and commercial and industrial banks, to enhance food security in the country and provide border markets to ensure the availability and diversity of food products in more effective ways.

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Drop seen in stock of strategic basics food commodities

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The compound Poisson distribution and return times in dynamical systems

Nicolai Haydn Mathematics Department, University of Southern California, Los Angeles, 90089-1113. E-mail: . This work was supported by a grant from the NSF (DMS-0301910) and by a grant from the Université de Toulon et du Var, France.    Sandro Vaienti Centre de Physique Théorique, UMR 6207, CNRS, Luminy Case 907, F-13288 Marseille Cedex 9, and Universities of Aix-Marseille I, II and Toulon-Var. Fédération de Recherche des Unités de Mathématiques de Marseille. E-mail: .

Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the limiting distribution is a compound Poissonian distribution. We also derive error terms for the convergence to the limiting distribution. We also prove a very general theorem that can be used to establish compound Poisson distributions in many other settings.

1 Introduction

In 1899 Poincaré showed that for a map on some space which has an invariant probability measure , almost every every point returns within finite time arbitrarily close. This means that for every (measurable) with the return time function is finite for -almost every . This result was quantified by Kac in 1947 for ergodic measures. His theorem states that , provided is ergodic, which implies that is on average equal to . Since 1990 there has been a growing interest in the statistics of return times and in particular in the distribution of . Considering that it was shown in [20, 19] that for ergodic measures the limiting distribution of a sequence of (rescaled) return functions for can be any arbitrarily prescribed distribution for suitably chosen sets , it is necessary to assume that the return sets are dynamically regular.

For the measure of maximal entropy on a subshift of finite type, Pitskel [25] showed that the return times are in the limit Poisson distributed for cylinder sets ( as ) where the set of suitable ‘centres’ form a full measure set. A similar result had independently been obtained by Hirata [15, 16] by a different method. For -mixing Gibbs measures Galves and Schmitt [10] showed in 1997 that the first return time is in the limit exponentially distributed and that the convergence is at an exponential rate. Subsequent results (e.g. [27, 8, 17, 13, 5, 1]) established limiting distribution results for first or multiple return times in various settings and sometimes with rates of convergence.

Almost all previous results look at the distribution of return times near generic points. The notable exception being the paper [15] by Hirata which gives the distribution of the first return time at a periodic point. In the present paper we consider periodic points for sufficiently well mixing invariant measures and show that the limiting distribution is compound Poissonian. The compound Poisson distribution has previously been used in various settings including the analysis of internet traffic where the waiting time between packets is exponential and the size of each packet is geometrically distributed. It has also been used to model the survival of capitalist enterprises in the free market system [21]. The main technical result, Proposition 1, provides conditions under which one obtains a compound Poissonian distribution with error terms. This result in itself will be of interest to a much larger community than the one of dynamicists addressed in this paper.

Let be a probability measure on a space which carries a transformation , preserving , and whose -algebra is generated by the joins , , of a given finite measurable partition . The elements of are called -cylinders. We assume is generating, i.e. the elements of are single points. Denote by the characteristic function of a (measurable) set and define the random variable:

. The value of measures the number of times a given point returns to within the time . Typically the obsevation time is chosen to be where is a parameter value. (The rescaling factor agrees with Kac’s theorem.) For instance, if is the measure of maximal entropy on a subshift of finite type, then Pitskel [25] showed that is for -almost every in the limit Poisson distributed (where and denotes the unique -cylinder that contains ). In [13] we have proven a similar result for a much wider class of systems and provided error estimates.

We develop a mechanism which allows to prove the compound Poisson distribution of return times at periodic points and also to obtain error estimates as the cylinder sets shrink in measure to zero.

To be more precise, if we denote by the counting function , with the observation time , we will study the following distribution:

where is a parameter and depends on the periodic point and will be given in Sect. 3. We will show that the limit is the compound Poisson distribution (see Section 2) if is a -mixing measure. We also provide rates of convergence. This then implies under some mild additional assumptions [14] the uniform integrability of the process .

We then extend this result to return times, i.e. to the distribution of the process restricted to the cylinder . The measure is then replaced by the conditional measure . We refer to this second case as the distribution of the number of visits for return times.

Our results for return times considerably improve on the work of Hirata [15], where he computed (without error) the distribution of the first return time (order ) around periodic points and for Gibbs measures on Axiom-A systems.

The plan of the paper is the following. The purpose of section 2 is to prove Proposition 1 that gives general conditions under which a sum of mutually dependent -valued random variables converges to the compound Poisson distribution and provides error terms. A similar result that had been inspired by a theorem of Sevast’yanov [26], was proved and used in [13] for the Poisson distribution.

The distribution of return times is tied to the mixing properties of the invariant measure considered. For that purpose we introduce in the third section the -mixing property. This property is more general that the widely used -mixing property and is reminiscent of Philipp and Stout [24] ‘retarded strong mixing property’. In this way one can obtain distribution results on return times of some well studied dynamical systems that are not -mixing, e.g. rational maps, parabolic maps, piecewise expanding maps in higher dimension ….

The third section is devoted to the proof of the existence of the limit distribution and rates of convergence for entry times (Theorem 7), while the fourth section extends those results to return times (Theorem 10). Section 5 contains a careful application to rational maps with critical points (Theorem 11).

We conclude this introduction with an interesting observation. Limit distributions for entry and return times have been provided along nested sequences of cylinder sets converging to points which were chosen almost everywhere or as periodic points. In section 3.4 we will show how to find points which do not have limit distributions at all, and this will be achieved by using our results on the compound Poisson distribution around periodic points.

2 Factorial moments and mixing

The main purpose of this section is to prove a very general result which we use to prove the main results in sections 3 and 5 but which can also be useful to establish compound Poisson distribution with respect to the geometric distributiion in many other settings. For more general compound Poisson distributions see [9]. More recently (e.g. [7, 2]) there have been efforts to approach compound Poisson distributions using the Chen-Stein method. The treatment in [7] has a more general setting, but the result is far from applicable to our situation.111We thank the referee for pointing us towards Chen and Roos’ work and also for other enlightening remarks. Proposition 1 is of general interest and is reminiscent of existing theorems which establish the Poisson distribution (cf. [26, 13]). from the convergence of the moments. It provides general conditions under which the distribution of a finite set of -valued random variables is close to compound Poisson (and provides error terms). In sections 3 and 5 we then use it to obtain the speed of convergence for the limiting distributions for -mixing systems, some non-Markovian systems and equilibrium states for rational maps with critical points.

2.1 Compound Poisson distribution

For a parameter let us define the polynomials

, where (). The distribution , is sometimes called the Pólya-Aeppli distribution [18]. It has the generating function

its mean is and its variance is . Note that for we recover the Poisson terms and the generating function which is analytic in the entire plane whereas for the generating function has an essential singularity at . The expansion at yields where

() are the factorial moments. Note that in particular and for all .

2.2 Return times patterns

Let and be given integers (typically ) and let be some (large) number. For we define the following:
(I) : We denote by the -vectors for which .
(II) : We divide the set into disjoint subsets where consists of all for which we can find indices , , so that if and so that for all .

For the values of will be identified with returns; returns that occur within less than time are called immediate returns and if the return time is then we call it a long return (i.e. if then we say is an immediate return and if the we call a long return). That means that consists of all return time patterns which have immediate returns that are clustered into blocks of immediate returns and long returns between those blocks. The entries , , are the beginnings (heads) of the blocks (of immediate returns). We assume from now on that all short returns are multiples of . (This reflects the periodic structure around periodic points, cf. condition (II) of Proposition 1.)
(III) : For the length of each block is , . Consequently let us put for the individual overlaps, for . Then is the overlap of the th block and the total overlap of . We now put . ( is a disjoint union.)
(IV) : For in we put

for the minimal distance between the ‘tail’ and the ‘head’ of successive blocks of immediate returns (or the length of the shortest one of the long gaps).

2.3 Compound Poisson approximations

The purpose of this section is to prove the following result on the approximation of the compound Poisson distribution.

Proposition 1

Let be as above. Let , , be -valued random variables on some for put . Choose and define the ‘rare set’ , where . Let be a probability measure on which satisfies the following conditions ( is a constant):
(I) for all (invariance of the measure).
(II) Suppose that there are numbers , so that for all

if all of the individual overlaps are multiples of , and

if some of the individual overlaps are not multiples of .
(III) There are some constants small (e.g. ), so that for all

Let us put and .

Then there exists a constant so that for every one has

Note that the constants and don’t enter the final estimate in an explicit way. The significant quantity here is which typically is where only have to be small enough of order .

The choice of is central to the application of this proposition. In the application however depends on and in fact as . Obviously a larger value for increases the error term as one sees from the expression, but also a smaller value increases the error term since the rare set becomes larger and the ‘mixing property’ in (II) will require larger and smaller , thus again increasing the error estimate. The trick is to optimise .

Proof. We compare the generating function for the process with the generating function for the compound Poissonian. In part (A) we compare their Taylor coefficients at and in part (B) we use Cauchy estimates to compare their Taylor coefficients at which then gives us the final result.

(A) The coefficients at (factorial moments) of the generating function are

while the coefficients of the generating function for the compound Poisson distribution are

where . We will now compare the coefficients to the coefficients . There are three parts to the comparison: (i) Assumption (II) is used to compare the terms for which ; (ii) Assumptions (I) and (III) are used to estimate the total contributions made by ; (iii) We have to estimate the contribution to that correspond to overlaps which do not occur for vectors in and therefore cannot be matched with terms in the sum that defines .

More precisely, we estimate as follows:

Before we proceed to bound the three terms on the right hand side let us estimate the cardinality of the sets . (Note that if is nonempty.) Since consists of all that have a total overlap (in blocks of immediate returns) we get

( blocks positioned ‘anywhere’ on an interval of length , overlaps distributed on immediate returns and blocks beginning on any of the return times).

Now we estimate the three terms in the coefficient comparison as follows:
(i) The first error term (difference between the dominating terms) is bounded using assumption (II):

(because ), where and .
(ii) For the second term let us note that where . Put for those where for exactly indices and put (obviously and ).

To estimate the cardinality of let us note that the number of possibilities of (entrance times for long returns bigger than ) is bounded above by (this is the upper bound for the number of possibilities to obtain intervals contained in the interval ), and each of the remaining return times less than assume no more than different values. Since the indices can be picked in many ways out of blocks, we obtain:

To estimate the contribution made by the portion of the sum in the definition of which corresponds to the vectors we obtain by summing over :

The corresponding term for the actual expected values of where is in the rare set is bounded by assumption (II). Hence we obtain

for some , and , .
(iii) Since the sum for contains many terms that cannot be paired with terms in the sum of let us look at those combinations of , , and that do not correspond to vectors in . Let us denote by the number of elements for the values of that occur in the representation of and are not in . Those overcounts occur for overlaps which have lengths . Denote by the individual overlaps of these fictitious ‘immediate returns’. Then, if the first intersection is of length (), then

Hence (for and )

where we used the identity . Let us put for the set of ficticious vectors that have individual overlaps () that are not allowed, i.e. where at least one overlap is longer than . Then we can estimate the contribution one gets by counting over as follows:

where we used the identity . Hence

Combining the three estimates (i), (ii) and (iii) yields

(B) The difference between the two generating functions splits into two parts, , which we analyse separately ( reflects the estimates of parts (A-i) and (A-iii), and reflects the estimate of (A-ii)):
(i) The function is majorised by the power series

The sum over is equal to (where ) which can be bounded by if . A Cauchy estimate with now yields

If is large so that then we can take and obtain for instance that (assuming )

using Stirling’s formula, where . If is small so that for instance then we take and thus obtain .
(ii) The second error function is majorised by the power series ()

if is small enough (e.g. ), where we have used the identity

(develop into a Taylor series with variable and use the identity ). Hence if we put () then

if we assume that is small enough (e.g. ). If then we get (using Stirling’s formula)

(if is close enough to ).

Since and we get by combining the estimates (i) and (ii)

(and ) from which follows the result of the proposition.

In the following we will apply this proposition to situations that typically arise in dynamical systems. There the stationarity condition (I) of the proposition is implied by the invariance of the measure. The random variables will be the indicator function of a cylinder set pulled back under the th iterate of the map. Condition (II) is then implied by the mixing property (see below Definition 2). The most difficult condition to satisfy is (III) because it involves ‘short range’ interaction over which one has little control and which require more delicate estimates (see Lemma 5 below). A simpler version of Proposition 1 is the following corollary () which is easily deduced by putting .

Corollary 2

Let be as above. Let , , be -valued random variables and for . For some let , where . Assume be a probability measure on which satisfies the following conditions ( is a constant, ):
(I) for all (invariance of the measure);
(II) Suppose there is a so that for all :

for all , and ;

for all .

Then there exists a constant so that for every one has ( and )

3 Measures that are -mixing

Let be a map on a space and a probability measure on . Moreover let be a measurable partition of and denote by its -th join which also is a measurable partition of for every . The atoms of are called -cylinders. Let us put for the collection of all cylinders in and put for the length of an -cylinder , i.e.  if .

We shall assume that is generating, i.e. that the atoms of are single points in .

In the following definition we generalise the ‘retarded strong mixing condition’ (see e.g. [24]). We consider mixing dynamical systems in which the function determines the rate of mixing while the separation function specifies a lower bound for the size of the gap that is necessary to get the mixing property.

Definition 3

Assume is a -invariant probability measure on and that there are functions and so that:
(i) () is non-decreasing
(ii) is non-increasing.

We say that the dynamical system is -mixing if

for all , , measurable (in the -algebra generated by ) and which are unions of -cylinders.

Systems that are -mixing are for instance:

  1. Classical -mixing systems (see, e.g. [6]): . These include equilibrium states for Hölder continuous potentials on Axiom A systems (which include subshifts of finite type) or on the Julia set of hyperbolic rational maps. In this case the partition is finite.

  2. Dispersing billiards [23]: is linear.

  3. Equilibrium states for Hölder continuous potentials (that satisfy the supremum gap (see section 5) on the Julia set of rational maps where the Julia set contains critical points: is linear, is exponential.

  4. Multidimensional piecewise continuous maps [22]: depends on the individual cylinders ().

For and (large) let as above be the -vectors for which . Let be a positive parameter, and put be the normalised time. Then the entries of the vector are the times at which all the points in hit the set during the time interval .

Lemma 4

Let be -mixing.

Then for all , unions of -cylinders, (), and all ‘hitting vectors’ with return times () one has