Math Formatting Problems

MathJax is not consistently rendering mathematical expressions properly on the homepage. Note that this problem is not limited to raw LaTex notation being displayed. In some posts, entire mathematical expressions are missing. Mathematical expressions appear to be correct when a specific post is opened in a new tab.

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From the “Preface to the English Edition” of “The Theory of Money and Credit” by Ludwig von Mises: “All proposals that aim to do away with the consequences of perverse economic and financial policy, merely by reforming the monetary and banking system, are fundamentally misconceived. Money is nothing but a medium of exchange and it completely fulfills its function when the exchange of goods and services is carried on more easily with its help than would be possible by means of barter. Attempts to carry out economic reforms from the monetary side can never amount to anything but an artificial stimulation of economic activity by an expansion of the circulation, and this, as must constantly be emphasized, must necessarily lead to crisis and depression. Recurring economic crises are nothing but the consequence of attempts, despite all the teachings of experience and all the warnings of the economists, to stimulate economic activity by means of additional credit.

Mathematicians of the day.

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Immunological mechanisms of the antitumor effects of supplemental oxygenation

From the abstract of “Immunological mechanisms of the antitumor effects of supplemental oxygenation“.

Antitumor T cells either avoid or are inhibited in hypoxic and extracellular adenosine-rich tumor microenvironments (TMEs) by A2A adenosine receptors. This may limit further advances in cancer immunotherapy. There is a need for readily available and safe treatments that weaken the hypoxia–A2-adenosinergic immunosuppression in the TME. Recently, we reported that respiratory hyperoxia decreases intratumoral hypoxia and concentrations of extracellular adenosine. We show that it also reverses the hypoxia-adenosinergic immunosuppression in the TME. This, in turn, stimulates (i) enhanced intratumoral infiltration and reduced inhibition of endogenously developed or adoptively transfered tumor-reactive CD8 T cells, (ii) increased proinflammatory cytokines and decreased immunosuppressive molecules, such as transforming growth factor–β (TGF-β), (iii) weakened immunosuppression by regulatory T cells, and (iv) improved lung tumor regression and long-term survival in mice. Respiratory hyperoxia also promoted the regression of spontaneous metastasis from orthotopically grown breast tumors. These effects are entirely T cell– and natural killer cell–dependent, thereby justifying the testing of supplemental oxygen as an immunological coadjuvant to combine with existing immunotherapies for cancer.

Additional information can be found in “Extra Oxygen and Immunotherapy Slows Cancerous Tumor Growth“.

Tripling the amount of oxygen in the air patients breathe could boost the effectiveness of cancer therapies, according to research published Wednesday.

A new study in the journal Science Translational Medicine proposes that adding oxygen to immunotherapy cancer treatments can weaken a tumor’s defenses against cancer-killing cells.

Dr. Michail Sitkovsky, director of the New England Inflammation and Tissue Protection Institute at Northeastern University in Boston, told Healthline that delivering 60 percent oxygen — the amount used in hospitals — could improve tumor rejection by flipping the tumor environment from hostile to permissive.

“The solution was embarrassingly simple,” Sitkovsky said.

Researchers made the discovery while experimenting on mouse models of lung and breast cancers. Mice kept in environments with 60 percent oxygen concentration had a much slower rate of cancer growth compared to mice in regular 21 percent oxygen settings.

This occurred, however, only when the mice also had the tumor-recognizing anti-tumor killer cells prompted by immunotherapy drugs.

The Link Between Cancer and Oxygen

Cancerous tissues are known to be low-oxygen environments. Not only is it a poor prognosis factor, the lack of oxygen produces adenosine, a molecule that blocks the body’s natural immune response.

Adenosine works against the body’s T-cells and natural killer cells by essentially putting them to sleep so that cancer cells can thrive. Tumors are worse off when adenosine production is decreased or when its effects are blocked.

The new research asserts that the supplemental oxygen decreases production of adenosine by tumors. This “wakes up” the inhibited anti-tumor killer cells to penetrate the tumor and deliver a lethal hit.

“When they are given oxygen, the immune killer cells are no longer sleepy or sluggish,” Sitkovsky said.

The paper published Wednesday offers additional therapies to improve the effectiveness of current immunotherapy and cancer vaccines.

“It must be emphasized that oxygen alone won’t help,” Sitkovsky said. “It must be given only together with other treatments that are designed to induce the expansion of anti-tumor killer cells.”

The rest of the article can be read here.

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From Fight Aging!: More of Brain Aging Than Thought May Be Vascular in Nature

Fight Aging! blog noted some recent research that suggests that cognitive decline in the elderly may be due to the same types of vascular deterioration that play a role in heart disease.

Age-related deterioration in blood vessels and the broader cardiovascular system generates damage in the brain. Blood vessel walls are elastic, a property that depends on the molecular structure of the proteins making up the extracellular matrix in that tissue. This structure is progressively degraded by the presence of sugary metabolic waste known as advanced glycation end-products (AGEs), which leads to the formation of cross-links between proteins and a consequent loss of elasticity. Stiffening of blood vessels causes hypertension and many of the cellular and molecular mechanisms involved overlap with those that speed the progression of atherosclerosis, a condition in which blood vessel walls become sources of chronic inflammation and are remodeled into fatty deposits by abnormal cellular activity. All of this causes a rising number of structural failures in the small blood vessels of the brain. Each one is effectively a tiny, unnoticed stroke, killing cells in a minuscule area of the brain. This harm adds up over time and is one of the contributing causes of age-related cognitive impairment.

A recently published paper suggests that more of the age-related changes observed in the brain may be due to vascular degeneration than previously thought. If so this implies that research aimed at removing cross-links has a greater importance, as do efforts to block the very early causes of atherosclerosis, such as the generation of oxidized lipids due to mitochondrial DNA damage.

The rest of the article can be read here.

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From The Guardian: Jaw bone fossil discovered in Ethiopia is oldest known human lineage remains

A lower jaw bone and five teeth discovered on a hillside in Ethiopia are the oldest remains ever found that belong to the genus Homo, the lineage that ultimately led to modern humans.

Fossil hunters spotted the jaw poking out of a rocky slope in the dry and dusty Afar region of the country about 250 miles from Addis Ababa.

The US-led research team believes the individual lived about 2.8m years ago, when the now parched landscape was open grassland and shrubs nourished by tree-lined rivers and wetlands.

The remains are about 400,000 years older than fossils which had previously held the record as the earliest known specimens on the Homo lineage.

The discovery sheds light on a profoundly important but poorly understood period in human evolution that played out between two and three million years ago, when humans began the crucial transformation from ape-like animals into forms that used tools and eventually began to resemble modern humans.

“This is the the first inkling we have of that transition to modern behaviour. We were no longer solving problems with our bodies but with our brains,” said Brian Villmoare at the University of Nevada in Las Vegas.

The new fossil, found at a site called Ledi-Geraru, has a handful of primitive features in common with an ancient forerunner of modern humans called Australopithecus afarensis. The most well-known specimen, the 3m-year-old Lucy, was unearthed in 1974 in Hadar, only 40 miles from the Ledi-Geraru site. But the latest fossil has more modern traits too. Some are seen only on the Homo lineage, such as a shallower chin bone.

The picture that emerges from the fossil record is that 3m years ago, the ape-like Australopithecus afarensis died out and was superseded by two very different human forms. One, called Paranthropus, had a small brain, large teeth and strong jaw muscles for chewing its food. The other was the Homo lineage, which found itself with much larger brains, a solution that turned out to be more successful.

“By finding this jaw bone we’ve figured out where that trajectory started,” said Villamoare. “This is the first Homo. It marks in all likelihood a major adaptive transition.”


The rest of the article can be read here.

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Understanding True Credit and False Credit by Frank Shostak

In this excellent article, Shostak provides a crystal clear example of how credit, the subsistence fund, and banking would function in a free economy without fraud (fractional reserve banking) and coercion (central bank and legal tender laws).

There are two kinds of credit: that which would be offered in a market economy with sound money and banking (true credit), and that which is made possible only through a system of central banking, artificially low interest rates, and fractional reserves (false credit).

Banks cannot expand true credit as such. All that they can do in reality is to facilitate the transfer of a given pool of savings from savers (i.e., those lending to the bank) to borrowers.

Consider the case of a baker who bakes ten loaves of bread. Out of his stock of real wealth (ten loaves of bread), the baker consumes two loaves and saves eight.

He lends his eight remaining loaves to the shoemaker in return for a pair of shoes in one-week’s time.

Note that credit here is the transfer of ”real stuff,” i.e., eight saved loaves of bread from the baker to the shoemaker in exchange for a future pair of shoes.

Also, observe that the amount of real savings determines the amount of available credit. If the baker had saved only four loaves of bread, the amount of credit would have only been four loaves instead of eight.

Note that the saved loaves of bread provide support to the shoemaker. That is, the bread sustains the shoemaker while he is busy making shoes.

This means that credit, by sustaining the shoemaker, gives rise to the production of shoes and therefore to the formation of more real wealth. This is the path to real economic growth.

Money and Credit

The introduction of money does not alter the essence of what credit is. Instead of lending his eight loaves of bread to the shoemaker, the baker can now exchange his saved eight loaves of bread for eight dollars and then lend them to the shoemaker.

With eight dollars the shoemaker can secure either eight loaves of bread or other goods to support him while he is engaged in the making of shoes. The baker is supplying the shoemaker with the facility to access the pool of real savings, which among other things also has eight loaves of bread that the baker has produced. Also note that without real savings the lending of money is an exercise in futility.

Money fulfills the role of a medium of exchange. Thus, when the baker exchanges his eight loaves for eight dollars he retains his real savings, so to speak, by means of the eight dollars.

The money in his possession will enable him, when he deems it necessary, to reclaim his eight loaves of bread or to secure any other goods and services.

There is one provision here that the flow of production of goods continues. Without the existence of goods, the money in the baker’s possession will be useless.

The existence of banks does not alter the essence of credit. Instead of the baker lending his money directly to the shoemaker, the baker lends his money to the bank, which in turn lends it to the shoemaker. In the process the baker earns interest for his loan, while the bank earns a commission for facilitating the transfer of money between the baker and the shoemaker.

The benefit that the shoemaker receives is that he can now secure real resources in order to be able to engage in his making of shoes.

Despite the apparent complexity that the banking system introduces, the essence of credit remains the transfer of saved real stuff from lender to borrower.

Without an increase in the pool of real savings, banks cannot create more credit. At the heart of the expansion of good credit by the banking system is an expansion of real savings.

Now, when the baker lends his eight dollars we must remember that he has exchanged for these dollars eight saved loaves of bread. In other words, he has exchanged something for eight dollars. So when a bank lends those eight dollars to the shoemaker, the bank lends fully “backed” dollars, so to speak.

The rest of the article can be read here.

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Playing with continued fractions and Khinchin’s constant by John Cook

Take a real number x and expand it as a continued fraction. Compute the geometric mean of the first n coefficients.

Aleksandr Khinchin proved that for almost all real numbers x, as n → ∞ the geometric means converge. Not only that, they converge to the same constant, known as Khinchin’s constant, 2.685452001…. (“Almost all” here mean in the sense of measure theory: the set of real numbers that are exceptions to Khinchin’s theorem have measure zero.)

The rest of the article can be read here.

Click here for a biography of Aleksandr Khinchin.


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Makers Versus Takers

mvtH/T V is For Voluntary.

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A Weekly Dose of Hazlitt: False Internationalism

False Internationalism” is the title of Henry Hazlitt’s Newsweek column from August 20, 1956. Here, Hazlitt summarizes a monograph written by Wilhelm Röpke in which he denounces the destruction of the 19th century international order via the destruction of the gold standard, trade barriers, and central planning.

There has recently appeared a 64-page pamphlet, by the
European economist Wilhelm Ropke, called Economic
Order and International Law. It is one of the most penetrating
analyses that have yet appeared of the modern
malady of false internationalism. Though it was a course
of lectures before the Academy of International Law, it
has been independently printed only for private circulation
(A.W. Sijthoff, Leyden) and its contents deserve to
be far more widely known.

Ropke’s thesis has so many facets and corollaries
that it is difficult to summarize in any short space. He
begins by pointing out that a central element in the
Socialist movement of the last hundred years has been
the idea of the international mission of Socialism. Yet
Socialism in practice (or any other brand of collectivism-
interventionism, “planning,” the Welfare State) has
led to nationalism, economic isolationism, autarky—in
brief, to international disintegration.

An As-If World Money

Ropke contrasts this international disintegration,
brought about by the interventionist, collectivist,
and inflationary policies followed by most governments
today, with the “universalist-liberal” solution
approached in the nineteenth century—and largely
retained, for that matter, up to about twenty years ago.
Nations did not surrender their sovereignty to some
international super-state. They did not set up endless
intergovernmental bodies like the United Nations,
with its maze of sub-agencies, or the International
Monetary Fund, or the European Payments Union, or
the Schuman Plan. But they did adhere to a far more
real international order, a sort of As-If World State,
with an As-If World Money.

International law respected private property. The
natural resources of the world were owned and developed
by private persons, or by corporations in which
anybody, whatever his nationality, could buy shares in
the world’s stock exchanges. International trade was
obstructed only by tariffs. It was not ripped into shreds
by exchange control, blocked currencies, devaluations,
bilateralism, import quotas, export subsidies, balance
of payments deficits, and “dollar shortages.”

But the great achievement of traditional liberalism
in the nineteenth century was the creation of a de
facto world currency, the international gold standard.
The gold standard meant that governments and central
banks, in their money and credit policies, were subjected
to a severe common discipline which prevented
anyone from stepping out of line and upsetting international
equilibrium. Continue reading

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