The lipid hypothesis of atherosclerosis says that high serum cholesterol levels come as a causative factor in the development of atherosclerosis. In other words, there exists a significant, real, statistical relationship between high cholesterol levels in the blood and atherosclerosis. It does not say that high blood cholesterol levels (hypercholesterolemia) causes atherosclerosis and consequent atherosclerotic events (heart attacks, strokes, angina, etc.) necessarily, but rather that blood cholesterol levels come as a causative factor. Since usually foods high in saturated fats and dietary cholesterol can raise serum cholesterol levels to a high level, or keep them at a high level, and since plant foods are not generally high in saturated fat and have no cholesterol in them, it would seem to follow that the lipid hypothesis would work out well for those who wish to advocate for a vegan diet.
However, the easiest and simplest way to advocate for a vegan diet comes as to advocate for a diet that qualifies as vegan while having as few other restrictions as possible. But, a diet developed with the lipid hypothesis in mind does not allow for this. First off, trans-fatty foods can significantly elevate blood cholesterol levels. Thus, the lipid hypothesis makes french fries, many brands of potato chips, foods with partially hydrogenated vegetable oil, and many other conventional vegan snack food products all potentially, if not actually, poor choices for your heart, your brain, and the blood flow in your body. Second, foods high in simple sugars can significantly elevate blood cholesterol levels. So, via the lipid hypothesis many, if not most brands of soft drinks, energy drinks, foods with high fructose corn syrup, fruit juices, etc. can elevate serum cholesterol levels. Third, refined sources of carbohydrates, such as white bread, semolina pasta, white rice, etc. can elevate serum cholesterol levels. Fourth, many oils due in part to their concentrated level of saturated fat can elevate serum cholesterol levels. There no doubt exist many more inconvenient "diet-heart" ideas in accordance with the lipid hypothesis, which do NOT work out as convenient for those that would advocate veganism, since they end up implying potential problems with some vegan diets. It is by no means impossible that, were they to understand it and its implications, some vegans might intensely dislike the lipid hypothesis for this very reason.
Friday, June 1, 2012
Monday, May 28, 2012
Caldwell Esselstyn's Study and Its Follow-Up
Harriet Hall here writes "
Caldwell Esselstyn
Esselstyn did an uncontrolled interventional study of patients with angiographically documented severe coronary artery disease who were not hypertensive, diabetics, or smokers. He wanted to test how effective one physician could be in helping patients achieve a total cholesterol level of 150 mg/dL or less, and what effect maintaining that level would have on coronary disease. Patients agreed to follow a plant-based diet with <10% of calories derived from fat. They were asked to eliminate oil, dairy products (except skim milk and no-fat yogurt), fish, fowl, and meat. They were encouraged to eat grains, legumes, lentils, vegetables, and fruit. Cholesterol-lowering medication was individualized.
There were originally 24 patients: 6 dropped out early on, 18 maintained the diet, one of these 18 died of an arrhythmia and 11 completed a mean of 5.5 years followup. Repeat angiography showed that of 25 coronary artery lesions, 11 regressed and 14 remained stable. At 10 years, 11 patients remained: 6 continued the diet and had no further coronary events; 5 resumed their pre-study diet and reported 10 coronary events.
In a 12 year followup report, the 6 who had maintained the diet at 10 years and the 5 who had gone off it and had coronary events had apparently somehow morphed into 17 patients who had remained adherent to the diet and who had had no coronary events. I couldn’t understand the discrepancy in numbers; perhaps readers can explain it to me if I missed something."
First off, it may seem that another number doesn't match in that the follow-up study says that the original study had 24 patients, while the first study above mentions 22. But, the first study says "The study included 22 patients with angiographically documented, severe coronary artery disease that was not immediately life threatening." So, there isn't any necessarily contradiction in numbers there.
Second, the first study says "Of the 22 participants, 5 dropped out within 2 years, and 17 maintained the diet, 11 of whom completed a mean of 5.5 years of follow-up." This does NOT say that 11 of them, implying that 6 quit the diet, but that 11 of them engaged in follow-up. As the follow-up study says: "At 5 years, 11 of these patients underwent angiographic analysis by the percent stenosis method, which demonstrated disease arrest in all 11 (100%) and regression in 8 (73%)." So, the 11 who completed the follow-up appears to refer to the patients who completed angiograms. 6 of the 17 didn't complete follow-up by not engaging in angiograms.
Another discrepancy in the numbers may appear to exist in that the follow study says "The remaining 18 patients adhered to the study diet and medication for 5 years.", while the first indicates 17 maintaining the diet. But, that 17 number appears in the passage about 5.5 years of follow-up and the second study says "One patient admitted to the study with <20% left ventricular output died from a ventricular arrhythmia just weeks after the 5-year follow-up angiogram had confirmed disease regression. Autopsy revealed no myocardial infarction. " So, there doesn't exist any contradiction there.
A further discrepancy may seem to exist in that the first study says "Among the 11 remaining patients after 10 years, six continued the diet and had no further coronary events, whereas the five dropouts who resumed their prestudy diet reported 10 coronary events." This might seem like 5 more patients (5 out of the 22 who had angiographically documented coronary artery disease) dropped out of the study, which would contradict 17 patients in the follow study. However, the five dropouts here probably refers to the original 5 of the original 22 angiographically documented patients who dropped out of the dietary program withing 2 years. Esselstyn may have only mentioned 6 continuing the diet here, because he was only able to verify 6 still on the dietary plan when he published this. The other 11 (not all angiographically documented patients) he may not have verified as still on the dietary plan until later... and that's perhaps part of the reason why he provided the update to the study in the first place.
Caldwell Esselstyn
Esselstyn did an uncontrolled interventional study of patients with angiographically documented severe coronary artery disease who were not hypertensive, diabetics, or smokers. He wanted to test how effective one physician could be in helping patients achieve a total cholesterol level of 150 mg/dL or less, and what effect maintaining that level would have on coronary disease. Patients agreed to follow a plant-based diet with <10% of calories derived from fat. They were asked to eliminate oil, dairy products (except skim milk and no-fat yogurt), fish, fowl, and meat. They were encouraged to eat grains, legumes, lentils, vegetables, and fruit. Cholesterol-lowering medication was individualized.
There were originally 24 patients: 6 dropped out early on, 18 maintained the diet, one of these 18 died of an arrhythmia and 11 completed a mean of 5.5 years followup. Repeat angiography showed that of 25 coronary artery lesions, 11 regressed and 14 remained stable. At 10 years, 11 patients remained: 6 continued the diet and had no further coronary events; 5 resumed their pre-study diet and reported 10 coronary events.
In a 12 year followup report, the 6 who had maintained the diet at 10 years and the 5 who had gone off it and had coronary events had apparently somehow morphed into 17 patients who had remained adherent to the diet and who had had no coronary events. I couldn’t understand the discrepancy in numbers; perhaps readers can explain it to me if I missed something."
First off, it may seem that another number doesn't match in that the follow-up study says that the original study had 24 patients, while the first study above mentions 22. But, the first study says "The study included 22 patients with angiographically documented, severe coronary artery disease that was not immediately life threatening." So, there isn't any necessarily contradiction in numbers there.
Second, the first study says "Of the 22 participants, 5 dropped out within 2 years, and 17 maintained the diet, 11 of whom completed a mean of 5.5 years of follow-up." This does NOT say that 11 of them, implying that 6 quit the diet, but that 11 of them engaged in follow-up. As the follow-up study says: "At 5 years, 11 of these patients underwent angiographic analysis by the percent stenosis method, which demonstrated disease arrest in all 11 (100%) and regression in 8 (73%)." So, the 11 who completed the follow-up appears to refer to the patients who completed angiograms. 6 of the 17 didn't complete follow-up by not engaging in angiograms.
Another discrepancy in the numbers may appear to exist in that the follow study says "The remaining 18 patients adhered to the study diet and medication for 5 years.", while the first indicates 17 maintaining the diet. But, that 17 number appears in the passage about 5.5 years of follow-up and the second study says "One patient admitted to the study with <20% left ventricular output died from a ventricular arrhythmia just weeks after the 5-year follow-up angiogram had confirmed disease regression. Autopsy revealed no myocardial infarction. " So, there doesn't exist any contradiction there.
A further discrepancy may seem to exist in that the first study says "Among the 11 remaining patients after 10 years, six continued the diet and had no further coronary events, whereas the five dropouts who resumed their prestudy diet reported 10 coronary events." This might seem like 5 more patients (5 out of the 22 who had angiographically documented coronary artery disease) dropped out of the study, which would contradict 17 patients in the follow study. However, the five dropouts here probably refers to the original 5 of the original 22 angiographically documented patients who dropped out of the dietary program withing 2 years. Esselstyn may have only mentioned 6 continuing the diet here, because he was only able to verify 6 still on the dietary plan when he published this. The other 11 (not all angiographically documented patients) he may not have verified as still on the dietary plan until later... and that's perhaps part of the reason why he provided the update to the study in the first place.
Tuesday, April 10, 2012
Mimic Operations
The author writes informal proofs in the following. The author uses Reverse Polish Notation also.
Suppose we have an infinite set S, and a operation "*". A mimic operation *' of * consists of an operation on S such that for all but a finite number of points a1, ..., an *=a1, ..., an *'. So, for a unary operation F on the natural numbers N, a mimic operation F' satisfies xF=xF' except for a finite set of natural numbers {a1,...,an}. For a binary operation G on N, a mimic of B, B' satisfies xyB=xyB' except for a finite number of pairs of natural numbers {(a, b)1,...,(a, b)n} and so on.
Theorem 1: For any n-ary operation O on an infinite set, there exists an infinity of mimic operations, O'.
Proof: An n-ary operation O can get defined by a set of n 1 + tuples. E. G. the binary operation of addition can get defined by the triples (2, 4, 6), (1, 1, 2) such that for (x, y, z), xy+=z. Now consider the set of such tuples T for O. Vary the n 1 + part of the tuples in T for some finite number of tuples. This forms a set of tuples T' which describes an n-ary operation distinct from O in but a finite number of points, and thus forms a mimic operation O'. Note that since there exist an infinity of tuples belonging to T, there exists an infinity of ways to form T' given T. Thus, given an n-ary operation O, there exists an infinity of mimic operations O'.
Define a k-mimic operation Mk of an operation M as an operation which differs from M by but k points, where both operations operate over an infinite set. In other words, for an operation Mn of arity n with mimic Mkn, a1...anMn=a1...anMkn, except for k tuples {(b1, ..., bn), ..., (l1, ..., ln)} where this equality fails.
Theorem 2: For any n-ary operation O on an infinite set, there exists an infinity of k mimic operations.
Proof: Since given the set of tuples T for an operation O there exist an infinity of ways to form T' (see the proof of Theorem 1). From T' we have an infinity of k-mimic operations O' of O.
Theorem 3: If a binary operation O satisfies commutativity, then if xxO=xxO1, O1 does not satisfy commutativity.
Proof: If O1 is a 1-mimic of O, then xyO=xyO1 for all but one pair (a, b). Suppose that for all x and y, if xyO=yxO, and xyO1=yxO1. Suppose that (a, b) consists of the point where O and O1 differ, by say letting abO=c, and letting abO1=d, where d does not equal c. It follows then that abO1=d=baO1 by supposition of commutation for O1. But, this implies that the pair (b, a) consists of a second point where O and O1 differ, which contradicts the supposition of O1 as a 1-mimic of O. Consequently, the theorem follows and if O1 satisfies commutation it at least consists of a 2-mimic.
Conjecture: If On and Ok are mimics of operation O, then On and Ok are mimics of each other.
The author thinks theorem 3 generalizes to o-mimics, where "o" indicates any positive odd number. The author also thinks that converse of the theorem holds in that if a 1-mimic does satisfy commutation, the operation which it mimics will not satisfy commutation also. Do there exist any relationships (or lack thereof) between an associative operation and its mimics? Between an idempotent operation and its mimics?
The author writes informal proofs in the following. The author uses Reverse Polish Notation also.
Suppose we have an infinite set S, and a operation "*". A mimic operation *' of * consists of an operation on S such that for all but a finite number of points a1, ..., an *=a1, ..., an *'. So, for a unary operation F on the natural numbers N, a mimic operation F' satisfies xF=xF' except for a finite set of natural numbers {a1,...,an}. For a binary operation G on N, a mimic of B, B' satisfies xyB=xyB' except for a finite number of pairs of natural numbers {(a, b)1,...,(a, b)n} and so on.
Theorem 1: For any n-ary operation O on an infinite set, there exists an infinity of mimic operations, O'.
Proof: An n-ary operation O can get defined by a set of n 1 + tuples. E. G. the binary operation of addition can get defined by the triples (2, 4, 6), (1, 1, 2) such that for (x, y, z), xy+=z. Now consider the set of such tuples T for O. Vary the n 1 + part of the tuples in T for some finite number of tuples. This forms a set of tuples T' which describes an n-ary operation distinct from O in but a finite number of points, and thus forms a mimic operation O'. Note that since there exist an infinity of tuples belonging to T, there exists an infinity of ways to form T' given T. Thus, given an n-ary operation O, there exists an infinity of mimic operations O'.
Define a k-mimic operation Mk of an operation M as an operation which differs from M by but k points, where both operations operate over an infinite set. In other words, for an operation Mn of arity n with mimic Mkn, a1...anMn=a1...anMkn, except for k tuples {(b1, ..., bn), ..., (l1, ..., ln)} where this equality fails.
Theorem 2: For any n-ary operation O on an infinite set, there exists an infinity of k mimic operations.
Proof: Since given the set of tuples T for an operation O there exist an infinity of ways to form T' (see the proof of Theorem 1). From T' we have an infinity of k-mimic operations O' of O.
Theorem 3: If a binary operation O satisfies commutativity, then if xxO=xxO1, O1 does not satisfy commutativity.
Proof: If O1 is a 1-mimic of O, then xyO=xyO1 for all but one pair (a, b). Suppose that for all x and y, if xyO=yxO, and xyO1=yxO1. Suppose that (a, b) consists of the point where O and O1 differ, by say letting abO=c, and letting abO1=d, where d does not equal c. It follows then that abO1=d=baO1 by supposition of commutation for O1. But, this implies that the pair (b, a) consists of a second point where O and O1 differ, which contradicts the supposition of O1 as a 1-mimic of O. Consequently, the theorem follows and if O1 satisfies commutation it at least consists of a 2-mimic.
Conjecture: If On and Ok are mimics of operation O, then On and Ok are mimics of each other.
The author thinks theorem 3 generalizes to o-mimics, where "o" indicates any positive odd number. The author also thinks that converse of the theorem holds in that if a 1-mimic does satisfy commutation, the operation which it mimics will not satisfy commutation also. Do there exist any relationships (or lack thereof) between an associative operation and its mimics? Between an idempotent operation and its mimics?
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