Probabilistic Horn Constraint for Natural Language Processing and More

Introduction Natural language processing (NLP) has employed statistical tools such as Hidden Markov Model (HMM) [4], Stochastic Context-Free Grammar (SCFG), Stochastic Tree-Adjoining Grammar (STAG) [2], Probabilistic Generalized LR Parser (PGLRP) [3], etc. Below we propose a general method which subsumes all of them. In this method, constraint is represented as a Horn logic program whose semantics is a probability distribution over candidates for solutions. Symbolic computation is to transform this program so as to figure out high-probability solutions while discarding wrong hypotheses. Structure sharing in the program guarantees efficient computation for both symbolic and probabilistic information. 2 Probabilistic Constraint A constraint is represented by a Horn program such as in Figure 1. Names beginning with capital (a) / s(A0,z) A0=a(A1) A1=b(A2) A2=a(z). (b) s(B,C) /<F

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What does it do? Calcium is the most abundant mineral in the human body. Of the two to three pounds of calcium contained in the average body, 99% is located in the bones and teeth. Calcium is needed to form bones and teeth and is also required for blood clotting, transmission of signals in nerve cells, and muscle contraction. The importance of calcium for preventing osteoporosis is probably its most well-known role. Although calcium plays at least some minor role in lowering blood pressure, the mechanisms involved appear complex and somewhat unclear.1 The level of calcium in the blood is tightly regulated by parathyroid hormone (PTH), and low intake of calcium causes elevations in PTH, which in turn have been implicated in the development of hypertension.2 High calcium intake has also been associated with a reduced risk of cardiovascular disease in postmenopausal women.3 By reducing absorption of oxalate,4 a substance found in many foods, calcium may be able to indirectly reduce the risk of kidney stones.5 However, people with a history of kidney stones must talk with a doctor before supplementing with calcium because such supplementation might actually increase the risk of forming stones for the small number of people who absorb too much calcium. Calcium also appears to partially bind some fats and cholesterol in the gastrointestinal tract. Perhaps as a result, some older research suggests that calcium supplementation may help lower cholesterol levels.6 Animal studies have established a role of calcium in the development of female egg cells (oocytes).7 8 Although the precise role of calcium is unclear, some researchers speculate that future studies may identify important uses for calcium in conditions of the human ovary, such as polycystic ovary syndrome (PCOS).9 Through a variety of mechanisms, calcium may have anticancer actions within the colon. Most preliminary studies have shown high calcium diets are associated with reduced colon cancer risk.10 Most11 12 13 but not all14 preliminary studies have found taking calcium supplements to also be associated with a reduced risk of colon cancer or precancerous conditions in the colon. One preliminary study reported that high dietary, but not supplemental, calcium intake was associated with a decreased risk of precancerous changes in the colon.15 In double-blind studies, calcium supplementation has significantly protected against precancerous changes in the colon in some 16 17 but not all studies.18 19 Where is it found? Most dietary calcium comes from dairy products. The myth that calcium from dairy products is not absorbed is not supported by scientific research.20 21 Other good sources include sardines, canned salmon, green leafy vegetables, and tofu. Choosing a form of calcium supplement can be confusing. While fewer pills of the calcium carbonate form are needed, some people may not absorb this form of calcium as well as some other forms. Most,22 23 but not all,24 studies suggest that calcium citrate is better absorbed than calcium carbonate. Virtually all comparative studies find that calcium citrate/malate (CCM) is absorbed somewhat better than calcium carbonate. CCM is increasingly the form of calcium recommended by doctors. Microcrystalline hydroxyapatite (MCHC), a variation on the bone meal form of calcium, has been shown to improve bone mass,25 but the absorption of MCHC appears to be poor.26 27 Only preliminary research exists regarding the amino acid chelates of calcium, and conclusions cannot be drawn at this time. Calcium has been used in connection with the following conditions (refer to the individual health concern for complete information): Rating Health Concerns Gestational hypertension Lactose intolerance (for preventing deficiency if dairy products are avoided only) Osteoporosis Preeclampsia (for deficiency) Premenstrual syndrome Rickets Celiac disease (for deficiency only) High blood pressure High cholesterol High triglycerides Amenorrhea (calcium for preventing bone loss) Colon cancer (reduces risk) Depression Dysmenorrhea (painful menstruation) Gingivitis (periodontal disease) Insulin resistance syndrome (Syndrome X) Kidney stones Migraine headaches Multiple sclerosis Pregnancy and postpartum support Warning: Calcium supplements should be avoided by prostate cancer patients. Reliable and relatively consistent scientific data showing a substantial health benefit. Contradictory, insufficient, or preliminary studies suggesting a health benefit or minimal health benefit. An herb is primarily supported by traditional use, or the herb or supplement has little scientific support and/or minimal health benefit. Who is likely to be deficient? Severe deficiency of either calcium or vitamin D leads to a condition called rickets in children and osteomalacia in adults. Since vitamin D is required for calcium absorption, people with conditions causing vitamin D deficiency (e.g., pancreatic insufficiency) may develop a deficiency of calcium as well. Vegans (pure vegetarians), people with dark skin, those who live in northern climates, and people who stay indoors almost all the time are more likely to be vitamin D deficient, than are other people. Vegans often eat less calcium and vitamin D than do other people. Most people eat well below the recommended amount of calcium. This lack of dietary calcium is thought to contribute to the risk of osteoporosis, particularly in white and Asian women. How much is usually taken? The National Academy of Sciences has established guidelines for calcium that are 25\u9650% higher than previous recommendations. For ages 19 to 50, calcium intake is recommended to be 1,000 mg dail