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By: Bertram G. Katzung MD, PhD
- Professor Emeritus, Department of Cellular & Molecular Pharmacology, University of California, San Francisco
These processes can be thought of as R-tree valued diffusion processes that are reversible with respect to generic 10mg duphaston the distribution of the Brownian continuum random tree duphaston 10mg line. Moving in a slightly different but related direction order duphaston 10mg without prescription, there is a large lit erature on random walks with state-space a given inﬁnite tree: [145 trusted duphaston 10 mg, 105] are excellent bibliographical references. In particular, there is a substantial 8 1 Introduction amount of research on the Martin boundary of such walks beginning with [52, 38, 122]. A general construction of diffusions on graphs using Dirichlet form methods is given in . Diffusions on tree–like objects are studied in [42, 93] using excursion theory ideas, local times of diffusions on graphs are investi gated in [53, 54], and an averaging principle for such processes is considered in . One particular process that has received a substantial amount of at tention is the so-called Walsh’s spider. The spider is a diffusion on the tree consisting of a ﬁnite number of semi–inﬁnite rays emanating from a single vertex – see [142, 26, 139, 25]. A higher dimensional diffusion with a structure somewhat akin to that of the spider, in which regions of higher dimensional spaces are “glued” to gether along lower dimensional boundaries, appears in the work of Sowers  on Hamiltonian systems perturbed by noise – see also . This construction was used in  to build diffusions on the interesting fractals introduced in  to answer a question posed in . In Chapter 7 we describe a particular Markov process with state–space an R-tree that does not have any leaves (in the sense that any path in the tree can be continued indeﬁnitely in both directions). The initial study of this process in  was motivated by Le Gall’s Brownian snake process – see, for example, [97, 98, 99, 100]. One agreeable feature of this process is that it serves as a new and convenient “test bed” on which we can study many of the objects of general Markov process theory such as Doob h-transforms, the classiﬁcation of entrance laws, the identiﬁcation of the Martin boundary and representation of excessive functions, and the existence of non-constant harmonic functions and the triviality of tail σ-ﬁelds. We use Dirichlet form methods in several chapters, so we have provided a brief summary of some of the more salient parts of the theory in Appen dix A. Similarly, we summarize some results on Hausdorff dimension, packing dimension and capacity that we use in various places in Appendix B. The Markov chain tree theorem gives an explicit formula for π, as opposed to the usual implicit description of π as the unique proba bility vector that solves the equation πP π. Let G V, E be the directed graph with vertex set V and directed edges consisting of pairs of vertices i, j such that pij 0. A rooted spanning tree of G is a directed subgraph of G that is a spanning tree as an undirected graph (that is, it is a connected subgraph without any cycles that has V as its vertex set) and is such that each vertex has out-degree 1, except for a distinguished vertex, the root, that has out-degree 0. Write A for the set of all rooted spanning trees of G and Ai for the set of rooted spanning trees that have i as their root. The weight of a rooted spanning tree this the product of its edge weights, which we write as weight T. Let X¯ X¯ be a two-sided stationary Markov chain with the n n Z transition matrix P (so that X¯ has distribution π for all n Z). The solid directed edges are in the tree, whereas dashed directed edges are edges in the underlying graph that are not in the tree. It is clear that f is well-deﬁned almost surely under the distribution of X¯ and so we can deﬁne a stationary, A-valued, Z-indexed stochastic process Y¯ Y¯ by n n Z ¯ n ¯ Yn : f θ X, n Z, where θ : V Z V Z denotes the usual shift operator deﬁned by θ x : x. More speciﬁcally, consider the following forward procedure that produces a spanning tree rooted at j from a spanning tree S rooted at i – see Figure 2. It is easy to see that a rooted spanning tree T A can be constructed from S A by the forward procedure if and only if S can be constructed from T by the following reverse procedure for a suitable vertex k. Let S and T be rooted spanning trees such that T can be obtained from S by the forward procedure, or, equivalently, such that S can be obtained from T by the reverse procedure. Write i and j for the roots of S and T, 12 2 Around the continuum random tree j i k j i k j i k Fig. The dashed line represents a directed path through the tree that may consist of several directed edges. Hence ρ is the stationary distribution cor responding to the irreducible transition matrix Q. We also note in passing that R is the transition matrix of the time-reversal of Y¯. Let Xj j N0 be the natural random walk on the complete graph K with transition matrix P given by P : 1 for i j and X n ij n 1 0 uniformly distributed. The set of rooted spanning trees of the complete graph Kn is just the set of of nn 1 rooted trees with vertices labeled by 1, 2. The most obvious thing to do would be to run the chain X until all n states had appeared and then con struct the tree T from the resulting sample path. The following algorithm, presented independently in [17, 35], improves on this naive approach by, in effect, generating X0 and the pairs Xτν 1, Xτν, ν X0 without generating the rest of the sample path of X. To complete the proof, we need only argue that this construction is equivalent to Algorithm 2. Thus, it will suﬃce to show that the conditional joint distribution of the 1 random variables πλ, i 2. Such a tree has a random number of vertices and if we further required that the random tree had a ﬁxed number n of vertices, then they would suggest simply conditioning the total number of vertices in the Galton-Watson tree to be n. Interestingly, special cases of this mechanism for generating random trees produce trees that are also natural from a combina torial perspective, as we shall soon see. Write T for the family tree of the Galton–Watson branching process with offspring distribution pi i N0 started with 1 individual in gen eration 0. For n 1 denote by Tn a random tree that arises by conditioning on the total population size T being n (we suppose that the event T n has positive probability). More precisely, we think of the trees T and Tn as rooted ordered trees: a rooted tree is ordered if we distinguish the offspring of a vertex according with a “birth order”.
Though licensure by specialty was considered briefly in the late 1920s generic duphaston 10mg free shipping, it was rejected in favor of exclusive control over specialization by self regulatory specialty boards buy generic duphaston 10mg. The system of private specialty boards that exercised this control was firmly established by the time the Advisory Board for Medical Specialties was formed in 1933 generic 10 mg duphaston with visa. The Struggle Against External Forces While mainstream American medicine has engaged in consolidating its power over contending schools of thought within the profession order 10 mg duphaston free shipping, it has also sought to block efforts by external forces to influence the standard of care. One set of forces consists of public and private health insurers who, beginning in the second half of the twentieth century, have attempted to 61 manipulate the standard of care in order to control their costs. This article focuses on the second major external force, the force of law, specifically, the legal standard of care to which defendants are held in medical 62 malpractice cases. Suits for medical malpractice were extremely rare in the new Republic: Even at a theoretical level, the medicolegal concept of malpractice was so arcane and so unimportant in the United States that American writers on medical jurisprudence, those most likely to be interested in the subject as an aspect of legal medicine, did not bother to mention it through the first 4 decades of the 19th 63 century. In an effort to curb health care spending, for example, both government and private health insurers have promulgated guidelines on what care is appropriate in particular circumstances. Mello, Of Swords and Shields: the Role of Clinical Practice Guidelines in Medical Malpractice Litigation, 149 U. Medical professionals have long confronted liability for providing substandard care. A 1374 case in which a surgeon was sued for improperly treating a patient’s hand wound was dismissed for using the wrong writ. Mohr notes that “[t]he general concept of professional malpractice was well embedded in English legal theory by the beginning of the 18th century,” and observes that Blackstone’s Commentaries on the Laws of England, which were widely read by the American colonists, “included under mala praxis (from which we derive the modern word malpractice), ‘Injuries. One was the elimination of licensing laws during the Jacksonian and Thompsonian period. As De Ville explains, “[l]icensure, in the Jacksonian mind, represented regulation from the top down and appeared to benefit the physician by creating an unfair monopoly and relying on artificial measures of merit. De Ville observed: Many Americans decisively changed their views on divine providence in the first half of the nineteenth century. This transformation allowed individuals to seek earthly causes for their misfortunes, assign blame, and demand compensation. At the same time, a variety of forces combined to make Americans dramatically more concerned with physical well-being and significantly more confident that they could do something about 72 it. Spiegel & Florence Kavaler, America’s First Medical Malpractice Crisis, 1835-1865, 22 J. The authors identify western New York State as the place where the proliferation of malpractice suits originated, id. The most common type of case after 1835 involved errors alleged to have occurred in orthopedic care. Mohr points out that “[t]he population rose about 85% during that period, which suggests that the rate of malpractice suits jumped abruptly by a factor of roughly 10-fold during the middle 2 decades of the 19th century. The medical profession stimulated malpractice suits in other ways than by relying on unsafe and ineffective treatments. Regulars seized upon malpractice liability as a way to curb the practice of irregulars. Mohr adds: [O]ver and over during the 1840s and 1850s, the nation’s best educated and most professionally minded physicians observed with a sort of defensive incredulity and disbelieving horror that many, if not most, of the burgeoning numbers of malpractice suits were being lodged not against charlatans and amateur hacks, but against others like themselves, the best-educated and most 74 successful physicians. Moreover, growing competition led practitioners to encourage patients to bring malpractice suits against practitioners who followed the same 75 doctrinal approach. Advances in medical science created unrealistic 76 expectations among patients, which practitioners fueled with self 77 promotion. Ironically, the regulars’ success in seizing control of the perfectionism, both of which were associated with the revivals of the 1820s and 1830s. As a result, even fervently religious Americans were less willing than earlier generations to accept physical afflictions as acts of divine providence. This same period also produced both the nation’s first widespread efforts to improve physical fitness and its first great food reforms. Americans were coming to the realization, or at least the hope, that bodily well-being could be controlled and, perhaps, even improved upon. As medical men of all types became more plentiful in the 1830s and 1840s, intraprofessional competition generated conflict, and many medical men incited suits against fellow practitioners. To improve their own status, individual physicians willingly denigrated the therapeutic practices of their competitors. Spiegel & Kavaler, supra note 65, at 301; see Mohr, supra note 27, at 1733 (“[T]here can be no malpractice without established practice; physicians cannot be convicted of deviating from accepted standards if no accepted standards exist. Amateurs and alternative healers had always delivered what patients came to them for, be it hot baths or herbal teas, and could not be sued for undesirable results. They claimed no fixed recipes and made a virtue of treating each case individually. Educated physicians, on the other hand, could have texts and advanced manuals (in steady production by 1840) used against them in court as codified norms from which they could be accused of diverging. As the nineteenth century progressed, malpractice suits were spurred on by additional developments. The number of lawyers increased as well as the number of doctors, and the demographics of the legal profession began to change. At the beginning of the century, explains De Ville, lawyers and doctors tended to come from the same social class, and were further allied by both being targeted by the Jacksonians.
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Plant Description: Papaya Leaf is an herbaceous tree with a stem of spongy cheap duphaston 10mg with visa, soft wood that is hollow in the center and bears melon-like fruit generic duphaston 10 mg online. It is an interesting tree discount duphaston 10 mg without prescription, in that the male and female parts exist in different trees purchase duphaston 10mg on line, and trees may grow to a height of twenty to thirty feet. This fussy plant needs a lot of water but must have good drainage, and it bears most fruit in light, porous, slightly acidic soils that are rich in organic matter. Said to be a native of the Caribbean and Central America, the Papaya is the true papaw that now grows abundantly throughout tropical America, Hawaii and many other tropical climates throughout the world. Medical Uses: Although grown to some extent in south Florida, the true papaw is not related to the North American papaw. The fruit is usually pear sized and has a central cavity filled with edible, pea-sized seed, which are said to have a similar flavor as capers. Papaya Leaves are cooked and considered a green vegetable and are a rich source of gummy, milky, white latex that contains the powerful enzyme, papain. This protein dissolving substance is an excellent remedy for stomach and digestive disorders. Papain is so powerful that Papaya Leaves have been wrapped around meats to break down the fibers and tenderize them. It is included in commercial preparations as a meat tenderizer and often used for that purpose in restaurants, and it also used commercially in chewing gums and as a stabilizing agent that is used to clarify beer. Treatments: Papaya Leaf is an excellent treatment for digestive disorders and extremely useful for any disturbances of the gastrointestinal tract. Papain, the powerful enzyme in Papaya, helps to dissolve and digest protein, thus easing stomach ailments and indigestion. Papain also breaks down wheat gluten, which may be helpful for those suffering from Celiac disease; and those who have difficulty digesting starchy foods, such as breads, cereals and potatoes, might find great relief in including Papaya in their diets. Another papayan enzyme, chymopapain, has been used in the treatment for slipped spinal disc and pinched nerves. Since many stomach problems are the direct result of indigestion, use of Papaya appears to help prevent many ailments. It stimulates digestive acids and the production of bile, which may also lead to a healthier liver and pancreas. Papaya is said to stimulate the bowels in times of constipation and is believed to be useful in treating inflammatory bowel disorders. Pregnant women should avoid Papaya, as it can be a uterine stimulant, (papain apparently dissolves a protein(s) responsible for adhering the newly fertilized egg to the wall of the uterus). Inhaling papaya powder (high in the enzymes, papain and chymopapain, can induce allergies. You will get a high dose of vitamins C and A, potassium (important for lowering blood pressure), calcium (good for osteoporosis) and folic acid (which may help prevent cardiovascular disease). Plant Description: Parsley Leafs is a biennial or perennial herb that originated in the eastern Mediterranean region as a wild plant, but is now found in cultivation everywhere. History: For more than two thousand years, it has been highly regarded as a medicinal herb to treat gastrointestinal disorders, and ancient Greeks valued Parsley for its soothing and diuretic effect on those with kidney and bladder ailments. The Greeks also adorned victors at the Isthmian games with wreaths of Parsley Leaves. What is now an indispensable and nutritious addition to our dinner table was never brought to the table of old, being held sacred to the dead, and it continued to be associated with death through the ages. Medical Uses: Nonetheless, it continued to be used in herbal medicine as an important digestive and circulatory aid. Saint Hildegard of Bingen, a Medieval German herbalist, prescribed Parsley wine to improve blood circulation and help heart conditions; and when Charlemagne had it planted in his garden in the Middle Ages, its cultivation was ensured, although its association with the underworld and the Devil continued for some time. Parsley supplies important minerals, beta carotene, essential oils, quercetin, rutin, flavonoids, chlorophyll and healthy doses of B-vitamins and vitamins A, C, E and K. Treatments: Parsley Leaves have been used to regulate blood sugar and are thought to be effective in cases of low blood sugar, if there is adrenal malfunction. Parsley Leaf stimulates and strengthens the activity of the digestive system, easing flatulence and indigestion. Its chlorophyll content is essential to healthy digestion, and it increases circulation to the digestive tract. The English herbalist, Culpepper, wrote that Parsley was "comfortable to the stomach and good for wind. The herbalist, Culpepper, also commented that Parsley "removed obstructions from the liver and spleen," and it is said today that Parsley helps to expel gallstones and kidney stones. Parsley is said to improve urination when it is painful or incomplete and accelerates the excretion of toxins. As a diuretic, Parsley relieves the bloating that some women experience before their periods. The leaves contain more vitamin C than oranges by weight and also provide a good source of iron (important for the proper formation of red blood cells), potassium (good for lowering blood pressure), calcium and manganese (helpful for osteoporosis) and folic acid (which may help prevent cardiovascular disease). Parsley Leaf is a superior breath freshener because of its high chlorophyll content. When applied externally, the ancients believed that Parsley Leaf was an effective treatment for skin problems, insect bites and stings, and would dispel skin tumors suspected to be cancerous. Precautions: Parsley is not recommended for pregnant women in large amounts, as it may cause uterine contractions, but used after delivery, it is said to tone the uterus. Dosages: For Botanical Powder: Take two (2) capsules, two (2) to three (3) times each day with water at mealtimes. For Botanical Extract: Take two (2) capsules, two (2) times each day with water at mealtimes. Do not forget to take Parsley for a healthy dose of vitamins, minerals and nutrients. Plant Description: Parsley Root is a biennial or perennial herb that originated as a wild plant in the eastern Mediterranean region but is found in cultivation everywhere.
Younger skin has Keloid scars can be distinguished from hypertrophic more tensile strength order duphaston 10mg without a prescription, which can lead to discount duphaston 10 mg widening of scars by spreading beyond the original wound 10mg duphaston visa. They include triamcinolone acetonide (Kenalog) and triam occur without race or age tendency and occur most fre cinolone diacetate (Aristocort) generic duphaston 10 mg on line. Wound color typically improves blast proliferation, reduce blood vessel formation, and to match the uninjured skin with time. By decreasing the production of collagen, a quently obliterating the rete pegs in the papillary der smaller scar is created. While collagen in normal dermis is 40 mg/mL are injected at 3 to 6-week intervals. Typi arranged in discrete fascicles separated by considerable cally, multiple injections are required to obtain the interstitial space, collagen nodules in keloids and in desired benefit. Complications of steroid injection hypertrophic scars appear avascular and unidirectional include atrophy of the subcutaneous layer, granuloma and are aligned in a highly stressed configuration. Col formation, pigmentary changes, and development of lagen synthesis is greater in keloids than hypertrophic telangiectasias. Collagen synthesis is three times greater in keloids New intralesional treatments have included the use of than hypertrophic scars and 20 times greater in normal antimitotic agents such as bleomycin and 5-fluorouracil scars. Small doses of these drugs may be injected into scars can be differentiated from keloids using light hypertrophic scar tissue with good results. Injections of bleomycin into a keloid demonstrate the randomly organized sheets of collagen using a multipuncture technique have also shown some with no obvious relationship to the skin surface in kel promise in scar flattening and preventing recurrence. Soft tissue fillers—Atrophic and depressed scars Skin is anisotropic and nonlinear and has time-depen may also be treated with injectable fillers in an attempt to provide bulk in areas of tissue deficiency. The term anisotropic indicates that monly used agents include bovine collagen (Zyderm, the mechanical properties of skin vary with direction. Silicone sheeting, hydration, and compression— Complications Silicone has been used with relative success in the man Complications of scar revision vary according to the agement of hypertrophic scars, although its mechanism method used. Viral tially hypothesized to work through pressure over the reactivation of the herpes zoster virus is a potential com scar tissue, the efficacy of silicone has been demon plication after dermabrasion or laser resurfacing. It appears that resurfacing can also cause postinflammatory hyperpig hydration, or rather the ability of silicone to prevent mentation, which may last several months. Patient expectations—As with any cosmetic proce alternative to silicone sheeting, silicone gel can be dure, the patient’s motivations and expectations for applied to the scar. Both silicone gel and silicone sheet seeking corrective surgery should be carefully consid ing have shown positive results in the reduction of scar ered. A patient Continuous pressure at 80 mm Hg provided by should understand that scar revision is a process to tight-fitting dressings has been shown to prevent and modify scar formation. The potential mechanisms of improve the appearance of the scar by adjusting, reposi tioning, or narrowing the scar and that complete elimi action are local tissue hypoxia and reduction of the intralesional population of mast cells, which may affect nation of the scar is impossible at this point. However, the physician should be sensitive to the fact that the fibroblast growth. If the revision does not meet the patient’s length laser can be effective in reducing scar erythema expectations, the patient may suffer additional trauma. Several treatments are Occasionally, psychological counseling should be rec usually required using a low to moderate fluence (5. Hypertrophic scars may also shrink with this treatment as a result of a reduction 2. Timing of scar revision—Scars in the inflamma tory phase are prone to hypertrophy. Although collagen mented scars may benefit from superficial abrasion of remodeling continues for 1–3 years, most significant the skin, which blends the scar with its surrounding tis changes occur in the first 4–6 months, and an average sue by changing the texture, color, and depth of the of 6 months’ delay before revision is reasonable. The technique of resurfacing depends on the theless, in clinical situations, where skin edges are nature of the deformity. The goal of this technique is to grossly misaligned or the scar lies in an unfavorable even out any uneven surfaces. The depth of the derm direction, scar revision may prove beneficial as early as abrasion depends on the depth of the scar. Scar analysis—Before embarking on a revision, the mis; otherwise, greater scarring or hypopigmentation primary scar, and its desired location when revised, will result. Laser resurfacing—Laser resurfacing has replaced according to their location, etiology, size, shape, con mechanical dermabrasion in many practices. Cosmetically favorable scars are similar tage of laser resurfacing over mechanical dermabrasion is in color to the surrounding tissue. Scars that are advantage is that there is no aerosolization of skin and located in the periphery of the face, at a transition line blood, thereby lowering the risk of viral transmission. The lack of one or more of advantageous in that it produces collagen contracture of these qualities results in an unsightly scar. However, the postoperative period of laser scars are wide, raised, or depressed, or are often hyper resurfacing is marked by prolonged erythema. The most pigmented or hypopigmented compared with the adja common lasers in use for resurfacing are the high-energy cent skin. Camouflage—Many patients who seek scar revisions may not be able to camouflage the scar or have minimal Appropriate scar management begins at the time of knowledge of available camouflage techniques. Good surgical technique is essential for normal hair, and accessories can sometimes offer excellent coverage wound healing. Newer makeup materials and techniques allow too tightly, and cauterizing too excessively may result in for better and more complete coverage of unsightly defects.