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A t rans ition state state 0 c an only occur if there is a new X (t) is equal which case (X(t + 8) = qOj 1 prostate cancer 3 months purchase genuine confido on-line. We approach this problem by studying the steady-state probabilities of the corresponding discrete-time chain Zn prostate oncology yakima cheap confido online mastercard. Since Zn = it is clear that the limit of P(Zn = j I Zo = i) prostate 90cc buy discount confido, if it exists prostate 24 reviews purchase confido without a prescription, is the same as the limit of P (X(t) = j I X(O) = i). It therefore suffices to consider the steady-state probabilities associated with Zn. Reasoning as in the discrete-time case, we see that for the steady-state probabilities to be independent of the initial state, we need the chain Zn to have a single recurrent class, which we will henceforth assume. Steady-State Convergence Theorem Consider a continuous-time Markov chain with a single recurrent class. Then, the states j are associated with steady-state probabilities j that have the followi ng properties. The steady-state probabilities 7I"j are to be distinguished from the steady state probabilities 1fj of the embedded Markov chain Xn. Indeed, the balance and normalization equations for the embedded Markov chain are Sec. The reason is that the process tends to spend more time during a typical visit to state 1 than during a typical visit to state 2. The main exception arises in the special case where the transition rates Vi are the same for all i; see the end-of-chapter problems. Birth-Death Processes As in the discrete-time case, the states in a birth-death process are linearly arranged and transitions can only occur to a neighboring state, or else leave the state unchanged; formally, we have qij = 0, for Ii - j I > 1. The local balance equations have the same structure as in the discrete-time case, leading to closed-form formulas for the steady-state probabilities. Coming up with a suitable Markov chain model of a given physical situ ation is to some extent an art. In general, we need to introduce a rich enough set of states so that the current state summarizes whatever information from the history of the process is relevant to its future evolution. Subject to this requirement, we usually aim at a model that does not involve more states than necessary. We have seen that we can calculate the probability that the process follows a particular path by multiplying the transition probabilities along the path. The probability of a more general event can be obtained by adding the probabilities of the various paths that lead to the occurrence of the event. In some cases, we can exploit the Markov property to avoid listing each and every path that corresponds to a particular event. A prominent example is the recursive calculation of the n-step transition probabilities, using the Chapman-Kolmogorov equations. To address such questions, we classified the states of a Markov chain as tran sient and recurrent. We discussed how the recurrent states can be divided into disjoint recurrent classes, so that each state in a recurrent class is ac cessible from every other state in the same class. The central result of Markov chain theory is that if a chain consists of a single aperiodic recur rent class, plus possibly some transient states, the probability Tij (n) that the state is equal to some j converges, as time goes to infinity, to a steady state probability 7rj, which does not depend on the initial state i. In other words, the identity of the initial state has no bearing on the statistics of Xn when n is very large. The steady-state probabilities can be found by solving a system of linear equations, consisting of the balance equations and the normalization equation Ej 7rj = 1. We dis cussed the absorption probabilities (the probability that the state eventu ally enters a given recurrent class, given that it starts at a given transient state), and the mean first passage times (the expected time until a particu lar recurrent state is entered, assuming that the chain has a single recurrent Sec. In both cases, we showed that the quantities of interest can be found by considering the unique solution to a system of linear equations. In such models, given the current state, the next state is determined by the same mechanism as in discrete-time Markov chains. However, the time until the next transition is an exponentially distributed random variable, whose parameter depends only the current state. Continuous-time Markov chains are in many ways similar to their discrete-time counterparts. They have the same Markov property (the future is independent from the past, given the present). In fact, we can visualize a continuous-time Markov chain in terms of a related discrete-time Markov chain obtained by a fine discretization of the time axis.

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Strict egalitarians (such as Temkin androgen hormone effects 60caps confido otc, 1993) make two moves to attempt to ward off the levelling down objection androgen hormone uterine buy confido 60caps lowest price. First prostate cancer xenograft purchase confido 60 caps free shipping, they argue that equality is only one of the values which we should deploy when deciding how goods should be distributed all things considered mens health lunch ideas order confido without a prescription. So while society A may be better from the perspective of equality, there may nonetheless be 22 23 24 Wolff and de-Shalit (2007: 89­107) propose a practical strategy for solving indexing problems in real world solutions, which looks like a promising avenue for further research. In this section I shall assume that health is a currency of justice in the relevant sense. I do not take it that this has been established by the argument in the previous section. I make this assumption simply because, unless health is a basic currency of justice, there will be little further to be said about how we should go about distributing health justly. For the purposes of simplicity I am making the rather unrealistic assumption that there are no individual health variations within the groups. Second, they argue that the levelling down objection presupposes a person-affecting requirement, namely that one situation cannot be better than another unless there is a person for whom it is better; however this requirement is false. To be told that strict egalitarianism is but one principle that needs to be weighed against as yet to be specified others, is not perhaps as helpful as one would have liked. So even if the person-affecting requirement were false, it would not follow that levelling down in health is acceptable. If a good which is a currency of justice is not only good for the person who has it, but is also impersonally good, then there would be reasons to object to levelling down in respect of that good that are separate from the person affecting requirement. Hurley (2007: 332­3) argues that health is just such a good: Health is a distinctive type of flourishing, with a specific natural character and basis. It is not just good for people to be healthy rather than unhealthy; it is also good in itself for there to be healthy people rather than unhealthy people. And so the objection to levelling down seems to stand, at least when we are distributing health. Prioritarianism Thinking about the problem of levelling down has led many to the view that the core commitments of egalitarian justice in health should not be strict egalitarianism, but rather to what has come to be known as prioritarianism, namely that we should give priority to improving the condition of those who are worst off (Parfit, 1997). Prioritarianism is very appealing as an account of what we owe to one another when it comes to health. However, while it may be true in most obvious cases that we should give priority to alleviating the condition of the worst off, giving an absolute priority to improving the condition of the worst off can have counterintuitive implications. For it may well be the case that it is much less cost effective to attempt to improve the condition of those who are the very worst off, than to attempt to improve the conditions of some other groups who are slightly better off. But where the levelling down objection concerns cases where no one gains and there is a significant loss to some, this objection concerns cases where there is a slight benefit to some, but a much more significant loss to others. Chapter 12: Health inequities 227 Prioritarians can address this challenge from efficiency in one of two ways: either they can deny that considerations of efficiency have any role to play here, and claim that even if much more good could be done to those who are less badly off, we should still focus our efforts on those who are worst off. Or they can shift to a position which has come to be known as weighted prioritarianism, which claims that priority to the worst off is to be given a high (but not absolute) weighting, so that in certain circumstances priority to the worst off can legitimately be overridden by the demands of efficiency. Sufficientarianism Sufficientarians (Frankfurt, 1987; Crisp, 2003a, 2003b) argue that priority is only to be given to those who are worse off than a certain threshold, and that if everyone is above this threshold, benefits to those who are comparatively better off count equally to those who are comparatively worse off. The policy implications of a sufficientarian approach to health would clearly depend on what we took the relevant threshold to be for health achievement. If the threshold was set high (for instance to 90 years of healthy life), then a sufficientarian approach would not be distinguishable in practice from a prioritarian approach. However, if the threshold was set low (for instance, to 50 years of moderately healthy life), then socioeconomic conditions which caused someone to die at 55 or 60 would not deprive someone of a share of healthy life to which they were entitled by justice. Crisp (2003a, 2003b) argues that we should set the level of sufficiency through the exercise of compassion from the perspective of an impartial observer. However, this seems not to be a very complete answer, given that what we reasonably feel compassion for is closely related to what we feel is to be expected. It is more plausible to think that there could be an objective standard for when a life of a given length is sufficiently healthy. But even here we would face the very difficult task of deciding what that level should be, a problem the prioritarian (who only needs to determine who is worse off) does not face. Conclusion Social scientists working on health inequalities have often thought that it is simple to identify health inequities.

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Understanding the extent to which movements in income come as a surprise is important because anticipated income increases or decreases have different implications for household finances and well-being than similarly large but surprising changes in income prostate cancer 51 confido 60 caps free shipping. Relevant examples of predictable income movement include changes in household earnings on account of seasonal work-say prostate 80cc discount generic confido canada, among construction workers or workers in temporary tourist jobs prostate cancer 02 psa with lupron cheapest generic confido uk. These kinds of changes are different from those associated with androgen hormone symptoms buy confido 60caps on line, for example, an unanticipated decline in hours or sales, or even a layoff, and we would expect households to react to such changes differently. Workers can also often anticipate, at least with some advance warning, a boost to earnings from a job promotion, or an increase in pay associated with years on the job. Reductions in income associated with a move to part-time work can sometimes be anticipated as well. The same is true for movements in individual or household earnings associated with changes in family structure, including marital status or number of children living at home. Walking the Tightrope 91 It is challenging to determine from even the best available data the extent to which households anticipate the changes in income that they encounter. Statistical models, augmented by economic theory, can identify changes in income that households ought to have been able to predict, or that they act as if they did predict. This makes sense in part because the expectations or behavior of households might reasonably differ from those derived from a particular, even very flexible econometric or theoretical model. Decompositions of income volatility, as in Larrimore, Mortenson, and Splinter (2016), which quantify the extent to which household income movements are associated with easily anticipated events like marriage or the birth of a child, suggest that substantial fractions of annual income volatility are predictable, but a comprehensive and robust quantification remains elusive. Recent Facts about Liquid Asset Holdings Even if substantial fractions of the changes in income were predictable, we would still expect households to maintain substantial liquid assets to buffer against unpredictable changes or simply in anticipation of predictable declines in income. For a large fraction of households, especially middle-income ones, this is not the case. A recent study using de-identified data from the users of a financial aggregation app, examines the levels and high-frequency variation in liquid asset holdings. That paper examines how liquid asset holdings change over the days between paychecks (the pay cycle). Figure 3, taken from that paper, shows median liquid assets over a two-week pay cycle, by terciles of the distribution of liquid assets. There is at least a one-day lag built into the data because the aggregator application collects balance information during the day, and will reflect a paycheck posted only on the previous day. Spending done just after the receipt of paycheck will therefore lead daily balances to understate gross asset balances right after the receipt of the paycheck. Without tapping into credit, or illiquid forms of savings, or any social or government support, this group could go more than a month without income and still maintain their usual levels of spending. Even on the day before their paycheck arrives, this part of the population has a substantial buffer in their liquid checking and savings accounts. For the bottom two-thirds of the liquid assets distribution, however, the financial situation looks much less secure. The money in their checking and savings accounts are not adequate for maintaining their typical levels of spending, even for a single pay period. The median number of days of average expenditure maintained in liquid assets is nearly eight for the middle tercile and three for the lowest tercile. Liquid assets are especially low the day just before a paycheck arrives, when the bottom third has a median balance of zero in their checking and savings accounts, and middle third has only four days. Despite, or perhaps because of, substantial income variation, this large part of the population lives, in effect, from paycheck to paycheck. The findings about income volatility and liquidity described above are not easily reconciled with standard frameworks of household finance. Insight can be gathered from studying how household finances respond to large and unambiguously unexpected shocks. The rest had to work for at least part of the shutdown, and so we would expect their work-related expenses to be little changed. While they did not know how long the shutdown would last, federal employees should have expected their missing earnings to be recouped as soon as the shutdown ended.

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As a 1991 report put it prostate cancer active surveillance purchase confido 60 caps, "The principle of selective centralization is a corollary theme [along with the principle of decentralization] which has also guided the evolution of the Office of the President mens health magazine cover 60 caps confido visa. However organized prostate cancer blogs buy genuine confido on line, the Office of the President must have the standing and resources to represent the interests of the University of California as a whole prostate cancer xenograft order confido overnight. The institutional assumption has long been that these interests are best served by the one-university principle, for reasons that date back to Sproul and that have been explored here. California gains from the geographic distribution of high-quality university campuses, each with its own character but the same mission, throughout the state. The University itself is stronger as a unified system of campuses than as ten separate institutions vying for public support and government funds. New campuses find room for realizing their aspirations and a legacy of academic quality that acts as a magnet for talented faculty and students. It unleashes fierce competition for resources and the spirit of suspicion, distrust, and jealousy Sproul warned about long ago. Although his functional university was not the answer, his analysis of the problem remains relevant. Multicampus institutions must deal regularly with external threats and pressures that threaten their goals, their institutional integrity, and their future. Within the system, campuses compete with each other for students, faculty, facilities, money, and prestige. The one-university idea has been a way of moderating competition and encouraging cooperation. Hard times offer campuses the opportunity to argue for greater independence from the system and less oversight. To date, the strongest statements of support for the one-university principle have come from the University-wide Academic Senate. The issue is not simply decentralization-the case for its utility was made long ago-but the future of the oneuniversity model. March, a well-known scholar of organization theory, has written about the growing influence of markets on thinking about institutions, including universities, in the past twenty years. The fall of the Soviet Union in 1991, March says, seemed the definitive validation of market systems and private sector strategies. Business schools, rather than political science or sociology departments, have become the locus of much of the research on organizations in recent years. And, it should be added, the conviction that research universities have a natural role in the marketplace. They are likely to bring pressures to take decentralization far beyond anything envisioned by the one-university idea and make short work of the notion that all campuses are "inherently equal. The one-university idea has been a brilliant strategy for presenting a united front in an uncertain political world, a force for internal coherence and cohesion, an act of collective imagination that created a great university system. The Chairman of the Board, with the consultation of the President, shall appoint a task force representative of the business community, students, the University, other segments of education, and organizations currently engaged in academic "outreach. The final report of this task force shall be presented to the Board of Regents within six months after its creation. Effective January 1, 1997, the University of California shall not use race, religion, sex, color, ethnicity, or national origin as criteria for admission to the University or to any program of study. The President shall confer with the Academic Senate of the University of California to develop supplemental criteria for consideration by the Board of Regents which shall be consistent with Section 2. In developing such criteria, which shall provide reasonable assurances that the applicant will successfully complete his or her course of study, consideration shall be given to individuals who, despite having suffered disadvantage economically or in terms of their social environment (such as an abusive or otherwise dysfunctional home or a neighborhood of unwholesome or antisocial influences), have nonetheless demonstrated sufficient character and determination in overcoming obstacles to warrant confidence that the applicant can pursue a course of study to successful completion, provided that any student admitted under this section must be academically eligible for admission. Effective January 1, 1997, not less than fifty (50) percent and not more than seventy-five (75) percent of any entering class on any campus shall be admitted solely on the basis of academic achievement. Nothing in Section 2 shall prohibit any action which is strictly necessary to establish or maintain eligibility for any federal or state program, where ineligibility would result in a loss of federal or state funds to the University. Nothing in Section 2 shall prohibit the University from taking appropriate action to remedy specific, documented cases of discrimination by the University, provided that such actions are expressly and specifically approved by the Board of Regents or taken pursuant to a final order of a court or administrative agency of competent jurisdiction.

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