5,755 research outputs found

    No double trouble: How to reopen the economy.

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    This policy introduces a measure of choice, consonant with our culture. Those younger than 65 can make their own personal tradeoffs between heath and livelihood, while older people, knowing that the virus will be spreading more quickly through the population will be even more cautious, thus preventing their early deaths. We return decisions to people while ensuring that the sum total of decisions does not overwhelm our hospitals. One felicitous result of this policy is that the virus will spread more quickly through the healthier population. This means that when the elderly re-engage in social life they will encounter fewer rather than more infected people reducing the likelihood that they will become sick and die themselves. Ironically, the best way to protect seniors is to let the virus spread in a controlled fashion among those who are not

    Functorial CW-approximation

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    The usual construction of a CW-approximation is functorial up to homotopy, but it is not functorial. In this note, we construct a functorial CW-approximation. Our construction takes inclusions of subspaces into inclusions of subcomplexes, and commutes with intersections of subspaces of a fixed space.Comment: 10 page

    Pandemic lockdown must fail: Save lives without crippling the economy

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    In the following working paper, I want to make a plea for what I am calling a “reverse quarantine”—quarantining people who are over 65 (who number 52 million), before they get sick. We need to complement this policy with federally funded and locally organized efforts to support seniors in place, drawing on the wellsprings of American pragmatism, the capacity to respond in emergencies, American volunteerism, and neighbor-to-neighbor assistance. We can’t turn quarantine into imprisonment. We must work as hard as we can to create a psychological sense of community at a moment when, paradoxically, social distancing is driving us apart. This may be utopian, but in the presence of disaster, hope can be motivating. Why do this? If the elderly stay in place this will both reduce deaths, as seniors are the most vulnerable, and reduce the number of people who can transmit the infection. We reduce the total burden on the health system. With the burden eased, we can let the virus spread more quickly, knowing that we have the hospital beds and equipment to help them. This would shorten the economic downturn leading to fewer business bankruptcies. After all, within the year, everyone who can be infected will be. The challenge that bedevils and threatens us, should we find no resolution, is to match pacing with the requisite supply of beds. In this note I provide the data and its analysis to back up this argument, to the best of my ability. I hope the latter was up to the task. This note is organized into six sections. In the first section, I introduce the HS and reproduce within the limits of my Excel modeling tools, their projection. In the second, I argue that social distancing will in all likelihood fail. We will have few of its benefits and most of its costs. In the third, I draw on a long theoretical tradition that connects long bouts of unemployment to deaths. I suggest that if social distancing provokes a long economic downturn, between 28,000 and 68,000 people will die in the years following the crisis. In the fourth, I briefly describe the Chinese and South Korean strategies for coping with the crisis. I argue that their successes are based on their distinctive culture and politics. We can’t use them here. In the fifth, I use a range of data sources, starting with HS, to estimate how many beds are “released” by quarantining seniors. I estimate that we can reduce the number of new beds we must build or re-purpose by over a million if we quarantine the elderly, decrease the length of stay in non-ICU beds, and repurpose current hospital beds. This may be an overestimate—a best case scenario—but I believe that the estimate is within an order of magnitude correct. In the sixth, I outline the rudiments of an American plan for tackling the crisis acknowledging that it may be still-born, with so little time left. It combines a war-economy with local initiative. I end with a plea that we expand the discourse about the crisis beyond the language and frameworks of the public health discipline. We need the voices of engineers, business leaders, economists and project managers. If we ever needed a “systems view,” it is now

    Overcategories and undercategories of model categories

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    If M is a model category and Z is an object of M, then there are model category structures on the category of objects of M over Z and the category of objects of M under Z under which a map is a cofibration, fibration, or weak equivalence if and only if its image in M under the forgetful functor is, respectively, a cofibration, fibration, or weak equivalence. It is asserted without proof in "Model categories and their localizations" that if M is cofibrantly generated, cellular, or proper, then so is the category of objects of M over Z. The purpose of this note is to fill in the proofs of those assertions and to state and prove the analogous results for undercategories.Comment: 6 page
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