Are We #StayingHome to Flatten the Curve?

The recent spread of COVID-19 across the U.S. led to concerted efforts by states to ``flatten the curve" through the adoption of stay-at-home mandates that encourage individuals to reduce travel and maintain social distance. Combining data on changes in travel activity with COVID-19 health outcomes and state policy adoption timing, we characterize nationwide changes in mobility patterns and isolate the portion attributable to statewide mandates. We find evidence of dramatic nationwide declines in mobility prior to adoption of any statewide mandates. Once states adopt a mandate, we estimate further mandate-induced declines between 2.1 and 7.0 percentage points across methods that account for states' differences in travel behavior prior to policy adoption. In addition, we investigate the effects of stay-at-home mandates on changes in COVID-19 health outcomes while controlling for pre-trends and observed pre-treatment mobility patterns. We estimate mandate-induced declines between 0.13 and 0.17 in deaths (5.6 to 6.0 in hospitalizations) per 100 thousand across methods. Across 43 adopting states, this represents 23,366-30,144 fewer deaths (and roughly one million averted hospitalizations) for the months of March and April - which indicates that death rates could have been 42-54% higher had states not adopted statewide policies. We further find evidence that changes in mobility patterns prior to adoption of statewide policies also played a role in reducing COVID-19 mortality and morbidity. Adding in averted deaths due to pre-mandate social distancing behavior, we estimate a total of 48-71,000 averted deaths from COVID-19 for the two-month period. Given that the actual COVID-19 death toll for March and April was 55,922, our estimates suggest that deaths would have been 1.86-2.27 times what they were absent any stay-at-home mandates during this period. These estimates represent a lower bound on the health impacts of stay-at-home policies, as they do not account for spillovers or undercounting of COVID-19 mortality. Our findings indicate that early behavior changes and later statewide policies reduced death rates and helped attenuate the negative consequences of COVID-19. Further, our findings of substantial reductions in mobility prior to state-level policies convey important policy implications for re-opening.Take Away Link https://are.berkeley.edu/sites/are.berkeley.edu/files/PolicyTakeAway_Web.pd

Julius and Julia: Mastering the art of the Schwarz lemma

This article discusses classical versions of the Schwarz lemma at the boundary of the unit disk in the complex plane. The exposition includes commentary on the history, the mathematics, and the applications.Comment: Expository article to appear in the American Mathematical Monthly. 19 pages, 4 figures, uses tik

Mocposite functions

Traditional mathematical notation can lead to confusion. Expressions that appear to define composite functions sometimes do not. A particular example with engineering applications is studied in detail.Comment: To appear in the American Mathematical Monthl

The Master Ward Identity

In the framework of perturbative quantum field theory (QFT) we propose a new, universal (re)normalization condition (called 'master Ward identity') which expresses the symmetries of the underlying classical theory. It implies for example the field equations, energy-momentum, charge- and ghost-number conservation, renormalized equal-time commutation relations and BRST-symmetry. It seems that the master Ward identity can nearly always be satisfied, the only exceptions we know are the usual anomalies. We prove the compatibility of the master Ward identity with the other (re)normalization conditions of causal perturbation theory, and for pure massive theories we show that the 'central solution' of Epstein and Glaser fulfills the master Ward identity, if the UV-scaling behavior of its individual terms is not relatively lowered. Application of the master Ward identity to the BRST-current of non-Abelian gauge theories generates an identity (called 'master BRST-identity') which contains the information which is needed for a local construction of the algebra of observables, i.e. the elimination of the unphysical fields and the construction of physical states in the presence of an adiabatically switched off interaction.Comment: 73 pages, version to appear in Rev. Math. Phy

Posterior Reversible Encephalopathy Syndrome and Azathioprine

Posterior reversible encephalopathy syndrome (PRES) is a rare syndrome that presents with neurological manifestations, often associated with arterial hypertension. Magnetic resonance imaging (MRI) shows bilateral white matter oedema in the posterior vascular territories. Immunosuppression, (pre) eclampsia and autoimmune diseases can be implicated. A 27-year-old woman, with mixed connective tissue disease under azathioprine, was admitted in the emergency room in status epilepticus and with severe hypertension. The MRI showed bilateral oedema in a pattern compatible with PRES. There was clinical improvement after azathioprine suspension. PRES is typically reversible with prompt recognition of the syndrome and its trigger. The association with azathioprine is rare. LEARNING POINTS: Posterior reversible encephalopathy syndrome should be considered in patients with sudden onset of headache, altered consciousness and seizures.Recognition of this entity and identification of the trigger are essential for reversal of the clinical picture.Autoimmune diseases and some immunosuppressive drugs have been identified as causative, but reports of an association with azathioprine are very rare.info:eu-repo/semantics/publishedVersio

Buyer Power through Producer's Differentiation

Cet article montre que des distributeurs peuvent décider d'offrir des produits différenciés, non pas pour relâcher la concurrence horizontale, mais pour accroître leur pouvoir d'achat vis-à-vis de leur fournisseur. Nous analysons un modèle simple où deux producteurs offrent des produits différenciés en qualité à deux distributeurs en activité sur des marches séparés qui ne peuvent offrir qu'un seul produit aux consommateurs. A la première étape du jeu, les distributeurs choisissent quel produit mettre en rayon, puis chaque distributeur et son fournisseur négocient sur un contrat de tarif binôme. Enfin, les distributeurs choisissent leur quantités. Lorsque les coûts de production sont convexes, la part des profits joint revenant au distributeur est plus élevée lorsque les distributeurs choisissent de se différencier. L'origine de la différenciation peut donc être uniquement liée au désir des distributeurs d'accroître leur pouvoir d'achat: via la différenciation des fournisseurs, le distributeur obtient une plus large part de profits joints plus faibles. Ce résultat est robuste lorsque l'on introduit de la concurrence en aval. Nous mettons en évidence les conséquences de cette stratégie de différenciation sur le surplus des consommateurs.Puissance d'achat;Gamme de produit;Différentiation des produits

Multiphoton Jaynes-Cummings Model: Arbitrary Rotations in Fock Space and Quantum Filters

The multiphoton Jaynes-Cummings model is investigated and applications in quantum information science are explored. Considering the strong atom-field coupling regime and an $N$-photon interaction, a nonlinear driving field can perform an arbitrary rotation in the Fock space of the cavity mode involving the vacuum and an $M$-Fock state, with $M<N$. Besides, driving the cavity mode with a linear coherent field (superposition of many Fock states), only the cavity states within the Fock subspace {$|0\rangle,|1\rangle,..., |N-1\rangle$} can be populated, i.e., we show how to implement a Fock state filter, or quantum scissor, that restricts the dynamics of a given bosonic mode to a limited Hilbert space. Such a device can be employed as a generator of finite-dimensional quantum-optical states and also as a quantum-optical intensity limiter, allowing as a special case the deterministic generation of single-photon pulses. On the other hand, our system also provides a very rich physics in the weak atom-field coupling regime, multiphoton electromagnetically-induced-transparency-like phenomena, inducing a narrow (controllable) reflectivity window for nonlinear probe fields. These results are useful for applications in quantum information processing and also motivate further investigations, e.g., the use of an $N$-photon Jaynes-Cummings system as a qudit with harmonic spectrum and the exploration of multiphoton quantum interference.Comment: 6+4 pages, 4 figures; close to the published versio