Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check

We show that when the Hornberger--Sipe calculation of collisional decoherence is carried out with the squared delta function a delta of energy instead of a delta of the absolute value of momentum, following a method introduced by Di\'osi, the corrected formula for the decoherence rate is simply obtained. The results of Hornberger and Sipe and of Di\'osi are shown to be in agreement. As an independent cross-check, we calculate the mean squared coordinate diffusion of a hard sphere implied by the corrected decoherence master equation, and show that it agrees precisely with the same quantity as calculated by a classical Brownian motion analysis.Comment: Tex: 14 pages 7/30/06: revisions to introduction, and references added 9/29/06: further minor revisions and references adde

Can the flyby anomaly be attributed to earth-bound dark matter?

We make preliminary estimates to assess whether the recently reported flyby anomaly can be attributed to dark matter interactions. We consider both elastic and exothermic inelastic scattering from dark matter constituents; for isotropic dark matter velocity distributions, the former decrease, while the latter increase, the final flyby velocity. The fact that the observed flyby velocity anomaly shows examples with both positive and negative signs, requires the dominance of different dark matter scattering processes along different flyby trajectories. The magnitude of the observed anomalies requires dark matter densities many orders of magnitude greater than the galactic halo density. Such a large density could result from an accumulation cascade, in which the solar system-bound dark matter density is much higher than the galactic halo density, and the earth-bound density is much higher than the solar system-bound density. We discuss a number of strong constraints on the hypothesis of a dark matter explanation for the flyby anomaly. These require dark matter to be non-self-annihilating, with the dark matter scattering cross section on nucleons much larger, and the dark matter mass much lighter, than usually assumed.Comment: Latex, 21 pages. v3: substantially revised and expanded; v4: version to appear in Phys. Rev.

Remarks on a Proposed Super-Kamiokande Test for Quantum Gravity Induced Decoherence Effects

Lisi, Marrone, and Montanino have recently proposed a test for quantum gravity induced decoherence effects in neutrino oscillations observed at Super-Kamiokande. We comment here that their equations have the same qualitative form as the energy conserving objective state vector reduction equations discussed by a number of authors. However, using the Planckian parameter value proposed to explain state vector reduction leads to a neutrino oscillation effect many orders of magnitude smaller than would be detectable at Super-Kamiokande. Similar estimates hold for the Ghirardi, Rimini, and Weber spontaneous localization approach to state vector reduction, and our remarks are relevant as well to proposed $K$ meson and $B$ meson tests of gravity induced decoherence.Comment: 10 pages, plain Tex, no figure

DISTRIBUTION OF LABELED LYMPH NODE CELLS IN MICE DURING THE LYMPHOCYTOSIS INDUCED BY BORDETELLA PERTUSSIS

The mechanism by which Bordetella pertussis organisms and their products induce lymphocytosis in mice was analyzed in terms of the localization of syngeneic Cr-51-labeled lymph node cells. Labeled lymphoid cells incubated in vitro with the supernatant of B. pertussis cultures and then injected intravenously into normal recipients, or labeled cells injected into pertussis-treated recipients were unable to "home" to lymphoid organs but persisted for long periods in the blood. In animals "equipped" with a population of Cr-51-labeled lymphoid cells, administration of B. pertussis organisms or culture supernatant effected a shift of radioactivity from lymph nodes and spleen into the peripheral blood, coincident with the lymphocytosis. In in vitro experiments it was found that the active principle could bind to both erythrocytes and lymphocytes and could spontaneously elute from these cells onto labeled lymphocytes which were then unable to home efficiently. The data suggest that Bordetella pertussis-induced lymphocytosis involves a reversible attachment of the pertussis factor onto the surfaces of lymphocytes which prevents their recirculation to lymphoid organs. Recirculating lymphocytes are presumably affected as they emerge from lymphoid organs to enter the blood

Weisskopf-Wigner Decay Theory for the Energy-Driven Stochastic Schr\"odinger Equation

We generalize the Weisskopf-Wigner theory for the line shape and transition rates of decaying states to the case of the energy-driven stochastic Schr\"odinger equation that has been used as a phenomenology for state vector reduction. Within the standard approximations used in the Weisskopf-Wigner analysis, and assuming that the perturbing potential inducing the decay has vanishing matrix elements within the degenerate manifold containing the decaying state, the stochastic Schr\"odinger equation linearizes. Solving the linearized equations, we find no change from the standard analysis in the line shape or the transition rate per unit time. The only effect of the stochastic terms is to alter the early time transient behavior of the decay, in a way that eliminates the quantum Zeno effect. We apply our results to estimate experimental bounds on the parameter governing the stochastic effects.Comment: 29 pages in RevTeX, Added Note, references adde

The Equilibrium Distribution of Gas Molecules Adsorbed on an Active Surface

We evaluate the exact equilibrium distribution of gas molecules adsorbed on an active surface with an infinite number of attachment sites. Our result is a Poisson distribution having mean $X = {\mu P P_s \over P_e}$, with $\mu$ the mean gas density, $P_s$ the sticking probability, $P_e$ the evaporation probability in a time interval $\tau$, and $P$ Smoluchowski's exit probability in time interval $\tau$ for the surface in question. We then solve for the case of a finite number of attachment sites using the mean field approximation, recovering in this case the Langmuir isotherm.Comment: 14 pages done in late

Ecological equivalence: a realistic assumption for niche theory as a testable alternative to neutral theory

Hubbell's 2001 neutral theory unifies biodiversity and biogeography by modelling steady-state distributions of species richness and abundances across spatio-temporal scales. Accurate predictions have issued from its core premise that all species have identical vital rates. Yet no ecologist believes that species are identical in reality. Here I explain this paradox in terms of the ecological equivalence that species must achieve at their coexistence equilibrium, defined by zero net fitness for all regardless of intrinsic differences between them. I show that the distinction of realised from intrinsic vital rates is crucial to evaluating community resilience. An analysis of competitive interactions reveals how zero-sum patterns of abundance emerge for species with contrasting life-history traits as for identical species. I develop a stochastic model to simulate community assembly from a random drift of invasions sustaining the dynamics of recruitment following deaths and extinctions. Species are allocated identical intrinsic vital rates for neutral dynamics, or random intrinsic vital rates and competitive abilities for niche dynamics either on a continuous scale or between dominant-fugitive extremes. Resulting communities have steady-state distributions of the same type for more or less extremely differentiated species as for identical species. All produce negatively skewed log-normal distributions of species abundance, zero-sum relationships of total abundance to area, and Arrhenius relationships of species to area. Intrinsically identical species nevertheless support fewer total individuals, because their densities impact as strongly on each other as on themselves. Truly neutral communities have measurably lower abundance/area and higher species/abundance ratios. Neutral scenarios can be parameterized as null hypotheses for testing competitive release, which is a sure signal of niche dynamics. Ignoring the true strength of interactions between and within species risks a substantial misrepresentation of community resilience to habitat los

Generalized stochastic Schroedinger equations for state vector collapse

A number of authors have proposed stochastic versions of the Schr\"odinger equation, either as effective evolution equations for open quantum systems or as alternative theories with an intrinsic collapse mechanism. We discuss here two directions for generalization of these equations. First, we study a general class of norm preserving stochastic evolution equations, and show that even after making several specializations, there is an infinity of possible stochastic Schr\"odinger equations for which state vector collapse is provable. Second, we explore the problem of formulating a relativistic stochastic Schr\"odinger equation, using a manifestly covariant equation for a quantum field system based on the interaction picture of Tomonaga and Schwinger. The stochastic noise term in this equation can couple to any local scalar density that commutes with the interaction energy density, and leads to collapse onto spatially localized eigenstates. However, as found in a similar model by Pearle, the equation predicts an infinite rate of energy nonconservation proportional to $\delta^3(\vec 0)$, arising from the local double commutator in the drift term.Comment: 24 pages Plain TeX. Minor changes, some new references. To appear in Journal of Physics

Comparative effectiveness of second line oral antidiabetic treatments among people with type 2 diabetes mellitus: emulation of a target trial using routinely collected health data

Objective: To compare the effectiveness of three commonly prescribed oral antidiabetic drugs added to metformin for people with type 2 diabetes mellitus requiring second line treatment in routine clinical practice. Design: Cohort study emulating a comparative effectiveness trial (target trial). Setting: Linked primary care, hospital, and death data in England, 2015-21. Participants: 75 739 adults with type 2 diabetes mellitus who initiated second line oral antidiabetic treatment with a sulfonylurea, DPP-4 inhibitor, or SGLT-2 inhibitor added to metformin. Main outcome measures: Primary outcome was absolute change in glycated haemoglobin A1c (HbA1c) between baseline and one year follow-up. Secondary outcomes were change in body mass index (BMI), systolic blood pressure, and estimated glomerular filtration rate (eGFR) at one year and two years, change in HbA1c at two years, and time to ≥40% decline in eGFR, major adverse kidney event, hospital admission for heart failure, major adverse cardiovascular event (MACE), and all cause mortality. Instrumental variable analysis was used to reduce the risk of confounding due to unobserved baseline measures. Results: 75 739 people initiated second line oral antidiabetic treatment with sulfonylureas (n=25 693, 33.9%), DPP-4 inhibitors (n=34 464 ,45.5%), or SGLT-2 inhibitors (n=15 582, 20.6%). SGLT-2 inhibitors were more effective than DPP-4 inhibitors or sulfonylureas in reducing mean HbA1c values between baseline and one year. After the instrumental variable analysis, the mean differences in HbA1c change between baseline and one year were −2.5 mmol/mol (95% confidence interval (CI) −3.7 to −1.3) for SGLT-2 inhibitors versus sulfonylureas and −3.2 mmol/mol (−4.6 to −1.8) for SGLT-2 inhibitors versus DPP-4 inhibitors. SGLT-2 inhibitors were more effective than sulfonylureas or DPP-4 inhibitors in reducing BMI and systolic blood pressure. For some secondary endpoints, evidence for SGLT-2 inhibitors being more effective was lacking—the hazard ratio for MACE, for example, was 0.99 (95% CI 0.61 to 1.62) versus sulfonylureas and 0.91 (0.51 to 1.63) versus DPP-4 inhibitors. SGLT-2 inhibitors had reduced hazards of hospital admission for heart failure compared with DPP-4 inhibitors (0.32, 0.12 to 0.90) and sulfonylureas (0.46, 0.20 to 1.05). The hazard ratio for a ≥40% decline in eGFR indicated a protective effect versus sulfonylureas (0.42, 0.22 to 0.82), with high uncertainty in the estimated hazard ratio versus DPP-4 inhibitors (0.64, 0.29 to 1.43). Conclusions: This emulation study of a target trial found that SGLT-2 inhibitors were more effective than sulfonylureas or DPP-4 inhibitors in lowering mean HbA1c, BMI, and systolic blood pressure and in reducing the hazards of hospital admission for heart failure (v DPP-4 inhibitors) and kidney disease progression (v sulfonylureas), with no evidence of differences in other clinical endpoints

Real-time pandemic surveillance using hospital admissions and mobility data

Forecasting the burden of COVID-19 has been impeded by limitations in data, with case reporting biased by testing practices, death counts lagging far behind infections, and hospital census reflecting time-varying patient access, admission criteria, and demographics. Here, we show that hospital admissions coupled with mobility data can reliably predict severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission rates and health-care demand. Using a forecasting model that has guided mitigation policies in Austin, TX, we estimate that the local reproduction number had an initial 7-d average of 5.8 (95% credible interval [CrI]: 3.6 to 7.9) and reached a low of 0.65 (95% CrI: 0.52 to0.77) after the summer 2020 surge. Estimated case detection rates ranged from 17.2% (95% CrI: 11.8 to 22.1%) at the outset to a high of 70% (95% CrI: 64 to 80%) in January 2021, and infection prevalence remained above 0.1% between April 2020 and March 1, 2021, peaking at 0.8% (0.7-0.9%) in early January 2021. As precautionary behaviors increased safety in public spaces, the relationship between mobility and transmission weakened. We estimate that mobility-associated transmission was 62% (95%CrI: 52 to 68%) lower in February 2021 compared to March 2020. In a retrospective comparison, the 95% CrIs of our 1, 2, and 3 wk ahead forecasts contained 93.6%, 89.9%, and 87.7% of reported data, respectively. Developed by a task force including scientists, public health officials, policy makers, and hospital executives, this model can reliably project COVID-19 healthcare needs in US cities.This work was supported by Grant U01IP001136 from the CDC, Grant NIH R01 AI151176 from the NIH, and a generous donation from Tito’s Handmade Vodka.StatisticsIntegrative BiologyOperations Research and Industrial EngineeringTexas Advanced Computing Center (TACC)Dell Medical SchoolInformation, Risk, and Operations Management (IROM