Robustly Optimal Auctions with Unknown Resale Opportunities

2018 ◽  
Vol 86 (4) ◽  
pp. 1527-1555 ◽  
Author(s):  
Gabriel Carroll ◽  
Ilya Segal
Keyword(s):  
Lagrange Multipliers ◽  
A Priori ◽  
Worst Case ◽  
Vickrey Auction ◽  
Optimal Auctions ◽  
Reserve Prices ◽  
Non Local ◽  
Incentive Constraints

Abstract The standard revenue-maximizing auction discriminates against a priori stronger bidders so as to reduce their information rents. We show that such discrimination is no longer optimal when the auction’s winner may resell to another bidder, and the auctioneer has non-Bayesian uncertainty about such resale opportunities. We identify a “worst-case” resale scenario, in which bidders’ values become publicly known after the auction and losing bidders compete Bertrand-style to buy the object from the winner. With this form of resale, misallocation no longer reduces the information rents of the high-value bidder, as he could still secure the same rents by buying the object in resale. Under regularity assumptions, we show that revenue is maximized by a version of the Vickrey auction with bidder-specific reserve prices, first proposed by Ausubel and Cramton (2004). The proof of optimality involves constructing Lagrange multipliers on a double continuum of binding non-local incentive constraints.

scholarly journals Bond-Length Distributions for Ions Bonded to Oxygen: Results for the Transition Metals and Quantification of the Factors Underlying Bond-Length Variation in Inorganic Solids

2020 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Frank Christopher Hawthorne
Keyword(s):  
Transition Metal ◽  
Bond Length ◽  
A Priori ◽  
Bond Formation ◽  
Length Variation ◽  
Electronic Effects ◽  
Coordination Polyhedra ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
Non Local

Bond-length distributions are examined for 63 transition-metal ions bonded to O2- in 147 configurations, for 7522 coordination polyhedra and 41,488 bond distances, providing baseline statistical knowledge of bond lengths for transi-tion metals bonded to O2-. A priori bond valences are calculated for 140 crystal structures containing 266 coordination poly-hedra for 85 transition-metal ion configurations with anomalous bond-length distributions. Two new indices, Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡, are proposed to quantify bond-length variation arising from bond-topological and crystallographic effects in extended solids. Bond-topological mechanisms of bond-length variation are [1] non-local bond-topological asymmetry, and [2] multi-ple-bond formation; crystallographic mechanisms are [3] electronic effects (with inherent focus on coupled electronic-vibra-tional degeneracy in this work), and [4] crystal-structure effects. The Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡 indices allow one to determine the primary cause(s) of bond-length variation for individual coordination polyhedra and ion configurations, quantify the dis-torting power of cations via electronic effects (by subtracting the bond-topological contribution to bond-length variation), set expectation limits regarding the extent to which functional properties linked to bond-length variations may be optimized in a given crystal structure (and inform how optimization may be achieved), and more. We find the observation of multiple bonds to be primarily driven by the bond-topological requirements of crystal structures in solids. However, we sometimes observe multiple bonds to form as a result of electronic effects (e.g. the pseudo Jahn-Teller effect); resolution of the origins of multiple-bond formation follows calculation of the Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡 indices on a structure-by-structure basis. Non-local bond-topological asymmetry is the most common cause of bond-length variation in transition-metal oxides and oxysalts, followed closely by the pseudo Jahn-Teller effect (PJTE). Non-local bond-topological asymmetry is further suggested to be the most widespread cause of bond-length variation in the solid state, with no a priori limitations with regard to ion identity. Overall, bond-length variations resulting from the PJTE are slightly larger than those resulting from non-local bond-topological asym-metry, comparable to those resulting from the strong JTE, and less than those induced by π-bond formation. From a compar-ison of a priori and observed bond valences for ~150 coordination polyhedra in which the strong JTE or the PJTE is the main reason underlying bond-length variation, the Jahn-Teller effect is found not to have a symbiotic relation with the bond-topo-logical requirements of crystal structures. The magnitude of bond-length variations caused by the PJTE decreases in the fol-lowing order for octahedrally coordinated d0 transition metals oxyanions: Os8+ > Mo6+ > W6+ >> V5+ > Nb5+ > Ti4+ > Ta5+ > Hf4+ > Zr4+ > Re7+ >> Y3+ > Sc3+. Such ranking varies by coordination number; for [4], it is Re7+ > Ti4+ > V5+ > W6+ > Mo6+ > Cr6+ > Os8+ >> Mn7+; for [5], it is Os8+ > Re7+ > Mo6+ > Ti4+ > W6+ > V5+ > Nb5+. We conclude that non-octahedral coordinations of d0 ion configurations are likely to occur with bond-length variations that are similar in magnitude to their octahedral counterparts. However, smaller bond-length variations are expected from the PJTE for non-d0 transition-metal oxyanions.<br>

How long have we got? The accuracy of physicians’ estimates and scenarios for survival time in 898 women with recurrent ovarian cancer (ROC).

2019 ◽  
Vol 37 (15_suppl) ◽  
pp. 5549-5549
Author(s):  
Felicia Roncolato ◽  
Rachel O'Connell ◽  
Florence Joly ◽  
Anne Lanceley ◽  
Felix Hilpert ◽  
...  
Keyword(s):  
Ovarian Cancer ◽  
Prognostic Factors ◽  
Survival Time ◽  
Cox Model ◽  
A Priori ◽  
Prognostic Significance ◽  
Recurrent Ovarian Cancer ◽  
Worst Case ◽  
Cox Models ◽  
Platinum Sensitive

5549 Background: Predicting, formulating, and communicating prognosis in women with ROC is difficult. Best-case, worst-case, and typical scenarios for survival time based on simple multiples of an individual’s expected survival time (EST) estimated by their oncologist have proven accurate and useful in a range of advanced cancers. We sought the accuracy and prognostic significance of such estimates in the GCIG Symptom Benefit Study: a multinational, prospective cohort study of women with ROC (platinum resistant and potentially platinum sensitive ROC who have had more than 2 lines of chemotherapy). Methods: Oncologists estimated EST at baseline for each woman they recruited to the GCIG Symptom Benefit Study in 11 countries. We hypothesised a priori that oncologists’ estimates of EST would be unbiased (equal proportions [approximately 50%] of women living longer versus shorter than their EST), imprecise ( < 33% living within 0.75 to 1.33 times their EST), and provide accurate scenarios for survival time (approximately 10% dying within ¼ of their EST, 10% living longer than 3 times their EST, and 50% living from half to double their EST). We also hypothesised that oncologists’ estimates of EST would be independently significant predictors of survival in a multivariable Cox model adjusting for prognostic factors established in previous studies. Results: Oncologists’ individualised estimates of EST in 898 women with ROC were unbiased (55% of women lived longer than their EST) and imprecise (23% lived within 0.75 to 1.33 times their EST). Scenarios for survival time based on oncologists’ estimates of EST were remarkably accurate: 7% of women died within ¼ of their EST, 13% lived longer than 3 times their EST, and 53% lived from half to double their EST. The median EST was 12 months (range 3-70), and median observed was 12.7 months. Oncologists’ estimates of EST were independently significant predictors of overall survival (HR 0.96, CI 0.94-0.98, p < 0.0001) in Cox models accounting for previously established prognostic factors. Conclusions: Oncologists’ estimates of EST were unbiased, imprecise, and independently significant predictors of survival time. Best-case, worst-case and typical scenarios based on simple multiples of EST were remarkably accurate, and provide a useful approach for predicting, formulating, and explaining prognosis in women with recurrent ovarian cancer. Clinical trial information: ACTRN: 12607000603415.

scholarly journals Tempered fractional LES modeling

2021 ◽  
Vol 932 ◽  
Author(s):  
Mehdi Samiee ◽  
Ali Akhavan-Safaei ◽  
Mohsen Zayernouri
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Equations ◽  
A Priori ◽  
Correlation Coefficients ◽  
Scale Model ◽  
Navier Stokes ◽  
Model Parameters ◽  
Subgrid Scale ◽  
Modelling Framework ◽  
Non Local

The presence of non-local interactions and intermittent signals in the homogeneous isotropic turbulence grant multi-point statistical functions a key role in formulating a new generation of large-eddy simulation (LES) models of higher fidelity. We establish a tempered fractional-order modelling framework for developing non-local LES subgrid-scale models, starting from the kinetic transport. We employ a tempered Lévy-stable distribution to represent the source of turbulent effects at the kinetic level, and we rigorously show that the corresponding turbulence closure term emerges as the tempered fractional Laplacian, $(\varDelta +\lambda )^{\alpha } (\cdot )$ , for $\alpha \in (0,1)$ , $\alpha \neq \frac {1}{2}$ and $\lambda >0$ in the filtered Navier–Stokes equations. Moreover, we prove the frame invariant properties of the proposed model, complying with the subgrid-scale stresses. To characterize the optimum values of model parameters and infer the enhanced efficiency of the tempered fractional subgrid-scale model, we develop a robust algorithm, involving two-point structure functions and conventional correlation coefficients. In an a priori statistical study, we evaluate the capabilities of the developed model in fulfilling the closed essential requirements, obtained for a weaker sense of the ideal LES model (Meneveau, Phys. Fluids, vol. 6, issue 2, 1994, pp. 815–833). Finally, the model undergoes the a posteriori analysis to ensure the numerical stability and pragmatic efficiency of the model.

scholarly journals Range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg–Marquardt method

2020 ◽  
Author(s):  
A Leitão ◽  
F Margotti ◽  
B F Svaiter
Keyword(s):  
Hilbert Spaces ◽  
Lagrange Multipliers ◽  
A Priori ◽  
Impedance Tomography ◽  
Nonlinear Operators ◽  
Marquardt Method ◽  
Exact Data ◽  
Levenberg Marquardt ◽  
Ill Posed ◽  
Novel Strategy

Abstract In this article we propose a novel strategy for choosing the Lagrange multipliers in the Levenberg–Marquardt method for solving ill-posed problems modeled by nonlinear operators acting between Hilbert spaces. Convergence analysis results are established for the proposed method, including monotonicity of iteration error, geometrical decay of the residual, convergence for exact data, stability and semi-convergence for noisy data. Numerical experiments are presented for an elliptic parameter identification two-dimensional electrical impedance tomography problem. The performance of our strategy is compared with standard implementations of the Levenberg–Marquardt method (using a priori choice of the multipliers).

Abstract 15568: Profound Increases in Out-of-Hospital Cardiopulmonary Arrest Cases Within Most Metropolitan Municipalities During the COVID-19 Pandemic

Circulation ◽  
2020 ◽  
Vol 142 (Suppl_3) ◽  
Author(s):  
Paul E Pepe ◽  
Kevin E McVaney ◽  
Lauren M Maloney ◽  
Eric Stein Bronsky ◽  
James J Augustine ◽  
...  
Keyword(s):  
Cardiopulmonary Arrest ◽  
A Priori ◽  
Large City ◽  
Absolute Number ◽  
Worst Case ◽  
Metropolitan Cities ◽  
High Prevalence ◽  
Large Populations ◽  
Metropolitan Municipalities ◽  
The U.S

Introduction: Even though most EMS systems globally experienced dramatic decreases in call volumes during the COVID-19 pandemic, many also reported unexpected increases in out-of-hospital cardiac arrest (OHCA) cases. Hypothesis: The pervasiveness of COVID-19 in metropolitan cities might be associated with a greater number of OHCA cases as compared to prior years. Methods: Large city EMS system medical directors responsible for about one-quarter of the U.S. population and millions of others in Europe/Australia were asked to tabulate the absolute number of OHCA cases to which EMS responded within their jurisdictions during the first 4 months of 2020. Results were compared to average numbers encountered during 2018 and 2019. A priori, considering the large populations (high corresponding OHCA frequencies) and case complexities, a 15% increase/decrease was to be considered highly significant (usual variation + 4-8% within the 28-31 days/month). Results: Of 35 major U.S. cities reporting to date, most had significant increases in OHCA, particularly in April with 71% (25/35) of the cities seeing a very large (>15%) increase. Nine cities (26%), all experiencing a high prevalence of COVID-19, had >50% (1.5-fold) increases. Three cities with highly-publicized inundations of COVID-19, experienced more than twice as many arrests (3.5-fold in the worst case). Meanwhile, 3 other cities with relatively low COVID-19 impact to date, had significantly fewer cases. Still, combining all of the 35 cities studied, OHCA increased from 5,009 (2 prior years’ average) to 8,701 (74% increase) during April (Fig 1). Participating cities outside the U.S. (e.g., Paris, London, Perth) mirrored these findings. Conclusions: To date, most, but not all, metropolitan cities have clearly experienced significant increases in OHCA that appear to parallel the prevalence of COVID-19 in their respective jurisdictions. These observations and available forensic data are now part of a work in progress.

scholarly journals Energy dissipation for hereditary and energy conservation for non-local fractional wave equations

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190295 ◽  
Author(s):  
Dušan Zorica ◽  
Ljubica Oparnica
Keyword(s):  
Energy Dissipation ◽  
Energy Conservation ◽  
Wave Equations ◽  
A Priori ◽  
Constitutive Models ◽  
Equation Of Motion ◽  
Constitutive Law ◽  
Energy Estimates ◽  
Fractional Wave Equations ◽  
Non Local

Using the method of a priori energy estimates, energy dissipation is proved for the class of hereditary fractional wave equations, obtained through the system of equations consisting of equation of motion, strain and fractional order constitutive models, that include the distributed-order constitutive law in which the integration is performed from zero to one generalizing all linear constitutive models of fractional and integer orders, as well as for the thermodynamically consistent fractional Burgers models, where the orders of fractional differentiation are up to the second order. In the case of non-local fractional wave equations, obtained using non-local constitutive models of Hooke- and Eringen-type in addition to the equation of motion and strain, a priori energy estimates yield the energy conservation, with the reinterpreted notion of the potential energy. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

Remarks on the Reynolds problem of elastohydrodynamic lubrication

1993 ◽  
Vol 4 (1) ◽  
pp. 83-96 ◽  
Author(s):  
José-Francisco Rodrigues
Keyword(s):  
Free Boundary ◽  
A Priori ◽  
Elastohydrodynamic Lubrication ◽  
Small Data ◽  
Existence Of A Solution ◽  
Pressure Dependent Viscosity ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
Dependent Viscosity ◽  
The Mathematical Model

The mathematical model of the flow of a viscous lubricant between elastic bearings leads to the study of a highly non-linear and non-local elliptic variational inequality. We discuss the existence of a solution by using an a prioriL∞-estimate. This method allows us to solve a large class of problems, including those arising from the linear Hertzian theory, and yields new existence results for the cases of a pressure-dependent viscosity or the inclusion of a load constraint. For small data the uniqueness of the solution holds, and we show that in the cylindrical journal bearing problem with small eccentricity ratio, the free boundary is given by two disjoint differentiable arcs close to the free boundary of the first-order approximate solution.

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