Self Equivalence of the Alternating Direction Method of Multipliers

The alternating direction method of multipliers (ADM or ADMM) breaks a complex optimization problem into much simpler subproblems. The ADM algorithms are typically short and easy to implement yet exhibit (nearly) state-of-the-art performance for large-scale optimization problems. To apply ADM, we first formulate a given problem into the "ADM-ready" form, so the final algorithm depends on the formulation. A problem like \mbox{minimize}_\mathbf{x} u(\mathbf{x}) + v(\mathbf{C}\mathbf{x}) has six different "ADM-ready" formulations. They can be in the primal or dual forms, and they differ by how dummy variables are introduced. To each "ADM-ready" formulation, ADM can be applied in two different orders depending on how the primal variables are updated. Finally, we get twelve different ADM algorithms! How do they compare to each other? Which algorithm should one choose? In this paper, we show that many of the different ways of applying ADM are equivalent. Specifically, we show that ADM applied to a primal formulation is equivalent to ADM applied to its Lagrange dual; ADM is equivalent to a primal-dual algorithm applied to the saddle-point formulation of the same problem. These results are surprising since the primal and dual variables in ADM are seemingly treated very differently, and some previous work exhibit preferences in one over the other on specific problems. In addition, when one of the two objective functions is quadratic, possibly subject to an affine constraint, we show that swapping the update order of the two primal variables in ADM gives the same algorithm. These results identify the few truly different ADM algorithms for a problem, which generally have different forms of subproblems from which it is easy to pick one with the most computationally friendly subproblems.Comment: 29 page

Asymmetric Dark Stars and Neutron Star Stability

We consider gravitationally bound states of asymmetric dark matter (ADM stars), and the impact of ADM capture on the stability of neutron stars. We derive and interpret the equation of state for ADM with both attractive and repulsive interactions, and solve the Tolman-Oppenheimer-Volkoff equations to find equilibrium sequences and maximum masses of ADM stars. Gravitational wave searches can utilize our solutions to model exotic compact objects (ECOs). Our results for attractive interactions differ substantially from those in the literature, where fermionic ADM with attractive self-interactions was employed to destabilize neutron stars more effectively than non-interacting fermionic ADM. By contrast, we argue that fermionic ADM with an attractive force is no more effective in destabilizing neutron stars than fermionic ADM with no self-interactions.Comment: 9 pages plus 2 appendices (15 pages total), 7 figures, 1 tabl

Plasma adrenomedullin is associated with short-term mortality and vasopressor requirement in patients admitted with sepsis

Introduction: The incidence of death among patients admitted for severe sepsis or septic shock is high. Adrenomedullin (ADM) plays a central role in initiating the hyperdynamic response during the early stages of sepsis. Pilot studies indicate an association of plasma ADM with the severity of the disease. In the present study we utilized a novel sandwich immunoassay of bioactive plasma ADM in patients hospitalized with sepsis in order to assess the clinical utility.Methods: We enrolled 101 consecutive patients admitted to the emergency department with suspected sepsis in this study. Sepsis was defined by fulfillment of at least two systemic inflammatory response syndrome (SIRS) criteria plus clinical suspicion of infection. Plasma samples for ADM measurement were obtained on admission and for the next four days. The 28-day mortality rate was recorded.Results: ADM at admission was associated with severity of disease (correlation with Acute Physiology and Chronic Health Evaluation II (APACHE II) score: r = 0.46; P <0.0001). ADM was also associated with 28-day mortality (ADM median (IQR): survivors: 50 (31 to 77) pg/mL; non-survivors: 84 (48 to 232) pg/mL; P <0.001) and was independent from and additive to APACHE II (P = 0.02). Cox regression analysis revealed an additive value of serial measurement of ADM over baseline assessment for prediction of 28-day mortality (P < 0.01). ADM was negatively correlated with mean arterial pressure (r = -0.39; P <0.0001), and it strongly discriminated those patients requiring vasopressor therapy from the others (ADM median (IQR): no vasopressors 48 (32 to 75) pg/mL; with vasopressors 129 (83 to 264) pg/mL, P <0.0001).Conclusions: In patients admitted with sepsis, severe sepsis or septic shock plasma ADM is strongly associated with severity of disease, vasopressor requirement and 28-day mortality

The Academy of Dental Materials: Providing roots and wings.

ObjectivesThe long history of the Academy of Dental Materials (ADM) is documented with its strategies (a) to rapidly communicate science among its members, (b) to establish special awards to stimulate new science, and (c) to develop new dental materials scientists.MethodsWe searched the history of the last 35 years of the ADM newsletters, transactions, journals, and officer notes. We document the (a) presidents, (b) meeting history, (c) membership growth, and (d) development of special awards through 2019 with the recent creation of the ADM Marshall Post-Doctoral Award.ResultsThere are 36 years of recent ADM history, 42 international meetings, membership growth to 400 individuals from 15 countries, service of 19 presidents, Paffenbarger annual Awardees since 1989, induction of >200 fellows, and recognition of the first winner of Marshall Post-Doctoral Award in 2018. New directions for recruiting members are suggested. Three potential new thrusts for the organization are presented: artificial intelligence, genetic engineering, and intensive member mentoring.SignificanceThese suggestions for the ADM provide a path for the ADM to continue to adapt to the ever changing scientific landscape

On the relation between ADM and Bondi energy-momenta

When a spacetime takes Bondi radiating metric, and is vacuum and asymptotically flat at spatial infinity which ensures the positive mass theorem, we prove that the standard ADM energy-momentum is the past limit of the Bondi energy-momentum. We also derive a formula relating the ADM energy-momentum of any asymptotically flat spacelike hypersurface to the Bondi energy-momentum of any null hypersurface. The formula indicates that the Bondi mass is always less than the ADM total energy if the system has {\it news}. The assumed asymptotic flatness precludes gravitational radiation. We therefore study further the relation between the ADM total energy and the Bondi mass when gravitational radiation emits. We find that in this case the ADM total energy is no longer the past limit of the Bondi mass. They differ by certain quantity relating to the {\it news} of the system.Comment: 21 pages, final versio

2D quantum dilaton gravitational Hamiltonian, boundary terms and new definition for total energy

The ADM and Bondi mass for the RST model have been first discussed from Hawking and Horowitz's argument. Expressing the localized RST action in terms of the ADM formulation, the RST Hamiltonian can be derived, meanwhile keeping track of all boundary terms. Then the total boundary terms can be taken as the total energy for the RST model. It has been found that there is a new contribution to the ADM and Bondi mass from the RST boundary due to the existence of the hidden dynamical field. The ADM and Bondi mass have been discussed respectively in detail, and some new properties have been found.Comment: 14 pages, Latex file, no figure, to appear in Phys. Lett.