A Randomness Threshold for Online Bipartite Matching, via Lossless Online Rounding

Over three decades ago, Karp, Vazirani and Vazirani (STOC'90) introduced the online bipartite matching problem. They observed that deterministic algorithms' competitive ratio for this problem is no greater than $1/2$, and proved that randomized algorithms can do better. A natural question thus arises: \emph{how random is random}? i.e., how much randomness is needed to outperform deterministic algorithms? The \textsc{ranking} algorithm of Karp et al.~requires $\tilde{O}(n)$ random bits, which, ignoring polylog terms, remained unimproved. On the other hand, Pena and Borodin (TCS'19) established a lower bound of $(1-o(1))\log\log n$ random bits for any $1/2+\Omega(1)$ competitive ratio. We close this doubly-exponential gap, proving that, surprisingly, the lower bound is tight. In fact, we prove a \emph{sharp threshold} of $(1\pm o(1))\log\log n$ random bits for the randomness necessary and sufficient to outperform deterministic algorithms for this problem, as well as its vertex-weighted generalization. This implies the same threshold for the advice complexity (nondeterminism) of these problems. Similar to recent breakthroughs in the online matching literature, for edge-weighted matching (Fahrbach et al.~FOCS'20) and adwords (Huang et al.~FOCS'20), our algorithms break the barrier of $1/2$ by randomizing matching choices over two neighbors. Unlike these works, our approach does not rely on the recently-introduced OCS machinery, nor the more established randomized primal-dual method. Instead, our work revisits a highly-successful online design technique, which was nonetheless under-utilized in the area of online matching, namely (lossless) online rounding of fractional algorithms. While this technique is known to be hopeless for online matching in general, we show that it is nonetheless applicable to carefully designed fractional algorithms with additional (non-convex) constraints

Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions

We study, by incorporating short-range ion-surface interactions, ionic profiles of electrolyte solutions close to a non-charged interface between two dielectric media. In order to account for important correlation effects close to the interface, the ionic profiles are calculated beyond mean-field theory, using the loop expansion of the free energy. We show how it is possible to overcome the well-known deficiency of the regular loop expansion close to the dielectric jump, and treat the non-linear boundary conditions within the framework of field theory. The ionic profiles are obtained analytically to one-loop order in the free energy, and their dependence on different ion-surface interactions is investigated. The Gibbs adsorption isotherm, as well as the ionic profiles are used to calculate the surface tension, in agreement with the reverse Hofmeister series. Consequently, from the experimentally-measured surface tension, one can extract a single adhesivity parameter, which can be used within our model to quantitatively predict hard to measure ionic profiles.Comment: 14 pages, 6 figure

Effective Potential for the Conformal Sector of Quantum Gravity with Torsion

The effective potential which describes the conformal dynamics of quantum gravity with torsion is discussed. The phase transitions induced by the combination of torsion and curvature are investigated. The mechanism for fixing the vacuum expectation values of the metric and torsion is presented.Comment: 9 pages, LaTeX, july 3

Evaluating the impact of policies recommending PrEP to subpopulations of men and transgender women who have sex with men based on demographic and behavioral risk factors.

IntroductionDeveloping guidelines to inform the use of antiretroviral pre-exposure prophylaxis (PrEP) for HIV prevention in resource-limited settings must necessarily be informed by considering the resources and infrastructure needed for PrEP delivery. We describe an approach that identifies subpopulations of cisgender men who have sex with men (MSM) and transgender women (TGW) to prioritize for the rollout of PrEP in resource-limited settings.MethodsWe use data from the iPrEx study, a multi-national phase III study of PrEP for HIV prevention in MSM/TGW, to build statistical models that identify subpopulations at high risk of HIV acquisition without PrEP, and with high expected PrEP benefit. We then evaluate empirically the population impact of policies recommending PrEP to these subpopulations, and contrast these with existing policies.ResultsA policy recommending PrEP to a high risk subpopulation of MSM/TGW reporting condomless receptive anal intercourse over the last 3 months (estimated 3.3% 1-year HIV incidence) yields an estimated 1.95% absolute reduction in 1-year HIV incidence at the population level, and 3.83% reduction over 2 years. Importantly, such a policy requires rolling PrEP out to just 59.7% of MSM/TGW in the iPrEx population. We find that this policy is identical to that which prioritizes MSM/TGW with high expected PrEP benefit. It is estimated to achieve nearly the same reduction in HIV incidence as the PrEP guideline put forth by the US Centers for Disease Control, which relies on the measurement of more behavioral risk factors and which would recommend PrEP to a larger subset of the MSM/TGW population (86% vs. 60%).ConclusionsThese findings may be used to focus future mathematical modelling studies of PrEP in resource-limited settings on prioritizing PrEP for high-risk subpopulations of MSM/TGW. The statistical approach we took could be employed to develop PrEP policies for other at-risk populations and resource-limited settings

Orientational order on curved surfaces - the high temperature region

We study orientational order, subject to thermal fluctuations, on a fixed curved surface. We derive, in particular, the average density of zeros of Gaussian distributed vector fields on a closed Riemannian manifold. Results are compared with the density of disclination charges obtained from a Coulomb gas model. Our model describes the disordered state of two dimensional objects with orientational degrees of freedom, such as vector ordering in Langmuir monolayers and lipid bilayers above the hexatic to fluid transition.Comment: final version, 13 Pages, 2 figures, uses iopart.cl

Higher spin fermions in the BTZ black hole

Recently it has been shown that the wave equations of bosonic higher spin fields in the BTZ background can be solved exactly. In this work we extend this analysis to fermionic higher spin fields. We solve the wave equations for arbitrary half-integer spin fields in the BTZ black hole background and obtain exact expressions for their quasinormal modes. These quasinormal modes are shown to agree precisely with the poles of the corresponding two point function in the dual conformal field theory as predicted by the AdS/CFT correspondence. We also obtain an expression for the 1-loop determinant in terms of the quasinormal modes and show it agrees with that obtained by integrating the heat kernel found by group theoretic methods.Comment: 29 page

Multifield Inflation after Planck: The Case for Nonminimal Couplings

Multifield models of inflation with nonminimal couplings are in excellent agreement with the recent results from Planck. Across a broad range of couplings and initial conditions, such models evolve along an effectively single-field attractor solution and predict values of the primordial spectral index and its running, the tensor-to-scalar ratio, and non-Gaussianities squarely in the observationally most-favored region. Such models can also amplify isocurvature perturbations, which could account for the low power recently observed in the cosmic microwave background power spectrum at low multipoles. Future measurements of primordial isocurvature perturbations could distinguish between the currently viable possibilities.United States. Dept. of Energy (Contract DE-FG02-05ER41360