On Volumes of Subregions in Holography and Complexity

The volume of the region inside the bulk Ryu-Takayanagi surface is a codimension-one object, and a natural generalization of holographic complexity to the case of subregions in the boundary QFT. We focus on time-independent geometries, and study the properties of this volume in various circumstances. We derive a formula for computing the volume for a strip entangling surface and a general asymptotically AdS bulk geometry. For an AdS black hole geometry, the volume exhibits non-monotonic behaviour as a function of the size of the entangling region (unlike the behaviour of the entanglement entropy in this setup, which is monotonic). For setups in which the holographic entanglement entropy exhibits transitions in the bulk, such as global AdS black hole, geometries dual to confining theories and disjoint entangling surfaces, the corresponding volume exhibits a discontinuous finite jump at the transition point (and so do the volumes of the corresponding entanglement wedges). We compute this volume discontinuity in several examples. Lastly, we compute the codim-zero volume and the bulk action of the entanglement wedge for the case of a sphere entangling surface and pure AdS geometry.Comment: 25 page

The Impact of the Medicare Drug Benefit on Health Care Spending by Older Households

This report uses data from the Bureau of Labor Statistics Consumer Expenditure Survey from 2004 to 2006 as well as data from the Congressional Budget Office to analyze the savings in prescription drug spending for seniors as a result of the Medicare Prescription Drug, Improvement, and Modernization Act of 2003 (MMA). The results show that the 1st income quintile of seniors experienced a fall in the rate of expenditures for prescription drugs and the 2nd income quintile saw a slowing of the rate of increase in expenditures. However, senior households in the middle- and upper-income quintiles saw a rise in expenditures for prescription drugs.medicare, prescription drugs, MMA, senior citizens, health care

Renormalization group flow of entanglement entropy on spheres

We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the cosmological constant and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in $d=2,3,4$. In three dimensions we find that while the renormalized entanglement entropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal `area law' for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.Comment: 38 pages, 2 figures; v2: references added, version accepted to JHE

Holographic Entanglement Entropy of Multiple Strips

We study holographic entanglement entropy (HEE) of $m$ strips in various holographic theories. We prove that for $m$ strips with equal lengths and equal separations, there are only 2 bulk minimal surfaces. For backgrounds which contain also "disconnected" surfaces, there are only 4 bulk minimal surfaces. Depending on the length of the strips and separation between them, the HEE exhibits first order "geometric" phase transitions between bulk minimal surfaces with different topologies. We study these different phases and display various phase diagrams. For confining geometries with $m$ strips, we find new classes of "disconnected" bulk minimal surfaces, and the resulting phase diagrams have a rich structure. We also study the "entanglement plateau" transition, where we consider the BTZ black hole in global coordinates with 2 strips. It is found that there are 4 bulk minimal surfaces, and the resulting phase diagram is displayed. We perform a general perturbative analysis of the $m$-strip system: including perturbing the CFT and perturbing the length or separation of the strips.Comment: 32 pages; v2: citations adde

Influence of the absorber dimensions on wavefront shaping based on volumetric optoacoustic feedback

The recently demonstrated control over light distribution through turbid media based on real-time three-dimensional optoacoustic feedback has offered promising prospects to interferometrically focus light within scattering objects. Nevertheless, the focusing capacity of the feedback-based approach is strongly conditioned by the number of effectively resolvable optical modes (speckles). In this letter, we experimentally tested the light intensity enhancement achieved with optoacoustic feedback measurements from different sizes of absorbing microparticles. The importance of the obtained results is discussed in the context of potential signal enhancement at deep locations within a scattering medium where the effective speckle sizes approach the minimum values dictated by optical diffraction

Two-Source Condensers with Low Error and Small Entropy Gap via Entropy-Resilient Functions

In their seminal work, Chattopadhyay and Zuckerman (STOC\u2716) constructed a two-source extractor with error epsilon for n-bit sources having min-entropy {polylog}(n/epsilon). Unfortunately, the construction\u27s running-time is {poly}(n/epsilon), which means that with polynomial-time constructions, only polynomially-small errors are possible. Our main result is a {poly}(n,log(1/epsilon))-time computable two-source condenser. For any k >= {polylog}(n/epsilon), our condenser transforms two independent (n,k)-sources to a distribution over m = k-O(log(1/epsilon)) bits that is epsilon-close to having min-entropy m - o(log(1/epsilon)). Hence, achieving entropy gap of o(log(1/epsilon)). The bottleneck for obtaining low error in recent constructions of two-source extractors lies in the use of resilient functions. Informally, this is a function that receives input bits from r players with the property that the function\u27s output has small bias even if a bounded number of corrupted players feed adversarial inputs after seeing the inputs of the other players. The drawback of using resilient functions is that the error cannot be smaller than ln r/r. This, in return, forces the running time of the construction to be polynomial in 1/epsilon. A key component in our construction is a variant of resilient functions which we call entropy-resilient functions. This variant can be seen as playing the above game for several rounds, each round outputting one bit. The goal of the corrupted players is to reduce, with as high probability as they can, the min-entropy accumulated throughout the rounds. We show that while the bias decreases only polynomially with the number of players in a one-round game, their success probability decreases exponentially in the entropy gap they are attempting to incur in a repeated game

Ben Bohane's portrayal of spirit and war in Melanesia

As a photojournalist, writer and producer of television documentaries, Ben Bohane has spent the past 12 years posting stories about life on the islands of Melanesia to the Western media—illuminating the struggles and the spirit worlds behind the news. Melanesia is as close to Australia as a 150km cruise from the tip of Cape York across the Torres Strait to Papua New Guinea, connecting Australasia to the rest of Oceania and Asia. Until recently, though, these islands have seemed distantly removed from Australia and New Zealand’s notion of its international community