Diversity Backpressure Scheduling and Routing with Mutual Information Accumulation in Wireless Ad-hoc Networks

We suggest and analyze algorithms for routing in multi-hop wireless ad-hoc networks that exploit mutual information accumulation as the physical layer transmission scheme, and are capable of routing multiple packet streams (commodities) when only the average channel state information is present and that only locally. The proposed algorithms are modifications of the Diversity Backpressure (DIVBAR) algorithm, under which the packet whose commodity has the largest "backpressure metric" is chosen to be transmitted and is forwarded through the link with the largest differential backlog (queue length). In contrast to traditional DIVBAR, each receiving node stores and accumulates the partially received packet in a separate "partial packet queue", thus increasing the probability of successful reception during a later possible retransmission. We present two variants of the algorithm: DIVBAR-RMIA, under which all the receiving nodes clear the received partial information of a packet once one or more receiving nodes firstly decode the packet; and DIVBAR-MIA, under which all the receiving nodes retain the partial information of a packet until the packet has reached its destination. We characterize the network capacity region with RMIA and prove that (under certain mild conditions) it is strictly larger than the network capacity region with the repetition (REP) transmission scheme that is used by the traditional DIVBAR. We also prove that DIVBAR-RMIA is throughput-optimum among the polices with RMIA, i.e., it achieves the network capacity region with RMIA, which in turn demonstrates that DIVBAR-RMIA outperforms traditional DIVBAR on the achievable throughput. Moreover, we prove that DIVBAR-MIA performs at least as well as DIVBAR-RMIA with respect to throughput. Simulations also confirm these results.Comment: 56 pages, 6 figure

Holographic entanglement entropy and the internal space

We elaborate on the role of extremal surfaces probing the internal space in AdS/CFT. Extremal surfaces in AdS quantify the "geometric" entanglement between different regions in physical space for the dual CFT. This, however, is just one of many ways to split a given system into subsectors, and extremal surfaces in the internal space should similarly quantify entanglement between subsectors of the theory. For the case of AdS$_5\times$S$^5$, their area was interpreted as entanglement entropy between U(n) and U(m) subsectors of U(n+m) N=4 SYM. Making this proposal precise is subtle for a number of reasons, the most obvious being that from the bulk one usually has access to gauge-invariant quantities only, while a split into subgroups is inherently gauge variant. We study N=4 SYM on the Coulomb branch, where some of the issues can be mitigated and the proposal can be sharpened. Continuing back to the original AdS$_5\times$S$^5$ geometry, we obtain a modified proposal, based on the relation of the internal space to the R-symmetry group.Comment: 11 pages, 6 figures; to appear in PR

Chemical bond and entanglement of electrons in the hydrogen molecule

We theoretically investigate the quantum correlations (in terms of concurrence of indistinguishable electrons) in a prototype molecular system (hydrogen molecule). With the assistance of the standard approximations of the linear combination of atomic orbitals and the configuration interaction methods we describe the electronic wavefunction of the ground state of the H2 molecule. Moreover, we managed to find a rather simple analytic expression for the concurrence (the most used measure of quantum entanglement) of the two electrons when the molecule is in its lowest energy. We have found that concurrence does not really show any relation to the construction of the chemical bond.Comment: 4 figures, 11 page

Calabi-Yau manifolds realizing symplectically rigid monodromy tuples

We define an iterative construction that produces a family of elliptically fibered Calabi-Yau $n$-folds with section from a family of elliptic Calabi-Yau varieties of one dimension lower. Parallel to the geometric construction, we iteratively obtain for each family with a point of maximal unipotent monodromy, normalized to be at t=0, its Picard-Fuchs operator and a closed-form expression for the period holomorphic at t=0, through a generalization of the classical Euler transform for hypergeometric functions. In particular, our construction yields one-parameter families of elliptically fibered Calabi-Yau manifolds with section whose Picard-Fuchs operators realize all symplectically rigid Calabi-Yau differential operators with three regular singular points classified by Bogner and Reiter, but also non-rigid operators with four singular points.Comment: 65 page

Orthogonal colorings of the sphere

An orthogonal coloring of the two-dimensional unit sphere $\mathbb{S}^2$, is a partition of $\mathbb{S}^2$ into parts such that no part contains a pair of orthogonal points, that is, a pair of points at spherical distance $\pi/2$ apart. It is a well-known result that an orthogonal coloring of $\mathbb{S}^2$ requires at least four parts, and orthogonal colorings with exactly four parts can easily be constructed from a regular octahedron centered at the origin. An intriguing question is whether or not every orthogonal 4-coloring of $\mathbb{S}^2$ is such an octahedral coloring. In this paper we address this question and show that if every color class has a non-empty interior, then the coloring is octahedral. Some related results are also given

Static and dynamic properties of Josephson weak links with singlet and triplet coupling

We theoretically study static and dynamic properties of short Josephson junctions (JJ) with singlet and triplet Josephson coupling. In singlet Josephson weak links, two singlet superconductors S are connected with each other by a normal film (N) or wire. Triplet JJs, which we denote S$_{\text{m}}$/N(F)/S$_{\text{m}}$, are formed by two singlet BCS superconductors covered by a thin layer of a weak ferromagnet F$_{\text{w}}$. These superconductors S$_{\text{m}}$ are separated from the N (or F) layer by spin filters, which pass electrons with only one spin orientation. The triplet Cooper pairs propagating from the left (right) superconductors S$_{\text{m}}$ differ from each other not only by polarizations, but also by chiralities. The latter is determined by the magnetization orientation in weak ferromagnets F$_{\text{w}}$. We obtain analytical formulas for the critical Josephson current in both types of the JJs. If chiralities of the triplet Cooper pairs penetrating into the N film in S$_{\text{m}}$/N(F)/S$_{\text{m}}$ JJs from the left and right S$_{\text{m}}$ are different, the Josephson current is not zero in the absence of the phase difference (spontaneous Josephson current). We also calculate the admittance $Y(\Omega)$ for arbitrary frequencies $\Omega$ in the case of singlet JJs and for low frequencies in the case of triplet JJs. At low temperatures $T$, the real part of the admittance $Y^{\prime}(\Omega)$ in singlet JJs starts to increase from zero at ${\hbar \Omega \geq \Delta_{\text{sg}}}$, but at ${T \geq \Delta_{\text{sg}}}$, it has a peak at low frequencies the magnitude of which is determined by inelastic processes. The subgap $\Delta_{\text{sg}}$ depends on transparencies of the S/N interfaces and on the phase difference $2 \chi_{0}$. The low-frequency peak in $Y^{\prime}(\Omega)$ in triplet JJs disappears.Comment: 11+ pages; 4 figures; published versio

Colorful theorems for strong convexity

We prove two colorful Carath\'eodory theorems for strongly convex hulls, generalizing the colorful Carat\'eodory theorem for ordinary convexity by Imre B\'ar\'any, the non-colorful Carath\'eodory theorem for strongly convex hulls by the second author, and the "very colorful theorems" by the first author and others. We also investigate if the assumption of a "generating convex set" is really needed in such results and try to give a topological criterion for one convex body to be a Minkowski summand of another

Soft-Output Sphere Decoder for Multiple-Symbol Differential Detection of Impulse-Radio Ultra-Wideband

Power efficiency of noncoherent receivers for impulse-radio ultra-wideband (IR-UWB) transmission systems can significantly be improved, on the one hand, by employing multiple-symbol differential detection (MSDD), and, on the other hand, by providing reliability information to the subsequent channel decoder. In this paper, we combine these two techniques. Incorporating the computation of the soft information into a single-tree-search sphere decoder (SD), the application of this soft-output MSDD in a typical IR-UWB system imposes only a moderate complexity increase at, however, improved performance over hard-output MSDD, and in particular, over conventional symbol-by-symbol noncoherent differential detection.Comment: accepted for presentation at 2010 IEEE International Symposium on Information Theory (ISIT 2010), Austin (TX), USA, as paper #106

Microrheology of supercooled liquids in terms of a continuous time random walk

Molecular dynamics simulations of a glass-forming model system are performed under application of a microrheological perturbation on a tagged particle. The trajectory of that particle is studied in its underlying potential energy landscape. Discretization of the configuration space is achieved via a metabasin analysis. The linear and nonlinear responses of drift and diffusive behavior can be interpreted and analyzed in terms of a continuous time random walk. In this way the physical origin of linear and nonlinear response can be identified. Critical forces are determined and compared with predictions from literature

Individual Preference Aware Caching Policy Design in Wireless D2D Networks

Cache-aided wireless device-to-device (D2D) networks allow significant throughput increase, depending on the concentration of the popularity distribution of files. Many studies assume that all users have the same preference distribution; however, this may not be true in practice. This work investigates whether and how the information about individual preferences can benefit cache-aided D2D networks. We examine a clustered network and derive a network utility that considers both the user distribution and channel fading effects into the analysis. We also formulate a utility maximization problem for designing caching policies. This maximization problem can be applied to optimize several important quantities, including throughput, energy efficiency (EE), cost, and hit-rate, and to solve different tradeoff problems. We provide a general approach that can solve the proposed problem under the assumption that users coordinate, then prove that the proposed approach can obtain the stationary point under a mild assumption. Using simulations of practical setups, we show that performance can improve significantly with proper exploitation of individual preferences. We also show that different types of tradeoffs exist between different performance metrics and that they can be managed through caching policy and cooperation distance designs.Comment: Accepted by IEEE Transactions on Wireless Communication