We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D 5 del Pezzo surfaces and the occurrence of free Z 2 quotients that lead to a new class of heterotic duals. 1

We characterize the capacity of Rayleigh blockfading multiple-input multiple-output (MIMO) channels in the noncoherent setting where transmitter and receiver have no a priori knowledge of the realizations of the fading channel. We prove that unitary space-time modulation (USTM) is not capacity-achieving in the high signal-to-noise ratio (SNR) regime when the total number of antennas exceeds the coherence time of the fading channel (expressed in multiples of the symbol duration), a situation that is relevant for MIMO systems with large antenna arrays (large-MIMO systems). This result settles a conjecture by Zheng & Tse (2002) in the affirmative. The capacity-achieving input signal, which we refer to as Beta-variate space-time modulation (BSTM), turns out to be the product of a unitary isotropically distributed random matrix, and a diagonal matrix whose nonzero entries are distributed as the square-root of the eigenvalues of a Beta-distributed random matrix of appropriate size. Numerical results illustrate that using BSTM instead of USTM in large-MIMO systems yields a rate gain as large as 13% for SNR values of practical interest.Here, ρ denotes the SNR, M * min{M, N, ⌊T /2⌋} with M and N standing for the number of transmit and receive antennas, respectively, and O(1) indicates a bounded function of ρ (for sufficiently large ρ). The high-SNR capacity expression given in (1) is insightful as it allows one to determine the capacity loss (at high SNR) due to lack of a priori channel knowledge. Recalling that in the coherent case C coh (ρ) = min{M, N } log(ρ) + O(1), ρ → ∞ one sees that this loss is pronounced when the channel's coherence time T is small. The capacity expression (1) also implies that, for a given coherence time T and number of receive antennas N , the capacity pre-log (i.e., the asymptotic ratio between the capacity in (1) and log(ρ) as ρ → ∞) is maximized by using M = min{N, ⌊T /2⌋} transmit antennas. 2 When T ≥ M + N (channel's coherence time larger or equal to the total number of antennas) the high-SNR expression (1) can be tightened as follows [4, Sec. IV.B]:Here, c, which is given in [4, Eq. (24)], depends on T , M , and N but not on ρ, and o(1) → 0 as ρ → ∞. Differently from (1), the high-SNR expression (2) describes capacity accurately already at moderate SNR values [11], because it captures the first two terms in the asymptotic expansion of C(ρ) for ρ → ∞. The key element exploited in [4] to establish (2) is the optimality of isotropically distributed unitary input signals [3, Sec. A.2] at high SNR. The isotropic unitary input distribution is often referred to as unitary space-time modulation (USTM) [12], [9], [13]. Capacity-approaching coding schemes that are based on 1 When T = 1, capacity grows double-logarithmically in ρ [10, Thm. 4.2]. 2 More generally, for fixed T and N , and for arbitrary SNR, the capacity for M > T is equal to the capacity for M = T [3, Thm. 1].

Interference alignment in the K-user MIMO interference channel with constant channel coefficients is considered. A novel constructive method for finding the interference alignment solution is proposed for the case where the number of transmit antennas equals the number of receive antennas (NT = NR = N ), the number of transmitter-receiver pairs equals K = N + 1, and all interference alignment multiplexing gains are one. The core of the method consists of solving an eigenvalue problem that incorporates the channel matrices of all interfering links. This procedure provides insight into the feasibility of signal vector spaces alignment schemes in finite dimensional MIMO interference channels.

We propose a Bayesian method for distributed sequential localization of mobile networks composed of both cooperative agents and noncooperative objects. Our method provides a consistent combination of cooperative self-localization (CS) and distributed tracking (DT). Multiple mobile agents and objects are localized and tracked using measurements between agents and objects and between agents. For a distributed operation and low complexity, we combine particle-based belief propagation with a consensus or gossip scheme. High localization accuracy is achieved through a probabilistic information transfer between the CS and DT parts of the underlying factor graph. Simulation results demonstrate significant improvements in both agent selflocalization and object localization performance compared to separate CS and DT, and very good scaling properties with respect to the numbers of agents and objects.

Abstract-We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixedpoint equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard constraints in the part of the factor graph corresponding to belief propagation. Finally, we demonstrate an application of our method to iterative channel estimation and decoding in an OFDM system.