Parameter-independent Iterative Approximate Byzantine Consensus

In this work, we explore iterative approximate Byzantine consensus algorithms that do not make explicit use of the global parameter of the graph, i.e., the upper-bound on the number of faults, f

2-D PSTD simulation of optical phase conjugation for turbidity suppression

Turbidity Suppression via Optical Phase Conjugation (TS-OPC) is an optical phenomenon that uses the back propagation nature of optical phase conjugate light field to undo the effect of tissue scattering. We use the computationally efficient and accurate pseudospectral time-domain (PSTD) simulation method to study this phenomenon; a key adaptation is the volumetric inversion of the optical wavefront E-field as a means for simulating a phase conjugate mirror. We simulate a number of scenarios and demonstrate that TS-OPC deteriorates with increased scattering in the medium, or increased mismatch between the random medium and the phase conjugate wave during reconstruction

Orbifold cup products and ring structures on Hochschild cohomologies

In this paper we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study the relation between this product and an $S^1$-equivariant version of the Chen--Ruan product. In particular, we give a de Rham model for this equivariant orbifold cohomology

Exact Byzantine Consensus on Arbitrary Directed Graphs Under Local Broadcast Model

We consider Byzantine consensus in a synchronous system where nodes are connected by a network modeled as a directed graph, i.e., communication links between neighboring nodes are not necessarily bi-directional. The directed graph model is motivated by wireless networks wherein asymmetric communication links can occur. In the classical point-to-point communication model, a message sent on a communication link is private between the two nodes on the link. This allows a Byzantine faulty node to equivocate, i.e., send inconsistent information to its neighbors. This paper considers the local broadcast model of communication, wherein transmission by a node is received identically by all of its outgoing neighbors, effectively depriving the faulty nodes of the ability to equivocate. Prior work has obtained sufficient and necessary conditions on undirected graphs to be able to achieve Byzantine consensus under the local broadcast model. In this paper, we obtain tight conditions on directed graphs to be able to achieve Byzantine consensus with binary inputs under the local broadcast model. The results obtained in the paper provide insights into the trade-off between directionality of communication links and the ability to achieve consensus

High Input Impedance Voltage-Mode Universal Biquadratic Filters With Three Inputs Using Three CCs and Grounding Capacitors

Two current conveyors (CCs) based high input impedance voltage-mode universal biquadratic filters each with three input terminals and one output terminal are presented. The first circuit is composed of three differential voltage current conveyors (DVCCs), two grounded capacitors and four resistors. The second circuit is composed of two DVCCs, one differential difference current conveyor (DDCC), two grounded capacitors and four grounded resistors. The proposed circuits can realize all the standard filter functions, namely, lowpass, bandpass, highpass, notch and allpass filters by the selections of different input voltage terminals. The proposed circuits offer the features of high input impedance, using only grounded capacitors and low active and passive sensitivities. Moreover, the x ports of the DVCCs (or DDCC) in the proposed circuits are connected directly to resistors. This design offers the feature of a direct incorporation of the parasitic resistance at the x terminal of the DVCC (DDCC), Rx, as a part of the main resistance