Abstract—A Gaussian interference channel (IC) with a relay is considered. The relay is assumed to operate over an orthogonal band with respect to the underlying IC, and the overall system is referred to as IC with an out-of-band relay (IC-OBR). The system can be seen as operating over two parallel interferencelimited channels: The first is a standard Gaussian IC and the second is a Gaussian relay channel characterized by two sources and destinations communicating through the relay without direct links. We refer to the second parallel channel as OBR Channel (OBRC). The main aim of this work is to identify conditions under which optimal operation, in terms of the capacity region of the IC-OBR, entails either signal relaying and/or interference forwarding by the relay, with either a separable or non-separable use of the two parallel channels, IC and OBRC. Here “separable ” refers to transmission of independent information over the two constituent channels. For a basic model in which the OBRC consists of four orthogonal channels from sources to relay and from relay to destinations (IC-OBR Type-I), a condition is identified under which signal relaying and separable operation is optimal. This condition entails the presence of a relay-to-destinations capacity bottleneck on the OBRC and holds irrespective of the IC. When this condition is not satisfied, various scenarios, which depend on the IC channel gains, are identified in which interference forwarding and non-separable operation are necessary to achieve optimal performance. In these scenarios, the system exploits the “excess capacity ” on the OBRC via interference forwarding to drive the IC-OBR system in specific interference regimes (strong or mixed). The analysis is then turned to a more complex IC-OBR, in which the OBRC consists of only two orthogonal channels, one from sources to relay and one from relay to destinations (IC-OBR Type-II). For this channel, some capacity resuls are derived that parallel the conclusions for IC-OBR Type-I and point to the additional analytical challenges. I.

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Fig 1 is incorrect, as it is missing Part M. A corrected version is here. The publisher apologizes for the error. Fig 1. Oocytes with asynapsed chromosomes are eliminated during diplonema. (A) XO pachytene oocyte with asynapsed X chromosome (arrow). SYCP3 (green) marks chromosome axes, γH2AFX (red

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Truncated Dyson–Schwinger equations represent finite subsets of the equations of motion for Green’s functions. Solutions to these non–linear integral equations can account for non–perturbative correlations. A closed set of coupled Dyson–Schwinger equations for the propagators of gluons and ghosts in Landau gauge QCD is obtained by neglecting all contributions from irreducible 4–point correlations and by implementing the Slavnov–Taylor identities for the 3–point vertex functions. We solve this coupled set in an one–dimensional approximation which allows for an analytic infrared expansion necessary to obtain numerically stable results. This technique, which was also used in our previous solution of the gluon Dyson–Schwinger equation in the Mandelstam approximation, is here extended to solve the coupled set of integral equations for the propagators of gluons and ghosts simultaneously. In particular, the gluon propagator is shown to vanish for small spacelike momenta whereas the previoulsy neglected ghost propagator is found to be enhanced in the infrared. The running coupling of the non–perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling, αc ≃ 9.5.

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mechanisms encountered in practice, namely in which each sampling function is obtained by applying a unitary operator on its predecessor. Examples include pointwise sampling at the output of an anti-aliasing filter and magnetic resonance imaging (MRI), which correspond respectively to the translation

the group elements are data structures in a computer. Matrices are unnecessarily large structures, and part of this thesis is concerned with small and efficient representations of a large class of Coxeter groups (including most Coxeter groups that anyone ever payed any attention to.) The main contents

Accounting for those errors, the real and imaginary parts of the source impedance should be written as Nam-Jin Oh Papers [1] and [2] corrected several equations in [3]–[5] on the analysis of low-noise amplifiers. However, there are more errors in [3]–[5] that require further correction. Based on [6

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