Most wireless communication networks are two-way, where nodes act as both sources and destinations of messages. This allows for "adaptation" at or "interaction" between the nodes -a node's channel inputs may be functions of its message(s) and previously received signals, in contrast to feedback-free one-way channels where inputs are functions of messages only. How to best adapt, or cooperate, is key to two-way communication, rendering it complex and challenging. However, examples exist of channels where adaptation is not beneficial from a capacity perspective; it is known that for the point-to-point two-way modulo 2 adder and Gaussian channels, adaptation does not increase capacity. We ask whether analogous results hold for several multi-user two-way networks.We first consider deterministic two-way channel models: the binary modulo-2 addition channel and a generalization of this, and the linear deterministic channel which models Gaussian channels at high SNR. For these deterministic models we obtain the capacity region for the two-way multiple access/broadcast channel, the two-way Z channel and the two-way interference channel (under certain "partial" adaptation constraints in some regimes). We permit all nodes to adapt their channel inputs to past outputs (except for portions of the linear high-SNR two-way interference channel where we only permit 2 of the 4 nodes to fully adapt). However, we show that this adaptation is useless from a capacity region perspective. That is, the two-way fully or partially adaptive capacity region consists of two parallel "one-way" regions operating simultaneously in opposite directions, achieved by strategies where the channel inputs at each use do not adapt to previous inputs. We next consider two noisy channel models: first, the Gaussian two-way MAC/BC, where we show that adaptation can at most increase the sum-rate by 1 2 bit in each direction. Next, for the two-way interference channel, partial adaptation is shown to be useless when the interference is very strong. In the strong and weak interference regimes, we show that the non-adaptive Han and Kobayashi scheme utilized in parallel in both directions achieves to within a constant gap for the symmetric rate of the fully (for some regimes) or partially (for the remaining regimes) adaptive models. The central technical contribution is the derivation of new, computable outer bounds which allow for adaptation. Inner bounds follow from known, non-adaptive achievability schemes of the corresponding one-way channel models.I. INTRODUCTION Two-way communication, where users A and B wish to exchange a stream of information, is a natural form of communication of relevance in present and future wireless networks. Applications include twoway high data-rate tele-medicine over wireless broadband links, mobile video conferencing over next generation cellular networks, the synchronization of data among terminals, and communication between a base station and clients. Indeed, much of our current wireless communication is already two-wa...

In a full-duplex bi-directional interference network with 2K transceivers, there are K communication pairs: each user transmits a message to and receives a message from one intended user and interferes with and experiences interference from all other users. All nodes may interact, or adapt inputs to past received signals, and may thus cooperate with each other. We derive a new outer bound, and use interference alignment to demonstrate that the optimal degrees of freedom (DoF, also known as the multiplexing gain) is K: full-duplex operation doubles the DoF, but interaction and cooperation does not further increase the DoF. We next characterize the DoF of a full-duplex bi-directional interference network with a MIMO, full-duplex relay. If the relay is non-causal/instantaneous (at time k forwards a function of its received signals up to time k) and has 2K antennas, we demonstrate a one-shot scheme where the relay mitigates all interference to achieve the interference-free 2K DoF. In contrast, if the relay is causal (at time k forwards a function of its received signals up to time k − 1), we show that a fullduplex MIMO relay cannot increase the DoF of the full-duplex bi-directional interference network beyond K, as if no relay or interaction is present.

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In two-way channels nodes are both sources and destinations of messages, allowing them to "adapt" or "interact" in the sense that their next channel input may be a function of their past received signals. This "adaptation" and how to best exploit it lies at the heart of two-way communication problems, rendering them particularly complex and challenging. It would be useful to know when adaptation is not beneficial from a capacity perspective. Certain examples exist: it is known that for the pointto-point two-way modulo 2 adder channel, and the point-to-point Gaussian two-way channel, adaptation does not increase capacity. In this work we show that the same is true for certain classes of deterministic multi-user two-way channels. In particular, we consider a class of multi-user two-way modulo 2 adder channels, which include the two-way modulo 2 adder MAC/BC channel, the two-way modulo 2 adder interference channel, and the twoway modulo 2 adder Z channel. For all three channel models we obtain the capacity region, which may be achieved using simple time-sharing.

iCn3D was initially developed as a web-based 3D molecular viewer. It then evolved from visualization into a full-featured interactive structural analysis software. It became a collaborative research instrument through the sharing of permanent, shortened URLs that encapsulate not only annotated visual molecular scenes, but also all underlying data and analysis scripts in a FAIR manner. More recently, with the growth of structural databases, the need to analyze large structural datasets systematically led us to use Python scripts and convert the code to be used in Node. js scripts. We showed a few examples of Python scripts at https://github.com/ncbi/icn3d/tree/master/icn3dpython to export secondary structures or PNG images from iCn3D. Users just need to replace the URL in the Python scripts to export other annotations from iCn3D. Furthermore, any interactive iCn3D feature can be converted into a Node. js script to be run in batch mode, enabling an interactive analysis performed on one or a handful of protein complexes to be scaled up to analysis features of large ensembles of structures. Currently available Node. js analysis scripts examples are available at https://github.com/ncbi/icn3d/tree/master/icn3dnode. This development will enable ensemble analyses on growing structural databases such as AlphaFold or RoseTTAFold on one hand and Electron Microscopy on the other. In this paper, we also review new features such as DelPhi electrostatic potential, 3D view of mutations, alignment of multiple chains, assembly of multiple structures by realignment, dynamic symmetry calculation, 2D cartoons at different levels, interactive contact maps, and use of iCn3D in Jupyter Notebook as described at https://pypi.org/project/icn3dpy.