Trade-offs between Selection Complexity and Performance when Searching the Plane without Communication

We consider the ANTS problem [Feinerman et al.] in which a group of agents collaboratively search for a target in a two-dimensional plane. Because this problem is inspired by the behavior of biological species, we argue that in addition to studying the {\em time complexity} of solutions it is also important to study the {\em selection complexity}, a measure of how likely a given algorithmic strategy is to arise in nature due to selective pressures. In more detail, we propose a new selection complexity metric $\chi$, defined for algorithm ${\cal A}$ such that $\chi({\cal A}) = b + \log \ell$, where $b$ is the number of memory bits used by each agent and $\ell$ bounds the fineness of available probabilities (agents use probabilities of at least $1/2^\ell$). In this paper, we study the trade-off between the standard performance metric of speed-up, which measures how the expected time to find the target improves with $n$, and our new selection metric. In particular, consider $n$ agents searching for a treasure located at (unknown) distance $D$ from the origin (where $n$ is sub-exponential in $D$). For this problem, we identify $\log \log D$ as a crucial threshold for our selection complexity metric. We first prove a new upper bound that achieves a near-optimal speed-up of $(D^2/n +D) \cdot 2^{O(\ell)}$ for $\chi({\cal A}) \leq 3 \log \log D + O(1)$. In particular, for $\ell \in O(1)$, the speed-up is asymptotically optimal. By comparison, the existing results for this problem [Feinerman et al.] that achieve similar speed-up require $\chi({\cal A}) = \Omega(\log D)$. We then show that this threshold is tight by describing a lower bound showing that if $\chi({\cal A}) < \log \log D - \omega(1)$, then with high probability the target is not found within $D^{2-o(1)}$ moves per agent. Hence, there is a sizable gap to the straightforward $\Omega(D^2/n + D)$ lower bound in this setting.Comment: appears in PODC 201

Multicriteria global optimization for biocircuit design

One of the challenges in Synthetic Biology is to design circuits with increasing levels of complexity. While circuits in Biology are complex and subject to natural tradeoffs, most synthetic circuits are simple in terms of the number of regulatory regions, and have been designed to meet a single design criterion. In this contribution we introduce a multiobjective formulation for the design of biocircuits. We set up the basis for an advanced optimization tool for the modular and systematic design of biocircuits capable of handling high levels of complexity and multiple design criteria. Our methodology combines the efficiency of global Mixed Integer Nonlinear Programming solvers with multiobjective optimization techniques. Through a number of examples we show the capability of the method to generate non intuitive designs with a desired functionality setting up a priori the desired level of complexity. The presence of more than one competing objective provides a realistic design setting where every design solution represents a trade-off between different criteria. The tool can be useful to explore and identify different design principles for synthetic gene circuits

Lower Bounds for Shoreline Searching With 2 or More Robots

Searching for a line on the plane with $n$ unit speed robots is a classic online problem that dates back to the 50's, and for which competitive ratio upper bounds are known for every $n\geq 1$. In this work we improve the best lower bound known for $n=2$ robots from 1.5993 to 3. Moreover we prove that the competitive ratio is at least $\sqrt{3}$ for $n=3$ robots, and at least $1/\cos(\pi/n)$ for $n\geq 4$ robots. Our lower bounds match the best upper bounds known for $n\geq 4$, hence resolving these cases. To the best of our knowledge, these are the first lower bounds proven for the cases $n\geq 3$ of this several decades old problem.Comment: This is an updated version of the paper with the same title which will appear in the proceedings of the 23rd International Conference on Principles of Distributed Systems (OPODIS 2019) Neuchatel, Switzerland, July 17-19, 201

Quantifying the Evolutionary Self Structuring of Embodied Cognitive Networks

We outline a possible theoretical framework for the quantitative modeling of networked embodied cognitive systems. We notice that: 1) information self structuring through sensory-motor coordination does not deterministically occur in Rn vector space, a generic multivariable space, but in SE(3), the group structure of the possible motions of a body in space; 2) it happens in a stochastic open ended environment. These observations may simplify, at the price of a certain abstraction, the modeling and the design of self organization processes based on the maximization of some informational measures, such as mutual information. Furthermore, by providing closed form or computationally lighter algorithms, it may significantly reduce the computational burden of their implementation. We propose a modeling framework which aims to give new tools for the design of networks of new artificial self organizing, embodied and intelligent agents and the reverse engineering of natural ones. At this point, it represents much a theoretical conjecture and it has still to be experimentally verified whether this model will be useful in practice.

MAC Aspects of Millimeter-Wave Cellular Networks

The current demands for extremely high data rate wireless services and the spectrum scarcity at the sub-6 GHz bands are forcefully motivating the use of the millimeter-wave (mmWave) frequencies. MmWave communications are characterized by severe attenuation, sparse-scattering environment, large bandwidth, high penetration loss, beamforming with massive antenna arrays, and possible noise-limited operation. These characteristics imply a major difference with respect to legacy communication technologies, primarily designed for the sub-6 GHz bands, and are posing major design challenges on medium access control (MAC) layer. This book chapter discusses key MAC layer issues at the initial access and mobility management (e.g., synchronization, random access, and handover) as well as resource allocation (interference management, scheduling, and association). The chapter provides an integrated view on MAC layer issues for cellular networks and reviews the main challenges and trade-offs and the state-of-the-art proposals to address them

Initial Access in 5G mm-Wave Cellular Networks

The massive amounts of bandwidth available at millimeter-wave frequencies (roughly above 10 GHz) have the potential to greatly increase the capacity of fifth generation cellular wireless systems. However, to overcome the high isotropic pathloss experienced at these frequencies, high directionality will be required at both the base station and the mobile user equipment to establish sufficient link budget in wide area networks. This reliance on directionality has important implications for control layer procedures. Initial access in particular can be significantly delayed due to the need for the base station and the user to find the proper alignment for directional transmission and reception. This paper provides a survey of several recently proposed techniques for this purpose. A coverage and delay analysis is performed to compare various techniques including exhaustive and iterative search, and Context Information based algorithms. We show that the best strategy depends on the target SNR regime, and provide guidelines to characterize the optimal choice as a function of the system parameters.Comment: 6 pages, 3 figures, 3 tables, 15 references, submitted to IEEE COMMAG 201