Parallel Search with no Coordination

We consider a parallel version of a classical Bayesian search problem. $k$ agents are looking for a treasure that is placed in one of the boxes indexed by $\mathbb{N}^+$ according to a known distribution $p$. The aim is to minimize the expected time until the first agent finds it. Searchers run in parallel where at each time step each searcher can "peek" into a box. A basic family of algorithms which are inherently robust is \emph{non-coordinating} algorithms. Such algorithms act independently at each searcher, differing only by their probabilistic choices. We are interested in the price incurred by employing such algorithms when compared with the case of full coordination. We first show that there exists a non-coordination algorithm, that knowing only the relative likelihood of boxes according to $p$, has expected running time of at most $10+4(1+\frac{1}{k})^2 T$, where $T$ is the expected running time of the best fully coordinated algorithm. This result is obtained by applying a refined version of the main algorithm suggested by Fraigniaud, Korman and Rodeh in STOC'16, which was designed for the context of linear parallel search.We then describe an optimal non-coordinating algorithm for the case where the distribution $p$ is known. The running time of this algorithm is difficult to analyse in general, but we calculate it for several examples. In the case where $p$ is uniform over a finite set of boxes, then the algorithm just checks boxes uniformly at random among all non-checked boxes and is essentially $2$ times worse than the coordinating algorithm.We also show simple algorithms for Pareto distributions over $M$ boxes. That is, in the case where $p(x) \sim 1/x^b$ for $0< b < 1$, we suggest the following algorithm: at step $t$ choose uniformly from the boxes unchecked in ${1, . . . ,min(M, \lfloor t/\sigma\rfloor)}$, where $\sigma = b/(b + k - 1)$. It turns out this algorithm is asymptotically optimal, and runs about $2+b$ times worse than the case of full coordination

Evacuating Two Robots from a Disk: A Second Cut

We present an improved algorithm for the problem of evacuating two robots from the unit disk via an unknown exit on the boundary. Robots start at the center of the disk, move at unit speed, and can only communicate locally. Our algorithm improves previous results by Brandt et al. [CIAC'17] by introducing a second detour through the interior of the disk. This allows for an improved evacuation time of $5.6234$. The best known lower bound of $5.255$ was shown by Czyzowicz et al. [CIAC'15].Comment: 19 pages, 5 figures. This is the full version of the paper with the same title accepted in the 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO'19

Fast Two-Robot Disk Evacuation with Wireless Communication

In the fast evacuation problem, we study the path planning problem for two robots who want to minimize the worst-case evacuation time on the unit disk. The robots are initially placed at the center of the disk. In order to evacuate, they need to reach an unknown point, the exit, on the boundary of the disk. Once one of the robots finds the exit, it will instantaneously notify the other agent, who will make a beeline to it. The problem has been studied for robots with the same speed~\cite{s1}. We study a more general case where one robot has speed $1$ and the other has speed $s \geq 1$. We provide optimal evacuation strategies in the case that $s \geq c_{2.75} \approx 2.75$ by showing matching upper and lower bounds on the worst-case evacuation time. For $1\leq s < c_{2.75}$, we show (non-matching) upper and lower bounds on the evacuation time with a ratio less than $1.22$. Moreover, we demonstrate that a generalization of the two-robot search strategy from~\cite{s1} is outperformed by our proposed strategies for any $s \geq c_{1.71} \approx 1.71$.Comment: 18 pages, 10 figure

Rendezvous on a Line by Location-Aware Robots Despite the Presence of Byzantine Faults

A set of mobile robots is placed at points of an infinite line. The robots are equipped with GPS devices and they may communicate their positions on the line to a central authority. The collection contains an unknown subset of "spies", i.e., byzantine robots, which are indistinguishable from the non-faulty ones. The set of the non-faulty robots need to rendezvous in the shortest possible time in order to perform some task, while the byzantine robots may try to delay their rendezvous for as long as possible. The problem facing a central authority is to determine trajectories for all robots so as to minimize the time until the non-faulty robots have rendezvoused. The trajectories must be determined without knowledge of which robots are faulty. Our goal is to minimize the competitive ratio between the time required to achieve the first rendezvous of the non-faulty robots and the time required for such a rendezvous to occur under the assumption that the faulty robots are known at the start. We provide a bounded competitive ratio algorithm, where the central authority is informed only of the set of initial robot positions, without knowing which ones or how many of them are faulty. When an upper bound on the number of byzantine robots is known to the central authority, we provide algorithms with better competitive ratios. In some instances we are able to show these algorithms are optimal

Density-dependence of functional development in spiking cortical networks grown in vitro

During development, the mammalian brain differentiates into specialized regions with distinct functional abilities. While many factors contribute to functional specialization, we explore the effect of neuronal density on the development of neuronal interactions in vitro. Two types of cortical networks, dense and sparse, with 50,000 and 12,000 total cells respectively, are studied. Activation graphs that represent pairwise neuronal interactions are constructed using a competitive first response model. These graphs reveal that, during development in vitro, dense networks form activation connections earlier than sparse networks. Link entropy analysis of dense net- work activation graphs suggests that the majority of connections between electrodes are reciprocal in nature. Information theoretic measures reveal that early functional information interactions (among 3 cells) are synergetic in both dense and sparse networks. However, during later stages of development, previously synergetic relationships become primarily redundant in dense, but not in sparse networks. Large link entropy values in the activation graph are related to the domination of redundant ensembles in late stages of development in dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specialization of nervous system tissue in vivo.Comment: 10 pages, 7 figure

Networked buffering: a basic mechanism for distributed robustness in complex adaptive systems

A generic mechanism - networked buffering - is proposed for the generation of robust traits in complex systems. It requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role within a system and 2) agents are degenerate, i.e. there exists partial overlap in the functional capabilities of agents. Given these prerequisites, degenerate systems can readily produce a distributed systemic response to local perturbations. Reciprocally, excess resources related to a single function can indirectly support multiple unrelated functions within a degenerate system. In models of genome:proteome mappings for which localized decision-making and modularity of genetic functions are assumed, we verify that such distributed compensatory effects cause enhanced robustness of system traits. The conditions needed for networked buffering to occur are neither demanding nor rare, supporting the conjecture that degeneracy may fundamentally underpin distributed robustness within several biotic and abiotic systems. For instance, networked buffering offers new insights into systems engineering and planning activities that occur under high uncertainty. It may also help explain recent developments in understanding the origins of resilience within complex ecosystems. \ud \u

Stochastic Responses May Allow Genetically Diverse Cell Populations to Optimize Performance with Simpler Signaling Networks

Two theories have emerged for the role that stochasticity plays in biological responses: first, that it degrades biological responses, so the performance of biological signaling machinery could be improved by increasing molecular copy numbers of key proteins; second, that it enhances biological performance, by enabling diversification of population-level responses. Using T cell biology as an example, we demonstrate that these roles for stochastic responses are not sufficient to understand experimental observations of stochastic response in complex biological systems that utilize environmental and genetic diversity to make cooperative responses. We propose a new role for stochastic responses in biology: they enable populations to make complex responses with simpler biochemical signaling machinery than would be required in the absence of stochasticity. Thus, the evolution of stochastic responses may be linked to the evolvability of different signaling machineries.National Institutes of Health (U.S.). Pioneer Awar

Mechanistic model of natural killer cell proliferative response to IL-15 receptor stimulation

Natural killer (NK) cells are innate lymphocytes that provide early host defense against intracellular pathogens, such as viruses. Although NK cell development, homeostasis, and proliferation are regulated by IL-15, the influence of IL-15 receptor (IL-15R)-mediated signaling at the cellular level has not been quantitatively characterized. We developed a mathematical model to analyze the kinetic interactions that control the formation and localization of IL-15/IL-15R complexes. Our computational results demonstrated that IL-15/IL-15R complexes on the cell surface were a key determinant of the magnitude of the IL-15 proliferative signal and that IL-15R occupancy functioned as an effective surrogate measure of receptor signaling. Ligand binding and receptor internalization modulated IL-15R occupancy. Our work supports the hypothesis that the total number and duration of IL-15/IL-15R complexes on the cell surface crosses a quantitative threshold prior to the initiation of NK cell division. Furthermore, our model predicted that the upregulation of IL-15Rα on NK cells substantially increased IL-15R complex formation and accelerated the expansion of dividing NK cells with the greatest impact at low IL-15 concentrations. Model predictions of the threshold requirement for NK cell recruitment to the cell cycle and the subsequent exponential proliferation correlated well with experimental data. In summary, our modeling analysis provides quantitative insight into the regulation of NK cell proliferation at the receptor level and provides a framework for the development of IL-15 based immunotherapies to modulate NK cell proliferation

The cytotoxic T cell proteome and its shaping by the kinase mTOR

High-resolution mass spectrometry maps the cytotoxic T lymphocyte (CTL) proteome and the impact of mammalian target of rapamycin complex 1 (mTORC1) on CTLs. The CTL proteome was dominated by metabolic regulators and granzymes and mTORC1 selectively repressed and promoted expression of subset of CTL proteins (~10%). These included key CTL effector molecules, signaling proteins and a subset of metabolic enzymes. Proteomic data highlighted the potential for mTORC1 negative control of phosphatidylinositol (3,4,5)-trisphosphate (PtdIns(3,4,5)P(3)) production in CTL. mTORC1 was shown to repress PtdIns(3,4,5)P(3) production and to determine the mTORC2 requirement for activation of the kinase Akt. Unbiased proteomic analysis thus provides a comprehensive understanding of CTL identity and mTORC1 control of CTL function

Network Analysis of Biochemical Logic for Noise Reduction and Stability: A System of Three Coupled Enzymatic AND Gates

We develop an approach aimed at optimizing the parameters of a network of biochemical logic gates for reduction of the "analog" noise buildup. Experiments for three coupled enzymatic AND gates are reported, illustrating our procedure. Specifically, starch - one of the controlled network inputs - is converted to maltose by beta-amylase. With the use of phosphate (another controlled input), maltose phosphorylase then produces glucose. Finally, nicotinamide adenine dinucleotide (NAD+) - the third controlled input - is reduced under the action of glucose dehydrogenase to yield the optically detected signal. Network functioning is analyzed by varying selective inputs and fitting standardized few-parameters "response-surface" functions assumed for each gate. This allows a certain probe of the individual gate quality, but primarily yields information on the relative contribution of the gates to noise amplification. The derived information is then used to modify our experimental system to put it in a regime of a less noisy operation.Comment: 31 pages, PD