Risk and Probability Premiums for CARA Utility Functions

The risk premium and the probability premium are used to determine appropriate coefficients of absolute risk aversion under CARA utility. A defensible range of risk-aversion coefficients is defined by the coefficients that correspond to risk premiums falling between 1 and 99% of the amount at risk or to probability premiums falling between .005 and ,49 for a lottery that pays or loses a given sum. The consequences of ignoring risk premiums when selecting risk-aversion coefficients for representative decision makers are illustrated by calculation of the implied risk premium associated with the levels of absolute risk aversion assumed in six selected studies

A sub-cm micromachined electron microscope

A new approach for fabricating macroscopic (approximately 10x10x10 mm(exp 3)) structures with micron accuracy has been developed. This approach combines the precision of semiconductor processing and fiber optic technologies. A (100) silicon wafer is anisotropically etched to create four orthogonal v-grooves and an aperture on each 10x12 mm die. Precision 308 micron optical fibers are sandwiched between the die to align the v-grooves. The fiber is then anodically bonded to the die above and below it. This procedure is repeated to create thick structures and a stack of 5 or 6 die will be used to create a miniature scanning electron microscope (MSEM). Two die in the structure will have a segmented electrode to deflect the beam and correct for astigmatism. The entire structure is UHV compatible. The performance of an SEM improves as its length is reduced and a sub-cm 2 keV MSEM with a field emission source should have approximately 1 nm resolution. A low voltage high resolution MSEM would be useful for the examination of biological specimens and semiconductors with a minimum of damage. The first MSEM will be tested with existing 6 micron thermionic sources. In the future a micromachined field emission source will be used. The stacking technology presented in this paper can produce an array of MSEMs 1 to 30 mm in length with a 1 mm or larger period. A key question being addressed by this research is the optimum size for a low voltage MSEM which will be determined by the required spatial resolution, field of view, and working distance

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

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

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

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

Single-cell quantification of IL-2 response by effector and regulatory T cells reveals critical plasticity in immune response

The sensitivity of T cells to interleukin-2 (IL-2) can vary by three orders of magnitude and is determined by the surface densities of the IL-2 receptor α subunits.Regulatory T cells inflict a double hit on effector T cells by lowering the bulk IL-2 concentration as well as the sensitivity of effector T cells to this crucial cytokine.This double hit deprives weakly activated effector T cells of pSTAT5 survival signals while having only minimal effects on strongly activated effector cells that express increased levels of the IL-2 receptor.Short-term signaling differences lead to a differential functional in terms of proliferation and cell division: regulatory T cell specifically suppress weakly activated effector T cells even at large numbers; small numbers of strongly activated effector T cells overcome the suppression

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

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