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The projected number of Internet of Things (IoT) sensors makes battery maintenance a challenging task. Although battery-less IoT is technologically viable, the sensors should be somehow energized, either locally or remotely. Unmanned aerial vehicles (UAVs) can respond to this quest via wireless power transfer (WPT). However, to achieve energy neutrality across the IoT networks and thus mitigate the maintenance issues, the UAVs providing energy and connectivity to IoT sensors must be supplied by recharging stations having multi-source energy harvesting (EH) capability. Yet, as these sensors rely solely on UAV-transferred power, the absence of UAVs causes sensor outages and hence loss of coverage when they visit recharging stations for battery replenishment. Hence, besides the UAV parameters (e.g., battery size and velocity), recharging duration and station density must be carefully determined to avoid these outages. To address that, this paper uses stochastic geometry to derive the coverage probability of UAV-powered sensors. Our analysis sheds light on the fundamental trade-offs and design guidelines for energy-neutral IoT networks with recharging stations in regard to the regulatory organization limitations, practical rectenna and UAV models, and the minimum power requirements of sensors., Comment: 7 pages, 5 figures, IEEE ICC'23

The reconstruction of spectral function from correlation function in Euclidean space is a challenging task. In this paper, we employ the Machine Learning techniques in terms of the radial basis functions networks to reconstruct the spectral function from a finite number of correlation data. To test our method, we first generate one type of correlation data using a mock spectral function by mixing several Breit-Wigner propagators. We found that compared with other traditional methods, TSVD, Tikhonov, and MEM, our approach gives a continuous and unified reconstruction for both positive definite and negative spectral function, which is especially useful for studying the QCD phase transition. Moreover, our approach has considerably better performance in the low frequency region. This has advantages for the extraction of transport coefficients which are related to the zero frequency limit of the spectral function. With the mock data generated through a model spectral function of stress energy tensor, we find our method gives a precise and stable extraction of the transport coefficients., Comment: 10 pages, 7 figures

A neutral network is a subgraph of a Hamming graph, and its principal eigenvalue determines its robustness: the ability of a population evolving on it to withstand errors. Here we consider the most robust small neutral networks: the graphs that interpolate pointwise between hypercube graphs of consecutive dimension (the point, line, line and point in the square, square, square and point in the cube, and so on). We prove that the principal eigenvalue of the adjacency matrix of these graphs is bounded by the logarithm of the number of vertices, and we conjecture an analogous result for Hamming graphs of alphabet size greater than two.

The growing demand for data has driven the Service Providers (SPs) to provide differential treatment of traffic to generate additional revenue streams from Content Providers (CPs). While SPs currently only provide best-effort services to their CPs, it is plausible to envision a model in near future, where CPs are willing to sponsor quality of service for their content in exchange of sharing a portion of their profit with SPs. This quality sponsoring becomes invaluable especially when the available resources are scarce such as in wireless networks, and can be accommodated in a non-neutral network. In this paper, we consider the problem of Quality-Sponsored Data (QSD) in a non-neutral network. In our model, SPs allow CPs to sponsor a portion of their resources, and price it appropriately to maximize their payoff. The payoff of the SP depends on the monetary revenue and the satisfaction of end-users both for the non-sponsored and sponsored content, while CPs generate revenue through advertisement. We analyze the market dynamics and equilibria in two different frameworks, i.e. sequential and bargaining game frameworks, and provide strategies for (i) SPs: to determine if and how to price resources, and (ii) CPs: to determine if and what quality to sponsor. The frameworks characterize different sets of equilibrium strategies and market outcomes depending on the parameters of the market., Comment: Submitted to IEEE/ACM Transaction on Networking

Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the same set. By linking every pair of genotypes that are mutually accessible through mutation, genotypes organize themselves into neutral networks (NN). These networks are known to be heterogeneous and assortative, and these properties affect the evolutionary dynamics of the population. By studying the dynamics of populations on NN with arbitrary topology we analyze the effect of assortativity, of NN (phenotype) fitness, and of network size. We find that the probability that the population leaves the network is smaller the longer the time spent on it. This progressive "phenotypic entrapment" entails a systematic increase in the overdispersion of the process with time and an acceleration in the fixation rate of neutral mutations. We also quantify the variation of these effects with the size of the phenotype and with its fitness relative to that of neighbouring alternatives., Comment: 31 pages, 4 figures

In this paper we present a novel framework for sequence to shape maps. These combinatorial maps realize exponentially many shapes, and have preimages which contain extended connected subgraphs of diameter n (neutral networks). We prove that all basic properties of RNA folding maps also hold for combinatorial maps. Our construction is as follows: suppose we are given a graph $H$ over the $\{1 >...,n\}$ and an alphabet of nucleotides together with a symmetric relation $\mathcal{R}$, implied by base pairing rules. Then the shape of a sequence of length n is the maximal H subgraph in which all pairs of nucleotides incident to H-edges satisfy $\mathcal{R}$. Our main result is to prove the existence of at least $\sqrt{2}^{n-1}$ shapes with extended neutral networks, i.e. shapes that have a preimage with diameter $n$ and a connected component of size at least $(\frac{1+\sqrt{5}}{2})^n+(\frac{1-\sqrt{5}}{2})^n$. Furthermore, we show that there exists a certain subset of shapes which carries a natural graph structure. In this graph any two shapes are connected by a path of shapes with respective neutral networks of distance one. We finally discuss our results and provide a comparison with RNA folding maps., Comment: 24 pages,4 figures

Our understanding of the evolutionary process has gone a long way since the publication, 150 years ago, of "On the origin of species" by Charles R. Darwin. The XXth Century witnessed great efforts to embrace replication, mutation, and selection within the framework of a formal theory, able eventually to predict the dynamics and fate of evolving populations. However, a large body of empirical evidence collected over the last decades strongly suggests that some of the assumptions of those classical models necessitate a deep revision. The viability of organisms is not dependent on a unique and optimal genotype. The discovery of huge sets of genotypes (or neutral networks) yielding the same phenotype --in the last term the same organism--, reveals that, most likely, very different functional solutions can be found, accessed and fixed in a population through a low-cost exploration of the space of genomes. The 'evolution behind the curtain' may be the answer to some of the current puzzles that evolutionary theory faces, like the fast speciation process that is observed in the fossil record after very long stasis periods., Comment: 7 pages, 7 color figures, uses a modification of pnastwo.cls called pnastwo-modified.cls (included)

RNA secondary structure is an important computational model to understand how genetic variation maps into phenotypic (structural) variation. Evolutionary innovation in RNA structures is facilitated by neutral networks, large connected sets of RNA sequences that fold into the same structure. Our work extends and deepens previous studies on neutral networks. First, we show that even the 1-mutant neighborhood of a given sequence (genotype) G0 with structure (phenotype) P contains many structural variants that are not close to P. This holds for biological and generic RNA sequences alike. Second, we analyze the relation between new structures in the 1-neighborhoods of genotypes Gk that are only a moderate Hamming distance k away from G0, and the structure of G0 itself, both for biological and for generic RNA structures. Third, we analyze the relation between mutational robustness of a sequence and the distances of structural variants near this sequence. Our findings underscore the role of neutral networks in evolutionary innovation, and the role that high robustness can play in diminishing the potential for such innovation., Comment: to be published in Biosystems

VEGAS (Varying Evolvability-Guided Adaptive Search) is a new methodology proposed to deal with the neutrality property of some optimization problems. ts main feature is to consider the whole neutral network rather than an arbitrary solution. Moreover, VEGAS is designed to escape from plateaus based on the evolvability of solution and a multi-armed bandit. Experiments are conducted on NK-landscapes with neutrality. Results show the importance of considering the whole neutral network and of guiding the search cleverly. The impact of the level of neutrality and of the exploration-exploitation trade-off are deeply analyzed., Comment: Genetic And Evolutionary Computation Conference, Dublin : Ireland (2011)

We study the relative importance of "top-speed" (long-term growth rate) and "acceleration" (how quickly the long-term growth rate can be reached) in the evolutionary race to increase population size. We observe that fitness alone does not capture growth rate: robustness, a property of neutral network shape, combines with fitness to include the effect of deleterious mutations, giving growth rate. Similarly, we show that growth rate alone does not capture population size: regularity, a different property of neutral network shape, combines with growth rate to include the effect of higher depletion rates early on, giving size. Whereas robustness is a function of the principal eigenvalue of the neutral network adjacency matrix, regularity is a function of the principal eigenvector. We show that robustness is not correlated with regularity, and observe in silico the selection for regularity by evolving RNA ribozymes. Despite having smaller growth rates, the more regular ribozymes have the biggest populations.

Hahn and Wallsten wrote that network neutrality "usually means that broadband service providers charge consumers only once for Internet access, do not favor one content provider over another, and do not charge content providers for sending information over broadband lines to end users." In this paper we study the implications of non-neutral behaviors under a simple model of linear demand-response to usage-based prices. We take into account advertising revenues and consider both cooperative and non-cooperative scenarios. In particular, we model the impact of side-payments between service and content providers. We also consider the effect of service discrimination by access providers, as well as an extension of our model to non-monopolistic content providers.

We study the dynamics of a population subject to selective pressures, evolving either on RNA neutral networks or in toy fitness landscapes. We discuss the spread and the neutrality of the population in the steady state. Different limits arise depending on whether selection or random drift are dominant. In the presence of strong drift we show that observables depend mainly on $M \mu$, $M$ being the population size and $\mu$ the mutation rate, while corrections to this scaling go as 1/M: such corrections can be quite large in the presence of selection if there are barriers in the fitness landscape. Also we find that the convergence to the large $M \mu$ limit is linear in $1/M \mu$. Finally we introduce a protocol that minimizes drift; then observables scale like 1/M rather than $1/(M\mu)$, allowing one to determine the large $M$ limit faster when $\mu$ is small; furthermore the genotypic diversity increases from $O(\ln M)$ to $O(M)$., Comment: 25 Pages, replaced with revised version,submitted to J Stat

Protein structures are much more conserved than sequences during evolution. Based on this observation, we investigate the consequences of structural conservation on protein evolution. We study seven of the most studied protein folds, finding out that an extended neutral network in sequence space is associated to each of them. Within our model, neutral evolution leads to a non-Poissonian substitution process, due to the broad distribution of connectivities in neutral networks. The observation that the substitution process has non-Poissonian statistics has been used against the original Kimura's neutral theory, while our model shows that this is a generic property of neutral evolution with structural conservation. Our model also predicts that the substitution rate can strongly fluctuate from one branch to another of the evolutionary tree. The average sequence similarity within a neutral network is close to the threshold of randomness, as observed for families of sequences sharing the same fold. Nevertheless, some positions are more difficult to mutate than others. We compare such structurally conserved positions to positions conserved in protein evolution, suggesting that our model can be a valuable tool to distinguish structural from functional conservation in databases of protein families. These results indicate that a synergy between database analysis and structurally-based computational studies can increase our understanding of protein evolution., Comment: 15 pages, 8 figures, revised

The problem of controlling higher-order interactions in neural networks is addressed with techniques commonly applied in the cluster analysis of quantum many-particle systems. For multi-neuron synaptic weights chosen according to a straightforward extension of the standard Hebbian learning rule, we show that higher-order contributions to the stimulus felt by a given neuron can be readily evaluated via Poly\`a's combinatoric group-theoretical approach or equivalently by exploiting a precise formal analogy with fermion diagrammatics., Comment: 11 pages, 1 figure

We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation takes place as regions with more advantageous distributions of neutral genotypes are discovered. Since these discoveries are typically rare events, the population dynamics can be subdivided into separate epochs, with rapid transitions between them. Within one epoch, the average fitness in the population is approximately constant. The transitions between epochs, however, are generally accompanied by a significant increase in the average fitness. We verify our theoretical considerations with two analytically tractable bitstring models., Comment: 16 pages, 4 eps figures, Latex (academic press style file), submitted to the Bulletin of Mathematical Biology

We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure $s$). By interpreting the secondary structure as biological information we can formulate the so called Error Threshold of Shapes as an extension of Eigen's et al. concept of an error threshold in the single peak landscape. Analogue to the approach of Derrida & Peliti for a of the population on the neutral network. On the one hand this model of a single shape landscape allows the derivation of analytical results, on the other hand the concept gives rise to study various scenarios by means of simulations, e.g. the interaction of two different networks. It turns out that the intersection of two sets of compatible sequences (with respect to the pair of secondary structures) plays a key role in the search for ''fitter'' secondary structures., Comment: 20 pages, uuencoded compressed postscript-file, Proc. of ECAL '95 conference, to appear., email: chris @ imb-jena.de