Collaborative routing and data delivery architecture for commercial wireless sensor networks Lately, wireless sensor network applications have emerged for provision of commercial services to end users. This results in commercial deployment of sensor networks which is as an important research area due to a number of design and quality of service challenges. An important technical challenge for sensor service provision to end users is managing dynamic network conditions such as unreliability of sensor nodes and network links which results in frequent service outages. This research is aimed at addressing this challenge. It presents a novel architecture which utilizes the availability of multiple sensor networks under different administrative domains, deployed in an area such that maximum network connectivity and high service availability are ensured. The architecture incorporates modifications and enhancements at the medium access control and the routing layers of sensor nodes for the collaborative operation of sensor networks. The design is based on IEEE 802.15.4 standard and ad hoc on demand distance vector routing protocol. The proposed architecture is mathematically analyzed with regards to overheads associated with the design such as routing and communication, and techniques to minimize these overheads are recommended. Through simulations using OMNET++, we show that the proposed architecture effectively provides connectivity for disconnected nodes achieving an overall increase in throughput for all the cooperating networks. Low-rate wireless personal area networks (LR-WPANs) such as IEEE 802.15.4 typify the more generalized form of wireless sensor networks (WSNs) with their unique design space. These networks comprise small, low power, low cost, and multi-functional sensing devices working in collaboration for sensing and data delivery under robust network conditions. These features render the design of WSN challenging as compared to the conventional networks. The design requirements in WSN that have consistently been addressed by the research community are energy efficiency, scalability, and adaptability to varying network conditions such as unreliable sensor nodes and flaky communication links. The design is also influenced by the type of sensing application and its specific demands. Lately, bulk manufacturing of inexpensive sensor node hardware has resulted in commercial deployment of these networks in order to provide on-demand sensor services to end users. Analogous to the fast proliferation of cellular network services to end users owing to mass production of low-cost mobile handsets, we anticipate swift commercial deployment of sensor networks for sensor services in the near future because research efforts are now rapidly directed towards designing concurrent applications for sensor networks and technical support for commercial sensor services [1] [2] [3] [4] [5] [6] .. Various experimental or commercial sensor networks that have been deployed lately support applications like vehicle tracking, industrial surveillance, home automation, seismic activities monitoring, remote health monitoring for patients, and even wildlife tracking. Similar to the simultaneous co-existence of multiple cellular networks in the same coverage area with distinct, at times overlapping clientage, it is expected that in near future multiple sensor networks with different sensing capabilities would co-exist in the same area. This anticipated scenario opens a new research dimension concerned with the co-existence of multiple sensor networks in the same geographical area which is maintaining quality of service for commercial users in the presence of link outages and limited resources. As of now, the research efforts directed towards addressing this issue remain insufficient. This mandates the attention and focus of the scientific community to design protocols and applications for co-existing sensor networks from the perspective of performance enhancement and reliability of services [1] .. In order to minimize service outage, commercially deployed voice and data networks maintain backup links and hardware thus mitigating the effects of possible failure of primary links or hardware. Since the idea of multiple co-existing sensor networks is new, the contemporary failure resilience efforts in WSN are geared to provide similar forms of redundancy. However, such over-provisioned sensor networks remain vulnerable to unpredictable scope and gravity of failures, raising questions on the very viability of this approach. In this article, we present a collaborative routing and data communication architecture for co-existing sensor networks that aims to resolve network outage problems due to coverage holes and maintains symbiotic backup connectivity of participating networks. The architecture proposes modifications both at the medium access control (MAC) layer and the network layer of sensor nodes. MAC layer changes are required for managing traffic flows for shared channel communication while modifications in the routing protocol are necessary to maintain and collect important management information for co-existing sensor networks. We analyze the proposed design in terms of various associated overheads and show that the architecture achieves the desired objectives with an acceptable increase in overheads.. There are three basic design elements of the proposed architecture.. MAC layer design: MAC layer algorithmic changes are required to realize native and foreign-channel access by multiple WSNs. A disconnected sensor node or even a group of such sensor nodes utilize the presence of other networks' nodes in its transmission range, communicating with them using certain channels. Algorithmic modifications are proposed in association procedure that allows native and foreign channel access and scheduling of nodes of co-existing sensor networks. Routing protocol design: Algorithmic changes are incorporated in the implementation of routing protocol in order to make multiple sensor networks mutually beneficial. The idea is to give sensor nodes the provision to employ nodes of other sensor networks for route discovery and data delivery.. Overhead modeling: The proposed architecture is mathematically modeled in terms of energy overheads associated with MAC layer design and routing.. The remainder of the article is organized as follows. In Section 2, we discuss the related work. Section 3 defines the problem. In Section 4, we present comprehensive design of our proposed architecture. Section 5 presents mathematical analysis of proposed architecture in terms of various overheads. Section 6 presents simulation results using OMNET++. Finally Section 7 concludes the article. Commercial sensor networks are aimed at providing persistent and stable sensor services to the end users. However, this type of service provision is negatively affected by the uncertain network conditions like node and link failures. This results in network partitions resulting in frequent undesirable service outages or unavailability of sensed data. In a scenario where multiple sensor networks overlap within a geographical area which may or may not be under the same administrative control, these networks could be enabled to utilize mutual resources in order to ensure desired network performance and quality of service. We presented a routing and data delivery architecture for mutually beneficial collaborative operation of commercial sensor networks with IEEE 802.15.4 and AODV as the building blocks. We conclude that collaborative operation of commercial sensor networks results in ensuring connectivity of isolated nodes and is mutually beneficial for all participating networks. We plan to take up pricing issues for the proposed collaborative design as future work. The collaborative design of multiple sensor networks located in an area is a novel idea. Multi-application sensor networks and multi-channel communication, where a single WSN can switch channels for data communication, can be found in the literature. This concept forms the baseline implementation of our idea. We review the related work in this section. Multi-application WSN is a network formed by sensor nodes that are equipped with multiple sensors and different applications run over these nodes independently. The research work in this domain relates to the software design aimed at efficiently utilizing the hardware resources of a sensor node. In an earlier work [2] , we presented the guidelines to bind multiple applications over a single sensor network at run time. The idea of virtual sensor network proposes virtualization of multiple applications running over a single sensor network [3] . Yu et al. [4] support concurrent application provisioning on a sensor network with an emphasis on over-the-air programming prospects. Mottola and Picco [5] propose a programming abstraction as a mean to support multiple applications over a single sensor network. Tsetsos et al. [6] discuss network architecture for sensor-based services and develop business model for such applications. Heinzelmanet al. [7] present middleware design to support multiple applications considering various real-life application scenarios. Bhattacharya et al. [8] present utility-based multi-application allocation and deployment environment as an integrated application deployment system for sensor network applications sharing the same infrastructure. Alomar and Akbar [9] propose a routing mechanism named "Carrefour Cast" that is based on aggregated 'Route Requests' and 'Route Replies' in order to decrease routing overhead in multi application set-up in multiple gateway environments. They optimize multiple applications provisioning by proposing network layer modifications.. In IEEE 802.15.4 standard, multi-channel communication is proposed for communication over multiple channels, and we use this design at the MAC layer in our proposed architecture for communication of co-existing WSNs. Multi-channel communication is an established operational requirement in wireless ad hoc and sensor networks. Jain et al. [10] and Li et al. [11] present the idea of a dedicated control channel for negotiation of data channel access and synchronization for ad hoc networks. Ramakrishnan and Ranjan [12] present a sensor multichannelMAC protocol for WSNs in a contention-based scheme that works with one control channel and eight data channels. MC-LMAC [13] is proposed for WSNs based on dedicated control channel but the goal is to maximize throughput using coordinated transmission over multiple frequency channels by scheduled access, where each sensor node is granted a timeslot and transmits without contention. Zhou et al. [14] propose multifrequency MAC protocol for WSN viewed as one of the initial multi-channel MAC protocols designed for WSN. It is a slotted CSMA protocol where nodes contend for the medium before they transmit at the beginning of timeslot. Y-MAC [15] is another recently proposed multichannel MAC protocol designed for WSNs that is based on scheduled access. Timeslots are assigned to receivers instead of senders and potential senders for the same receiver contend for medium at the beginning of each timeslot.. Recently, some researchers have investigated the usage of multiple channels to defy the limitations of single channel MAC protocols. In this regard, Ansari et al. [16] and Liu and Wu [17] designed a multi-radio MAC protocol, running on a sensor node platform equipped with two radio transceivers. This approach is economically unsuitable for WSNs due to an increase in hardware cost, battery consumption, and design complexity. Moreover, a multi-channel MAC protocol using single radio transceiver is fairly plausible since most commercial radio devices such as CC1000 [18] and CC2420 [19] provide programmable channel selection to support multiple channel operation.

B I O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B I I O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Topological characterization of neuronal arbor morphology via sequence representation: I - motif analysis Background: The morphology of neurons offers many insights into developmental processes and signal processing. Numerous reports have focused on metrics at the level of individual branches or whole arbors; however, no studies have attempted to quantify repeated morphological patterns within neuronal trees. We introduce a novel sequential encoding of neurite branching suitable to explore topological patterns. The proposed sequence representation of binary trees is effective for quantifying the topological patterns of neuronal arbors. Motif analysis offers a measure to validate or refine models and hypotheses. It reveals that the local topological features of both axons and non-apical dendrites are similarly consistent with terminal growth-like processes despite substantially different overall size and function. In contrast, pyramidal apical dendrites exhibit a motif profile indicative of segmental growth.. The methods described here and in the following paper can generally be applied to any tree structure of sufficient complexity. Research in glia [58, 59] , brain vasculature [60] , botany [61] , rivers/watersheds, and phylogenetics are all potential targets of a sequence analysis approach. Moreover, while the topological sequence representation is powerful as it is, it also can serve as a basis on which other morphological features are added. The novel method of representing neuronal trees as sequences of bifurcations introduced in this work facilitates detection and analysis of branching patterns. Using an exclusively topological approach we show that sequence length and subsequences up to three characters long almost completely capture the local topology of neuronal axons, dendrites, and apical dendrites.. Node type distributions highlight the most substantial differences between axons and dendrites, with axons having higher proportions of terminal side-branches (C nodes). The vast majority of dendrites exhibit particularly low proportions of C nodes, but the proportion increases considerably for dendrites with greater than 40 bifurcations. Dimer and trimer motifs show much greater similarity than difference between axons and dendrites, highlighting a primarily terminal growth effect with some particular and likely complex segmental growth process occurring in axons and larger dendrites. Pyramidal neuron apical dendrites (mainly cortical), on the other hand, stand out as having a k-mer profile very similar to a basic segmental growth model with relatively small deviation from the baseline of tree shapes. Neuronal morphology is determined by a number of factors, including physical and biological constraints and requirements of axonal, dendritic, and network function. Branching topology is a complex feature of arbor morphology and is generally measured via one of several metrics: number of branches, maximum branch order (i.e. number of bifurcations between root and tip), partition asymmetry [1] , and caulescence (i.e. prominence of a main path [2] ). While these metrics have proven useful in many studies, they do not necessarily capture the detailed branching patterns of neurons. We introduce a method for representing a neuronal tree as a sequence of characters, each encoding for select features of a branch. We tested this method on a large set of neuronal reconstructions from NeuroMorpho.Org [3] . Specifically, we analyzed the branching sequences for motifs to identify patterns (subsequences) representative of arbor types (axons, dendrites, and pyramidal apical dendrites).. Branch diameter and neurite length have long been known to impact passive and active electrical propagation [4, 5] , and branching patterns can influence the order and timing of input signal integration and postsynaptic receipt [6, 7] . Ultimately it is the combination of features, including non-morphological features such as channel composition and density, which determine electrophysiological function. Moreover, arbor size and branching patterns reflect the distribution of synaptic (pre or post) targets of a neuron given metabolic and volumetric constraints [8] [9] [10] . Beyond the functional focus, branching features result from particular growth processes and thus can be used to validate growth models driven by biophysics [11, 12] , molecular and signaling dynamics [13] [14] [15] [16] , statistical relationships [17] [18] [19] [20] , or more abstract positional and branch-type rules [21, 22] .. Until recently, the challenges of generating relevant biological data have limited cell type growth analyses to a single type or a few related cell types at a time. However, accelerating data production and curation of datasets from a growing number of laboratories by NeuroMorpho.Org have enabled large-scale analysis. Some studies have used these data to detect general principles of neuronal organization [10, 23] . New imaging and semi-to fullyautomated reconstruction processes [24, 25] are contributing to increased throughput, with ever larger datasets to be expected in the near future [26] . For detecting relationships between cell types, this influx of data calls for new methods of analysis [27] .. Other fields have seen similarly dramatic growth in data, most notably genomics. Statisticians and computer scientists responded by creating a wide and still growing array of techniques to sort through the data in a practical timeframe in search of significant relationships and findings. These techniques broadly include local and global alignment [28] [29] [30] ; as well as multiple sequence alignment [31] , each with many specific algorithms designed for targeted sensitivity and/or efficiency. We leveraged the underlying bases of these techniques to analyze neuronal morphology by representing axonal and dendritic trees as sequences of branches encoded by their features. We began by sequentially encoding local topology based on a simple binary tree representation of neuronal structure. We then applied motif analysis [32] to determine the defining topological patterns across arbor types from a broad range of species, neuron classes, and brain regions. Highly over-or under-expressed patterns constitute motifs and anti-motifs, respectively. All code is available open source at http://krasnow1.gmu. edu/cn3/NeuriteSequence/, including Java implementation, R analysis scripts, and related documentation.

O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Analyzing Th17 cell differentiation dynamics using a novel integrative modeling framework for time-course RNA sequencing data AbstractThe differentiation of naive CD4 + helper T (Th) cells into effector Th17 cells is steered by extracellular cytokines that activate and control the lineage specific transcriptional program. While the inducing cytokine signals and core transcription factors driving the differentiation towards Th17 lineage are well known, detailed mechanistic interactions between the key components are poorly understood. Results: We develop an integrative modeling framework which combines RNA sequencing data with mathematical modeling and enables us to construct a mechanistic model for the core Th17 regulatory network in a data-driven manner. Conclusions: Our results show significant evidence, for instance, for inhibitory mechanisms between the transcription factors and reveal a previously unknown dependency between the dosage of the inducing cytokine TGFβ and the expression of the master regulator of competing (induced) regulatory T cell lineage. Further, our experimental validation approves this dependency in Th17 polarizing conditions. While the cytokines that induce naive CD4 + T cells to differentiate into specific subsets are well known, the mechanistic detailed interactions between the key transcription factors are not known. As a comprehensive experimental determination of the detailed dynamics is out of reach, mathematical modeling is an indispensable aid to learn more about the differentiation processes. In this study, we observe Th17 specific transcription factor dynamics through time-course mRNA data (RNA-seq measurements) and use objective computational tools to learn the mechanistic interactions of the key transcription factors. By integrating the mathematical models with our comprehensive set of time-course RNA-seq data as well as qualitative information about the differentiation dynamics, we construct an experimentally-based dynamic model that is capable of producing meaningful predictions that we also validate experimentally. We model the Th17 differentiation process on the same level as the process is typically experimentally observed. Our modeling approach is unique in three ways. First, we use time-course RNA-seq data as a basis of our work and integrate the data with dynamic modeling using a framework that makes use of statistical characterization of sequencing data. Second, we apply powerful statistical methodology that allows us to evaluate the alternative model topologies and, even more importantly, allows us to estimate the posterior predictive distributions for any process included into the model. Because we have a statistical model for the experimental data, the predictive distributions conveniently reflect the uncertainty in the observations as well as in the structure of our models. Third, we can generate probabilistic predictions in a continuous range of cytokine conditions on contrary to just knocking down a gene or removing a cytokine input from the model. In other words, we are able to make predictions in a continuous range of cytokine conditions (e.g. different dilution levels for TGFβ, see Fig. 2 ).. Previously published models for Th17 differentiation have been a part of larger studies which have aimed at modeling CD4 + T cell differentiation into various subsets [17, 18, 22] or have been especially designed to describe the reciprocal differentiation into Th17 and iTreg cells [20, 21] . Although these studies provide us with valuable information about the Th17 cell differentiation process, the models do not allow efficient use of time-course data and, more importantly, the model structure cannot be quantitatively judged by experimental observations.. The applicability of our modeling approach is not restricted to the modeling of Th17 cell differentiation. The statistical framework that we develop to combine mathematical models with sequencing data is fully general and can be used to analyze any RNA-seq data given an adequate continuous-state dynamic model. Our framework incorporates all available information on the statistical properties of sequencing data into the likelihood function which has the form of the negative binomial (NB) distribution. The NB distribution is also used in state-of-the-art data analysis methods [24, 28] and, thus, all important features of data, such as time-dependent gene-wise overdispersion, can be automatically taken into account when constructing the likelihood function. Further, the NB likelihood function conveniently links the discrete read count data with continuous-state dynamic models. The NB distribution is unarguably the most well suited distribution for read count data [24, 28] and, for this reason, our framework is inherently better suited for linking dynamic models with sequencing data than standard methods such as maximum likelihood fit via normal distribution. In some parameter regimes, the NB distribution can be approximated using the normal distribution and, in these cases, maximum likelihood fit might also well approximate the best fit obtained from our rigorous model. However, to construct this kind of normal approximations, one still needs to extract information from the sequencing data to incorporate, for example, time-dependent features and, importantly, one needs to check that the normal approximation is valid in all ranges of data at all time points considered. In general, normal approximations for count data are noted to perform poorly [26, 27] and by means of our framework, these kinds of cumbersome approximations can be simply avoided.. In summary, we introduce an experimentally-based modeling approach for Th17 cell differentiation and use it to generate predictions that are experimentally validated. The modeling is carried out within a novel statistical framework and, by using statistical methodology, we carry out experimentally based construction of a mathematical model. Our study approves the important role of quantitative dynamic modeling in identifying and studying regulatory mechanisms. Advanced application of mathematical modeling takes the analysis of timecourse data well beyond the standard statistical analyses and offers powerful means to test the existing knowledge against data as well as to hypothesize alternative mechanisms that can generate the observed data. There are two central requirements for successful application of mathematical modeling to these kinds of analysis tasks. First, the model construction process needs to be data and knowledge driven and, second, the resulting models must be suitable for quantitative evaluation. Our experimentally-based modeling framework for Th17 cell differentiation is designed to serve these needs in the best possible way and can be regarded powerful in the sense that it enables us to fully account for the uncertainty in the data as well in the model structure. Adaptive immunity is largely mediated by CD4 + T cells which are a subclass of lymphocytes [1] . When a naive CD4 + T cell encounters an antigen in the presence of cytokine signals, the cell is activated through T cell receptor and the differentiation into one of the effector T helper (Th) cell subsets can be initiated [1] . There are four well characterized subsets of CD4 + T cells, Th1, Th2, Th17, and induced regulatory T (iTreg) cells, all of them having distinct functions in the adaptive immune system [1] . The subset of Th17 cells is the most recently discovered subset and, consequently, there has been a keen interest in studying the properties of this subset during the past decade [2] [3] [4] [5] . The primary function of Th17 cells is to clear pathogens during host defense reactions and, in *Correspondence: jukka.intosalmi@aalto.fi 1 Department of Computer Science, Aalto University, FI-00076, Aalto, Finland Full list of author information is available at the end of the article general, Th17 cells have been noted to have important functions in various autoimmune diseases such as psoriasis, rheumatoid arthritis, multiple sclerosis, asthma, and inflammatory bowel disease [4, 5] .. The differentiation from a naive CD4 + T cell into a Th17 cell is induced by two cytokines, transforming growth factor β (TGFβ) and interleukin 6 (IL6) and both of these cytokines are required for a successful differentiation [4, 6] . The key transcription factors for Th17 cell generation are the retinoic acid receptor-related orphan receptor gamma t (RORγ t) and signal transducer and activator of transcription 3 (STAT3) [4, 6] . In the course of the differentiation, STAT3 is activated through an extracellular IL6 signal and, in the presence of a sufficient TGFβ level, STAT3 induces RORγ t expression which leads to Th17 differentiation and interleukin 17 secretion [4, 6] . Th17 cell differentiation is also closely related to the generation of iTreg cells. The relation between iTreg and Th17 lineages is reciprocal in nature, differentiation into both subtypes requires a sufficient amount of TGFβ, and these subtypes have also been shown to exhibit plasticity [4, [7] [8] [9] . Recent experimental studies provide a plethora of information about the Th17 lineage specific regulatory network [6, 10] but precise mechanistic understanding of the transcription factor dynamics is yet to be attained. In this study, we take the first steps towards a mechanistic characterization of the Th17 specific core regulatory network by using mathematical modeling that is employed to extract information from time-course measurements of mRNA kinetics.. Mathematical modeling can be used to construct detailed descriptions for kinetics of molecular processes and, consequently, it offers rigorous and objective means to test whether the current understanding about the molecular system is in agreement with observed data or otherwise expected behavior. During the past years, mathematical models have been developed to study the differentiation from naive CD4 + T cells into Th1, Th2, Th17, and iTreg subsets [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] . Some of the published models describe the differentiation into several distinct subsets and, in the context of lineage specification, these models describe also the differentiation into Th17 subset [17, 18, [20] [21] [22] . However, to our best knowledge, a detailed dynamic model describing the dynamics of core transcription factors behind Th17 cell differentiation has not been published. Developing this kind of detailed model is timely because recent experimental studies provide us with sufficient amount of information about the dependencies between the key transcription factors and, on the other hand, learning the mechanistic underpinnings of regulatory relationships during the differentiation process is crucial, for instance, for the design of experimental approaches to modulate the immune response.. In this study, we construct a dynamic description for the core molecular mechanisms steering Th17 cell differentiation and use mathematical modeling to quantitatively predict the resulting molecular dynamics. The dynamic description is calibrated in a data-driven manner, and both the calibrated dynamic model and biological findings are further validated experimentally. Our analysis rests upon comprehensive time-course RNA sequencing measurements that provide us with a system level understanding of dynamic gene expression kinetics during the Th17 cell differentiation of primary murine T cells in vitro. In order to combine mathematical modeling with these data and enable experimentally-based modeling, we develop a statistical framework that is designed specifically for time-course RNA sequencing data and, further, we elaborate the statistical techniques that are essential for obtaining our results. Our treatment of sequencing data is based on the negative binomial distribution that is also used in the state-of-the-art statistical data analysis methods and this approach enables us to integrate mathematical modeling with sequencing data in a natural way.. In summary, we present a computational framework that is used to derive the first detailed dynamic model for the core network behind Th17 cell differentiation and, further, we validate the model experimentally. Our results show significant evidence, for instance, for inhibitory mechanisms between the transcription factors and also reveal a previously unknown dependency between the dosage of TGFβ and the expression of the master regulator of competing iTreg lineage in Th17 polarizing conditions.

O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


LP/WLP Hybrid Scheme for Quality Improvement of TCX Coders Operating at Low Bit Rates In this paper, we propose a switchable linear prediction (LP)/warped linear prediction (WLP) hybrid scheme for the transform coded excitation (TCX) coder, which is adopted as a core codec in AMR-WB+ and USAC. The proposed algorithm selects either an LP or WLP filter on a per-frame basis. To provide a smooth transitions between LP and WLP frames, a window switching scheme is developed using sine and rectangular windows. In addition, a Gaussian Mixture Model (GMM)-based classification module is used to determine the prediction mode. Through a subjective listening test it was confirmed that the proposed LP/WLP switching scheme offers improved sound quality. key words: warped linear prediction (WLP), linear prediction, audio coding, TCX, low bit rate Maintaining transparent audio quality while reducing the bit rates is very important for efficiently store and transmit audio data through media with limited bandwidth. The stateof-the-art codecs such as AMR-WB+ [1] and unified speech and audio codec (USAC) [2] promise high quality for speech and audio contents at low bit rates. Those codecs switch between a speech core coder, algebraic code excited linear prediction (ACELP), and a transform-based core coder, transform coded excitation (TCX). TCX in the AMR-WB+ originally employed DFT [1] . Later, to improve coding efficiency, a modified MDCT-based TCX was developed [3] .. Both ACELP and TCX coders operate with a linear prediction (LP) filter. LP is an effective tool for modeling both speech and audio, so it has been widely used in a variety of speech/audio codecs. For audio signals, especially when the signals are nearly stationary, it was indicated that warped linear prediction (WLP) could be more effective than LP in terms of bit saving [4] . Therefore, perceptual quality could be improved by using WLP rather than LP at the same bit rates.. In this paper, we propose a switchable LP/WLP hybrid scheme for the TCX coder operating at low bit rates. The main motivation of this study is that, in some frames containing fairly stationary low-frequency components, the use of WLP instead of LP can improve the coding efficiency of TCX. To provide a smooth transition between LP and WLP, we propose a window switching scheme based on sine We proposed an LP/WLP switching scheme and applied it to the TCX coder adopted in AMR-WB+. For seamless connection between LP and WLP frames, we proposed a new window switching scheme, together with a GMM-based classification module. Test results indicated that the proposed scheme could provide improved results, especially for items containing dominant spectral peaks in low frequency bands.

O O O O O O O B O O O O O O O O O O O O O B I O B I O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I B I B I B B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B B O O O O O O O O O O O O O O O O B O O O O O O O B O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


MRL and SuperFine+MRL: new supertree methods Background: Supertree methods combine trees on subsets of the full taxon set together to produce a tree on the entire set of taxa. Of the many supertree methods, the most popular is MRP (Matrix Representation with Parsimony), a method that operates by first encoding the input set of source trees by a large matrix (the "MRP matrix") over {0,1, ?}, and then running maximum parsimony heuristics on the MRP matrix. Experimental studies evaluating MRP in comparison to other supertree methods have established that for large datasets, MRP generally produces trees of equal or greater accuracy than other methods, and can run on larger datasets. A recent development in supertree methods is SuperFine+MRP, a method that combines MRP with a divide-and-conquer approach, and produces more accurate trees in less time than MRP. In this paper we consider a new approach for supertree estimation, called MRL (Matrix Representation with Likelihood). MRL begins with the same MRP matrix, but then analyzes the MRP matrix using heuristics (such as RAxML) for 2-state Maximum Likelihood.We compared MRP and SuperFine+MRP with MRL and SuperFine+MRL on simulated and biological datasets. We examined the MRP and MRL scores of each method on a wide range of datasets, as well as the resulting topological accuracy of the trees. Our experimental results show that MRL, coupled with a very good ML heuristic such as RAxML, produced more accurate trees than MRP, and MRL scores were more strongly correlated with topological accuracy than MRP scores.Conclusions: SuperFine+MRP, when based upon a good MP heuristic, such as TNT, produces among the best scores for both MRP and MRL, and is generally faster and more topologically accurate than other supertree methods we tested.We show the number of source trees, total taxa, resolution of the strict consensus merger tree, and the source of the original data for each of the biological datasets. The scaffold density is the proportion of the total taxa present in the largest source tree.Nguyen et al. Algorithms for Molecular Biology 2012, 7:3 Several key observations are noted. First, SuperFine +TNT gave the best results for Sum-FN, but other than on the seabirds and THPL datasets, all methods produced trees with similar Sum-FN scores. MRL(RAxML) typically resulted in the best MRL scores, and SuperFine +MRP(TNT) often produced trees with the second best MRL scores. SuperFine+MRP(TNT) also resulted in the best MRP scores for all datasets. SuperFine+MRP(TNT) was among the fastest methods, and on the largest dataset it was substantially faster than any other method. Thus, although we cannot evaluate the topological accuracy of any of these estimated supertrees, SuperFine +MRP(TNT) had a good overall performance for all criteria we evaluate (MRP, MRL, Sum-FN, and running time). Supertree estimation methods need to be both highly accurate and also reasonably fast, as otherwise they will not be useful in estimating large phylogenies. Our discussion thus addresses both running time and topological accuracy.. The results for the simulated datasets show clearly that all the methods produce trees with about the same accuracy on datasets with very dense scaffolds, but differ substantially in terms of accuracy on the datasets with sparser scaffolds. Since sparser scaffolds are common We show the average running times, in minutes, to calculate the 1000-taxon supertrees estimated from 25 clade-based source trees and 1 scaffold tree. The standard deviation is shown in parenthesis. The lowest running time for each scaffold factor is shown in bold. We give the average running times, in minutes, to calculate the 500-taxon supertrees estimated from 15 clade-based source trees and 1 scaffold tree. The standard deviation is shown in parenthesis. The lowest running time for each scaffold factor is shown in bold.. for biological supertree inputs, the differences in accuracy on sparse scaffolds is important.. In general we found that all the SuperFine variants we studied (whether using MRL or MRP to refine polytomies in the SCM tree) produced very accurate trees, and that differences between them were largely in terms of running time, or with respect to MRL, MRP, or Sum-FN score. With respect to running time, SuperFine +MRP(TNT) was the fastest of all the methods we studied, finishing in at most 4 minutes on all the datasets (including the largest one with 2228 taxa and 39 source trees). Furthermore, SuperFine+MRP(TNT) produced very good MRP and MRL scores, outperforming TNT and PAUP* with respect to MRP score optimization. On the biological datasets, we also observed similar results, including that SuperFine+MRP(TNT) generally produced very good Sum-FN scores. Thus, although SuperFine+MRP(TNT) was not designed to be a Figure 2 Scatterplot of average missing branch rates versus running times for 1000-taxon 50% scaffold density model conditions. The average missing branch rate versus running times (in minutes) for the supertree methods for 9 replicates of the 1000-taxon 50% scaffold density model conditions. We show the average Spearman's rank correlation coefficient between different statistics and the FN error rates of trees generated around each of the six estimated supertrees for the 1000-taxon model conditions. For each of the estimated six supertrees, 100 trees were generated using a p-ECR move, for a total of 606 trees (600 p-ECR trees plus 6 supertrees) per replicate. MRP score is the MP score of the estimated tree with respect to the MRP matrix. MRL score is the negative log-likelihood score of the estimated tree with respect to the MRP matrix. Sum-FN is the sum of the bipartitions in the source trees not present in the estimated tree divided by the total number bipartitions in the source trees. Coefficients with larger magnitude represent stronger correlation between the test statistic and FN error rates. The largest correlation coefficient for each scaffold density is shown in bold. We show the average Spearman's rank correlation coefficient between different statistics and the FN error rates of trees generated around each of the six estimated supertrees for the 500-taxon model conditions. For each of the six estimated supertrees, 100 trees were generated using a p-ECR move, for a total of 606 trees (600 p-ECR trees plus 6 supertrees) per replicate. MRP score is the MP score of the estimated tree with respect to the MRP matrix. MRL score is the negative log-likelihood score of the estimated tree with respect to the MRP matrix. Sum-FN is the sum of the bipartitions in the source trees not present in the estimated tree divided by the total number bipartitions in the source trees. Coefficients with larger magnitude represent stronger correlation between the test statistic and FN error rates. The largest correlation coefficient for each scaffold density is shown in bold.. heuristic for any of these criteria, it has excellent performance across the board. It is worth discussing in greater depth the results we showed for Sum-FN scores. Our study shows that neither MRP nor Sum-FN scores have the best correlation with tree error, except when the scaffold factor is very dense. This result suggests that optimizing MRP or Sum-FN may not be the best strategy (except with dense scaffolds), and that evaluating supertree methods with respect to Sum-FN may not be the best way of distinguishing methods (except for dense scaffold datasets, perhaps). These observations were made earlier in [24] , but are worth repeating here, because of the increased interest in an approach to supertree estimation proposed by Steel and Rodrigo [15] , called "maximum likelihood supertrees". This method is based upon an exponential error model, and can be based upon different ways of measuring distances between trees and weights on the input trees. However, in the simplest case, where the weights on trees are all the same and the distance between trees is the RF distance, finding the ML supertree is identical to optimizing Sum-RF (minimizing the total topological distance, using Robinson-Foulds scores, to the input trees), a criterion that is almost identical to Sum-FN. Indeed, when the input estimated trees are binary, these criteria are exactly the same. Since our simulation study estimated supertrees from binary source trees, our correlation analysis also shows that optimizing Sum-RF is not likely to be the best strategy, except for dense scaffold datasets, and thus suggests that the use of RF distance metric within the ML supertree approach proposed by Steel and Rodrigo may not be appropriate. We note here a potential shortcoming of the ML supertree approach in general: it seems likely that the probability of a particular estimated tree will not depend only on the topological distance it has to the true tree, but rather also on the parameters of the true tree (especially the branch lengths), since very short branches are more likely to fail to be recovered in a phylogenetic estimation than longer branches.. A fundamental observation in this study is that searching for supertrees that optimize the maximum likelihood score under the S2+CAT model improved tree accuracy, a trend that we found quite surprising. The MRP matrix is a collection of partial binary characters defined by the input source trees. When these trees are compatible, the MRP matrix will exhibit no homoplasy at all, a condition under which the MRP solution will yield the true tree. Therefore, when there is no homoplasy, the ML solution under a no-commonmechanism model [33] (in which every combination of edge and site has its own rate parameter) will also produce the true tree, since then ML and MP produce the The lowest MRP score for each dataset is shown in bold. The lowest running time for each dataset is shown in bold. same trees. However, standard ML models (including the model used in this study) assume i.i.d. rates across sites, which does not yield the same result. Thus, we do not have a theoretical explanation for why optimizing likelihood under S2+CAT should lead to good supertrees. All we can say is that the data suggest that there may be some value (even if only approximate, and perhaps only under some conditions, not yet understood) in using maximum likelihood under this model as an optimization criterion for estimating supertrees. Future work should investigate whether optimizing the MRL score continues to return good solutions when the source trees are estimated from sequences that evolve under more realistic conditions, including indels, heterotachy, and non-stationarity.. As has been noted in [34] , supertree analyses are not always able to completely identify the true tree, because the conditions required for such identification include correct source trees and overlap properties that may not be true of any given set of source trees. However, alternatives -such as combined analyses, in which a phylogeny estimation method is applied to a concatenation of the gene sequence alignments -also have only limited guarantees. From a practical standpoint, the evidence suggests that while combined analyses can yield more accurate trees [20, 24] than supertree methods, there are conditions in which combined analysis methods cannot be used (e.g., heterogeneous data, including morphology, gene orders, or different types of molecular data), or are simply too computationally intensive. In these cases, improved supertree methods can be important tools in the phylogenetics toolkit.. In summary, this study introduces a new set of supertree methods based upon combining the divide-andconquer strategy within SuperFine with fast supertree methods. In particular, the combination of SuperFine with TNT is extremely fast and produces very accurate supertrees, even on the largest datasets we studied. Earlier work [24] showed that SuperFine (based upon MRP, and using PAUP*) came very close to the accuracy of combined analysis based upon maximum likelihood. Future work should investigate statistical approaches to supertree estimation (along the lines of maximum likelihood supertrees, but taking branch lengths or support into account). The combination of SuperFine with such statistically-based supertree methods might close the gap between combined analysis and supertree methods. Because estimation of large trees is computationally challenging [1-3] and topological error tends to increase with the number of taxa [4] [5] [6] [7] , supertree methods (which estimate trees on full sets of taxa from sets of smaller trees) may be key to accurate estimations of the Tree of Life. Many supertree methods have been proposed: see [8] for an overview of early methods, and also [9] [10] [11] [12] [13] [14] [15] [16] [17] . Some of these (e.g., the Robinson-Foulds supertree approach in [9] ) operate only on rooted source trees, while others (e.g., the Maximum Likelihood Supertree Method in [15] ) are only theoretical (i.e., have not yet been implemented). Of the various methods that are implemented, MRP (Matrix Representation with Parsimony) [18, 19] is by far the most frequently used. Furthermore, studies have shown that of these methods, only MRP produces highly accurate supertrees on datasets of unrooted source trees with large numbers of taxa [17, 20] .. MRP operates in two steps. Given a set T of source trees with set S of taxa, the first step produces a large matrix, called the MRP matrix, with one row for every taxon in S and one column for every edge of every tree in T . For a given edge e in a given source tree t, the column in the MRP matrix has entries over {0,1, ?}, with 0 given for the taxa that are on one side of the edge e, 1 for the taxa on the other side, and ? for all the remaining taxa (i.e., the ones that do not appear in the tree t). This way of encoding each source tree is called the "Baum-Ragan" coding; however, when the source trees are rooted, other techniques (e.g., the Purvis coding) can be used (see a comparison between these coding methods in [20] ). The second step then uses the maximum parsimony criterion to produce a tree on the MRP matrix. The MRP approach thus depends on whether substitutions from 0 to 1 have the same cost as substitutions from 1 to 0, and hence also depends on how the states 0 and 1 are assigned to the leaves in each source tree, for each given edge. In particular, the MRP matrix definition depends upon whether the trees in T are rooted or unrooted. The simplest version of MRP (and the one we study in this paper) treats all input trees as unrooted and uses the standard maximum parsimony criterion in which all substitutions have equal cost (this is called "reversible Fitch parsimony"). For this very simple version of MRP (i.e., Baum-Ragan encoding, followed by reversible Fitch parsimony), the choice of state (i.e., 0 or 1) for each side of each edge has no impact on the output, and so can be made arbitrarily. Methods for MRP are based upon techniques for the NP-hard maximum parsimony problem [21] . The most popular MRP heuristics therefore use good heuristics for maximum parsimony (MP), such as PAUP* [22] and TNT [23] .. Recently, Swenson et al. [24] introduced a new supertree method, SuperFine+MRP, that operates in two steps: in the first step, an incompletely resolved tree called the "strict consensus merger" (SCM) tree is computed, and in the second step MRP heuristics are used to refine each high degree node (polytomy) in the SCM tree. Their study showed that SuperFine+MRP produced topologically more accurate trees than MRP (both methods based upon the same MP heuristics in PAUP* [22] ) and also ran in much less time. However, in some cases (in particular on very large supertree datasets), the SCM tree contained very large polytomies, so that refining the large polytomies could require a substantial time effort, thus reducing the running time advantage of SuperFine +MRP over MRP. Speeding up the analysis through a parallelization of SuperFine's refinement step is also hampered by the fact that refinement of very large polytomies using MRP is the most computationally intensive part of the SuperFine analysis [25] .. Our objective was therefore to find an alternative to MRP for the refinement step within SuperFine. In this paper we examine supertrees estimated by analyzing the MRP matrix using RAxML's [26] fast heuristics for maximum likelihood under the symmetric 2-state model (so that the change from 0 to 1 is as likely as the change from 1 to 0) with CAT distribution of rates across sites, and we refer to this as the S2+CAT model. We call the optimization problem in this approach to supertree estimation "matrix representation with likelihood", or MRL. Thus, MRL is the counterpart to MRP, and uses S2 +CAT maximum likelihood instead of maximum parsimony as a criterion for estimating a supertree from the MRP matrix.. We report on a simulation study we performed to compare MRP to MRL (using fast heuristics for both) as supertree methods, and also to refine the SCM tree computed by SuperFine. Our study shows that using RAxML for MRL produces topologically more accurate trees than the MRP heuristics (PAUP* and TNT [23] ) we studied, and that MRL scores (under GTR+gamma, see discussion below) correlate very well with tree accuracy (and in general better than MRP scores). These results suggest that MRL may be a useful optimality criterion for supertree estimation. Second, we show that SuperFine can be used to obtain better scores for MRP and good scores for MRL, and faster than the standard heuristics for these problems.

B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O B O O O O B O O O O O B O O O O O O O O O O O B O O O B O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O


Biogeography-based optimization for voltage stability improvement and reactive reserve management Abstract: This paper proposes a biogeography-based optimization algorithm to enhance the voltage stability of a power system. It computes the optimal quantity of reactive power support with a view to place the static VAR compensator at the most appropriate nodes. The scheme inflicts an effective management of VAR resources in the process of improving the voltage profile and reducing the network losses. It includes the results of IEEE 30-node system to illustrate the feasibility of the approach. Voltage instability, characterized by a monotonic voltage drop that is slow initially and becomes abrupt after some time, is triggered either by some kind of disturbances or an increase in reactive power demand that is beyond the capability of the system. It has been realized that major blackouts were caused by voltage instability. It is therefore necessary to predict the occurrence of voltage instability and carry out corrective measures with a view toward ensuring stable operation [1, 2] .. Static VAR compensators (SVCs) and other flexible alternating current transmission system (FACTS) devices have been installed in power systems to provide reactive power support. The determination of the node location for such devices and the amount of reactive power support is of great significance for reducing the real power losses in addition to enhancing voltage stability (VS). It also increases the available transfer capacity of the transmission lines, thereby improving the feeder voltage profile. Several methods for solving this problem have been suggested in the literature [3] [4] [5] [6] [7] [8] [9] [10] [11] .. Numerous methods for prevention of voltage instability using FACTS devices in power systems were surveyed in [3] . An operation strategy involving SVCs for improving voltage profile and minimizing real power loss reduction was suggested in [4] . A bacterial foraging-based algorithm was used to improve the voltage stability limit and to reduce the loss by optimally placing the unified power flow controller (UPFC) in [5] . An operation scheme based on a UPFC in order to ensure security through the line over load control and low voltage control was given in [6] . A method for installing a UPFC with the view of enhancing the VS margin under contingent conditions was presented in [7] . A strategy for maintaining reactive power reserve with the view of * Correspondence: annamalaiasmani@gmail.com avoiding voltage collapse was presented in [8] . An analytical procedure for minimizing voltage deviations in order to indirectly enhance VS was proposed through reactive power compensation in [9] . A particle swarm optimization (PSO)-based algorithm was suggested in [10] to ensure voltage security by controlling the reactive power and node voltages. An adoptive immune algorithm for the reactive power optimization was outlined in [11] .. Recently, a biogeography-based optimization (BBO) algorithm was suggested for solving optimization problems [12] . It was developed based on the theory of biogeography, studying the geographical distribution of biological species. In this approach, the islands or habitats are modeled to represent problem solutions, and the immigration and emigration of species between islands denote sharing of features between solutions. It has been applied to several optimization problems, such as optimal reactive power control [13] , economic load dispatch [14] , and power flow [15] .. A novel BBO-based algorithm for enhancing VS in power systems through optimal placement of SVCs is detailed in this paper. The algorithm has been tested on the IEEE 30-node system and the results are offered. The paper is divided into 4 segments. Section 1 gives the introduction, Section 2 explains the BBO algorithm, Section 3 explains the proposed strategy, Section 4 discusses the results, and Section 5 gives the conclusions. A new BBO-based algorithm for enhancing voltage stability by placing the SVC at the most appropriate node and computing the optimal quantity of reactive power support has been proposed. The simulation results have clearly illustrated that the proposed strategy requires the lowest VAR support, minimizes net voltage deviations, reduces system losses, offers better a voltage profile, and takes the lowest computation time and makes it suitable for practical implementations as compared to the other 2 methods.

B I O B I O O O O O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


An n log n algorithm for hyper-minimizing a (minimized) deterministic automaton We improve a recent result [Badr: Hyper-minimization in O@n P A. Int. J. Found. Comput. Sci. 20, 2009] for hyper-minimized nite automata. Namely, we present an O@n log nA algorithm that computes for a given deterministic nite automaton (dfa) an almostequivalent dfa that is as small as possiblesuch an automaton is called hyper-minimal. 6 This is an extended and revised version of: M. Holzer, A. Maletti. An n log n algorithm for hyperminimizing states in a (minimized) deterministic automaton. Early studies in automata theory revealed that nondeterministic and deterministic nite automata are equivalent [1] . However, nondeterministic automata can be exponentially more succinct [2, 3] (with respect to the number of states). In fact, nite automata are probably best known for being equivalent to right-linear context-free grammars, and thus, for capturing the lowest level of the Chomsky-hierarchy, which is the family of regular languages. Over the last 50 years, a vast literature documenting the importance of nite automata as an enormously valuable concept has been developed. Although, there are a lot of similarities between nondeterministic and deterministic nite automata, one important dierence is that of the minimization problem. The study of this problem also dates back to the early beginnings of automata theory. It is of practical relevance because regular languages are used in many applications, and one may like to represent the languages succinctly. While for nondeterministic automata the computation of an equivalent minimal automaton is PSPACE-complete [4] and thus highly intractable, the corresponding problem for deterministic automata is known to be eectively solvable in polynomial time [5] . An automaton is minimal if every other automaton with fewer states disagrees on acceptance for at least one input. Minimizing deterministic nite automata (dfa) is based on computing an equivalence relation on the states of the automaton and collapsing states that are equivalent. Here two states p; q P Q, where Q is the set of states of the automaton under consideration, are equivalent, if the automaton starting its computation in state p accepts the same language as the automaton if q is taken as the start state. Minimization of two equivalent dfa leads to minimal dfa that are isomorphic up to the renaming of states. Hence, minimal dfa are unique. This yields a nice characterization: A dfa M is minimal if and only if in M :. (i) there are no unreachable states and (ii) there is no pair of dierent but equivalent states.. The computation of this equivalence can be implemented in a straightforward fashion by repeatedly rening partitions starting with the partition that groups accepting and rejecting states together [5] . This yields a polynomial-time algorithm of O@n P A.. Hopcroft's algorithm [6] for minimization slightly improves the naïve implementation to a running time of O@m log nA with m a jQ ¢ ¦j and n a jQj, where ¦ is the alphabet of input symbols of the nite automaton. It is up to now the best known minimization algorithm for dfa in general. Recent developments have shown that this bound is tight for Hopcroft's algorithm [7, 8] . Thus, minimization can be seen as a form of lossless compression that can be done eectively while preserving the accepted language exactly.. Recently, a new form of minimization, namely hyper-minimization, was studied in the literature [9, 10, 11] . There the minimization or compression is done while giving up the preservation of the semantics of nite automata; i.e., the accepted language. It is clear that the semantics cannot vary arbitrarily. A related minimization method based on cover automata is presented in [12, 13] . Hyper-minimization [9, 10, 11] allows the accepted language to dier in acceptance on a nite number of inputs, which is called almost-equivalence. Thus, hyper-minimization aims to nd an almost-equivalent dfa that is as small as possible. Here an automaton is hyper-minimal if every other automaton with fewer states disagrees on acceptance for an innite number of inputs.. In [9] basic properties of hyper-minimization and hyper-minimal dfa are investigated.. Most importantly, a characterization of hyper-minimal dfa is given, which is similar to the characterization of minimal dfa mentioned above. Namely, a dfa M is hyper-minimal if and only if in M : (i) there are no unreachable states, (ii) there is no pair of dierent but equivalent states, and (iii) there is no pair of dierent but almost-equivalent states such that at least one of them is a preamble state. Here a state is called a preamble state if it is reachable from the start state by a nite number of inputs, only. Otherwise the state is called a kernel state. These properties allow a structural characterization of hyper-minimal dfa. Roughly speaking, the kernels (all states that are kernel states) of two almost-equivalent hyper-minimal automata are isomorphic in the standard sense, and their preambles are also isomorphic except for acceptance values. Thus, it turns out that hyper-minimal dfa are not necessarily unique. Nevertheless, it was shown in [9] that hyper-minimization can be done in time O@mn P A, where m a j¦ ¢ Qj and n a jQj. For a constant alphabet size this gives an O@n Q A algorithm. Later, the bound was improved [10, 11] to O@mnA. In this paper we improve this upper bound further to O@m log nA. If the alphabet size is constant, then this yields an O@n log nA algorithm. In addition, we argue that this is reasonably good because any upper bound t@nA a @nA for hyper-minimization implies that (classical) minimization can be done within t@nA. To this end, we linearly reduce minimization to hyper-minimization. Similar results were independently obtained in [14] .. The results of this paper were rst reported in [15] . This version contains the full, detailed proofs of the claims, a more elaborate example, and a few minor corrections. The paper is organized as follows: In the next section we introduce the necessary notation.. Then in Section 3 we rst describe the general background needed to perform hyperminimization, namely identifying kernel states, computing almost-equivalent states, and nally merging almost-equivalent states. Next we present a running example, and show how to implement these three sub-tasks in time O@m log nA. The formal time-complexity and correctness proofs are presented in Sections 4 and 5. In Section 4 we also show the linear reduction from minimization to hyper-minimization. Finally we summarize our results and state some open problems. We have designed an O@m log nA algorithm, where m a jQ ¢ ¦j and n a jQj, that computes a hyper-minimized dfa from a given dfa @Q; ¦; q H ; ; F A. The hyper-minimized dfa may have fewer states than the classical minimized dfa. Its accepted language is almost-equal to the original one, which means that it diers in acceptance on only a nite number of inputs. Since hyper-minimization is a very new eld of research, most of the standard questions related to descriptional complexity such as, for example, nondeterministic automata to dfa conversion with respect to hyper-minimality, are problems of further research.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O