Why neighbor-joining works

We show that the neighbor-joining algorithm is a robust quartet method for constructing trees from distances. This leads to a new performance guarantee that contains Atteson's optimal radius bound as a special case and explains many cases where neighbor-joining is successful even when Atteson's criterion is not satisfied. We also provide a proof for Atteson's conjecture on the optimal edge radius of the neighbor-joining algorithm. The strong performance guarantees we provide also hold for the quadratic time fast neighbor-joining algorithm, thus providing a theoretical basis for inferring very large phylogenies with neighbor-joining

Quartet consistency count method for reconstructing phylogenetic trees

Among the distance based algorithms in phylogenetic tree reconstruction, the neighbor-joining algorithm has been a widely used and effective method. We propose a new algorithm which counts the number of consistent quartets for cherry picking with tie breaking. We show that the success rate of the new algorithm is almost equal to that of neighbor-joining. This gives an explanation of the qualitative nature of neighbor-joining and that of dissimilarity maps from DNA sequence data. Moreover, the new algorithm always reconstructs correct trees from quartet consistent dissimilarity maps.Comment: 11 pages, 5 figure

SunStar: an implementation of the generalized STAR method

Master's Project (M.S.) University of Alaska Fairbanks, 2017STAR ... is a method of computing species trees from gene trees. Later, STAR was generalized and proven to be statistically consistent given a few conditions (Allman, Degnan, and Rhodes 2013). Using these conditions, it is possible to investigate robustness in the species tree inference process, the lack of which will produce instabilities in the tree resulting from STAR. We have developed a software package that estimates support for inferred trees called SunStar

On the optimality of the neighbor-joining algorithm

The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME) tree associated to a dissimilarity map. From this point of view, NJ is ``optimal'' when the algorithm outputs the tree which minimizes the balanced minimum evolution criterion. We use the fact that the NJ tree topology and the BME tree topology are determined by polyhedral subdivisions of the spaces of dissimilarity maps ${\R}_{+}^{n \choose 2}$ to study the optimality of the neighbor-joining algorithm. In particular, we investigate and compare the polyhedral subdivisions for $n \leq 8$. A key requirement is the measurement of volumes of spherical polytopes in high dimension, which we obtain using a combination of Monte Carlo methods and polyhedral algorithms. We show that highly unrelated trees can be co-optimal in BME reconstruction, and that NJ regions are not convex. We obtain the $l_2$ radius for neighbor-joining for $n=5$ and we conjecture that the ability of the neighbor-joining algorithm to recover the BME tree depends on the diameter of the BME tree

Unfolding Latent Tree Structures using 4th Order Tensors

Discovering the latent structure from many observed variables is an important yet challenging learning task. Existing approaches for discovering latent structures often require the unknown number of hidden states as an input. In this paper, we propose a quartet based approach which is \emph{agnostic} to this number. The key contribution is a novel rank characterization of the tensor associated with the marginal distribution of a quartet. This characterization allows us to design a \emph{nuclear norm} based test for resolving quartet relations. We then use the quartet test as a subroutine in a divide-and-conquer algorithm for recovering the latent tree structure. Under mild conditions, the algorithm is consistent and its error probability decays exponentially with increasing sample size. We demonstrate that the proposed approach compares favorably to alternatives. In a real world stock dataset, it also discovers meaningful groupings of variables, and produces a model that fits the data better

Emergence of scale-free behavior in networks from limited-horizon linking and cost trade-offs

We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are not too far apart on the sphere may be considered for being joined by an edge. Given two such nodes, the joining occurs only if the gain of doing it surpasses the cost. Our model is based on a multiplicative parameter lambda that regulates, in a function of node degrees, the maximum geodesic distance that is allowed between nodes for them to be considered for joining. For n nodes distributed uniformly on the sphere, and for lambda*sqrt(n) within limits that depend on cost-related parameters, we have found that our growth mechanism gives rise to power-law distributions of node degree that are invariant for constant lambda*sqrt(n). We also study connectivity- and distance-related properties of the networks

The New Grid

The New Grid seeks to provide mobile users with an additional method for off-grid communication, or communication without connection to Internet infrastructure. The motivation for this project was to find another alternative to Internet-dependent communication. Current Internet infrastructure is antiquated; it is expensive to maintain and expand, it has numerous vulnerabilities and high-impact points of failure, and can be rendered unusable for lengthy periods of time by natural disasters or other catastrophes. This current grid will eventually need to be replaced by a more modern, scalable, and adaptive infrastructure. The results of the projects research showed that implementing a library to allow for the creation of mobile peer-to-peer mesh networks could serve as a starting point for a transition from current Internet infrastructure to a more scalable, adaptive, and reliable Internet- independent network grid. Development of The New Grid largely followed the Rational Unified Process, in which the development process is split into four phases: requirements gathering, system design, implementation, and testing. Most of fall quarter was spent outlining functional requirements for the system, designing possible methods of implementation, and researching similar solutions that seek to transition mass mobile communication to a newer, more modern network grid. The New Grid differs from similar solutions because it has been implemented as a modular library. Current systems that allow for off-grid mobile connection exist as independent applications with a defined context and predetermined usability scope. We, the design team, found that implementing the system in the form of a modular library has multiple benefits. Primarily, this implementation would allow The New Grid to be deployed as widely as possible. Developers can both write applications around our library as well as include specific modules into existing applications without impacting other modules or introducing additional overhead into a system. Another benefit of deploying the system as a modular library is adaptability. The current, initial stable build of The New Grid uses Bluetooth Low Energy as its backbone for facilitating communication within large networks of mobile devices; however, this library could use any existing or future communication protocol to facilitate connection as long as a hook is written to allow The New Grid to interface with that protocol. Thus, The New Grid is not limited by which connection protocols currently exist, a property that other similar systems do not possess. The New Grid can be used in any application that requires connection between users. The most common applications would likely be messaging, file sharing, or social networking. While developers may find a variety of uses for The New Grid, its primary purpose is to facilitate reliable connection and secure data transfer in an environment with a large user base. Achieving this goal was proven feasible through research and testing the library with a small cluster of Android devices communicating solely with Bluetooth Low Energy. Expanding this group of a few phones to a larger mesh network of hundreds of devices was shown to be feasible through testing the librarys algorithms and protocols on a large network of virtual devices. As long as developers seek to create applications that allow users to communicate independent of Internet infrastructure, The New Grid will allow smartphone users to communicate off-grid and hopefully spur a switch from infrastructure-dependent mobile communication to user-centric, adaptive, and flexible connection