1,721,030 research outputs found
Toward the Darwinian transition: Switching between distributed and speciated states in a simple model of early life
No full textIt has been hypothesized that in the era just before the last universal common ancestor emerged, life on earth was fundamentally collective. Ancient life forms shared their genetic material freely through massive horizontal gene transfer (HGT). At a certain point, however, life made a transition to the modern era of individuality and vertical descent. Here we present a minimal model for stochastic processes potentially contributing to this hypothesized “Darwinian transition.” The model suggests that HGT-dominated dynamics may have been intermittently interrupted by selection-driven processes during which genotypes became fitter and decreased their inclination toward HGT. Stochastic switching in the population dynamics with three-point (hypernetwork) interactions may have destabilized the HGT-dominated collective state and essentially contributed to the emergence of vertical descent and the first well-defined species in early evolution. A systematic nonlinear analysis of the stochastic model dynamics covering key features of evolutionary processes (such as selection, mutation, drift and HGT) supports this view. Our findings thus suggest a viable direction out of early collective evolution, potentially enabling the start of individuality and vertical Darwinian evolution
STATISTICAL MODELING AND INFERENCE FOR SOCIAL NETWORKS
No full text275 pagesThe main contributions of this thesis can be organized under two main themes: knowledge discovery from social networks via human social sensing (Theme 1) and systematic emergence of societal consequences via individual actions and decisions (Theme 2). The key aim of Theme 1 is to devise algorithmic methods that can elicit useful information from humans in a social network. In particular, three statistical inference methods that exploit the graph theoretic consequence named the friendship paradox are presented: an algorithm to estimate heavy-tailed (power-law) degree distributions of social networks, a polling algorithm to estimate the fraction of nodes in a network with a specific attribute (e.g., a particular political ideology, a contagious disease, etc.) and an algorithm to dynamically track the fraction of people in a social network who have been exposed to a specific piece of information (e.g., a URL to a news article on Facebook, a hashtag on Twitter). It is shown that the proposed methods outperform the alternative methods via theoretical, numerical and empirical results. The contributions under the Theme 2 aim to understand how various societal consequences systematically emerge as collective consequences of individual actions, decisions and observations. In particular, the second theme explores the emergence of perception bias (i.e., the tendency of individuals to overestimate the prevalence of some attributes) and the glass ceiling effect (i.e., the existence of an invisible barrier that prevents certain social groups from rising to influential positions) in directed social networks (e.g., Twitter, author-citation networks). First, it is shown how the friendship paradox in directed social networks can explain why people on average overestimate the prevalence of certain traits (i.e., the perception bias in directed social networks), and strategies are proposed to mitigate its adverse effects. Then, a novel dynamical model (Directed Mixed Preferential Attachment model) is presented to explain how the glass ceiling effect in directed social networks emerges as a collective consequence of homophily (i.e., preference of individuals to associate with others who have similar attributes), size of the minority, level of preferential attachment (i.e., the preference of individuals to link to others who are already more popular) and growth dynamics (i.e., how frequently new individuals join, how they are incorporated into the social network, etc.). Additionally, the Directed Mixed Preferential Attachment model and its theoretical analysis is also used to shed light on the interplay between the structure and the dynamics of directed networks (which have been relatively less studied compared to their undirected counterparts)
Parallel Machine Learning Algorithms In Bioinformatics And Global Optimization
Full text linkThis is a dissertation in three parts, in each we explore the development and analysis of a parallel statistical or machine learning algorithm and its implementation. First, we examine the Assembly Likelihood Evaluation (ALE) framework. This algorithm defines a rigorous statistical likelihood metric used to validate and score genome and metagenome assemblies. This algorithm can be used to identify specific errors within assemblies and their locations; enable comparison between assemblies allowing for optimization of the assembly process; and using re-sequencing data, detect structural variations. Second, we develop an algorithm for Expected Parallel Improvement (EPI). This optimization method allows us to optimally sample many points concurrently from an expensive to evaluate and unknown function. Instead of sampling sequentially, which can be inefficient when the available resources allow for simultaneous evaluation, EPI identifies the best set of points to sample next, allowing multiple samplings to be performed in unison. Finally, we explore Velvetrope: a parallel, bitwise algorithm for finding homologous regions within sequences. This algorithm employs a two-part filter between sequences. It first finds offsets where two sequences share a higher than expected amount of identity. It then filters areas within these offsets with higher than expected identity. The resulting positions along each sequence represent regions of statistically significant similarity
L2 Minimal Algorithms
No full text43 pagesWe consider putting certain tensors into forms with approximately minimum L2 norm. These tensors describe strategies for computing linear or bilinear maps. Such forms are of interest from a practical perspective because they are particularly numerically stable. They are of interest from a theoretical perspective because they may be unique up to certain orthogonal or unitary transformations. The main tensors of interest represent (commutative, real) "matrix multiplication algorithms" or "bilinear algorithms." We explain how an algorithm's L2 minimal form might be thought of as optimally stable and as close to attaining the nuclear norm as possible. We demonstrate an algorithm "Strop" that has minimum L2 norm among all rank 7 algorithms for 2x2 matrix multiplication. This leads to better error for typical large matrices than Strassen, at the cost of more operations. Putting Strassen's (or any such) algorithm into this form requires "only" a convex optimization problem on positive definite matrices. In some situations, this optimization enables us to check when algorithms are equivalent in a natural sense. As a stepping stone we consider L2 minimal forms for analogous "linear algorithms." Such forms have been the subject of extensive study by invariant theorists, but are less known in other circles. We give simple examples of when the existence of these forms, and their use in equivalence testing, is apparent from an optimization perspective
ULTRAFAST FIBER LASERS ENABLED BY HIGHLY NONLINEAR PULSE EVOLUTIONS
No full textUltrafast lasers have had tremendous impact on both science and applications, far beyond what their inventors could have imagined. Commercially-available solid-state lasers can readily generate coherent pulses lasting only a few tens of femtoseconds. The availability of such short pulses, and the huge peak intensities they enable, has allowed scientists and engineers to probe and manipulate materials to an unprecedented degree. Nevertheless, the scope of these advances has been curtailed by the complexity, size, and unreliability of such devices. For all the progress that laser science has made, most ultrafast lasers remain bulky, solid-state systems prone to misalignments during heavy use. The advent of fiber lasers with capabilities approaching that of traditional, solid-state lasers offers one means of solving these problems. Fiber systems can be fully integrated to be alignment-free, while their waveguide structure ensures nearly perfect beam quality. However, these advantages come at a cost: the tight confinement and long interaction lengths make both linear and nonlinear effects significant in shaping pulses. Much research over the past few decades has been devoted to harnessing and managing these effects in the pursuit of fiber lasers with higher powers, stronger intensities, and shorter pulse durations. This thesis focuses on less quantitative metrics of fiber laser performance, with an emphasis on furthering the versatility and practicality of ultrafast sources. Much of this work relies on the calculated use of strong fiber nonlinearities, turning conventionally-undesirable phenomena into crucial tools for enabling new capabilities. First, the generation of femtosecond-scale pulses from much slower, more robust sources is investigated, conferring not only reliability advantages but also a fundamentally greater scope for repetition rate tuning. Next, prospects for fiber lasers operating at wavelengths far from any gain media are explored. By leveraging optical parametric gain alongside chirped-pulse evolutions, energy and bandwidth generated at one wavelength can be efficiently converted to another, while keeping the pulse's phase and compressibility intact. Both the scaling properties and the underlying theoretical considerations of this approach are discussed. Prospects for realizing optical parametric sources in birefringent step-index fibers are then studied. By using the polarization modes in a telecom-grade fiber to obtain phase-matching, new wavelengths can be generated while eschewing photonic crystal fiber and its inherent practical disadvantages. Finally, more speculative ideas for future work along these themes are discussed
Three Problems In Nonlinear Dynamics: Time Delay, Fractionality And Synchronization
Full text linkThree problems in nonlinear dynamics are studied with concern to the effects of time history dependent functions on steady state behavior. In each problem we consider either a single oscillator or a system of oscillators. The appearance of the time history dependence varies over the problems, and is be introduced either as a delayed term or a fractional derivative. In our first problem, a van der Pol type system with delayed feedback is explored by employing a two variable expansion perturbation method. The resulting amplitude-delay relation predicts two Hopf bifurcation curves, such that in the region between these two curves oscillations will be quenched. The perturbation results are verified by comparison with numerical integration. The second and third problems are on the subject of fractional derivatives. In analyzing these problems we look to extend classic perturbation methods to the treatment of fractional derivatives. In the second problem we also consider a single oscillator. The oscillator may be described as a damped Mathieu type where the damping term has been replaced by a fractional derivative. The order of the fractional derivative considered ranges from 0 to 1. Both lowest order and higher order approximations for the n = 1 transition curves, which separate regions of stability from instability, are found using the method of harmonic balance. An approximation for the n = 0 transition curve is also obtained. In the limiting cases of the fractional derivative's order, [alpha], being 0 or 1, the fractional Mathieu equation being considered respectively reduces to the familiar undamped and damped Mathieu equations. The undamped and damped Mathieu equations are well studied and our results may be compared with the known results in these cases. Through these comparisons conclusions are drawn as to the validity of assumptions made in applying the method of harmonic balance as well as the effect of the fractional derivative. In the third problem, the stability of the in-phase and out-of-phase modes of a pair of fractionally-coupled van der Pol oscillators is studied. A two variable perturbation method is applied to the system's corresponding variational equations to obtain expressions for the transition curves separating regions of stability from instability. The perturbation results are validated with numerics and, as in the second problem, through direct comparison with known results in the limiting cases of fractional derivative order taking on the values of [alpha] = 0 and [alpha] = 1
Mathematical Models For The Evolution And Development Of The Cerebral Cortex In Mammals
Full text linkThis is a pivotal time in neuroscience as modern imaging techniques and methods in network reconstruction are elucidating the structure of the brain as never before. Ultimately, our insights into these networks of connections will be the foundation for a better understanding of cognitive function and dysfunction in humans and other species. Comprehending why these structures are as we find them can be helped by knowing their developmental programs. Mathematical models will play a key role in understanding how developmental programs are orchestrated by the genome and refined by evolution to construct the brain. In this thesis I present mathematical models for two early stages of the development of the cerebral cortex in mammals: neurogenesis and the emergence of early network structure. Both models are informed by empirical developmental and anatomical data. The first, an ordinary differential equation model for the kinetics of cortical neurogenesis, shows how those kinetics shape the basic architecture of the cortex. A massive increase in the number of cortical neurons, driving the size of the cortex to increase by 5 orders of magnitude, is a key feature of mammalian evolution. Not only are there systematic variations in the cortical architecture across species, but also within a given cortex (affecting the type of information processing which happens in each part of the cortex). The mathematical model presented here accounts for both the cross-species and within-cortex variation as arising from the same developmental mechanism. For the second model, data from an axon-tracing study in rodents informs a network model of early connectivity between neurons in the cerebral cortex. Analysis of the model shows that early axon out-growth has an anisotropic spatial distribution which reduces the volume occupied by the axons without causing a significant decrease in the efficiency of the resulting network. Moreover, the preferential connectivity observed along the medial-lateral axis of the cortex my seed the emerging layout of the cortical areas which are specialized for various types of information processing
Synchronization unlocked: spirals, zetas, rings, and glasses
No full textSupplemental file(s) description: Video1a, Video1b, Video2a, Video2b, Video2c, Video3, Video5, Video6, Video8Here, we study networks of coupled oscillators. Specifically, we identify phenomenology at or near a synchronization threshold in four distinct cases. First, we identify a novel spatiotemporal pattern in the two-dimensional Kuramoto lattice with periodic boundary conditions. This pattern appears as a two-armed rotating spiral in the spatial variation of the oscillators' instantaneous frequencies; hence the name ``frequency spirals.'' Second, we look at a large (but finite) number N of globally coupled oscillators in the special case where the natural frequencies are evenly spaced on a given interval. With these conditions, a leading order correction to the locking threshold is derivable, and scales according to N^{-3/2}. Thirdly, we do a case study on how topology can affect synchronization by comparing the locking threshold for a ring and chain of oscillators. Given identical initial phases and random natural frequencies, the ratio of locking thresholds is given upper and lower bounds which depend only on the shape of the coupling function. Finally, we examine a population of oscillators with random coupling strengths distributed across zero. A quarter century ago, a ``volcano transition'' was identified in such a model, but by using a particular coupling matrix construction, we present the first results analytically characterizing the transition point
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