Gradient descent for sparse rank-one matrix completion for crowd-sourced aggregation of sparsely interacting workers

We consider worker skill estimation for the singlecoin Dawid-Skene crowdsourcing model. In practice skill-estimation is challenging because worker assignments are sparse and irregular due to the arbitrary, and uncontrolled availability of workers. We formulate skill estimation as a rank-one correlation-matrix completion problem, where the observed components correspond to observed label correlation between workers. We show that the correlation matrix can be successfully recovered and skills identifiable if and only if the sampling matrix (observed components) is irreducible and aperiodic. We then propose an efficient gradient descent scheme and show that skill estimates converges to the desired global optima for such sampling matrices. Our proof is original and the results are surprising in light of the fact that even the weighted rank-one matrix factorization problem is NP hard in general. Next we derive sample complexity bounds for the noisy case in terms of spectral properties of the signless Laplacian of the sampling matrix. Our proposed scheme achieves state-of-art performance on a number of real-world datasets.Published versio

Minimal Reachability is Hard To Approximate

In this note, we consider the problem of choosing which nodes of a linear dynamical system should be actuated so that the state transfer from the system's initial condition to a given final state is possible. Assuming a standard complexity hypothesis, we show that this problem cannot be efficiently solved or approximated in polynomial, or even quasi-polynomial, time

Efficient Information Aggregation Strategies for Distributed Control and Signal Processing

This thesis is concerned with distributed control and coordination of networks consisting of multiple, potentially mobile, agents. This is motivated mainly by the emergence of large scale networks characterized by the lack of centralized access to information and time-varying connectivity. Control and optimization algorithms deployed in such networks should be completely distributed, relying only on local observations and information, and robust against unexpected changes in topology such as link failures. We will describe protocols to solve certain control and signal processing problems in this setting. We will demonstrate that a key challenge for such systems is the problem of computing averages in a decentralized way. Namely, we will show that a number of distributed control and signal processing problems can be solved straightforwardly if solutions to the averaging problem are available. The rest of the thesis will be concerned with algorithms for the averaging problem and its generalizations. We will (i) derive the fastest known averaging algorithms in a variety of settings and subject to a variety of communication and storage constraints (ii) prove a lower bound identifying a fundamental barrier for averaging algorithms (iii) propose a new model for distributed function computation which reflects the constraints facing many large-scale networks, and nearly characterize the general class of functions which can be computed in this model.Comment: Ph.D. thesis, Department of Electrical Engineering and Computer Science, MIT, September 201

Convergence speed in distributed consensus and averaging

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 71-75).We propose three new algorithms for the distributed averaging and consensus problems: two for the fixed-graph case, and one for the dynamic-topology case. The convergence times of our fixed-graph algorithms compare favorably with other known methods, while our algorithm for the dynamic-topology case is the first to be accompanied by a polynomial-time bound on the worst-case convergence time.by Alexander Olshevsky.S.M

Search for lightest neutralino and stau pair production in light gravitino scenarios with stau NLSP

Promptly decaying lightest neutralinos and long-lived staus are searched for in the context of light gravitino scenarios. It is assumed that the stau is the next to lightest supersymmetric particle (NLSP) and that the lightest neutralino is the next to NLSP (NNLSP). Data collected with the Delphi detector at centre-of-mass energies from 161 to 183 \GeV are analysed. No evidence of the production of these particles is found. Hence, lower mass limits for both kinds of particles are set at 95% C.L.. The mass of gaugino-like neutralinos is found to be greater than 71.5 GeV/c^2. In the search for long-lived stau, masses less than 70.0 to 77.5 \GeVcc are excluded for gravitino masses from 10 to 150 \eVcc . Combining this search with the searches for stable heavy leptons and Minimal Supersymmetric Standard Model staus a lower limit of 68.5 \GeVcc may be set for the stau mas

Shake a tail feather: the evolution of the theropod tail into a stiff aerodynamic surface

Theropod dinosaurs show striking morphological and functional tail variation; e.g., a long, robust, basal theropod tail used for counterbalance, or a short, modern avian tail used as an aerodynamic surface. We used a quantitative morphological and functional analysis to reconstruct intervertebral joint stiffness in the tail along the theropod lineage to extant birds. This provides new details of the tail's morphological transformation, and for the first time quantitatively evaluates its biomechanical consequences. We observe that both dorsoventral and lateral joint stiffness decreased along the non-avian theropod lineage (between nodes Theropoda and Paraves). Our results show how the tail structure of non-avian theropods was mechanically appropriate for holding itself up against gravity and maintaining passive balance. However, as dorsoventral and lateral joint stiffness decreased, the tail may have become more effective for dynamically maintaining balance. This supports our hypothesis of a reduction of dorsoventral and lateral joint stiffness in shorter tails. Along the avian theropod lineage (Avialae to crown group birds), dorsoventral and lateral joint stiffness increased overall, which appears to contradict our null expectation. We infer that this departure in joint stiffness is specific to the tail's aerodynamic role and the functional constraints imposed by it. Increased dorsoventral and lateral joint stiffness may have facilitated a gradually improved capacity to lift, depress, and swing the tail. The associated morphological changes should have resulted in a tail capable of producing larger muscular forces to utilise larger lift forces in flight. Improved joint mobility in neornithine birds potentially permitted an increase in the range of lift force vector orientations, which might have improved flight proficiency and manoeuvrability. The tail morphology of modern birds with tail fanning capabilities originated in early ornithuromorph birds. Hence, these capabilities should have been present in the early Cretaceous, with incipient tail-fanning capacity in the earliest pygostylian birds

Local Helioseismology of Sunspots: Current Status and Perspectives (Invited Review)

Mechanisms of the formation and stability of sunspots are among the longest-standing and intriguing puzzles of solar physics and astrophysics. Sunspots are controlled by subsurface dynamics hidden from direct observations. Recently, substantial progress in our understanding of the physics of the turbulent magnetized plasma in strong-field regions has been made by using numerical simulations and local helioseismology. Both the simulations and helioseismic measurements are extremely challenging, but it becomes clear that the key to understanding the enigma of sunspots is a synergy between models and observations. Recent observations and radiative MHD numerical models have provided a convincing explanation to the Evershed flows in sunspot penumbrae. Also, they lead to the understanding of sunspots as self-organized magnetic structures in the turbulent plasma of the upper convection zone, which are maintained by a large-scale dynamics. Local helioseismic diagnostics of sunspots still have many uncertainties, some of which are discussed in this review. However, there have been significant achievements in resolving these uncertainties, verifying the basic results by new high-resolution observations, testing the helioseismic techniques by numerical simulations, and comparing results obtained by different methods. For instance, a recent analysis of helioseismology data from the Hinode space mission has successfully resolved several uncertainties and concerns (such as the inclined-field and phase-speed filtering effects) that might affect the inferences of the subsurface wave-speed structure of sunspots and the flow pattern. It becomes clear that for the understanding of the phenomenon of sunspots it is important to further improve the helioseismology methods and investigate the whole life cycle of active regions, from magnetic-flux emergence to dissipation.Comment: 34 pages, 18 figures, submitted to Solar Physic

Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised protons

Measurements of the Collins and Sivers asymmetries for charged pions and charged and neutral kaons produced in semi-inclusive deep-inelastic scattering of high energy muons off transversely polarised protons are presented. The results were obtained using all the available COMPASS proton data, which were taken in the years 2007 and 2010. The Collins asymmetries exhibit in the valence region a non-zero signal for pions and there are hints of non-zero signal also for kaons. The Sivers asymmetries are found to be positive for positive pions and kaons and compatible with zero otherwise. © 2015

On the NP-hardness of checking matrix polytope stability and continuous-time switching stability

Motivated by questions in robust control and switched linear dynamical systems, we consider the problem checking whether all convex combinations of k matrices in R[superscript ntimesn] are stable. In particular, we are interested whether there exist algorithms which can solve this problem in time polynomial in n and k. We show that if k=n[superscript d] for any fixed real d > 0, then the problem is NP-hard, meaning that no polynomial-time algorithm in n exists provided that P ne NP, a widely believed conjecture in computer science. On the other hand, when k is a constant independent of n, then it is known that the problem may be solved in polynomial time in n. Using these results and the method of measurable switching rules, we prove our main statement: verifying the absolute asymptotic stability of a continuous-time switched linear system with more than n[superscript d] matrices A[subscript i] isin R[superscript ntimesn] satisfying 0 ges A[subscript i] + A[subscript i] [superscript T] is NP-hard