A semidefinite program for unbalanced multisection in the stochastic block model

We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure. We prove that our algorithm achieves exact recovery of the latent communities, up to the information-theoretic limits determined by Abbe and Sandon (2015). Our result extends prior SDP approaches by allowing for many communities of different sizes. By virtue of a semidefinite approach, our algorithms succeed against a semirandom variant of the stochastic block model, guaranteeing a form of robustness and generalization. We further explore how semirandom models can lend insight into both the strengths and limitations of SDPs in this setting.Comment: 29 page

Estimation under group actions: recovering orbits from invariants

Motivated by geometric problems in signal processing, computer vision, and structural biology, we study a class of orbit recovery problems where we observe very noisy copies of an unknown signal, each acted upon by a random element of some group (such as Z/p or SO(3)). The goal is to recover the orbit of the signal under the group action in the high-noise regime. This generalizes problems of interest such as multi-reference alignment (MRA) and the reconstruction problem in cryo-electron microscopy (cryo-EM). We obtain matching lower and upper bounds on the sample complexity of these problems in high generality, showing that the statistical difficulty is intricately determined by the invariant theory of the underlying symmetry group. In particular, we determine that for cryo-EM with noise variance $\sigma^2$ and uniform viewing directions, the number of samples required scales as $\sigma^6$. We match this bound with a novel algorithm for ab initio reconstruction in cryo-EM, based on invariant features of degree at most 3. We further discuss how to recover multiple molecular structures from heterogeneous cryo-EM samples.Comment: 54 pages. This version contains a number of new result

How robust are reconstruction thresholds for community detection?

The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection. In an exciting sequence of developments, motivated by deep but non-rigorous ideas from statistical physics, Decelle et al. conjectured a sharp threshold for when community detection is possible in the sparse regime. Mossel, Neeman and Sly and Massoulié proved the conjecture and gave matching algorithms and lower bounds. Here we revisit the stochastic block model from the perspective of semirandom models where we allow an adversary to make 'helpful' changes that strengthen ties within each community and break ties between them. We show a surprising result that these 'helpful' changes can shift the information-theoretic threshold, making the community detection problem strictly harder. We complement this by showing that an algorithm based on semidefinite programming (which was known to get close to the threshold) continues to work in the semirandom model (even for partial recovery). This suggests that algorithms based on semidefinite programming are robust in ways that any algorithm meeting the information-theoretic threshold cannot be. These results point to an interesting new direction: Can we find robust, semirandom analogues to some of the classical, average-case thresholds in statistics? We also explore this question in the broadcast tree model, and we show that the viewpoint of semirandom models can help explain why some algorithms are preferred to others in practice, in spite of the gaps in their statistical performance on random models.National Science Foundation (U.S.). Faculty Early Career Development Program (Award CCF-1453261)Google Faculty Research AwardNihon Denki Kabushiki Kaish

Youths\u27 Perspectives on the Reasons Underlying School Truancy and Opportunities to Improve School Attendance

School truancy is common in the United States; however, youths’ perspectives on the underlying reasons for and the best ways to curtail this phenomenon are lacking. This project sought to better understand what factors contribute to youths’ decisions to skip classes or ditch full days of school over time and to solicit youths’ recommendations on how to reduce truancy and improve system functioning. We used a community partnered qualitative descriptive approach to conduct in-depth interviews with 39 youths with a history of truancy from South and East Los Angeles. Youths’ experiences and recommendations illustrate the multiple factors that influence school truancy and suggest potential leverage points for reducing truancy, including modifications to the school environment to increase student engagement; a more effective school response to address truancy; and further involvement and engagement of parents. Researchers, policy makers, and school practitioners can use results to help inform efforts to address school truancy

Quantitative microscopic methods for crystal growth and dissolution processes

The aim of this thesis was to investigate crystal nucleation, growth and dissolution processes, focussing particularly on the behaviour of the crystal surface. To facilitate this various methods of microscopy were used, as well as electrochemical techniques, with the goal to separate mass transport towards the crystal surface and the processes which occur close to the crystal surface, and measure intrinsic growth/dissolution rates. In order to do this, crystal systems were screened for their relevance to applications in industrial processes, and those chosen were related to pharmaceutical crystallization and scale formation in o↵ shore oil wells. For each system, different methods of electrochemical measurement and microscopy were investigated to chose a technique which works best for the problem in hand. Further to the experimental data produced, these were supported by mass transfer models, with the aim of finding out more quantitative information about the surface behaviour of the crystal systems observed. Firstly, salicylic acid micro-crystals were observed in aqueous solution by optical microscopy to visualise growth/dissolution rates of individual faces. It was found from finite element method (FEM) simulations that the most active (001) face was strongly mass transport controlled, and that the (110) and ( ¯ 110) were closer to the surface controlled regime. Salicylic acid crystals were further analysed by scanning electrochemical microscopy (SECM) using 3 dimensional (3D) scans containing a series of approaches to the surface. By inducing dissolution on the crystal surface, and measuring a change in ultramicroelectrode (UME) current, the dissolution rate constant of the (110) face of salicylic acid was determined for this heterogeneous surface. Barite nucleation and growth was observed by optical microscopy, using a flow cell with hydrodynamic flow. High supersaturations were used and the crystals were deposited onto foreign surfaces with differing surface charge. It was found that the flux of material, once initial nucleation was achieved, matched closely to simulated mass transport fluxes. Finally, nanoprecipitation was induced at the opening of a nanopipette (ca. 100 nm) diameter and an ion current was applied to induce the early stages of barite nucleation. It was possible to observe nucleation and blockage of the nanopipette from the current transient produced. This process was used to test the effectiveness of different phosphonate inhibitors

Overcomplete Independent Component Analysis via SDP

We present a novel algorithm for overcomplete independent components analysis (ICA), where the number of latent sources k exceeds the dimension p of observed variables. Previous algorithms either suffer from high computational complexity or make strong assumptions about the form of the mixing matrix. Our algorithm does not make any sparsity assumption yet enjoys favorable computational and theoretical properties. Our algorithm consists of two main steps: (a) estimation of the Hessians of the cumulant generating function (as opposed to the fourth and higher order cumulants used by most algorithms) and (b) a novel semi-definite programming (SDP) relaxation for recovering a mixing component. We show that this relaxation can be efficiently solved with a projected accelerated gradient descent method, which makes the whole algorithm computationally practical. Moreover, we conjecture that the proposed program recovers a mixing component at the rate k < p^2/4 and prove that a mixing component can be recovered with high probability when k < (2 - epsilon) p log p when the original components are sampled uniformly at random on the hyper sphere. Experiments are provided on synthetic data and the CIFAR-10 dataset of real images.Comment: Appears in: Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS 2019). 21 page

Hopping intermittent contact-scanning electrochemical microscopy (HIC-SECM) as a new local dissolution kinetic probe : application to salicylic acid dissolution in aqueous solution

Dissolution kinetics of the (110) face of salicylic acid in aqueous solution is determined by hopping intermittent contact-scanning electrochemical microscopy (HIC-SECM) using a 2.5 μm diameter platinum ultramicroelectrode (UME). The method operates by translating the probe UME towards the surface at a series of positions across the crystal and inducing dissolution via the reduction of protons to hydrogen, which titrates the weak acid and promotes the dissolution reaction, but only when the UME is close to the crystal. Most importantly, as dissolution is only briefly and transiently induced at each location, the initial dissolution kinetics of an as-grown single crystal surface can be measured, rather than a surface which has undergone significant dissolution (pitting), as in other techniques. Mass transport and kinetics in the system are modelled using finite element method simulations which allows dissolution rate constants to be evaluated. It is found that the kinetics of an ‘as-grown’ crystal are much slower than for a surface that has undergone partial bulk dissolution (mimicking conventional techniques), which can be attributed to a dramatic change in surface morphology as identified by atomic force microscopy (AFM). The ‘as-grown’ (110) surface presents extended terrace structures to the solution which evidently dissolve slowly, whereas a partially dissolved surface has extensive etch features and step sites which greatly enhance dissolution kinetics. This means that crystals such as salicylic acid will show time-dependent dissolution kinetics (fluxes) that are strongly dependent on crystal history, and this needs to be taken into account to fully understand dissolution

KELT-1b: A Strongly Irradiated, Highly Inflated, Short Period, 27 Jupiter-mass Companion Transiting a mid-F Star

We present the discovery of KELT-1b, the first transiting low-mass companion from the wide-field Kilodegree Extremely Little Telescope-North (KELT-North) survey. The V=10.7 primary is a mildly evolved, solar-metallicity, mid-F star. The companion is a low-mass brown dwarf or super-massive planet with mass of 27.23+/-0.50 MJ and radius of 1.110+0.037-0.024 RJ, on a very short period (P=1.21750007) circular orbit. KELT-1b receives a large amount of stellar insolation, with an equilibrium temperature assuming zero albedo and perfect redistribution of 2422 K. Upper limits on the secondary eclipse depth indicate that either the companion must have a non-zero albedo, or it must experience some energy redistribution. Comparison with standard evolutionary models for brown dwarfs suggests that the radius of KELT-1b is significantly inflated. Adaptive optics imaging reveals a candidate stellar companion to KELT-1, which is consistent with an M dwarf if bound. The projected spin-orbit alignment angle is consistent with zero stellar obliquity, and the vsini of the primary is consistent with tidal synchronization. Given the extreme parameters of the KELT-1 system, we expect it to provide an important testbed for theories of the emplacement and evolution of short-period companions, and theories of tidal dissipation and irradiated brown dwarf atmospheres.Comment: 30 pages, 19 figures. Submitted to Ap