Depth-Independent Lower bounds on the Communication Complexity of Read-Once Boolean Formulas

We show lower bounds of $\Omega(\sqrt{n})$ and $\Omega(n^{1/4})$ on the randomized and quantum communication complexity, respectively, of all $n$-variable read-once Boolean formulas. Our results complement the recent lower bound of $\Omega(n/8^d)$ by Leonardos and Saks and $\Omega(n/2^{\Omega(d\log d)})$ by Jayram, Kopparty and Raghavendra for randomized communication complexity of read-once Boolean formulas with depth $d$. We obtain our result by "embedding" either the Disjointness problem or its complement in any given read-once Boolean formula.Comment: 5 page

Online Fault Classification in HPC Systems through Machine Learning

As High-Performance Computing (HPC) systems strive towards the exascale goal, studies suggest that they will experience excessive failure rates. For this reason, detecting and classifying faults in HPC systems as they occur and initiating corrective actions before they can transform into failures will be essential for continued operation. In this paper, we propose a fault classification method for HPC systems based on machine learning that has been designed specifically to operate with live streamed data. We cast the problem and its solution within realistic operating constraints of online use. Our results show that almost perfect classification accuracy can be reached for different fault types with low computational overhead and minimal delay. We have based our study on a local dataset, which we make publicly available, that was acquired by injecting faults to an in-house experimental HPC system.Comment: Accepted for publication at the Euro-Par 2019 conferenc

White matter integrity is associated with gait impairment and falls in mild cognitive impairment. Results from the gait and brain study

© 2019 The Authors Background: Mild Cognitive Impairment (MCI) is an intermediate state between normal cognition and dementia that is associated with twice the risk of falls. It is unknown whether white matter integrity (WMI) is associated with increased risk of falls in MCI. The purpose of this study was to evaluate if early changes in WMI were associated with gait impairment and falls. Methods: Forty-three participants with MCI from the Gait and Brain Study underwent standardized assessment of cognition, gait performance under single and dual-task conditions (walking while talking), and WMI using 3 Tesla diffusion tensor imaging (DTI). Macro-structural imaging characteristics (white and grey matter morphology) as well as microstructural WMI parameters were examined for associations with falls and gait performance. Significantly associated WM tracts were then used to test the interplay between WMI and history of falls, after adjusting for other important covariates. Results: Multiple WM tracts (corpus callosum, forceps minor, and the left inferior fronto-occipital fasciculus) were significantly associated with history of falls and lower dual-task gait performance. A multivariable regression model showed that fall history was associated with the radial diffusivity in the forceps minor, even after adjusting for education, sex, BMI, MMSE scores, comorbidities, gait velocity and WMH volume as covariates. Conclusions: Multiple WM tracts that are known to be involved in executive and visuospatial functions were preferentially affected in MCI individuals with history of falls. Our preliminary findings support the notion that WMI in key brain regions may increase risk of falls in older adults with MCI

Structural motifs of biomolecules

Biomolecular structures are assemblies of emergent anisotropic building modules such as uniaxial helices or biaxial strands. We provide an approach to understanding a marginally compact phase of matter that is occupied by proteins and DNA. This phase, which is in some respects analogous to the liquid crystal phase for chain molecules, stabilizes a range of shapes that can be obtained by sequence-independent interactions occurring intra- and intermolecularly between polymeric molecules. We present a singularityfree self-interaction for a tube in the continuum limit and show that this results in the tube being positioned in the marginally compact phase. Our work provides a unified framework for understanding the building blocks of biomolecules.Comment: 13 pages, 5 figure

Superuniversality from disorder at two-dimensional topological phase transitions

We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles (`anyons') identified with `electric charge' excitations of a phase with intrinsic topological order. All other anyons have nontrivial mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is `superuniversal' across a wide range of such condensation transitions, and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases.Comment: 33 pages, 35 figures; published versio

RELEASE: A High-level Paradigm for Reliable Large-scale Server Software

Erlang is a functional language with a much-emulated model for building reliable distributed systems. This paper outlines the RELEASE project, and describes the progress in the first six months. The project aim is to scale the Erlang’s radical concurrency-oriented programming paradigm to build reliable general-purpose software, such as server-based systems, on massively parallel machines. Currently Erlang has inherently scalable computation and reliability models, but in practice scalability is constrained by aspects of the language and virtual machine. We are working at three levels to address these challenges: evolving the Erlang virtual machine so that it can work effectively on large scale multicore systems; evolving the language to Scalable Distributed (SD) Erlang; developing a scalable Erlang infrastructure to integrate multiple, heterogeneous clusters. We are also developing state of the art tools that allow programmers to understand the behaviour of massively parallel SD Erlang programs. We will demonstrate the effectiveness of the RELEASE approach using demonstrators and two large case studies on a Blue Gene

Measurement induced criticality in quasiperiodic modulated random hybrid circuits

We study one-dimensional hybrid quantum circuits perturbed by quenched quasiperiodic (QP) modulations across the measurement-induced phase transition (MIPT). Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent $\beta$ to exceed the Luck bound $\nu \ge 1/(1-\beta)$ for the stability of the MIPT where $\nu\cong 4/3$. Via large-scale numerical simulations of random Clifford circuits interleaved with local projective measurements, we find that sufficiently large QP structural fluctuations destabilize the MIPT and induce a flow to a broad family of critical dynamical phase transitions of the infinite QP type that is governed by the wandering exponent, $\beta$. We numerically determine the associated critical properties, including the correlation length exponent consistent with saturating the Luck bound, and a universal activated dynamical scaling with activation exponent $\psi \cong \beta$, finding excellent agreement with the conclusions of real space renormalization group calculations.Comment: 14 pages, 13 figure