arXiv subjects

Brian Williams

Publications and source records attributed to Brian Williams.

At least 55 records · Page 3Linked to original sources

arXiv2019

Efficiently Exploring Ordering Problems through Conflict-directed Search

In planning and scheduling, solving problems with both state and temporal constraints is hard since these constraints may be highly coupled. Judicious orderings of events enable solvers to efficiently make decisions over sequences of actions to satisfy complex hybrid specifications. The ordering problem is thus fundamental to planning. Promising recent works have explored the ordering problem as search, incorporating a special tree structure for efficiency. However, such approaches only reason over partial order specifications. Having observed that an ordering is inconsistent with respect to underlying constraints, prior works do not exploit the tree structure to efficiently generate orderings that resolve the inconsistency. In this paper, we present Conflict-directed Incremental Total Ordering (CDITO), a conflict-directed search method to incrementally and systematically generate event total orders given ordering relations and conflicts returned by sub-solvers. Due to its ability to reason over conflicts, CDITO is much more efficient than Incremental Total Ordering. We demonstrate this by benchmarking on temporal network configuration problems that involve routing network flows and allocating bandwidth resources over time.

cs.AI↗

arXiv2019

Toroidal prefactorization algebras associated to holomorphic fibrations and a relationship to vertex algebras

Let $X$ be a complex manifold, $π: E \rightarrow X$ a locally trivial holomorphic fibration with fiber $F$, and $\mathfrak{g}$ a Lie algebra with an invariant symmetric form. We associate to this data a holomorphic prefactorization algebra $\mathcal{F}_{\mathfrak{g}, π}$ on $X$ in the formalism of Costello-Gwilliam. When $X=\mathbb{C}$, $\mathfrak{g}$ is simple, and $F$ is a smooth affine variety, we extract from $\mathcal{F}_{\mathfrak{g}, π}$ a vertex algebra which is a vacuum module for the universal central extension of the Lie algebra $\mathfrak{g} \otimes H^{0}(F, \mathcal{O})[z,z^{-1}]$. As a special case, when $F$ is an algebraic torus $(\mathbb{C}^{*})^n$, we obtain a vertex algebra naturally associated to an $(n+1)$--toroidal algebra, generalizing the affine vacuum module.

math.QA↗

arXiv2019

Complexity Bounds for the Controllability of Temporal Networks with Conditions, Disjunctions, and Uncertainty

In temporal planning, many different temporal network formalisms are used to model real world situations. Each of these formalisms has different features which affect how easy it is to determine whether the underlying network of temporal constraints is consistent. While many of the simpler models have been well-studied from a computational complexity perspective, the algorithms developed for advanced models which combine features have very loose complexity bounds. In this paper, we provide tight completeness bounds for strong, weak, and dynamic controllability checking of temporal networks that have conditions, disjunctions, and temporal uncertainty. Our work exposes some of the subtle differences between these different structures and, remarkably, establishes a guarantee that all of these problems are computable in PSPACE.

cs.AI↗

arXiv2018

Chance Constrained Motion Planning for High-Dimensional Robots

This paper introduces Probabilistic Chekov (p-Chekov), a chance-constrained motion planning system that can be applied to high degree-of-freedom (DOF) robots under motion uncertainty and imperfect state information. Given process and observation noise models, it can find feasible trajectories which satisfy a user-specified bound over the probability of collision. Leveraging our previous work in deterministic motion planning which integrated trajectory optimization into a sparse roadmap framework, p-Chekov shows superiority in its planning speed for high-dimensional tasks. P-Chekov incorporates a linear-quadratic Gaussian motion planning approach into the estimation of the robot state probability distribution, applies quadrature theories to waypoint collision risk estimation, and adapts risk allocation approaches to assign allowable probabilities of failure among waypoints. Unlike other existing risk-aware planners, p-Chekov can be applied to high-DOF robotic planning tasks without the convexification of the environment. The experiment results in this paper show that this p-Chekov system can effectively reduce collision risk and satisfy user-specified chance constraints in typical real-world planning scenarios for high-DOF robots.

cs.RO↗

arXiv2018

Improving Trajectory Optimization using a Roadmap Framework

We present an evaluation of several representative sampling-based and optimization-based motion planners, and then introduce an integrated motion planning system which incorporates recent advances in trajectory optimization into a sparse roadmap framework. Through experiments in 4 common application scenarios with 5000 test cases each, we show that optimization-based or sampling-based planners alone are not effective for realistic problems where fast planning times are required. To the best of our knowledge, this is the first work that presents such a systematic and comprehensive evaluation of state-of-the-art motion planners, which are based on a significant amount of experiments. We then combine different stand-alone planners with trajectory optimization. The results show that the combination of our sparse roadmap and trajectory optimization provides superior performance over other standard sampling-based planners combinations. By using a multi-query roadmap instead of generating completely new trajectories for each planning problem, our approach allows for extensions such as persistent control policy information associated with a trajectory across planning problems. Also, the sub-optimality resulting from the sparsity of roadmap, as well as the unexpected disturbances from the environment, can both be overcome by the real-time trajectory optimization process.

cs.RO↗

arXiv2018

The holomorphic bosonic string

We present a holomorphic version of the bosonic string in the formalism of quantum field theory developed by Costello and collaborators. In this paper we focus on the case in which space-time is flat and construct a one-loop exact quantization. Starting from first principles, we arrive at the critical dimension as an obstruction to satisfying the quantum master equation. Moreover, we show how the factorization algebra recovers the BRST cohomology of the string and give another construction of the Gerstenhaber structure. Finally, we show how the factorization homology along closed manifolds encodes the determinant line bundle over the moduli space of Riemann surfaces.

math-ph↗

arXiv2017

Asymptotic Freedom in the BV Formalism

We define the beta-function of a perturbative quantum field theory in the mathematical framework introduced by Costello -- combining perturbative renormalization and the BV formalism -- as the cohomology class of a certain element in the obstruction-deformation complex. We show that the one-loop beta-function is a well-defined element of the local deformation complex for translation-invariant and classically scale-invariant theories, and furthermore that it is locally constant as a function on the space of classical interactions and computable as a rescaling anomaly, or as the logarithmic one-loop counterterm. We compute the one-loop beta-function in first-order Yang--Mills theory, recovering the famous asymptotic freedom for Yang--Mills in a mathematical context.

math-ph↗

arXiv2016

Time Resource Networks

The problem of scheduling under resource constraints is widely applicable. One prominent example is power management, in which we have a limited continuous supply of power but must schedule a number of power-consuming tasks. Such problems feature tightly coupled continuous resource constraints and continuous temporal constraints. We address such problems by introducing the Time Resource Network (TRN), an encoding for resource-constrained scheduling problems. The definition allows temporal specifications using a general family of representations derived from the Simple Temporal network, including the Simple Temporal Network with Uncertainty, and the probabilistic Simple Temporal Network (Fang et al. (2014)). We propose two algorithms for determining the consistency of a TRN: one based on Mixed Integer Programing and the other one based on Constraint Programming, which we evaluate on scheduling problems with Simple Temporal Constraints and Probabilistic Temporal Constraints.

cs.AI↗

arXiv2015

Discussion: The NoMax Strategy and Correlated Outputs

This is a discussion of the paper "Modeling an Augmented Lagrangian for Improved Blackbox Constrained Optimization," (Gramacy, R.~B., Gray, G.~A., Digabel, S.~L., Lee, H.~K.~H., Ranjan, P., Wells, G., and Wild, S.~M., Technometrics, 61, 1--38, 2015).

math.OC↗

arXiv2014

Ending AIDS in Gabon: How long will it take? How much will it cost?

The prevalence of HIV in West Africa is lower than elsewhere in Africa but Gabon has one of the highest rates of HIV in that region. Gabon has a small population and a high per capita gross domestic product making it an ideal place to carry out a programme of early treatment for HIV. The effectiveness, availability and affordability of triple combination therapy make it possible to contemplate ending AIDS deaths and HIV transmission in the short term and HIV prevalence in the long term. Here we consider what would have happened in Gabon without the development of potent anti-retroviral therapy (ART), the impact that the current roll-out of ART has had on HIV, and what might be possible if early treatment with ART becomes available to all. We fit a dynamic transmission model to trends in the adult prevalence of HIV and infer trends in incidence, mortality and the impact of ART. The availability of ART has reduced the prevalence of HIV among adults not on ART from 4.2% to 2.9%, annual incidence from 0.43% to 0.27%, and the proportion of adults dying from AIDS illnesses each year from 0.36% to 0.13% saving the lives of 2.3 thousand people in 2013 alone. The provision of ART has been highly cost effective saving the country at least $18 million up to 2013.

q-bio.QM↗

arXiv2014

Elimination of HIV in South Africa through expanded access to antiretroviral therapy: Cautions, caveats and the importance of parsimony

In a recent article Hontelez and colleagues investigate the prospects for elimination of HIV in South Africa through expanded access to antiretroviral therapy (ART) using STDSIM, a micro-simulation model. One of the first published models to suggest that expanded access to ART could lead to the elimination of HIV, referred to by the authors as the Granich Model, was developed and implemented by the present author. The notion that expanded access to ART could lead to the end of the AIDS epidemic gave rise to considerable interest and debate and remains contentious. In considering this notion Hontelez et al. start by stripping down STDSIM to a simple model that is equivalent to the model developed by the present author3 but is a stochastic event driven model. Hontelez and colleagues then reintroduce levels of complexity to explore ways in which the model structure affects the results. In contrast to our earlier conclusions Hontelez and colleagues conclude that universal voluntary counselling and testing with immediate ART at 90% coverage should result in the elimination of HIV but would take three times longer than predicted by the model developed by the present author. Hontelez et al. suggest that the current scale-up of ART at CD4 cell counts less than 350 cells/microL will lead to elimination of HIV in 30 years. I disagree with both claims and believe that their more complex models rely on unwarranted and unsubstantiated assumptions.

q-bio.QM↗

arXiv2014

Drake: An Efficient Executive for Temporal Plans with Choice

This work presents Drake, a dynamic executive for temporal plans with choice. Dynamic plan execution strategies allow an autonomous agent to react quickly to unfolding events, improving the robustness of the agent. Prior work developed methods for dynamically dispatching Simple Temporal Networks, and further research enriched the expressiveness of the plans executives could handle, including discrete choices, which are the focus of this work. However, in some approaches to date, these additional choices induce significant storage or latency requirements to make flexible execution possible. Drake is designed to leverage the low latency made possible by a preprocessing step called compilation, while avoiding high memory costs through a compact representation. We leverage the concepts of labels and environments, taken from prior work in Assumption-based Truth Maintenance Systems (ATMS), to concisely record the implications of the discrete choices, exploiting the structure of the plan to avoid redundant reasoning or storage. Our labeling and maintenance scheme, called the Labeled Value Set Maintenance System, is distinguished by its focus on properties fundamental to temporal problems, and, more generally, weighted graph algorithms. In particular, the maintenance system focuses on maintaining a minimal representation of non-dominated constraints. We benchmark Drakes performance on random structured problems, and find that Drake reduces the size of the compiled representation by a factor of over 500 for large problems, while incurring only a modest increase in run-time latency, compared to prior work in compiled executives for temporal plans with discrete choices.

cs.AI↗

arXiv2013

Destriping Cosmic Microwave Background Polarimeter data

Destriping is a well-established technique for removing low-frequency correlated noise from Cosmic Microwave Background (CMB) survey data. In this paper we present a destriping algorithm tailored to data from a polarimeter, i.e. an instrument where each channel independently measures the polarization of the input signal. We also describe a fully parallel implementation in Python released as Free Software and analyze its results and performance on simulated datasets, both the design case of signal and correlated noise, and with additional systematic effects. Finally we apply the algorithm to 30 days of 37.5 GHz polarized microwave data gathered from the B-Machine experiment, developed at UCSB. The B-Machine data and destriped maps are made publicly available. The purpose is the development of a scalable software tool to be applied to the upcoming 12 months of temperature and polarization data from LATTE (Low frequency All sky TemperaTure Experiment) at 8 GHz and to even larger datasets.

astro-ph.IM↗

arXiv2013

The Coyote Universe III: Simulation Suite and Precision Emulator for the Nonlinear Matter Power Spectrum

Many of the most exciting questions in astrophysics and cosmology, including the majority of observational probes of dark energy, rely on an understanding of the nonlinear regime of structure formation. In order to fully exploit the information available from this regime and to extract cosmological constraints, accurate theoretical predictions are needed. Currently such predictions can only be obtained from costly, precision numerical simulations. This paper is the third in a series aimed at constructing an accurate calibration of the nonlinear mass power spectrum on Mpc scales for a wide range of currently viable cosmological models, including dark energy. The first two papers addressed the numerical challenges, and the scheme by which an interpolator was built from a carefully chosen set of cosmological models. In this paper we introduce the "Coyote Univers"' simulation suite which comprises nearly 1,000 N-body simulations at different force and mass resolutions, spanning 38 wCDM cosmologies. This large simulation suite enables us to construct a prediction scheme, or emulator, for the nonlinear matter power spectrum accurate at the percent level out to k~1 h/Mpc. We describe the construction of the emulator, explain the tests performed to ensure its accuracy, and discuss how the central ideas may be extended to a wider range of cosmological models and applications. A power spectrum emulator code is released publicly as part of this paper.

astro-ph.CO↗

arXiv2013

HIV, TB and ART: the CD4 enigma

The concentration of CD4 T-lymphocytes (CD4 count), in a person's plasma is widely used to decide when to start HIV-positive people on anti-retroviral therapy (ART) and to predict the impact of ART on the future course of HIV and tuberculosis (TB). However, CD4 cell-counts vary widely within and among populations and depend on many factors besides HIV-infection. The way in which CD4 counts decline over the course of HIV infection is neither well understood nor widely agreed. We review what is known about CD4 counts in relation to HIV and TB and discuss areas in which more research is needed to build a consensus on how to interpret and use CD4 counts in clinical practice and to develop a better understanding of the dynamics and control of HIV and HIV-related TB.

q-bio.QM↗

arXiv2013

Mission to the Trojan Asteroids: lessons learned during a JPL Planetary Science Summer School mission design exercise

The 2013 Planetary Science Decadal Survey identified a detailed investigation of the Trojan asteroids occupying Jupiter's L4 and L5 Lagrange points as a priority for future NASA missions. Observing these asteroids and measuring their physical characteristics and composition would aid in identification of their source and provide answers about their likely impact history and evolution, thus yielding information about the makeup and dynamics of the early Solar System. We present a conceptual design for a mission to the Jovian Trojan asteroids: the Trojan ASteroid Tour, Exploration, and Rendezvous (TASTER) mission, that is consistent with the NASA New Frontiers candidate mission recommended by the Decadal Survey and the final result of the 2011 NASA-JPL Planetary Science Summer School. Our proposed mission includes visits to two Trojans in the L4 population: a 500 km altitude fly-by of 1999 XS143, followed by a rendezvous with and detailed observations of 911 Agamemnon at orbital altitudes of 1000 - 100 km over a 12 month nominal science data capture period. Our proposed instrument payload - wide- and narrow-angle cameras, a visual and infrared mapping spectrometer, and a neutron/gamma ray spectrometer - would provide unprecedented high-resolution, regional-to-global datasets for the target bodies, yielding fundamental information about the early history and evolution of the Solar System. Although our mission design was completed as part of an academic exercise, this study serves as a useful starting point for future Trojan mission design studies. In particular, we identify and discuss key issues that can make large differences in the complex trade-offs required when designing a mission to the Trojan asteroids.

astro-ph.EP↗

arXiv2011

Resistance to TB drugs in KwaZulu-Natal: causes and prospects for control

In 2005 there was an outbreak of XDR (extensively drug resistant) TB in Tugela Ferry, which is served by the Church of Scotland Hospital (COSH), in the uMzinyathi District, KwaZulu-Natal, South Africa. An investigation was carried out to determine if XDR TB was occurring elsewhere in the province, and to develop hypotheses for the rise in drug resistance with a view to developing a strategy for the control of MDR (multi-drug resistant) and XDR TB in the province and elsewhere. TB incidence and treatment success rates, for each of the 11 districts in the province, were obtained from the provincial electronic TB register for the years 2002-2007. The results of culture and drug sensitivity tests for the years 2002 to 2007 in each of the districts were compiled and culture taking practices were compared to the number of MDR TB cases. Interviews were conducted with key personnel in affected sites. In 2007, 2799, or 2.3% of 119,218 notified TB cases in the province were multi-drug resistant (MDR), and of these 270 (9.6%) were XDR. The two worst affected districts were uMzinyathi where 226 (4.1%) of 5522 notified TB cases were MDR, and of these 120 (53%) were extensively drug resistant (XDR), and uMkhanyakude where 337 (4.8%) of 6991 notified TB cases were MDR, but of these only four or (1.2%) were XDR. The worst affected medical centre was COSH where 164 or 9.8% of notified TB cases were MDR and of these 99 (60%) were XDR. Very high rates of XDR TB in the province are only found in uMzinyathi district even though MDR TB is common in most other districts. XDR may arisen at COSH because of the early and effective integration of the TB and HIV programmes in overcrowded and poorly ventilated facilities particular to COS.H To control XDR TB better management of both susceptible and resistant forms of TB is needed including treatment supervision, infection control and HIV management.

q-bio.CB↗

arXiv2010

Modeling the frequency response of microwave radiometers with QUCS

Characterization of the frequency response of coherent radiometric receivers is a key element in estimating the flux of astrophysical emissions, since the measured signal depends on the convolution of the source spectral emission with the instrument band shape. Laboratory Radio Frequency (RF) measurements of the instrument bandpass often require complex test setups and are subject to a number of systematic effects driven by thermal issues and impedance matching, particularly if cryogenic operation is involved. In this paper we present an approach to modeling radiometers bandpasses by integrating simulations and RF measurements of individual components. This method is based on QUCS (Quasi Universal Circuit Simulator), an open-source circuit simulator, which gives the flexibility of choosing among the available devices, implementing new analytical software models or using measured S-parameters. Therefore an independent estimate of the instrument bandpass is achieved using standard individual component measurements and validated analytical simulations. In order to automate the process of preparing input data, running simulations and exporting results we developed the Python package python-qucs and released it under GNU Public License. We discuss, as working cases, bandpass response modeling of the COFE and Planck Low Frequency Instrument (LFI) radiometers and compare results obtained with QUCS and with a commercial circuit simulator software. The main purpose of bandpass modeling in COFE is to optimize component matching, while in LFI they represent the best estimation of frequency response, since end-to-end measurements were strongly affected by systematic effects.

astro-ph.IM↗