arXiv subjects

Alan Williams

Publications and source records attributed to Alan Williams.

26 records · Page 2Linked to original sources

arXiv2023

Semi-Global Practical Extremum Seeking with Practical Safety

We introduce a type of safe extremum seeking (ES) controller, which minimizes an unknown objective function while also maintaining practical positivity of an unknown barrier function. We show semi-global practical asymptotic stability of our algorithm and present an analogous notion of practical safety. The dynamics of the controller are inspired by the quadratic program (QP) based safety filter designs which, in the literature, are more commonly used in cases where the barrier function is known. Conditions on the barrier and objective function are explored showing that non convex problems can be solved. A Lyapunov argument is proposed to achieve the main results of the paper. Finally, an example is given of the algorithm which solves the constrained optimization problem.

math.OC↗

arXiv2023

Experimental Safe Extremum Seeking for Accelerators

We demonstrate the recent designs of Safe Extremum Seeking (Safe ES) on the 1 kilometer-long charged particle accelerator at the Los Alamos Neutron Science Center (LANSCE). Safe ES is a modification of ES which, in addition to minimizing an analytically unknown cost, also employs a safety filter based on an analytically unknown control barrier function (CBF) safety metric. Accelerator tuning is necessitated by the accelerators being large, with many drifting parameters due to thermal effects and degradation. At the same time, safe operation (the maintenance of state constraints) is crucial, as damage brings astronomical costs, both financially and in operation downtime. Our measured (but analytically unknown) safety metric is the beam current. We perform multivariable Safe ES on three accelerator applications, in which we adapt 4, 6, and 3 magnet strength parameters, respectively. Two of the three applications are for validated simulation models of beamlines at LANSCE: the first for the Proton Radiography (pRad) beamline of 800 MeV protons for spot size tuning; the second on a high performance code, HPSim, for tuning the low energy beam transport (LEBT) region of of 750 keV protons. The third is an experimental tuning of the steering magnets in the LEBT at LANSCE.

physics.acc-ph↗

arXiv2021

Workflows Community Summit: Advancing the State-of-the-art of Scientific Workflows Management Systems Research and Development

Scientific workflows are a cornerstone of modern scientific computing, and they have underpinned some of the most significant discoveries of the last decade. Many of these workflows have high computational, storage, and/or communication demands, and thus must execute on a wide range of large-scale platforms, from large clouds to upcoming exascale HPC platforms. Workflows will play a crucial role in the data-oriented and post-Moore's computing landscape as they democratize the application of cutting-edge research techniques, computationally intensive methods, and use of new computing platforms. As workflows continue to be adopted by scientific projects and user communities, they are becoming more complex. Workflows are increasingly composed of tasks that perform computations such as short machine learning inference, multi-node simulations, long-running machine learning model training, amongst others, and thus increasingly rely on heterogeneous architectures that include CPUs but also GPUs and accelerators. The workflow management system (WMS) technology landscape is currently segmented and presents significant barriers to entry due to the hundreds of seemingly comparable, yet incompatible, systems that exist. Another fundamental problem is that there are conflicting theoretical bases and abstractions for a WMS. Systems that use the same underlying abstractions can likely be translated between, which is not the case for systems that use different abstractions. More information: https://workflowsri.org/summits/technical

cs.DC↗

arXiv2021

$N$-detachable pairs in 3-connected matroids III: the theorem

math.CO↗

arXiv2020

$N$-detachable pairs in 3-connected matroids II: life in $X$

Let $M$ be a 3-connected matroid, and let $N$ be a 3-connected minor of $M$. A pair $\{x_1,x_2\} \subseteq E(M)$ is $N$-detachable if one of the matroids $M/x_1/x_2$ or $M \backslash x_1 \backslash x_2$ is both 3-connected and has an $N$-minor. This is the second in a series of three papers where we describe the structures that arise when it is not possible to find an $N$-detachable pair in $M$. In the first paper in the series, we showed that, under mild assumptions, either $M$ has an $N$-detachable pair, $M$ has one of three particular 3-separators that can appear in a matroid with no N-detachable pairs, or there is a 3-separating set $X$ with certain strong structural properties. In this paper, we analyse matroids with such a structured set $X$, and prove that they have either an $N$-detachable pair, or one of five particular 3-separators that can appear in a matroid with no $N$-detachable pairs.

math.CO↗

arXiv2020

$N$-detachable pairs in 3-connected matroids I: unveiling $X$

Let $M$ be a 3-connected matroid, and let $N$ be a 3-connected minor of $M$. We say that a pair $\{x_1,x_2\} \subseteq E(M)$ is $N$-detachable if one of the matroids $M/x_1/x_2$ or $M \backslash x_1 \backslash x_2$ is both 3-connected and has an $N$-minor. This is the first in a series of three papers where we describe the structures that arise when it is not possible to find an $N$-detachable pair in $M$. In this paper, we prove that if $M$ has no $N$-detachable pairs, then either $M$ has a 3-separating set, which we call $X$, with certain strong structural properties, or $M$ has one of three particular 3-separators that can appear in a matroid with no $N$-detachable pairs.

math.CO↗

arXiv2003

Random Walks for Spike-Timing Dependent Plasticity

Random walk methods are used to calculate the moments of negative image equilibrium distributions in synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of sensory electric fields. Of particular behavioral importance to the fish is the variance of the equilibrium postsynaptic potential in the presence of noise, which is determined by the variance of the equilibrium weight distribution. Recurrence relations are derived for the moments of the equilibrium weight distribution, for arbitrary postsynaptic potential functions and arbitrary learning rules. For the case of homogeneous network parameters, explicit closed form solutions are developed for the covariances of the synaptic weight and postsynaptic potential distributions.

q-bio.NC↗

arXiv2003

Stability of Negative Image Equilibria in Spike-Timing Dependent Plasticity

We investigate the stability of negative image equilibria in mean synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of external electric fields. We derive a necessary and sufficient condition for stability, for arbitrary postsynaptic potential functions and arbitrary learning rules. We then apply the general result to several examples of biological interest.

physics.bio-ph↗