47,316 research outputs found
Diffusion model approach to simulating electron-proton scattering events
Generative AI is a fast-growing area of research offering various avenues for
exploration in high-energy nuclear physics. In this work, we explore the use of
generative models for simulating electron-proton collisions relevant to
experiments like CEBAF and the future Electron-Ion Collider (EIC). These
experiments play a critical role in advancing our understanding of nucleons and
nuclei in terms of quark and gluon degrees of freedom. The use of generative
models for simulating collider events faces several challenges such as the
sparsity of the data, the presence of global or event-wide constraints, and
steeply falling particle distributions. In this work, we focus on the
implementation of diffusion models for the simulation of electron-proton
scattering events at EIC energies. Our results demonstrate that diffusion
models can accurately reproduce relevant observables such as momentum
distributions and correlations of particles, momentum sum rules, and the
leading electron kinematics, all of which are of particular interest in
electron-proton collisions. Although the sampling process is relatively slow
compared to other machine learning architectures, we find diffusion models can
generate high-quality samples. We foresee various applications of our work
including inference for nuclear structure, interpretable generative machine
learning, and searches of physics beyond the Standard Model.Comment: 14 pages, 10 figure
A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems
We propose a technique to detect and generate patterns in a network of
locally interacting dynamical systems. Central to our approach is a novel
spatial superposition logic, whose semantics is defined over the quad-tree of a
partitioned image. We show that formulas in this logic can be efficiently
learned from positive and negative examples of several types of patterns. We
also demonstrate that pattern detection, which is implemented as a model
checking algorithm, performs very well for test data sets different from the
learning sets. We define a quantitative semantics for the logic and integrate
the model checking algorithm with particle swarm optimization in a
computational framework for synthesis of parameters leading to desired patterns
in reaction-diffusion systems
An Exact Auxiliary Variable Gibbs Sampler for a Class of Diffusions
Stochastic differential equations (SDEs) or diffusions are continuous-valued
continuous-time stochastic processes widely used in the applied and
mathematical sciences. Simulating paths from these processes is usually an
intractable problem, and typically involves time-discretization approximations.
We propose an exact Markov chain Monte Carlo sampling algorithm that involves
no such time-discretization error. Our sampler is applicable to the problem of
prior simulation from an SDE, posterior simulation conditioned on noisy
observations, as well as parameter inference given noisy observations. Our work
recasts an existing rejection sampling algorithm for a class of diffusions as a
latent variable model, and then derives an auxiliary variable Gibbs sampling
algorithm that targets the associated joint distribution. At a high level, the
resulting algorithm involves two steps: simulating a random grid of times from
an inhomogeneous Poisson process, and updating the SDE trajectory conditioned
on this grid. Our work allows the vast literature of Monte Carlo sampling
algorithms from the Gaussian process literature to be brought to bear to
applications involving diffusions. We study our method on synthetic and real
datasets, where we demonstrate superior performance over competing methods.Comment: 37 pages, 13 figure
Complexity, parallel computation and statistical physics
The intuition that a long history is required for the emergence of complexity
in natural systems is formalized using the notion of depth. The depth of a
system is defined in terms of the number of parallel computational steps needed
to simulate it. Depth provides an objective, irreducible measure of history
applicable to systems of the kind studied in statistical physics. It is argued
that physical complexity cannot occur in the absence of substantial depth and
that depth is a useful proxy for physical complexity. The ideas are illustrated
for a variety of systems in statistical physics.Comment: 21 pages, 7 figure
Intrinsic Gaussian processes on complex constrained domains
We propose a class of intrinsic Gaussian processes (in-GPs) for
interpolation, regression and classification on manifolds with a primary focus
on complex constrained domains or irregular shaped spaces arising as subsets or
submanifolds of R, R2, R3 and beyond. For example, in-GPs can accommodate
spatial domains arising as complex subsets of Euclidean space. in-GPs respect
the potentially complex boundary or interior conditions as well as the
intrinsic geometry of the spaces. The key novelty of the proposed approach is
to utilise the relationship between heat kernels and the transition density of
Brownian motion on manifolds for constructing and approximating valid and
computationally feasible covariance kernels. This enables in-GPs to be
practically applied in great generality, while existing approaches for
smoothing on constrained domains are limited to simple special cases. The broad
utilities of the in-GP approach is illustrated through simulation studies and
data examples
Simulating Brain Tumor Heterogeneity with a Multiscale Agent-Based Model: Linking Molecular Signatures, Phenotypes and Expansion Rate
We have extended our previously developed 3D multi-scale agent-based brain
tumor model to simulate cancer heterogeneity and to analyze its impact across
the scales of interest. While our algorithm continues to employ an epidermal
growth factor receptor (EGFR) gene-protein interaction network to determine the
cells' phenotype, it now adds an explicit treatment of tumor cell adhesion
related to the model's biochemical microenvironment. We simulate a simplified
tumor progression pathway that leads to the emergence of five distinct glioma
cell clones with different EGFR density and cell 'search precisions'. The in
silico results show that microscopic tumor heterogeneity can impact the tumor
system's multicellular growth patterns. Our findings further confirm that EGFR
density results in the more aggressive clonal populations switching earlier
from proliferation-dominated to a more migratory phenotype. Moreover, analyzing
the dynamic molecular profile that triggers the phenotypic switch between
proliferation and migration, our in silico oncogenomics data display spatial
and temporal diversity in documenting the regional impact of tumorigenesis, and
thus support the added value of multi-site and repeated assessments in vitro
and in vivo. Potential implications from this in silico work for experimental
and computational studies are discussed.Comment: 37 pages, 10 figure
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