19,907 research outputs found
Maximizing Activity in Ising Networks via the TAP Approximation
A wide array of complex biological, social, and physical systems have
recently been shown to be quantitatively described by Ising models, which lie
at the intersection of statistical physics and machine learning. Here, we study
the fundamental question of how to optimize the state of a networked Ising
system given a budget of external influence. In the continuous setting where
one can tune the influence applied to each node, we propose a series of
approximate gradient ascent algorithms based on the Plefka expansion, which
generalizes the na\"{i}ve mean field and TAP approximations. In the discrete
setting where one chooses a small set of influential nodes, the problem is
equivalent to the famous influence maximization problem in social networks with
an additional stochastic noise term. In this case, we provide sufficient
conditions for when the objective is submodular, allowing a greedy algorithm to
achieve an approximation ratio of . Additionally, we compare the
Ising-based algorithms with traditional influence maximization algorithms,
demonstrating the practical importance of accurately modeling stochastic
fluctuations in the system
Nuclides as a liquid phase of chiral perturbation theory I: emergence of pion-less SU(2) PT
The Standard Model of particle physics, augmented with neutrino mixing, is at
least very nearly the complete theory of interactions of known particles at
energies accessible to Nature on Earth. Candidate effective theories of nuclear
structure must therefore reflect SM symmetries, especially the chiral global
symmetry of two-massless-quark QCD. For ground-state
nuclei, SU(2) chiral perturbation theory (XPT) enables perturbation in inverse
powers of , with analytic operators renormalized to
all loop orders. We show that pion-less "Static Chiral Nucleon Liquids" (SXNL)
emerge as a liquid phase of SU(2) XPT of protons, neutrons and 3
Nambu-Goldstone boson pions. Far-IR pions decouple from SXNL, simplifying the
derivation of saturated nuclear matter and microscopic liquid drops
(ground-state nuclides). We trace to the global symmetries of
two-massless-quark QCD the power of pion-less SU(2) XPT to capture experimental
ground-state properties of certain nuclides with even parity, spin zero, even
proton number Z, and neutron number N.
We derive the SXNL effective SU(2) XPT Lagrangian, including all order
operators. These include: all 4-nucleon
operators that survive Fierz rearrangement in the non-relativistic limit, and
effective Lorentz-vector iso-vector neutral "-exchange" operators. SXNL
motivate nuclear matter as non-topological solitons at zero pressure: the
Nuclear Liquid Drop Model and Bethe-Weizsacker Semi-Empirical Mass Formula
emerge in an explicit Thomas-Fermi construction provided in the companion
paper. For chosen nuclides, nuclear Density Functional and Skyrme models are
justified to order . We conjecture that inclusion of
higher order operators will result in accurate "natural" Skyrme, No-Core-Shell,
and neutron star models
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