95 research outputs found
Many-body correlations from integral geometry
In a recent letter we presented a framework for predicting the concentrations
of many-particle local structures inside the bulk liquid as a route to
assessing changes in the liquid approaching dynamical arrest. Central to this
framework was the morphometric approach, a synthesis of integral geometry and
liquid state theory, which has traditionally been derived from fundamental
measure theory. We present the morphometric approach in a new context as a
generalisation of scaled particle theory, and derive several morphometric
theories for hard spheres of fundamental and practical interest. Our central
result is a new theory which is particularly suited to the treatment of
many-body correlation functions in the hard sphere liquid, which we demonstrate
by numerical tests against simulation.Comment: 12 pages, 6 figure
Halo Excitation of He in Inelastic and Charge-Exchange Reactions
Four-body distorted wave theory appropriate for nucleon-nucleus reactions
leading to 3-body continuum excitations of two-neutron Borromean halo nuclei is
developed. The peculiarities of the halo bound state and 3-body continuum are
fully taken into account by using the method of hyperspherical harmonics. The
procedure is applied for A=6 test-bench nuclei; thus we report detailed studies
of inclusive cross sections for inelastic He(p,p')He and
charge-exchange Li(n,p)He reactions at nucleon energy 50 MeV. The
theoretical low-energy spectra exhibit two resonance-like structures. The first
(narrow) is the excitation of the well-known three-body resonance. The
second (broad) bump is a composition of overlapping soft modes of
multipolarities whose relative weights depend on
transferred momentum and reaction type. Inelastic scattering is the most
selective tool for studying the soft dipole excitation mode.Comment: Submitted to Phys. Rev. C., 11 figures using eps
Optimal Phase Transitions in Compressed Sensing
Compressed sensing deals with efficient recovery of analog signals from
linear encodings. This paper presents a statistical study of compressed sensing
by modeling the input signal as an i.i.d. process with known distribution.
Three classes of encoders are considered, namely optimal nonlinear, optimal
linear and random linear encoders. Focusing on optimal decoders, we investigate
the fundamental tradeoff between measurement rate and reconstruction fidelity
gauged by error probability and noise sensitivity in the absence and presence
of measurement noise, respectively. The optimal phase transition threshold is
determined as a functional of the input distribution and compared to suboptimal
thresholds achieved by popular reconstruction algorithms. In particular, we
show that Gaussian sensing matrices incur no penalty on the phase transition
threshold with respect to optimal nonlinear encoding. Our results also provide
a rigorous justification of previous results based on replica heuristics in the
weak-noise regime.Comment: to appear in IEEE Transactions of Information Theor
On the existence of solutions to adversarial training in multiclass classification
We study three models of the problem of adversarial training in multiclass
classification designed to construct robust classifiers against adversarial
perturbations of data in the agnostic-classifier setting. We prove the
existence of Borel measurable robust classifiers in each model and provide a
unified perspective of the adversarial training problem, expanding the
connections with optimal transport initiated by the authors in previous work
and developing new connections between adversarial training in the multiclass
setting and total variation regularization. As a corollary of our results, we
prove the existence of Borel measurable solutions to the agnostic adversarial
training problem in the binary classification setting, a result that improves
results in the literature of adversarial training, where robust classifiers
were only known to exist within the enlarged universal -algebra of the
feature space
Dispersion relations for
We present a dispersive analysis of the decay amplitude for
that is based on the fundamental principles of analyticity
and unitarity. In this framework, final-state interactions are fully taken into
account. Our dispersive representation relies only on input for the
and scattering phase shifts. Isospin symmetry allows us to describe
both the charged and neutral decay channel in terms of the same function. The
dispersion relation contains subtraction constants that cannot be fixed by
unitarity. We determine these parameters by a fit to Dalitz-plot data from the
VES and BES-III experiments. We study the prediction of a low-energy theorem
and compare the dispersive fit to variants of chiral perturbation theory.Comment: 22 pages, 10 figures; v2: added footnote, version published in EPJ
Anomalous transport in the crowded world of biological cells
A ubiquitous observation in cell biology is that diffusion of macromolecules
and organelles is anomalous, and a description simply based on the conventional
diffusion equation with diffusion constants measured in dilute solution fails.
This is commonly attributed to macromolecular crowding in the interior of cells
and in cellular membranes, summarising their densely packed and heterogeneous
structures. The most familiar phenomenon is a power-law increase of the MSD,
but there are other manifestations like strongly reduced and time-dependent
diffusion coefficients, persistent correlations, non-gaussian distributions of
the displacements, heterogeneous diffusion, and immobile particles. After a
general introduction to the statistical description of slow, anomalous
transport, we summarise some widely used theoretical models: gaussian models
like FBM and Langevin equations for visco-elastic media, the CTRW model, and
the Lorentz model describing obstructed transport in a heterogeneous
environment. Emphasis is put on the spatio-temporal properties of the transport
in terms of 2-point correlation functions, dynamic scaling behaviour, and how
the models are distinguished by their propagators even for identical MSDs.
Then, we review the theory underlying common experimental techniques in the
presence of anomalous transport: single-particle tracking, FCS, and FRAP. We
report on the large body of recent experimental evidence for anomalous
transport in crowded biological media: in cyto- and nucleoplasm as well as in
cellular membranes, complemented by in vitro experiments where model systems
mimic physiological crowding conditions. Finally, computer simulations play an
important role in testing the theoretical models and corroborating the
experimental findings. The review is completed by a synthesis of the
theoretical and experimental progress identifying open questions for future
investigation.Comment: review article, to appear in Rep. Prog. Phy
Precision theoretical methods for large-scale structure of the Universe
We develop new analytic methods to accurately describe the formation of cosmic large-scale structure. These methods are based on the path integral formalism and allows one to efficiently address a number of long-standing problems in the field.
We describe the non-linear evolution of the baryon acoustic oscillations (BAO) in the distribution of matter. We argue for the need for resummation of large infrared (IR) enhanced contributions from bulk flows. We show how this can be done via a systematic resummation of Feynman diagrams guided by well-defined power counting rules. We formulate IR resummation both in real and redshift spaces. For the latter we develop a new method that maps cosmological correlation functions from real to redshift space and retains their IR finiteness. Our results agree well with the N-body simulation data at the BAO scales. This establishes IR resummation within our approach as a robust and complete procedure and provides a consistent theoretical model for the BAO feature in the statistics of matter and biased tracers in real and redshift spaces.
Eventually, we perform a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. We evaluate the PDF in the saddle-point approximation and show how it factorizes into an exponent given by a spherically symmetric saddle-point solution and a prefactor produced by fluctuations. The prefactor splits into a monopole contribution which is evaluated exactly, and a factor corresponding to aspherical fluctuations. The latter is crucial for the consistency of the calculation: neglecting it would make the PDF incompatible with translational invariance. We compute the aspherical prefactor using a combination of analytic and numerical techniques, identify the sensitivity to the short-scale physics and argue that it must be properly renormalized. Finally, we compare our result with N-body simulation data and find an excellent agreement
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