2,581 research outputs found
Exponential Reduction in Sample Complexity with Learning of Ising Model Dynamics
The usual setting for learning the structure and parameters of a graphical
model assumes the availability of independent samples produced from the
corresponding multivariate probability distribution. However, for many models
the mixing time of the respective Markov chain can be very large and i.i.d.
samples may not be obtained. We study the problem of reconstructing binary
graphical models from correlated samples produced by a dynamical process, which
is natural in many applications. We analyze the sample complexity of two
estimators that are based on the interaction screening objective and the
conditional likelihood loss. We observe that for samples coming from a
dynamical process far from equilibrium, the sample complexity reduces
exponentially compared to a dynamical process that mixes quickly.Comment: Accepted to ICML 202
Time reflection and refraction in synthetic frequency dimension
The duality of space and time in Maxwell's equations has prompted interest in
time boundaries and the accompanying temporal analog of spatial reflection and
refraction. However, achieving observable time boundary effects at optical
frequencies in real materials is challenging. In this work, we demonstrate that
time reflection and refraction can be observed in a two-band model centered
around a non-zero reference energy. Our model can be physically implemented in
the synthetic frequency dimension as a system of two coupled
dynamically-modulated ring resonators. We find that modulation at microwave
frequencies is sufficient to observe time boundary effects for optical waves in
synthetic frequency dimension. Our work shows that implementing multi-band
models in synthetic dimensions opens a new avenue for further exploration of
time boundaries.Comment: 9 pages, 4 figures; fixed typo in equation labe
Unforgeable Noise-Tolerant Quantum Tokens
The realization of devices which harness the laws of quantum mechanics
represents an exciting challenge at the interface of modern technology and
fundamental science. An exemplary paragon of the power of such quantum
primitives is the concept of "quantum money". A dishonest holder of a quantum
bank-note will invariably fail in any forging attempts; indeed, under
assumptions of ideal measurements and decoherence-free memories such security
is guaranteed by the no-cloning theorem. In any practical situation, however,
noise, decoherence and operational imperfections abound. Thus, the development
of secure "quantum money"-type primitives capable of tolerating realistic
infidelities is of both practical and fundamental importance. Here, we propose
a novel class of such protocols and demonstrate their tolerance to noise;
moreover, we prove their rigorous security by determining tight fidelity
thresholds. Our proposed protocols require only the ability to prepare, store
and measure single qubit quantum memories, making their experimental
realization accessible with current technologies.Comment: 18 pages, 5 figure
Rho-omega mixing in asymmetric nuclear matter via QCD sum rule approach
We evaluate the operator product expansion (OPE) for a mixed correlator of
the isovector and isoscalar vector currents in the background of the nucleon
density with intrinsic isospin asymmetry [i.e. excess of neutrons over protons]
and match it with its imaginary part, given by resonances and continuum, via
the dispersion relation. The leading density-dependent contribution to
mixing is due the scattering term, which turns out to be larger
than any density dependent piece in the OPE. We estimate that the asymmetric
density of induces the amplitude
of mixing, equal in magnitude to the mixing amplitude in vacuum,
with the constructive interference for positive and destructive for negative
values of . We revisit sum rules for vector meson masses at finite
nucleon density to point out the numerical importance of the screening term in
the isoscalar channel, which turns out to be one order of magnitude larger than
any density-dependent condensates over the Borel window. This changes the
conclusions about the density dependence of , indicating
MeV increase at nuclear saturation density.Comment: 8 pages, Revte
Mass independence and asymmetry of the reaction: Multi-fragmentation as an example
We present our recent results on the fragmentation by varying the mass
asymmetry of the reaction between 0.2 and 0.7 at an incident energy of 250
MeV/nucleon. For the present study, the total mass of the system is kept
constant (ATOT = 152) and mass asymmetry of the reaction is defined by the
asymmetry parameter (? = | (AT - AP)/(AT + AP) |). The measured distributions
are shown as a function of the total charge of all projectile fragments,
Zbound. We see an interesting outcome for rise and fall in the production of
intermediate mass fragments (IMFs) for large asymmetric colliding nuclei. This
trend, however, is completely missing for large asymmetric nuclei. Therefore,
experiments are needed to verify this prediction
Graded extension of SO(2,1) Lie algebra and the search for exact solutions of Dirac equation by point canonical transformations
SO(2,1) is the symmetry algebra for a class of three-parameter problems that
includes the oscillator, Coulomb and Morse potentials as well as other problems
at zero energy. All of the potentials in this class can be mapped into the
oscillator potential by point canonical transformations. We call this class the
"oscillator class". A nontrivial graded extension of SO(2,1) is defined and its
realization by two-dimensional matrices of differential operators acting in
spinor space is given. It turns out that this graded algebra is the
supersymmetry algebra for a class of relativistic potentials that includes the
Dirac-Oscillator, Dirac-Coulomb and Dirac-Morse potentials. This class is, in
fact, the relativistic extension of the oscillator class. A new point canonical
transformation, which is compatible with the relativistic problem, is
formulated. It maps all of these relativistic potentials into the
Dirac-Oscillator potential.Comment: Replaced with a more potrable PDF versio
High Accuracy Protein Identification: Fusion of solid-state nanopore sensing and machine learning
Proteins are arguably the most important class of biomarkers for health
diagnostic purposes. Label-free solid-state nanopore sensing is a versatile
technique for sensing and analysing biomolecules such as proteins at
single-molecule level. While molecular-level information on size, shape, and
charge of proteins can be assessed by nanopores, the identification of proteins
with comparable sizes remains a challenge. Here, we present methods that
combine solid-state nanopore sensing with machine learning to address this
challenge. We assess the translocations of four similarly sized proteins using
amplifiers with bandwidths (BWs) of 100 kHz (sampling rate=200 ksps) and 10 MHz
(sampling rate=40 Msps), the highest bandwidth reported for protein sensing,
using nanopores fabricated in <10 nm thick silicon nitride membranes. F-values
of up to 65.9% and 83.2% (without clustering of the protein signals) were
achieved with 100 kHz and 10 MHz BW instruments, respectively, for
identification of the four proteins. The accuracy of protein identification was
significantly improved by grouping the signals into several clusters depending
on the event features, resulting in F-value and specificity reaching as high as
88.7% and 96.4%, respectively, for combinations of four proteins. The combined
improvement in sensor signals through the use of high bandwidth instruments,
advanced clustering, machine learning, and other advanced data analysis methods
allows identification of proteins with high accuracy
Scattering of relativistic particles with Aharonov-Bohm-Coulomb interaction in two dimensions
The Aharonov-Bohm-Coulomb potentials in two dimensions may describe the
interaction between two particles carrying electric charge and magnetic flux,
say, Chern--Simons solitons, or so called anyons. The scattering problem for
such two-body systems is extended to the relativistic case, and the scattering
amplitude is obtained as a partial wave series. The electric charge and
magnetic flux is (, ) for one particle and (, ) for the
other. When , and takes on integer
or half integer values, the partial wave series is summed up approximately to
give a closed form. The results exhibit some nonperturbative features and
cannot be obtained from perturbative quantum electrodynamics at the tree level.Comment: revtex, 11 pages, no figur
Ma-Xu quantization rule and exact WKB condition for translationally shape invariant potentials
For translationally shape invariant potentials, the exact quantization rule
proposed by Ma and Xu is a direct consequence of exactness of the modified WKB
quantization condition proved by Barclay. We propose here a very direct
alternative way to calculate the appropriate correction for the whole class of
translationally shape invariant potentials
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