15,148 research outputs found
Differential Privacy and the Fat-Shattering Dimension of Linear Queries
In this paper, we consider the task of answering linear queries under the
constraint of differential privacy. This is a general and well-studied class of
queries that captures other commonly studied classes, including predicate
queries and histogram queries. We show that the accuracy to which a set of
linear queries can be answered is closely related to its fat-shattering
dimension, a property that characterizes the learnability of real-valued
functions in the agnostic-learning setting.Comment: Appears in APPROX 201
Phase separation dynamics in colloid-polymer mixtures: the effect of interaction range
Colloid-polymer mixtures may undergo either fluid-fluid phase separation or
gelation. This depends on the depth of the quench (polymer concentration) and
polymer-colloid size ratio. We present a real-space study of dynamics in phase
separating colloid-polymer mixtures with medium- to long-range attractions
(polymer-colloid size ratio q_R=0.45-0.89, with the aim of understanding the
mechanism of gelation as the range of the attraction is changed. In contrast to
previous studies of short-range attractive systems, where gelation occurs
shortly after crossing the equilibrium phase boundary, we find a substantial
region of fluid-fluid phase separation. On deeper quenches the system undergoes
a continuous crossover to gel formation. We identify two regimes, `classical'
phase separation, where single particle relaxation is faster than the dynamics
of phase separation, and `viscoelastic' phase separation, where demixing is
slowed down appreciably due to slow dynamics in the colloid-rich phase.
Particles at the surface of the strands of the network exhibit significantly
greater mobility than those buried inside the gel strand which presents a
method for coarsening.Comment: 8 page
Degradation of a quantum directional reference frame as a random walk
We investigate if the degradation of a quantum directional reference frame
through repeated use can be modeled as a classical direction undergoing a
random walk on a sphere. We demonstrate that the behaviour of the fidelity for
a degrading quantum directional reference frame, defined as the average
probability of correctly determining the orientation of a test system, can be
fit precisely using such a model. Physically, the mechanism for the random walk
is the uncontrollable back-action on the reference frame due to its use in a
measurement of the direction of another system. However, we find that the
magnitude of the step size of this random walk is not given by our classical
model and must be determined from the full quantum description.Comment: 5 pages, no figures. Comments are welcome. v2: several changes to
clarify the key results. v3: journal reference added, acknowledgements and
references update
Optimal measurements for relative quantum information
We provide optimal measurement schemes for estimating relative parameters of
the quantum state of a pair of spin systems. We prove that the optimal
measurements are joint measurements on the pair of systems, meaning that they
cannot be achieved by local operations and classical communication. We also
demonstrate that in the limit where one of the spins becomes macroscopic, our
results reproduce those that are obtained by treating that spin as a classical
reference direction.Comment: 6 pages, 1 figure, published versio
Some Remarks on the Question of Charge Densities in Stationary-Current-Carrying Conductors
Recently, some discussions arose as to the definition of charge and the value
of the density of charge in stationary-current-carrying conductors. We stress
that the problem of charge definition comes from a misunderstanding of the
usual definition. We provide some theoretical elements which suggest that
positive and negative charge densities are equal in the frame of the positive
ions.Comment: 14 pages, TeX, macro newsym.tex include
Formulating answerable questions: question negotiation in evidence-based practice
Objective: This review explores the different question formulation structures proposed in the literature that may be helpful to librarians for conducting the reference interview and for teaching students and clinicians. Method: We present and compare several known question formulation structures identified in the health and social sciences literature. Discussion: Health and social care professionals should be made aware of the plurality of question formulation structures and their applicability to different fields of practice, as well as their utility for different types of questions within a field of practice
A Classical Bound on Quantum Entropy
A classical upper bound for quantum entropy is identified and illustrated,
, involving the variance
in phase space of the classical limit distribution of a given system. A
fortiori, this further bounds the corresponding information-theoretical
generalizations of the quantum entropy proposed by Renyi.Comment: Latex2e, 7 pages, publication versio
Fluctuations and oscillations in a simple epidemic model
We show that the simplest stochastic epidemiological models with spatial
correlations exhibit two types of oscillatory behaviour in the endemic phase.
In a large parameter range, the oscillations are due to resonant amplification
of stochastic fluctuations, a general mechanism first reported for
predator-prey dynamics. In a narrow range of parameters that includes many
infectious diseases which confer long lasting immunity the oscillations persist
for infinite populations. This effect is apparent in simulations of the
stochastic process in systems of variable size, and can be understood from the
phase diagram of the deterministic pair approximation equations. The two
mechanisms combined play a central role in explaining the ubiquity of
oscillatory behaviour in real data and in simulation results of epidemic and
other related models.Comment: acknowledgments added; a typo in the discussion that follows Eq. (3)
is corrected
- …