4,382 research outputs found
Bayesian Inference of Arrival Rate and Substitution Behavior from Sales Transaction Data with Stockouts
When an item goes out of stock, sales transaction data no longer reflect the
original customer demand, since some customers leave with no purchase while
others substitute alternative products for the one that was out of stock. Here
we develop a Bayesian hierarchical model for inferring the underlying customer
arrival rate and choice model from sales transaction data and the corresponding
stock levels. The model uses a nonhomogeneous Poisson process to allow the
arrival rate to vary throughout the day, and allows for a variety of choice
models. Model parameters are inferred using a stochastic gradient MCMC
algorithm that can scale to large transaction databases. We fit the model to
data from a local bakery and show that it is able to make accurate
out-of-sample predictions, and to provide actionable insight into lost cookie
sales
Extensions of positive definite functions on amenable groups
Let be a subset of a amenable group such that and
. The main result of the paper states that if the Cayley graph of
with respect to has a certain combinatorial property, then every positive
definite operator-valued function on can be extended to a positive definite
function on . Several known extension results are obtained as a corollary.
New applications are also presented
Noninvasive imaging of receptor function: signal transduction pathways and physiological readouts
Intracellular signaling describes the process of information propagation from the cell surface to the location within the cell where a biological response is executed. Signaling pathways involve a complex network of interacting molecular species. It is obvious that information on the activation of individual pathways is highly relevant in biomedical research, both from a diagnostic point of view and for evaluating therapeutic interventions. Modern molecular imaging approaches are capable of providing such information in a temporo-spatially resolved manner. Two strategies can be pursued: imaging individual pathway molecules or targeting protein-protein interactions, which are key elements of the signaling networks. Assays such as fluorescence resonance energy transfer, two-hybrid, protein fragment complementation or protein splicing have been adapted to allow studies in live mice. The major issues in imaging signal transduction are sensitivity, as critical species occur at low concentration, and the fact that the processes targeted are intracellular, that is, exogenous probes have to cross the cell membrane. Currently, the majority of these imaging methods are based on genetic engineering approaches and are therefore confined to experimental studies in animals. Exogenous probes for targeting intracellular pathway molecules are being developed and may allow translation into the clinic
Matched detectors as definers of force
Although quantum states nicely express interference effects, outcomes of
experimental trials show no states directly; they indicate properties of
probability distributions for outcomes. We prove categorically that probability
distributions leave open a choice of quantum states and operators and
particles, resolvable only by a move beyond logic, which, inspired or not, can
be characterized as a guess. By recognizing guesswork as inescapable in
choosing quantum states and particles, we free up the use of particles as
theoretical inventions by which to describe experiments with devices, and
thereby replace the postulate of state reductions by a theorem. By using the
freedom to invent probe particles in modeling light detection, we develop a
quantum model of the balancing of a light-induced force, with application to
models and detecting devices by which to better distinguish one source of weak
light from another. Finally, we uncover a symmetry between entangled states and
entangled detectors, a dramatic example of how the judgment about what light
state is generated by a source depends on choosing how to model the detector of
that light.Comment: 30 pages, 4 figs, LaTeX; new Introduction; new material in Secs. 4 &
5; new Sec. 6; 1 new figure, added reference
The horizon problem for prevalent surfaces
We investigate the box dimensions of the horizon of a fractal surface defined
by a function . In particular we show that a prevalent surface
satisfies the `horizon property', namely that the box dimension of the horizon
is one less than that of the surface. Since a prevalent surface has box
dimension 3, this does not give us any information about the horizon of
surfaces of dimension strictly less than 3. To examine this situation we
introduce spaces of functions with surfaces of upper box dimension at most
\alpha, for \alpha [2,3). In this setting the behaviour of the horizon is
more subtle. We construct a prevalent subset of these spaces where the lower
box dimension of the horizon lies between the dimension of the surface minus
one and 2. We show that in the sense of prevalence these bounds are as tight as
possible if the spaces are defined purely in terms of dimension. However, if we
work in Lipschitz spaces, the horizon property does indeed hold for prevalent
functions. Along the way, we obtain a range of properties of box dimensions of
sums of functions
Density of states of a two-dimensional electron gas in a non-quantizing magnetic field
We study local density of electron states of a two-dimentional conductor with
a smooth disorder potential in a non-quantizing magnetic field, which does not
cause the standart de Haas-van Alphen oscillations. It is found, that despite
the influence of such ``classical'' magnetic field on the average electron
density of states (DOS) is negligibly small, it does produce a significant
effect on the DOS correlations. The corresponding correlation function exhibits
oscillations with the characteristic period of cyclotron quantum
.Comment: 7 pages, including 3 figure
Effects of two dimensional plasmons on the tunneling density of states
We show that gapless plasmons lead to a universal
correction to the tunneling
density of states of a clean two dimensional Coulomb interacting electron gas.
We also discuss a counterpart of this effect in the "composite fermion metal"
which forms in the presence of a quantizing perpendicular magnetic field
corresponding to the half-filled Landau level. We argue that the latter
phenomenon might be relevant for deviations from a simple scaling observed by
A.Chang et al in the tunneling characteristics of Quantum Hall liquids.Comment: 12 pages, Latex, NORDITA repor
Adjointness Relations as a Criterion for Choosing an Inner Product
This is a contribution to the forthcoming book "Canonical Gravity: {}From
Classical to Quantum" edited by J. Ehlers and H. Friedrich. Ashtekar's
criterion for choosing an inner product in the quantisation of constrained
systems is discussed. An erroneous claim in a previous paper is corrected and a
cautionary example is presented.Comment: 6 pages, MPA-AR-94-
A subalgebra of the Hardy algebra relevant in control theory and its algebraic-analytic properties
We denote by A_0+AP_+ the Banach algebra of all complex-valued functions f
defined in the closed right half plane, such that f is the sum of a holomorphic
function vanishing at infinity and a ``causal'' almost periodic function. We
give a complete description of the maximum ideal space M(A_0+AP_+) of A_0+AP_+.
Using this description, we also establish the following results:
(1) The corona theorem for A_0+AP_+.
(2) M(A_0+AP_+) is contractible (which implies that A_0+AP_+ is a projective
free ring).
(3) A_0+AP_+ is not a GCD domain.
(4) A_0+AP_+ is not a pre-Bezout domain.
(5) A_0+AP_+ is not a coherent ring.
The study of the above algebraic-anlaytic properties is motivated by
applications in the frequency domain approach to linear control theory, where
they play an important role in the stabilization problem.Comment: 17 page
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