13,408 research outputs found
On the Inverse Problem for a Size-Structured Population Model
We consider a size-structured model for cell division and address the
question of determining the division (birth) rate from the measured stable size
distribution of the population. We formulate such question as an inverse
problem for an integro-differential equation posed on the half line. We develop
firstly a regular dependency theory for the solution in terms of the
coefficients and, secondly, a novel regularization technique for tackling this
inverse problem which takes into account the specific nature of the equation.
Our results rely also on generalized relative entropy estimates and related
Poincar\'e inequalities
Information Revelation in Auctions.
Auction theory has emphasized the importance of private information to the profits of bidders. However, the theory has failed to consider the question of whether or not bidders will be able to keep their information private. We show that in a variety of contexts bidders will reveal all their information, even if this information revelation is (ex ante) detrimental to them. Similarly, a seller may reveal all her information even when this revelation lowers revenues. We also show that bidders may be harmed by private information.WINNERS CURSE; LINKAGE PRINCIPLE; REVELATION BY BIDDERS
Weak Convergence in the Prokhorov Metric of Methods for Stochastic Differential Equations
We consider the weak convergence of numerical methods for stochastic
differential equations (SDEs). Weak convergence is usually expressed in terms
of the convergence of expected values of test functions of the trajectories.
Here we present an alternative formulation of weak convergence in terms of the
well-known Prokhorov metric on spaces of random variables. For a general class
of methods, we establish bounds on the rates of convergence in terms of the
Prokhorov metric. In doing so, we revisit the original proofs of weak
convergence and show explicitly how the bounds on the error depend on the
smoothness of the test functions. As an application of our result, we use the
Strassen - Dudley theorem to show that the numerical approximation and the true
solution to the system of SDEs can be re-embedded in a probability space in
such a way that the method converges there in a strong sense. One corollary of
this last result is that the method converges in the Wasserstein distance,
another metric on spaces of random variables. Another corollary establishes
rates of convergence for expected values of test functions assuming only local
Lipschitz continuity. We conclude with a review of the existing results for
pathwise convergence of weakly converging methods and the corresponding strong
results available under re-embedding.Comment: 12 pages, 2nd revision for IMA J Numerical Analysis. Further minor
errors correcte
Specialization of the rostral prefrontal cortex for distinct analogy processes
Analogical reasoning is central to learning and abstract thinking. It involves using a more familiar situation (source) to make inferences about a less familiar situation (target). According to the predominant cognitive models, analogical reasoning includes 1) generation of structured mental representations and 2) mapping based on structural similarities between them. This study used functional magnetic resonance imaging to specify the role of rostral prefrontal cortex (PFC) in these distinct processes. An experimental paradigm was designed that enabled differentiation between these processes, by temporal separation of the presentation of the source and the target. Within rostral PFC, a lateral subregion was activated by analogy task both during study of the source (before the source could be compared with a target) and when the target appeared. This may suggest that this subregion supports fundamental analogy processes such as generating structured representations of stimuli but is not specific to one particular processing stage. By contrast, a dorsomedial subregion of rostral PFC showed an interaction between task (analogy vs. control) and period (more activated when the target appeared). We propose that this region is involved in comparison or mapping processes. These results add to the growing evidence for functional differentiation between rostral PFC subregions
Concepts of Moral Geography in Dante Alighieri and James Joyce
Moral geography illustrates the relationship between the landscape and the moral, religious, and psychological structures that are in place in the text. In literature, moral geography is present vis-à-vis how the physical landscape reflects the mental landscape of the characters, and vice versa. This is especially pertinent in Dante, who can be seen as the most prominent example of moral geographical frameworks in the Western canon. Joyce, who was an avid reader of Dante, understood Dante’s use of the concept and redefined the concept to suit his purpose in Ulysses. This thesis operates upon the premise that the moral geographical framework laid by Dante laid the groundwork for Joyce’s moral geographical framework, and though Joyce altered Dante’s to a fair degree, he is indebted to Dante for this framework
Numerical simulation of the magnetization of high-temperature superconductors: 3D finite element method using a single time-step iteration
We make progress towards a 3D finite-element model for the magnetization of a
high temperature superconductor (HTS): We suggest a method that takes into
account demagnetisation effects and flux creep, while it neglects the effects
associated with currents that are not perpendicular to the local magnetic
induction. We consider samples that are subjected to a uniform magnetic field
varying linearly with time. Their magnetization is calculated by means of a
weak formulation in the magnetostatic approximation of the Maxwell equations
(A-phi formulation). An implicit method is used for the temporal resolution
(Backward Euler scheme) and is solved in the open source solver GetDP. Picard
iterations are used to deal with the power law conductivity of HTS. The finite
element formulation is validated for an HTS tube with large pinning strength
through the comparison with results obtained with other well-established
methods. We show that carrying the calculations with a single time-step (as
opposed to many small time-steps) produce results with excellent accuracy in a
drastically reduced simulation time. The numerical method is extended to the
study of the trapped magnetization of cylinders that are drilled with different
arrays of columnar holes arranged parallel to the cylinder axis
Unexpected D-type Interlopers in the Inner Main Belt
Very red featureless asteroids (spectroscopic D-types) are expected to have
formed in the outer solar system far from the sun. They comprise the majority
of asteroids in the Jupiter Trojan population, and are also commonly found in
the outer main belt and among Hildas. The first evidence for D-types in the
inner and middle parts of the main belt was seen in the Sloan Digital Sky
Survey (SDSS). Here we report follow-up observations of SDSS D-type candidates
in the near-infrared. Based on follow up observations of 13 SDSS D-type
candidates, we find a ~20% positive confirmation rate. Known inner belt D-types
range in diameter from roughly 7 to 30 kilometers. Based on these detections we
estimate there are ~100 inner belt D-types with diameters between 2.5 and 20km.
The lower and upper limits for total mass of inner belt D-types is 2x
kg to 2x kg which represents 0.01% to 0.1% of the mass of the inner
belt. The inner belt D-types have albedos at or above the upper end typical for
D-types which raises the question as to whether these inner belt bodies
represent only a subset of D-types, they have been altered by external factors
such as weathering processes, or if they are compositionally distinct from
other D-types. All D-types and candidates have diameters less than 30km, yet
there is no obvious parent body in the inner belt. Dynamical models have yet to
show how D-types originating from the outer solar system could penetrate into
the inner reaches of the Main Belt under current scenarios of planet formation
and subsequent Yarkovsky drift.Comment: 16 pages, 3 figures, 4 tables -- accepted for publication in Icaru
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