Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Bounds on multisecant lines

The purpose of this paper is two fold. First, we give an upper bound on the orderof a multisecant line to an integral arithmetically Cohen-Macaulay subscheme in Pn of codimension two in terms of the Hilbert function. Secondly, we givean explicit description of the singular locus of the blow up of an arbitrary local ring at a complete intersection ideal. This description is used to refine standardlinking theorem. These results are tied together by the construction of sharp examples for the bound, which uses the linking theorems.

Semi-purity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the study of covariant arithmetic Chow groups. The semipurity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties.

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

Image restoration in astronomy: a Bayesian perspective

When preparing an article on image restoration in astronomy, it is obvious that some topics have to be dropped to keep the work at reasonable length. We have decided to concentrate on image and noise models and on the algorithms to find the restoration. Topics like parameter estimation and stopping rules are also commented on. We start by describing the Bayesian paradigm and then proceed to study the noise and blur models used by the astronomical community. Then the prior models used to restore astronomical images are examined. We describe the algorithms used to find the restoration for the most common combinations of degradation and image models. Then we comment on important issues such as acceleration of algorithms, stopping rules, and parameter estimation. We also comment on the huge amount of information available to, and made available by, the astronomical community.

A pseudo-spectral method for simulating of poro-elastic seismic wave propagation in complex borehole environments

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in cylindrical coordinates. An important application of this method is the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the center, the borehole casing and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction, Fourier expansions in the other directions, and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method based on the method of characteristics is used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces. The viability and accuracy of the proposed method has been tested and verified in 2D polar coordinates through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. The proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is handled adequately.

The set of undominated imputations and the core: an axiomatic approach

This paper provides an axiomatic framework to compare the D-core (the set of undominatedimputations) and the core of a cooperative game with transferable utility. Theorem1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms alsocharacterize the core on the domain of convex games, totally balanced games, balancedgames, and superadditive games

Differential equations driven by fractional Brownian motion

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

A Transportation Safety Planning Tool for the City of Ames, August 2011

The historically-reactive approach to identifying safety problems and mitigating them involves selecting black spots or hot spots by ranking locations based on crash frequency and severity. The approach focuses mainly on the corridor level without taking the exposure rate (vehicle miles traveled) and socio-demographics information of the study area, which are very important in the transportation planning process, into consideration. A larger study analysis unit at the Transportation Analysis Zone (TAZ) level or the network planning level should be used to address the needs of development of the community in the future and incorporate safety into the long-range transportation planning process. In this study, existing planning tools (such as the PLANSAFE models presented in NCHRP Report 546) were evaluated for forecasting safety in small and medium-sized communities, particularly as related to changes in socio-demographics characteristics, traffic demand, road network, and countermeasures. The research also evaluated the applicability of the Empirical Bayes (EB) method to network-level analysis. In addition, application of the United States Road Assessment Program (usRAP) protocols at the local urban road network level was investigated. This research evaluated the applicability of these three methods for the City of Ames, Iowa. The outcome of this research is a systematic process and framework for considering road safety issues explicitly in the small and medium-sized community transportation planning process and for quantifying the safety impacts of new developments and policy programs. More specifically, quantitative safety may be incorporated into the planning process, through effective visualization and increased awareness of safety issues (usRAP), the identification of high-risk locations with potential for improvement, (usRAP maps and EB), countermeasures for high-risk locations (EB before and after study and PLANSAFE), and socio-economic and demographic induced changes at the planning-level (PLANSAFE).

Low energy excitations of double quantum dots in the lowest Landau level regime

We study the spectrum and magnetic properties of double quantum dots in the lowest Landau level for different values of the hopping and Zeeman parameters by means of exact diagonalization techniques in systems of N=6 and 7 electrons and a filling factor close to 2. We compare our results with those obtained in double quantum layers and single quantum dots. The Kohn theorem is also discussed.

Correlations derived from modern nucleon-nucleon potentials

Various modern nucleon-nucleon (NN) potentials yield a very accurate fit to the nucleon-nucleon scattering phase shifts. The differences between these interactions in describing properties of nuclear matter are investigated. Various contributions to the total energy are evaluated employing the Hellmann-Feynman theorem. Special attention is paid to the two-nucleon correlation functions derived from these interactions. Differences in the predictions of the various interactions can be traced back to the inclusion of nonlocal terms.

Heat fluctuations in Brownian transducers

The heat fluctuation probability distribution function in Brownian transducers operating between two heat reservoirs is studied. We find, both analytically and numerically, that the recently proposed fluctuation theorem for heat exchange [C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)] has to be applied carefully when the coupling mechanism between both baths is considered. We also conjecture how to extend such a relation when an external work is present.

On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Scaling in relativistic Thomas-Fermi approach for nuclei

By using the scaling method we derive the virial theorem for the relativistic mean field model of nuclei treated in the ThomasFermi approach. The ThomasFermi solutions statisfy the stability condition against scaling. We apply the formalism to study the excitation energy of the breathing mode in finite nuclei with several relativistic parameter sets of common use.

Lattice-gas model of orientable molecules: Application to liquid crystals

We have analyzed a two-dimensional lattice-gas model of cylindrical molecules which can exhibit four possible orientations. The Hamiltonian of the model contains positional and orientational energy interaction terms. The ground state of the model has been investigated on the basis of Karl¿s theorem. Monte Carlo simulation results have confirmed the predicted ground state. The model is able to reproduce, with appropriate values of the Hamiltonian parameters, both, a smectic-nematic-like transition and a nematic-isotropic-like transition. We have also analyzed the phase diagram of the system by mean-field techniques and Monte Carlo simulations. Mean-field calculations agree well qualitatively with Monte Carlo results but overestimate transition temperatures.