DMSA and its complexes with radioisotopes: review

Meso-2,3-dimercaptosuccinic acid (DMSA) forms stable complexes with a remarkable wide range of metal ions. This relatively small molecule has attracted increasing attention in the field of radiopharmacy, treatment of heavy metal intoxications and nanoparticles preparation. In this review detailed summary of all physical, chemical and biological properties of DMSA and its complex compounds with ^99mTc, ^186/188Re, ¹⁶⁶Ho, ¹⁷⁷Lu and ⁹⁰Y is provided. The clinical utilisation of DMSA complexes in the nuclear medicine and its use for treatment of heavy metal intoxication is briefly summarised. The aspects of its application in the field of nanoparticles preparation is behind the scope of this review, therefore it is only shortly described.     

Approximation algorithms for scheduling unrelated parallel machines

We consider the following scheduling problem. There arem parallel machines andn independent jobs. Each job is to be assigned to one of the machines. The processing of jobj on machinei requires timep _ij . The objective is to find a schedule that minimizes the makespan.Our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum. We also present a polynomial approximation scheme for the case that the number of machines is fixed. Both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations. In particular, we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints.In contrast to our main result, we prove that no polynomial algorithm can achieve a worst-case ratio less than 3/2 unlessP = NP. We finally obtain a complexity classification for all special cases with a fixed number of processing times.A preliminary version of this paper appeared in theProceedings of the 28th Annual IEEE Symposium on the Foundations of Computer Science (Computer Society Press of the IEEE, Washington, D.C., 1987) pp. 217–224.     

Generalized solutions to free boundary problems for hyperbolic systems of functional partial differential equations

Summary Local a.e. solutions to a free boundary (Stefan) problem for a quasilinear hyperbolic system of functional PDE's of first order in two independent variables and diagonal form are investigated. The formulation includes retarded arguments and hereditary Volterra terms.     

A continuous parametric shape model

In this paper we propose a flexible continuous parametric shape model for star-shaped planar objects. The model is based on a polar Fourier expansion of the normalized radius-vector function. The expected phase amplitudes are modelled by a simple regression with parameters having nice geometric interpretations. The suggestedgeneralized p-order model is an extension of first- and second-order Gaussian shape models, and in particular the Gaussian assumption is relaxed. The statistical analysis is straightforward, as demonstrated by an application concerning shape discrimination of two cell nuclei populations.     

Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems

Summary. A domain with possibly non-Lipschitz boundary is defined as a limit of monotonically expanding or shrinking domains with Lipschitz boundary. A uniquely solvable Dirichlet boundary value problem (DBVP) is defined on each of the Lipschitz domains and the limit of these solutions is investigated. The limit function also solves a DBVP on the limit domain but the problem can depend on the sequences of domains if the limit domain is unstable with respect to the DBVP. The core of the paper consists in estimates of the difference between the respective solutions of the DBVP on two close domains, one of which is Lipschitz and the other can be unstable. Estimates for starshaped as well as rather general domains are derived. Their numerical evaluation is possible and can be done in different ways. Received October 16, 2001 / Revised version received January 16, 2002 / Published online: April 17, 2002 RID="*" ID="*" The research was funded partially by the National Science Foundation under the grants NSF–Czech Rep. INT-9724783 and NSF DMS-9802367 RID="**" ID="**" Support for Jan Chleboun coming from the Grant Agency of the Czech Republic through grant 201/98/0528 is appreciated     

On the structure ofn-point sets

Letn be an integer greater than one. Our main result, called the “Structure Theorem” is that a set that containsn−1 disjoint continua that are cut by a single line cannot be ann-point set, that is, a set that meets every line in preciselyn points. This theorem unifies and significantly improves upon a number of known theorems. The second part of the paper is devoted to several theorems that address the question when a set that meets every line in at mostn points can be extended to ann-point set. These theorems also highlight the sharpness of the Structure Theorem.     

Theory of electronic transport in two-dimensional systems in the presence of magnetic fields

Three parts of the paper [Czech. J. Phys.41 (1991) 620,7 are focused on the Landauer-Büttiker approach to the study of transport in two-dimensional electron systems, with particular attention to the influence of an external magnetic field. In the previous parts the Landauer formalism was generalized for two-dimensional systems in quantizing magnetic fields. In the present part we applied the formalism to an analysis of magnetoresistance measurements. The two-dimensional electron gas preserved in the non-dissipative quantum Hall regime acts as the ideal leads necessary in the Landauer-Büttiker approach. The voltage, applied to the gate, forms a scattering region in the gated part of the sample, in between of its undisturbed parts (ideal leads). The dependence of the resistance on the gate voltage and the number of available channels within the ideal leads are discussed.The author wishes to thank to Professor P. Steda for cooperation and to Professor L. Smrka for his encouragement and support. Dr. R. J. Haug should be acknowledged for providing his experimental results.     

Graphs that are not complete pluripolar

Let be domains in . Under very mild conditions on we show that there exist holomorphic functions , defined on with the property that is nowhere extendible across , while the graph of over is not complete pluripolar in . This refutes a conjecture of Levenberg, Martin and Poletsky (1992).

     

Polyèdre de Newton et distributionf + s . II

Sans résumé

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Relating neural dynamics to neural coding

We demonstrate that two key theoretical objects used widely in computational neuroscience, the phase-resetting curve (PRC) from dynamics and the spike triggered average (STA) from statistical analysis, are closely related when neurons fire in a nearly regular manner and the stimulus is sufficiently small. We prove that the STA due to injected noisy current is proportional to the derivative of the PRC. We compare these analytic results with numerical calculations for the Hodgkin-Huxley neuron and we apply the method to neurons in the olfactory bulb of mice. This observation allows us to relate the stimulus-response properties of a neuron to its dynamics, bridging the gap between dynamical and information theoretic approaches to understanding brain computations and facilitating the interpretation of changes in channels and other cellular properties as influencing the representation of stimuli.