698 research outputs found
A triangle model of criminality
This paper is concerned with a quantitative model describing the interaction of three sociological species, termed as owners, criminals and security guards, and denoted by X, Y and Z respectively. In our model, Y is a predator of the species X, and so is Z with respect to Y . Moreover, Z can also be thought of as a predator of X, since this last population is required to bear the costs of maintaining Z. We propose a system of three ordinary differential equations to account for the time evolution of X(t), Y (t) and Z(t) according to our previous assumptions. Out of the various parameters that appear in that system, we select two of them, denoted by H, and h, which are related with the efficiency of the security forces as a control parameter in our discussion. To begin with, we consider the case of large and constant owners population, which allows us to reduce (3)â(5) to a bidimensional system for Y (t) and Z(t). As a preliminary step, this situation is first discussed under the additional assumption that Y (t) + Z(t) is constant. A bifurcation study is then performed in terms of H and h, which shows the key role played by the rate of casualties in Y and Z, that results particularly in a possible onset of bistability. When the previous restriction is dropped, we observe the appearance of oscillatory behaviours in the full two-dimensional system. We finally provide a exploratory study of the complete model (3)â(5), where a number of bifurcations appear as parameter H changes, and the corresponding solutions behaviours are described
A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators
This chapter offers a detailed survey on intrinsically localized frames and
the corresponding matrix representation of operators. We re-investigate the
properties of localized frames and the associated Banach spaces in full detail.
We investigate the representation of operators using localized frames in a
Galerkin-type scheme. We show how the boundedness and the invertibility of
matrices and operators are linked and give some sufficient and necessary
conditions for the boundedness of operators between the associated Banach
spaces.Comment: 32 page
An optimally concentrated Gabor transform for localized time-frequency components
Gabor analysis is one of the most common instances of time-frequency signal
analysis. Choosing a suitable window for the Gabor transform of a signal is
often a challenge for practical applications, in particular in audio signal
processing. Many time-frequency (TF) patterns of different shapes may be
present in a signal and they can not all be sparsely represented in the same
spectrogram. We propose several algorithms, which provide optimal windows for a
user-selected TF pattern with respect to different concentration criteria. We
base our optimization algorithm on -norms as measure of TF spreading. For
a given number of sampling points in the TF plane we also propose optimal
lattices to be used with the obtained windows. We illustrate the potentiality
of the method on selected numerical examples
A spoonful of Lâfucoseâan efficient therapy for GFUSâCDG, a new glycosylation disorder
Abstract Congenital disorders of glycosylation are a genetically and phenotypically heterogeneous family of diseases affecting the coâ and posttranslational modification of proteins. Using exome sequencing, we detected biallelic variants in GFUS (NM_003313.4) c.[632G>A];[659C>T] (p.[Gly211Glu];[Ser220Leu]) in a patient presenting with global developmental delay, mild coarse facial features and faltering growth. GFUS encodes GDPâLâfucose synthase, the terminal enzyme in de novo synthesis of GDPâLâfucose, required for fucosylation of Nâ and Oâglycans. We found reduced GFUS protein and decreased GDPâLâfucose levels leading to a general hypofucosylation determined in patient's glycoproteins in serum, leukocytes, thrombocytes and fibroblasts. Complementation of patient fibroblasts with wildâtype GFUS cDNA restored fucosylation. Making use of the GDPâLâfucose salvage pathway, oral fucose supplementation normalized fucosylation of proteins within 4Â weeks as measured in serum and leukocytes. During the followâup of 19Â months, a moderate improvement of growth was seen, as well as a clear improvement of cognitive skills as measured by the Kaufmann ABC and the Nijmegen Pediatric CDG Rating Scale. In conclusion, GFUSâCDG is a new glycosylation disorder for which oral Lâfucose supplementation is promising
Abstract composition laws and their modulation spaces
On classes of functions defined on R^2n we introduce abstract composition
laws modelled after the pseudodifferential product of symbols. We attach to
these composition laws modulation mappings and spaces with useful algebraic and
topological properties.Comment: 19 page
Constructions of regular algebras
Criterion of (Shilov) regularity for weighted algebras on a
locally compact abelian group is known by works of Beurling (1949) and
Domar (1956). In the present paper this criterion is extended to translation
invariant weighted algebras with . Regular algebras
are constructed on any sigma-compact abelian group . It was proved earlier
by the author that sigma-compactness is necessary (in the abelian case) for the
existence of weighted algebras with .Comment: Submitted to Mat. Sborni
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