589 research outputs found
A Number-Theoretic Error-Correcting Code
In this paper we describe a new error-correcting code (ECC) inspired by the
Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the
proposed ECC happens to be more efficient than some established ECCs for
certain sets of parameters. The new ECC adds an appendix to the message. The
appendix is the modular product of small primes representing the message bits.
The receiver recomputes the product and detects transmission errors using
modular division and lattice reduction
Lower Bounds for Heights in Relative Galois Extensions
The goal of this paper is to obtain lower bounds on the height of an
algebraic number in a relative setting, extending previous work of Amoroso and
Masser. Specifically, in our first theorem we obtain an effective bound for the
height of an algebraic number when the base field is a
number field and is Galois. Our second result
establishes an explicit height bound for any non-zero element which is
not a root of unity in a Galois extension , depending on
the degree of and the number of conjugates of
which are multiplicatively independent over . As a consequence, we
obtain a height bound for such that is independent of the
multiplicative independence condition
Quantitative Chevalley-Weil theorem for curves
The classical Chevalley-Weil theorem asserts that for an \'etale covering of
projective varieties over a number field K, the discriminant of the field of
definition of the fiber over a K-rational point is uniformly bounded. We obtain
a fully explicit version of this theorem in dimension 1.Comment: version 4: minor inaccuracies in Lemma 3.4 and Proposition 5.2
correcte
The International-Trade Network: Gravity Equations and Topological Properties
This paper begins to explore the determinants of the topological properties
of the international - trade network (ITN). We fit bilateral-trade flows using
a standard gravity equation to build a "residual" ITN where trade-link weights
are depurated from geographical distance, size, border effects, trade
agreements, and so on. We then compare the topological properties of the
original and residual ITNs. We find that the residual ITN displays, unlike the
original one, marked signatures of a complex system, and is characterized by a
very different topological architecture. Whereas the original ITN is
geographically clustered and organized around a few large-sized hubs, the
residual ITN displays many small-sized but trade-oriented countries that,
independently of their geographical position, either play the role of local
hubs or attract large and rich countries in relatively complex
trade-interaction patterns
Boolean Dynamics with Random Couplings
This paper reviews a class of generic dissipative dynamical systems called
N-K models. In these models, the dynamics of N elements, defined as Boolean
variables, develop step by step, clocked by a discrete time variable. Each of
the N Boolean elements at a given time is given a value which depends upon K
elements in the previous time step.
We review the work of many authors on the behavior of the models, looking
particularly at the structure and lengths of their cycles, the sizes of their
basins of attraction, and the flow of information through the systems. In the
limit of infinite N, there is a phase transition between a chaotic and an
ordered phase, with a critical phase in between.
We argue that the behavior of this system depends significantly on the
topology of the network connections. If the elements are placed upon a lattice
with dimension d, the system shows correlations related to the standard
percolation or directed percolation phase transition on such a lattice. On the
other hand, a very different behavior is seen in the Kauffman net in which all
spins are equally likely to be coupled to a given spin. In this situation,
coupling loops are mostly suppressed, and the behavior of the system is much
more like that of a mean field theory.
We also describe possible applications of the models to, for example, genetic
networks, cell differentiation, evolution, democracy in social systems and
neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical
Sciences Serie
Modeling complex ecological economic systems: toward an evolutionary, dynamic understanding of people and nature
Recent understanding about system dynamics and predictability that has emerged from the study of complex systems is creating new tools for modeling interactions between anthropogenic and natural systems. A range of techniques has become available through advances in computer speed and accessibility and by implementing a broad, interdisciplinary systems view
Mathematical Explanations and Mathematical Applications
One of the key questions in the philosophy of mathematics is the role and status of mathematical applications in the natural sciences. The importance of mathematics for science is indisputable, but philosophers have disagreed on what the relation between mathematical theories and scientific theories are. This chapter presents these topics through a distinction between mathematical applications and mathematical explanations. Particularly important is the question whether mathematical applications are ever indispensable. If so, it has often been argued, such applications should count as proper mathematical explanations. Following Quine, many philosophers have also contended that if there are indispensable mathematical applications in the natural sciences, then the mathematical objects posited in those applications have an independent existence like the scientific objects. Thus the question of mathematical explanations and applications has an important relevance for the ontology of mathematics.Peer reviewe
Geographical Affinities of the HapMap Samples
The HapMap samples were collected for medical-genetic studies, but are also widely used in population-genetic and evolutionary investigations. Yet the ascertainment of the samples differs from most population-genetic studies which collect individuals who live in the same local region as their ancestors. What effects could this non-standard ascertainment have on the interpretation of HapMap results?We compared the HapMap samples with more conventionally-ascertained samples used in population- and forensic-genetic studies, including the HGDP-CEPH panel, making use of published genome-wide autosomal SNP data and Y-STR haplotypes, as well as producing new Y-STR data. We found that the HapMap samples were representative of their broad geographical regions of ancestry according to all tests applied. The YRI and JPT were indistinguishable from independent samples of Yoruba and Japanese in all ways investigated. However, both the CHB and the CEU were distinguishable from all other HGDP-CEPH populations with autosomal markers, and both showed Y-STR similarities to unusually large numbers of populations, perhaps reflecting their admixed origins.The CHB and JPT are readily distinguished from one another with both autosomal and Y-chromosomal markers, and results obtained after combining them into a single sample should be interpreted with caution. The CEU are better described as being of Western European ancestry than of Northern European ancestry as often reported. Both the CHB and CEU show subtle but detectable signs of admixture. Thus the YRI and JPT samples are well-suited to standard population-genetic studies, but the CHB and CEU less so
Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector
Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente
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