120,710 research outputs found
Software for cut-generating functions in the Gomory--Johnson model and beyond
We present software for investigations with cut generating functions in the
Gomory-Johnson model and extensions, implemented in the computer algebra system
SageMath.Comment: 8 pages, 3 figures; to appear in Proc. International Congress on
Mathematical Software 201
A consistent model for leptogenesis, dark matter and the IceCube signal
We discuss a left-right symmetric extension of the Standard Model in which
the three additional right-handed neutrinos play a central role in explaining
the baryon asymmetry of the Universe, the dark matter abundance and the ultra
energetic signal detected by the IceCube experiment. The energy spectrum and
neutrino flux measured by IceCube are ascribed to the decays of the lightest
right-handed neutrino , thus fixing its mass and lifetime, while the
production of in the primordial thermal bath occurs via a freeze-in
mechanism driven by the additional interactions. The constraints
imposed by IceCube and the dark matter abundance allow nonetheless the heavier
right-handed neutrinos to realize a standard type-I seesaw leptogenesis, with
the asymmetry dominantly produced by the next-to-lightest neutrino .
Further consequences and predictions of the model are that: the
production implies a specific power-law relation between the reheating
temperature of the Universe and the vacuum expectation value of the
triplet; leptogenesis imposes a lower bound on the reheating temperature of the
Universe at 7\times10^9\,\mbox{GeV}. Additionally, the model requires a
vanishing absolute neutrino mass scale .Comment: 19 pages, 4 figures. Constraints from cosmic-ray antiprotons and
gamma rays added, with hadrophobic assignment of the matter multiplets to
satisfy bounds. References added. Matches version published in JHE
On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem
We investigate three competing notions that generalize the notion of a facet
of finite-dimensional polyhedra to the infinite-dimensional Gomory-Johnson
model. These notions were known to coincide for continuous piecewise linear
functions with rational breakpoints. We show that two of the notions, extreme
functions and facets, coincide for the case of continuous piecewise linear
functions, removing the hypothesis regarding rational breakpoints. We then
separate the three notions using discontinuous examples.Comment: 18 pages, 2 figure
Designing probiotic therapies with broad-spectrum activity against a wildlife pathogen
Host-associated microbes form an important component of immunity that protect
against infection by pathogens. Treating wild individuals with these protective microbes,
known as probiotics, can reduce rates of infection and disease in both wild and captive
settings. However, the utility of probiotics for tackling wildlife disease requires that
they offer consistent protection across the broad genomic variation of the pathogen
that hosts can encounter in natural settings. Here we develop multi-isolate probiotic
consortia with the aim of effecting broad-spectrum inhibition of growth of the lethal
amphibian pathogen Batrachochytrium dendrobatidis (Bd) when tested against nine
Bd isolates from two distinct lineages. Though we achieved strong growth inhibition
between 70 and 100% for seven Bd isolates, two isolates appeared consistently
resistant to inhibition, irrespective of probiotic strategy employed. We found no evidence
that genomic relatedness of the chytrid predicted similarity of inhibition scores, nor that
increasing the genetic diversity of the bacterial consortia could offer stronger inhibition
of pathogen growth, even for the two resistant isolates. Our findings have important
consequences for the application of probiotics to mitigate wildlife diseases in the face of
extensive pathogen genomic variation
Towards a novel wave-extraction method for numerical relativity
We present the recent results of a research project aimed at constructing a
robust wave extraction technique for numerical relativity. Our procedure makes
use of Weyl scalars to achieve wave extraction. It is well known that, with a
correct choice of null tetrad, Weyl scalars are directly associated to physical
properties of the space-time under analysis in some well understood way. In
particular it is possible to associate with the outgoing gravitational
radiation degrees of freedom, thus making it a promising tool for numerical
wave--extraction. The right choice of the tetrad is, however, the problem to be
addressed. We have made progress towards identifying a general procedure for
choosing this tetrad, by looking at transverse tetrads where .
As a direct application of these concepts, we present a numerical study of
the evolution of a non-linearly disturbed black hole described by the
Bondi--Sachs metric. This particular scenario allows us to compare the results
coming from Weyl scalars with the results coming from the news function which,
in this particular case, is directly associated with the radiative degrees of
freedom. We show that, if we did not take particular care in choosing the right
tetrad, we would end up with incorrect results.Comment: 6 pages, 1 figure, to appear in the Proceedings of the Albert
Einstein Century International Conference, Paris, France, 200
The structure of the infinite models in integer programming
The infinite models in integer programming can be described as the convex
hull of some points or as the intersection of halfspaces derived from valid
functions. In this paper we study the relationships between these two
descriptions. Our results have implications for corner polyhedra. One
consequence is that nonnegative, continuous valid functions suffice to describe
corner polyhedra (with or without rational data)
Chain Reduction for Binary and Zero-Suppressed Decision Diagrams
Chain reduction enables reduced ordered binary decision diagrams (BDDs) and
zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the
others' ability to symbolically represent Boolean functions in compact form.
For any Boolean function, its chain-reduced ZDD (CZDD) representation will be
no larger than its ZDD representation, and at most twice the size of its BDD
representation. The chain-reduced BDD (CBDD) of a function will be no larger
than its BDD representation, and at most three times the size of its CZDD
representation. Extensions to the standard algorithms for operating on BDDs and
ZDDs enable them to operate on the chain-reduced versions. Experimental
evaluations on representative benchmarks for encoding word lists, solving
combinatorial problems, and operating on digital circuits indicate that chain
reduction can provide significant benefits in terms of both memory and
execution time
- …