3,275 research outputs found
Stable Isotropic Cosmological Singularities in Quadratic Gravity
We show that, in quadratic lagrangian theories of gravity, isotropic
cosmological singularities are stable to the presence of small scalar, vector
and tensor inhomogeneities. Unlike in general relativity, a particular exact
isotropic solution is shown to be the stable attractor on approach to the
initial cosmological singularity. This solution is also known to act as an
attractor in Bianchi universes of types I, II and IX, and the results of this
paper reinforce the hypothesis that small inhomogeneous and anisotropic
perturbations of this attractor form part of the general cosmological solution
to the field equations of quadratic gravity. Implications for the existence of
a 'gravitational entropy' are also discussed.Comment: 18 pages, no figure
On the String Consensus Problem and the Manhattan Sequence Consensus Problem
In the Manhattan Sequence Consensus problem (MSC problem) we are given
integer sequences, each of length , and we are to find an integer sequence
of length (called a consensus sequence), such that the maximum
Manhattan distance of from each of the input sequences is minimized. For
binary sequences Manhattan distance coincides with Hamming distance, hence in
this case the string consensus problem (also called string center problem or
closest string problem) is a special case of MSC. Our main result is a
practically efficient -time algorithm solving MSC for sequences.
Practicality of our algorithms has been verified experimentally. It improves
upon the quadratic algorithm by Amir et al.\ (SPIRE 2012) for string consensus
problem for binary strings. Similarly as in Amir's algorithm we use a
column-based framework. We replace the implied general integer linear
programming by its easy special cases, due to combinatorial properties of the
MSC for . We also show that for a general parameter any instance
can be reduced in linear time to a kernel of size , so the problem is
fixed-parameter tractable. Nevertheless, for this is still too large
for any naive solution to be feasible in practice.Comment: accepted to SPIRE 201
Matching Reads to Many Genomes with the r-Index
The r-index is a tool for compressed indexing of genomic databases for exact pattern matching, which can be used to completely align reads that perfectly match some part of a genome in the database or to find seeds for reads that do not. This article shows how to download and install the programs ri-buildfasta and ri-align; how to call ri-buildfasta on an FASTA file to build an r-index for that file; and how to query that index with ri-align
Efficient Construction of a Complete Index for Pan-Genomics Read Alignment
While short read aligners, which predominantly use the FM-index, are able to easily index one or a few human genomes, they do not scale well to indexing databases containing thousands of genomes. To understand why, it helps to examine the main components of the FM-index in more detail, which is a rank data structure over the Burrows-Wheeler Transform () of the string that will allow us to find the interval in the string\u2019s suffix array () containing pointers to starting positions of occurrences of a given pattern; second, a sample of the that\u2014when used with the rank data structure\u2014allows us access to the . The rank data structure can be kept small even for large genomic databases, by run-length compressing the , but until recently there was no means known to keep the sample small without greatly slowing down access to the . Now that Gagie et al. (SODA 2018) have defined an sample that takes about the same space as the run-length compressed \u2014we have the design for efficient FM-indexes of genomic databases but are faced with the problem of building them. In 2018 we showed how to build the of large genomic databases efficiently (WABI 2018) but the problem of building Gagie et al.\u2019s sample efficiently was left open. We compare our approach to state-of-the-art methods for constructing the sample, and demonstrate that it is the fastest and most space-efficient method on highly repetitive genomic databases. Lastly, we apply our method for indexing partial and whole human genomes and show that it improves over Bowtie with respect to both memory and time
Prefix-free parsing for building big BWTs
High-throughput sequencing technologies have led to explosive growth of genomic databases; one of which will soon reach hundreds of terabytes. For many applications we want to build and store indexes of these databases but constructing such indexes is a challenge. Fortunately, many of these genomic databases are highly-repetitive - a characteristic that can be exploited to ease the computation of the Burrows-Wheeler Transform (BWT), which underlies many popular indexes. In this paper, we introduce a preprocessing algorithm, referred to as prefix-free parsing, that takes a text T as input, and in one-pass generates a dictionary D and a parse P of T with the property that the BWT of T can be constructed from D and P using workspace proportional to their total size and O(|T|)-time. Our experiments show that D and P are significantly smaller than T in practice, and thus, can fit in a reasonable internal memory even when T is very large. In particular, we show that with prefix-free parsing we can build an 131-MB run-length compressed FM-index (restricted to support only counting and not locating) for 1000 copies of human chromosome 19 in 2 h using 21 GB of memory, suggesting that we can build a 6.73 GB index for 1000 complete human-genome haplotypes in approximately 102 h using about 1 TB of memory
Cation distribution in manganese cobaltite spinels Co3âxMnxO4 (0 †x †1) determined by thermal analysis
Thermogravimetric analysis was used in order to study the reduction in air of submicronic powders of Co3âx Mn x O4 spinels, with 0 †x †1. For x = 0 (i.e. Co3O4), cation reduction occurred in a single step. It involved the CoIII ions at the octahedral sites, which were reduced to Co2+ on producing CoO. For 0 < x †1, the reduction occurred in two stages at increasing temperature with increasing amounts of manganese. The first step corresponded to the reduction of octahedral CoIII ions and the second was attributed to the reduction of octahedral Mn4+ ions to Mn3+. From the individual weight losses and the electrical neutrality of the lattice, the CoIII and Mn4+ ion concentrations were calculated. The distribution of cobalt and manganese ions present on each crystallographic site of the spinel was determined. In contrast to most previous studies that took into account either CoIII and Mn3+ or Co2+, CoIII and Mn4+ only, our thermal analysis study showed that Co2+/CoIII and Mn3+/Mn4+ pairs occupy the octahedral sites. These results were used to explain the resistivity measurements carried out on dense ceramics prepared from our powders sintered at low temperature (700â750 °C) in a Spark Plasma Sintering apparatus
Influence of conformational fluctuations on enzymatic activity: modelling the functional motion of beta-secretase
Considerable insight into the functional activity of proteins and enzymes can
be obtained by studying the low-energy conformational distortions that the
biopolymer can sustain. We carry out the characterization of these large scale
structural changes for a protein of considerable pharmaceutical interest, the
human -secretase. Starting from the crystallographic structure of the
protein, we use the recently introduced beta-Gaussian model to identify, with
negligible computational expenditure, the most significant distortion occurring
in thermal equilibrium and the associated time scales. The application of this
strategy allows to gain considerable insight into the putative functional
movements and, furthermore, helps to identify a handful of key regions in the
protein which have an important mechanical influence on the enzymatic activity
despite being spatially distant from the active site. The results obtained
within the Gaussian model are validated through an extensive comparison against
an all-atom Molecular Dynamics simulation.Comment: To be published in a special issue of J. Phys.: Cond. Mat. (Bedlewo
Workshop
Soliton-Magnon Scattering in Two-Dimensional Isotropic Ferromagnets
It is studied the scattering of magnons by the 2d topological
Belavin-Polyakov soliton in isotropic ferromagnet. Analytical solutions of the
scattering problem are constructed: (i) exactly for any magnon wave vectors for
the partial wave with the azimuthal number m=1 (translational mode), and (ii)
in the long- and short-wave limits for the rest modes. The magnon mode
frequencies are found for the finite size magnets. An effective equation of the
soliton motion is constructed. The magnon density of states, connected with the
soliton-magnon interaction, is found in a long-wave approximation.Comment: 4 pages, REVTe
Internal Modes and Magnon Scattering on Topological Solitons in 2d Easy-Axis Ferromagnets
We study the magnon modes in the presence of a topological soliton in a 2d
Heisenberg easy-axis ferromagnet. The problem of magnon scattering on the
soliton with arbitrary relation between the soliton radius R and the "magnetic
length" Delta_0 is investigated for partial modes with different values of the
azimuthal quantum numbers m. Truly local modes are shown to be present for all
values of m, when the soliton radius is enough large. The eigenfrequencies of
such internal modes are calculated analytically on limiting case of a large
soliton radius and numerically for arbitrary soliton radius. It is demonstrated
that the model of an isotropic magnet, which admits an exact analytical
investigation, is not adequate even for the limit of small radius solitons,
R<<Delta_0: there exists a local mode with nonzero frequency. We use the data
about local modes to derive the effective equation of soliton motion; this
equation has the usual Newtonian form in contrast to the case of the easy-plane
ferromagnet. The effective mass of the soliton is found.Comment: 33 pages (REVTeX), 12 figures (EPS
Wetland Manipulation in the Yalahau Region of the Northern Maya Lowlands
Manipulation of wetlands for agricultural purposes by the ancient Maya of southern Mexico and Central America has been a subject of much research and debate since the 1970s. Evidence for wetland cultivation systems, in the form of drained or channelized fields, and raised planting platforms, has been restricted primarily to the southern Maya Lowlands. New research in the Yalahau region of Quintana Roo, Mexico, has recorded evidence for wetland manipulation in the far northern lowlands, in the form of rock alignments that apparently functioned to control water movement and soil accumulation in seasonally inundated areas. Nearby ancient settlements date primarily to the Late Preclassic period (ca. 100 B.C. to A.C. 350), and this age is tentatively attributed to wetland management in the area
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