3,262 research outputs found
The partition bundle of type A_{N-1} (2, 0) theory
Six-dimensional (2, 0) theory can be defined on a large class of
six-manifolds endowed with some additional topological and geometric data (i.e.
an orientation, a spin structure, a conformal structure, and an R-symmetry
bundle with connection). We discuss the nature of the object that generalizes
the partition function of a more conventional quantum theory. This object takes
its values in a certain complex vector space, which fits together into the
total space of a complex vector bundle (the `partition bundle') as the data on
the six-manifold is varied in its infinite-dimensional parameter space. In this
context, an important role is played by the middle-dimensional intermediate
Jacobian of the six-manifold endowed with some additional data (i.e. a
symplectic structure, a quadratic form, and a complex structure). We define a
certain hermitian vector bundle over this finite-dimensional parameter space.
The partition bundle is then given by the pullback of the latter bundle by the
map from the parameter space related to the six-manifold to the parameter space
related to the intermediate Jacobian.Comment: 15 pages. Minor changes, added reference
Reinstated episodic context guides sampling-based decisions for reward.
How does experience inform decisions? In episodic sampling, decisions are guided by a few episodic memories of past choices. This process can yield choice patterns similar to model-free reinforcement learning; however, samples can vary from trial to trial, causing decisions to vary. Here we show that context retrieved during episodic sampling can cause choice behavior to deviate sharply from the predictions of reinforcement learning. Specifically, we show that, when a given memory is sampled, choices (in the present) are influenced by the properties of other decisions made in the same context as the sampled event. This effect is mediated by fMRI measures of context retrieval on each trial, suggesting a mechanism whereby cues trigger retrieval of context, which then triggers retrieval of other decisions from that context. This result establishes a new avenue by which experience can guide choice and, as such, has broad implications for the study of decisions
D-brane anomaly inflow revisited
Axial and gravitational anomaly of field theories, when embedded in string
theory, must be accompanied by canceling inflow. We give a self-contained
overview for various world-volume theories, and clarify the role of smeared
magnetic sources in I-brane/D-brane cases. The proper anomaly descent of the
source, as demanded by regularity of RR field strengths H's, turns out to be an
essential ingredient. We show how this allows correct inflow to be generated
for all such theories, including self-dual cases, and also that the mechanism
is now insensitive to the choice between the two related but inequivalent forms
of D-brane Chern-Simons couplings. In particular, SO(6)_R axial anomaly of d=4
maximal SYM is canceled by the inflow onto D3-branes via the standard minimal
coupling to C_4. We also propose how, for the anomaly cancelation, the four
types of Orientifold planes should be coupled to the spacetime curvatures, of
which conflicting claims existed previously.Comment: 41 pages, references updated; version to appear in JHE
M5 spikes and operators in the HVZ membrane theory
In this note we study some aspects of the so-called dual ABJM theory
introduced by Hanany, Vegh & Zaffaroni. We analyze the spectrum of chiral
operators, and compare it with the spectrum of functions on the mesonic moduli
space M=C^2\times C^2/Z_k, finding expected agreement for the coherent branch.
A somewhat mysterious extra branch of dimension N^2 opens up at the orbifold
fixed point. We also study BPS solutions which represent M2/M5 intersections.
The mesonic moduli space suggests that there should be two versions of this
spike: one where the M5 lives in the orbifolded C^2 and another where it lives
in the unorbifolded one. While expectedly the first class turns out to be like
the ABJM spike, the latter class looks like a collection of stacks of M5 branes
with fuzzy S^3 profiles. This shows hints of the appearance of the global SO(4)
at the non-abelian level which is otherwise not present in the bosonic
potential. We also study the matching of SUGRA modes with operators in the
coherent branch of the moduli space. As a byproduct, we present some formulae
for the laplacian in conical CY_4 of the form C^n\times CY_{4-n}.Comment: 22 pages, 1 figure. Published version with corrected typos
Orientifolds and the Refined Topological String
We study refined topological string theory in the presence of orientifolds by
counting second-quantized BPS states in M-theory. This leads us to propose a
new integrality condition for both refined and unrefined topological strings
when orientifolds are present. We define the SO(2N) refined Chern-Simons theory
which computes refined open string amplitudes for branes wrapping Seifert
three-manifolds. We use the SO(2N) refined Chern-Simons theory to compute new
invariants of torus knots that generalize the Kauffman polynomials. At large N,
the SO(2N) refined Chern-Simons theory on the three-sphere is dual to refined
topological strings on an orientifold of the resolved conifold, generalizing
the Gopakumar-Sinha-Vafa duality. Finally, we use the (2,0) theory to define
and solve refined Chern-Simons theory for all ADE gauge groups
The effect of intervertebral cartilage on neutral posture and range of motion in the necks of sauropod dinosaurs
The necks of sauropod dinosaurs were a key factor in their evolution. The habitual posture and range of motion of these necks has been controversial, and computer-aided studies have argued for an obligatory sub-horizontal pose. However, such studies are compromised by their failure to take into account the important role of intervertebral cartilage. This cartilage takes very different forms in different animals. Mammals and crocodilians have intervertebral discs, while birds have synovial joints in their necks. The form and thickness of cartilage varies significantly even among closely related taxa. We cannot yet tell whether the neck joints of sauropods more closely resembled those of birds or mammals. Inspection of CT scans showed cartilage:bone ratios of 4.5% for Sauroposeidon and about 20% and 15% for two juvenile Apatosaurus individuals. In extant animals, this ratio varied from 2.59% for the rhea to 24% for a juvenile giraffe. It is not yet possible to disentangle ontogenetic and taxonomic signals, but mammal cartilage is generally three times as thick as that of birds. Our most detailed work, on a turkey, yielded a cartilage:bone ratio of 4.56%. Articular cartilage also added 11% to the length of the turkey's zygapophyseal facets. Simple image manipulation suggests that incorporating 4.56% of neck cartilage into an intervertebral joint of a turkey raises neutral posture by 15°. If this were also true of sauropods, the true neutral pose of the neck would be much higher than has been depicted. An additional 11% of zygapophyseal facet length translates to 11% more range of motion at each joint. More precise quantitative results must await detailed modelling. In summary, including cartilage in our models of sauropod necks shows that they were longer, more elevated and more flexible than previously recognised
Microevolution of Helicobacter pylori during prolonged infection of single hosts and within families
Our understanding of basic evolutionary processes in bacteria is still very limited. For example, multiple recent dating estimates are based on a universal inter-species molecular clock rate, but that rate was calibrated using estimates of geological dates that are no longer accepted. We therefore estimated the short-term rates of mutation and recombination in Helicobacter pylori by sequencing an average of 39,300 bp in 78 gene fragments from 97 isolates. These isolates included 34 pairs of sequential samples, which were sampled at intervals of 0.25 to 10.2 years. They also included single isolates from 29 individuals (average age: 45 years) from 10 families. The accumulation of sequence diversity increased with time of separation in a clock-like manner in the sequential isolates. We used Approximate Bayesian Computation to estimate the rates of mutation, recombination, mean length of recombination tracts, and average diversity in those tracts. The estimates indicate that the short-term mutation rate is 1.4×10−6 (serial isolates) to 4.5×10−6 (family isolates) per nucleotide per year and that three times as many substitutions are introduced by recombination as by mutation. The long-term mutation rate over millennia is 5–17-fold lower, partly due to the removal of non-synonymous mutations due to purifying selection. Comparisons with the recent literature show that short-term mutation rates vary dramatically in different bacterial species and can span a range of several orders of magnitude
Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds
The six-dimensional effective action of F-theory compactified on a singular
elliptically fibred Calabi-Yau threefold is determined by using an M-theory
lift. The low-energy data are derived by comparing a circle reduction of a
general six-dimensional (1,0) gauged supergravity theory with the effective
action of M-theory on the resolved Calabi-Yau threefold. The derivation
includes six-dimensional tensor multiplets for which the (anti-) self-duality
constraints are imposed on the level of the five-dimensional action. The vector
sector of the reduced theory is encoded by a non-standard potential due to the
Green-Schwarz term in six dimensions. This Green-Schwarz term also contains
higher curvature couplings which are considered to establish the full map
between anomaly coefficients and geometry. F-/M-theory duality is exploited by
moving to the five-dimensional Coulomb branch after circle reduction and
integrating out massive vector multiplets and matter hypermultiplets. The
associated fermions then generate additional Chern-Simons couplings at
one-loop. Further couplings involving the graviphoton are induced by quantum
corrections due to excited Kaluza-Klein modes. On the M-theory side integrating
out massive fields corresponds to resolving the singularities of the Calabi-Yau
threefold, and yields intriguing relations between six-dimensional anomalies
and classical topology.Comment: 55 pages, v2: typos corrected, discussion of loop corrections
improve
Statistical analysis and significance testing of serial analysis of gene expression data using a Poisson mixture model
<p>Abstract</p> <p>Background</p> <p>Serial analysis of gene expression (SAGE) is used to obtain quantitative snapshots of the transcriptome. These profiles are count-based and are assumed to follow a Binomial or Poisson distribution. However, tag counts observed across multiple libraries (for example, one or more groups of biological replicates) have additional variance that cannot be accommodated by this assumption alone. Several models have been proposed to account for this effect, all of which utilize a continuous prior distribution to explain the excess variance. Here, a Poisson mixture model, which assumes excess variability arises from sampling a mixture of distinct components, is proposed and the merits of this model are discussed and evaluated.</p> <p>Results</p> <p>The goodness of fit of the Poisson mixture model on 15 sets of biological SAGE replicates is compared to the previously proposed hierarchical gamma-Poisson (negative binomial) model, and a substantial improvement is seen. In further support of the mixture model, there is observed: 1) an increase in the number of mixture components needed to fit the expression of tags representing more than one transcript; and 2) a tendency for components to cluster libraries into the same groups. A confidence score is presented that can identify tags that are differentially expressed between groups of SAGE libraries. Several examples where this test outperforms those previously proposed are highlighted.</p> <p>Conclusion</p> <p>The Poisson mixture model performs well as a) a method to represent SAGE data from biological replicates, and b) a basis to assign significance when testing for differential expression between multiple groups of replicates. Code for the R statistical software package is included to assist investigators in applying this model to their own data.</p
D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades
We perform a systematic analysis of the D-brane charges associated with
string theory realizations of d=3 gauge theories, focusing on the examples of
the N=4 supersymmetric U(N)xU(N+M) Yang-Mills theory and the N=3 supersymmetric
U(N)xU(N+M) Yang-Mills-Chern-Simons theory. We use both the brane construction
of these theories and their dual string theory backgrounds in the supergravity
approximation. In the N=4 case we generalize the previously known gravitational
duals to arbitrary values of the gauge couplings, and present a precise mapping
between the gravity and field theory parameters. In the N=3 case, which (for
some values of N and M) flows to an N=6 supersymmetric Chern-Simons-matter
theory in the IR, we argue that the careful analysis of the charges leads to a
shift in the value of the B-field in the IR solution by 1/2, in units where its
periodicity is one, compared to previous claims. We also suggest that the N=3
theories may exhibit, for some values of N and M, duality cascades similar to
those of the Klebanov-Strassler theory.Comment: 47 pages, 9 figures; minor changes, references adde
- …