474 research outputs found
Proalgebraic crossed modules of quasirational presentations
We introduce the concept of quasirational relation modules for discrete and
pro- presentations of discrete and pro- groups and show that aspherical
presentations and their subpresentations are quasirational. In the pro--case
quasirationality of pro--groups with a single defining relation holds. For
every quasirational (pro-)relation module we construct the so called
-adic rationalization, which is a pro-fd-module
. We provide the isomorphisms
and , where and
stands for continuous prounipotent completions and corresponding
prounipotent presentations correspondingly. We show how
embeds into a sequence of abelian prounipotent
groups. This sequence arises naturally from a certain prounipotent crossed
module, the latter bring concrete examples of proalgebraic homotopy types. The
old-standing open problem of Serre, slightly corrected by Gildenhuys, in its
modern form states that pro--groups with a single defining relation are
aspherical. Our results give a positive feedback to the question of Serre.Comment: This is a corrected version of the paper which appeared in the
Extended Abstracts Spring 2015, Interactions between Representation Theory,
Algebraic Topology and Commutative Algebra, Research Perspectives CRM
Barcelona, Vol.5, 201
On p-adic lattices and Grassmannians
It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive
group G over a field k, carry the geometric structure of an inductive limit of
projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for
G. From the point of view of number theory it would be interesting to obtain an
analogous geometric interpretation of quotients of the form
G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of
p-typical Witt vectors, k is a perfect field of characteristic p and G is a
reductive group scheme over W(k). The present paper is an attempt to describe
which constructions carry over from the function field case to the p-adic case,
more precisely to the situation of the p-adic affine Grassmannian for the
special linear group G=SL_n. We start with a description of the R-valued points
of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R),
where R is a perfect k-algebra. In order to obtain a link with geometry we
further construct projective k-subvarieties of the multigraded Hilbert scheme
which map equivariantly to the p-adic affine Grassmannian. The images of these
morphisms play the role of Schubert varieties in the p-adic setting. Further,
for any reduced k-algebra R these morphisms induce bijective maps between the
sets of R-valued points of the respective open orbits in the multigraded
Hilbert scheme and the corresponding Schubert cells of the p-adic affine
Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math.
Zeitschrift, of the previously published preprint "On p-adic loop groups and
Grassmannians
On Birch and Swinnerton-Dyer's cubic surfaces
In a 1975 paper of Birch and Swinnerton-Dyer, a number of explicit norm form
cubic surfaces are shown to fail the Hasse Principle. They make a
correspondence between this failure and the Brauer--Manin obstruction, recently
discovered by Manin. We generalize their work, making use of modern computer
algebra software to show that a larger set of cubic surfaces have a
Brauer--Manin obstruction to the Hasse principle, thus verifying the
Colliot-Th\'el\`ene--Sansuc conjecture for infinitely many cubic surfaces
Perverse coherent t-structures through torsion theories
Bezrukavnikov (later together with Arinkin) recovered the work of Deligne
defining perverse -structures for the derived category of coherent sheaves
on a projective variety. In this text we prove that these -structures can be
obtained through tilting torsion theories as in the work of Happel, Reiten and
Smal\o. This approach proves to be slightly more general as it allows us to
define, in the quasi-coherent setting, similar perverse -structures for
certain noncommutative projective planes.Comment: New revised version with important correction
How Can Selection of Biologically Inspired Features Improve the Performance of a Robust Object Recognition Model?
Humans can effectively and swiftly recognize objects in complex natural scenes. This outstanding ability has motivated many computational object recognition models. Most of these models try to emulate the behavior of this remarkable system. The human visual system hierarchically recognizes objects in several processing stages. Along these stages a set of features with increasing complexity is extracted by different parts of visual system. Elementary features like bars and edges are processed in earlier levels of visual pathway and as far as one goes upper in this pathway more complex features will be spotted. It is an important interrogation in the field of visual processing to see which features of an object are selected and represented by the visual cortex. To address this issue, we extended a hierarchical model, which is motivated by biology, for different object recognition tasks. In this model, a set of object parts, named patches, extracted in the intermediate stages. These object parts are used for training procedure in the model and have an important role in object recognition. These patches are selected indiscriminately from different positions of an image and this can lead to the extraction of non-discriminating patches which eventually may reduce the performance. In the proposed model we used an evolutionary algorithm approach to select a set of informative patches. Our reported results indicate that these patches are more informative than usual random patches. We demonstrate the strength of the proposed model on a range of object recognition tasks. The proposed model outperforms the original model in diverse object recognition tasks. It can be seen from the experiments that selected features are generally particular parts of target images. Our results suggest that selected features which are parts of target objects provide an efficient set for robust object recognition
Derivations and automorphisms of free nilpotent Lie algebras and their quotiens
Let \n_{d,t} be the free nilpotent Lie algebra of type and nilindex
. Starting out with the derivation algebra and the automorphism group of
\n_{d,t}, we get a natural description of derivations and automorphisms of
any generic nilpotent Lie algebra of the same type and nilindex. Moreover,
along the paper we discuss several examples to illustrate the obtained results.Comment: 13 page
A Stable Biologically Motivated Learning Mechanism for Visual Feature Extraction to Handle Facial Categorization
The brain mechanism of extracting visual features for recognizing various objects has consistently been a controversial issue in computational models of object recognition. To extract visual features, we introduce a new, biologically motivated model for facial categorization, which is an extension of the Hubel and Wiesel simple-to-complex cell hierarchy. To address the synaptic stability versus plasticity dilemma, we apply the Adaptive Resonance Theory (ART) for extracting informative intermediate level visual features during the learning process, which also makes this model stable against the destruction of previously learned information while learning new information. Such a mechanism has been suggested to be embedded within known laminar microcircuits of the cerebral cortex. To reveal the strength of the proposed visual feature learning mechanism, we show that when we use this mechanism in the training process of a well-known biologically motivated object recognition model (the HMAX model), it performs better than the HMAX model in face/non-face classification tasks. Furthermore, we demonstrate that our proposed mechanism is capable of following similar trends in performance as humans in a psychophysical experiment using a face versus non-face rapid categorization task
Temporal Patterns of Nucleotide Misincorporations and DNA Fragmentation in Ancient DNA
DNA that survives in museum specimens, bones and other tissues recovered by archaeologists is invariably fragmented and chemically modified. The extent to which such modifications accumulate over time is largely unknown but could potentially be used to differentiate between endogenous old DNA and present-day DNA contaminating specimens and experiments. Here we examine mitochondrial DNA sequences from tissue remains that vary in age between 18 and 60,000 years with respect to three molecular features: fragment length, base composition at strand breaks, and apparent C to T substitutions. We find that fragment length does not decrease consistently over time and that strand breaks occur preferentially before purine residues by what may be at least two different molecular mechanisms that are not yet understood. In contrast, the frequency of apparent C to T substitutions towards the 5âČ-ends of molecules tends to increase over time. These nucleotide misincorporations are thus a useful tool to distinguish recent from ancient DNA sources in specimens that have not been subjected to unusual or harsh treatments
Observation of associated near-side and away-side long-range correlations in âsNN=5.02ââTeV proton-lead collisions with the ATLAS detector
Two-particle correlations in relative azimuthal angle (ÎÏ) and pseudorapidity (Îη) are measured in âsNN=5.02ââTeV p+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using approximately 1ââÎŒb-1 of data as a function of transverse momentum (pT) and the transverse energy (ÎŁETPb) summed over 3.1<η<4.9 in the direction of the Pb beam. The correlation function, constructed from charged particles, exhibits a long-range (2<|Îη|<5) ânear-sideâ (ÎÏâŒ0) correlation that grows rapidly with increasing ÎŁETPb. A long-range âaway-sideâ (ÎÏâŒÏ) correlation, obtained by subtracting the expected contributions from recoiling dijets and other sources estimated using events with small ÎŁETPb, is found to match the near-side correlation in magnitude, shape (in Îη and ÎÏ) and ÎŁETPb dependence. The resultant ÎÏ correlation is approximately symmetric about Ï/2, and is consistent with a dominant cosâĄ2ÎÏ modulation for all ÎŁETPb ranges and particle pT
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