1,613 research outputs found
Which canonical algebras are derived equivalent to incidence algebras of posets?
We give a full description of all the canonical algebras over an
algebraically closed field that are derived equivalent to incidence algebras of
finite posets. These are the canonical algebras whose number of weights is
either 2 or 3.Comment: 8 pages; slight revision; to appear in Comm. Algebr
Determining topological order from a local ground state correlation function
Topological insulators are physically distinguishable from normal insulators
only near edges and defects, while in the bulk there is no clear signature to
their topological order. In this work we show that the Z index of topological
insulators and the Z index of the integer quantum Hall effect manifest
themselves locally. We do so by providing an algorithm for determining these
indices from a local equal time ground-state correlation function at any
convenient boundary conditions. Our procedure is unaffected by the presence of
disorder and can be naturally generalized to include weak interactions. The
locality of these topological indices implies bulk-edge correspondence theorem.Comment: 7 pages, 3 figures. Major changes: the paper was divided into
sections, the locality of the order in 3D topological insulators is also
discusse
The double Ringel-Hall algebra on a hereditary abelian finitary length category
In this paper, we study the category of semi-stable
coherent sheaves of a fixed slope over a weighted projective curve. This
category has nice properties: it is a hereditary abelian finitary length
category. We will define the Ringel-Hall algebra of and
relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type
theorem to describe the indecomposable objects in this category, i.e. the
indecomposable semi-stable sheaves.Comment: 29 page
Deep levels in a-plane, high Mg-content MgxZn1-xO epitaxial layers grown by molecular beam epitaxy
Deep level defects in n-type unintentionally doped a-plane MgxZn1−xO, grown by molecular beam epitaxy on r-plane sapphire were fully characterized using deep level optical spectroscopy (DLOS) and related methods. Four compositions of MgxZn1−xO were examined with x = 0.31, 0.44, 0.52, and 0.56 together with a control ZnO sample. DLOS measurements revealed the presence of five deep levels in each Mg-containing sample, having energy levels of Ec − 1.4 eV, 2.1 eV, 2.6 V, and Ev + 0.3 eV and 0.6 eV. For all Mg compositions, the activation energies of the first three states were constant with respect to the conduction band edge, whereas the latter two revealed constant activation energies with respect to the valence band edge. In contrast to the ternary materials, only three levels, at Ec − 2.1 eV, Ev + 0.3 eV, and 0.6 eV, were observed for the ZnO control sample in this systematically grown series of samples. Substantially higher concentrations of the deep levels at Ev + 0.3 eV and Ec − 2.1 eV were observed in ZnO compared to the Mg alloyed samples. Moreover, there is a general invariance of trap concentration of the Ev + 0.3 eV and 0.6 eV levels on Mg content, while at least and order of magnitude dependency of the Ec − 1.4 eV and Ec − 2.6 eV levels in Mg alloyed samples
Direct Measurement of Quantum Confinement Effects at Metal to Quantum-Well Nanocontacts
Model metal-semiconductor nanostructure Schottky nanocontacts were made on cleaved heterostructures containing GaAs quantum wells (QWs) of varying width and were locally probed by ballistic electron emission microscopy. The local Schottky barrier was found to increase by ∼0.140 eV as the QW width was systematically decreased from 15 to 1 nm, due mostly to a large (∼0.200 eV) quantum-confinement increase to the QW conduction band. The measured barrier increase over the full 1 to 15 nm QW range was quantitatively explained when local "interface pinning" and image force lowering effects are also considered
Quantum groups and double quiver algebras
For a finite dimensional semisimple Lie algebra and a root
of unity in a field we associate to these data a double quiver
It is shown that a restricted version of the quantized
enveloping algebras is a quotient of the double quiver algebra
Comment: 15 page
LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies
We extend the classical LR characterization of chirotopes of finite planar
families of points to chirotopes of finite planar families of pairwise disjoint
convex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is a
chirotope of finite planar families of pairwise disjoint convex bodies if and
only if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to the
set of 3-subsets of J is a chirotope of finite planar families of pairwise
disjoint convex bodies. Our main tool is the polarity map, i.e., the map that
assigns to a convex body the set of lines missing its interior, from which we
derive the key notion of arrangements of double pseudolines, introduced for the
first time in this paper.Comment: 100 pages, 73 figures; accepted manuscript versio
The Design Space of Generative Models
Card et al.'s classic paper "The Design Space of Input Devices" established
the value of design spaces as a tool for HCI analysis and invention. We posit
that developing design spaces for emerging pre-trained, generative AI models is
necessary for supporting their integration into human-centered systems and
practices. We explore what it means to develop an AI model design space by
proposing two design spaces relating to generative AI models: the first
considers how HCI can impact generative models (i.e., interfaces for models)
and the second considers how generative models can impact HCI (i.e., models as
an HCI prototyping material)
Alterations in composition and diversity of the intestinal microbiota in patients with diarrhea-predominant irritable bowel syndrome: Alterations in composition and diversity of the intestinal microbiota in D-IBS
The intestinal microbiota has been implicated in the pathophysiology of Irritable Bowel Syndrome (IBS). Due to the variable resolutions of techniques used to characterize the intestinal microbiota, and the heterogeneity of IBS, the defined alterations of the IBS intestinal microbiota are inconsistent. We analyzed the composition of the intestinal microbiota in a defined subgroup of IBS patients (diarrhea-predominant IBS, D-IBS) using a technique that provides the deepest characterization available for complex microbial communities
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