20,366 research outputs found
The differential graded odd nilHecke algebra
We equip the odd nilHecke algebra and its associated thick calculus category
with digrammatically local differentials. The resulting differential graded
Grothendieck groups are isomorphic to two different forms of the positive part
of quantum sl(2) at a fourth root of unity.Comment: 53 page
Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit
Subspace clustering methods based on , or nuclear norm
regularization have become very popular due to their simplicity, theoretical
guarantees and empirical success. However, the choice of the regularizer can
greatly impact both theory and practice. For instance, regularization
is guaranteed to give a subspace-preserving affinity (i.e., there are no
connections between points from different subspaces) under broad conditions
(e.g., arbitrary subspaces and corrupted data). However, it requires solving a
large scale convex optimization problem. On the other hand, and
nuclear norm regularization provide efficient closed form solutions, but
require very strong assumptions to guarantee a subspace-preserving affinity,
e.g., independent subspaces and uncorrupted data. In this paper we study a
subspace clustering method based on orthogonal matching pursuit. We show that
the method is both computationally efficient and guaranteed to give a
subspace-preserving affinity under broad conditions. Experiments on synthetic
data verify our theoretical analysis, and applications in handwritten digit and
face clustering show that our approach achieves the best trade off between
accuracy and efficiency.Comment: 13 pages, 1 figure, 2 tables. Accepted to CVPR 2016 as an oral
presentatio
Quantum duality under the theta-exact Seiberg-Witten map
We show that in the perturbative regime defined by the coupling constant, the
theta-exact Seiberg-Witten map applied to noncommutative U(N) Yang-Mills --with
or without Supersymmetry-- gives an ordinary gauge theory which is, at the
quantum level, dual to the former. We do so by using the on-shell DeWitt
effective action and dimensional regularization. We explicitly compute the
one-loop two-point function contribution to the on-shell DeWitt effective
action of the ordinary U(1) theory furnished by the theta-exact Seiberg-Witten
map. We find that the non-local UV divergences found in the propagator in the
Feynman gauge all but disappear, so that they are not physically relevant. We
also show that the quadratic noncommutative IR divergences are gauge-fixing
independent and go away in the Supersymmetric version of the U(1) theory.Comment: 47 pages, 21 figures. Version published in JHEP under the reference:
JHEP09(2016)05
Provable Self-Representation Based Outlier Detection in a Union of Subspaces
Many computer vision tasks involve processing large amounts of data
contaminated by outliers, which need to be detected and rejected. While outlier
detection methods based on robust statistics have existed for decades, only
recently have methods based on sparse and low-rank representation been
developed along with guarantees of correct outlier detection when the inliers
lie in one or more low-dimensional subspaces. This paper proposes a new outlier
detection method that combines tools from sparse representation with random
walks on a graph. By exploiting the property that data points can be expressed
as sparse linear combinations of each other, we obtain an asymmetric affinity
matrix among data points, which we use to construct a weighted directed graph.
By defining a suitable Markov Chain from this graph, we establish a connection
between inliers/outliers and essential/inessential states of the Markov chain,
which allows us to detect outliers by using random walks. We provide a
theoretical analysis that justifies the correctness of our method under
geometric and connectivity assumptions. Experimental results on image databases
demonstrate its superiority with respect to state-of-the-art sparse and
low-rank outlier detection methods.Comment: 16 pages. CVPR 2017 spotlight oral presentatio
Quantum noncommutative ABJM theory: first steps
We introduce ABJM quantum field theory in the noncommutative spacetime by
using the component formalism and show that it is N=6 supersymmetric. For the
U(1)_{\kappa} x U(1)_{-\kappa} case, we compute all one-loop 1PI two and three
point functions in the Landau gauge and show that they are UV finite and have
well-defined commutative limits theta^{\mu\nu} -> 0, corresponding exactly to
the 1PI functions of the ordinary ABJM field theory. This result also holds for
all one-loop functions which are UV finite by power counting. It seems that the
quantum noncommutative ABJM field theory is free from the noncommutative IR
instabilities.Comment: 43 pages and 25 figures, corrected trivial typos, misprints,
misplaced symbols et
Super Yang-Mills and theta-exact Seiberg-Witten map: Absence of quadratic noncommutative IR divergences
We compute the one-loop 1PI contributions to all the propagators of the
noncommutative N=1, 2, 4 super Yang-Mills (SYM) U(1) theories defined by the
means of the theta-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then
we extract the UV divergent contributions and the noncommutative IR
divergences. We show that all the quadratic noncommutative IR divergences add
up to zero in each propagator.Comment: 55 pages, 53 figures, version published in JHE
Rigorous Proof of Pseudospin Ferromagnetism in Two-Component Bosonic Systems with Component-Independent Interactions
For a two-component bosonic system, the components can be mapped onto a
pseudo-spin degree of freedom with spin quantum number S=1/2. We provide a
rigorous proof that for a wide-range of real Hamiltonians with component
independent mass and interaction, the ground state is a ferromagnetic state
with pseudospin fully polarized. The spin-wave excitations are studied and
found to have quadratic dispersion relations at long wave length.Comment: 4 pages, no figur
Intra-organizational integration and innovation: organizational structure, environmental contingency and R&D performance
It is widely thought that intra-firm integration has a positive effect on organizational performance, especially in environments characterized by complex and uncertain information. However, counter arguments suggest that integration may limit flexibility and thereby reduce performance in the face of uncertainty. Research and development activities of a firm are especially likely to face complex and uncertain information environments. Following prior work in contingency theory, this paper analyzes the effects of intra-organizational integration on manufacturing firms’ innovative performance. Based on a survey of R&D units in US manufacturing firms and patent data from the NBER patent database, we examine the relation between mechanisms for linking R&D to other units of the firm and the relative innovativeness of the firm. Furthermore, we argue that the impact of integration may vary by the importance of secrecy in protecting firms’ innovation advantages. We find that intra-firm integration is associated with higher self-reported innovativeness and more patents. We also find some evidence that this effect is moderated by the appropriability regime the firm faces, with the benefits of cross-functional integration being weaker in industries where secrecy is especially important. These results both support and develop the contingency model of organizational performance.Innovation; Organizations; Contingency theory;
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