6,891 research outputs found
For the Jubilee of Vladimir Mikhailovich Chernov
On April 25, 2019, Vladimir Chernov celebrated his 70th birthday, Doctor of Physics and Mathematics, Chief Researcher at the Laboratory of Mathematical Methods of Image Processing of the Image Processing Systems Institute of the Russian Academy of Sciences (IPSI RAS), a branch of the Federal Science Research Center "Crystallography and Photonics RAS and part-Time Professor at the Department of Geoinformatics and Information Security of the Samara National Research University named after academician S.P. Korolev (Samara University). The article briefly describes the scientific and pedagogical achievements of the hero of the day. © Published under licence by IOP Publishing Ltd
Honeycomb tessellations and canonical bases for permutohedral blades
This paper studies two families of piecewise constant functions which are
determined by the -skeleta of collections of honeycomb tessellations of
with standard permutohedra. The union of the codimension
cones obtained by extending the facets which are incident to a vertex of such a
tessellation is called a blade. We prove ring-theoretically that such a
honeycomb, with 1-skeleton built from a cyclic sequence of segments in the root
directions , decomposes locally as a Minkowski sum of
isometrically embedded components of hexagonal honeycombs: tripods and
one-dimensional subspaces. For each triangulation of a cyclically oriented
polygon there exists such a factorization. This consequently gives resolution
to an issue proposed and developed by A. Ocneanu, to find a structure theory
for an object he discovered during his investigations into higher Lie theories:
permutohedral blades. We introduce a certain canonical basis for a vector space
spanned by piecewise constant functions of blades which is compatible with
various quotient spaces appearing in algebra, topology and scattering
amplitudes. Various connections to scattering amplitudes are discussed, giving
new geometric interpretations for certain combinatorial identities for one-loop
Parke-Taylor factors. We give a closed formula for the graded dimension of the
canonical blade basis. We conjecture that the coefficients of the generating
function numerators for the diagonals are symmetric and unimodal.Comment: Added references; new section on configuration space
An Introduction To The Web-Based Formalism
This paper summarizes our rather lengthy paper, "Algebra of the Infrared:
String Field Theoretic Structures in Massive Field Theory In
Two Dimensions," and is meant to be an informal, yet detailed, introduction and
summary of that larger work.Comment: 50 pages, 40 figure
ForestHash: Semantic Hashing With Shallow Random Forests and Tiny Convolutional Networks
Hash codes are efficient data representations for coping with the ever
growing amounts of data. In this paper, we introduce a random forest semantic
hashing scheme that embeds tiny convolutional neural networks (CNN) into
shallow random forests, with near-optimal information-theoretic code
aggregation among trees. We start with a simple hashing scheme, where random
trees in a forest act as hashing functions by setting `1' for the visited tree
leaf, and `0' for the rest. We show that traditional random forests fail to
generate hashes that preserve the underlying similarity between the trees,
rendering the random forests approach to hashing challenging. To address this,
we propose to first randomly group arriving classes at each tree split node
into two groups, obtaining a significantly simplified two-class classification
problem, which can be handled using a light-weight CNN weak learner. Such
random class grouping scheme enables code uniqueness by enforcing each class to
share its code with different classes in different trees. A non-conventional
low-rank loss is further adopted for the CNN weak learners to encourage code
consistency by minimizing intra-class variations and maximizing inter-class
distance for the two random class groups. Finally, we introduce an
information-theoretic approach for aggregating codes of individual trees into a
single hash code, producing a near-optimal unique hash for each class. The
proposed approach significantly outperforms state-of-the-art hashing methods
for image retrieval tasks on large-scale public datasets, while performing at
the level of other state-of-the-art image classification techniques while
utilizing a more compact and efficient scalable representation. This work
proposes a principled and robust procedure to train and deploy in parallel an
ensemble of light-weight CNNs, instead of simply going deeper.Comment: Accepted to ECCV 201
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