Multipartite Ranking-Selection of Low-Dimensional Instances by Supervised Projection to High-Dimensional Space

Pruning of redundant or irrelevant instances of data is a key to every successful solution for pattern recognition. In this paper, we present a novel ranking-selection framework for low-length but highly correlated instances. Instead of working in the low-dimensional instance space, we learn a supervised projection to high-dimensional space spanned by the number of classes in the dataset under study. Imposing higher distinctions via exposing the notion of labels to the instances, lets to deploy one versus all ranking for each individual classes and selecting quality instances via adaptive thresholding of the overall scores. To prove the efficiency of our paradigm, we employ it for the purpose of texture understanding which is a hard recognition challenge due to high similarity of texture pixels and low dimensionality of their color features. Our experiments show considerable improvements in recognition performance over other local descriptors on several publicly available datasets.Comment: 15 pages, 1 figure, 2 tables, 3 algorithms, 1 appendi

Approximation on abelian varieties by its subgroups

In this paper, we introduce an algebro-geometric formulation for Faltings' theorem on diophantine approximation on abelian varieties using an improvement of Faltings-Wustholz observation over number fields. In fact, we prove that, for any geometrically irreducible sub-variety E of an abelian variety A and any finitely generated subgroup F of A(C) we have an estimate of the form d_v(E;x) >cH(x)^d for for some constant c where d_v(E;x) denotes the distance of a point x in F outside E and v is a place of K. This was proved before, only for F being the set of rational points of A over a number field.Comment: 6 pages. arXiv admin note: substantial text overlap with arXiv:math/040449

Linkage of finite G_C-dimension modules

Let R be a semiperfect commutative Noetherian ring and C a semidualizing R-module. We study the theory of linkage for modules of finite G_C-dimension. For a horizontally linked R-module M of finite G_C-dimension, the connection of the Serre condition (S_n) with the vanishing of certain relative cohomology modules of its linked module is discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1407.654

Deformation of Outer Representations of Galois Group II

This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for functors on Artin local rings. In the second part, we use a version of Schlessinger criteria for functors on the Artinian category of nilpotent Lie algebras which is formulated by Pridham, and explore arithmetic applications.Comment: 8 page

μ\mu Problem, SO(10) SUSY GUT and Heavy Gluino LSP

We present a solution to the $\mu$ problem in an SO(10) supersymmetric grand unified (SUSY GUT) model with gauge mediated (GMSB) and D-term supersymmetry breaking. A Peccei-Quinn ({\bf PQ}) symmetry is broken at the messenger scale and enables the generation of the $\mu$ term. The invisible axion (Goldstone boson of {\bf PQ} symmetry breaking) is a cold dark matter candidate. At low energy, our model leads to a phenomenologically acceptable version of the minimal supersymmetric standard model (MSSM) with novel particle phenomenology. Either the gluino or the gravitino is the lightest supersymmetric particle (LSP). The phenomenological constraints on the model result in a Higgs with mass $\sim 86 - 91$ GeV and $\tan\beta \sim 9 - 14$.Comment: Talk given at The Meeting of The Division of Particles and Fields of The American Physical Society (DPF 2000), Columbus, Ohio, August 9-12, 2000, 3 p

Distributed Deep Transfer Learning by Basic Probability Assignment

Transfer learning is a popular practice in deep neural networks, but fine-tuning of large number of parameters is a hard task due to the complex wiring of neurons between splitting layers and imbalance distributions of data in pretrained and transferred domains. The reconstruction of the original wiring for the target domain is a heavy burden due to the size of interconnections across neurons. We propose a distributed scheme that tunes the convolutional filters individually while backpropagates them jointly by means of basic probability assignment. Some of the most recent advances in evidence theory show that in a vast variety of the imbalanced regimes, optimizing of some proper objective functions derived from contingency matrices prevents biases towards high-prior class distributions. Therefore, the original filters get gradually transferred based on individual contributions to overall performance of the target domain. This largely reduces the expected complexity of transfer learning whilst highly improves precision. Our experiments on standard benchmarks and scenarios confirm the consistent improvement of our distributed deep transfer learning strategy

Toward Robustness against Label Noise in Training Deep Discriminative Neural Networks

Collecting large training datasets, annotated with high-quality labels, is costly and time-consuming. This paper proposes a novel framework for training deep convolutional neural networks from noisy labeled datasets that can be obtained cheaply. The problem is formulated using an undirected graphical model that represents the relationship between noisy and clean labels, trained in a semi-supervised setting. In our formulation, the inference over latent clean labels is tractable and is regularized during training using auxiliary sources of information. The proposed model is applied to the image labeling problem and is shown to be effective in labeling unseen images as well as reducing label noise in training on CIFAR-10 and MS COCO datasets.Comment: To appear in Neural Information Processing Systems (NIPS) 201

On Atkin-Lehner correspondences on Siegel spaces

We introduce a higher dimensional Atkin-Lehner theory for Siegel-Parahoric congruence subgroups of $GSp(2g)$. Old Siegel forms are induced by geometric correspondences on Siegel moduli spaces which commute with almost all local Hecke algebras. We also introduce an algorithm to get equations for moduli spaces of Siegel-Parahoric level structures, once we have equations for prime levels and square prime levels over the level one Siegel space. This way we give equations for an infinite tower of Siegel spaces after N. Elkies who did the genus one case.Comment: 20 page

Deformation of Outer Representations of Galois Group

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than those coming from deformations of "abelian" Galois representations induced by the Tate module of associated Jacobian variety. We develop an arithmetic deformation theory of graded Lie algebras with finite dimensional graded components to serve our purpose.Comment: 20 pages, some corrections are implemented in the revised versio

Self-Similar Fractals and Arithmetic Dynamics

The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a finite and disjoint union of `similar' copies. Fractals provide a framework in which, one can unite some results and conjectures in Diophantine geometry. We define a well-behaved notion of dimension for self-similar fractals. We also prove a fractal version of Roth's theorem for algebraic points on a variety approximated by elements of a fractal subset. As a consequence, we get a fractal version of Siegel's theorem on finiteness of integral points on hyperbolic curves and a fractal version of Falting's theorem on Diophantine approximation on abelian varieties.Comment: 19 page