The C-spectral sequence was introduced by Vinogradov in the late Seventies as a fundamental tool for the study of algebro-geometric properties of jet spaces and differential equations. A spectral sequence arise from the contact filtration of the modules of forms on jet spaces of a fibring (or on a differential equation…
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48 results for “Vinogradov sequence”
New diffiety theory leads to a well-posed KP hierarchy.
problem Formalizing diffieties for better hierarchy analysis.
method Definition of diffiety based on Frolicher structures.
result Formation of a well-posed Kadomtsev-Petviashvili hierarchy.
Introduces internal Lagrangians for differential equations and connects them to presymplectic structures.
problem Understanding the geometry of differential equations and their solutions.
method Develops a spectral sequence related to internal Lagrangians and investigates connections to presymplectic structures.
result Interprets a term in Vinogradov's spectral sequence for gauge theories.
The Koszul-Tate resolution is described in the context of the geometry of jet spaces and differential equations. The application due to Barnich, Brandt, and Henneaux of this resolution to computing the horizontal cohomology is analyzed. Relations with the Vinogradov spectral sequence are discussed.
This paper is devoted to the horizontal (``characteristic'') cohomology of systems of differential equations. Recent results on computing the horizontal cohomology via the compatibility complex are generalized. New results on the Vinogradov C-spectral sequence and the Krasil'shchik C-cohomology are obtained. As an appl…
These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequence and the C-cohomology, including the formulation in terms of the horizontal (characteristic) cohomology. Applications to computing invar…
On -ary Lie algebras of type math.RT
These notes are devoted to the multiple generalization of a Lie algebra introduced by A.M.Vinogradov and M.M.Vinogradov. We compare definitions of such algebras in the usual and invariant case. Furthermore, we show that there are no simple -ary Lie algebras of type for .
We study the geometry of jets of submanifolds with special interest in the relationship with the calculus of variations. We give a new proof of the fact that higher order jets of submanifolds are affine bundles; as a by-product we obtain a new expression for the associated vector bundles. We use Green-Vinogradov formul…
Secondary Calculus formalizes PDEs using cohomology, simplifying their study.
problem Formalizing and simplifying the study of partial differential equations (PDEs).
method Using cohomology of diffieties to formalize PDEs and their properties.
result Differential calculus on PDE solution spaces is homotopy calculus on horizontal De Rham algebras of diffieties.
Derived bracketsmath.DG
We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and Vinogradov, and we prove that the Vinogradov bracket is the skew-symmetrization of a derived bracket. Odd (resp…
Differential Calculus over Graded Commutative Algebras and Vector Bundles with Inner Structuresmath.DG
New calculus framework for vector bundles with metrics.
problem Developing calculus for vector bundles with fiber metrics.
method Adapting differential calculus to graded commutative algebras and focusing on diole and triole algebras.
result Triole algebra provides a suitable environment for vector bundle calculus with fiber metrics.
Integrable symmetries of diffieties are studied, leading to local morphisms.
problem Understanding local integrable symmetries of diffieties.
method Integrable infinitesimal symmetries defined as a one-parameter pseudogroup of local diffiety morphisms. Reduction of computation to solving PDEs.
result Preliminary results and examples show integrable symmetries can be reduced to solving linear systems.
In this note we generalize a result by Alekseev and Strobl for the case of -branes. We show that there is a relation between anomalous free current algebras and "isotropic" involutive subbundles of with the Vinogradov bracket, that is a generalization of the Courant bracket. As an application …
Following I. S. Krasilshchik and A. M. Vinogradov, we regard PDEs as infinite-dimensional manifolds with involutive distributions and consider their special morphisms called differential coverings, which include constructions like Lax pairs and Backlund transformations. We show that, similarly to usual coverings in top…
New method extends invariant reduction to rescaled geometric structures.
problem Computing invariant geometric structures under symmetries.
method Extends invariant reduction to rescaled structures using shift rule.
result Emergence and loss of invariance in reductions.
We solve higher-order morphisms for twisted Courant algebras.
problem Construct canonical -morphisms for higher Courant algebroids.
method Develop a general framework for arbitrary .
result Affirmative answer to Zambon's question for higher degrees.
A novel sequence-to-sequence model predicts missing sensor data.
problem Missing sensor data in sequences.
method Formulated a novel sequence-to-sequence model using forward and backward RNNs.
result The model produces the lowest errors in 12% more cases than the current state-of-the-art.
Classifies intrinsically linked tournaments by their score sequences.
problem Classifying intrinsically linked tournaments using their score sequences.
method Examining the score sequences of tournaments and identifying linkless sequences.
result The vast majority of score sequences for 8-vertex tournaments are linkless.
Enhances sequence memory capacity in neural networks.
problem Limited sequence capacity in Hopfield-like neural networks.
method Introducing a nonlinear interaction term and a generalized pseudoinverse rule.
result Significantly increased sequence capacity with novel scaling laws.
Deep generative models have been successfully used to learn representations for high-dimensional discrete spaces by representing discrete objects as sequences and employing powerful sequence-based deep models. Unfortunately, these sequence-based models often produce invalid sequences: sequences which do not represent a…
Equivalent condition found for q-holonomic sequences.
problem Characterizing q-holonomic sequences.
method Elimination property for subsets of variables.
result Proved equivalence of q-holonomicity and elimination property.
The abstract discusses a spectral sequence for Lie algebroids.
problem The abstract tackles the spectral sequence of Lie algebroids.
method The abstract presents a spectral sequence for Lie algebroids, generalizing classical constructions.
result The spectral sequence converges to Lie algebroid cohomology for wide Lie subalgebroids and to formal Lie algebroid cohomology for Lie subalgebroids over proper submanifolds.
Many machine learning tasks can be expressed as the transformation---or \emph{transduction}---of input sequences into output sequences: speech recognition, machine translation, protein secondary structure prediction and text-to-speech to name but a few. One of the key challenges in sequence transduction is learning to …
Mining tasks over sequential data, such as clickstreams and gene sequences, require a careful design of embeddings usable by learning algorithms. Recent research in feature learning has been extended to sequential data, where each instance consists of a sequence of heterogeneous items with a variable length. However, m…
Paper proposes using LSTM for LSH-based sequence alignment.
problem Sequence alignment using deep learning models.
method Deep bidirectional LSTM for feature learning and LSH-based sequence alignment.
result Higher accuracy achieved with LSTM-based model.
Study on continuous sequence classification with distribution uncertainty.
problem Classifying continuous sequences with varying distribution uncertainty.
method Proposes distribution-free tests for three test designs: fixed-length, sequential, and two-phase tests.
result Error probabilities decay exponentially fast for all test designs.
Deep learning models optimize protein sequences.
problem Optimizing protein properties through sequence design.
method Deep generative models guided by machine learning.
result Improved protein sequence generation from prior knowledge.
Sequence classification is an important data mining task in many real world applications. Over the past few decades, many sequence classification methods have been proposed from different aspects. In particular, the pattern-based method is one of the most important and widely studied sequence classification methods in …
We study the Thompson sampling algorithm in an adversarial setting, specifically, for adversarial bit prediction. We characterize the bit sequences with the smallest and largest expected regret. Among sequences of length with zeros, the sequences of largest regret consist of alternating zeros and …
Unimodal sequences of moves connect 3-manifold triangulations.
problem Understanding the structure of sequences of bistellar flips.
method Examined unimodal sequences of moves that increase and decrease triangulation size.
result Proved that any two one-vertex triangulations are connected by a unimodal sequence of moves.
This paper presents a novel end-to-end approach to program repair based on sequence-to-sequence learning. We devise, implement, and evaluate a system, called SequenceR, for fixing bugs based on sequence-to-sequence learning on source code. This approach uses the copy mechanism to overcome the unlimited vocabulary probl…
This work compresses sequences by treating them as continuous-time processes, enabling efficient discretization.
problem Efficient compression of sequences, especially with deep learning models that scale with sequence length.
method Treat sequences as continuous-time processes, learn efficient discretization, and decode at different time intervals.
result Automatic bit rate reductions in video and motion capture sequences using learned discretization.
Characterizes sequences from two-component link diagrams.
problem Understanding information from non-self crossing sequences of link diagrams.
method Investigated and characterized pairs of non-self OU sequences of two-component link diagrams.
result Completely characterized pairs of non-self OU sequences of diagrams of two-component links.
In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we introduce the inconstancy of a sequence and we show why it seems more pertinent …
Generative adversarial nets (GAN) has been successfully introduced for generating text to alleviate the exposure bias. However, discriminators in these models only evaluate the entire sequence, which causes feedback sparsity and mode collapse. To tackle these problems, we propose a novel mechanism. It first segments th…
Researchers develop flexible kernels for biological sequences with guaranteed reliability.
problem Challenges in applying machine learning to biological sequences, including unreliable methods.
method Theoretical analysis and development of modified kernels to ensure reliability and accuracy.
result Developed kernels that are universal, characteristic, and metrize the space of distributions for biological sequences.
A convolutional sequence to sequence non-intrusive load monitoring model is proposed in this paper. Gated linear unit convolutional layers are used to extract information from the sequences of aggregate electricity consumption. Residual blocks are also introduced to refine the output of the neural network. The partiall…
Using sequence to sequence algorithms for query expansion has not been explored yet in Information Retrieval literature nor in Question-Answering's. We tried to fill this gap in the literature with a custom Query Expansion engine trained and tested on open datasets. Starting from open datasets, we built a Query Expansi…
P3BO optimizes biological sequence design by combining multiple methods.
problem Variability in performance of black-box optimization methods for biological sequence design.
method Population-Based Black-Box Optimization (P3BO) that samples sequences from an ensemble of methods, weighting by past performance.
result P3BO outperforms individual methods, proposing higher quality and more diverse sequences.
Undirected neural sequence models such as BERT (Devlin et al., 2019) have received renewed interest due to their success on discriminative natural language understanding tasks such as question-answering and natural language inference. The problem of generating sequences directly from these models has received relativel…
New concordance invariant from spectral sequence on Khovanov homology.
problem Concordance invariants from spectral sequences.
method Constructing from spectral sequence on Khovanov homology.
result Provides a bound on the nonorientable slice genus.
The availability of large amounts of time series data, paired with the performance of deep-learning algorithms on a broad class of problems, has recently led to significant interest in the use of sequence-to-sequence models for time series forecasting. We provide the first theoretical analysis of this time series forec…
Random Fragments Classification of Microbial Marker Clades with Multi-class SVM and N-Best Algorithmq-bio.QM
Microbial clades modeling is a challenging problem in biology based on microarray genome sequences, especially in new species gene isolates discovery and category. Marker family genome sequences play important roles in describing specific microbial clades within species, a framework of support vector machine (SVM) base…
nTreeClus clusters categorical sequences using tree-based learners and k-mers.
problem Challenges in clustering categorical and sequential data.
method nTreeClus uses Tree-based Learners, k-mers, and autoregressive models for categorical time series.
result nTreeClus outperformed baseline methods in various validation metrics.
New sequences prove some link diagrams can't be transformed by specific moves.
problem Proving some link diagrams can't be transformed by specific sequences of Reidemeister moves.
method Proved the existence of I-generalized ordered sequences to create simple transformations.
result Some link diagrams cannot be transformed by sequences of moves that increase, then decrease crossings.
Sequence-to-Sequence (seq2seq) modeling has rapidly become an important general-purpose NLP tool that has proven effective for many text-generation and sequence-labeling tasks. Seq2seq builds on deep neural language modeling and inherits its remarkable accuracy in estimating local, next-word distributions. In this work…
Existence of an infinite sequence of harmonic maps between spheres of certain dimensions was proven by Bizon and Chmaj. This sequence shares many features of the Bartnik-McKinnon sequence of solutions to the Einstein-Yang-Mills equations as well as sequences of solutions that have arisen in other physical models. We ap…
New flexible confidence sequences for robust statistical inference.
problem Creating robust statistical inference methods that work under mild assumptions.
method Proposed a new class of asymptotic time-uniform confidence sequences.
result Sharp asymptotic time-uniform confidence sequences achieved under mild assumptions.