A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We use the theory of pseudo-holomorphic quilts to establish a counterpart, in symplectic Floer homology, to the Gysin sequence for the homology of a sphere-bundle. In a motivating class of examples, this "symplectic Gysin sequence" is precisely analogous to an exact sequence describing the behaviour of Seiberg-Witten m…
Researchers use Gysin sequence to show sl(N) homology of T(2,m) is cohomology of SU(N) representations.
New Smith-Gysin sequence for non-semi-free actions without semi-free condition.
In this paper we construct Cech cohomology groups that form a Gysin-type long exact sequence for principal torus bundles. This sequence is modeled on a de Rham cohomology sequence published in earlier work by Bouwknegt, Hannabuss and Mathai, which was developed to compute the global properties of T-duality in the prese…
Study spherical T-duality and Massey products in iterated sphere bundles.
The blow-down map is studied in Lie algebroid cohomology.
The paper proves a pointwise Gysin formula for vector bundles and applies it to show positivity of polynomials.
This paper introduces persistent equivariant cohomology and applies it to circle actions.
Part 2 discusses compatibility between analytic and topological Gysin maps.
In this paper we study the topological T-dual of spaces with a non-free circle action mainly using the stack theory method of Bunke and co-workers \cite{Bunke1}. We first compare three formalisms for obtaining the Topological T-dual of a semi-free -space in a simple example. Then, we calculate the T-dual of genera…
In this paper, we investigate the behaviour of the Serre spectral sequence with respect to the algebraic structures of string topology in generalized homology theories, specificially with the Chas-Sullivan product and the corresponding coproduct and module structures. We prove compatibility for two kinds of fibre bundl…
Spherical T-duality for iterated sphere bundles
New method defines Gysin maps for stratified spaces, preserving signatures.
We give two generalizations of the Atiyah-Bott-Berline-Vergne localization theorem for the equivariant cohomology of a torus action: 1) replacing the torus action by a compact connected Lie group action, 2) replacing the manifold having a torus action by an equivariant map. This provides a systematic method for calcula…
We develop a new approach to the pulling back fixed point theorem of W. Browder and use it in order to prove various generalizations of this result.
In this paper we use tools from differential topology to give a geometric description of cohomology for Hilbert manifolds. Our model is Quillen's geometric description of cobordism groups for finite dimensional smooth manifolds \cite{Q}. Quillen stresses the fact that this construction allows the definition of Gysin ma…
Reciprocity laws for line bundles on circle fibrations over complex manifolds.
Generalizes double transgression formulas on complex manifolds.
Study normal bundle and deformation to get new pushforward maps.
Develops a new theory of localization in algebraic geometry.
Paper develops equivariant basic cohomology for Lie groupoids.
The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular connections. There are many different spaces of currents which yield the character groups. …
A novel sequence-to-sequence model predicts missing sensor data.
Classifies intrinsically linked tournaments by their score sequences.
Enhances sequence memory capacity in neural networks.
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.
The abstract discusses a spectral sequence for Lie algebroids.
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.
Study on continuous sequence classification with distribution uncertainty.
Deep learning models optimize protein sequences.
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.
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.
Characterizes sequences from two-component link diagrams.
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.
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.
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.
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…