The Mittag-Leffler theorem is extended to meromorphic curves and minimal surfaces.
problem Extending the Mittag-Leffler theorem to meromorphic curves and minimal surfaces.
method Established a Mittag-Leffler-type theorem for meromorphic curves and minimal immersions, including interpolation and approximation.
result Complete minimal ends in R^5 are generically embedded, and open Riemann surfaces are characterized for minimal surfaces.
The paper explores when end summing is unique for manifolds at infinity.
problem Nonuniqueness of end summing in manifolds with specific fundamental group behavior at infinity.
method Examines various categories (TOP, PL, DIFF) and types of 0- and 1-handles.
result Uniqueness is proved for Mittag-Leffler ends and generalized to handle slides and cancellations.
The paper proves uniform approximation for minimal surfaces with applications to a Mittag-Leffler theorem.
problem Approximating complete conformal minimal surfaces with finite curvature.
method Uniform approximation theorem with interpolation for minimal surfaces.
result Obtained a Mittag-Leffler type theorem for minimal immersions.
The paper defines a new condition for Fano manifolds and shows its implications on their asymptotic behavior.
problem Understanding the asymptotic behavior of Fano manifolds.
method Introducing the asymptotically Mittag-Leffler condition and proving its implications on the J-function. result The J-function of a Fano manifold exhibits exponential growth if it is asymptotically Mittag-Leffler. In this paper we prove that if we consider the standard real metric on simplicial rooted trees then the category Tower-Set of inverse sequences can be described by means of the bounded coarse geometry of the naturally associated trees. Using this we give a geometrical characterization of Mittag-Leffler property in inve…
Extends rough Heston model solution to general λ.
problem Improving the rough Heston model for various λ values.
method Generalized rational approximation for Mittag-Leffler kernel.
result Convergence of the solution for general λ.
Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely, a distribution derived from the so-called Mittag-Lef…
We analyse the dynamics of the Warsaw Stock Exchange index WIG at a daily time horizon before and after its well defined local maxima of the cusp-like shape decorated with oscillations. The rising and falling paths of the index peaks can be described by the Mittag-Leffler function superposed with various types of oscil…
New method estimates travel times more accurately with fewer components.
problem Dynamic number of travel time modes and skewed distributions.
method Gamma mixture densities with sparse estimation and recursive algorithm.
result Improved travel time estimation with fewer components and better fitting accuracy.
The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poiss…
This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…
The paper develops theory for holomorphic null curves in SL2(C).
problem Developing theory for holomorphic null curves in SL2(C).
method Establish Runge, Mergelyan, Mittag-Leffler, and Carleman type theorems for holomorphic null immersions.
result Proves every open Riemann surface admits a proper holomorphic null embedding into SL2(C).
This paper focuses on the development of harmonic and Clifford analysis techniques in the context of some conformally flat manifolds that arise from factoring out a simply-connected domain from Rn by special arithmetic subgroups of the conformal group. Our discussion encompasses in particular the Hopf manifold $S^1 …
Study of coupled Hawkes processes with rough-volatility limits.
problem Understanding coupled Hawkes processes with rough-volatility limits.
method Proving weak convergence of rescaled intensity vector to stochastic Volterra equations.
result Limiting components exhibit different degrees of roughness and cross-decorrelation law.
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that includes the Ito and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is…
NeuroMem-FHP framework estimates FHP parameters efficiently.
problem Estimating parameters of fractional Hawkes process (FHP) with long-range dependence.
method Developed LSTM and Transformer neural architectures to estimate FHP parameters directly from inter-arrival times.
result Transformer achieves highest estimation accuracy (MSE = 0.1634) compared to classical MLE (MSE = 2.8032).
The paper proves a Whitehead theorem for fine shape spaces.
problem Proving a Whitehead theorem for fine shape spaces.
method Using Steenrod-Sitnikov homotopy groups and ind-groups.
result Fine shape morphisms are equivalences if they induce isomorphisms on π_i.
Steenrod homotopy theory is a framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; from another viewpoint, it studies the topology of the lim^1 functor (for inverse sequences of groups). This paper is primarily concerned with the case of compacta, in which Steenrod homot…
Ends and cohomology theory for noncompact spaces.
problem Study of noncompact spaces and their invariants.
method Exposition of ends theory, introduction of reduced end cohomology, proof of theorems.
result Proof of a theorem on end cohomology of end sums of manifolds.
End-to-end portfolio system accounts for model risk.
problem Model risk in portfolio selection.
method Distributionally robust optimization with convex duality.
result Explicitly accounts for model risk in portfolio selection.
Improved speech recognition models with data augmentation and dropout.
problem Overfitting in end-to-end speech recognition models.
method Data augmentation and dropout applied to all layers of the network.
result Combination of data augmentation and dropout gives over 20% performance improvement.
New family of trinoids with irregular end found.
problem Finding constant mean curvature trinoids with irregular ends.
method Constructing a five-parameter family of trinoids.
result New family of trinoids with one irregular end.
Develops Bayesian approach for end-to-end learning in stochastic optimization.
problem Stochastic optimization problems under uncertainty.
method Bayesian interpretation and new end-to-end learning algorithms.
result Improved decision maps for empirical risk minimization and distributionally robust optimization.
Study shows mapping class groups are one-ended for surfaces with at least one end.
problem Analyzing the number of ends in mapping class groups of surfaces.
method Proving the associated translatable curve graph is one-ended, quasi-isometric to the mapping class group.
result Mapping class groups are one-ended for surfaces with at least one end of discrete type.
We give a mathematical foundation for, and numerical demonstration of, the existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1 surface is an ``elliptic end'' (resp. a ``hyperbolic end'') if the monodromy matrix at the …
End-to-end models perform better with learned log-scaled mel-spectrogram features.
problem End-to-end neural network models struggle with performance compared to models using high-level data representations.
method Trained first layers of a CNN model on log-scaled mel-spectrogram transformation and then used these learned features to initialize an end-to-end CNN classifier.
result Convergence and performance on ESC-50 dataset are similar to a model trained on pre-processed log-scaled mel-spectrogram features.
End-to-end speech recognition system trained on GPUs and CPUs.
problem Building state-of-the-art speech recognition systems.
method Utilizes CPUs and GPUs for training, data augmentation, and neural network updates. Uses vocal tract length perturbation and acoustic simulator for data augmentation. Employed Horovod allreduce for training.
result Achieved 7.92% WER on proprietary English Bixby open domain test set using a Bidirectional Full Attention (BFA) model.
End-to-end autonomous driving models get better uncertainty estimates.
problem Uncertainty quantification for end-to-end autonomous driving models.
method Approximate inference for implicit copula neural linear model.
result Densities for steering angle are marginally calibrated.
End-to-end TTS framework uses hard alignment to improve accuracy.
problem End-to-end TTS systems struggle with accurate alignment between input text and output acoustic features.
method Proposes a constrained alignment scheme with hard monotonic alignments, marginalized during training.
result Improves alignment learning and prediction in end-to-end TTS systems.
This work proposes splitting deep neural networks into smaller sub-networks for faster and more efficient distillation.
problem Challenges in training deep neural networks, including local optima, gradient issues, and computational demands.
method Proposes a non-end-to-end distillation approach by splitting networks into smaller, independent sub-networks (neighbourhoods).
result Independent training of smaller sub-networks can speed up distillation and improve efficiency in various applications.
End-to-end autonomous driving perception learns latent features for better performance.
problem Current autonomous driving systems are complex and require human engineering.
method Sequential latent representation learning for end-to-end perception.
result End-to-end perception model solves detection, tracking, localization, and mapping problems.
End-to-end learning refers to training a possibly complex learning system by applying gradient-based learning to the system as a whole. End-to-end learning system is specifically designed so that all modules are differentiable. In effect, not only a central learning machine, but also all "peripheral" modules like repre…
End-to-end TTS learns context features from text input.
problem Lack of understanding of context features learned by end-to-end TTS.
method Evaluated encoder outputs against context criteria derived from parametric TTS.
result Encoder outputs reflect linguistic and phonetic context features.
End-to-end model extracts nested terms without extra features.
problem Automatic term extraction for nested terms.
method Deep learning model that predicts conceptual terms within fixed sentence lengths.
result High recall and comparable precision on term extraction task.
Study end sum for surfaces and prove uniqueness results.
problem Uniqueness of end sum for surfaces and related manifolds.
method Analyzing end sum and adding a 1-handle at infinity for surfaces.
result The end sum of two surfaces with compact boundary is uniquely determined by the chosen ends.
Study of non-metrizable manifolds' ends, generalizing Nyikos's theorem.
problem Characterizing non-metrizable surfaces with ends.
method Introducing short and long ends, developing theory of spaces of ends.
result Characterization of surfaces as metrizable manifolds plus long pipes.
Machine learning optimizes fiber communication rates without channel knowledge.
problem Achieving information rates in nonlinear fiber communication.
method Jointly optimizes input and auxiliary channel distributions using end-to-end autoencoder learning.
result Computes achievable information rates without explicit channel knowledge.
Hybrid and end-to-end models compare in syllable recognition.
problem Comparing hybrid and end-to-end models for syllable recognition.
method Traditional hybrid system (kaldi) vs. end-to-end (TensorFlow) models.
result Hybrid models with explicit syllable knowledge outperform end-to-end models.
End-to-end autonomous driving framework using guided auxiliary supervision.
problem Learning to drive in highly stochastic urban settings.
method Multi-task Learning from Demonstration (MT-LfD) framework with end-to-end trainable network and supervised auxiliary tasks.
result Joint learning and supervised guidance facilitate faster and better driving performance.
Kauri is a novel unsupervised binary tree for clustering that outperforms existing methods.
problem Learning a tree end-to-end for clustering without labels is an open challenge.
method Greedy maximization of the kernel KMeans objective without centroids.
result Kauri often outperforms existing unsupervised clustering methods, especially with non-linear kernels.
Paper constructs a minimal surface with specific ends and curvature.
problem Constructing a minimal surface with specific topological and geometric properties.
method Weierstrass representation, elliptic functions, and solving the period problem.
result Existence of a complete immersed minimal surface of genus one with specified ends and total Gauss curvature.
Researchers found multiple ways to end-sum 4-manifolds, contradicting a previous conjecture.
problem Nonuniqueness of end-sums in 4-manifolds.
method Explicit examples and detailed discussion of end-cohomology algebra.
result Uncountably many distinct proper homotopy types from end-sums.
End-to-end solution for recognizing handwritten numerals, avoiding traditional preprocessing steps.
problem Handwritten numeral string recognition with traditional preprocessing steps.
method YoLo-based model for automatic detection and recognition, avoiding heuristic-based preprocessing and segmentation.
result Proposed method reduces complexity and is a feasible end-to-end solution for numeral string recognition.
New Hilbert bundles with ends defined from indexed bases.
problem Defining new structures in Hilbert bundles.
method Indexed bases and unitary operators of finite propagation.
result Characteristic classes of Hilbert bundles with ends.
End-to-end policy learning improves statistical arbitrage trading.
problem Traditional mean reversion trading strategies in statistical arbitrage are limited.
method We use Autoencoder architectures and policy learning to develop trading strategies.
result End-to-end training yields superior gross returns.
Estimates ends of Ricci shrinkers, focusing on smooth and singular cases.
problem Understanding the structure of ends in Ricci shrinkers, especially singular ones.
method Analyzes general and asymptotically conical ends, applies to weak convergence.
result No new conical end can form in the limit of sequences of Ricci shrinkers.
End-to-end audio recognition system improves accuracy.
problem Improving accuracy in auditory object recognition.
method Proposes an end-to-end deep neural network with an 'inception nucleus' to learn features from raw waveforms.
result Bests current state-of-the-art approaches by 10.4 percentage points on Urbansound8k dataset.
FPETS speeds up TTS by 600X and reduces errors.
problem High latency and errors in end-to-end TTS systems.
method Non-autoregressive, fully parallel approach with UFANS and trainable position encoding.
result Significant speed up and better quality audios with fewer errors.