arXiv research

We tackle the problem of protein secondary structure prediction using a common task framework. This lead to the introduction of multiple ideas for neural architectures based on state of the art building blocks, used in this task for the first time. We take a principled machine learning approach, which provides genuine,…

DEUP directly predicts epistemic uncertainty, improving model optimization and exploration.

Spatial Adapter adds structured spatial representation to frozen predictors.

Machine learning improves RNA secondary structure prediction.

This paper defines systematic value investing as an empirical optimization problem. Predictive modeling is introduced as a systematic value investing methodology with dynamic and optimization features. A predictive modeling process is demonstrated using financial metrics from Gray & Carlisle and Buffett & Clark. A 31-y…

FOLKLORE algorithm speeds up online multiclass logistic regression.

Study of spectral flow in symmetric Toeplitz operator families.

The knot invariant Upsilon, defined by Ozsvath, Stipsicz, and Szabo, induces a homomorphism from the smooth knot concordance group to the group of piecewise linear functions on the interval [0,2]. Here we define a set of related secondary invariants, each of which assigns to a knot a piecewise linear function on [0,2].…

The paper tackles online learning with two types of losses and shows it's impossible without certain assumptions.

The problem of distributed learning and channel access is considered in a cognitive network with multiple secondary users. The availability statistics of the channels are initially unknown to the secondary users and are estimated using sensing decisions. There is no explicit information exchange or prior agreement amon…

Deep Convolutional Neural Networks (DCNN) has shown excellent performance in a variety of machine learning tasks. This manuscript presents Deep Convolutional Neural Fields (DeepCNF), a combination of DCNN with Conditional Random Field (CRF), for sequence labeling with highly imbalanced label distribution. The widely-us…

Fuses ITRs for primary and secondary outcomes to minimize harm.

We introduce two invariants called the secondary cuspidal curvature and the bias on $5/2$-cuspidal edges, and investigate their basic properties. While the secondary cuspidal curvature is an analog of the cuspidal curvature of (ordinary) cuspidal edges, there are no invariants corresponding to the bias. We prove that t…

In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by p…

Secondary Calculus formalizes PDEs using cohomology, simplifying their study.

We verify that the formula of X. Ma for the analytic torsion form of an iterated fibration implies that Lott's secondary analytic index is functorial.

Paper constructs a cohomology class related to McDuff's secondary class, proving it transgresses to the Euler class of foliated sphere bundles.

The study improves credit evaluation in peer-to-peer lending using machine learning.

A famous construction of Gelfand, Kapranov and Zelevinsky associates to each finite point configuration $A \subset \mathbb{R}^d$ a polyhedral fan, which stratifies the space of weight vectors by the combinatorial types of regular subdivisions of $A$. That fan arises as the normal fan of a convex polytope. In a complete…

New stability theorem for nonorientable surfaces mapping class groups.

E2Efold predicts RNA secondary structures better than previous methods.

We introduce a notion of secondary characteristic classes of Lie algebra extensions. As a spin-off of our construction we obtain a new proof of Lecomte's generalization of the Chern-Weil homomorphism.

PS8-Net improves eight-state protein secondary structure prediction accuracy.

Defines and proves CR invariants on five-manifolds.

Deep learning helps remove secondary $B$-mode polarization to detect primordial gravitational waves.

The Dirac equation for massive free electrically neutral spin 1/2 particles in a gravitation field is considered. The secondary quantization procedure is applied to it and the Hilbert space of multiparticle quantum states is constructed.

In this paper we construct an infinite family of knots with vanishing Upsilon invariant $Υ$, although their secondary Upsilon invariants $Υ^2$ show that they are linearly independent in the smooth knot concordance group. We also prove a conjecture in a paper by Allen.

We discuss some aspects of index and secondary index theory for flat bundles with duality. This theory was first developed by J. Lott. Our main purpose in the present paper is to provide a modification with better functorial properties.

In this paper, we introduce six axioms for relative Bott-Chern secondary characteristic classes and prove the uniqueness and existence theorem for them. Such a work provides us a natural way to understand and hence to prove the arithmetic Grothendieck-Riemann-Roch theorem.

We define and study the secondary Chern-Euler class for a general submanifold of a Riemannian manifold. Using this class, we define and study index for a vector field with non-isolated singularities on a submanifold. As an application, our studies give conceptual proofs of a classical result of Chern.

In this paper we define K-theoretic secondary invariants attached to a Lie groupoid $G$. The K-theory of $C^*_r(G_{ad}^0)$ (where $G_{ad}^0$ is the adiabatic deformation $G$ restricted to the interval $[0,1)$) is the receptacle for K-theoretic secondary invariants. We give a Lie groupoid version of construction given b…

The Law of Vector Fields is a term coined by Gottlieb for a relative Poincaré-Hopf theorem. It was first proved by Morse and expresses the Euler characteristic of a manifold with boundary in terms of the indices of a generic vector field and the inner part of its tangential projection on the boundary. We give two diffe…

In this paper we study the variability and rigidity of secondary characteristic classes which arise from flat connections on a manifold. Considering the connection as a Lie-algebra valued one-form, we study the characteristic map from Lie algebra cohomology to de Rham cohomology of the manifold, and prove that if the L…

Neural network predicts cardiovascular events from EHRs with high accuracy.

We introduce partial secondary invariants associated to complete Riemannian metrics which have uniformly positive scalar curvature outside a prescribed subset on a spin manifold. These can be used to distinguish such Riemannian metrics up to concordance relative to the prescribed subset. We exhibit a general external p…

For a Riemannian foliation on a closed manifold, the first secondary invariant of Molino's central sheaf is an obstruction to tautness. Another obstruction is the class defined by the basic component of the mean curvature with respect to some metric. Both obstructions are proved to be the same up to a constant, and oth…

Symmetric CNNs improve sequential recommendation and protein structure prediction.

We refine the intersection product in homology to an equivariant setting, which unifies several known constructions. As an application, we give a common generalisation of the Chas-Sullivan string product on a manifold and the Chataur-Menichi string product on the classifying space by defining a string product on the Bo…

Two multifidelity trust-region methods use low-fidelity models for efficient optimization.

In this paper, we address the general case of a coordinated secondary network willing to exploit communication opportunities left vacant by a licensed primary network. Since secondary users (SU) usually have no prior knowledge on the environment, they need to learn the availability of each channel through sensing techn…

We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are introduced and discussed, including expansion rate, local entropy, and orbit growth …

For a manifold with boundary, the restriction of Chern's transgression form of the Euler curvature form over the boundary is closed. Its cohomology class is called the secondary Chern-Euler class and used by Sha to formulate a relative Poincaré-Hopf theorem, under the condition that the metric on the manifold is locall…

Multi-task learning (MTL) has recently contributed to learning better representations in service of various NLP tasks. MTL aims at improving the performance of a primary task, by jointly training on a secondary task. This paper introduces automated tasks, which exploit the sequential nature of the input data, as second…

CRF model improves protein secondary structure prediction.

Let xi be a smooth oriented vector bundle, with n-dimensional fibre, over a smooth manifold M. Denote by xi-hat the fibrewise one-point compactification of xi. The main purpose of this paper is to define geometrically a canonical element Upsilon(xi) in H^n(xi-hat,Q) (H^n(xi-hat,Z) tensor 1/2, to be more precise). The e…

By analyzing how the Borel regulator classes vanish on various groups related to $\mathrm{GL}(n,\mathrm{Z})$, we define three series of secondary characteristic classes for subgroups of automorphism groups of free groups. The first case is the $\mathrm{IA}$-automorphism groups and we show that our classes coincide with…

Extends Adams' theorem to periodic cohomology.

Constructs combinatorial 2D topological field theories from cyclic A-infinity algebras.