Machine learning improves RNA secondary structure prediction.
problem Stagnant performance of RNA secondary structure prediction methods.
method Machine learning, especially deep learning, is used to predict RNA secondary structures.
result Machine learning methods have improved the prediction of RNA secondary structures.
Study on involution in double jet bundles.
problem Exploring involution in double jet bundles.
method Generalized double tangent bundles to double jet bundles, presented secondary vector bundle structure, proved involution.
result Existence of a natural involution on double jet bundles.
E2Efold predicts RNA secondary structures better than previous methods.
problem RNA secondary structure prediction with constraints.
method End-to-end deep learning model using unrolled algorithms to enforce constraints.
result E2Efold predicts significantly better structures, especially for pseudoknotted structures.
PS8-Net improves eight-state protein secondary structure prediction accuracy.
problem Precise prediction of eight-state protein secondary structure (PSS) is crucial in bioinformatics.
method PS8-Net is a new deep convolutional neural network (DCNN) that uses a PS8 module with skip connections to enhance accuracy.
result PS8-Net achieves 76.89% Q8 accuracy on benchmark datasets.
Improved protein Q8 secondary structure prediction to 70.7% accuracy.
problem Protein secondary structure prediction accuracy improvement.
method Diverse neural network architectures, ensemble approach, unbiased performance measures.
result 70.7% accuracy on Q8 secondary structure prediction, statistically indistinguishable from top predictors.
Symmetric CNNs improve sequential recommendation and protein structure prediction.
problem Improving prediction accuracy in sequential recommendation and protein structure inference.
method Developed a CNN architecture that preserves symmetry in convolutional layers, using parameterized convolutional kernels.
result Symmetric structured CNNs achieve better performance with fewer parameters.
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.
CRF model improves protein secondary structure prediction.
problem Improving secondary structure prediction of proteins.
method Applied Conditional Random Fields (CRF) to protein classification.
result CRF model leads to extremely accurate protein secondary structure predictions.
Mathematician summarizes protein geometry and mutation effects.
problem Understanding how proteins mutate and their structure-function relationship.
method Mathematical analysis of protein structures and functions, focusing on hydrogen bonds and secondary structure.
result Protein secondary structure regulates mutation by stabilizing or destabilizing regions.
The paper defines K-theoretic secondary invariants for Lie groupoids and proves related index theorems.
problem Constructing secondary invariants for Lie groupoids and proving their properties.
method Lie groupoid version of constructions from Piazza and Schick, focusing on adiabatic deformations and geometric operators.
result Lie groupoid version of Delocalized APS Index Theorem and product formula for secondary invariants.
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 …
Deep learning helps remove secondary B-mode polarization to detect primordial gravitational waves.
problem Removing secondary B-mode polarization from CMB data to detect primordial gravitational waves. method Applied deep learning (ResUNet-CMB) to estimate and remove multiple sources of secondary B-mode polarization. result Deep learning can produce nearly optimal, unbiased estimates of the amplitude of primordial gravitational waves.
We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as wel…
Paper finds knots with vanishing Upsilon but non-trivial secondary Upsilon.
problem Understanding the Upsilon invariant and its secondary version.
method Constructing infinite families of knots and proving conjectures.
result Secondary Upsilon invariant can be non-trivial even if Upsilon is zero.
Let G be a simple Lie group of real rank one, and S the ideal boundary of the corresponding symmetric space of noncompact type (H^n_R, H^n_C, H^n_H or H^2_O). We show the finiteness of the possible values of the secondary characteristic classes of transversely homogeneous foliations on a fixed manifold whose transverse…
Constructs combinatorial 2D topological field theories from cyclic A-infinity algebras.
problem Developing a combinatorial framework for 2D topological field theories.
method Using triangulations and polygonal decompositions, constructing cochains on a CW complex.
result Existence of combinatorial 2D topological field theories based on cyclic A-infinity algebras.
We introduce the secondary Stiefel-Whitney class w~2 of homotopically trivial diffeomorphisms and show that a homotopically trivial symplectomorphism of a ruled 4-manifold is isotopic to identity if and only if the class w~2 vanishes. Using this, we give a detailed description of the combinatorial str…
Study of spectral flow in symmetric Toeplitz operator families.
problem Understanding spectral flow in families of symmetric Toeplitz operators.
method Analog of Atiyah-Singer-Robbin-Salamon theorem for Z2-valued spectral flow. result Graded secondary spectral flow equals secondary index of a Callias-type operator.
The paper tackles online learning with two types of losses and shows it's impossible without certain assumptions.
problem Online learning with primary and secondary losses where the secondary loss is bounded by a linear threshold.
method Analyzes the feasibility of achieving low regret with respect to the primary loss while keeping the secondary loss within a linear threshold.
result Achieving the goal is impossible without bounded variance assumption on the secondary loss.
New classes for Lie algebra extensions discovered.
problem No specific problem stated; focuses on Lie algebra extensions.
method Introducing secondary characteristic classes.
result New proof of Lecomte's generalization of the Chern-Weil homomorphism.
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…
Researchers introduce new invariants for a specific type of edge geometry.
problem Investigating geometric properties of 5/2-cuspidal edges. method Introducing secondary cuspidal curvature and bias, proving their properties and product's invariance.
result Real analytic 5/2-cuspidal edges with non-vanishing limiting normal curvature admit non-trivial isometric deformations. Fuses ITRs for primary and secondary outcomes to minimize harm.
problem Learn an ITR maximizing primary outcome while minimizing harm to secondary outcomes.
method Introduces fusion penalty to encourage similar recommendations for different outcomes. Two algorithms estimate the ITR using surrogate loss functions.
result Agreement rate between primary and secondary optimal ITRs converges faster than ignoring secondary outcomes.
New knot invariants bound genus and concordance genus.
problem Bounding knot genus and concordance genus.
method Defining secondary Upsilon invariants as piecewise linear functions.
result Secondary invariants detect knots not detected by Upsilon.
What are called secondary characteristic classes in Chern-Weil theory are a refinement of ordinary characteristic classes of principal bundles from cohomology to differential cohomology. We consider the problem of refining the construction of secondary characteristic classes from cohomology sets to cocycle spaces; and …
A new method for optimizing hierarchical multi-objective problems.
problem Symmetry and neglect of objective hierarchy in existing multi-objective methods.
method Priority-Constrained Descent (PCD) framework exploiting hierarchical objective structures.
result Pareto dominance and better per-objective performance with secondary progress guarantees.
The paper extends Gelfand-Kapranov-Zelevinsky construction to hyperbolic Riemann surfaces with punctures.
problem Stratifying the space of weight vectors for hyperbolic Riemann surfaces with punctures.
method Analogous to Gelfand-Kapranov-Zelevinsky construction, associates polyhedral fans to hyperbolic Riemann surfaces with punctures.
result The secondary fan of a hyperbolic Riemann surface with punctures is the normal fan of a convex polyhedron, the secondary polyhedron.
We study algebraic structures (L∞ and A∞-algebras) introduced by Gaiotto, Moore and Witten in their recent work devoted to certain supersymmetric 2-dimensional massive field theories. We show that such structures can be systematically produced in any number of dimensions by using the geometry of seconda…
Paper constructs a cohomology class related to McDuff's secondary class, proving it transgresses to the Euler class of foliated sphere bundles.
problem Finding higher-dimensional analogs of the Calabi invariant and its transgression to the Euler class.
method Constructing a cohomology class of volume-preserving diffeomorphisms and proving transgression to the Euler class of foliated sphere bundles.
result The cohomology class transgresses to the Euler class of foliated sphere bundles.
The study improves credit evaluation in peer-to-peer lending using machine learning.
problem Traditional credit histories are insufficient for distinguishing good from bad borrowers.
method Used machine learning classification and clustering algorithms to predict creditworthiness.
result Achieved 65% F1 and 73% AUC on LendingClub data, identifying key secondary attributes.
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.
The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) "presymplectic structure" w …
The paper studies connections in superintegrable systems, revealing geometric insights.
problem Understanding non- and semi-degenerate superintegrable systems.
method Analyzes two torsion-free connections associated with superintegrable systems.
result Semi-degenerate secondary structure tensor is the Ricci curvature of a natural torsion-free connection.
New stability theorem for nonorientable surfaces mapping class groups.
problem Stability of homology groups of mapping class groups of nonorientable surfaces.
method Galatius--Kupers--Randal-Williams framework of cellular E2-algebras. result New best known stability range for homology of nonorientable surfaces.
RNA structures show that a significant portion of bases do not form hydrogen bonds.
problem Understanding the unpaired bases in RNA secondary structures.
method Comparing random words in free groups to RNA sequences, analyzing word lengths.
result The expected fraction of unpaired bases converges to a constant λ2. Automorphisms of Kodaira surfaces are shown to be affine transformations.
problem Characterizing automorphisms of Kodaira surfaces.
method Analyzing lifts to the universal cover and conditions on affine transformations.
result Precise description of Kodaira surfaces' automorphism groups.
Defines and proves CR invariants on five-manifolds.
problem Defines and studies CR invariants on CR five-manifolds.
method Defines global secondary CR invariants and proves their linear combination.
result Any global secondary CR invariant is a linear combination of total Q′-curvature, total I′-curvature, and a local CR invariant. A strategy for spectrum sharing in CRNs with multiple PT power levels.
problem Efficient spectrum usage for secondary users in CRNs with multiple PT power levels.
method Data-driven/machine learning based multi-level spectrum sensing and prediction-transmission structures.
result The proposed strategy effectively aligns the ST with the PT power levels, improving spectrum usage.
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.
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.
The note answers a question about Betti numbers for 1D Euclidean space.
problem Understanding Betti numbers for vector fields and differential forms in 1D Euclidean space.
method Using Euler vector field and Lie superalgebra structure.
result The Betti numbers are 1 for the case where primary and secondary weights are equal.
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.
Moduli spaces of doubly periodic monopoles, also called monopole walls or monowalls, are hyperkähler; thus, when four-dimensional, they are self-dual gravitational instantons. We find all monowalls with lowest number of moduli. Their moduli spaces can be identified, on the one hand, with Coulomb branches of five-dimens…
Study controls bifurcations in Eulerian flows with multiple Hopf singularities.
problem Bifurcation analysis and control of nonlinear Eulerian flows with non-resonant n-tuple Hopf singularities.
method Analysis of CW complex bifurcations of flow-invariant Clifford hypertori, using leaf-bifurcation varieties.
result Tertiary toral CW complex bifurcates from and persists outside a secondary toral CW complex.
Global invariant for path structures and differential equations defined on torus.
problem Global invariant for path structures and differential equations.
method Computed as a secondary invariant from a Cartan connection on a canonical bundle.
result Formula for global invariant of second order differential equations on torus.
This paper constructs an explicit {e}-structure for certain 2-nondegenerate hypersurfaces.
problem Characterizing and classifying 2-nondegenerate Levi rank 1 hypersurfaces in complex space.
method Normalization of group parameters and construction of an explicit {e}-structure.
result An explicit {e}-structure is constructed for hypersurfaces where primary invariants do not vanish.
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…