The classical Schläfli formula, and its ``higher'' analogs given in [SS03], are relations between the variations of the volumes and ``curvatures'' of faces of different dimensions of a polyhedra (which can be Euclidean, spherical or hyperbolic) under a first-order deformation. We describe here analogs of those formulas…
On-device research index
arXiv research
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.
169,341 papers · 148 categories
Trend · papers per month
48 results for “differential Schläfli”
siRF identifies transcription factor binding near enhancers in flies.
problem Identifying functional transcription factor binding near enhancers.
method Signed iterative random forests (siRF) for machine learning.
result Infers regulatory interactions among transcription factors and enhancers.
Most animals possess the ability to actuate a vast diversity of movements, ostensibly constrained only by morphology and physics. In practice, however, a frequent assumption in behavioral science is that most of an animal's activities can be described in terms of a small set of stereotyped motifs. Here we introduce a m…
New framework learns interaction rules from animal trajectories.
problem Challenges in extracting interaction rules from animal movement data.
method Augmented behavioral models with neural networks and theory-guided regularization.
result Improved performance over baselines and novel biological insights.
Double descent phenomenon explained in simple terms.
problem Understanding the surprising drop in test error in overparameterized models.
method Informal explanation using linear algebra and probability, visual intuition with polynomial regression, mathematical analysis with ordinary linear regression.
result Three factors create double descent: data undersampling, model size, and parameter count. Ablating any one of these factors prevents double descent.
Co-eye: A Multi-resolution Symbolic Representation to TimeSeries Diversified Ensemble Classificationcs.LG
Co-eye combines multiple symbolic representations to improve time series classification accuracy.
problem Challenges in time series classification due to domain diversity.
method Inspired by compound eyes, Co-eye uses multiple symbolic representations and hyper-parameterised lenses to classify time series data.
result Co-eye outperforms state-of-the-art techniques in accuracy and robustness across various domains.
The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the properties and specific features of the differential-geometrical structures. The…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for the existence of a complete uniform differential structure on a given differenti…
In this paper we give explicit formulas of differential characteristic classes of principal -bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, differential Pontryagin classes and differential Euler class. Furthermore, we show that…
We define the Simons-Sullivan differential analytic index by translating the Freed-Lott differential analytic index via explicit ring isomorphisms between Freed-Lott differential K-theory and Simons-Sullivan differential K-theory. We prove the differential Grothendieck-Riemann-Roch theorem in Simons-Sullivan differenti…
Introduces exterior differential systems for grad students.
problem No specific problem stated; introduces a topic.
method No specific method mentioned; brief introduction.
result Introduces exterior differential systems.
Study differential invariants for line bundle operators.
problem Conditions for equivalence of differential operators in line bundles.
method Use differential invariants and groups of automorphisms.
result Find conditions for equivalence of differential operators.
We generalize stochastic smoothing for gradient estimation of non-differentiable functions.
problem Gradient estimation for non-differentiable functions.
method Developed a general framework for relaxation and gradient estimation of non-differentiable black-box functions using stochastic smoothing with reduced assumptions.
result Empirically validated the effectiveness of variance reduction strategies for various non-differentiable tasks.
The paper proves Gorenstein contractions for multiscale differentials on nodal curves.
problem Proving Gorenstein contractions for multiscale differentials on nodal curves.
method Addressing the conjecture by Ranganathan and Wise, showing contractions level by level.
result Multiscale differentials can be contracted to Gorenstein singularities, level by level, from the top down.
Study third order differential operators on 2D manifolds, finding equivalence conditions.
problem Finding conditions for equivalence of third order differential operators on 2D manifolds.
method Use differential invariants and groups of automorphisms to study equivalence.
result Conditions for equivalence of differential operators on 2D manifolds.
Classifies components of strata of k-differentials on Riemann surfaces.
problem Classifying connected components of strata of k-differentials.
method Developed new techniques to study connected components of strata of k-differentials for general k.
result Complete classification of connected components of the strata of quadratic differentials with arbitrary poles.
Monotonic differentiable sorting networks improve upon previous methods.
problem Non-monotonicity in differentiable sorting networks.
method Relaxation of conditional swap operations using sigmoid functions to ensure monotonicity.
result Monotonic differentiable sorting networks improve upon previous methods.
Lecture notes introduce differential geometry using sheaves and differential operators.
problem Exploring differential geometry concepts.
method Using sheaves, differential operators, and horizontal subbundles.
result Presented an approach to fundamental differential geometry structures.
New compact support differential cohomology theory with Pontryagin duality proof.
problem Developing a new mathematical framework for differential cohomology with compact support.
method Adapting Cheeger-Simons approach to introduce differential cohomology with compact support, proving functoriality, excision theorem, and using Pontryagin duality.
result Pontryagin duality for differential cohomology, showing isomorphism between ordinary differential cohomology and the smooth Pontryagin dual of compactly supported differential cohomology.
Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differentia…
Talks about new methods in differential geometry.
problem None explicitly stated in the abstract.
method Stresses the neighbor relation as a basic notion.
result Not explicitly stated in the abstract.
Extends abelian differentials to log twisted differentials with spin and hyperelliptic structures.
problem Compactify the moduli space of abelian differentials with spin and hyperelliptic structures.
method Introduce log twisted differentials and hyperelliptic differentials using stable log maps and admissible covers.
result Proves the existence of up to three connected components in the open strata of log twisted differentials.
A new deep learning method using differential flows and Gaussian processes.
problem Improving deep learning performance through more flexible transformations.
method Differential flows and Gaussian processes to learn stochastic differential equations.
result Exceeds performance of deep Gaussian processes and neural networks.
The paper integrates DGLA to DGLG using HCPs and Hopf algebras.
problem Integrating DGLA to DGLG.
method Definition of DGLG and HCPs, use of graded Hopf algebras.
result Construction of DGLG from DGLA and vice versa.
DiffEqFlux.jl integrates neural networks with differential equations.
problem Combining machine learning and differential equations for modeling complex systems.
method Fusing neural networks and differential equations using DiffEqFlux.jl.
result Demonstrates the integration of differential equations into neural networks and vice versa.
Paper defines quasi-Strebel structures for meromorphic k-differentials and proves their existence.
problem Existence of quasi-Strebel structures for meromorphic k-differentials.
method Introduced quasi-Strebel structures and proved their existence for meromorphic k-differentials.
result Every differential of even order k > 2 satisfying certain conditions admits a quasi-Strebel structure.
Finite intersection numbers between horizontal foliations of quadratic differentials.
problem Intersection properties of horizontal foliations in quadratic differentials.
method Joint continuity of intersection number in -norm.
result Intersection number is finite and jointly continuous.
Develops differential KO-theory with constructions and applications.
problem Constructing differential refinements in KO-theory.
method Explicit constructions and refinements of spectral sequences.
result Identification of differentials in differential KO-theory.
We give chain homotopy maps of Khovanov-type link homology of a universal differential. The universal differential, discussed by Mikhail Khovanov, Marco Mackaay, Paul Turner and Pedro Vaz, contains the original Khovanov's differential and Lee's differential. We also consider the conditions of any differential ensuring …
We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds admit a unique differential, coinciding with the usual one. Thus smooth manifolds fo…
Paper solves a class of differential equations with specific solutions.
problem Identifying solutions to a class of nonlinear ODEs.
method Solves using a proposed side condition involving a third-order linear ODE.
result New closed and integral-form solutions for the Tzitzeica curve equation.
We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra a…
Systematic approach to twisting differential KO-theory with applications in geometry, topology, and physics.
problem Constructing and understanding twisted differential KO-theory and its spectral sequence.
method Developed a systematic approach to twisting differential KO-theory, relating and contrasting degree two and degree one twists, and providing explicit identifications of differentials.
result Illustrated applications in geometry, topology, and physics, including integrality results and characterizations of twisted differential Spin structures.
We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomo…
Strata of -differentialsmath.AG
The paper describes the stratification and compactification of -differentials on Riemann surfaces.
problem Understanding the structure of -differentials on Riemann surfaces.
method Complete description of strata of -differentials in terms of pointed stable -differentials.
result Global -residue condition and admissible covers of stable curves.
New privacy framework tailored to specific data distributions.
problem Protecting individual data points in decision-making processes.
method Introducing tangent differential privacy, a new form of differential privacy.
result Entropic regularization guarantees tangent differential privacy under general conditions.
Studies projective geometry and partial differential equations prolongation.
problem Understanding the prolongation of overdetermined geometric partial differential equations.
method Introduction to differential geometry and tractor calculus, study of prolongation of equations.
result Recovery of projective tractor and cotractor connections via partial differential equations prolongation.
Develops differential K-theory for noncommutative algebras.
problem Creating a differential extension of algebraic K-theory for noncommutative algebras.
method Introduces secondary transgression forms and a differential refinement of the smooth Serre--Swan correspondence.
result Subsumes differential K-theory for smooth manifolds and fits into a noncommutative differential cohomology hexagon diagram.
Extends differential geometry concepts to manifolds with super tangent bundles.
problem No specific problem stated; extending differential geometry to super tangent bundles.
method Introduces super tangent bundle and extends differential geometry concepts.
result Basic notions of differential geometry extended to manifolds with super tangent bundles.
Poincaré and Sobolev inequalities for differential forms on Heisenberg balls are derived.
problem Establishing inequalities for differential forms on Heisenberg balls.
method Using Rumin's differentials and a global homotopy of Rumin's complex.
result Global homotopy improves differentiability of Rumin forms on bounded geometry contact manifolds.
Generalized differential cohomology theories, in particular differential K-theory (often called "smooth K-theory"), are becoming an important tool in differential geometry and in mathematical physics. In this survey, we describe the developments of the recent decades in this area. In particular, we discuss axiomatic ch…
Differentiable pipeline replaces non-differentiable CAE components for shape optimization.
problem Gradient-based optimization is limited by non-differentiable components in CAE workflows.
method Surrogate models replace non-differentiable pipeline components, enabling gradient-based optimization.
result Gradient-based shape optimization possible without differentiable solvers.
Differentiable programming aids in solving differential equations and their sensitivities.
problem Computing gradients of numerical solutions of differential equations.
method Review of existing techniques and mathematical foundations.
result Established a coherent framework for combining differential equations with data-driven approaches.
Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequencemath.AT
Constructs AHSS for twisted differential generalized cohomology theories.
problem Generalizing AHSS for twisted settings and differential cohomology.
method Builds on previous work, uses bundles of spectra with flat connections.
result Establishes twisted differential spectra as bundles of spectra with flat connections.
Efficient neural networks compute various differential operators cheaply.
problem Efficient computation of higher time complexity differential operators.
method Restricted neural network architectures with diagonal and hollow Jacobian matrices, allowing efficient extraction of dimension-wise derivatives.
result Demonstrated efficient computation of differential operators for various applications.
The purpose of this paper is to connect two subjects: the theory of quantum integrable systems (complete commutative rings of differential operators), and differential Galois theory. We define quantum completely integrable systems (QCIS), algebraically integrable QCIS, the differential Galois group of a QCIS. We show t…
Characterizes primary operations in differential cohomology using stacks.
problem Understanding primary operations in differential cohomology.
method Characterization via stacks, explicit refinement of Steenrod squares and powers, interplay between different cohomology types.
result Developed techniques for differential cohomology, including Künneth decomposition.
Differential K-theory gets a -ring structure.
problem Establishing a -ring structure in differential K-theory.
method Splitting principle for differential K-theory, Adams operations construction.
result Differential -ring admits a -ring structure.