We study heterotic supergravity at , first described in detail in 1989 by Bergshoeff and de Roo. In particular, we discuss an ambiguity of a connection choice on the tangent bundle. It is well known that at the Hull connection gives a consistent supergravity theory with supersymmetry …
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.
169,051 papers · 148 categories
Trend · papers per month
48 results for “differential redefinition”
Injectivity of geodesic X-ray transform on low-regularity manifolds.
problem Injectivity of geodesic X-ray transform on manifolds with low regularity.
method Calculus of differential and curvature operators on non-smooth structures.
result Injectivity of geodesic X-ray transform on simple Riemannian manifolds with -regularity.
Colored knot polynomials possess a peculiar Z-expansion in certain combinations of differentials, which depends on the representation. The coefficients of this expansion are functions of the three variables (A,q,t) and can be considered as new distinguished coordinates on the space of knot polynomials, analogous to the…
The notion of a causal boundary for a spacetime has been a controversial topic during the last three decades. Moreover, recently the role of the boundary in the AdS/CFT correspondence for plane waves, have stimulated its redefinition with some possible alternatives. Our aim is threefold. First, to review the different …
This paper extends Khovanov homology to categorify Kauffman bracket skein module for non-orientable surface.
problem Categorify Kauffman bracket skein module for non-orientable surface .
method Redefined the differential in the Khovanov chain complex for the twisted -bundle over .
result Categorified the Kauffman bracket skein module for the non-orientable surface .
We explore homotopies in quantum field theory formalism.
problem Constructing homotopies in Batalin-Vilkovisky formalism.
method Review and construction of homotopies from renormalization group flow and gauge fixing changes.
result Constructing spans of quantum master actions with isomorphic effective actions using homotopies.
Holomorphic supergravity theory simplifies anomaly cancellation in heterotic moduli.
problem Anomaly cancellation in heterotic moduli space.
method Formulated a ten-dimensional version of Kodaira-Spencer gravity, quantized fluctuations, and showed partition function simplification.
result Holomorphic supergravity theory simplifies anomaly cancellation and relates to type I Kodaira-Spencer theory.
New combinatorial approach to Goldman-Turaev Lie bialgebra using cyclic word partitions.
problem Defining the Goldman bracket and Turaev cobracket combinatorially.
method Focus on partitions of cyclic words to define the bracket and cobracket.
result Combinatorial definition of the bracket and cobracket.
Although portfolio management didn't change much during the 40 years after the seminal works of Markowitz and Sharpe, the development of risk budgeting techniques marked an important milestone in the deepening of the relationship between risk and asset management. Risk parity then became a popular financial model of in…
Paper proposes a new model to assess risks in energy storage systems considering both exogenous and endogenous uncertainties.
problem Current risk assessment ignores the stochastic nature of energy storage availability.
method Data-driven unified model with exogenous and endogenous uncertainty description for four types of generic energy storage.
result Comparative results show more severe risks for endogenous uncertainty, suggesting new strategies for system operators.
New insights into BNN optimization redefine latent weights as inertia.
problem Optimizing Binarized Neural Networks (BNNs) with latent weights.
method Interpreted latent weights as inertia and introduced Binary Optimizer (Bop).
result Demonstrated improved performance of Bop on CIFAR-10 and ImageNet.
Geometrically describes pseudo-gauge freedom in relativistic hydrodynamics.
problem Pseudo-gauge ambiguity in relativistic hydrodynamics.
method Develops -contact geometry to describe thermodynamic states and conservation laws.
result Identifies pseudo-gauge freedom as the non-uniqueness of thermodynamic equilibrium redefinition.
DER uses neural nets to better handle uncertainty in machine learning.
problem Need for principled uncertainty reasoning in safety-critical domains.
method Uncertainty-aware regression-based neural networks (NNs) with evidential distributions.
result DER shows promise over traditional methods but is a heuristic.
A new k-means variant minimizes pairwise distances within clusters.
problem The need for improved clustering methods.
method A stochastic optimization procedure that minimizes the k-sums target function.
result The new k-sums method outperforms k-means and its variants.
Community detection for correlation matricesphysics.data-an
A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are …
We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation of the expression describing the declining long-term tail of a social discount c…
Perelman's Ricci flow emerges in quantum gravity, linking math and physics.
problem Understanding Perelman's Ricci flow equations in quantum gravity.
method Mapping Perelman's Ricci flow equations to localization equations in topological quantum gravity.
result Perelman's dilaton and fixed volume condition emerge dynamically.
Paper presents a unified approach to interpolation and geodesics in latent spaces of generative models.
problem Finding geodesics and interpolating in latent spaces of non-Gaussian densities.
method General approach to interpolation and geodesics in latent space for arbitrary density.
result Maximizing quality measure of an interpolating curve is equivalent to finding geodesic.
We educe a perspective on how best to regulate the bank of tomorrow in frames of debate launched by the International Centre for Financial Regulation and Financial Times. Our goal is to create a conceptual framework for policymakers and regulators to shape the international financial system in century of globalization …
This paper improves error estimation in covariate shift by incorporating target information.
problem Error estimation is inaccurate in covariate shift scenarios.
method Proposes a redefinition of importance using target information for better error estimation.
result Incorporating target information leads to more accurate error estimation, especially with KLIEP.
In this thesis, we study moduli in compactifications of ten-dimensional heterotic supergravity. We consider supersymmetric compactifications to four-dimensional maximally symmetric space, commonly referred to as the Strominger system. The compact part of space-time is a six-dimensional manifold of what we refer to …
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…
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.
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…
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…
By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology …
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…
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.
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.