arXiv research

Machine learning detects type Ia supernovae from photometric data.

DiTSNe-Ia model accurately reconstructs supernovae spectra from light curves.

In the present work, torsion energy is defined. Its law of conservation is given. It is shown that this type of energy gives rise to a repulsive force which can be used to interpret supernovae type Ia observations, and consequently the accelerating expansion of the Universe. This interpretation is a pure geometric one …

CNNs improve transient detection in DES-SN images.

The ability to build a model on a source task and subsequently adapt such model on a new target task is a pervasive need in many astronomical applications. The problem is generally known as transfer learning in machine learning, where domain adaptation is a popular scenario. An example is to build a predictive model on…

We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By co…

Measuring supernova neutrinos removes spacetime's conformal freedom.

Cosmologists are facing the problem of the analysis of a huge quantity of data when observing the sky. The methods used in cosmology are, for the most of them, relying on astrophysical models, and thus, for the classification, they usually use a machine learning approach in two-steps, which consists in, first, extracti…

Genetic algorithms optimize neural networks for cosmological data analysis.

A new category of Lie algebras, called generalized Lie algebras, is presented such that classical Lie algebras and Lie-Rinehart algebras are objects of this new category. A new philosophy over generalized Lie algebroids theory is presented using the notion of generalized Lie algebra and examples of objects of the categ…

Let F_n be the free group on n generators. Define IA_n to be group of automorphisms of F_n that act trivially on first homology. The Johnson homomorphism in this setting is a map from IA_n to its abelianization. The first goal of this paper is to determine how much this map contributes to the second rational cohomology…

The paper constructs finite generating sets for complex algebraic structures.

Let IA_n be the Torelli subgroup of Aut(F_n). We give an explicit finite set of generators for H_2(IA_n) as a GL_n(Z)-module. Corollaries include a version of surjective representation stability for H_2(IA_n), the vanishing of the GL_n(Z)-coinvariants of H_2(IA_n), and the vanishing of the second rational homology grou…

Certain subgroups of the groups $Aut(F_n)$ of automorphisms of a free group $F_n$ are considered. Comparing Alexander polynomials of two poly-free groups $Cb_4^+$ and $P_4$ we prove that these groups are not isomorphic, despite the fact that they have a lot of common properties. This answers the question of Cohen-Pakia…

The virtually cyclic dimension of Out(F_N) is finite and related properties are established.

Refundable income annuities offer a money-back guarantee, now the majority of sales.

The study explores automorphisms and centralizers in free group outer automorphisms.

IA-BMA adapts model weights to inputs for better predictions.

Abstract commensurators of ${ m{Aut}}(F_N)$ and ${ m{IA}}_N$ are the same.

Adversarial attacks reduce deep learning beam selection performance in mmWave 5G.

Study automorphism group actions on Jacobi diagrams spaces.

Given a Lagrangian submanifold $L$ of the affine symplectic $2n$-space, one can canonically and uniquely define a center-chord and a special improper affine sphere of dimension $2n$, both of whose sets of singularities contain $L$. Although these improper affine spheres (IAS) always present other singularities away fro…

The study examines aperiodicity properties of automorphism groups of free products of groups.

This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.

The study examines spaces of non-extendable quasimorphisms for group pairs.

Efficient methods for Lévy models using SINH-regular processes.

Calibrated PRMs improve inference efficiency for LLMs by dynamically adjusting compute budgets.

We show that for a $C^1$ residual subset of diffeomorphisms far away from tangency, every non-trivial chain recurrent class that is accumulated by sources ia a homoclinic class contains periodic points with index 1 and it's the Hausdorff limit of a family of sources.

Cross-validation (CV) is a technique for evaluating the ability of statistical models/learning systems based on a given data set. Despite its wide applicability, the rather heavy computational cost can prevent its use as the system size grows. To resolve this difficulty in the case of Bayesian linear regression, we dev…

Study closed G2-structures with T3-symmetry, classifying them into types and deriving hypersymplectic structures.

The paper analyzes zero modes on product manifolds and provides estimates for their norms.

This work proves that large models can be compressed significantly without losing performance.

Paper proves convergence of warped product manifolds to a nonnegative scalar curvature limit.

For a Morse map $f:M\to S^1$ Novikov [11] has introduced an analog of Morse complex, defined over the ring $\ZZZ[[t]][t^{-1}]$ of integer Laurent power series. Novikov conjectured, that generically the matrix entries of the differentials in this complex are of the form $\sum_ia_it^i$, where $a_i$ grow at most exponenti…

We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we emphasize geometric aspects. The beginning chapters give a general discussion about su…

A quantum framework optimizes collateral allocation for derivatives.

First sample-efficient algorithm for learning EFCE in bandit feedback settings.

Ensemble methods for supervised machine learning have become popular due to their ability to accurately predict class labels with groups of simple, lightweight "base learners." While ensembles offer computationally efficient models that have good predictive capability they tend to be large and offer little insight into…

Proposes a method to improve learning when training data is not representative.

In previous work a relation between a large class of Kac-Moody algebras and meromorphic connections on global curves was established---notably the Weyl group gives isomorphisms between different moduli spaces of connections, and the root system is also seen to play a role. This involved a modular interpretation of many…

Paper proves a spinor inequality for magnetic fields on spin manifolds.

Predicts the age of astronomical transients from real-time data.

IAs is well known, when D6 branes wrap a special lagrangian cycle on a non compact CY 3-fold in such a way that the internal string frame metric is Kahler there exists a dual description, which is given in terms of a purely geometrical eleven dimensional background with an internal metric of $G_2$ holonomy. It is also …

The paper proves inequalities for zero mode equations on spin manifolds.

Surveying conjectures on compactness and scalar curvature.

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…

In this paper, we briefly review some of the known results concerning the cohomological structures of the mapping class group of surfaces, the outer automorphism group of free groups, the diffeomorphism group of surfaces as well as various subgroups of them such as the Torelli group, the IA outer automorphism group of …

Paper proposes a federated learning framework for relative fairness.