arXiv research

DG algorithms often fail to generalize well in limited domains, highlighting necessary vs. sufficient conditions.

New conditions prevent gaps in optimal control problems.

Establishes a condition for multiclass classification-calibration of Gamma-Phi losses.

Study abelianization of Lie algebroids and groupoids, providing conditions for existence.

New findings on flatness for specific driftless systems.

Paper proves min-vol NMF robust to noise under expanded condition.

Condition found for spinc structures on a specific type of manifold.

New condition for reconstructing Morse functions on 3D manifolds.

We study the necessary and sufficient conditions for a Finsler surface with $(α,β)$-metrics to be with reversible geodesics.

The Hilbert map's image is discussed, showing when it's surjective.

The paper simplifies conditions for optimal paths on manifolds avoiding obstacles.

Develops a nonparametric graphical model for conditional independence.

The paper modifies a warped product space to find conditions for constant height functions.

Easy conditions found for simplifying complex systems.

We give a sufficient condition for a branched surface in a 3 dimensional manifold to fully carry a lamination, giving a piece of answer to a classical question of D. Gabai.

The study finds necessary and sufficient conditions for $C^1$-hypersurfaces to have nowhere $C^1$-regular parallel sets.

Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two…

Unified neural network for linear and nonlinear dimension reduction.

We give topological conditions to ensure that a noncollapsed almost Ricci-flat 4-manifold admits a Ricci-flat metric. One sufficient condition is that the manifold is spin and has a nonzero A-hat genus. Another condition is that the fundamental group is infinite or, more generally, of sufficiently large cardinality.

Necessary and sufficient condition is given for a set $A\subset R^1$ to be a subset of the critical values set for a $C^k$ function $f:R^m \to R^1$.

We address some theoretical guarantees for Schatten-$p$ quasi-norm minimization ($p \in (0,1]$) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition…

Guilbault and author prove sufficient conditions for $\mathcal{Z}$-compactifiability of certain manifolds.

In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-Émery condition $BE (K, N)$. The sufficient condition is satisfied for the glued space of any two (not necessary same dimensional) closed pointed Riemannian manifolds at their base points. This tells …

We find a necessary and sufficient condition for a compact 7-manifold to admit a $\tilde G_2$-structure. As a result we find a sufficient condition for an open 7-manifold to admit a closed 3-form of $\tilde G_2$-type.

Defines and studies Clairaut Riemannian maps between manifolds and Ricci solitons.

New Milnor's invariant condition for topologically slice links.

I.A.B. Strachan introduced the notion of a natural Frobenius submanifold of a Frobenius manifold and gave a sufficient but not necessary condition for a submanifold to be a natural Frobenius submanifold. This paper will give a necessary and sufficient condition and classify the natural Frobenius hypersurfaces.

New conditions ensure geodesic connectedness of affine manifolds.

We formulate a sufficient condition for the existence of a consistent price system (CPS), which is weaker than the conditional full support condition (CFS) introduced by Guasoni, Rasonyi, and Schachermayer [Ann. Appl. Probab., 18(2008), pp. 491-520] . We use the new condition to show the existence of CPSs for certain p…

In this paper, we give sufficient conditions for a Perron number, given as the leading eigenvalue of an aperiodic matrix, to be a pseudo-Anosov dilatation of a compact surface. We give an explicit construction of the surface and the map when the sufficient condition is met.

Low-rank matrix recovery has found many applications in science and engineering such as machine learning, signal processing, collaborative filtering, system identification, and Euclidean embedding. But the low-rank matrix recovery problem is an NP hard problem and thus challenging. A commonly used heuristic approach is…

New method uses sufficient statistics to infer causal relationships from observational data.

The paper analyzes the convergence of CART under a SID condition, improving previous results.

In this paper, we use less topological restrictions and more geometric and analytic conditions to obtain some sufficient conditions on Yamabe solitons such that their metrics are Yamabe metrics, that is, metrics of constant scalar curvature. More precisely, we use properties of conformal vector fields to find several s…

Listing has recently extended results of Kozameh, Newman and Tod for four-dimensional spacetimes and presented a set of necessary and sufficient conditions for a metric to be locally conformally equivalent to an Einstein metric in all semi-Riemannian spaces of dimension n>3 -- subject to a non-degeneracy restriction on…

We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition sharpens and improves on previous results. We connect the condition, and hence the pr…

Quantized neural networks can represent all fixed-point functions under certain conditions.

Adam and RMSProp are two of the most influential adaptive stochastic algorithms for training deep neural networks, which have been pointed out to be divergent even in the convex setting via a few simple counterexamples. Many attempts, such as decreasing an adaptive learning rate, adopting a big batch size, incorporatin…

New approach proves convergence of SA and SGD with weaker conditions.

We give necessary and sufficient conditions for existence of solutions to a general system of complex Monge-Ampère equations on Fano horosymmetric manifolds. In particular, we get necessary and sufficient conditions for existence of coupled Kähler-Ricci solitons, Mabuchi metrics and twisted Kähler-Einstein metrics in t…

The object of this paper is to obtain the concircular curvature tensor of the semi symmetric non-metric connection on the Weyl manifold and to give a necessary and sufficient condition for a semi symmetric non-metric connection to be S-concircular.

In this paper, we propose new conditions guaranteeing that the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the lite…

The paper establishes conditions for strict power concavity in convolutions.

Paper finds conditions for non-Einstein relative Yamabe metrics.

The paper defines conditions for para-Kaehler immersions and classifies them between forms.

Let Pi: M -> B be an onto maximal rank map or a Riemannian submersion between Riemannian manifolds M and B. Initially, we prove necessary and sufficient conditions for any fiber F to be roughly isometric to M. Then, we prove necessary and sufficient conditions for Pi to be a rough isometry. As a corollary M is roughly …

We consider a problem of optimal investment with intermediate consumption in the framework of an incomplete semimartingale model of a financial market. We show that a necessary and sufficient condition for the validity of key assertions of the theory is that the value functions of the primal and dual problems are finit…

The paper studies maps between Riemannian and Kähler manifolds, focusing on Clairaut semi-invariant Riemannian maps.