arXiv research

Adam-type optimizers show one-sided convergence in GAN training, not reaching critical points.

We derive some results on contrarian and one-sided strategies by Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk \cite{sv}. In particular, concerning the rate of convergence of the strong law of large numbers (SLLN), we prove that Skeptic can force that the convergen…

New method learns from biased data, outperforming existing approaches.

This work improves polynomial approximations for functions with asymmetric behavior.

We define a notion of Hempel distance for one-sided Heegaard splittings and show that the existence of alternate surfaces restricts distance for one-sided splittings in a manner similar to Hartshorn's and Scharlemann-Tomova's results for two-sided splittings. We also show that every geometrically compressible one-sided…

DS-GDA solves nonconvex-nonconcave problems without regularity conditions.

When a Dehn filled link manifold contains a geometrically incompressible one-sided surface, it is shown there is a unique boundary incompressible position that the surface can take in the link space. The proof uses a version of the sweep-out technique from two-sided Heegaard splitting theory. When applied to one-sided …

In this paper we prove an extrinsic one-sided curvature estimate for disks embedded in $\mathbb{R}^3$ with constant mean curvature which is independent of the value of the constant mean curvature. We apply this extrinsic one-sided curvature estimate in [24] to prove to prove a weak chord arc type result for these disks…

Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S^3 are standard.

The stability and the index of complete one-sided minimal surfaces of certain three-dimensional Riemannian manifolds with positive scalar curvature are studied.

In the closed, non-Haken, hyperbolic class of examples generated by (2p,q) Dehn fillings of Figure 8 knot space, the geometrically incompressible one-sided surfaces are identified by the filling ratio p/q and determined to be unique in all cases. When applied to one-sided Heegaard splittings, this can be used to classi…

Various structural properties are developed for non-orientable surfaces in link spaces. The Möbius band tree is described to represent genus growth of one-sided surfaces in solid tori. The structure of the Tree allows various insights into the change of genus under boundary slope, which are not possible using the exist…

We extend the results of Hardt and Simon on area-minimizing cones to prove that isolated singularities of stationary one-sided area-minimizing hypersurfaces can be locally perturbed away on the side that they are minimizing.

The one-bit quantization is implemented by one single comparator that operates at low power and a high rate. Hence one-bit compressive sensing (1bit-CS) becomes attractive in signal processing. When measurements are corrupted by noise during signal acquisition and transmission, 1bit-CS is usually modeled as minimizing …

Study non-orientable surfaces to find loops winding around punctures.

We give a sufficient and necessary condition of the fundamental group homomorphism of a map between manifolds to induce homology equivalences. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen's plus construction with Whitehead torsions.

Left orderability proven for certain 3-manifolds with specific foliations.

This dissertation investigates the use of one-sided classification algorithms in the application of separating hazardous chlorinated solvents from other materials, based on their Raman spectra. The experimentation is carried out using a new one-sided classification toolkit that was designed and developed from the groun…

Study of bandit problem with Poisson decision times and Lévy processes.

A new method for selective classification trades off accuracy for coverage.

Study one-sided matrix completion with two observations per row.

Investigates VaR behavior for sums of one-sided random variables, showing impossibilities and conditions for super-additivity.

The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal processing and communication (SPCOM) problems. Despite its popularity, most exist…

Online learning with one-sided feedback aims to maximize accuracy while ensuring fairness.

We prove that there is a true asymptotic formula for the number of one sided simple closed curves of length $\leq L$ on any Fuchsian real projective plane with three points removed. The exponent of growth is independent of the hyperbolic structure, and it is noninteger, in contrast to counting results of Mirzakhani for…

We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential Lévy models driven by one-sided stable or tempered stable processes. Pricing formulas take the form of fast converging series of powers of the log-forward moneyness and of …

A new framework improves VaR recalibration by balancing reliance on imperfect volatility proxies.

Let $Σ$ be a codimension one submanifold of an $n$-dimensional Riemannian manifold $M$, $n\geqslant 2$. We give a necessary condition for an isometric immersion of $Σ$ into $\mathbb R^q$ equipped with the standard Euclidean metric, $q\geqslant n+1$, to be locally isometrically $C^1$-extendable to $M$. Even if this cond…

Study on CNNs' learning rates and approximation capacities.

We prove some half-space theorems for minimal surfaces in the Heisenberg group Nil_3 and the Lie group Sol_3 endowed with their left-invariant Riemannian metrics. If S is a properly immersed minimal surface in Nil_3 that lies on one side of some entire minimal graph G, then S is the image of G by a vertical translation…

New Q-learning algorithms reduce regret in inventory control problems.

A new SOHP filter improves trend estimation in economic time series.

We discuss possible relationships between geometric and topological interactions on one side and physical interactions on the other side.

Functor connects Lie groupoid algebras to bornological structures.

For a Catalan state $C$ of a lattice crossing $L\left( m,n\right)$ with no returns on one side, we find its coefficient $C\left( A\right)$ in the Relative Kauffman Bracket Skein Module expansion of $L\left( m,n\right)$. We show, in particular, that $C\left( A\right)$ can be found using the plucking polynomial of a …

The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian case correspond to one-sided bounds on the sectional curvatures. Starting from 2-d…

We prove several sharp one-sided pinching estimates for immersed and embedded hypersurfaces evolving by various fully nonlinear, one-homogeneous curvature flows by the method of Stampacchia iteration. These include sharp estimates for the largest principal curvature and the inscribed curvature ('cylindrical estimates')…

In this paper we develop a Morse theory for the uniform energy. We use the one-sided directional derivative of the distance function to study the minimizing properties of variations through closed geodesics. This derivative is then used to define a one-sided directional derivative for the uniform energy which allows us…

New algorithms improve convergence of minimax optimization.

In this paper, we study the stochastic version of the one-sided full information bandit problem, where we have $K$ arms $[K] = \{1, 2, \ldots, K\}$, and playing arm $i$ would gain reward from an unknown distribution for arm $i$ while obtaining reward feedback for all arms $j \ge i$. One-sided full information bandit ca…

The Generalized Smale Conjecture asserts that if M is a closed 3-manifold with constant positive curvature, then the inclusion of the group of isometries into the group of diffeomorphisms is a homotopy equivalence. For the 3-sphere, this was the classical Smale Conjecture proved by A. Hatcher. N. Ivanov proved the Gene…

This manuscript provides optimization guarantees, generalization bounds, and statistical consistency results for AdaBoost variants which replace the exponential loss with the logistic and similar losses (specifically, twice differentiable convex losses which are Lipschitz and tend to zero on one side). The heart of the…

New methods improve online matrix optimization with reduced computational cost.

This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an $\R_+$-valued best bid price process and an $L^2_{loc}$-valued volume process. …

We show that for a taut foliation F with one-sided branching of an atoroidal 3-manifold M, one can construct a pair of genuine laminations with solid torus complementary regions which bind every leaf of F in a geodesic lamination. These laminations come from a universal circle, a refinement of the universal circles pro…

Method detects jumps in high-frequency order prices using local minima.

Efficient algorithm approximates discrete random variables with minimal Kolmogorov distance.

Study problem-dependent rates in statistical learning theory, achieving optimal generalization error bounds.