arXiv research

For positive integers $p$ and $q$ let $G:=\textrm{PSO}(p,q)$ be the projective indefinite special-orthogonal group of signature $(p,q)$. We study counting problems in the Riemannian symmetric space $X_G$ of $G$ and in the pseudo-Riemannian hyperbolic space $\mathbb{H}^{p,q-1}$. Let $S\subset X_G$ be a totally geodesic …

Study on geodesics proving index and intersection bounds, with examples of multiplicity.

The study examines growth of quadratic forms under Anosov subgroups.

Let $σ$ be the scattering relation on a compact Riemannian manifold $M$ with non-necessarily convex boundary, that maps initial points of geodesic rays on the boundary and initial directions to the outgoing point on the boundary and the outgoing direction. Let $\ell$ be the length of that geodesic ray. We study the que…

We show that some hyperbolic 3-manifolds which are tessellated by copies of the regular ideal hyperbolic tetrahedron embed geodesically in a complete, finite volume, hyperbolic 4-manifold. This allows us to prove that the complement of the figure-eight knot geometrically bounds a complete, finite volume hyperbolic 4-ma…

We discuss the homotopy type and the cohomology of spaces of locally convex parametrized curves gamma: [0,1] -> S^2, i.e., curves with positive geodesic curvature. The space of all such curves with gamma(0) = gamma(1) = e_1 and gamma'(0) = gamma'(1) = e_2 is known to have three connected components X_{-1,c}, X_1, X_{-1…

Given a smooth non-trapping compact manifold with strictly con- vex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. This data consist of the exit directions of geodesics that are emaneted from interior points of the manifold. We show that…

A smooth curve $γ: [0,1] \to S^2$ is locally convex if its geodesic curvature is positive at every point. J. A. Little showed that the space of all locally positive curves $γ$ with $γ(0) = γ(1) = e_1$ and $γ'(0) = γ'(1) = e_2$ has three connected components $L_{-1,c}$, $L_{+1}$, $L_{-1,n}$. The space $L_{-1,c}$ is know…

We study model-agnostic copies of machine learning classifiers. We develop the theory behind the problem of copying, highlighting its differences with that of learning, and propose a framework to copy the functionality of any classifier using no prior knowledge of its parameters or training data distribution. We identi…

In this paper by using Teichmuller theory of a sphere with four holes/orbifold points, we obtain a system of flat coordinates on the general affine cubic surface having a D_4 singularity at the origin. We show that the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere coincides with the Etingo…

We construct the first examples of complete, properly embedded minimal surfaces in $\mathbb{H}^2 \times \mathbb{R}$ with finite total curvature and positive genus. These are constructed by gluing copies of horizontal catenoids or other nondegenerate summands. We also establish that every horizontal catenoid is nondegen…

This paper introduces DPI, a new metric to assess data-copying risk in tabular data.

New seq2seq model can copy entire spans, outperforming simpler models in editing tasks.

Paper analyzes gradient descent with noisy data copies for linear regression, showing regularization and acceleration effects.

In many real-world systems, information can be transmitted in two qualitatively different ways: by copying or by transformation. Copying occurs when messages are transmitted without modification, e.g., when an offspring receives an unaltered copy of a gene from its parent. Transformation occurs when messages are modifi…

New test detects when generative models memorize training data.

In this paper, we consider the formal power series whose n-th coefficient is the number of copies of a given finite graph in the ball of radius n centred at the identity element in the Cayley graph of a finitely generated group and call it the growth function. Epstein, Iano-Fletcher and Uri Zwick proved that the growth…

Shapes can roll downhill following any curve, but often return to initial orientation after crossing multiple copies.

Every lens space has a locally flat embedding in a connected sum of 8 copies of the complex projective plane and a smooth embedding in n copies of the complex projective plane for some positive integer n. We show that there is no n such that every lens space smoothly embeds in n copies of the complex projective plane.

New system resists meme coin copy trading bots.

GMC benchmark isolates retrieval in Transformers, revealing max-margin alignment.

The paper adapts metrics to anti-de Sitter structures, characterizing their degeneracies.

Bayesian theory explains abrupt emergence of copy subcircuit in attention.

A condition for the existence of false gauge field copies in terms of the Lefschetz number of a certain differential operator is presented.

CN-SBM clusters cancer samples and regions based on copy number variants.

Under-parameterized networks can either copy or average teacher weights, leading to universal optimal solutions.

Automatic question generation is an important problem in natural language processing. In this paper we propose a novel adaptive copying recurrent neural network model to tackle the problem of question generation from sentences and paragraphs. The proposed model adds a copying mechanism component onto a bidirectional LS…

The paper introduces a new method to improve model generalization by routing model copies through permutations.

Copies have been proposed as a viable alternative to endow machine learning models with properties and features that adapt them to changing needs. A fundamental step of the copying process is generating an unlabelled set of points to explore the decision behavior of the targeted classifier throughout the input space. I…

We prove that an odd pretzel knot is doubly slice if it has $2n+1$ twist parameters consisting of $n+1$ copies of $a$ and $n$ copies of $-a$ for some odd integer $a$. Combined with the work of Issa and McCoy, it follows that these are the only doubly slice odd pretzel knots.

Is it possible to generally construct a dynamical system to simulate a black system without recovering the equations of motion of the latter? Here we show that this goal can be approached by a learning machine. Trained by a set of input-output responses or a segment of time series of a black system, a learning machine …

We show that the maximal orbit dimension of a simultaneous Lie group action on n copies of a manifold does not pseudo-stabilize when n increases. We also show that if a Lie group action is (locally) effective on subsets of a manifold, then the induced Cartesian action is locally free on an open subset of a sufficiently…

A free action of the direct product of two copies of the symmetric group on 3 elements on the cartesian product of two copies of the 3-sphere is constructed. This nonlinear action is constructed using surgery. The action provides a counterexample to a conjecture of Lewis made in 1968.

For a closed 4-manifold X and closed 3-manifold M we investigate the smallest integer n (perhaps infinity) such that M embeds in the connected sum of n copies of X. It is proven that any lens space (or homology lens space) embeds topologically locally flatly in a connected sum of 8 copies of the complex projective plan…

A fibration of ${\mathbb R}^n$ by oriented copies of ${\mathbb R}^p$ is called skew if no two fibers intersect nor contain parallel directions. Conditions on $p$ and $n$ for the existence of such a fibration were given by Ovsienko and Tabachnikov. A classification of smooth fibrations of ${\mathbb R}^3$ by skew oriente…

We construct branched double coverings by certain direct products of manifolds for connected sums of copies of sphere bundles over the 2-sphere. As an application we answer a question of Kotschick and Loeh up to dimension five. More precisely, we show that: (1) every simply connected, closed four-manifold admits a bran…

New algorithms for fair item allocation with limited copies.

Anosov representations are linked to specific spacetimes.

Proves stability of cone-volume measure with nearly constant density.

We discuss the relationship between the m-th homotopy group of the one-point union of r copies of the two-dimensional sphere and the m-th homotopy group of the one-point union of r+1 copies of the Thom space of the oriented two-dimensional universal vector bundle. Using a suitably choosen isomorphism between them a for…

Characterizes a specific type of Courant algebroid with a Calabi-Yau structure.

Special shadow-complexity equals k+1 for k copies of S1×S3.

Generating logical form equivalents of human language is a fresh way to employ neural architectures where long short-term memory effectively captures dependencies in both encoder and decoder units. The logical form of the sequence usually preserves information from the natural language side in the form of similar token…

We study how convergence of an observer whose state lives in a copy of the given system's space can be established using a Riemannian metric. We show that the existence of an observer guaranteeing the property that a Riemannian distance between system and observer solutions is nonincreasing implies that the Lie derivat…

Study shows $k$-NN classifier is not universally consistent on $(0,1)$ but consistent on discrete and specific measure spaces.

A new model for graph sampling that preserves structure without explicit targeting.

Let G be either SU(p,2) with p>=2, Sp(2,R) or SO(p,2) with p>=3. The symmetric spaces associated to these G's are the classical bounded symmetric domains of rank 2, with the exceptions of SO*(8)/U(4) and SO*(10)/U(5). Using the correspondence between representations of fundamental groups of Kähler manifolds and Higgs b…

In the past few years, Convolutional Neural Networks (CNNs) have been achieving state-of-the-art performance on a variety of problems. Many companies employ resources and money to generate these models and provide them as an API, therefore it is in their best interest to protect them, i.e., to avoid that someone else c…