Paper improves group sparse recovery bounds using ℓ1-norm minimization.
problem Recovering group sparse vectors from few measurements.
method Introduces GRNSP and GRIP, and uses convex relaxations.
result New bounds for group sparse recovery, including equal and unequal group sizes.
Constructs Lorentzian harmonic maps and associated timelike surfaces.
problem Lorentzian harmonic maps and timelike surfaces properties.
method Constructs framed null curves and solves eigenvalue equation.
result Characterizes singularities on timelike minimal surfaces.
Study properties of null string congruences in complex and real pseudo-Riemannian spaces.
problem Analyze properties of null string congruences in 4D spaces.
method Investigate the geometry of null strings and their congruences in complex and real pseudo-Riemannian spaces.
result Relations between null string congruences, Petrov-Penrose types, and Ricci tensor algebraic types are established.
Small coherence guarantees a weak Null Space Property.
problem Ensuring the Null Space Property for matrices with small coherence.
method Established a connection between small coherence and the weak Null Space Property.
result A small coherence implies a weak Null Space Property for most index subsets.
In this study, we define a family of null curves in Minkowski 3-space and called null similar curves. We obtain some properties of these special curves. We show that two null curves are null similar curves if and only if these curves form a null Bertrand pair. Moreover, we obtain that the family of null geodesics and n…
The paper describes timelike surfaces with a canonical null direction in Minkowski space.
problem Characterizing timelike surfaces with a canonical null direction.
method Analyzing ruled and non-ruled surfaces, using the Gauss map.
result Properties of timelike surfaces with a canonical null direction in different dimensions.
Study recasts learning non-linear functions from noisy data as robust regression, proving reconstruction guarantees.
problem Learning non-linear functions from corrupted and dependent data.
method Sparse robust linear regression with ℓ1-optimization, incorporating unknown coefficients and corruptions. result Reconstruction guarantees for ℓ1-optimization problem with dependent data, proving null and stable null space properties. The study characterizes and analyzes spacelike surfaces with a canonical normal null direction in Minkowski 4-space.
problem Characterizing and analyzing spacelike surfaces with a specific null direction in Minkowski space.
method Using geometric properties, Gauss map, and a nonlinear partial differential equation, the study characterizes and analyzes these surfaces.
result Characterizations and properties of spacelike surfaces with a canonical normal null direction are obtained.
Defines null G-structures on Lorentzian manifolds and explores their symmetries.
problem Understanding geometric properties of null G-structures on Lorentzian manifolds.
method Definition and investigation of null G-structures, identification of induced geometries, algebra of diffeomorphisms.
result Interpolates between BMS and Lorentz symmetry algebras in some cases.
Enhances robustness of one-class classification framework.
problem Susceptibility to training data corruptions and inability to rank observations.
method Regularization of null-space kernel Fisher methodology in OC-KSR.
result Enhanced robustness against contamination in training set.
New algebraic parametrizations for harmonic maps to orthogonal group.
problem Finding solutions to harmonic maps from surfaces to O(n).
method Algebraic parametrizations and free holomorphic data.
result Reveals correspondence with null curves and minimal surfaces.
The paper develops theory for holomorphic null curves in SL2(C).
problem Developing theory for holomorphic null curves in SL2(C).
method Establish Runge, Mergelyan, Mittag-Leffler, and Carleman type theorems for holomorphic null immersions.
result Proves every open Riemann surface admits a proper holomorphic null embedding into SL2(C).
New binary matrices improve compressed sensing with faster and less storage requirements.
problem Achieving robust sparse recovery with binary measurement matrices.
method Derived bounds and conditions for binary matrices to satisfy the robust null space property (RNSP).
result Binary matrices with girth six are nearly optimal for compressed sensing.
A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions (null, space- or timelike). The metrics are classified according to their group of…
Minimal surfaces in Heisenberg group have null curves and lines.
problem Characterizing timelike minimal surfaces in the Heisenberg group.
method Characterization through null curves and lines with prescribed curvatures.
result Minimal surfaces are defined by the multiplication of null curves and affine null lines.
Integrable flows on null curves in anti-de Sitter 3-space studied.
problem Analyzing integrable flows on null curves in anti-de Sitter 3-space.
method Formulated integrable flows related to the KdV hierarchy on null curves exploiting the geometry of anti-de Sitter 3-space.
result Explicitly found closed stationary solutions in terms of periodic solutions of a Lamé equation.
Study improves distributed linear estimation under adversarial conditions.
problem Mean estimation of a random vector with adversarial measurements and asynchrony.
method Two-timescale ℓ1-minimization algorithm with tight convergence rates.
result Unified finite-time characterization of robustness, identifiability, and statistical efficiency.
Study left-invariant pseudo-Riemannian metrics on Lie groups using moving bracket approach.
problem Characterize left-invariant pseudo-Riemannian metrics on Lie groups with vanishing scalar curvature invariants.
method Using the moving bracket approach, analyze Lie algebras of dimensions ≤ 6 and semi-simple Lie algebras.
result All Lie algebras of dimension ≤ 6 except 3-dimensional solvable Lie algebra are in the null cone, leading to VSI metrics.
The study examines null curves in specific geometric manifolds and their properties.
problem Characterizing null curves in Sasaki-like almost contact B-metric manifolds.
method Expressed Frenet frames and curvatures, proved curvature constancy conditions, and found necessary conditions for generalized helices and null cubic.
result Curvatures of specific null curves are constant if a function on the manifold is constant.
Study on null helices in semi-Riemannian manifolds with special submanifolds.
problem Investigating geometric properties of null helices on totally umbilical submanifolds in 3D semi-Riemannian manifolds.
method Using the null Frenet frame and degenerate metric condition, equations and invariants characterizing null helices are derived.
result Equations and invariants characterizing null helices on totally umbilical submanifolds in 3D semi-Riemannian manifolds are obtained.
The paper develops a robust test for nonlinear effects using Gaussian processes.
problem Detecting nonlinear interactions between continuous features.
method Hypothesis test based on Gaussian processes, robust to kernel mis-specification, and using ensemble estimators.
result Demonstrates interesting connections between machine learning and statistical inference.
New bounds on null-cobordism complexity and homotopy results.
problem Understanding the minimal geometric complexity of null-cobordisms.
method Combining geometric and homotopy techniques to analyze Riemannian manifolds and spaces.
result The minimal geometric complexity of null-cobordisms is at most a polynomial of degree dependent on the dimension.
We study the geodesic orbit property for nilpotent Lie groups N when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries. When N acts on itself by left-translations we show that it is a geodesic orbit space if and only if the metric…
In this paper we survey some recent contributions by the authors to the theory of null holomorphic curves in the complex Euclidean space C3, as well as their applications to null holomorphic curves in the special linear group SL2(C), minimal surfaces in the Euclidean space R3, and const…
New concepts of barriers and black regions defined for Lorentzian manifolds.
problem Understanding causal world-lines and horizons in Lorentzian manifolds.
method Proving properties of null hypersurfaces and their causal world-lines.
result Null hypersurfaces are semi-permeable, leading to new concepts of barriers and black regions.
New properties on null hypersurfaces using rigging technique.
problem Existence and completeness of rigged Riemannian structures on null hypersurfaces.
method Rigging technique to induce Riemannian structure and study geometric/topological properties.
result New properties and applications of rigging fields under geometric/topological constraints.
We fully develop the concept of causal symmetry introduced in Class. Quant. Grav. 20 (2003) L139. A causal symmetry is a transformation of a Lorentzian manifold (V,g) which maps every future-directed vector onto a future-directed vector. We prove that the set of all causal symmetries is not a group under the usual comp…
Null distance metric studies spacetime convergence.
problem Investigate convergence in spacetime geometry.
method Introduced null distance metric for Lorentzian manifolds, proving convergence results.
result Null distance metric leads to distinct limiting behavior under non-uniform convergence of warping functions.
Study left-invariant pseudo-Riemannian metrics on Lie groups focusing on null cone Lie algebras.
problem Characterize left-invariant pseudo-Riemannian metrics on Lie groups in the null cone.
method Use bracket flow on Lie algebra to study metrics on Lie groups.
result Classify all cases of null cone Lie algebras in signatures (1,q) and (2,q).
Study on null-projectability of Levi-Civita connections in neutral metrics.
problem Characterizing projectability of Levi-Civita connections along null parallel distributions.
method Analyzing projectability of torsion-free connections along foliations on manifolds, focusing on neutral metric signatures and mid-dimensional distributions.
result Extension of Patterson and Walker's Riemann extension metrics to null parallel distributions of any dimension.
All inextendible null geodesics in four dimensional de Sitter space dS^4 are complete and globally achronal. This achronality is related to the fact that all observer horizons in dS^4 are eternal, i.e. extend from future infinity scri^+ all the way back to past infinity scri^-. We show that the property of having a nul…
Convex optimization with expander matrices improves sparse recovery efficiency.
problem Sparse recovery from linear measurements using expander matrices.
method Use of expander matrices for linear sketches in convex optimization to recover block-sparse matrices.
result The recovery error can be expressed in terms of the model-based norm, ensuring the solution is within the model.
New privacy-preserving method controls false discovery rate in hypothesis testing.
problem Controlling false discovery rate in multiple hypothesis testing with privacy.
method Adapting Benjamini-Hochberg procedure to differential privacy, using new proof techniques.
result Proves FDR control of differentially private BHq variants under weak assumptions.
The study explores Lorentzian manifolds with specific null vector fields and their geometric properties.
problem Characterizing Lorentzian manifolds with shearfree null vector fields and their quotient structures.
method Analyzing quotient spaces and constructing metrics on total spaces of bundles.
result Existence of non-trivial generalized electromagnetic plane waves and Einstein metrics.
We construct a Kähler structure (J,Ω,G) on the space L(H3) of oriented geodesics of hyperbolic 3-space H3 and investigate its properties. We prove that (L(H3),J) is biholomorphic to ${\mathbb{P}}^1\times{\mathbb{P}}^1-\ba…
Finite resources limit false discovery rate control in structured hypothesis spaces.
problem Controlling false discovery rate in hypothesis testing with finite data and structured hypothesis spaces.
method Framework for exact FDR control and adaptive power maximization.
result Exact FDR control and adaptive power maximization.
We study the full holonomy group of Lorentzian manifolds with a parallel null line bundle. We prove several results that are based on the classification of the restricted holonomy groups of such manifolds and provide a construction method for manifolds with disconnected holonomy which starts from a Riemannian manifold …
Synthetic framework for null hypersurfaces in non-smooth spacetimes.
problem Analyzing null hypersurfaces in non-smooth spacetimes.
method Develops synthetic null hypersurfaces using optimal transport and Lorentzian geometry.
result Synthetic null energy condition stabilizes under convergence and applies to low-regularity spacetimes.
The paper studies convergence of cosmological spacetimes using null distance.
problem Convergence of cosmological spacetimes with compact slices.
method Using null distance and Gromov-Hausdorff convergence, the paper establishes convergence results for spacetimes with mild extension properties.
result Uniform convergence of null distances and Gromov-Hausdorff convergence for monotone sequences of spacetimes.
In this paper we study the non-geodesic non-null biharmonic curves in 3-dimensional hyperbolic Heisenberg group. We prove that all of the non-geodesic non-null biharmonic curves in 3-dimensional hyperbolic Heisenberg group are helices. Moreover, we obtain explicit parametric equations for non-geodesic non-null biharmon…
Study on null Penrose inequality using geodesic foliations and functional properties.
problem Proving the null Penrose inequality using functional properties and geodesic foliations.
method Introducing a functional on surfaces, studying its properties along a null hypersurface, and using geodesic foliations to derive inequalities.
result Derivation of a general Penrose-type inequality and conditions for the null Penrose inequality.
The paper extends spacetime topology results using codimension 2 null cut locus properties.
problem Understanding spacetime topology with and without horizons.
method Review and extension of existing literature on spacetime topology, utilizing codimension 2 null cut locus properties.
result Results for spacetimes with and without horizons, including asymptotically AdS settings.
Using twistor methods, we explicitly construct all local forms of four--dimensional real analytic neutral signature anti--self--dual conformal structures (M,[g]) with a null conformal Killing vector. We show that M is foliated by anti-self-dual null surfaces, and the two-dimensional leaf space inherits a natural pr…
New piracy-resistant watermarks for deep neural networks prevent false claims.
problem Protecting deep learning models from false claims by embedding pirate watermarks.
method Null embedding, a new approach to build watermarks that resist removal and addition.
result Null embedding achieves piracy resistance and other watermark properties over various tasks and models.
New surgery problems solved for 4D topological surgery.
problem Intermediate 4D surgery problems for 1/2-π1-null groups. method Group-theoretic 2-Engel relation and geometric applications.
result 1/2-π1-null surgery problems are universal. We study the geometric properties of a 2m-dimensional complex manifold M admitting a holomorphic reduction of the frame bundle to the structure group P⊂Spin(2m,C), the stabiliser of the line spanned by a pure spinor at a point. Geometrically, M is endowed with a hol…
Study shows knots with specific properties avoid certain topological surgeries.
problem Understanding knots and their behavior under specific surgeries.
method Analyzes null-homotopic knots in 3-manifolds and their effect on surgeries.
result Zero surgery on null-homotopic knots in certain 3-manifolds avoids summands of S1imesS2. Study characterizes geometric properties of QGCR-null submanifolds in cosymplectic manifolds.
problem Characterizing geometric properties of QGCR-null submanifolds in cosymplectic manifolds.
method Characterization through totally umbilical and irrotational properties, and discussion of geodesity conditions.
result Characterizes geometric properties of ascreen QGCR-null submanifolds.