A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study of rigid body displacements in a projective space over dual numbers with geometric interpretations.
Paper solves dual Minkowski problem in 2D plane for specific curvature cases.
Unified geometric framework for quantum states using dual number algebras.
The article provides formulas for the number of terms in connected sums of sphere products associated with dual-neighborly polytopes.
Solves a generalized dual Minkowski problem for specific values of q.
We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is much larger than the number of observations because of the dual formulation. More…
Previous studies on stochastic primal-dual algorithms for solving min-max problems with faster convergence heavily rely on the bilinear structure of the problem, which restricts their applicability to a narrowed range of problems. The main contribution of this paper is the design and analysis of new stochastic primal-d…
We present DUAL-LOCO, a communication-efficient algorithm for distributed statistical estimation. DUAL-LOCO assumes that the data is distributed according to the features rather than the samples. It requires only a single round of communication where low-dimensional random projections are used to approximate the depend…
New metric found for 4-manifolds with specific properties.
We present a construction of complete self-dual Einstein metrics of negative scalar curvature on an uncountable family of manifolds of infinite topological type, which are enumerated by continued fraction expansions of irrational numbers. These manifolds may be regarded as limits of the resolutions of cyclic quotient s…
Drago optimizes DRO problems with faster convergence.
We present a dual subspace ascent algorithm for support vector machine training that respects a budget constraint limiting the number of support vectors. Budget methods are effective for reducing the training time of kernel SVM while retaining high accuracy. To date, budget training is available only for primal (SGD-ba…
We construct self-dual(SD) but not locally conformally flat(LCF) metrics on families of non-simply connected 4-manifolds with small signature. We construct various sequences with bounded or unbounded Betti numbers and Euler characteristic. These metrics have negative scalar curvature. As an application, this addresses …
Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study sketching from an optimization point of view: we first show that the iterative Hessia…
Sharp bounds for Kirby-Thompson invariants of knotted surfaces computed.
An Alexander self-dual complex gives rise to a compactification of , called ASD compactification, which is a smooth algebraic variety. ASD compactifications include (but are not exhausted by) the polygon spaces, or the moduli spaces of flexible polygons. We present an explicit description of the Chow rings of …
This paper proves that on any tamed closed almost complex four-manifold whose dimension of -anti-invariant cohomology is equal to the self-dual second Betti number minus one, there exists a new symplectic form compatible with the given almost complex structure . In particular, if the self-dual second Bett…
Study finds obstacles to solutions for specific equations on compact surfaces.
We explain why numbers occurring in the classification of polygon spaces coincide with numbers of self-dual equivalence classes of threshold functions, or of regular Boolean functions, or of decisive weighted majority games.
Dual explanation method using convex hulls and example-based vectors.
Unified framework for Arnold-type invariants via dual complexes and finite-difference structures.
We compute the quotient of the self-duality equation for conformal metrics by the action of the diffeomorphism group. We also determine Hilbert polynomial, counting the number of independent scalar differential invariants depending on the jet-order, and the corresponding Poincaré function. We describe the field of rati…
Utilizing a number of results of Dittmann, we investigate the nature of the Yang-Mills field over the eight-dimensional convex set, endowed with the Bures metric, of three-level quantum systems. Adopting a numerical strategy, we first decompose the field into self-dual and anti-self-dual components, by implementing the…
Dual regularized graph Laplacian improves spectral clustering for community detection.
Unified framework for complex, split-complex, and dual numbers.
We prove dual attainment for multi-asset financial derivatives pricing.
We give lower bounds for the tunnel number of knots and handlebody-knots. We also give a lower bound for the cutting number, which is a "dual" notion to the tunnel number in the handlebody-knot theory. We provide necessary conditions for constituent handlebody-knots by using -family of quandles colorings. The above …
New connections share geodesics with superintegrable systems.
Researchers find examples of real Bott manifolds with nonzero dual Stiefel-Whitney class wbar_{n-ahat(n)} for all n nonzero mod 4.
Unified algorithm solves convex optimization problems with optimal rates.
DCCNNs reduce computational overhead and ambiguity in convolutional neural networks.
The split version of the Freudenthal-Tits magic square stems from Lie theory and constructs a Lie algebra starting from two split composition algebras [3, 17, 18]. The geometries appearing in the second row are Severi-Brauer varieties [20]. We provide an easy uniform axiomatization of these geometries and related ones,…
We provide theoretical complexity analysis for new algorithms to compute the optimal transport (OT) distance between two discrete probability distributions, and demonstrate their favorable practical performance over state-of-art primal-dual algorithms and their capability in solving other problems in large-scale, such …
Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R-torsion and linking numbers respectively. The new feature which makes this possible is the introduction o…
This paper improves upper bounds on ribbonlength for certain alternating links.
Study shows gap between de Rham and symplectic-Bott-Chern harmonic forms for specific almost-Kähler manifolds.
New scalable methods for unbalanced optimal transport improve efficiency and applicability.
Solves dual imbalance in detecting sparse anomalies in MIL.
Smooth manifolds can be triangulated with graphs of bounded twin-width.
We give a unified description of tetrahedra with lightlike faces in 3d anti-de Sitter, de Sitter and Minkowski spaces and of their duals in 3d anti-de Sitter, hyperbolic and half-pipe spaces. We show that both types of tetrahedra are determined by a generalized cross-ratio with values in a commutative 2d real algebra t…
David Gabai recently proved a smooth 4-dimensional "Light Bulb Theorem" in the absence of 2-torsion in the fundamental group. We extend his result to 4-manifolds with arbitrary fundamental group by showing that an invariant of Mike Freedman and Frank Quinn gives the complete obstruction to "homotopy implies isotopy" fo…
In 1995 D. Joyce explicitly constructed a series of self-dual metrics with torus action on the connected sums of complex projective planes. In this paper we explicitly construct the twistor spaces of some of Joyce's self-dual metrics. Starting from a fiber space whose fibers are compact singular toric surfaces, we appl…
We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view…
We present a construction of self-dual Yang-Mills connections on the Taub-NUT space. We illustrate it by finding explicit expressions for all SU(2) instantons of instanton number one and generic monodromy at infinity.
Lasso is a widely used regression technique to find sparse representations. When the dimension of the feature space and the number of samples are extremely large, solving the Lasso problem remains challenging. To improve the efficiency of solving large-scale Lasso problems, El Ghaoui and his colleagues have proposed th…
In modern large-scale machine learning applications, the training data are often partitioned and stored on multiple machines. It is customary to employ the "data parallelism" approach, where the aggregated training loss is minimized without moving data across machines. In this paper, we introduce a novel distributed du…
This paper proves the following: A volume preserving vector field on a compact 3-manifold whose dual 2-form is exact can not generate uniquely ergodic dynamics unless its asymptotic linking number is zero.
We present a dual-view mixture model to cluster users based on their features and latent behavioral functions. Every component of the mixture model represents a probability density over a feature view for observed user attributes and a behavior view for latent behavioral functions that are indirectly observed through u…