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.
The paper extends ternary algebra concepts using cube roots of unity.
The paper constructs new algebraic structures from Lie algebras and ternary Nambu-Lie algebras, leading to Yang-Baxter operators.
We introduce a notion of ternary distributive algebraic structure, give examples, and relate it to the notion of a quandle. Classification is given for low order structures of this type. Constructions of such structures from ternary bialgebras are provided. We also describe ternary distributive algebraic structures com…
New algebraic structure for vector bundles with special properties.
We define homology of ternary algebras satisfying axioms derived from particle scattering or, equivalently, from the third Reidemeister move. We show that ternary quasigroups satisfying these axioms appear naturally in invariants of Reidemeister, Yoshikawa, and Roseman moves. Our homology has a degenerate subcomplex. T…
Lectures explore how differential methods improve understanding of algebraic group orbit spaces.
We show that some ternary quasigroups appear naturally as invariants of classical links and links on surfaces. We also note how to obtain from them invariants of Yoshikawa moves. In our previous paper, we defined homology theory for algebras satisfying two axioms derived from the third Reidemeister move. In this paper,…
We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, one obtains the relations from the knot group, and from the core group. Using the ternary o…
Quantum invariant derived from ternary cohomology of self-distributive structures.
New braided Frobenius algebras created from specific Hopf algebras.
We review supervised learning and deep neural network design for learning membership on algebraic varieties. We demonstrate that these trained artificial neural networks can predict the entanglement type for quantum states. We give examples for detecting degenerate states, as well as border rank classification for up t…
We introduce \textit{Niebrzydowski algebras}, algebraic structures with a ternary operation and a partially defined multiplication, with axioms motivated by the Reidemeister moves for -oriented trivalent spatial graphs and handlebody-links. As part of this definition, we identify generating sets of -oriented Reid…
We define a homology for ternary groups using both associativity and skew elements. We describe the odd-even construction which yields many examples of ternary groups. We define the ternary knot group, consider its homomorphisms into ternary groups, and discuss the applications.
We describe various properties and give several characterizations of ternary groups satisfying two axioms derived from the third Reidemeister move in knot theory. Using special attributes of such ternary groups, such as semi-commutativity, we construct a ternary invariant of curves immersed in compact surfaces, conside…
Novel ternary structures reveal new interpretations of linear connections.
We prove that the quotients of the group algebra of the braid group introduced by L. Funar in Comm. Math. Phys., 1995, collapses in characteristic distinct from 2. In characteristic 2 we define several quotients of it, which are connected to the classical Hecke and Birman-Wenzl-Murakami quotients, but which admit in ad…
Motivated by large-scale Collaborative-Filtering applications, we present a Non-Commuting Latent Factor (NCLF) tensor-completion approach for modeling three-way arrays, which is diagonal like the standard PARAFAC, but wherein different terms distinguish different kinds of three-way relations of co-clusters, as determin…
Heap theory applied to framed links yields new invariants.
Introduces Lie semiheaps and their relation to Lie groups and bundles.
Heaps are para-associative ternary operations bijectively exemplified by groups via the operation . They are also ternary self-distributive, and have a diagrammatic interpretation in terms of framed links. Motivated by these properties, we define para-associative and heap cohomology theories…
Study of SO(3)-irreducible geometry in complex 5D and ternary Pauli exclusion principle.
EC2T creates sparse and ternary neural networks for resource-constrained devices.
Recurrent neural networks (RNNs) have shown excellent performance in processing sequence data. However, they are both complex and memory intensive due to their recursive nature. These limitations make RNNs difficult to embed on mobile devices requiring real-time processes with limited hardware resources. To address the…
MobileNets family of computer vision neural networks have fueled tremendous progress in the design and organization of resource-efficient architectures in recent years. New applications with stringent real-time requirements on highly constrained devices require further compression of MobileNets-like already compute-eff…
Unified cosmological and Einstein polytope theories.
The paper describes topological properties of arcs and crossings in knot theory.
Neural network models are resource hungry. It is difficult to deploy such deep networks on devices with limited resources, like smart wearables, cellphones, drones, and autonomous vehicles. Low bit quantization such as binary and ternary quantization is a common approach to alleviate this resource requirements. Ternary…
Paper ranks stocks by compression risk, not volatility.
New inequality for ternary variables improves on existing measures.
A notion of n-Lie algebra introduced by V.T. Filippov can be viewed as a generalization of a concept of binary Lie algebra to the algebras with n-ary multiplication law. A notion of Lie algebra can be extended to Z_2-graded structures giving a notion of Lie superalgebra. Analogously a notion of n-Lie algebra can be ext…
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS theory is based on random Gaussian projection matrices, which satisfy recovery guara…
Algorithm identifies Copeland winners in dueling bandits with ternary feedback.
Selective classification improves trading strategies by abstaining from predictions.
Study examines null vector fields on Lorentzian manifolds.
The group of -diffeomorphisms of any sparse Cantor subset of a manifold is countable and discrete (possibly trivial). Thompson's groups come out of this construction when we consider central ternary Cantor subsets of an interval. Brin's higher dimensional generalizations of Thompson's group arise…
FTTQ optimizes quantized networks in federated learning, reducing communication costs.
The use of deep neural networks in edge computing devices hinges on the balance between accuracy and complexity of computations. Ternary Connect (TC) \cite{lin2015neural} addresses this issue by restricting the parameters to three levels , and , thus eliminating multiplications in the forward pass of the net…
Study curvature loci of 3-manifolds in R^6 and R^5.
GOCPD detects change points by maximizing the probability of two independent models.
Recent breakthroughs in computer vision make use of large deep neural networks, utilizing the substantial speedup offered by GPUs. For applications running on limited hardware, however, high precision real-time processing can still be a challenge. One approach to solving this problem is training networks with binary or…
Machine learning-based applications are increasingly prevalent in IoT devices. The power and storage constraints of these devices make it particularly challenging to run modern neural networks, limiting the number of new applications that can be deployed on an IoT system. A number of compression techniques have been pr…
TRF uses ternary random features to improve ML performance without extra computation.
We inductively define layers of colorings of knot and knotted surface diagrams using ternary quasigroups. Homological invariants from such systems of colorings use shorter differentials and of higher degree than the standard homology differentials, and give access to typically more complex homology groups.
The paper is based on relations between a ternary symmetric form defining the SO(3) geometry in dimension five and Cartan's works on isoparametric hypersurfaces in spheres. As observed by Bryant such a ternary form exists only in dimensions n_k=3k+2, where k=1,2,4,8. In these dimensions it reduces the orthogonal group …
Proposes volumization for neural networks to control bias-variance tradeoff.
This paper introduces Hausdorff measure and its applications in fractal geometry.
Box Thirding identifies the best arm efficiently under limited samples.
In this paper are given explicit calculations of Laplace operator spectrum for smooth real/complex-valued functions on all connected compact simple rank three Lie groups with biinvariant Riemannian metric and established a connection of obtained formulas with the number theory and integer ternary and binary quadratic f…