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 builds non-bi-orderable groups without generalized torsion.
In this article, we extend the conventional framework of convolutional-Restricted-Boltzmann-Machine to learn highly abstract features among abitrary number of time related input maps by constructing a layer of multiplicative units, which capture the relations among inputs. In many cases, more than two maps are strongly…
Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a…
Well-quasi-orders proved on embedded planar graphs.
Strict partial order is a mathematical structure commonly seen in relational data. One obstacle to extracting such type of relations at scale is the lack of large-scale labels for building effective data-driven solutions. We develop an active learning framework for mining such relations subject to a strict order. Our a…
We define an order relation among oriented -complexes. We show that with respect to this relation, two -complexes over the same complex are homotopy equivalent if and only if there is an isometry between the second homology groups. We also consider minimal objects of this relation.
The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.
We show that a knot has a non left-orderable surgery if the knot group admits a generalized Baumslag-Solitar relator and satisfies certain conditions on a longitude of the knot. As an application, it is shown that certain positively twisted torus knots admit non left-orderable surgeries.
Study convex embeddability in linear and circular orders, applying to knots.
Study compares hypergraph and graph-level models for higher-order relational learning.
We study the price impact of order book events - limit orders, market orders and cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow imbalance, defined as the imbalance between supply and demand at the best bid and ask pri…
H-GAT improves stock selection by capturing complex higher-order stock relations and integrating both technical and fundamental analysis.
Graph Neural Network improves volatility forecasting for 500 S&P stocks.
Paper introduces OMD for ordered state transitions in SSMs.
Study optimality conditions for interval-valued optimization problems on Riemannian manifolds.
We determine the L^2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups (surface-plus-one-relation groups were introduced by Hempel who called them one-relator surface groups). In particular we show that for all such groups G, the L^2-Betti numbers b_n^{(2)}(G) are 0 for all n>1. We also o…
Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its or…
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a …
Study on heavy tails in closing auction returns, explaining imbalance through limit order submission.
Paper introduces a new framework combining deep learning and logic for relational data.
The forcing relation of braids has been introduced for a 2-dimensional analogue of the Sharkovskii order on periods for maps of the interval. In this paper, by making use of the Nielsen fixed point theory and a representation of braid groups, we deduce a trace formula for the computation of the forcing order.
Recently Swatee Naik and Theodore Stanford proved that two S-equivalent knots are related by a finite sequence of doubled-delta moves on their knot diagrams. We show that classical S-equivalence is not sufficient to extend their result to ordered links. We define a new algebraic relation on Seifert matrices, called Str…
New method for learning on heterogeneous graphs without meta-paths.
We study the order of tangency between two manifolds of same dimension and give that notion three quite different geometric interpretations. Related aspects of the order of tangency, e.g., regular separation exponents, are also discussed.
Estimates multiple related causal graphs with shared causal order.
We develop a method to show the fundamental group of the double branched covering of a link is not left-orderable by introducing the notion of the coarse presentation. As in the usual group presentations, a coarse presentation is given by a set of generators and relations, but inequalities are allowed as relations. By …
Paper proves Reshetikhin-Turaev link invariants appear in higher order terms of re-normalized link invariants for plumbed links.
We discuss some open problems and recent progress related to the 4th order Paneitz operator and Q curvature in dimensions other than 4.
New tools analyze the complexity of left-ordering equivalence relations in groups and 3-manifolds.
Recent work in learning ontologies (hierarchical and partially-ordered structures) has leveraged the intrinsic geometry of spaces of learned representations to make predictions that automatically obey complex structural constraints. We explore two extensions of one such model, the order-embedding model for hierarchical…
Proposes a method to measure model parameter similarity for visual tasks.
Given a linearly ordered set I, every surjective map p: A --> I endows the set A with a structure of set of preferences by "replacing" the elements of I with their inverse images via p considered as "balloons" (sets endowed with an equivalence relation), lifting the linear order on A, and "agglutinating" this structure…
Statistical relational AI (StarAI) aims at reasoning and learning in noisy domains described in terms of objects and relationships by combining probability with first-order logic. With huge advances in deep learning in the current years, combining deep networks with first-order logic has been the focus of several recen…
Advances combinatorial complexes for better modeling of hierarchical and set-type relations.
We analyze oversquashing in topological message-passing using relational structures.
Sharing information between multiple tasks enables algorithms to achieve good generalization performance even from small amounts of training data. However, in a realistic scenario of multi-task learning not all tasks are equally related to each other, hence it could be advantageous to transfer information only between …
Different variants of MFDFA technique are applied in order to investigate various (artificial and real-world) time series. Our analysis shows that the calculated singularity spectra are very sensitive to the order of the detrending polynomial used within the MFDFA method. The relation between the width of the multifrac…
Given a set S of n points in general position, we consider all k-th order Voronoi diagrams on S, for k=1,...,n, simultaneously. We deduce symmetry relations for the number of faces, number of vertices and number of circles of certain orders. These symmetry relations are independent of the position of the sites in S. As…
For a 3-manifold with boundary, we study the Kauffman module with indeterminate equal to where . We conjecture an explicit relation between this module and the Reidemeister torsion of which we prove in particular cases. As a maybe useful tool, we then introduce a notion of twisted self-linking and…
RWTNs improve NTN performance in SRL tasks.
Strong geodesic convex function and strong monotone vector field of order on Riemannian manifolds have been established. A characterization of strong geodesic convex function of order for the continuously differentiable functions has been discussed. The relation between the solution of a new variational inequal…
We give different proofs and prove new results on the non complete solvability of some systems of complex first order p.d.e.'s, especially related to the analysis on CR manifolds.
We generalize the notion of involutivity to systems of differential equations of different orders and show that the classical results due to Guillemin and Quillen relating involutivity, restrictions, characteristics and characteristicity, known for first order systems, extend to the general context, though in a modifie…
Disproves Fedotov's conjecture on higher-order Shephard inequalities.
Simple algorithm for computing link polynomials using skein relations.
Sharkovskii proved that the existence of a periodic orbit in a one-dimensional dynamical system implies existence of infinitely many periodic orbits. We obtain an analog of Sharkovskii's theorem for periodic orbits of shear homeomorphisms of the torus. This is done by obtaining a dynamical order relation on the set of …
GraIL predicts relations by reasoning over subgraphs, outperforming embeddings.
Proposes a novel SAM operator for separate item and relational memories.