arXiv research

Improved Random Forests detect pure interactions better.

In blind hyperspectral unmixing (HU), the pure-pixel assumption is well-known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no pure-pixel case, a good blind…

This work introduces CAET, an algorithm for cost-aware pairwise pure exploration.

We define invariants of braids rather than invariants of conjugacy classes of braids. For any pure three-braid we give effective upper and lower bounds for these invariants. This is done in terms of a natural syllable decomposition of the word representing the image of the braid in the braid group modulo its center. Th…

A new method purifies interaction effects in models to improve interpretability.

In many healthcare settings, intuitive decision rules for risk stratification can help effective hospital resource allocation. This paper introduces a novel variant of decision tree algorithms that produces a chain of decisions, not a general tree. Our algorithm, $α$-Carving Decision Chain (ACDC), sequentially carves o…

Study pure exploration in high-dimensional feature spaces using adaptive embeddings.

Study of dynamic competition between old and new technologies using a nonlinear map.

CryptoGAT improves cryptocurrency price prediction by treating it as a graph problem.

PureTS uses simple linear models to improve long-term time series forecasting.

New mechanism for pure differential privacy on functional summaries using Laplace-like process.

This paper extends a Kyle model to include price-responsive traders, revealing new dynamics and equilibria.

Proposes a new method for clustering tasks in multi-task learning.

A new invariant for pure braids is defined and shown not to be trivial.

The concept of pure spinor is generalized, giving rise to the notion of pure subspaces, spinorial subspaces associated to isotropic vector subspaces of non-maximal dimension. Several algebraic identities concerning the pure subspaces are proved here, as well as some differential results. Furthermore, the freedom in the…

Characterizes optimal-speed quantum state evolution Hamiltonians.

In this study, we propose the leveraging of interpretability for tasks beyond purely the purpose of explainability. In particular, this study puts forward a novel strategy for leveraging gradient-based interpretability in the realm of adversarial examples, where we use insights gained to aid adversarial learning. More …

Estimates joint causal effects using single-variable interventions on nonlinear models.

The CN matrix of a pure braid projection is characterized and applied.

We develop a formalism to study linearized perturbations around the equilibria of a pure exchange economy. With the use of mean field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous preferences and probabilistic interaction between agents. We are able to show that i…

A spacetime denotes a pure radiation field if its energy momentum tensor represents a situation in which all the energy is transported in one direction with the speed of light. In 1989, Wils and later in 1997 Ludwig and Edgar studied the physical properties of pure radiation metrics, which are conformally related to a …

Corrects earlier work on surface orbifold pure braid groups.

In this mostly survey paper, we investigate the resonance varieties, the lower central series ranks, and the Chen ranks, as well as the residual and formality properties of several families of braid-like groups: the pure braid groups $P_n$, the welded pure braid groups $wP_n$, the virtual pure braid groups $vP_n$, as w…

We find finite presentations for the automorphism group of the Artin pure braid group and the automorphism group of the pure braid group associated to the full monomial group.

In this paper it is proved that the pure braided Thompson's group BF admits a bi-order, analog to the bi-order of the pure braid groups.

Summary of pure cactus groups and circle points.

Study automorphisms of pure braid groups on sphere homotopy groups.

New braid representations using virtual knot theory.

In this paper we introduce the framed pure braid group on $n$ strands of an oriented surface, a topological generalisation of the pure braid group $P_n$. We give different equivalents definitions for framed pure braid groups and we study exact sequences relating these groups with other generalisations of $P_n$, usually…

The question of whether a representation of Artin's pure braid group is faithful is translated to certain properties of the Lie algebra arising from the descending central series of the pure braid group, and thus the Vassiliev invariants of pure braids via work of T. Kohno \cite{kohno1,kohno2}. The main result is a Lie…

We show that the Artin pure braid group on at least four strands is not residually free. Our results also show that the pure braid group on at least three strands has corank two.

We prove that the pure braid groups on closed, orientable surfaces are bi-orderable, and that the pure braid groups on closed, non-orientable surfaces have generalized torsion, thus they are not bi-orderable.

Study of pure mapping class groups on infinite graphs.

3-braid knots can't have purely cosmetic surgeries.

Algorithm balances online and offline data for linear bandits.

Study of pure spinors on neutral manifolds with applications to supersymmetric solutions.

New proof shows homomorphisms from pure braid groups to hyperbolic groups have cyclic images or factor through forgetful maps.

In this paper we use game theory to model poisoning attack scenarios. We prove the non-existence of pure strategy Nash Equilibrium in the attacker and defender game. We then propose a mixed extension of our game model and an algorithm to approximate the Nash Equilibrium strategy for the defender. We then demonstrate th…

We demonstrate that the lowest possible price change (tick-size) has a large impact on the structure of financial return distributions. It induces a microstructure as well as it can alter the tail behavior. On small return intervals, the tick-size can distort the calculation of correlations. This especially occurs on s…

Proves certain subgroups of genus 2 handlebody group are convex cocompact.

Defines crisis transitions in pure exchange economies rigorously.

The paper tackles pure exploration in multi-armed bandits with low rank structure using oblivious sampling.

The study proves large alternating Montesinos knots cannot have purely cosmetic surgeries.

It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such obstacle follows that manifold as pseudo-Riemannian manifold is locally non-reducible.…

Two knot families meet cosmetic surgery conjecture.

New dual approach for hedging Bermudan options efficiently.

Framework purifies approximate differential privacy to pure differential privacy.

Study on sample complexity for pure exploration in feedback graph settings.