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 shows physical drift affects put-call parity enforcement, not just option payoffs.
New method solves tensor equations including parity odd and even terms in 4D.
Although portfolio management didn't change much during the 40 years after the seminal works of Markowitz and Sharpe, the development of risk budgeting techniques marked an important milestone in the deepening of the relationship between risk and asset management. Risk parity then became a popular financial model of in…
Proposes a framework to create fair IDRs by enforcing demographic parity constraints.
Researchers solved a number-theoretic hypothesis to determine the spin parity of k-differentials.
This paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial and categorifications of the arrow polynomial. The paper is relatively self-contained and it describes virtual knot theory bot…
We construct various functorial maps (projections) from virtual knots to classical knots. These maps are defined on diagrams of virtual knots; in terms of Gauss diagram each of them can be represented as a deletion of some chords. The construction relies upon the notion of parity. As corollaries, we prove that the mini…
Investigates MAD-RP portfolios for asset allocation.
Parity functors assign labels to knot diagrams based on crossing parity.
Any optimization algorithm based on the risk parity approach requires the formulation of portfolio total risk in terms of marginal contributions. In this paper we use the independence of the underlying factors in the market to derive the centered moments required in the risk decomposition process when the modified vers…
Parity defined for based matrices, a new example of virtual knot parity.
We introduce the 2-colour parity. It is a theory of parity for a large class of virtual links, defined using the interaction between orientations of the link components and a certain type of colouring. The 2-colour parity is an extension of the Gaussian parity, to which it reduces on virtual knots. We show that the 2-c…
In the present paper, we develop the parity theory invented in \cite{ManSb}; we construct new parities for two-component (virtual and free) links. New parities significantly depend on geometrical properties of diagrams; in particular, they are mutation-sensitive. New parities can be used practically in all problems, wh…
In \cite {FrKn,Sbornik} it was shown that in some knot theories the crucial role is played by {\em parity}, i.e.\ a function on crossings valued in and behaving nicely with respect to Reidemeister moves. Any parity allows one to construct functorial mappings from knots to knots, to refine many invariants and …
We identify conditional parity as a general notion of non-discrimination in machine learning. In fact, several recently proposed notions of non-discrimination, including a few counterfactual notions, are instances of conditional parity. We show that conditional parity is amenable to statistical analysis by studying ran…
Universal Gaussian parity proven for 2D knots.
New parities defined on virtual knots linked to crossing indices.
Differentially private fair binary classification algorithm developed.
Blockchain funds balance risk and return for various investors.
This paper tackles fair Bayes-optimal classifiers under predictive parity, proving their limitations and proposing a new algorithm.
Parity calibration aims to predict increase-decrease events, not values.
We use crossing parity to construct a generalization of biquandles for virtual knots which we call Parity Biquandles. These structures include all biquandles as a standard example referred to as the even parity biquandle. Additionally, we find all Parity Biquandles arising from the Alexander Biquandle and Quaternionic …
Diversified risk parity strategies outperform equally-weighted portfolios in various asset universes.
Functorial maps and weak parities are equivalent descriptions of rules of substitution virtual crossings for classical in diagrams of a knot in a way compatible with Reidemeister moves. We introduce the notion of maximal weak parity and describe it for knots in a given closed oriented surface. This weak parity defines …
Introduce a two-variable parity polynomial for virtual knotoids
Paper solves k-sparse parity problem with sign SGD, matching SQ lower bound.
Neural networks struggle with learning fixed parities.
In [3] we constructed the parity-biquandle bracket valued in {\em pictures} (linear combinations of -valent graphs). We gave no example of classical links such that the parity-biquandle bracket of which is not trivial. In the present paper we slightly change the notation of the parity-biquandle bracket and give exam…
The study of fairness in intelligent decision systems has mostly ignored long-term influence on the underlying population. Yet fairness considerations (e.g. affirmative action) have often the implicit goal of achieving balance among groups within the population. The most basic notion of balance is eventual equality bet…
Parity mappings from the chords of a Gauss diagram to the integers is defined. The parity of the chords is used to construct families of invariants of Gauss diagrams and virtual knots. One family consists of degree Vassiliev invariants.
We define counting and cocycle enhancement invariants of virtual knots using parity biquandles. These invariants are determined by pairs consisting of a biquandle 2-cocycle φ^0 and a map φ^1 with certain compatibility conditions leading to one-variable or two-variable polynomial invariants of virtual knots. We provide …
Counterfactual fairness not equivalent to demographic parity, finds study.
Transformers solve parity problems efficiently with step-by-step reasoning.
Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate a necklace (in combinatorial sense). We express rational local formulas for all…
2-dimensional knots and links are studied in the article. The notion of parity is introduced via techniques similar to the ones used by the second named author in 1-dimensional case. By using parity new invariants are constructed and known invariants are refined.
In [14], the second named author constructed the bracket invariant [.] of virtual knots valued in pictures (linear combinations of virtual knot diagrams with some crossing information omitted), such that for many diagrams K, the following formula holds: [K]=K', where K' is the underlying graph of the diagram, i.e., the…
Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute. However, the exact tradeoff between fairness and accuracy is not entirely clear, even f…
New causal analysis reconciles predictive and statistical fairness.
New method controls bias in training data for fair outcomes.
The article develops a model for skewness risk in risk parity portfolios.
In previous papers, the author realized the following principle for many knot theories: if a knot diagram is complicated enough then it reproduces itself, i.e., is a subdiagram of any other diagram equivalent to it. This principle is realized by diagram-valued invariants [ ] of knots such that [K]=K. It turns out that …
We mathematically compare four competing definitions of group-level nondiscrimination: demographic parity, equalized odds, predictive parity, and calibration. Using the theoretical framework of Friedler et al., we study the properties of each definition under various worldviews, which are assumptions about how, if at a…
We consider knot theories possessing a {\em parity}: each crossing is decreed {\em odd} or {\em even} according to some universal rule. If this rule satisfies some simple axioms concerning the behaviour under Reidemeister moves, this leads to a possibility of constructing new invariants and proving minimality and non-t…
The paper models exchange rate risk premium using mean-reverting dynamics.
We investigate an application of crossing parity for the bracket expansion of the Jones polynomial for virtual knots. In addition we consider an application of parity for the arrow polynomial as well as for the categorifications of both polynomials. We present a number of examples found through our calculations. We pro…
Incorrect parity-based descriptions of realizable Gauss diagrams found, but bipartite graphs provide a valid approach.
Algorithm ensures demographic parity in regression without sensitive attribute data.
New framework tackles fairness in link prediction beyond demographic parity.