arXiv research

Study optimal investment with herd behavior using rational decision decomposition.

Subjective expected utility theory assumes that decision-makers possess unlimited computational resources to reason about their choices; however, virtually all decisions in everyday life are made under resource constraints - i.e. decision-makers are bounded in their rationality. Here we experimentally tested the predic…

Abstract: Rational decomposition of homeomorphism spaces for manifolds.

We construct an open book decomposition compatible with a contact structure given by a rational contact surgery on a Legendrian link in the standard contact $S^3$. As an application we show that some rational contact surgeries on certain Legendrian knots induce overtwisted contact structures.

New theorem allows transverse links to be braided with rational book structure.

Smooth 4-manifolds have simple horizontal decompositions.

Study homotopy groups of open books and their pages, pages, and bindings.

Classifies 4-manifolds with genus one horizontal handlebody decomposition.

Rational maps structure theorem with geometric decomposition and realizability proof.

Given a rational homology sphere which bounds rational homology balls, we investigate the complexity of these balls as measured by the number of 1-handles in a handle decomposition. We use Casson-Gordon invariants to obtain lower bounds which also lead to lower bounds on the fusion number of ribbon knots. We use Levine…

In this paper the theory of semi-bounded rationality is proposed as an extension of the theory of bounded rationality. In particular, it is proposed that a decision making process involves two components and these are the correlation machine, which estimates missing values, and the causal machine, which relates the cau…

Paper finds new realizable data for maps with three branch points.

The theory of rational choice assumes that when people make decisions they do so in order to maximize their utility. In order to achieve this goal they ought to use all the information available and consider all the choices available to choose an optimal choice. This paper investigates what happens when decisions are m…

Let $(X,ω)$ be a symplectic rational 4 manifold. We study the space of tamed almost complex structures $\mathcal{J}_ω$ using a fine decomposition via smooth rational curves and a relative version of the infinite-dimensional Alexander duality. This decomposition provides new understandings of both the variation and stab…

Bounded rationality, that is, decision-making and planning under resource limitations, is widely regarded as an important open problem in artificial intelligence, reinforcement learning, computational neuroscience and economics. This paper offers a consolidated presentation of a theory of bounded rationality based on i…

In this paper we determine a complete list of rational surface singularities which have metrically conical bilipschitz type of its inner metric. We achieve this by using the thick-thin decomposition of Birbrair, Neumann and Pichon.

Every negative amphichiral knot is rationally slice.

The study analyzes when Bayesian averaging over decision trees is reliable.

Paper develops a framework for learning interpretable representations of sequential decision behavior.

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In…

The Availability bias, manifested in the over-representation of extreme eventualities in decision-making, is a well-known cognitive bias, and is generally taken as evidence of human irrationality. In this work, we present the first rational, metacognitive account of the Availability bias, formally articulated at Marr's…

New mechanism designs regulate herding in financial markets.

We give new rational blowdown constructions of exotic CP^2#n(-CP^2) (5\leq n\leq 9) without using elliptic fibrations. We also show that our 4-manifolds admit handle decompositions without 1- and 3-handles, for 7\leq n\leq 9. A strategy for rational blowdown constructions of exotic CP^2#n(-CP^2) (1\leq n\leq 4) is also…

We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of ``optimal'' solutions is generically exponentially large: rationality is thus de fact…

Model captures decision-making under bounded rationality with prior beliefs and market feedback.

It is known that for coprime integers $p>q\geq 1$, the lens space $L(p^2,pq-1)$ bounds a rational ball, $B_{p,q}$, arising as the 2-fold branched cover of a (smooth) slice disk in $B^4$ bounding the associated 2-bridge knot. Lekilli and Maydanskiy give handle decompositions for each $B_{p,q}$. Whereas, Yamada gives an …

We study canonical decompositions of postcritically finite branched coverings of the 2-sphere, as defined by K. Pilgrim. We show that every hyperbolic cycle in the decomposition does not have a Thurston obstruction. It is thus Thurston equivalent to a rational map.

We investigate the duality between local (complex analytic) projective structures on surfaces and two dimensional (complex analytic) neighborhoods of rational curves having self-intersection +1. We study the analytic classification, existence of normal forms, pencil/fibration decomposition, infinitesimal symmetries. We…

We give an upper bound on the z-degree of the Kauffman polynomial of a link, using bridges of length greater than one which are separated in some tangle decomposition of a link diagram. We construct some examples by wiring together rational tangles.

Instanton Floer homology matches Heegaard Floer for almost-rational plumbings.

The paper classifies certain singular projective varieties with specific properties.

Study of knot surgeries and JSJ decompositions to tackle $L$-space conjecture.

Study models human investors' sub-rational behavior in financial markets.

Information-theoretic bounded rationality describes utility-optimizing decision-makers whose limited information-processing capabilities are formalized by information constraints. One of the consequences of bounded rationality is that resource-limited decision-makers can join together to solve decision-making problems …

Bounded rationality investigates utility-optimizing decision-makers with limited information-processing power. In particular, information theoretic bounded rationality models formalize resource constraints abstractly in terms of relative Shannon information, namely the Kullback-Leibler Divergence between the agents' pr…

Paper formalizes Simon's satisficing through FFSD, proving its equivalence to expected utility theory.

By recent results of Baker--Etnyre--Van Horn-Morris, a rational open book decomposition defines a compatible contact structure. We show that the Heegaard Floer contact invariant of such a contact structure can be computed in terms of the knot Floer homology of its (rationally null-homologous) binding. We then use this …

If K is a rationally null-homologous knot in a 3-manifold M, the rational genus of K is the infimum of -χ(S)/2p over all embedded orientable surfaces S in the complement of K whose boundary wraps p times around K for some p (hereafter: S is a p-Seifert surface for K). Knots with very small rational genus can be constru…

We consider a framework involving behavioral economics and machine learning. Rationally inattentive Bayesian agents make decisions based on their posterior distribution, utility function and information acquisition cost Renyi divergence which generalizes Shannon mutual information). By observing these decisions, how ca…

The paper studies foliations on smooth projective varieties and their properties.

The paper explains credit decisions using Shapley decomposition for adverse actions.

Torus decomposition shows foliation detected slopes for glued knot manifolds.

Two approaches study the homotopy of blow ups in algebraic and symplectic geometry.

We prove that for every integer k>1 there is a simply connected rational homology 5-sphere $\scriptstyle{M^5_k}$ with spin such that $\scriptstyle{H_2(M^5_k,\bbz)}$ has order $\scriptstyle{k^2},$ and $\scriptstyle{M^5_k}$ admits a Riemannian metric of positive Ricci curvature. Moreover, if the prime number decompositio…

Inferring a person's goal from their behavior is an important problem in applications of AI (e.g. automated assistants, recommender systems). The workhorse model for this task is the rational actor model - this amounts to assuming that people have stable reward functions, discount the future exponentially, and construc…

Transforms uniform learners to work under arbitrary distributions efficiently.

The study classifies manifolds that can be split into two disk bundles.

New symplectic caps and embeddings found in complex projective plane.