arXiv research

Proposes a new method for completing swap cycles in decentralized exchanges.

Money was invented to address the difficulty in the double coincidence of wants between the supply and demand when people exchanged their goods and services. There are two information states in society: one is the initial state that people have goods and services due to division of labor; the other is the final state t…

In this paper, we investigate the structure of the Gardiner-Masur boundary of Teichmuller space. Indeed, we will give a geometric description of boundary comparing to the Duchin-Leininger-Rafi compactification of the space of singular flat structures. We will obtain the coincidence between the Gardiner-Masur boundary a…

In today's economy, selling a new zero-marginal cost product is a real challenge, as it is difficult to determine a product's "correct" sales price based on its profit and dissemination. As an example, think of the price of a new app or video game. New sales mechanisms for selling this type of product need to be design…

We give a construction to remove coincidence points of continuous maps on graphs (1-complexes) by changing the maps by homotopies. When the codomain is not homeomorphic to the circle, we show that any pair of maps can be changed by homotopies to be coincidence free. This means that there can be no nontrivial coincidenc…

The elbow method for choosing k in k-means is unreliable and should be avoided.

this is a duplicate submission(original is arXiv:1612.02141). Hence want to withdraw it

The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to topological (Nielsen) coincidence theory. We demonstrate that three natural axioms are su…

Jones polynomial coincidences explored for rational knots.

We consider sufficient conditions of local removability of coincidences of maps f,g:N->M, where M,N are manifolds with dimensions dimN>dimM. The coincidence index is the only obstruction to the removability for maps with fibers either acyclic or homeomorphic to spheres of certain dimensions. We also address the normali…

We study a distributed estimation problem in which two remotely located parties, Alice and Bob, observe an unlimited number of i.i.d. samples corresponding to two different parts of a random vector. Alice can send $k$ bits on average to Bob, who in turn wants to estimate the cross-correlation matrix between the two par…

Model-free approach to hedge path-dependent options using min-max optimization.

Deep learning models are now used in many different industries, while in certain domains safety is not a critical issue in the medical field it is a huge concern. Not only, we want the models to generalize well but we also want to know the models confidence respect to its decision and which features matter the most. Ou…

We give a homotopy invariant construction of the Reidemeister trace for the coincidence of two maps between closed manifolds of not necessarily the same dimensions. It is realized as a homology class of the homotopy equalizer, which coincides with the Hurewicz image of Koschorke's stabilized bordism invariant. To defin…

Optimizes liquidation strategies for assets with Levy process price dynamics.

The paper finds a geometric explanation for coinciding Thom polynomials of cusp and corank-2 singularities.

We construct link invariants using the $D_{2n}$ subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories inv…

Jordan algebras in information geometry linked to metrics on probability distributions.

Using standard analysis only, we present an extension ${^\bullet\R}$ of the real field containing nilpotent infinitesimals. On the one hand we want to present a very simple setting to formalize infinitesimal methods in Differential Geometry, Analysis and Physics. On the other hand we want to show that these infinitesim…

Coincidences of maps between smooth manifolds are studied via a geometric approach which involves (nonstabilized) normal bordism theory and pathspaces.

This article examines the coincidence of the projective and conformal Weyl tensors associated to a given connection D. The connection may be a general Weyl connection associated to a conformal class of metrics [g]. The main result for n>3 is that the Weyl tensors coincide iff D is the Levi-Civita connection of an Einst…

Best arm identification (or, pure exploration) in multi-armed bandits is a fundamental problem in machine learning. In this paper we study the distributed version of this problem where we have multiple agents, and they want to learn the best arm collaboratively. We want to quantify the power of collaboration under limi…

In this paper we study geometric coincidence problems in the spirit of the following problems by B. Grünbaum: How many affine diameters of a convex body in $\mathbb R^n$ must have a common point? How many centers (in some sense) of hyperplane sections of a convex body in $\mathbb R^n$ must coincide? One possible approa…

We present three case studies of organizations using a data science competition to answer a pressing question. The first is in education where a nonprofit that creates smart school budgets wanted to automatically tag budget line items. The second is in public health, where a low-cost, nonprofit women's health care prov…

In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. Here we extend it to pairs (f_1, f_2) of maps between manifolds of arbitrary dimensions. This leads to estimates of the minimum numbers MCC(f_1, f_2) (and MC(f_1, f_2), resp.) of pathcomponents (and of poi…

Problems for the graduate students who want to improve problem-solving skills in geometry. Every problem has a short elegant solution -- this gives a hint which was not available when the problem was discovered.

Bidders in day-ahead electricity markets want to sell/buy electricity when their bids generate positive surplus and not to take an action when the reverse holds. However, non-convexities in these markets cause conflicts between the actions that the bidders want to take and the actual market results. In this work, we in…

The study derives formulas for functionals on surface with boundary under harmonic Ricci flow.

In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. We extend it to pairs (f_1,f_2) of maps between manifolds of arbitrary dimensions, using nonstabilized normal bordism theory as our main tool. This leads to estimates of the minimum numbers MCC(f_1,f_2) (a…

Minimum numbers of fixed points or of coincidence components (realized by maps in given homotopy classes) are the principal objects of study in topological fixed point and coincidence theory. In this paper we investigate fiberwise analoga and represent a general approach e.g. to the question when two maps can be deform…

A new scheme for private computation splits client data into shares for server operations.

As technology become more advanced, those who design, use and are otherwise affected by it want to know that it will perform correctly, and understand why it does what it does, and how to use it appropriately. In essence they want to be able to trust the systems that are being designed. In this survey we present assura…

Facial attribute editing aims to manipulate single or multiple attributes of a face image, i.e., to generate a new face with desired attributes while preserving other details. Recently, generative adversarial net (GAN) and encoder-decoder architecture are usually incorporated to handle this task with promising results.…

BlackJAX simplifies Bayesian inference with modular, fast implementations.

In this paper we give a proof of Lichnerowicz Conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids the {\it Nice Embeddings} into eigen spaces of the Laplacian. Even if one wants to use these embeddings this paper gives a more streamlined proof.

We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.

For any two continuous maps $f,g$ between two solvmanifolds of same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence number of $f,g$. This result is an extension of the result of Ha, Lee and Penninckx for completely solvable case.

A single algebraic identity unifies information-theoretic variational results.

The main result of the present paper is a coincidence formula for foliated manifolds. To prove this we establish Kuenneth formula, Poincare duality and intersection product in the context of tangential de Rham cohomology and homology of tangential currents. We apply the formula to get a dynamical Lefschetz formula for …

Unified framework for uniform signal recovery in nonlinear GCS with 1-bit/quantized measurements.

This paper centers around two basic problems of topological coincidence theory. First, try to measure (with help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free maps. Secondly, describe the set of loose pairs of homotopy classes. …

Given two maps f_1, f_2 : M^m \longrightarrow N^n between manifolds of the indicated arbitrary dimensions, when can they be deformed away from one another? More generally: what is the minimum number MCC (f_1, f_2) of pathcomponents of the coincidence space of maps f'_1, f'_2 where f'_i is homotopic to f_i, i = 1, 2? Ap…

We compare various notions of weak subsolutions to degenerate complex Monge-Amp{è}re flows, showing that they all coincide. This allows us to show that the viscosity solution coincides with the envelope of pluripotential subsolutions. Dedicated to Duong Hong Phong on the occasion of his 65th birthday.

An interesting problem in classical differential geometry is to find methods to prove that two surfaces defined by different charts actually coincide up to position in space. In a previous paper we proposed a method in this direction for minimal surfaces. Here we explain not only how this method works but also how we c…

The purpose of this paper is to point out that `supremum' in two inequalities of Brooks should be replaced with `infimum'. The results of this paper are already known by Professor Higuci. Hence, I want to delete this paper from this preprint server.

In this paper we prove that the zeroth Milnor-Thurston homology group coincides with singular homology for Peano Continua. More- over, we show that the canonical homomorphism between these ho- mology theories may not be injective. However, it is proved that it is injective when a space has Borel path-components.

In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be explicitly and consistently incorporated in the valuation of decisions, using the theory …

The main theme of this paper is to study for a symplectomorphism of a compact surface, the asymptotic invariant which is defined to be the growth rate of the sequence of the total dimensions of symplectic Floer homologies of the iterates of the symplectomorphism. We prove that the asymptotic invariant coincides with as…