arXiv subjects

Bo Lin

Publications and source records attributed to Bo Lin.

84 records · Page 5Linked to original sources

arXiv2019

Computing Committor Functions for the Study of Rare Events Using Deep Learning

The committor function is a central object of study in understanding transitions between metastable states in complex systems. However, computing the committor function for realistic systems at low temperatures is a challenging task, due to the curse of dimensionality and the scarcity of transition data. In this paper, we introduce a computational approach that overcomes these issues and achieves good performance on complex benchmark problems with rough energy landscapes. The new approach combines deep learning, data sampling and feature engineering techniques. This establishes an alternative practical method for studying rare transition events between metastable states in complex, high dimensional systems.

physics.comp-ph↗

arXiv2019

Two-player incentive compatible outcome functions are affine maximizers

In mechanism design, for a given type space, there may be incentive compatible outcome functions which are not affine maximizers. Using tools from linear algebra and tropical geometry, we prove that for two-player games on a discrete type space, any given outcome function can be turned into an affine maximizer through a nontrivial perturbation of the type space. Furthermore, our theorems are the strongest possible in this setup.

math.CO↗

arXiv2018

3D characterization of ultrasonic melt processing on the microstructural refinement of Al-Cu alloys by synchrotron X-ray tomography

The effect of ultrasonic melting processing on three-dimensional architecture of intermetallic phases and pores in two multicomponent cast Al-5.0Cu-0.6Mn-0.5 Fe alloys is characterized using conventional microscopy and synchrotron X-ray microtomography. The two alloys are found to contain intermetallic phases such as Al15(FeMn)3Cu2, Al7Cu2Fe, Al3(FeMn), Al6(FeMn), and Al2Cu that have complex networked morphology in 3D. The application of USP in alloys can obtained refined and equiaxed microstructures. The grain size of 0.5Fe and 1.0 Fe alloys is greatly decreased from 16.9 m, 15.8 m without USP to 13.3 m, 12.2 m with USP, respectively. The results show that USP significantly reduce the volume fraction, grain size, interconnectivity, and equivalent diameter of the intermetallic phases in both alloys. The volume fraction of pores in both alloys is reduced due to the USP degassing effect. The refinement mechanism of USP induced fragmentation of primary and secondary dendrites via acoustic bubbles and acoustic streaming flow were discussed.

cond-mat.mtrl-sci↗

arXiv2018

Tropical Fermat-Weber points

In a metric space, the Fermat-Weber points of a sample are statistics to measure the central tendency of the sample and it is well-known that the Fermat-Weber point of a sample is not necessarily unique in the metric space. We investigate the computation of Fermat-Weber points under the tropical metric on the quotient space $\mathbb{R}^{n} \!/ \mathbb{R} {\bf 1}$ with a fixed $n \in \mathbb{N}$, motivated by its application to the space of equidistant phylogenetic trees with $N$ leaves (in this case $n=\binom{N}{2}$) realized as the tropical linear space of all ultrametrics. We show that the set of all tropical Fermat-Weber points of a finite sample is always a classical convex polytope, and we present a combinatorial formula for a key value associated to this set. We identify conditions under which this set is a singleton. We apply numerical experiments to analyze the set of the tropical Fermat-Weber points within a space of phylogenetic trees. We discuss the issues in the computation of the tropical Fermat-Weber points.

math.CO↗

arXiv2017

From Clarity to Efficiency for Distributed Algorithms

This article describes a very high-level language for clear description of distributed algorithms and optimizations necessary for generating efficient implementations. The language supports high-level control flows where complex synchronization conditions can be expressed using high-level queries, especially logic quantifications, over message history sequences. Unfortunately, the programs would be extremely inefficient, including consuming unbounded memory, if executed straightforwardly. We present new optimizations that automatically transform complex synchronization conditions into incremental updates of necessary auxiliary values as messages are sent and received. The core of the optimizations is the first general method for efficient implementation of logic quantifications. We have developed an operational semantics of the language, implemented a prototype of the compiler and the optimizations, and successfully used the language and implementation on a variety of important distributed algorithms.

cs.PL↗

arXiv2017

Towards a tropical Hodge bundle

The moduli space $M_g^{trop}$ of tropical curves of genus $g$ is a generalized cone complex that parametrizes metric vertex-weighted graphs of genus $g$. For each such graph $Γ$, the associated canonical linear system $\vert K_Γ\vert$ has the structure of a polyhedral complex. In this article we propose a tropical analogue of the Hodge bundle on $M_g^{trop}$ and study its basic combinatorial properties. Our construction is illustrated with explicit computations and examples.

math.AG↗

arXiv2016

Computing Linear Systems on Metric Graphs

The linear system $|D|$ of a divisor $D$ on a metric graph has the structure of a cell complex. We introduce the anchor divisors and anchor cells in it - they serve as the landmarks for us to compute the f-vector of the complex and find all cells in the complex. A linear system can also be identified as a tropical convex hull of rational functions. We compute its extremal generators using the landmarks. We apply these methods to some examples - namely the canonical linear systems of some small trivalent graphs.

math.CO↗

arXiv2016

Demand-Driven Incremental Object Queries

Object queries are essential in information seeking and decision making in vast areas of applications. However, a query may involve complex conditions on objects and sets, which can be arbitrarily nested and aliased. The objects and sets involved as well as the demand---the given parameter values of interest---can change arbitrarily. How to implement object queries efficiently under all possible updates, and furthermore to provide complexity guarantees? This paper describes an automatic method. The method allows powerful queries to be written completely declaratively. It transforms demand as well as all objects and sets into relations. Most importantly, it defines invariants for not only the query results, but also all auxiliary values about the objects and sets involved, including those for propagating demand, and incrementally maintains all of them. Implementation and experiments with problems from a variety of application areas, including distributed algorithms and probabilistic queries, confirm the analyzed complexities, trade-offs, and significant improvements over prior work.

cs.PL↗

arXiv2016

Convexity in Tree Spaces

We study the geometry of metrics and convexity structures on the space of phylogenetic trees, which is here realized as the tropical linear space of all \ ultrametrics. The ${\rm CAT}(0)$-metric of Billera-Holmes-Vogtman arises from the theory of orthant spaces. While its geodesics can be computed by the Owen-Provan algorithm, geodesic triangles are complicated. We show that the dimension of such a triangle can be arbitrarily high. Tropical convexity and the tropical metric behave better. They exhibit properties desirable for geometric statistics, such as geodesics of small depth.

math.MG↗

arXiv2014

Almost-toric Hypersurfaces

An almost-toric hypersurface is parameterized by monomials multiplied by polynomials in one extra variable. We determine the Newton polytope of such a hypersurface, and apply this to give an algorithm for computing the implicit equation.

math.AG↗

arXiv2010

Compact graphene mode-locked wavelength-tunable erbium-doped fiber lasers: from all anomalous dispersion towards all normal dispersion

Soliton operation and soliton wavelength tuning of erbium-doped fiber lasers mode locked with atomic layer graphene was experimentally investigated under various cavity dispersion conditions. It was shown that not only wide range soliton wavelength tuning but also soltion pulse width variation could be obtained in the fiber lasers. Our results show that the graphene mode locked erbium-doped fiber lasers provide a compact, user friendly and low cost wavelength tunable ultrahsort pulse source.

physics.optics↗

arXiv2010

Inverse-Gaussian-Apodized Fiber Bragg Grating for Dual Wavelength Lasing

A fiber Bragg grating (FBG) with an inverse-Gaussian apodization function is proposed and fabricated. It is shown that such a FBG possesses easily controllable dual-wavelength narrow transmission peaks. Incorporating such a FBG filter in a fiber laser with a linear cavity, stable dual-wavelength emission with 0.146 nm wavelength spacing is obtained. It provides a simple and low cost approach of achieving the dual-wavelength fiber laser operation.

physics.atom-ph↗