arXiv subjects

Kai Jin

Publications and source records attributed to Kai Jin.

44 records · Page 3Linked to original sources

arXiv2018

Finding all Maximal Area Parallelograms in a Convex Polygon

Polygon inclusion problems have been studied extensively in geometric optimization. In this paper, we consider the variant of computing the maximum area parallelograms (MAPs) and all the locally maximal area parallelograms (LMAPs) in a given convex polygon. By proving and utilizing several structural properties of the LMAPs, we compute all of them (including all the MAPs) in $O(n^2)$ time, where $n$ denotes the number of edges of the given polygon. In addition, we prove that the LMAPs interleave each other and thus the number of LMAPs is $O(n)$. We discuss applications of our result to, among others, the problem of computing the maximum area centrally-symmetric convex body inside a convex polygon, and the simplest case of the Heilbronn triangle problem.

cs.CG↗

arXiv2018

DeepTracker: Visualizing the Training Process of Convolutional Neural Networks

Deep convolutional neural networks (CNNs) have achieved remarkable success in various fields. However, training an excellent CNN is practically a trial-and-error process that consumes a tremendous amount of time and computer resources. To accelerate the training process and reduce the number of trials, experts need to understand what has occurred in the training process and why the resulting CNN behaves as such. However, current popular training platforms, such as TensorFlow, only provide very little and general information, such as training/validation errors, which is far from enough to serve this purpose. To bridge this gap and help domain experts with their training tasks in a practical environment, we propose a visual analytics system, DeepTracker, to facilitate the exploration of the rich dynamics of CNN training processes and to identify the unusual patterns that are hidden behind the huge amount of training log. Specifically,we combine a hierarchical index mechanism and a set of hierarchical small multiples to help experts explore the entire training log from different levels of detail. We also introduce a novel cube-style visualization to reveal the complex correlations among multiple types of heterogeneous training data including neuron weights, validation images, and training iterations. Three case studies are conducted to demonstrate how DeepTracker provides its users with valuable knowledge in an industry-level CNN training process, namely in our case, training ResNet-50 on the ImageNet dataset. We show that our method can be easily applied to other state-of-the-art "very deep" CNN models.

cs.CV↗

arXiv2018

LOCld65, A Dual-Channel VCSEL Driver ASIC For Detector Front-End Readout

We present the design and the test results of a dual-channel Vertical-Cavity Surface-Emitting Laser (VCSEL) driver ASIC LOCld65 for detector front-end readout. LOCld65 is designed in a commercial 65-nm CMOS technology with a power supply of 1.2 V. LOCld65 contains two separate channels with the same structure and the two channels share an I2C slave. Each channel consists of an input amplifier, four stages of limiting amplifiers (LAs), a high-current output driver, and a bias-current generator. In order to extend the bandwidth, the input amplifier uses an inductive peaking technique and the LAs use a shared inductive peaking technique. The input amplifier and the output driver each utilize a Continuous-Time Linear Equalizer (CTLE). The LAs employ active feedback. The modulation current, the bias current, the peaking strength of the CTLEs, and the feedback strength of LAs are programmable through an I2C interface. In order to protect from the radiation damage, the I2C slave is implemented with triple modular redundancy. Each channel of LOCld65 is tested to operate up to 14 Gbps with typical power dissipations (the VCSEL included) of 68.3 mW/channel and 62.1 mW/channel at the VCSEL voltages of 3.3 V and 2.5 V, respectively. LOCld65 survives 4.9 kGy(SiO2). LOCld65 is an excellent match for the serializer-deserializer ASIC lpGBT in single- or dual-channel optical transmitters in HL-LHC upgrade applications.

physics.ins-det↗

arXiv2017

Linear Time Approximation Schemes for Geometric Maximum Coverage

We study approximation algorithms for the following geometric version of the maximum coverage problem: Let $\mathcal{P}$ be a set of $n$ weighted points in the plane. Let $D$ represent a planar object, such as a rectangle, or a disk. We want to place $m$ copies of $D$ such that the sum of the weights of the points in $\mathcal{P}$ covered by these copies is maximized. For any fixed $\varepsilon>0$, we present efficient approximation schemes that can find a $(1-\varepsilon)$-approximation to the optimal solution. In particular, for $m=1$ and for the special case where $D$ is a rectangle, our algorithm runs in time $O(n\log (\frac{1}{\varepsilon}))$, improving on the previous result. For $m>1$ and the rectangular case, our algorithm runs in $O(\frac{n}{\varepsilon}\log (\frac{1}{\varepsilon})+\frac{m}{\varepsilon}\log m +m(\frac{1}{\varepsilon})^{O(\min(\sqrt{m},\frac{1}{\varepsilon}))})$ time. For a more general class of shapes (including disks, polygons with $O(1)$ edges), our algorithm runs in $O(n(\frac{1}{\varepsilon})^{O(1)}+\frac{m}ε\log m + m(\frac{1}{\varepsilon})^{O(\min(m,\frac{1}{\varepsilon^2}))})$ time.

cs.CG↗

arXiv2016

A Sodium laser guide star coupling efficiency measurement method

Large telescope's adaptive optics (AO) system requires one or several bright artificial laser guide stars to improve its sky coverage. The recent advent of high power sodium laser is perfect for such application. However, besides the output power, other parameters of the laser also have significant impact on the brightness of the generated sodium laser guide star mostly in non-linear relationships. When tuning and optimizing these parameters it is necessary to tune based on a laser guide star generation performance metric. Although return photon flux is widely used, variability of atmosphere and sodium layer make it difficult to compare from site to site even within short time period for the same site. A new metric, coupling efficiency is adopted in our field tests. In this paper, we will introduce our method for measuring the coupling efficiency of a 20W class pulse sodium laser for AO application during field tests that were conducted during 2013-2015.

astro-ph.IM↗

arXiv2016

On the power of dominated players in team competitions

We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect recall and can be solved efficiently by standard methods. We are interested in the properties of the subgame perfect equilibria of this game. We first show that uniformly random strategy is a subgame perfect equilibrium strategy for both teams when there are no redundant players (i.e., the number of players in each team equals to the number of rounds of the competition). Secondly, a team can safely abandon its weak players if it has redundant players and the strength of players is transitive. We then focus on the more interesting case where there are redundant players and the strength of players is not transitive. In this case, we obtain several counterintuitive results. First of all, a player might help improve the payoff of its team, even if it is dominated by the entire other team. We give a necessary condition for a dominated player to be useful. We also study the extent to which the dominated players can increase the payoff. These results bring insights into playing and designing general team competitions.

cs.GT↗

arXiv2013

A Generic Position Based Method for Real Root Isolation of Zero-Dimensional Polynomial Systems

We improve the local generic position method for isolating the real roots of a zero-dimensional bivariate polynomial system with two polynomials and extend the method to general zero-dimensional polynomial systems. The method mainly involves resultant computation and real root isolation of univariate polynomial equations. The roots of the system have a linear univariate representation. The complexity of the method is $\tilde{O}_B(N^{10})$ for the bivariate case, where $N=\max(d,τ)$, $d$ resp., $τ$ is an upper bound on the degree, resp., the maximal coefficient bitsize of the input polynomials. The algorithm is certified with probability 1 in the multivariate case. The implementation shows that the method is efficient, especially for bivariate polynomial systems.

cs.SC↗

arXiv2012

Certified Rational Parametric Approximation of Real Algebraic Space Curves with Local Generic Position Method

In this paper, an algorithm to compute a certified $G^1$ rational parametric approximation for algebraic space curves is given by extending the local generic position method for solving zero dimensional polynomial equation systems to the case of dimension one. By certified, we mean the approximation curve and the original curve have the same topology and their Hausdauff distance is smaller than a given precision. Thus, the method also gives a new algorithm to compute the topology for space algebraic curves. The main advantage of the algorithm, inhering from the local generic method, is that topology computation and approximation for a space curve is directly reduced to the same tasks for two plane curves. In particular, the error bound of the approximation space curve is obtained from the error bounds of the approximation plane curves explicitly. Nontrivial examples are used to show the effectivity of the method.

cs.CG↗