Uniform Sampling on the Standard Simplex

AbstractOver the last decades, algorithms have been developed for checking copositivity of a matrix. Methods are based on several principles, such as spatial branch and bound, transformation to Mixed Integer Programming, implicit enumeration of KKT points or face-based search. Our research question focuses on exploiting the mathematical properties of the relative interior minima of the standard quadratic program (StQP) and monotonicity. We derive several theoretical properties related to convexity and monotonicity of the standard quadratic function over faces of the standard simplex. We illustrate with numerical instances up to 28 dimensions the use of monotonicity in face-based algorithms. The question is what traversal through the face graph of the standard simplex is more appropriate for which matrix instance; top down or bottom up approaches. This depends on the level of the face graph where the minimum of StQP can be found, which is related to the density of the so-called convexity graph.

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Non-uniform sampling in pulse dipolar spectroscopy by EPR: the redistribution of noise and the optimization of data acquisition

Physical Chemistry Chemical Physics ◽

10.1039/d1cp00705j ◽

2021 ◽

Author(s):

Anna G. Matveeva ◽

Victoria N. Syryamina ◽

Vyacheslav M. Nekrasov ◽

Michael K. Bowman

Keyword(s):

Data Acquisition ◽

Spectroscopy Data ◽

Distance Spectrum ◽

Uniform Sampling ◽

Increased Sensitivity ◽

Non Uniform Sampling

Non-uniform schemes for collection of pulse dipole spectroscopy data can decrease and redistribute noise in the distance spectrum for increased sensitivity and throughput.

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An Optimized Triggering Algorithm for Event-Triggered Control of Networked Control Systems

Mathematics ◽

10.3390/math9111262 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1262

Author(s):

Sunil Kumar Mishra ◽

Amitkumar V. Jha ◽

Vijay Kumar Verma ◽

Bhargav Appasani ◽

Almoataz Y. Abdelaziz ◽

...

Keyword(s):

Control Systems ◽

Networked Control Systems ◽

Networked Control ◽

Pendulum System ◽

Uniform Sampling ◽

Inverted Pendulum System ◽

Event Triggering ◽

Non Uniform Sampling ◽

System States ◽

Event Triggered

This paper presents an optimized algorithm for event-triggered control (ETC) of networked control systems (NCS). Initially, the traditional backstepping controller is designed for a generalized nonlinear plant in strict-feedback form that is subsequently extended to the ETC. In the NCS, the controller and the plant communicate with each other using a communication network. In order to minimize the bandwidth required, the number of samples to be sent over the communication channel should be reduced. This can be achieved using the non-uniform sampling of data. However, the implementation of non-uniform sampling without a proper event triggering rule might lead the closed-loop system towards instability. Therefore, an optimized event triggering algorithm has been designed such that the system states are always forced to remain in stable trajectory. Additionally, the effect of ETC on the stability of backstepping control has been analyzed using the Lyapunov stability theory. Two case studies on an inverted pendulum system and single-link robot system have been carried out to demonstrate the effectiveness of the proposed ETC in terms of system states, control effort and inter-event execution time.

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Faster Motif Counting via Succinct Color Coding and Adaptive Sampling

ACM Transactions on Knowledge Discovery from Data ◽

10.1145/3447397 ◽

2021 ◽

Vol 15 (6) ◽

pp. 1-27

Author(s):

Marco Bressan ◽

Stefano Leucci ◽

Alessandro Panconesi

Keyword(s):

Adaptive Sampling ◽

Relative Frequency ◽

State Of The Art ◽

Color Coding ◽

Input Graph ◽

Large Graphs ◽

Running Time ◽

Uniform Sampling ◽

Current State ◽

Connected Subgraphs

We address the problem of computing the distribution of induced connected subgraphs, aka graphlets or motifs , in large graphs. The current state-of-the-art algorithms estimate the motif counts via uniform sampling by leveraging the color coding technique by Alon, Yuster, and Zwick. In this work, we extend the applicability of this approach by introducing a set of algorithmic optimizations and techniques that reduce the running time and space usage of color coding and improve the accuracy of the counts. To this end, we first show how to optimize color coding to efficiently build a compact table of a representative subsample of all graphlets in the input graph. For 8-node motifs, we can build such a table in one hour for a graph with 65M nodes and 1.8B edges, which is times larger than the state of the art. We then introduce a novel adaptive sampling scheme that breaks the “additive error barrier” of uniform sampling, guaranteeing multiplicative approximations instead of just additive ones. This allows us to count not only the most frequent motifs, but also extremely rare ones. For instance, on one graph we accurately count nearly 10.000 distinct 8-node motifs whose relative frequency is so small that uniform sampling would literally take centuries to find them. Our results show that color coding is still the most promising approach to scalable motif counting.

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Information-Efficient, Off-Center Sampling Results in Improved Precision in 3D Single-Particle Tracking Microscopy

Entropy ◽

10.3390/e23050498 ◽

2021 ◽

Vol 23 (5) ◽

pp. 498

Author(s):

Chen Zhang ◽

Kevin Welsher

Keyword(s):

Fisher Information ◽

Particle Tracking ◽

Single Particle ◽

Biological Samples ◽

Tracking System ◽

Single Particle Tracking ◽

Uniform Sampling ◽

Single Dimension ◽

3D Localization ◽

Particle Localization

In this work, we present a 3D single-particle tracking system that can apply tailored sampling patterns to selectively extract photons that yield the most information for particle localization. We demonstrate that off-center sampling at locations predicted by Fisher information utilizes photons most efficiently. When performing localization in a single dimension, optimized off-center sampling patterns gave doubled precision compared to uniform sampling. A ~20% increase in precision compared to uniform sampling can be achieved when a similar off-center pattern is used in 3D localization. Here, we systematically investigated the photon efficiency of different emission patterns in a diffraction-limited system and achieved higher precision than uniform sampling. The ability to maximize information from the limited number of photons demonstrated here is critical for particle tracking applications in biological samples, where photons may be limited.

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