Stability Analysis of Discrete-Time Linear Complementarity Systems

A Discrete-Time Linear Complementarity System (DLCS) is a dynamical system in discrete time whose state evolution is governed by linear dynamics in states and algebraic variables that solve a Linear Complementarity Problem (LCP). The DLCS is the hybrid dynamical system that is the discrete-time counterpart of the well-known Linear Complementarity System (LCS). We derive sufficient conditions for Lyapunov stability of a DLCS when using a quadratic Lyapunov function that depends only on the state variables and a quadratic Lyapunov function that depends both on the state and the algebraic variables. The sufficient conditions require checking the feasibility of a copositive program over nonconvex cones. Our results only assume that the LCP is solvable and do not require the solutions to be unique. We devise a novel, exact cutting plane algorithm for the verification of stability and the computation of the Lyapunov functions. To the best of our knowledge, our algorithm is the first exact approach for stability verification of DLCS. A number of numerical examples are presented to illustrate the approach. Though our main object of study in this paper is the DLCS, the proposed algorithm can be readily applied to the stability verification of LCS. In this context, we show the equivalence between the stability of a LCS and the DLCS, resulting from a time-stepping procedure applied to the LCS for all sufficiently small time steps

Data‐enabled cognitive modeling: Validating student engineers’ fuzzy design‐based decision‐making in a virtual design problem

The ability of future engineering professionals to solve complex real‐world problems depends on their design education and training. Because engineers engage with open‐ended problems in which there are unknown parameters and multiple competing objectives, they engage in fuzzy decision‐making, a method of making decisions that takes into account inherent imprecisions and uncertainties in the real world. In the design‐based decision‐making field, few studies have applied fuzzy decision‐making models to actual decision‐making process data. Thus, in this study, we use datasets on student decision‐making processes to validate approximate fuzzy models of student decision‐making, which we call data‐enabled cognitive modeling. The results of this study (1) show that simulated design problems provide rich datasets that enable analysis of student design decision‐making and (2) validate models of student design cognition that can inform future design curricula and help educators understand how students think about design problems

Transcriptome-Based Exon Capture Enables Highly Cost-Effective Comparative Genomic Data Collection At Moderate Evolutionary Scales

Background: To date, exon capture has largely been restricted to species with fully sequenced genomes, which has precluded its application to lineages that lack high quality genomic resources. We developed a novel strategy for designing array-based exon capture in chipmunks (Tamias) based on de novo transcriptome assemblies. We evaluated the performance of our approach across specimens from four chipmunk species. Results: We selectively targeted 11,975 exons (similar to 4 Mb) on custom capture arrays, and enriched over 99% of the targets in all libraries. The percentage of aligned reads was highly consistent (24.4-29.1%) across all specimens, including in multiplexing up to 20 barcoded individuals on a single array. Base coverage among specimens and within targets in each species library was uniform, and the performance of targets among independent exon captures was highly reproducible. There was no decrease in coverage among chipmunk species, which showed up to 1.5% sequence divergence in coding regions. We did observe a decline in capture performance of a subset of targets designed from a much more divergent ground squirrel genome (30 My), however, over 90% of the targets were also recovered. Final assemblies yielded over ten thousand orthologous loci (similar to 3.6 Mb) with thousands of fixed and polymorphic SNPs among species identified. Conclusions: Our study demonstrates the potential of a transcriptome-enabled, multiplexed, exon capture method to create thousands of informative markers for population genomic and phylogenetic studies in non-model species across the tree of life

Temporal genomic contrasts reveal rapid evolutionary responses in an alpine mammal during recent climate change

Many species have experienced dramatic changes in their abundance and distribution during recent climate change, but it is often unclear whether such ecological responses are accompanied by evolutionary change. We used targeted exon sequencing of 294 museum specimens (160 historic, 134 modern) to generate independent temporal genomic contrasts spanning a century of climate change (1911–2012) for two co-distributed chipmunk species: an endemic alpine specialist (Tamias alpinus) undergoing severe range contraction and a stable mid-elevation species (T. speciosus). Using a novel analytical approach, we reconstructed the demographic histories of these populations and tested for evidence of recent positive directional selection. Only the retracting species showed substantial population genetic fragmentation through time and this was coupled with positive selection and substantial shifts in allele frequencies at a gene, Alox15, involved in regulation of inflammation and response to hypoxia. However, these rapid population and gene-level responses were not detected in an analogous temporal contrast from another area where T. alpinus has also undergone severe range contraction. Collectively, these results highlight that evolutionary responses may be variable and context dependent across populations, even when they show seemingly synchronous ecological shifts. Our results demonstrate that temporal genomic contrasts can be used to detect very recent evolutionary responses within and among contemporary populations, even in the face of complex demographic changes. Given the wealth of specimens archived in natural history museums, comparative analyses of temporal population genomic data have the potential to improve our understanding of recent and ongoing evolutionary responses to rapidly changing environments

Topics in parallel integer optimization

Ph.D.Martin Savelsberg

Congestion analysis for global routing via integer programming

Abstract — This work presents a fast and flexible framework for congestion analysis at the global routing stage. It captures various factors that contribute to congestion in modern designs. The framework is a practical realization of a proposed parameterized integer programming formulation. The formulation minimizes overflow inside a set of regions covering the layout which is defined by an input resolution parameter. A resolution lower than the global routing grid-graph creates regions that are larger in size than the global-cells. The maximum resolution case simplifies the formulation to minimizing the total overflow which has been traditionally used as a metric to evaluate routability. A novel contribution of this work is to demonstrate that for a small analysis time budget, regional minimization of overflow with a lower resolution allows a more accurate identification of the routing congestion hotspot locations, compared to minimizing the total overflow. It allows generating a more accurate congestion heatmap. The other contributions include several new ideas for a practical realization of the formulation for industrysized benchmark instances some of which are also improvements to existing global routing procedures. This work also describes coalesCgrip, a simpler variation of our framework which was used to evaluate the ISPD 2011 contest. I