Optimal Subharmonic Entrainment

For many natural and engineered systems, a central function or design goal is the synchronization of one or more rhythmic or oscillating processes to an external forcing signal, which may be periodic on a different time-scale from the actuated process. Such subharmonic synchrony, which is dynamically established when N control cycles occur for every M cycles of a forced oscillator, is referred to as N:M entrainment. In many applications, entrainment must be established in an optimal manner, for example by minimizing control energy or the transient time to phase locking. We present a theory for deriving inputs that establish subharmonic N:M entrainment of general nonlinear oscillators, or of collections of rhythmic dynamical units, while optimizing such objectives. Ordinary differential equation models of oscillating systems are reduced to phase variable representations, each of which consists of a natural frequency and phase response curve. Formal averaging and the calculus of variations are then applied to such reduced models in order to derive optimal subharmonic entrainment waveforms. The optimal entrainment of a canonical model for a spiking neuron is used to illustrate this approach, which is readily extended to arbitrary oscillating systems

Complex Dynamics in Dedicated / Multifunctional Neural Networks and Chaotic Nonlinear Systems

We study complex behaviors arising in neuroscience and other nonlinear systems by combining dynamical systems analysis with modern computational approaches including GPU parallelization and unsupervised machine learning. To gain insights into the behaviors of brain networks and complex central pattern generators (CPGs), it is important to understand the dynamical principles regulating individual neurons as well as the basic structural and functional building blocks of neural networks. In the first section, we discuss how symbolic methods can help us analyze neural dynamics such as bursting, tonic spiking and chaotic mixed-mode oscillations in various models of individual neurons, the bifurcations that underlie transitions between activity types, as well as emergent network phenomena through synergistic interactions seen in realistic neural circuits, such as network bursting from non-intrinsic bursters. The second section is focused on the origin and coexistence of multistable rhythms in oscillatory neural networks of inhibitory coupled cells. We discuss how network connectivity and intrinsic properties of the cells affect the dynamics, and how even simple circuits can exhibit a variety of mono/multi-stable rhythms including pacemakers, half-center oscillators, multiple traveling-waves, fully synchronous states, as well as various chimeras. Our analyses can help generate verifiable hypotheses for neurophysiological experiments on central pattern generators. In the last section, we demonstrate the inter-disciplinary nature of this research through the applications of these techniques to identify the universal principles governing both simple and complex dynamics, and chaotic structure in diverse nonlinear systems. Using a classical example from nonlinear laser optics, we elaborate on the multiplicity and self-similarity of key organizing structures in 2D parameter space such as homoclinic and heteroclinic bifurcation curves, Bykov T-point spirals, and inclination flips. This is followed by detailed computational reconstructions of the spatial organization and 3D embedding of bifurcation surfaces, parametric saddles, and isolated closed curves (isolas). The generality of our modeling approaches could lead to novel methodologies and nonlinear science applications in biological, medical and engineering systems

Control strategies of 3-cell Central Pattern Generator via global stimuli

The study of the synchronization patterns of small neuron networks that control several biological processes has become an interesting growing discipline. Some of these synchronization patterns of individual neurons are related to some undesirable neurological diseases, and they are believed to play a crucial role in the emergence of pathological rhythmic brain activity in different diseases, like Parkinson''s disease. We show how, with a suitable combination of short and weak global inhibitory and excitatory stimuli over the whole network, we can switch between different stable bursting patterns in small neuron networks (in our case a 3-neuron network). We develop a systematic study showing and explaining the effects of applying the pulses at different moments. Moreover, we compare the technique on a completely symmetric network and on a slightly perturbed one (a much more realistic situation). The present approach of using global stimuli may allow to avoid undesirable synchronization patterns with nonaggressive stimuli

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity

This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasi-local black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity. Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24 November, 2006), part of the "General Relativity Trimester" at the Institut Henri Poincare (Fall 2006). Comments and references added. Typos corrected. Submitted to Classical and Quantum Gravit

Research and Creative Activity, July 1, 2020-June 30, 2021: Major Sponsored Programs and Faculty Accomplishments in Research and Creative Activity, University of Nebraska-Lincoln

Foreword by Bob Wilhelm, Vice Chancellor for Research and Economic Development, University of Nebraska-Lincoln: This booklet highlights successes in research, scholarship and creative activity by University of Nebraska–Lincoln faculty during the fiscal year running July 1, 2020, to June 30, 2021. It lists investigators, project titles and funding sources on major grants and sponsored awards received during the year; fellowships and other recognitions and honors bestowed on our faculty; books and chapters published by faculty; performances, exhibitions and other examples of creative activity; patents and licensing agreements issued; National Science Foundation I-CORPS teams; and peer-reviewed journal articles and conference presentations. In recognition of the important role faculty have in the undergraduate experience at Nebraska, this booklet notes the students and mentors participating in the Undergraduate Creative Activities and Research Experience (UCARE) and the First-Year Research Experience (FYRE) programs. While metrics cannot convey the full impact of our work, they are tangible measures of growth. A few achievements of note: • UNL achieved a record $320 million in total research expenditures in FY 2020, a 43• Our faculty earned 1,508 sponsored research awards in FY 2020. University-sponsored industry activity also spurred economic growth for Nebraska. • Nebraska Innovation Campus created 1,948 jobs statewide and had a total economic impact of$372 million. • Industry sponsorship supported $19.2 million in research expenditures. • NUtech Ventures brought in$6.48 million in licensing income. I applaud the Nebraska Research community for its determination and commitment during a challenging year. Your hard work has made it possible for our momentum to continue growing. Our university is poised for even greater success. The Grand Challenges initiative provides a framework for developing bold ideas to solve society’s greatest issues, which is how we will have the greatest impact as an institution. Please visit research.unl.edu/grandchallenges to learn more. We’re also renewing our campus commitment to a journey of anti-racism and racial equity, which is among the most important work we’ll do. I am pleased to present this record of accomplishments. Contents Awards of $5 Million or More Awards of$1 Million to $4,999,999 Awards of$250,000 to $999,999 50 Early Career Awards Arts and Humanities Awards of$250,000 or More Arts and Humanities Awards of $50,000 to$249,999 Arts and Humanities Awards of $5,000 to$49,999 Patents License Agreements National Science Foundation Innovation Corps Teams Creative Activity Books Recognitions and Honors Journal Articles 105 Conference Presentations UCARE and FYRE Projects Glossar

Annual Research Report, 2010-2011

Annual report of collaborative research projects of Old Dominion University faculty and students in partnership with business, industry and government.https://digitalcommons.odu.edu/or_researchreports/1000/thumbnail.jp