Digital Commons Network^™

Almost Finite-Time Observers For A Family Of Nonlinear Continuous-Time Systems, Frederic Mazenc, Michael Malisoff

Faculty Publications

We provide a new class of observers for a class of nonlinear systems which are not required to be affine in the unmeasured states. The observers ensure exponential convergence of the observation errors to zero, under linear output measurements. The rate of exponential convergence converges to infinity, as the growth rate of the nonlinear state-dependent part of the dynamics converges to zero, so we call the observers almost finite-time. Under global Lipschitz conditions on the state-dependent part of the dynamics, our global result ensures convergence of the observers, for all initial states. For cases where the nonlinearity is of order …

New Finite-Time And Fast Converging Observers With A Single Delay, Frédéric Mazenc, Michael Malisoff

Faculty Publications

We provide new reduced order observer designs for a key class of nonlinear dynamics. When continuous output measurements are available, we prove that our observers converge in a fixed finite time in the absence of perturbations, and we prove a robustness result under uncertainties in the output measurements and in the dynamics, which bounds the observation error in terms of bounds on the uncertainties. The observers contain a dynamic extension with only one pointwise delay, and they use the observability Gramian to eliminate an invertibility condition that was present in earlier finite time observer designs. We also provide analogs for …

On A Capacitary Strong Type Inequality And Related Capacitary Estimates, Keng Hao Ooi, Nguyen Cong Phuc

Faculty Publications

We establish a Maz'ya type capacitary inequality which resolves a special case of a conjecture by David R. Adams. As a consequence, we obtain several equivalent norms for Choquet integrals associated to Bessel or Riesz capacities. This enables us to obtain bounds for the Hardy-Littlewood maximal function in a sublinear setting.

2-Modular Matrices, James Oxley, Zach Walsh

Faculty Publications

An integer matrix A is Δ -modular if the determinant of each rank(A) × rank(A) submatrix has absolute value at most Δ. The class of 1-modular, or unimodular, matrices is of fundamental significance in both integer programming theory and matroid theory. A 1957 result of Heller shows that the maximum number of nonzero, pairwise non-parallel columns of a rank-r unimodular matrix is (r+1/2). We prove that, for each sufficiently large integer r, the maximum number of nonzero, pairwise non-parallel columns of a rank-r 2-modular matrix is (r+2/2) - 2.

Small Cocircuits In Minimally Vertically 4-Connected Matroids, James Oxley, Zach Walsh

Faculty Publications

Halin proved that every minimally k-connected graph has a vertex of degree k. More generally, does every minimally vertically k-connected matroid have a k-element cocircuit? Results of Murty and Wong give an affirmative answer when k \leq 3. We show that every minimally vertically 4-connected matroid with at least six elements has a 4-element cocircuit, or a 5-element cocircuit that contains a triangle, with the exception of a specific nonbinary 9-element matroid. Consequently, every minimally vertically 4-connected binary matroid with at least six elements has a 4-element cocircuit.

Strengthened Chain Theorems For Different Versions Of 4-Connectivity, Guoli Ding, Chengfu Qin

Faculty Publications

The chain theorem of Tutte states that every 3-connected graph can be constructed from a wheel Wn by repeatedly adding edges and splitting vertices. It is not difficult to prove the following strengthening of this theorem: every non-wheel 3-connected graph can be constructed from W4 by repeatedly adding edges and splitting vertices. In this paper, we similarly strengthen several chain theorems for various versions of 4-connectivity.

On The Asymptotic Convergence And Acceleration Of Gradient Methods, Yakui Huang, Yu Hong Dai, Xin Wei Liu, Hongchao Zhang

Faculty Publications

We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each method in the family will asymptotically zigzag between two directions. Asymptotic convergence results of the objective value, gradient norm, and stepsize are presented as well. To accelerate the family of gradient methods, we further exploit spectral properties of stepsizes to break the zigzagging pattern. In particular, a new stepsize is derived by imposing finite termination on minimizing two-dimensional strictly convex quadratic function. It is shown that, for the general quadratic function, the …

Forecasting Equity Index Volatility By Measuring The Linkage Among Component Stocks∗, Yue Qiu, Tian Xie, Jun Yu, Qiankun Zhou

Faculty Publications

The linkage among the realized volatilities of component stocks is important when modeling and forecasting the relevant index volatility. In this article, the linkage is measured via an extended Common Correlated Effects (CCEs) approach under a panel heterogeneous autoregression model where unobserved common factors in errors are assumed. Consistency of the CCE estimator is obtained. The common factors are extracted using the principal component analysis. Empirical studies show that realized volatility models exploiting the linkage effects lead to significantly better out-of-sample forecast performance, for example, an up to 32% increase in the pseudo R2. We also conduct various forecasting exercises …

Hybrid Quantum-Classical Unit Commitment, Reza Mahroo, Amin Kargarian

Faculty Publications

This paper proposes a hybrid quantum-classical algorithm to solve a fundamental power system problem called unit commitment (UC). The UC problem is decomposed into a quadratic subproblem, a quadratic unconstrained binary optimization (QUBO) subproblem, and an unconstrained quadratic subproblem. A classical optimization solver solves the first and third subproblems, while the QUBO subproblem is solved by a quantum algorithm called quantum approximate optimization algorithm (QAOA). The three subproblems are then coordinated iteratively using a three-block alternating direction method of multipliers algorithm. Using Qiskit on the IBM Q system as the simulation environment, simulation results demonstrate the validity of the proposed …

Flood-Aware Optimal Power Flow For Proactive Day-Ahead Transmission Substation Hardening, Mohadese Movahednia, Amin Kargarian

Faculty Publications

Power system components, particularly electrical substations, may be severely damaged due to flooding, resulting in prolonged power outages and resilience degradation. This problem is more severe in low-elevated regions such as Louisiana. Protective operational actions such as placing tiger dams around substations before flooding can reduce substation vulnerability, damage costs, and energy not supplied cost, thus enhancing power grid resilience. This paper proposes a stochastic mixed-integer programming model for protecting transmission substations one day before flood events using tiger dams. A flood-aware optimal power flow problem is formulated for transmission system operators with respect to the protected/unprotected status of substations. …

A Deep Learning Approach To Optimal Sampling Problems, Xinxin Wang, Xiangyu Meng, Fangfei Li

Faculty Publications

Time-triggered and event-triggered sampling methods have been widely adopted in control systems. Optimal sampling problems of the two mechanisms have also received great attentions. However, for high-dimensional systems, analytical methods have some limitations. In this study, we propose a model-free method, called soft greedy policy for neural network fitting, to calculate the optimal sampling period of the time-triggered impulse control and the optimal threshold of the event-triggered impulse control. A neural network is used to approximate the objective function and then is trained. This approach is more widely applicable than the analytical method. At the same time, compared with different …

Event-Triggered Control For Discrete-Time Systems Using A Positive Systems Approach, Frederic Mazenc, Michael Malisoff, Corina Barbalata, Zhong Ping Jiang

Faculty Publications

We provide an output feedback event-triggered controller for discrete-time linear systems. We make novel use of positive systems, interval observers, an event-triggered state estimator, and triggering times that are computed from estimator values. This provides a discrete-time analog of our recent positive systems approach for continuous-time systems. A key novel ingredient in our discrete-time event triggers is their use of vectors of absolute values, instead of the usual Euclidean norm. We illustrate the benefits of our method using a model for event-triggered BlueROV2 underwater vehicles.

Cable Decoupling And Cable-Based Stiffening Of Continuum Robots, Parsa Molaei, Nekita A. Pitts, Genevieve Palardy, Ji Su, Matthew K. Mahlin, James H. Neilan, Hunter B. Gilbert

Faculty Publications

Cable-driven continuum robots, which are robots with a continuously flexible backbone and no identifiable joints that are actuated by cables, have shown great potential for many applications in unstructured, uncertain environments. However, the standard design for a cable-driven continuum robot segment, which bends a continuous backbone along a circular arc, has many compliant modes of deformation which are uncontrolled, and which may result in buckling or other undesirable behaviors if not ameliorated. In this paper, we detail an approach for using additional cables to selectively stiffen planar cable-driven robots without substantial coupling to the actuating cables. A mechanics-based model based …

Classification Of Surface Pavement Cracks As Top-Down, Bottom-Up, And Cement-Treated Reflective Cracking Based On Deep Learning Methods, Nirmal Dhakal, Mostafa A. Elseifi, Zia U.A. Zihan, Zhongjie Zhang, Christophe N. Fillastre, Jagannath Upadhyay

Faculty Publications

The treatment and repair strategies for reflective and fatigue cracking that initiate at the pavement surface (i.e., top-down cracking) and at the bottom of the asphalt concrete layer (i.e., bottom-up cracking) are noticeably different. However, pavement management engineers are facing difficulties in identifying these cracks in the field because they usually appear in visually identical patterns. The objective of this study was to develop artificial neural network (ANN) and convolutional neural network (CNN) applications to differentiate and classify top-down, bottom-up, and cement-treated reflective cracking in in-service flexible pavements using deep-learning models. The developed CNN model achieved an accuracy of 93.8% …

Event-Triggered Prediction-Based Delay Compensation Approach, Frederic Mazenc, Michael Malisoff, Corina Barbalata

Faculty Publications

We provide a new event-triggered delay compensation approach for linear systems with arbitrarily long constant input delays. Our prediction map is expressible as a solution of a discrete time system. Our method ensures input-to-state stability. We also provide an analog under measurement delays, where the prediction map is expressible as a solution of a continuous-discrete system. Significant novel features are our combined use of matrices of absolute values and our prediction based event triggers, instead of Euclidean norms, and the fact that the predictor dynamics always has the same dimension as that of the original system. Our marine robotic example …

Estimation For Model Parameters And Maximum Power Points Of Photovoltaic Modules Using Stochastic Fractal Search Algorithms, Duy C. Huynh, Matthew W. Dunnigan, Corina Barbalata

Faculty Publications

The performance of a photovoltaic (PV) power generation system could be improved through the optimal control and operation of a PV module which is one of the fundamental components of this system. Thus, an appropriate PV module model along with precise knowledge of its parameters is necessary. This paper proposes a novel technique to estimate the source current, the saturation current of diodes, the shunt resistance, the series resistance, the ideality coefficient of diodes and the maximum power points (MPPs) of PV modules at the same time. This estimation problem can be described by the minimization of the root mean …

Event-Triggered Control For Continuous-Time Linear Systems With A Delay In The Input, Frederic Mazenc, Michael Malisoff, Corina Barbalata

Faculty Publications

We provide an event-triggered control technique for a family of linear time-varying continuous-time systems with a constant known pointwise delay in the input. We adopt a subpredictor based prediction technique, and we provide sufficient conditions that ensure that Zeno behavior does not occur. At each time, only delayed measurements are needed to implement the control. Also, the delay can be an arbitrarily large constant. We prove an input-to-state stability property for the closed-loop system, using the theory of cooperative systems. We apply our method to a gyroscopic control problem for a curve tracking dynamics arising in marine robotics.

Thermodynamic Characterization Of Grease Oxidation–Thermal Stability Via Pressure Differential Scanning Calorimetry, Jude A. Osara, Piet M. Lugt, Michael D. Bryant, Michael M. Khonsari

Faculty Publications

This study investigates and characterizes, via thermodynamic laws, a widely employed standard for measuring oxidation-thermal stability of lubricating greases—ASTM 5483—based on first-order chemical kinetics, using pressure differential scanning calorimetry (PDSC). Steps and active mechanisms in the controlled test are analyzed and modeled using energy and entropy transformations. Applying the degradation-entropy generation (DEG) theorem, oxidation induction time is related to accumulated oxidation entropy and entropy transfer by mass flow to obtain characteristic degradation coefficients. These DEG coefficients are calibrated using available measured data from the literature and subsequently used to predict induction times at various temperatures. DEG elements—trajectories, planes, and domain—presented …

Supercongruences For Rigid Hypergeometric Calabi–Yau Threefolds, Ling Long, Fang Ting Tu, Noriko Yui, Wadim Zudilin

Faculty Publications

We establish the supercongruences for the fourteen rigid hypergeometric Calabi–Yau threefolds over Q conjectured by Rodriguez-Villegas in 2003. Our first method is based on Dwork's theory of p-adic unit roots and it allows us to establish the supercongruences between the truncated hypergeometric series and the corresponding unit roots for ordinary primes. The other method makes use of the theory of hypergeometric motives, in particular, adapts the techniques from the recent work of Beukers, Cohen and Mellit on finite hypergeometric sums over Q. Essential ingredients in executing the both approaches are the modularity of the underlying Calabi–Yau threefolds and a p-adic …

Droplet-Based Fuel Property Measurements, Wanjun Dang

LSU Doctoral Dissertations

Ongoing work to find renewable biofuels to function as drop-in replacements or blending components with gasoline has identified a large number of fuel candidates. Given the vast number of potential biomass-derived fuel molecules and limited sample sizes, screening tools are required to down-select candidate fuels having desired physical properties to ensure good engine performance. This work investigates approaches for rapid screening of candidate fuels using micro-liter sample sizes targeting four properties -- surface tension, viscosity, heat of vaporization (HOV), and vapor pressure. Measurement techniques for fuel properties are developed based on unit phenomena for liquid fuel droplets including droplet oscillation …

Functional Structure Of Biomacromolecules In Plant Biomass Using Solid-State Nmr And Dynamic Nuclear Polarization, Alex Kipchirchir Kirui

LSU Doctoral Dissertations

This dissertation summarizes the recent findings on complex biomacromolecules in cell wall of plants and fungi which perform important roles in cell recognition, structural build up, and energy storage. Because of the technical difficulty in characterizing these biomacromolecules, which are often polymorphic and disordered in structure, the functional structure of these biomacromolecules remains elusive. In this dissertation, I present two solid-state nuclear magnetic resonance (ssNMR) and dynamic nuclear polarization (DNP) studies of carbohydrate-rich biosystems: the energy-rich plant biomass and disease-relevant, pathogenic fungi.

First, we have investigated the secondary cell wall of plant biomass which is a carbohydrate-rich biosystem using solid …

Limits On Parameter Estimation Of Quantum Channels, Vishal Katariya

LSU Doctoral Dissertations

The aim of this thesis is to develop a theoretical framework to study parameter estimation of quantum channels. We begin by describing the classical task of parameter estimation that we build upon. In its most basic form, parameter estimation is the task of obtaining an estimate of an unknown parameter from some experimental data. This experimental data can be seen as a number of samples of a parameterized probability distribution. In general, the goal of such a task is to obtain an estimate of the unknown parameter while minimizing its error.

We study the task of estimating unknown parameters which …

Inductor Free Methods For Breaking Dc Currents, Sudipta Sen

LSU Doctoral Dissertations

The current interruption in dc circuits is more difficult to achieve compared to the ac circuits because, unlike ac systems, dc circuits do not have the natural current zero-crossing. Presently there are three categories of basic dc breaker models namely mechanical, static, and hybrid dc breakers. As current power systems is moving more towards microgrids, DERs, Electric Vehicles (EVs), and with recent advancements in dc circuits, wide verities of dc power sources, and loads, dc breakers are very important in future system protection.

New alternate methods to break dc currents for low-voltage applications are proposed in this work. The proposed …

An Intrinsic Proof Of An Extension Of Itô’S Isometry For Anticipating Stochastic Integrals, Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha

Journal of Stochastic Analysis

No abstract provided.

First Record Of Fungal Diversity In The Tropical And Warm-Temperate Middle Miocene Climate Optimum Forests Of Eurasia, Ingrid C. Romero, Noelia B. Nuñez Otaño, Martha E. Gibson, Tyler M. Spears, C. Jolene Fairchild, Laikin Tarlton, Savannah Jones, Harvey E. Belkin, Sophie Warny, Matthew J. Pound, Jennifer M.K. O’Keefe

Faculty Publications

The middle Miocene Climate Optimum (MMCO) was the warmest interval of the last 23 million years and is one of the best analogs for proposed future climate change scenarios. Fungi play a key role in the terrestrial carbon cycle as dominant decomposers of plant debris, and through their interactions with plants and other organisms as symbionts, parasites, and endobionts. Thus, their study in the fossil record, especially during the MMCO, is essential to better understand biodiversity changes and terrestrial carbon cycle dynamics in past analogous environments, as well as to model future ecological and climatic scenarios. The fossil record also …

Point Absorber Limits To Future Gravitational-Wave Detectors, W X. Jia, H Yamamoto, K Kuns, A Effler, W X. Jia, P Fritschel, R Abbott, C Adams, R X. Adhikari, A Ananyeva, S Appert, K Arai, J S. Areeda, Y Asali, S M. Aston, C Austin, A Baer, M Ball, S W. Ballmer, S Banagiri, D Barker, L Barsotti, J Bartlett, B K. Berger, G Betzwieser, D Bhattacharjee, G Billingsley, S Biscans, C D. Blair, R M. Blair, N Bode, P Booker, R Bork, A Bramley

Faculty Publications

High-quality optical resonant cavities require low optical loss, typically on the scale of parts per million. However, unintended micron-scale contaminants on the resonator mirrors that absorb the light circulating in the cavity can deform the surface thermoelastically and thus increase losses by scattering light out of the resonant mode. The point absorber effect is a limiting factor in some high-power cavity experiments, for example, the Advanced LIGO gravitational-wave detector. In this Letter, we present a general approach to the point absorber effect from first principles and simulate its contribution to the increased scattering. The achievable circulating power in current and …

Genomics And Transcriptomics Landscapes Associated To Changes In Insulin Sensitivity In Response To Endurance Exercise Training, Louise Y. Takeshita, Peter K. Davidsen, John M. Herbert, Philipp Antczak, Matthijs K.C. Hesselink, Patrick Schrauwen, S. John Weisnagel, Jeremy M. Robbins, Robert E. Gerszten, Sujoy Ghosh, Mark A. Sarzynski, Claude Bouchard, Francesco Falciani

Division of Basic Science Faculty Publications

Despite good adherence to supervised endurance exercise training (EET), some individuals experience no or little improvement in peripheral insulin sensitivity. The genetic and molecular mechanisms underlying this phenomenon are currently not understood. By investigating genome-wide variants associated with baseline and exercise-induced changes (∆) in insulin sensitivity index (Si) in healthy volunteers, we have identified novel candidate genes whose mouse knockouts phenotypes were consistent with a causative effect on Si. An integrative analysis of functional genomic and transcriptomic profiles suggests genetic variants have an aggregate effect on baseline Si and ∆Si, focused around cholinergic signalling, including downstream calcium and chemokine signalling. …

Culture And Economics: A Literature Review, Faith Howard

Honors Capstones

No abstract provided.

An Argument For The Second Nuclear Era: Salvaging The Atomic Age In Response To Climate Change, Ian Sager

Honors Capstones

No abstract provided.

A Gravitational-Wave Measurement Of The Hubble Constant Following The Second Observing Run Of Advanced Ligo And Virgo (Vol 908, 218, 2021), B. P. Abbott, R. Abbott, T. D. Abbott

Faculty Publications

No abstract provided.