Deciphering protein folding and unfolding pathways under tension is essential for deepening our understanding of fundamental biological mechanisms. Such insights hold the promise of developing treatments for a range of debilitating and fatal conditions, including muscular disorders like Duchenne Muscular Dystrophy and neurodegenerative diseases such as Parkinson's disease. Single molecule force spectroscopy (SMFS) is a powerful technique for investigating forces involved in protein domains folding and unfolding. However, SMFS trials often involve multiple protein molecules, necessitating filtering to isolate measurements from single-molecule trials. Currently, manual visual inspection is the primary method for classifying single-molecule data; a process that is both time-consuming and requires significant expertise. Here, we both apply state-of-the-art machine learning models and present a novel deep learning model tailored to SMFS data. The proposed model employs a dual-branch fusion strategy; one branch integrates the physics of protein molecules, and the other operates independently of physical constraints. This model automates the isolation of single-molecule measurements, significantly enhancing data processing efficiency. To train and validate our approach, we developed a physics-based Monte Carlo engine to simulate force spectroscopy datasets, including trials involving single molecules, multiple molecules, and no molecules. Our model achieves state-of-the-art performance, outperforming five baseline methods on both simulated and experimental datasets. It attains nearly 100\% accuracy across all simulated datasets and an average accuracy of $79.6 \pm 5.2$\% on experimental datasets, using only $\sim$30 training samples, surpassing baseline methods by 11.4\%. Notably, even without expert annotations on experimental data, the model achieves an average accuracy of $72.0 \pm 5.9$\% when pre-trained on corresponding simulated datasets. With our deep learning approach, the time required to extract meaningful statistics from single-molecule SMFS trials is reduced from a day to under an hour. This work results in SMFS experimental datasets from four important protein molecules crucial to many biological pathways. To support further research, we have made our datasets publicly available and provided a Python-based toolbox (https://github.com/SalapakaLab-SIMBioSys/SMFS-Identification).

In this article, the optimal sample complexity of learning the underlying interactions or dependencies of a Linear Dynamical System (LDS) over a Directed Acyclic Graph (DAG) is studied. We call such a DAG underlying an LDS as dynamical DAG (DDAG). In particular, we consider a DDAG where the nodal dynamics are driven by unobserved exogenous noise sources that are wide-sense stationary (WSS) in time but are mutually uncorrelated, and have the same power spectral density (PSD). Inspired by the static DAG setting, a metric and an algorithm based on the PSD matrix of the observed time series are proposed to reconstruct the DDAG. It is shown that the optimal sample complexity (or length of state trajectory) needed to learn the DDAG is $n=\Theta(q\log(p/q))$, where $p$ is the number of nodes and $q$ is the maximum number of parents per node. To prove the sample complexity upper bound, a concentration bound for the PSD estimation is derived, under two different sampling strategies. A matching min-max lower bound using generalized Fano’s inequality also is provided, thus showing the order optimality of the proposed algorithm. The codes used in the paper are available at \url{https://github.com/Mishfad/Learning-Dynamical-DAGs}

A distributed controller for secondary control problems in microgrids with grid-forming (GFM) inverter-based resources (IBRs) is developed. The controller is based on distributed optimization and is synthesized and implemented distributively enabling each GFM IBR to utilize decentralized measurements and the neighborhood information in the communication network. We present a convergence analysis establishing voltage regulation and reactive power sharing properties. A controller-hardware-in-the-loop experiment is conducted to evaluate the performance of the proposed controller. The experimental results corroborate the efficacy of the proposed distributed controller for secondary control.

We consider the framework of distributed aggregation of Distributed Energy Resources (DERs) in power networks to provide ancillary services to the power grid. Existing aggregation schemes work under the assumption of trust and honest behavior of the DERs and can suffer when that is not the case. In this article, we develop a distributed detection scheme that allows the DERs to detect and isolate the maliciously behaving DERs. We propose a model for the maliciously behaving DERs and show that the proposed distributed scheme leads to the detection of the malicious DERs. Further, augmented with the distributed power apportioning algorithm the proposed scheme provides a framework for resilient distributed power apportioning for ancillary service dispatch in power networks. A controller-hardware-in-the-loop (CHIL) experimental setup is developed to evaluate the performance of the proposed resilient distributed power apportioning scheme on an 8-commercial building distribution network (Central Core) connected to a 55 bus distribution network (External Power Network) based on the University of Minnesota Campus. A diversity of DERs and loads are included in the network to generalize the applicability of the framework. The experimental results corroborate the efficacy of the proposed resilient distributed power apportioning for ancillary service dispatch in power networks.

We consider a networked linear dynamical system with p agents/nodes. We study the problem of learning the underlying graph of interactions/dependencies from observations of the nodal trajectories over a time-interval T. We present a regularized non-casual consistent estimator for this problem and analyze its sample complexity over two regimes: (a) where the interval T consists of n i.i.d. observation windows of length T/n (restart and record), and (b) where T is one continuous observation window (consecutive). Using the theory of M-estimators, we show that the estimator recovers the underlying interactions, in either regime, in a time-interval that is logarithmic in the system size p. To the best of our knowledge, this is the first work to analyze the sample complexity of learning linear dynamical systems driven by unobserved not-white wide-sense stationary (WSS) inputs.

Power-hardware-in-the-loop (PHIL) simulations of grid-forming (GFM) inverter systems facilitate the testing of drastic scenarios, such as on-grid to off-grid transitions and islanded microgrid operations without a stiff grid. To the authors’ best knowledge, most studies in the literature focus on PHIL simulations for grid-following inverter systems. Only a few studies focus on GFM inverters, and those are challenging and problematic, especially for high-power applications. This article proposes a novel PHIL simulation platform that enables interfacing high-power GFM inverter systems. The paper proposes the concept of a virtual GFM inverter as a part of the proposed PHIL interface. This addition of a virtual GFM inverter in the PHIL interface expands the conventional ideal transformer model (ITM) method and enables it to overcome the issues of instability of existing ITM methods. In the validation stage, a PHIL experiment is conducted on a three-phase, 480-V, 125-kVA GFM inverter system with the proposed interfacing method. The results corroborate that the proposed PHIL simulation method performs well and is stable for GFM inverter systems.

For smooth transition from islanded mode to grid-tied mode, synchronization to the incoming grid is required for any islanded microgrid. This paper is proposing a novel active synchronization method for such islanded microgrids. In this method, the proposed synchronization controller compensates the phase angle and voltage magnitude difference between islanded microgrid side and the incoming grid side to zero by adjusting the droop laws of all grid-forming (GFM) inverter systems of the microgrid dynamically via secondary control layer of microgrid hierarchical control architecture. It is analytically shown that compensation on only phase angle and voltage magnitude is sufficient for synchronization as frequency is compensated by this proposed method indirectly by the phase angle compensation. A systematic approach for tuning the proposed synchronization controllers are provided. For validation, a controller hardware-in-the-loop-based real-time simulation is conducted using OP5700 RT-simulator manufactured by OPAL-RT on a 3-phase, 480V, 500kVA, 55-bus urban microgrid system with 6 GFM inverters where control of 2 GFM inverters are realized on low-cost Texas-Instruments TMS28379D Delfino controller boards. The proposed method is relatively fast and enables a smooth re-connection of microgrid with grid with less transients.

Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of mixture distributions is of fundamental importance in many of these applications. This article provides sharp bounds on the entropy concavity deficit, which is the difference between the differential entropy of the mixture and the weighted sum of differential entropies of constituent components. Toward establishing lower and upper bounds on the concavity deficit, results that are of importance in their own right are obtained. In order to obtain nontrivial upper bounds, properties of the skew-divergence are developed and notions of “skew”$f$-divergences are introduced; a reverse Pinsker inequality and a bound on Jensen-Shannon divergence are obtained along the way. Complementary lower bounds are derived with special attention paid to the case that corresponds to independent summation of a continuous and a discrete random variable. Several applications of the bounds are delineated, including to mutual information of additive noise channels, thermodynamics of computation, and functional inequalities.

Consensus-based distributed algorithms are well suited for coordination among agents in a cyber-physical system. These distributed schemes, however, suffer from their vulnerability to cyber attacks that are aimed at manipulating data and control ow. In this article, we present a novel distributed method for detecting the presence of such intrusions for a distributed multi-agent system following ratio consensus. We employ a Max-Min protocol to develop low cost, easy to implement detection strategies where each participating node detects the intrusion independently, eliminating the need for a trusted certifying agent in the network. The effectiveness of the detection method is demonstrated by numerical simulations on a 1000 node network to demonstrate the efficacy and simplicity of implementation.

Motivated by the entropy computations relevant to the evaluation of decrease in entropy in bit reset operations, the authors investigate the deficit in an entropic inequality involving two independent random variables, one continuous and the other discrete. In the case where the continuous random variable is Gaussian, we derive strong quantitative bounds on the deficit in the inequality. More explicitly it is shown that the decay of the deficit is sub-Gaussian with respect to the reciprocal of the standard deviation of the Gaussian variable. What is more, up to rational terms these results are shown to be sharp.

Intracellular transport is an essential function in eucaryotic cells, facilitated by motor proteins-proteins converting chemical energy into kinetic energy. It is understood that motor proteins work in teams enabling unidirectional and bidirectional transport of intracellular cargo over long distances. Disruptions of the underlying transport mechanisms, often caused by mutations that alter single motor characteristics, are known to cause neurodegenerative diseases. For example, phosphorylation of kinesin motor domain at the serine residue is implicated in Huntington's disease, with a recent study of phosphorylated and phosphomimetic serine residues indicating lowered single motor stalling forces. In this article we report the effects of mutations of this nature on transport properties of cargo carried by multiple wild-type and mutant motors. Results indicate that mutants with altered stall forces might determine the average velocity and run-length even when they are outnumbered by wild type motors in the ensemble. It is shown that mutants gain a competitive advantage and lead to an increase in the expected run-length when the load on the cargo is in the vicinity of the mutant's stalling force or a multiple of its stalling force. A separate contribution of this article is the development of a semi-analytic method to analyze transport of cargo by multiple motors of multiple types. The technique determines transition rates between various relative configurations of motors carrying the cargo using the transition rates between various absolute configurations. This enables a computation of biologically relevant quantities like average velocity and run-length without resorting to Monte Carlo simulations. It can also be used to introduce alterations of various single motor parameters to model a mutation and to deduce effects of such alterations on the transport of a common cargo by multiple motors. Our method is easily implementable and we provide a software package for general use.

Inter-symbol interference (ISI) channels with data dependent Gauss Markov noise have been used to model read channels in magnetic recording and other data storage systems. The Viterbi algorithm can be adapted for performing maximum likelihood sequence detection in such channels. However, the problem of finding an analytical upper bound on the bit error rate of the Viterbi detector in this case has not been fully investigated. Current techniques rely on an exhaustive enumeration of short error events and determine the BER using a union bound. In this work, we consider a subset of the class of ISI channels with data dependent Gauss-Markov noise. We derive an upper bound on the pairwise error probability (PEP) between the transmitted bit sequence and the decoded bit sequence that can be expressed as a product of functions depending on current and previous states in the (incorrect) decoded sequence and the (correct) transmitted sequence. In general, the PEP is asymmetric. The average BER over all possible bit sequences is then determined using a pairwise state diagram. Simulations results which corroborate the analysis of upper bound, demonstrate that analytic bound on BER is tight in high SNR regime. In the high SNR regime, our proposed upper bound obviates the need for computationally expensive simulation.

There is an increasing need for high density data storage devices driven by the increased demand of consumer electronics. In this work, we consider a data storage system that operates by encoding information as topographic profiles on a polymer medium. A cantilever probe with a sharp tip (few nm radius) is used to create and sense the presence of topographic profiles, resulting in a density of few Tb per in.2. The prevalent mode of using the cantilever probe is the static mode that is harsh on the probe and the media. In this article, the high quality factor dynamic mode operation, that is less harsh on the media and the probe, is analyzed. The read operation is modeled as a communication channel which incorporates system memory due to inter-symbol interference and the cantilever state. We demonstrate an appropriate level of abstraction of this complex nanoscale system that obviates the need for an involved physical model. Next, a solution to the maximum likelihood sequence detection problem based on the Viterbi algorithm is devised. Experimental and simulation results demonstrate that the performance of this detector is several orders of magnitude better than the performance of other existing schemes.

There is an ever increasing need for storing data in small form factors driven by the ubiquitous use and increased demands of consumer electronics. A new data storage approach that achieves a few Tb per in2areal densities, utilizes a cantilever probe with a sharp tip that can be used to deform and assess the topography of a polymer medium. The information may be encoded by means of topographic profiles on the medium. The prevalent mode of using the cantilever probe is the static mode that is known to be harsh on the probe and the media. In this paper, the high quality factor dynamic mode operation, which is known to be less harsh on the media and the probe, is analyzed for probe based high density data storage purposes. It is demonstrated that an appropriate level of abstraction is possible that obviates the need for an involved physical model. The read operation is modeled as a communication channel which incorporates the inherent system memory due to the intersymbol interference and the cantilever state that can be identified using training data. Using the identified model, a solution to the maximum likelihood sequence detection problem based on the Viterbi algorithm is devised. Experimental and simulation results demonstrate that the performance of this detector is several orders of magnitude better than the other existing schemes and confirms performance gains that can render the dynamic mode operation feasible for high density data storage purposes.

Several methods have been developed for joint working and spare capacity planning in survivable wavelength-division-multiplexing (WDM) networks. These methods have considered a static traffic demand and optimized the network cost assuming various cost models and survivability paradigms. Our interest primarily lies in network operation under dynamic traffic. We formulate various operational phases in survivable WDM networks as a single integer linear programming (ILP) optimization problem. This common framework avoids service disruption to the existing connections. However, the complexity of the optimization problem makes the formulation applicable only for network provisioning and offline reconfiguration. The direct use of this method for online reconfiguration remains limited to small networks with few tens of wavelengths. Our goal in this paper is to develop an algorithm for fast online reconfiguration. We propose a heuristic algorithm based on LP relaxation technique to solve this problem. Since the ILP variables are relaxed, we provide a way to derive a feasible solution from the relaxed problem. The algorithm consists of two steps. In the first step, the network topology is processed based on the demand set to be provisioned. This preprocessing step is done to ensure that the LP yields a feasible solution. The preprocessing step in our algorithm is based on: (a) the assumption that in a network, two routes between any given node pair are sufficient to provide effective fault tolerance and (b) an observation on the working of the ILP for such networks. In the second step, using the processed topology as input, we formulate and solve the LP problem. Interestingly, the LP relaxation heuristic yielded a feasible solution to the ILP in all our experiments. We provide insights into why the LP formulation yields a feasible solution to the ILP We demonstrate the use of our algorithm on practical size backbone networks with hundreds of wavelengths per link. The results indicate that the run time of our heuristic algorithm is fast enough (in order of seconds) to be used for online reconfiguration.