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It is common for researchers to record long, multiple time series from experiments or calculations. But sometimes there are no good models for the systems or no applicable mathematical theorems that can tell us when there are basic relationships between subsets of the time series data such as continuity, differentiability, embeddings, etc. The data is often higher dimensional and simple plotting will not guide us. At that point fitting the data to polynomials, Fourier series, etc. becomes uncertain. Even at the simplest level, having data that shows there is a function between the data subsets is useful and a negative answer means that more particular data fitting or analysis will be suspect and probably fail. We show here statistics that test time series subsets for basic mathematical properties and relations between them that not only indicate when more specific analyses are safe to do, but whether the systems are operating correctly. We apply these statistics to examples from reservoir computing where an important property of reservoir computers is that the reservoir system establishes an embedding of the drive system in order to make any other calculations with the reservoir computer successful., Comment: 15 pages, 10 figures

The CHIPS R&D project focuses on development of low-cost water Cherenkov neutrino detectors through novel design strategies and resourceful engineering. This work presents an end-to-end DAQ solution intended for a recent 5 kt CHIPS prototype, which is largely based on affordable mass-produced components. Much like the detector itself, the presented instrumentation is composed of modular arrays that can be scaled up and easily serviced. A single such array can carry up to 30 photomultiplier tubes (PMTs) accompanied by electronics that generate high voltage in-situ and deliver time resolution of up to 0.69 ns. In addition, the technology is compatible with the White Rabbit timing system, which can synchronize its elements to within 100 ps. While deployment issues did not permit the presented DAQ system to operate beyond initial evaluation, the presented hardware and software successfully passed numerous commissioning tests that demonstrated their viability for use in a large-scale neutrino detector, instrumented with thousands of PMTs., Comment: 30 pages, 28 figures, submitted to MDPI Applied Sciences, Special Issue: Advanced Neutrino Detector Development and Application

A static electric field of a few V/cm shifts the energy levels of ultracold Rydberg atoms in a magneto-optical trap. For a given principle quantum number, most of the energy levels are nearly degenerate at zero field and fan out with increasing field to form a manifold. We excite Rydberg atoms to energy levels near the center of the manifold, where the spacing is nearly harmonic, and allow them to exchange energy via resonant dipole-dipole interactions. We measure the time evolution as energy spreads away from the center of the manifold, which reveals that the system fails to thermalize for long interaction times. A computational model that includes only a few essential features of the system qualitatively agrees with this result., Comment: 6 pages, 4 figures

This paper investigates in detail the effects of noise on the performance of reservoir computing. We focus on an application in which reservoir computers are used to learn the relationship between different state variables of a chaotic system. We recognize that noise can affect differently the training and testing phases. We find that the best performance of the reservoir is achieved when the strength of the noise that affects the input signal in the training phase equals the strength of the noise that affects the input signal in the testing phase. For all the cases we examined, we found that a good remedy to noise is to low-pass filter the input and the training/testing signals; this typically preserves the performance of the reservoir, while reducing the undesired effects of noise.

Reservoir computing, a recurrent neural network paradigm in which only the output layer is trained, has demonstrated remarkable performance on tasks such as prediction and control of nonlinear systems. Recently, it was demonstrated that adding time-shifts to the signals generated by a reservoir can provide large improvements in performance accuracy. In this work, we present a technique to choose the time-shifts by maximizing the rank of the reservoir matrix using a rank-revealing QR algorithm. This technique, which is not task dependent, does not require a model of the system, and therefore is directly applicable to analog hardware reservoir computers. We demonstrate our time-shift selection technique on two types of reservoir computer: one based on an opto-electronic oscillator and the traditional recurrent network with a $tanh$ activation function. We find that our technique provides improved accuracy over random time-shift selection in essentially all cases.

While there have been many publications on potential applications of chaos to fields such as communications, radar, sonar, random signal generation, channel equalization and others, designing continuous chaotic systems is still an unsolved problem. There are a number of well known chaotic systems used for applications, but if any application is to become widely used, some way of generating many different chaotic signals is necessary. This work shows that one may use a reservoir computer to create a set of chaotic signals that are correlated but easily distinguishable from one chaotic signal with desirable properties. The ability to distinguish the new signals is demonstrated with a simple communications example., Comment: 24 pages 8 figures

We simulate the dynamics of Rydberg atoms resonantly exchanging energy via two-, three-, and four-body dipole-dipole interactions in a one-dimensional array. Using simplified models of a realistic experimental system, we study the initial state survival probability, mean level spacing, spread of entanglement, and properties of the energy eigenstates. By exploring a range of disorders and interaction strengths, we find regions in parameter space where the three- and four-body dynamics either fail to thermalize or do so slowly. The interplay between the stronger hopping and weaker field-tuned interactions gives rise to quantum many-body scar states, which play a critical role in slowing the dynamics of the three- and four-body interactions., Comment: 21 pages, 19 figures

Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters. These discrete analyses successfully determine cell types and markers; however, continuous variation within and between cell types may not be detected. We propose three topologically motivated mathematical methods for unsupervised feature selection that consider discrete and continuous transcriptional patterns on an equal footing across multiple scales simultaneously. Eigenscores ($\text{eig}_i$) rank signals or genes based on their correspondence to low-frequency intrinsic patterning in the data using the spectral decomposition of the Laplacian graph. The multiscale Laplacian score (MLS) is an unsupervised method for locating relevant scales in data and selecting the genes that are coherently expressed at these respective scales. The persistent Rayleigh quotient (PRQ) takes data equipped with a filtration, allowing the separation of genes with different roles in a bifurcation process (e.g., pseudo-time). We demonstrate the utility of these techniques by applying them to published single-cell transcriptomics data sets. The methods validate previously identified genes and detect additional biologically meaningful genes with coherent expression patterns. By studying the interaction between gene signals and the geometry of the underlying space, the three methods give multidimensional rankings of the genes and visualisation of relationships between them., Comment: 32 pages, 15 figures, 1 table. Revised and published in Entropy, special issue Applications of Topological Data Analysis in the Life Sciences

A reservoir computer is a type of dynamical system arranged to do computation. Typically, a reservoir computer is constructed by connecting a large number of nonlinear nodes in a network that includes recurrent connections. In order to achieve accurate results, the reservoir usually contains hundreds to thousands of nodes. This high dimensionality makes it difficult to analyze the reservoir computer using tools from dynamical systems theory. Additionally, the need to create and connect large numbers of nonlinear nodes makes it difficult to design and build analog reservoir computers that can be faster and consume less power than digital reservoir computers. We demonstrate here that a reservoir computer may be divided into two parts; a small set of nonlinear nodes (the reservoir), and a separate set of time-shifted reservoir output signals. The time-shifted output signals serve to increase the rank and memory of the reservoir computer, and the set of nonlinear nodes may create an embedding of the input dynamical system. We use this time-shifting technique to obtain excellent performance from an opto-electronic delay-based reservoir computer with only a small number of virtual nodes. Because only a few nonlinear nodes are required, construction of a reservoir computer becomes much easier, and delay-based reservoir computers can operate at much higher speeds.

This letter reports the design, construction, and experimental validation of a novel hand-held robot for in-office laser surgery of the vocal folds. In-office endoscopic laser surgery is an emerging trend in Laryngology: It promises to deliver the same patient outcomes of traditional surgical treatment (i.e., in the operating room), at a fraction of the cost. Unfortunately, office procedures can be challenging to perform; the optical fibers used for laser delivery can only emit light forward in a line-of-sight fashion, which severely limits anatomical access. The robot we present in this letter aims to overcome these challenges. The end effector of the robot is a steerable laser fiber, created through the combination of a thin optical fiber (0.225 mm) with a tendon-actuated Nickel-Titanium notched sheath that provides bending. This device can be seamlessly used with most commercially available endoscopes, as it is sufficiently small (1.1 mm) to pass through a working channel. To control the fiber, we propose a compact actuation unit that can be mounted on top of the endoscope handle, so that, during a procedure, the operating physician can operate both the endoscope and the steerable fiber with a single hand. We report simulation and phantom experiments demonstrating that the proposed device substantially enhances surgical access compared to current clinical fibers.

A reservoir computer is a way of using a high dimensional dynamical system for computation. One way to construct a reservoir computer is by connecting a set of nonlinear nodes into a network. Because the network creates feedback between nodes, the reservoir computer has memory. If the reservoir computer is to respond to an input signal in a consistent way (a necessary condition for computation), the memory must be fading; that is, the influence of the initial conditions fades over time. How long this memory lasts is important for determining how well the reservoir computer can solve a particular problem. In this paper I describe ways to vary the length of the fading memory in reservoir computers. Tuning the memory can be important to achieve optimal results in some problems; too much or too little memory degrades the accuracy of the computation.

The topology of a network associated with a reservoir computer is often taken so that the connectivity and the weights are chosen randomly. Optimization is hardly considered as the parameter space is typically too large. Here we investigate this problem for a class of reservoir computers for which we obtain a decomposition of the reservoir dynamics into modes, which can be computed independently of one another. Each mode depends on an eigenvalue of the network adjacency matrix. We then take a parametric approach in which the eigenvalues are parameters that can be appropriately designed and optimized. In addition, we introduce the application of a time shift to each individual mode. We show that manipulations of the individual modes, either in terms of the eigenvalues or the time shifts, can lead to dramatic reductions in the training error.

It has been demonstrated that cellular automata had the highest computational capacity at the edge of chaos, the parameter at which their behavior transitioned from ordered to chaotic. This same concept has been applied to reservoir computers; a number of researchers have stated that the highest computational capacity for a reservoir computer is at the edge of chaos, although others have suggested that this rule is not universally true. Because many reservoir computers do not show chaotic behavior but merely become unstable, it is felt that a more accurate term for this instability transition is the "edge of stability"Here I find two examples where the computational capacity of a reservoir computer decreases as the edge of stability is approached; in one case, because generalized synchronization breaks down, and in the other case because the reservoir computer is a poor match to the problem being solved. The edge of stability as an optimal operating point for a reservoir computer is not in general true, although it may be true in some cases.

In this paper, we describe the iterative participatory design of SOPHIE, an online virtual patient for feedback-based practice of sensitive patient-physician conversations, and discuss an initial qualitative evaluation of the system by professional end users. The design of SOPHIE was motivated from a computational linguistic analysis of the transcripts of 383 patient-physician conversations from an essential office visit of late stage cancer patients with their oncologists. We developed methods for the automatic detection of two behavioral paradigms, lecturing and positive language usage patterns (sentiment trajectory of conversation), that are shown to be significantly associated with patient prognosis understanding. These automated metrics associated with effective communication were incorporated into SOPHIE, and a pilot user study identified that SOPHIE was favorably reviewed by a user group of practicing physicians.

Reservoir computers are a type of neuromorphic computer that may be built a an analog system, potentially creating powerful computers that are small, light and consume little power. Typically a reservoir computer is build by connecting together a set of nonlinear nodes into a network; connecting the nonlinear nodes may be difficult or expensive, however. This work shows how a reservoir computer may be expanded by adding functions to its output. The particular functions described here are linear filters, but other functions are possible. The design and construction of linear filters is well known, and such filters may be easily implemented in hardware such as field programmable gate arrays (FPGA's). The effect of adding filters on the reservoir computer performance is simulated for a signal fitting problem, a prediction problem and a signal classification problem.

A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. In this work, three dimension estimation methods, false nearest neighbor, covariance and Kaplan-Yorke dimensions, are used to estimate the dimension of the reservoir dynamical system. It is shown that the signals in the reservoir system exist on a relatively low dimensional surface. Changing the spectral radius of the reservoir network can increase the fractal dimension of the reservoir signals, leading to an increase in testing error., Comment: submitted to Chaos