Spatiotemporal patterns of firearm acquisition in the United States in different presidential terms.

This study develops mathematical tools and approaches to investigate spatiotemporal patterns of firearm acquisition in the U.S. complemented by hypothesis testing and statistical analysis. First, state-level and nation-level instant background check (BC) data are employed as proxy of firearm acquisition corresponding to 1999-2021. The relative-phase time-series of BC in each U.S. state is recovered and utilized to calculate the time-series of the U.S. states' synchronization degree. We reveal that U.S. states present a high-level degree of synchronization except in 2010-2011 and after 2018. Comparing these results with respect to a sitting U.S. president provides additional information: specifically, any two presidential terms are characterized by statistically different synchronization degrees except G. W. Bush's first term and B. H. Obama's second term. Next, to detail variations of BC, short-time Fourier transform, dimensionality reduction techniques, and diffusion maps are implemented within a time-frequency representation. Firearm acquisition in the high frequency band is described by a low-dimensional embedding, in the form of a plane with two embedding coordinates. Data points on the embedding plane identify separate clusters that signify state transitions in the original BC data with respect to different time windows. Through this analysis, we reveal that the frequency content of the BC data has a time-dependent characteristic. By comparing the diffusion map at hand with respect to a presidential term, we find that at least one of the embedding coordinates presents statistically significant variations between any two presidential terms except B. H. Obama's first term and D. J. Trump's pre-COVID term. The results point at a possible interplay between firearm acquisition in the U.S. and a presidential term.

Cellular automata modeling suggests symmetric stem-cell division, cell death, and cell drift as key mechanisms driving adult spinal cord growth in teleost fish.

Adult neurogenesis - the generation of neurons during adulthood - is intensively studied, yet little is known about its consequences at the tissue level. In the teleost fish Apteronotus leptorhynchus, morphometric analysis has revealed that the total number of cells in the spinal cord increases continuously throughout adulthood, driven by the activity of neurogenic stem/progenitor cells in both the ependymal layer at the central canal and in the radially located parenchyma. This net increase in cell numbers demonstrates cellular addition, as opposed to cellular turnover which appears to be the common outcome of adult neurogenesis in mammals. Grounded on a comprehensive set of quantitative data generated through high-resolution mapping of stem cells and their progeny, we constructed a cellular automata model of the stem-cell-driven growth of the spinal cord. Simulations based on this model suggest that three cellular mechanisms play a critical role for promoting sustained tissue growth and acquisition of correct form of the spinal cord, including the development of the ependymal layer and the parenchyma: the number of symmetric stem-cell divisions versus asymmetric divisions; the probability of the progeny of progenitor cells to undergo cell death; and the radial drifting of cells.

Improving on transfer entropy-based network reconstruction using time-delays: Approach and validation.

Transfer entropy constitutes a viable model-free tool to infer causal relationships between two dynamical systems from their time-series. In an information-theoretic sense, transfer entropy associates a cause-and-effect relationship with directed information transfer, such that one may improve the prediction of the future of a dynamical system from the history of another system. Recent studies have proposed the use of transfer entropy to reconstruct networks, but the inherent dyadic nature of this metric challenges the development of a robust approach that can discriminate direct from indirect interactions between nodes. In this paper, we seek to fill this methodological gap through the cogent integration of time-delays in the transfer entropy computation. By recognizing that information transfer in the network is bound by a finite speed, we relate the value of the time-delayed transfer entropy between two nodes to the number of walks between them. Upon this premise, we lay out the foundation of an alternative framework for network reconstruction, which we illustrate through closed-form results on three-node networks and numerically validate on larger networks, using examples of Boolean models and chaotic maps.

Stochastic cellular automata model of tumorous neurosphere growth: Roles of developmental maturity and cell death.

The neurosphere assay is a powerful in vitro system for studying stem/progenitor-cell-driven tissue growth. By employing a stochastic cellular automata model, we simulated the development of tumorous neurospheres in response to transformation of a randomly selected progenitor cell into a brain tumor stem cell. Simulated tumorous neurospheres were distinguished from normal neurospheres by their size, which exceeded that of normal neurospheres typically manifold. A decisive factor that determined whether brain tumor stem cells gave rise to tumorous neurospheres was their ability to escape encapsulation by neighboring cells, which suppressed mitotic activity through contact inhibition. In our simulations, the likelihood of tumorigenesis was strongly negatively correlated with the developmental maturity of the neurospheres in which the transformation of a progenitor cell into a brain tumor stem cell was induced. This likelihood was furthermore modulated by the probability of the progeny of dividing cells to undergo cell death. In developmentally immature neurospheres, the number of normal neurospheres, relative to the number of tumorous neurospheres, increased with increasing cell death probability. Markedly, in developmentally mature neurospheres the opposite effect was observed. This dichotomous effect of cell death on simulated tumor progression provides theoretical support for the seemingly paradoxical finding made by other authors in experimental studies that anti-cancer therapies based on induction of apoptosis may both promote and suppress tumor growth.

Fast consensus in a large-scale multi-agent system with directed graphs using time-delayed measurements.

This article is on fast-consensus reaching in a class of multi-agent systems (MAS). We present an analytical approach to tune controllers for the agents based on the premise that delayed measurements in the controller can be preferable to standard controllers relying only on current measurements. Controller tuning in this setting is however challenging due to the presence of delays. To tackle this problem, we propose an analytic geometry approach. The key contribution is that the tuning can be implemented for complex eigenvalues of the arising graph Laplacian of the network, complementing the current state of the art, which is limited to real eigenvalues. Results, therefore, extend our knowledge beyond symmetric graphs and enable the study of the MAS under directed graphs. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Stochastic cellular automata model of neurosphere growth: Roles of proliferative potential, contact inhibition, cell death, and phagocytosis.

Neural stem and progenitor cells isolated from the central nervous system form, under specific culture conditions, clonal cell clusters known as neurospheres. The neurosphere assay has proven to be a powerful in vitro system to study the behavior of such cells and the development of their progeny. However, the theory of neurosphere growth has remained poorly understood. To overcome this limitation, we have, in the present paper, developed a cellular automata model, with which we examined the effects of proliferative potential, contact inhibition, cell death, and clearance of dead cells on growth rate, final size, and composition of neurospheres. Simulations based on this model indicated that the proliferative potential of the founder cell and its progenitors has a major influence on neurosphere size. On the other hand, contact inhibition of proliferation limits the final size, and reduces the growth rate, of neurospheres. The effect of this inhibition is particularly dramatic when a stem cell becomes encapsulated by differentiated or other non-proliferating cells, thereby suppressing any further mitotic division - despite the existing proliferative potential of the stem cell. Conversely, clearance of dead cells through phagocytosis is predicted to accelerate growth by reducing contact inhibition. A surprising prediction derived from our model is that cell death, while resulting in a decrease in growth rate and final size of neurospheres, increases the degree of differentiation of neurosphere cells. It is likely that the cellular automata model developed as part of the present investigation is applicable to the study of tissue growth in a wide range of systems.

Growth of adult spinal cord in knifefish: Development and parametrization of a distributed model.

The study of indeterminate-growing organisms such as teleost fish presents a unique opportunity for improving our understanding of central nervous tissue growth during adulthood. Integrating the existing experimental data associated with this process into a theoretical framework through mathematical or computational modeling provides further research avenues through sensitivity analysis and optimization. While this type of approach has been used extensively in investigations of tumor growth, wound healing, and bone regeneration, the development of nervous tissue has been rarely studied within a modeling framework. To address this gap, the present work introduces a distributed model of spinal cord growth in the knifefish Apteronotus leptorhynchus, an established teleostean model of adult growth in the central nervous system. The proposed model incorporates two mechanisms, cell proliferation by active stem/progenitor cells and cell drift due to population pressure, both of which are subject to global constraints. A coupled reaction-diffusion equation approach was adopted to represent the densities of actively-proliferating and non-proliferating cells along the longitudinal axis of the spinal cord. Computer simulations using this model yielded biologically-feasible growth trajectories. Subsequent comparisons with whole-organism growth curves allowed the estimation of previously-unknown parameters, such as relative growth rates.

Analysis of Subjects' Vulnerability in a Touch Screen Game Using Behavioral Metrics.

In this article, we report results on an experimental study conducted with volunteer subjects playing a touch-screen game with two unique difficulty levels. Subjects have knowledge about the rules of both game levels, but only sufficient playing experience with the easy level of the game, making them vulnerable with the difficult level. Several behavioral metrics associated with subjects' playing the game are studied in order to assess subjects' mental-workload changes induced by their vulnerability. Specifically, these metrics are calculated based on subjects' finger kinematics and decision making times, which are then compared with baseline metrics, namely, performance metrics pertaining to how well the game is played and a physiological metric called pnn50 extracted from heart rate measurements. In balanced experiments and supported by comparisons with baseline metrics, it is found that some of the studied behavioral metrics have the potential to be used to infer subjects' mental workload changes through different levels of the game. These metrics, which are decoupled from task specifics, relate to subjects' ability to develop strategies to play the game, and hence have the advantage of offering insight into subjects' task-load and vulnerability assessment across various experimental settings.

A consensus dynamics with delay-induced instability can self-regulate for stability via agent regrouping.

Dynamics of many multi-agent systems is influenced by communication/activation delays τ. In the presence of delays, there exists a certain margin called the delay margin τ*, less than which system stability holds. This margin depends strongly on agents' dynamics and the agent network. In this article, three key elements, namely, the delay margin, network graph, and a distance threshold conditioning two agents' connectivity are considered in a multi-agent consensus dynamics under delay τ. We report that when the dynamics is unstable under this delay, its states can be naturally bounded, even for arbitrarily large threshold values, preventing agents to disperse indefinitely. This mechanism can also make the system recover stability in a self-regulating manner, mainly induced by network separation and enhanced delay margin. Under certain conditions, unstable consensus dynamics can keep separating into smaller stable subnetwork dynamics until all agents stabilize in their respective subnetworks. Results are then demonstrated on a previously validated robot coordination model, where specifically robustness of τ* is studied against the delay τinh inherently present in the orientation measurements of the robots. To this end, a mathematical framework to compute τ* with respect to τinh in quasi-state is developed, demonstrating that τ* can be sensitive to τinh, yet robot regrouping and stabilization of subnetworks is still possible.

Formative reasons for state-to-state influences on firearm acquisition in the U.S.

Objectives: Firearm-related crimes and self-inflicted harms pose a significant threat to the safety and well-being of Americans. Investigation of firearm prevalence in the United States (U.S.) has therefore been a center of attention. A critical aspect in this endeavor is to explain whether there are identifiable patterns in firearm acquisition. Methods: We view firearm acquisition patterning as a spatio-temporal dynamical system distributed across U.S. states that co-evolves with crime rates, political ideology, income levels, population, and the legal environment. We leverage transfer entropy and exponential random graph models along with publicly available data, to statistically reveal the formative factors in how each state's temporal patterning of firearm acquisition influences other states. Results: Results help to explain how and why U.S. states influence each other in their firearm acquisition. We establish that state-to-state influences, or lack thereof, in firearm acquisition patterning are explained by states' percent of gun homicide, firearm law strictness, geographic neighborhood, and citizen ideology. Network-based characteristics, namely, mutuality and transitivity, are also important to explain such influence. Conclusions: Results suggest that state policies or programs that reduce gun homicides will also help suppress that state's influence on the patterning of firearm acquisition in other states. Furthermore, states with stricter firearm laws are more likely to influence firearm acquisition in other states, but are themselves shielded from the effects of other states' firearm acquisition patterns. These results inform future research in public health, criminology, and policy making.

Multiple Intentional Delays Can Facilitate Fast Consensus and Noise Reduction in a Multiagent System.

We investigate the use of a derivative-free control scheme called the multiple-delay proportional-retarded (PR) protocol to achieve fast consensus in a large-scale multiagent system. The delays are intentionally introduced in the PR with the purpose of creating derivative-like controllers that rely only on position measurements, thus mitigating undesirable noise effects. The main result places the spectral abscissa of the consensus dynamics at a desired locus and also achieves a user-defined spectral "separation," both of which directly influence convergence to consensus. Design rules and limitations arising from analytical derivations to achieve these results are laid out. Case studies are provided to demonstrate the concepts.

Portable Motion-Analysis Device for Upper-Limb Research, Assessment, and Rehabilitation in Non-Laboratory Settings.

This study presents the design and feasibility testing of an interactive portable motion-analysis device for the assessment of upper-limb motor functions in clinical and home settings. The device engages subjects to perform tasks that imitate activities of daily living, e.g. drinking from a cup and moving other complex objects. Sitting at a magnetic table subjects hold a 3D printed cup with an adjustable magnet and move this cup on the table to targets that can be drawn on the table surface. A ball rolling inside the cup can enhance the task challenge by introducing additional dynamics. A single video camera with a portable computer tracks real-time kinematics of the cup and the rolling ball using a custom-developed, color-based computer-vision algorithm. Preliminary verification with marker-based 3D-motion capture demonstrated that the device produces accurate kinematic measurements. Based on the real-time 2D cup coordinates, audio-visual feedback about performance can be delivered to increase motivation. The feasibility of using this device in clinical diagnostics is demonstrated on 2 neurotypical children and also 3 children with upper-extremity impairments in the hospital, where conventional motion-analysis systems are difficult to use. The device meets key needs for clinical practice: 1) a portable solution for quantitative motor assessment for upper-limb movement disorders at non-laboratory clinical settings, 2) a low-cost rehabilitation device that can increase the volume of in-home physical therapy, and 3) the device affords testing and training a variety of motor tasks inspired by daily challenges to enhance self-confidence to participate in day-to-day activities.

Media coverage and firearm acquisition in the aftermath of a mass shooting.

With an alarming frequency, the United States is experiencing mass shooting events, which often result in heated public debates on firearm control. Whether such events play any role in recent dramatic increases in firearm prevalence remains an open question. This study adopts an information-theoretic framework to analyse the complex interplay between the occurrence of a mass shooting, media coverage on firearm control policies and firearm acquisition at both national and state levels. Through the analysis of time series from 1999 to 2017, we identify a correlation between the occurrence of a mass shooting and the rate of growth in firearm acquisition. More importantly, a transfer entropy analysis pinpoints media coverage on firearm control policies as a potential causal link in a Wiener-Granger sense that establishes this correlation. Our results demonstrate that media coverage may increase public worry about more stringent firearm control and partially drive increases in firearm prevalence.

Toward Monitoring Parkinson's Through Analysis of Static Handwriting Samples: A Quantitative Analytical Framework.

Detection of changes in micrographia as a manifestation of symptomatic progression or therapeutic response in Parkinson's disease (PD) is challenging as such changes can be subtle. A computerized toolkit based on quantitative analysis of handwriting samples would be valuable as it could supplement and support clinical assessments, help monitor micrographia, and link it to PD. Such a toolkit would be especially useful if it could detect subtle yet relevant changes in handwriting morphology, thus enhancing resolution of the detection procedure. This would be made possible by developing a set of metrics sensitive enough to detect and discern micrographia with specificity. Several metrics that are sensitive to the characteristics of micrographia were developed, with minimal sensitivity to confounding handwriting artifacts. These metrics capture character size-reduction, ink utilization, and pixel density within a writing sample from left to right. They are used here to "score" handwritten signatures of 12 different individuals corresponding to healthy and symptomatic PD conditions, and sample control signatures that had been artificially reduced in size for comparison purposes. Moreover, metric analyses of samples from ten of the 12 individuals for which clinical diagnosis time is known show considerable informative variations when applied to static signature samples obtained before and after diagnosis. In particular, a measure called pixel density variation showed statistically significant differences ( ) between two comparison groups of remote signature recordings: earlier versus recent, based on independent and paired t-test analyses on a total of 40 signature samples. The quantitative framework developed here has the potential to be used in future controlled experiments to study micrographia and links to PD from various aspects, including monitoring and assessment of applied interventions and treatments. The inherent value in this methodology is further enhanced by its reliance solely on static signatures, not requiring dynamic sampling with specialized equipment.

Experimental Evaluation of a Braille-Reading-Inspired Finger Motion Adaptive Algorithm.

Braille reading is a complex process involving intricate finger-motion patterns and finger-rubbing actions across Braille letters for the stimulation of appropriate nerves. Although Braille reading is performed by smoothly moving the finger from left-to-right, research shows that even fluent reading requires right-to-left movements of the finger, known as "reversal". Reversals are crucial as they not only enhance stimulation of nerves for correctly reading the letters, but they also show one to re-read the letters that were missed in the first pass. Moreover, it is known that reversals can be performed as often as in every sentence and can start at any location in a sentence. Here, we report experimental results on the feasibility of an algorithm that can render a machine to automatically adapt to reversal gestures of one's finger. Through Braille-reading-analogous tasks, the algorithm is tested with thirty sighted subjects that volunteered in the study. We find that the finger motion adaptive algorithm (FMAA) is useful in achieving cooperation between human finger and the machine. In the presence of FMAA, subjects' performance metrics associated with the tasks have significantly improved as supported by statistical analysis. In light of these encouraging results, preliminary experiments are carried out with five blind subjects with the aim to put the algorithm to test. Results obtained from carefully designed experiments showed that subjects' Braille reading accuracy in the presence of FMAA was more favorable then when FMAA was turned off. Utilization of FMAA in future generation Braille reading devices thus holds strong promise.

Can improved specialty access moderate emergency department overuse?: Effect of neurology appointment delays on ED visits.

BACKGROUND: Delayed access to specialty care may increase inappropriate emergency department (ED) visits. However, the details of this relationship after referral to a specialist are unknown. METHODS: The correlations in an academic medical center between time to new neurology patient appointments and nonurgent ED use are explored in this study. Access was measured as the number of days between the scheduling and outpatient appointment dates. A series of statistical analyses including correlation analysis, regressions, and hypothesis tests were conducted to investigate possible associations between delayed access to specialty care and ED visits, as well as the effect of ED visits on specialty care cancellation and no-show rates. RESULTS: Of 19,505 new neurology patients, 310 visited an ED prior to their appointment, 95.2% (295) of whom had poor access (defined here as exceeding 21 days). Patients with access >21 days for new visits were 6.6 times more likely to visit the ED before their appointment date, 19% within the first week after scheduling. Patients who visited the ED between their booking and appointment dates were 2.3 times more likely to cancel or fail to attend their appointment. CONCLUSION: These results suggest that long access delays in specialty referrals can significantly increase ED costs and congestion. Further studies in other specialties to explore this relationship are warranted.

Rules and limitations of building delay-tolerant topologies for coupled systems.

This paper investigates the equilibrium behavior of broadly studied synchronization dynamics of coupled systems, among which shared information is delayed. The underlying relationship is established between graph structures and the largest amount of delay the dynamics can withstand without losing stability. In particular, based on Cartesian product of graphs, we present the rules and limitations for synthesizing the graphs of large-scale systems that can remain stable for as large delays as possible. Examples are provided to demonstrate the results.

Stability of car following with human memory effects and automatic headway compensation.

This paper addresses the study of some appropriate control strategies in order to guarantee the exponential stability of a class of deterministic microscopic car-following models including human drivers' memory effects and automated headway controllers. More precisely, the delayed action/decision of human drivers is represented using distributed delays with a gap and the considered automated controller is of proportional derivative type. The analysis is performed in both delay parameter and controller gain parameter spaces, and appropriate algorithms are proposed. Surprisingly, large delays and/or gains improve stability for the corresponding closed-loop schemes. Finally, some illustrative examples as well as various interpretations of the results complete the presentation.