Behaviors of the synthetic characters in current military simulations are limited since they are generally generated by rule-based and reactive computational models with minimal intelligence. Such computational models cannot adapt to reflect the experience of the characters, resulting in brittle intelligence for even the most effective behavior models devised via costly and labor-intensive processes. Observation-based behavior model adaptation that leverages machine learning and the experience of synthetic entities in combination with appropriate prior knowledge can address the issues in the existing computational behavior models to create a better training experience in military training simulations. In this paper, we introduce a framework that aims to create autonomous synthetic characters that can perform coherent sequences of believable behavior while being aware of human trainees and their needs within a training simulation. This framework brings together three mutually complementary components. The first component is a Unity-based simulation environment - Rapid Integration and Development Environment (RIDE) - supporting One World Terrain (OWT) models and capable of running and supporting machine learning experiments. The second is Shiva, a novel multi-agent reinforcement and imitation learning framework that can interface with a variety of simulation environments, and that can additionally utilize a variety of learning algorithms. The final component is the Sigma Cognitive Architecture that will augment the behavior models with symbolic and probabilistic reasoning capabilities. We have successfully created proof-of-concept behavior models leveraging this framework on realistic terrain as an essential step towards bringing machine learning into military simulations.
We present a simple phenomenological formula which approximates the hyperbolic volume of a knot using only a single evaluation of its Jones polynomial at a root of unity. The average error is just $2.86$% on the first $1.7$ million knots, which represents a large improvement over previous formulas of this kind. To find the approximation formula, we use layer-wise relevance propagation to reverse engineer a black box neural network which achieves a similar average error for the same approximation task when trained on $10$% of the total dataset. The particular roots of unity which appear in our analysis cannot be written as $e^{2\pi i / (k+2)}$ with integer $k$; therefore, the relevant Jones polynomial evaluations are not given by unknot-normalized expectation values of Wilson loop operators in conventional $SU(2)$ Chern$\unicode{x2013}$Simons theory with level $k$. Instead, they correspond to an analytic continuation of such expectation values to fractional level. We briefly review the continuation procedure and comment on the presence of certain Lefschetz thimbles, to which our approximation formula is sensitive, in the analytically continued Chern$\unicode{x2013}$Simons integration cycle.
This paper proposes a fractional-order reset element whose architecture allows for the suppression of nonlinear effects for a range of frequencies. Suppressing the nonlinear effects of a reset element for the desired frequency range while maintaining it for the rest is beneficial, especially when it is used in the framework of a "Constant in gain, Lead in phase" (CgLp) filter. CgLp is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation -- the waterbed effect. The ideal behaviour of such a filter in the frequency domain is unity gain while providing a phase lead for a broad range of frequencies. However, CgLp's ideal behaviour is based on the describing function, which is a first-order approximation that neglects the effects of the higher-order harmonics in the output of the filter. Although CgLp is fundamentally a nonlinear filter, its nonlinearity is not required for all frequencies. Thus, it is shown in this paper that using the proposed reset element architecture, CgLp gets closer to its ideal behaviour for a range of frequencies, and its performance will be improved accordingly.
Ambient backscatter communication (AmBC) leverages the existing ambient radio frequency (RF) environment to implement communication with battery-free devices. The key challenge in the development of AmBC is the very weak RF signals backscattered by the AmBC Tag. To overcome this challenge, we propose the use of orthogonal space-time block codes (OSTBC) by incorporating multiple antennas at the Tag as well as at the Reader. Our approach considers both coherent and non-coherent OSTBC so that systems with and without channel state information can be considered. To allow the application of OSTBC, we develop an approximate linearized and normalized multiple-input multiple-output (MIMO) channel model for the AmBC system. This MIMO channel model is shown to be accurate for a wide range of useful operating conditions. Two coherent detectors and a non-coherent detector are also provided based on the proposed AmBC channel model. Simulation results show that enhanced bit error rate performance can be achieved, demonstrating the benefit of using multiple antennas at the Tag as well as the Reader.
A novel IV estimation method, that we term Locally Trimmed LS (LTLS), is developed which yields estimators with (mixed) Gaussian limit distributions in situations where the data may be weakly or strongly persistent. In particular, we allow for nonlinear predictive type of regressions where the regressor can be stationary short/long memory as well as nonstationary long memory process or a nearly integrated array. The resultant t-tests have conventional limit distributions (i.e. N(0; 1)) free of (near to unity and long memory) nuisance parameters. In the case where the regressor is a fractional process, no preliminary estimator for the memory parameter is required. Therefore, the practitioner can conduct inference while being agnostic about the exact dependence structure in the data. The LTLS estimator is obtained by applying certain chronological trimming to the OLS instrument via the utilisation of appropriate kernel functions of time trend variables. The finite sample performance of LTLS based t-tests is investigated with the aid of a simulation experiment. An empirical application to the predictability of stock returns is also provided.
The SIR evolutionary model predicts too sharp a decrease of the fractions of people infected with COVID-19 in France after the start of the national lockdown, compared to what is observed. I fit the daily hospital data: arrivals in regular and critical care units, releases and deaths, using extended SEIR models. These involve ratios of evolutionary timescales to branching fractions, assumed uniform throughout a country, and the basic reproduction number, $R_0$, before and during the national lockdown, for each region of France. The joint-region Bayesian analysis allows precise evaluations of the time/fraction ratios and pre-hospitalized fractions. The hospital data are well fit by the models, except the arrivals in critical care, which decrease faster than predicted, indicating better treatment over time. Averaged over France, the analysis yields $R_0$= 3.4$\pm$0.1 before the lockdown and 0.65$\pm$0.04 (90% c.l.) during the lockdown, with small regional variations. On 11 May 2020, the Infection Fatality Rate in France was 4 $\pm$1% (90% c.l.), while the Feverish vastly outnumber the Asymptomatic, contrary to the early phases. Without the lockdown nor social distancing, over 2 million deaths from COVID-19 would have occurred throughout France, while a lockdown that would have been enforced 10 days earlier would have led to less than 1000 deaths. The fraction of immunized people reached a plateau below 1% throughout France (3% in Paris) by late April 2020 (95% c.l.), suggesting a lack of herd immunity. The widespread availability of face masks on 11 May, when the lockdown was partially lifted, should keep $R_0$ below unity if at least 46% of the population wear them outside their home. Otherwise, without enhanced other social distancing, a second wave is inevitable and cause the number of deaths to triple between early May and October (if $R_0$=1.2) or even late June (if $R_0$=2).
A simple coherent-imaging method due to Paganin et al. is widely employed for phase-amplitude reconstruction of samples using a single paraxial x-ray propagation-based phase-contrast image. The method assumes that the sample-to-detector distance is sufficiently small for the associated Fresnel number to be large compared to unity. The algorithm is particularly effective when employed in a tomographic setting, using a single propagation-based phase-contrast image for each projection. Here we develop a simple extension of the method, which improves the reconstructed contrast of very fine sample features. This provides first-principles motivation for boosting fine spatial detail associated with high Fourier frequencies, relative to the original method, and was inspired by several recent works employing empirically-obtained Fourier filters to a similar end.
We study the SIR epidemiological model, with a variable contagion rate, applied to the evolution of COVID19 in Cuba. It is highlighted that an increase in the predictive character depends on understanding the dynamics for the temporal evolution of the rate of contagion $\beta^*$. A semi-empirical model for this dynamics is formulated, where reaching $\beta^*\approx0$ due to isolation is achieved after the mean duration of the disease $\tau=1/\gamma$, in which the number of infected in the confined families has decreased. It is considered that $\beta^*(t)$ should have an abrupt decrease on the day of initiation of confinement and decrease until canceling at the end of the interval $\tau$. The analysis describes appropriately the infection curve for Germany. The model is applied to predict an infection curve for Cuba, which estimates a maximum number of infected as less than 2000 in the middle of May, depending on the rigor of the isolation. This is suggested by the ratio between the daily detected cases and the total. We consider the ratio between the observed and real infected cases (k) less than unity. The low value of k decreases the maximum obtained when $\beta^*-\gamma>0$. The observed evolution is independent of k in the linear region. The value of $\beta^*$ is also studied by time intervals, adjusting to the data of Cuba, Germany and South Korea. We compare the extrapolation of the evolution of Cuba with the contagion rate until 16.04.20 with that obtained by a strict quarantine at the end of April. This model with variable $\beta^*$ correctly describes the observed infected evolution curves. We emphasize that the desired maximum of the SIR infected curve is not the maximum standard with constant $\beta^*$, but one achieved due to quarantine when $\tilde R_0=\beta^*/\gamma<1$. For the countries controlling the epidemic the maxima are in the region in which SIR equations are linear.
It has been known since Elliott (1998) that standard methods of inference on cointegrating relationships break down entirely when autoregressive roots are near but not exactly equal to unity. We consider this problem within the framework of a structural VAR, arguing this it is as much a problem of identification failure as it is of inference. We develop a characterisation of cointegration based on the impulse response function, which allows long-run equilibrium relationships to remain identified even in the absence of exact unit roots. Our approach also provides a framework in which the structural shocks driving the common persistent components continue to be identified via long-run restrictions, just as in an SVAR with exact unit roots. We show that inference on the cointegrating relationships is affected by nuisance parameters, in a manner familiar from predictive regression; indeed the two problems are asymptotically equivalent. By adapting the approach of Elliott, M\"uller and Watson (2015) to our setting, we develop tests that robustly control size while sacrificing little power (relative to tests that are efficient in the presence of exact unit roots).
We investigate state-dependent effects of fiscal multipliers and allow for endogenous sample splitting to determine whether the US economy is in a slack state. When the endogenized slack state is estimated as the period of the unemployment rate higher than about 12 percent, the estimated cumulative multipliers are significantly larger during slack periods than non-slack periods and are above unity. We also examine the possibility of time-varying regimes of slackness and find that our empirical results are robust under a more flexible framework. Our estimation results point out the importance of the heterogenous effects of fiscal policy and shed light on the prospect of fiscal policy in response to economic shocks from the current COVID-19 pandemic.
Background: Multi-articulate prostheses are capable of performing dexterous hand movements. However, clinically available control strategies fail to provide users with intuitive, independent and proportional control over multiple degrees of freedom (DOFs) in real-time. New Method: We detail the use of a modified Kalman filter (MKF) to provide intuitive, independent and proportional control over six-DOF prostheses such as the DEKA "LUKE" Arm. Input features include neural firing rates recorded from Utah Slanted Electrode Arrays and mean absolute value of intramuscular electromyographic (EMG) recordings. Ad-hoc modifications include thresholds and non-unity gains on the output of a Kalman filter. Results: We demonstrate that both neural and EMG data can be combined effectively. We also highlight that modifications can be optimized to significantly improve performance relative to an unmodified Kalman filter. Thresholds significantly reduced unintended movement and promoted more independent control of the different DOFs. Gain were significantly greater than one and served to amplify participant effort. Optimal modifications can be determined quickly offline and translate to functional improvements online. Using a portable take-home system, participants performed various activities of daily living. Comparison with Existing Methods: In contrast to pattern recognition, the MKF allows users to continuously modulate their force output, which is critical for fine dexterity. The MKF is also computationally efficient and can be trained in less than five minutes. Conclusions: The MKF can be used to explore the functional and psychological benefits associated with long-term, at-home control of dexterous prosthetic hands.
The rise of antimicrobial drug resistance is an imminent threat to global health that has warranted, and duly received, considerable attention within the medical, microbiological and modelling communities. Outbreaks of drug-resistant pathogens are ignited by the emergence and transmission of mutant variants descended from wild-type strains circulating in the community. In this work we investigate the stochastic dynamics of the emergence of a novel disease strain, introduced into a population in which it must compete with an existing endemic strain. In analogy with past work on single-strain epidemic outbreaks, we apply a branching process approximation to calculate the probability that the new strain becomes established. As expected, a critical determinant of the survival prospects of any invading strain is the magnitude of its reproduction number relative to that of the background endemic strain. Whilst in most circumstances this ratio must exceed unity in order for invasion to be viable, we show that differential control scenarios can lead to less-fit novel strains invading populations hosting a fitter endemic one. This analysis and the accompanying findings will inform our understanding of the mechanisms that have led to past instances of successful strain invasion, and provide valuable lessons for thwarting future drug-resistant strain incursions.
In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratio R0 is less than unity and unstable otherwise. The stability of equilibria with delays shows that the endemic equilibrium is locally stable without delays and stable if the delays are under conditions. The existence of Hopf-bifurcation is investigated and transversality conditions proved. The model results suggest that as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability through the process of local birth or death of oscillations. Further, a decrease or an increase in the delays leads to asymptotic stability or instability of the endemic equilibrium respectively. The analytical results, are supported by numerical simulations. Keywords: Time delay, Pneumococcal pneumonia, Vaccination, Stability, Hopf-bifurcation
I start from the fundamental principles of non-relativistic quantum mechanics, without probability, and interpret them using the notion of coexistence: a quantum state can be read, not uniquely, as a coexistence of other quantum states, which are pairwise orthogonal. In this formalism, I prove that a conscious observer is necessarily a physical object that can memorize local events by setting one of its parts in an exactly specified constant quantum state (hypotheses H1, H2 and H3). Then I define the probability of a future event as the proportion of initial observers, all identical, who will actually experience that event. It then becomes possible to establish the usual results of quantum mechanics. Furthermore, I detail the link between probabilities and relative frequencies. Additionally, I study the biological feasibility of this modelling of observer's mind. The second part of this paper completes the neuronal description of the mind functions, based on current neuroscientific knowledge. It provides a model that is compatible with the assumptions of the first part and consistent with our daily conscious experience. In particular, it develops a model of self-consciousness based on an explicit use of the random component of neuron behaviour; according to the first part, that random is in fact the coexistence of a multiplicity of possibilities. So, when the mind measures the random part of certain neurons in the brain, he goes himself within each of these possibilities. The mind has a decision-making component that is active in this situation, appearing then as the cause of the choice of this possibility among all the others. This models the self-consciousness which then ensures the unity of our conscious experience by equating this experience with ``what the ego is conscious about''. The conclusion details the points that remain to be developed.
The Cascaded Integrator Comb filters (CIC) find many applications in recent electronic devices such as frequency selection functions in a digital radio or modem and any filter structure that is required to efficiently process large sample rate factor. These filters are normally located after the sigma-delta modulator and have a regular structure. These types of filters do not require multipliers and the coefficient storage unlike in the normal digital FIR and IIR filters because of all filter coefficients are unity. Hence, it can be efficiently implemented to operate at high speed. Hence, this book describes the Very Large Scale Integration (VLSI) implementation of the CIC filters that are suitable for high-performance audio applications.
In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields. We present a general simple algorithm to generate such copulas on the basis of the empirical copula from high-dimensional data sets. In particular, our constructions also allow for an implementation of positive tail dependence which sometimes is a desirable property of copula modelling, in particular for internal models under Solvency II.
Models that accurately predict the output voltage ripple magnitude are essential for applications with stringent performance target for it. Impact of dc input ripple on the output ripple for a Series Resonant Converter (SRC) using discrete domain exact discretization modelling method is analysed in this paper. A novel discrete state space model along with a small signal model for SRC considering 3 state variables is presented. The audiosusceptibility (AS) transfer function which relates the input to output ripple is derived from the small signal model. Analysis of the AS transfer function indicates a resonance peak and an expression is derived connecting the AS resonance frequency for input ripple with different SRC component values. Further analysis is done to show that a set of values for SRC parameter exists, which forms a design region, for which the normalized gain offered by the SRC for input ripple is less than unity at any input ripple frequency. A test setup to introduce the variable frequency ripple at the input of SRC for the experimental evaluation of AS transfer function is also proposed. Influence of stray parameters on AS gain, AS resonance frequency and on SRC tank resonance frequency is addressed. An SRC is designed at a power level of 10kW. The analysis using the derived model, simulations, and experimental results are found to be closely matching.
The probability that the frequency of a particular trait will eventually become unity, the so-called fixation probability, is a central issue in the study of population evolution. Its computation, once we are given a stochastic finite population model without mutations and a (possibly frequency dependent) fitness function, is straightforward and it can be done in several ways. Nevertheless, despite the fact that the fixation probability is an important macroscopic property of the population, its precise knowledge does not give any clear information about the interaction patterns among individuals in the population. Here we address the inverse problem: From a given fixation pattern and population size, we want to infer what is the game being played by the population. This is done by first exploiting the framework developed in FACC Chalub and MO Souza, J. Math. Biol. 75: 1735, 2017., which yields a fitness function that realises this fixation pattern in the Wright-Fisher model. This fitness function always exists, but it is not necessarily unique. Subsequently, we show that any such fitness function can be approximated, with arbitrary precision, using $d$-player game theory, provided $d$ is large enough. The pay-off matrix that emerges naturally from the approximating game will provide useful information about the individual interaction structure that is not itself apparent in the fixation pattern. We present extensive numerical support for our conclusions.
This paper considers a mathematical model based on the transmission dynamics of hepatitis C virus (HCV) infection. In addition to the usual compartments for susceptible, exposed, and infected individuals, this model includes compartments for individuals who are under treatment and those who have had vaccination against HCV infection. It is assumed that the immunity provided by the vaccine fades with time. The basic reproduction number, $R_0$, and the equilibrium solutions of the model are determined. The model exhibits the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists with a stable endemic equilibrium whenever $R_0$ is less than unity. It is shown that the use of only a perfect vaccine can eliminate backward bifurcation completely. Furthermore, a unique endemic equilibrium of the model is proved to be globally asymptotically stable under certain restrictions on the parameter values. Numerical simulation results are given to support the theoretical predictions. [epidemiological model; equilibrium solutions; backward bifurcation; global asymptotic stability; Lyapunov function.]
We propose two localized Radial Basis Function (RBF) methods, the Radial Basis Function Partition of Unity method (RBF-PUM) and the Radial Basis Function generated Finite Differences method (RBF-FD), for solving financial derivative pricing problems arising from market models with multiple stochastic factors. We demonstrate the useful features of the proposed methods, such as high accuracy, sparsity of the differentiation matrices, mesh-free nature and multi-dimensional extendability, and show how to apply these methods for solving time-dependent higher-dimensional PDEs in finance. We test these methods on several problems that incorporate stochastic asset, volatility, and interest rate dynamics by conducting numerical experiments. The results illustrate the capability of both methods to solve the problems to a sufficient accuracy within reasonable time. Both methods exhibit similar orders of convergence, which can be further improved by a more elaborate choice of the method parameters. Finally, we discuss the parallelization potentials of the proposed methods and report the speedup on the example of RBF-FD.