Elementary Model Research Articles

Estimation of the Elementary Chirp Model Parameters

In this paper, we propose some estimation techniques to estimate the elementary chirp model parameters, which are encountered in sonar, radar, acoustics, and other areas. We derive asymptotic theoretical properties of least squares estimators and approximate least squares estimators for the one component elementary chirp model. It is proved that the proposed estimators are strongly consistent and follow the normal distribution asymptotically. We also suggest how to obtain proper initial values for these methods. The problem of finding initial values is a difficult problem when the number of components in the model is large, or when the signal-to-noise ratio is low, or when two frequency rates are close to each other. We propose sequential procedures to estimate the multiple component elementary chirp model parameters. We prove that the theoretical properties of sequential least squares estimators and sequential approximate least squares estimators coincide with those of least squares estimators and approximate least squares estimators, respectively. Further, the asymptotic variances of the proposed estimators attain the Cramér-Rao lower bounds asymptotically when errors are normal random variables and independently and identically distributed. To evaluate the performance of the proposed estimators, numerical experiments are performed. It is observed that the proposed sequential estimators perform well even in situations where least squares estimators do not perform well. We illustrate the performance of the proposed sequential algorithm on a bat data.

Внутригодовая изменчивость температуры приземного воздуха и её моделирование для города Ставрополя

Introduction. It is known that the time course of temperature during the year is seasonal. However, the rates of temperature growth in transition periods are different. This complicates the prediction of such an important parameter, in particular for agriculture, as the air temperature of the surface layer of the atmosphere. Accordingly, the article analyzes the intra-annual variability of air temperature and compares it with a sinusoidal model of the annual temperature course. Materials and research methods. The time series of the air temperature of the surface layer of the atmosphere for the city of Stavropol are considered and the task is to compare the actual and theoretical values of annual amplitudes. In the elementary (sinusoidal) model, this theoretical value turns out to be directly proportional to the annual variance. The time series of temperature differences (inter-monthly changes), the so-called discrete derivatives, is also considered, and the comparison of the usual and discrete derivative of the sine function as an elementary model of the annual temperature course is carried out. A new value is introduced – the standard deviation of variability, which also characterizes the variance, yet not for a number of temperatures, but their differences. Research results and their discussion. It is noted that the theoretical (i.e., valid for the sinusoidal model) and the actual value of the amplitude of the annual temperature course are quite well matched. However, due to non-periodic deviations, the difference between these values can reach 2 °C, which is characterized by asymmetry on the intra-annual variability chart. In addition, the average annual temperature course is considered and its analysis is carried out using discrete derivatives. It is shown that the ratio of the annual temperature amplitude to the amplitude of the discrete derivative of this value is equal to the cyclic frequency of fluctuations of the annual temperature course. Conclusions. The results obtained confirm the possibility of using a sinusoidal model of the annual temperature course (although with some limitations related to the asymmetry and shift of intra-annual peak points). The analysis of the annual temperature course using discrete derivatives and its comparison with the sinusoidal model revealed the features of the average annual intra-annual variability of surface air temperature for the city of Stavropol for the period 1944 – 2022. Sometimes there is a change in the rate of heating or cooling; in rare cases, there is an inversion when considering the time series of average monthly temperatures).

An Elementary Model of VC Financing and Growth

This article uses an endogenous growth model to study how the improvements in financing for innovative start-ups brought by venture capital (VC) affect firm innovation and growth. Partial equilibrium results show how lending contracts change as financing efficiency improves, while general equilibrium results show that better screening and development of projects by VC investors leads to higher aggregate productivity growth.

The Prediction of the exchange rate between the us dollar and rmb through liner regression and arima model

The exchange rate between the US dollar and the RMB has been changing over the past year. Through the analysis of daily changing data, the direct calculation of linear regression will lead to the overall upward trend of the data, but not the rise and fall of the exchange rate. Therefore, it is necessary to introduce a more accurate ARIMA model to predict the possible development and change of data in a short period of time and analyze what policy causes the sharp fluctuations of data in a short period of time. In the process of applying the ARIMA model, this paper analyzed the shortcomings of ordinary linear regression and therefore proposed how to select the appropriate model for different data processing. The research results of this article provide more beginners in statistics with ideas for solving problems: prediction problems that cannot be solved by simple linear regression and existing elementary models can be analyzed using certain time series models, and reasonable explanations for data changes can be given based on existing policy reasons, Including irresistible inflation and the United States' own adjustment to the Federal Reserve's interest rate hike.

Analysis of the use of vector autoregressions in economic forecasting

Using vector autoregressions is a promising direction in short-term economic forecasting. They do not simply model the relationship between different factors, but also model the time-distributed relationship of these factors. Vector autoregressions are suitable for modeling complex dynamic economic multifactor processes. The complexity of the problem of estimating coefficients, which increases with the dimensionality of vectors, prevents the widespread use of autoregressions in practice. Vector autoregressions in complex-valued form with the same dimensionality as the modeled vector contain a much smaller number of coefficients. This facilitates the estimation of the coefficients of vector autoregressions. Some problems requiring further investigation arise when using vector autoregressions in complex form. Among them is the problem of selecting the best model. The information criteria used for this purpose limit the variety of vector autoregressions, reducing them to elementary models. The study was supported by the Russian Science Foundation grant No. 23-28-01213, https://rscf.ru/project/23-28-01213.

Things We Must Never Do (if Any)

Are there things that we must never do, no matter how untypical the circumstances and “unorthodox” our deontic ideas might be? In this essay I try to make evident that acts I call “pure sadist acts” satisfy this description. I discuss several examples of such acts and alert to their being not always easy to distinguish from certain others. Norms prohibiting such acts I call “true”, and I suggest that other, less suggestive, norms might also be (derivatively) true, if the pertinent acts stand in certain relations with the former ones. I incorporate some ideas from Hume, as well as from elementary model theory, to make mine clearer.

Origin of the efficiency of spike timing-based neural computation for processing temporal information

Although the advantage of spike timing-based over rate-based network computation has been recognized, the underlying mechanism remains unclear. Using Tempotron and Perceptron as elementary neural models, we examined the intrinsic difference between spike timing-based and rate-based computations. For more direct comparison, we modified Tempotron computation into rate-based computation with the retention of some temporal information. Previous studies have shown that spike timing-based computation are computationally more powerful than rate-based computation in terms of the number of computational units required and the capability in classifying random patterns. Our study showed that spike timing-based and rate-based Tempotron computations provided similar capability in classifying random spike patterns, as well as in text sentiment classification and spam text detection. However, spike timing-based computation is superior in performing a task involving discriminating forward vs. reverse sequence of events, i.e., information mainly temporal in nature. Further studies revealed that this superiority required the asymmetry in the profile of the postsynaptic potential (PSP), and that temporal sequence information was converted to biased spatial distribution of synaptic weight modifications during learning. Thus, the intrinsic PSP asymmetry is a mechanistic basis for the high efficiency of spike timing-based computation for processing temporal information.

Hyperbolic Topological Band Insulators.

Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a new paradigm of synthetic matter, and their energy levels were characterized by a band structure in a four- (or higher-) dimensional momentum space. To explore the uncharted topological aspects arising in hyperbolic band theory, we here introduce elementary models of hyperbolic topological band insulators: the hyperbolic Haldane model and the hyperbolic Kane-Mele model; both obtained by replacing the hexagonal cells of their Euclidean counterparts by octagons. Their nontrivial topology is revealed by computing topological invariants in both position and momentum space. The bulk-boundary correspondence is evidenced by comparing bulk and boundary density of states, by modeling propagation of edge excitations, and by their robustness against disorder.

Полуэмпирический анализ начальной стадии роста очага разложения за фронтом ударной волны

The paper presents analysis results of the initial stage of decomposition of phlegmatized RDX behind the front of a shock wave with pressure at the front approximately equal to 2 GPa, presumably during the time preceding the merging of the initially isolated decomposition centers. In this case, the time dependences of the mass fraction of explosive decomposition products behind the shock wave front and their specific volume obtained by processing the results of experiments carried out by the method of quasi-thin layers (layers tenths of millimeters thick placed between blocks of an inert reference material) are used. Based on the dynamics of changes in the parameters of the state of the reacting charge revealed from the results of the experiment, the time dependences of the characteristics of the matrix explosive movement around the decomposition site were established within the framework of an elementary spherical charge cell model. It is taken in the form of a sphere containing a central pore filled initially with air. Time dependences (within tenths of a microsecond) of the radius of the decomposition site, represented as a spherical cavity filled with explosive combustion products and compressible initial pore gas, are obtained; tangential deformation and its velocity on control spherical surfaces located at different distances from the surface of the decomposition site; strains and strain rates on the spherical combustion surface are revealed. The influence on the estimates of these characteristics of the concentration of decomposition sites in the range of variation 1012....1013 m–3 and the residual air pressure in the pores remaining after the pressing of charges (0,1 MPa and 1 MPa). Deformations and strain rates on the surface of the decomposition site, considered as a combustion surface, can reach values equal to 25% and 106 1/s, respectively. The surface area of the decomposition site can be an order of magnitude greater than the combustion surface area, which would be if the specific volume of decomposition products was not significantly less than that of the explosive. The speed of displacement of the surface of the decomposition site can exceed the linear combustion rate by an order of magnitude.

Optimal capacity allocation for heavy-traffic fixed-cycle traffic-light queues and intersections

Setting traffic light signals is a classical topic in traffic engineering, and important in heavy-traffic conditions when green times become scarce and longer queues are inevitably formed. For the fixed-cycle traffic-light queue, an elementary queueing model for one traffic light with cyclic signaling, we obtain heavy-traffic limits that capture the long-term queue behavior. We leverage the limit theorems to obtain sharp performance approximations for one queue in heavy traffic. We also consider optimization problems that aim for optimal division of green times among multiple conflicting traffic streams. We show that inserting heavy-traffic approximations leads to tractable optimization problems and close-to-optimal signal prescriptions.

Solving the Schrödinger Equation with Genetic Algorithms: A Practical Approach

The Schrödinger equation is one of the most important equations in physics and chemistry and can be solved in the simplest cases by computer numerical methods. Since the beginning of the 1970s, the computer began to be used to solve this equation in elementary quantum systems, and, in the most complex case, a ‘hydrogen-like’ system. Obtaining the solution means finding the wave function, which allows predicting the physical and chemical properties of the quantum system. However, when a quantum system is more complex than a ‘hydrogen-like’ system, we must be satisfied with an approximate solution of the equation. During the last decade, application of algorithms and principles of quantum computation in disciplines other than physics and chemistry, such as biology and artificial intelligence, has led to the search for alternative techniques with which to obtain approximate solutions of the Schrödinger equation. In this work, we review and illustrate the application of genetic algorithms, i.e., stochastic optimization procedures inspired by Darwinian evolution, in elementary quantum systems and in quantum models of artificial intelligence. In this last field, we illustrate with two ‘toy models’ how to solve the Schrödinger equation in an elementary model of a quantum neuron and in the synthesis of quantum circuits controlling the behavior of a Braitenberg vehicle.

Landslide susceptibility assessment in the rocky coast subsystem of Essaouira, Morocco

Abstract. In recent decades, multiple researchers have produced landslide susceptibility maps using different techniques and models, including the information value method, which is a statistical model that is widely applied to various coastal environments. This study aimed to evaluate susceptibility to landslides in the Essaouira coastal area using bivariate statistical methods. In this study, 588 distinct landslides were identified, inventoried, and mapped. Landslides are performed by means of observation and interpretation of different data sources, namely high-resolution satellite images, aerial photographs, topographic maps, and extensive field surveys. The rocky coastal system of Essaouira is located in the middle of the Atlantic coast of Morocco. The study area was split into 1534 cliff terrain units that were 50 m in width. For training and validation purposes, the landslide inventory was divided into two independent groups: 70 % for training and 30 % for validation. Twenty-two layers of landslide conditioning factors were prepared – namely, elevation, slope angle, slope aspect, plan curvature, profile curvature, cliff height, topographic wetness index, topographic position index, slope over area ratio, solar radiation, presence of faulting, lithological units, toe lithology, presence and type of cliff toe protection, layer tilt, rainfall, streams, land-use patterns, normalised difference vegetation index, lithological material grain size, and presence of springs. The statistical relationship between the conditioning factors and the different landslide types was calculated using the bivariate information value method in a pixel-based model and in the elementary terrain units-based model. Coastal landside susceptibility maps were validated using landslide training group partitions. The receiver operating characteristic curve and area under the curve were used to assess the accuracy and prediction capacity of the different coastal landslide susceptibility models. Two methodologies, considering a pixel-based approach and using coastal terrain units, were adopted to evaluate coastal landslide susceptibility. The results allowed for the classification of 38 % of the rocky coast subsystem as having high susceptibility to landslides, which were mostly located in the southern part of the Essaouira coastal area. These susceptibility maps will be useful for future planned development activities as well as for environmental protection.

Hybrid form of quantum theory with non-Hermitian Hamiltonians

In Schrödinger picture the unitarity of evolution is usually guaranteed by the Hermiticity of the Hamiltonian operator h=h† in a conventional Hilbert space Htextbook. After a Dyson-inspired operator-transformation (OT) non-unitary preconditioning Ω:h→H the simplified Hamiltonian H is, in its manifestly unphysical Hilbert space Hauxiliary, non-Hermitian. Besides its natural OT-based physical interpretation it can also be “Hermitized” (i.e., made compatible with the unitarity) via a metric-amendment (MA) change of the Hilbert space, Hauxiliary→Hphysical. In our present letter we propose another, third, hybrid form (HF) of the Hermitization of H in which the change involves, simultaneously, both the Hamiltonian and the metric. Formally this means that the original Dyson map is assumed factorizable, Ω=ΩMΩH. A key practical advantage of the new HF approach lies in the model-dependent adaptability of such a factorization. The flexibility and possible optimality of the balance between the MA-related (i.e., metric-amending) factor ΩM and the OT-related (i.e., Hamiltonian-changing) factor ΩH are explicitly illustrated via an elementary two-state quantum model.

A Compliant Teleoperation System by Utilizing Haptic Guidance and Series Elastic Actuator-Based Gripper

Abstract This article introduces a haptic-guided teleoperation framework using a series elastic actuator (SEA)-based compliant gripper. The proposed teleoperation system involves one local haptic device, one layer of virtual reality, and one remote industrial manipulator with a compliant gripper. The overall compliance of the teleoperation is distributed between the software and hardware components of the bilateral loop. On the one hand, the implemented haptic guidance is based on an elementary coupling model uniquely defined and established for all interactions among the user, remote manipulator, and virtual interface. On the other hand, the manipulator operating in the remote environment is equipped with a novel compliant gripper based on series elastic actuators, providing passive compliance at the interactions with the environment. Introducing the gripper into the haptic loop is expected to compensate for disturbances due to inaccurate modeling and/or unmodeled dynamics of the remote environment and external effects. The teleoperation system is implemented for manipulation and tracking tasks and tested with different users. Experimental results show that the haptic guidance and the compliant gripper together significantly improve the teleoperation performances in terms of transparency.

Learning ocean circulation models with reservoir computing

Two elementary models of ocean circulation, the well-known double-gyre stream function model and a single-layer quasi-geostrophic (QG) basin model, are used to generate flow data that sample a range of possible dynamical behavior for particular flow parameters. A reservoir computing (RC) machine learning algorithm then learns these models from the stream function time series. In the case of the QG model, a system of partial differential equations with three physically relevant dimensionless parameters is solved, including Munk- and Stommel-type solutions. The effectiveness of a RC approach to learning these ocean circulation models is evident from its ability to capture the characteristics of these ocean circulation models with limited data including predictive forecasts. Further assessment of the accuracy and usefulness of the RC approach is conducted by evaluating the role of both physical and numerical parameters and by comparison with particle trajectories and with well-established quantitative assessments, including finite-time Lyapunov exponents and proper orthogonal decomposition. The results show the capability of the methods outlined in this article to be applied to key research problems on ocean transport, such as predictive modeling or control.

Molecular Dynamics Study of CO2 Phase Change Transport in the Near-Critical Region: Model Parameter Optimization

The technical development of supercritical CO2, energy systems, CO2 capture, and other applications has become a hot topic in recent years. Therefore, molecular dynamics simulation (MD) of CO2, especially the investigation at the CO2 supercritical region is urgently needed. This study focused on the optimization of common CO2 potential model EPM2 (elementary physical model—2) combined MD forcefield OPLS-AA (optimized potentials for liquid simulations—all atom) and CHARMM (chemistry at Harvard macromolecular mechanics for MD simulation). Through adjusting angle parameters according to EPM2, vapor-liquid equilibrium curve, critical point and supercritical region could be well corresponding with experiments, which can be more accurate than previous approaches. The simulated results using 179.63° in OPLS-AA forcefield can not only correspond to supercritical phase of near-critical region (within ±10% error range under CO2 is at 468 kg/m3, 304.2–320 K, 7.2–10.0 MPa), but also be consistent with actual CO2 properties in gas phase of near-critical region (temperature range can reach 304.2–350 K while the density scope can reach 15–168 kg/m3). Besides, optimized potential model also has a certain reliability on the investigation of CO2 diffusion properties. The values simulated have the same order of magnitude as literature values, especially simulated diffusion coefficient values at gas phase. The CO2 property of heat capacity is also simulated, and the errors are within ±15%. That is to say, the optimized CO2 potential parameter also has a certain accuracy to analyze CO2 heat transfer. The angle value optimized in this study may be useful for the fundamental understanding of the supercritical state and it can well be applied in the further investigation of CO2 systems.

The effect of ligand and acid promoter on hydroesterification of ethylene to methyl propionate and kinetic studies

A new palladium/tris(4-fluorophenyl)phosphine/p-toluenesulfonic acid catalytic system was developed to synthesize methyl propionate from ethylene hydroesterification. The influence of phosphine ligands and acid promoters on catalytic activity was systematically studied. A volcano relationship between the catalytic activity and the electric effect of phosphine ligand was achieved through the characterization of 31P NMR of selenium phosphine compounds. An acid strength range favorable to the hydroesterification of ethylene was found by characterizing the pKa value of Brønsted acid. Then, the effect of phosphine ligand/Pd(OAc)2 ratio, p-toluenesulfonic/Pd(OAc)2 ratio, temperature, time, and pressure on this reaction were investigated. Finally, the elementary reaction-based kinetic model was developed, which indicated that nucleophilic attack of methanol on the Pd-acyl intermediate to give methyl propionate is the rate-determining step. The activation barrier of rate-determining step is 83.1 kJ·mol−1.

Shell model foundations of the proxy-SU(3) symmetry: Nucleon pairs creating nuclear deformation

Abstract Proxy-SU(3) symmetry is an approximation scheme extending the Elliott SU(3) algebra of the sd shell to heavier shells, in order to make possible the application of the symmetry properties in cutting down the size of the required calculations. When introduced in 2017, the approximation had been justified by calculations carried out within the Nilsson model, an elementary shell model based on a 3-dimensional harmonic oscillator with cylindrical symmetry, applicable to deformed nuclei. Recently our group managed to map the cartesian basis of the Elliott SU(3) model onto the spherical shell model basis, fully clarifying the approximations used within the proxy-SU(3) scheme and paving the way for using the proxy-SU(3) approximation in shell model calculations for heavy nuclei. As a by-product, the relation of the 0[110] Nilsson pairs used in proxy-SU(3) to the earlier used de Shalit-Goldhaber pairs and Federman-Pittel pairs has been clarified. The connection between the proxy-SU(3) scheme and the spherical shell model has also been worked out in the original framework of the Nilsson model, with identical results.

An Elementary Model of Focal Adhesion Detachment and Reattachment During Cell Reorientation Using Ideas from the Kinetics of Wiggly Energies

A simple, transparent, two-dimensional, nonlinear model of cell reorientation is constructed in this paper. The cells are attached to a substrate by “focal adhesions” that transmit the deformation of the substrate to the “stress fibers” in the cell. When the substrate is subjected to a deformation, say an in-plane bi-axial deformation with stretches λ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\lambda _{1}$\\end{document} and λ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\lambda _{2}$\\end{document}, the stress fibers deform with it and change their length and orientation. In addition, the focal adhesions can detach from the substrate and reattach to it at new nearby locations, and this process of detachment and reattachment can happen many times. In this scenario the (varying) fiber angle Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\Theta $\\end{document}in the reference configuration plays the role of an internal variable. 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The evolution of this system is studied using a gradient flow kinetic law, which is homogenized for ϵ→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\epsilon \ o 0$\\end{document} using results from weak convergence. The results determine (a)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(a)$\\end{document} a region of the λ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\lambda _{1}$\\end{document}, λ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\lambda _{2}$\\end{document}-plane in which the (referential) fiber orientation remains stuck at the angle Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\Theta $\\end{document} and does not evolve, and (b)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(b)$\\end{document} the evolution of the orientation when the stretches move out of this region as the fibers seek to minimize energy.

Dual STDP processes at Purkinje cells contribute to distinct improvements in accuracy and speed of saccadic eye movements.

Saccadic eye-movements play a crucial role in visuo-motor control by allowing rapid foveation onto new targets. However, the neural processes governing saccades adaptation are not fully understood. Saccades, due to the short-time of execution (20-100 ms) and the absence of sensory information for online feedback control, must be controlled in a ballistic manner. Incomplete measurements of the movement trajectory, such as the visual endpoint error, are supposedly used to form internal predictions about the movement kinematics resulting in predictive control. In order to characterize the synaptic and neural circuit mechanisms underlying predictive saccadic control, we have reconstructed the saccadic system in a digital controller embedding a spiking neural network of the cerebellum with spike timing-dependent plasticity (STDP) rules driving parallel fiber-Purkinje cell long-term potentiation and depression (LTP and LTD). This model implements a control policy based on a dual plasticity mechanism, resulting in the identification of the roles of LTP and LTD in regulating the overall quality of saccade kinematics: it turns out that LTD increases the accuracy by decreasing visual error and LTP increases the peak speed. The control policy also required cerebellar PCs to be divided into two subpopulations, characterized by burst or pause responses. To our knowledge, this is the first model that explains in mechanistic terms the visual error and peak speed regulation of ballistic eye movements in forward mode exploiting spike-timing to regulate firing in different populations of the neuronal network. This elementary model of saccades could be extended and applied to other more complex cases in which single jerks are concatenated to compose articulated and coordinated movements.