Approximate Point Research Articles

End-to-end Privacy Preserving Training and Inference for Air Pollution Forecasting with Data from Rival Fleets

Privacy-preserving machine learning (PPML) promises to train machine learning (ML) models by combining data spread across multiple data silos. Theoretically, secure multiparty computation (MPC) allows multiple data owners to train models on their joint data without revealing the data to each other. However, the prior implementations of this secure training using MPC have three limitations: they have only been evaluated on CNNs, and LSTMs have been ignored; fixed point approximations have affected training accuracies compared to training in floating point; and due to significant latency overheads of secure training via MPC, its relevance for practical tasks with streaming data remains unclear. The motivation of this work is to report our experience of addressing the practical problem of secure training and inference of models for urban sensing problems, e.g., traffic congestion estimation, or air pollution monitoring in large cities, where data can be contributed by rival fleet companies while balancing the privacy-accuracy trade-offs using MPC-based techniques.Our first contribution is to design a custom ML model for this task that can be efficiently trained with MPC within a desirable latency. In particular, we design a GCN-LSTM and securely train it on time-series sensor data for accurate forecasting, within 7 minutes per epoch. As our second contribution, we build an end-to-end system of private training and inference that provably matches the training accuracy of cleartext ML training. This work is the first to securely train a model with LSTM cells. Third, this trained model is kept secret-shared between the fleet companies and allows clients to make sensitive queries to this model while carefully handling potentially invalid queries. Our custom protocols allow clients to query predictions from privately trained models in milliseconds, all the while maintaining accuracy and cryptographic security.

Comparing Multiple Extended Object Tracking with Point Based Multi Object Tracking for LiDAR in a Maritime Context

In this paper, we compare a recently developed multiple extended object tracking method with a point-based tracker for maritime applications by evaluating the methods on both real and simulated LiDAR data. Being able to track other vessels is a key part of maritime situational awareness, and multi-object tracking is well suited to this task. Traditionally, multi-object tracking uses the point approximation to simplify the target tracking problem, meaning that an object is assumed to only generate a single measurement. With recent advances in sensor technology, this approximation is no longer valid. Multiple extended object tracking instead makes use of methods that estimates the extent of a target using all available measurements. However, the target models used in extended object tracking are by necessity more complex. We compare these two approaches on real and simulated LiDAR data, which was gathered by tracking smaller vessels. We find that the extended object method has greater performance on simulated data and experimental data with comparatively little wake clutter. However, on experimental data with more wake clutter, the point-based method outperforms the extended object method since it is less sensitive to the disturbance caused by wake clutter. We can conclude that multiple extended object tracking methods have the potential to be more accurate for LiDAR data, but since the models are more complex, measurement sources need to be modeled correctly.

Математическое моделирование интервальнозаданной системы управления движением искусственного спутника Земли в среде MatLab

The article discusses the features of studying complex intervals-given systems. An approach of point approximation of intermediate systems based on key matrices is proposed. Based on the proposed approach, a group of point matrices is obtained and, accordingly, a group of objects with conditions for applying the decomposition procedure, for which the conditions for studying dynamic properties, such as controlled and controlled for them, are set. The developed theoretical apparatus is designed for motion control systems of an artificial satellite of the Earth, for which a model is developed, represented by a system of differential equations with intervals, the key matrix method is applied and a fourpoint model is obtained. Modeling schemes were created for each process in the MatLab environment, modeling characteristics were obtained. A description of a multi-link system consisting of several movable models manufactured at the Center for Space Technology and Microgravity (ZARM) of the University of Bremen (Germany) is given. A mathematical model of the motion of this system has been created. The results of mathematical modeling of a motion control algorithm that ensures the movement of system elements along a given trajectory are presented. Several configurations of the system, ways of interaction of its elements are considered, the dependence of the system parameters on the motion parameters is investigated, the control accuracy is investigated.

Parsimony and parameter estimation for mixtures of multivariate leptokurtic-normal distributions

Mixtures of multivariate leptokurtic-normal distributions have been recently introduced in the clustering literature based on mixtures of elliptical heavy-tailed distributions. They have the advantage of having parameters directly related to the moments of practical interest. We derive two estimation procedures for these mixtures. The first one is based on the majorization-minimization algorithm, while the second is based on a fixed point approximation. Moreover, we introduce parsimonious forms of the considered mixtures and we use the illustrated estimation procedures to fit them. We use simulated and real data sets to investigate various aspects of the proposed models and algorithms.

Quantum evolution with random phase scattering

We consider the quantum evolution of a fermion–hole pair in a d-dimensional gas of non-interacting fermions in the presence of random phase scattering. This system is mapped onto an effective Ising model, which enables us to show rigorously that the probability of recombining the fermion and the hole decays exponentially with the distance of their initial spatial separation. In contrast, without random phase scattering the recombination probability decays like a power law, which is reflected by an infinite mean square displacement. The effective Ising model is studied within a saddle point approximation and yields a finite mean square displacement that depends on the evolution time and on the spectral properties of the deterministic part of the evolution operator.

Differential dynamic programming for finite‐horizon zero‐sum differential games of nonlinear systems

AbstractIn this article, we present an iterative algorithm based on differential dynamic programming (DDP) for finite‐horizon two‐person zero‐sum differential games. The technique of DDP is used to expand the Hamilton–Jacobi–Isaacs (HJI) partial differential equation into higher‐order differential equations. Using value function and saddle point approximations, the DDP expansion is transformed into algebraic matrix equation in integral form. Based on the algebraic matrix equation, a DDP iterative algorithm is developed to learn the solution to the differential games. Strict proof is proposed to guarantee the iterative convergences of the value function and saddle point. The new algorithm is fundamentally different from existing results, in the sense that it overcome the technical obstacle to address the time‐varying behavior of HJI partial differential equation. Simulation examples are given to demonstrate the effectiveness of the proposed method.

Magnetocaloric effect in the Jx−Jy Blume–Capel model

The magnetocaloric properties of the Jx−Jy Blume–Capel model with Jx/Jy=−0.5 are studied using the two point approximation of the Cluster Variation Method. The phase diagrams exhibit different phases depending on the anisotropy parameter, magnetic field, temperature and exchange interaction ratio. It is shown how the nature of the phase transition changes as parameters are varied. For an anisotropy parameter value of D=1.45, a tricritical point and a reentrant behavior are identified. It was found inverse and direct magnetocaloric effect. The inverse magnetocaloric effect of the model is enhanced at low fields and temperatures around jumps between plateaus of magnetization.

Entropy of causal diamond ensembles

We define a canonical ensemble for a gravitational causal diamond by introducing an artificial York boundary inside the diamond with a fixed induced metric and temperature, and evaluate the partition function using a saddle point approximation. For Einstein gravity with zero cosmological constant there is no exact saddle with a horizon, however the portion of the Euclidean diamond enclosed by the boundary arises as an approximate saddle in the high-temperature regime, in which the saddle horizon approaches the boundary. This high-temperature partition function provides a statistical interpretation of the recent calculation of Banks, Draper and Farkas, in which the entropy of causal diamonds is recovered from a boundary term in the on-shell Euclidean action. In contrast, with a positive cosmological constant, as well as in Jackiw-Teitelboim gravity with or without a cosmological constant, an exact saddle exists with a finite boundary temperature, but in these cases the causal diamond is determined by the saddle rather than being selected a priori.

The effect of coating concentration of curcumin: H2O on copper winding characteristics

Each coil of copper produces a magnetic field and the total field inside the solenoid will be the sum of the fields caused by each coil of current. If the solenoid coils are very closely spaced, the internal field will be essentially parallel to the axis except at the very ends. To find out the magnitude of the magnetic field inside the solenoid, you can use Ampere’s law, namely B=μo∙N∙I, where B is the magnetic field strength (T), µo is air permeability (4×10‒7 T m/A), N is the number of turns and I is an electric current. The value of B depends on the number of turns per unit length, N, and current I. The field is independent of the position inside the solenoid, so the value of B is uniform. This only applies to infinite solenoids, but is a good approximation for actual points that are not near the ends of the solenoid. The research object is 4 identical copper coils with a length of 3 cm, a coil diameter of 2 cm, a cross section of 1.5 mm2 with an inductance value of 2.17 µH. Before coating curcumin on the copper winding, the initial value of the magnetic field strength was 2.54 µTesla. After the coating process of curcumin:H2O concentration, the value of the magnetic field strength increased. The method used was immersing 4 copper coils with an inductance value of 2.17 µH in curcumin:H2O concentration in a 100 ml volume measuring cup, with the respective concentrations: (20 %:80 %), (40 %:60 %), (60 %:40 %), (80 %:20 %) in a certain time. Then the copper coil conductor is supplied with a 5-volt DC voltage source. Then the value of the magnetic field strength (B) and electric current is measured, the results are compared with the system before immersing the copper coil. The measurement results showed that the values of electric current and magnetic field strength increased after curcumin coating compared to before treatment. To see the bonding performance of curcumin and copper, the FTIR test and simulation of the curcumin: copper bond were carried out using Avogadro software. In the IR test, there is a strong absorption of aromatic C-C from 1,650 cm-1 to 1,500 cm-1. Whereas in the simulation, the bond between copper and curcumin produces a bond energy of 164.532 kJ/mol or equivalent to 171.12×10-2 eV

Comment on the Vacuum Energy Density for λϕ4 Theory in d Spacetime Dimensions

In a recent article we showed that the vacuum energy density in two spacetime dimensions for a wide variety of integrable quantum field theories has the form ρvac=−m2/2g where m is a physical mass and g is a generalized coupling, where in the free field limit g→0, ρvac diverges. This vacuum energy density has the form ⟨Tμν⟩=−ρvacgμν, and has previously been considered as a contribution to the stress energy tensor in Einstein’s gravity as a “cosmological constant”. We speculated that in four spacetime dimensions ρvac takes a similar form ρvac=−m4/2g, but did not support this idea in any specific model. In this article, we study this problem for λϕ4 theory in d spacetime dimensions. We show how to obtain the exactρvac for the sinh–Gordon theory in the weak coupling limit by using a saddle point approximation. This calculation indicates that the vacuum energy can be well-defined, positive or negative, without spontaneous symmetry breaking. We also show that ρvac satisfies a Callan–Symanzik type of renormalization group equation. For the most interesting case physically, ρvac is positive and can arise from a marginally relevant negative coupling g and the vacuum energy flows to zero at low energies.

High temperature expansion of double scaled SYK

We study the high temperature (or small inverse temperature β) expansion of the free energy of double scaled SYK model. We find that this expansion is a convergent series with a finite radius of convergence. It turns out that the radius of convergence is determined by the first zero of the partition function on the imaginary β-axis. We also show that the semi-classical expansion of the free energy obtained from the saddle point approximation of the exact result is consistent with the high temperature expansion of the free energy.

Classical observables from partial wave amplitudes

We study the formalism of Kosower-Maybee-O’Connell (KMOC) to extract classical impulse from quantum amplitude in the context of the partial wave expansion of a 2-to-2 elastic scattering. We take two complementary approaches to establish the connection. The first one takes advantage of Clebsch-Gordan relations for the base amplitudes of the partial wave expansion. The second one is a novel adaptation of the traditional saddle point approximation in the semi-classical limit. In the former, an interference between the S-matrix and its conjugate leads to a large degree of cancellation such that the saddle point approximation to handle a rapidly oscillating integral is no longer needed. As an example with a non-orbital angular momentum, we apply our methods to the charge-monopole scattering problem in the probe limit and reproduce both of the two angles characterizing the classical scattering. A spinor basis for the partial wave expansion, a non-relativistic avatar of the spinor-helicity variables, plays a crucial role throughout our computations.

Biophysical modeling of the electric field magnitude and distribution induced by electrical stimulation with intracerebral electrodes

Intracranial electrodes are used clinically for diagnostic or therapeutic purposes, notably in drug-refractory epilepsy (DRE) among others. Visualization and quantification of the energy delivered through such electrodes is key to understanding how the resulting electric fields modulate neuronal excitability, i.e. the ratio between excitation and inhibition. Quantifying the electric field induced by electrical stimulation in a patient-specific manner is challenging, because these electric fields depend on a number of factors: electrode trajectory with respect to folded brain anatomy, biophysical (electrical conductivity / permittivity) properties of brain tissue and stimulation parameters such as electrode contacts position and intensity. Here, we aimed to evaluate various biophysical models for characterizing the electric fields induced by electrical stimulation in DRE patients undergoing stereoelectroencephalography (SEEG) recordings in the context of pre-surgical evaluation. This stimulation was performed with multiple-contact intracranial electrodes used in routine clinical practice. We introduced realistic 3D models of electrode geometry and trajectory in the neocortex. For the electrodes, we compared point (0D) and line (1D) sources approximations. For brain tissue, we considered three configurations of increasing complexity: a 6-layer spherical model, a toy model with a sulcus representation, replicating results from previous approaches; and went beyond the state-of-the-art by using a realistic head model geometry. Electrode geometry influenced the electric field distribution at close distances (∼3 mm) from the electrode axis. For larger distances, the volume conductor geometry and electrical conductivity dominated electric field distribution. These results are the first step towards accurate and computationally tractable patient-specific models of electric fields induced by neuromodulation and neurostimulation procedures.

Auxiliary superfield method for statistical predictions of complex, structural acoustics systems: Saddle point approximation for the mean field.

The auxiliary superfield approach is proposed as a method to obtain statistical predictions of the acoustic response of complex elastic structures. The potential advantage of the method is the full retention of interference and resonance effects associated with the degrees of freedom being averaged over. It is not known whether this approach leads to tractable problems for structural acoustics systems, however. We have applied the method to the idealized case of an infinite, thin plate with attached oscillators to obtain the mean Green's function. The oscillators are assumed to have an uncorrelated, Gaussian distributed mass and stiffness distribution representing a simple form of complex internal structure. Using the auxiliary superfield approach, the mean Green's functions are expressed exactly as a functional integral. For relatively small disorder, the integral may be estimated by a saddle point approximation which leads to coupled integral equations for effective mass and stiffness matrices that can be solved numerically for a given spatial distribution of the disorder. With the solutions for these matrices, one obtains a self-consistently determined, generalized fuzzy structure model. We give analytical solutions for the simple case of a uniform spatial distribution. The results are promising for the application of the method to more challenging geometries.

Partition Function for a Volume of Space.

We consider the quantum gravity partition function that counts the dimension of the Hilbert space of a spatial region with topology of a ball and fixed proper volume, and evaluate it in the leading order saddle point approximation. The result is the exponential of the Bekenstein-Hawking entropy associated with the area of the saddle ball boundary, and is reliable within effective field theory provided the mild curvature singularity at the ball boundary is regulated by higher curvature terms. This generalizes the classic Gibbons-Hawking computation of the de Sitter entropy for the case of positive cosmological constant and unconstrained volume, and hence exhibits the holographic nature of nonperturbative quantum gravity in generic finite volumes of space.

A queuing model for ventilator capacity management during the COVID-19 pandemic.

We applied a queuing model to inform ventilator capacity planning during the first wave of the COVID-19 epidemic in the province of British Columbia (BC), Canada. The core of our framework is a multi-class Erlang loss model that represents ventilator use by both COVID-19 and non-COVID-19 patients. Input for the model includes COVID-19 case projections, and our analysis incorporates projections with different levels of transmission due to public health measures and social distancing. We incorporated data from the BC Intensive Care Unit Database to calibrate and validate the model. Using discrete event simulation, we projected ventilator access, including when capacity would be reached and how many patients would be unable to access a ventilator. Simulation results were compared with three numerical approximation methods, namely pointwise stationary approximation, modified offered load, and fixed point approximation. Using this comparison, we developed a hybrid optimization approach to efficiently identify required ventilator capacity to meet access targets. Model projections demonstrate that public health measures and social distancing potentially averted up to 50 deaths per day in BC, by ensuring that ventilator capacity was not reached during the first wave of COVID-19. Without these measures, an additional 173 ventilators would have been required to ensure that at least 95% of patients can access a ventilator immediately. Our model enables policy makers to estimate critical care utilization based on epidemic projections with different transmission levels, thereby providing a tool to quantify the interplay between public health measures, necessary critical care resources, and patient access indicators.

Thermal fluctuations of black holes with non-linear electrodynamics and charged Renyi entropy

We extend the charged Renyi entropy to a more general holographic scenario. Coupling an arbitrary non-linear electrodynamics Lagrangian density to AdS gravity, we analyse the thermodynamic features of non-linearly charged hyperbolic black holes and the thermal fluctuations in the grand canonical ensemble. We provide a general form for the relevant holographic quantities that describes a CFT with a global U(1) symmetry in terms of horizon data and we compute the first thermal fluctuation of the charged Renyi entropy. We demonstrate the validity of the formulae through an analytic example; the Coulomb source in 2 + 1 dimensions. We propose this model to be dual to charged free bosons in 1 + 1 dimensions. The corrections generates a subleading logarithmic divergence in the entanglement entropy which appear in some Condensed Matter systems with spontaneous symmetry breaking due to IR effects in the ground state. We comment on the possibility of interpreting these results in terms of holography beyond the saddle point approximation.

DC operating points of nonlinear circuits and generalized Carleman linearization

PurposeThe purpose of this paper is to present a procedure for approximating DC operating points of nonlinear circuits. The presented approach can also be applied in case of multiple DC operating points.Design/methodology/approachA generalized Carleman linearization is used, which transforms an algebraic nonlinear equation into an equivalent infinite-dimensional linear system. In general, no close-form solution can be given for the infinite-dimensional linear system. Hence, the infinite-dimensional linear system is approximated by a finite one over a predefined interval using a self-consistent technique. The presented procedure allows to approximate all possible DC operating points within a predefined interval. To isolate all DC operating points, the initial interval is gradually divided into subintervals.FindingsIt is shown that the presented approach is not restricted to the polynomial case and allows to approximate all DC operating points. The presented approach can be applied in case of multiple DC operating points and does not depend on the domain of attraction of the DC operating points.Originality/valueA new procedure for the approximation of DC operating points of nonlinear circuits based on a generalized Carleman linearization is presented. This approach can be applied in case of multiple DC operating points and is independent of the domain of attraction. Further, this generalized approach is not restricted to the polynomial case and can be applied to a variety of circuits.

A numerical scheme for the optimal control of groundwater pollution

AbstractA scheme is proposed for the numerical study of optimal control problems related to groundwater quality management in the case of nonpoint‐source pollution. The corresponding state equation is a system of coupled nonlinear partial differential equations. The approximation is given by a finite volume scheme based on a two‐point flux approximation with upwind mobilities embedded in an iterative fixed point approximation. The analysis of the convergence of the scheme allows to establish existence and uniqueness results under reasonable assumptions. Numerical illustrations of the performance of the algorithm are given in realistic situations.

Minisuperspace quantum cosmology from the Einstein-Cartan path integral

We derive the fixed-$\mathrm{\ensuremath{\Lambda}}$ and unimodular propagators using the path integral formalism as applied to the Einstein-Cartan action. The simplicity of the action (which is linear in the lapse function) allows for an exact integration starting from the lapse function and the enforcement of the Hamiltonian constraint, leading to a product of Chern-Simons states if the connection is fixed at the endpoints. No saddle point approximation is needed. Should the metric be fixed at the endpoints, then, depending on the contour chosen for the connection, Hartle-Hawking or Vilenkin propagators are obtained. Thus, in this approach one trades a choice of contour in the lapse function for one in the connection, where appropriate. The unimodular propagators are also trivial to obtain via the path integral, and the previously derived expressions are recovered.