Space-time Volume Research Articles

Guided Event Filtering: Synergy Between Intensity Images and Neuromorphic Events for High Performance Imaging.

Many visual and robotics tasks in real-world scenarios rely on robust handling of high speed motion and high dynamic range (HDR) with effectively high spatial resolution and low noise. Such stringent requirements, however, cannot be directly satisfied by a single imager or imaging modality, rather by multi-modal sensors with complementary advantages. In this paper, we address high performance imaging by exploring the synergy between traditional frame-based sensors with high spatial resolution and low sensor noise, and emerging event-based sensors with high speed and high dynamic range. We introduce a novel computational framework, termed Guided Event Filtering (GEF), to process these two streams of input data and output a stream of super-resolved yet noise-reduced events. To generate high quality events, GEF first registers the captured noisy events onto the guidance image plane according to our flow model. it then performs joint image filtering that inherits the mutual structure from both inputs. Lastly, GEF re-distributes the filtered event frame in the space-time volume while preserving the statistical characteristics of the original events. When the guidance images under-perform, GEF incorporates an event self-guiding mechanism that resorts to neighbor events for guidance. We demonstrate the benefits of GEF by applying the output high quality events to existing event-based algorithms across diverse application categories, including high speed object tracking, depth estimation, high frame-rate video synthesis, and super resolution/HDR/color image restoration.

Globally-Optimal Contrast Maximisation for Event Cameras.

Event cameras are bio-inspired sensors that perform well in challenging illumination conditions and have high temporal resolution. However, their concept is fundamentally different from traditional frame-based cameras. The pixels of an event camera operate independently and asynchronously. They measure changes of the logarithmic brightness and return them in the highly discretised form of time-stamped events indicating a relative change of a certain quantity since the last event. New models and algorithms are needed to process this kind of measurements. The present work looks at several motion estimation problems with event cameras. The flow of the events is modelled by a general homographic warping in a space-time volume, and the objective is formulated as a maximisation of contrast within the image of warped events. Our core contribution consists of deriving globally optimal solutions to these generally non-convex problems, which removes the dependency on a good initial guess plaguing existing methods. Our methods rely on branch-and-bound optimisation and employ novel and efficient, recursive upper and lower bounds derived for six different contrast estimation functions. The practical validity of our approach is demonstrated by a successful application to three different event camera motion estimation problems.

Quantitative Detection of Financial Fraud Based on Deep Learning with Combination of E-Commerce Big Data

At present, there are more and more frauds in the financial field. The detection and prevention of financial frauds are of great significance for regulating and maintaining a reasonable financial order. Deep learning algorithms are widely used because of their high recognition rate, good robustness, and strong implementation. Therefore, in the context of e-commerce big data, this paper proposes a quantitative detection algorithm for financial fraud based on deep learning. First, the encoders are used to extract the features of the behaviour. At the same time, in order to reduce the computational complexity, the feature extraction is restricted to the space-time volume of the dense trajectory. Second, the neural network model is used to transform features into behavioural visual word representations, and feature fusion is performed using weighted correlation methods to improve feature classification capabilities. Finally, sparse reconstruction errors are used to judge and detect financial fraud. This method builds a deep neural network model with multiple hidden layers, learns the characteristic expression of the data, and fully depicts the rich internal information of the data, thereby improving the accuracy of financial fraud detection. Experimental results show that this method can effectively learn the essential characteristics of the data, and significantly improve the detection rate of fraud detection algorithms.

Toward Measuring the Level of Spatiotemporal Clustering of Multi-Categorical Geographic Events

Human activity events are often recorded with their geographic locations and temporal stamps, which form spatial patterns of the events during individual time periods. Temporal attributes of these events help us understand the evolution of spatial processes over time. A challenge that researchers still face is that existing methods tend to treat all events as the same when evaluating the spatiotemporal pattern of events that have different properties. This article suggests a method for assessing the level of spatiotemporal clustering or spatiotemporal autocorrelation that may exist in a set of human activity events when they are associated with different categorical attributes. This method extends the Voronoi structure from 2D to 3D and integrates a sliding-window model as an approach to spatiotemporal tessellations of a space-time volume defined by a study area and time period. Furthermore, an index was developed to evaluate the partial spatiotemporal clustering level of one of the two event categories against the other category. The proposed method was applied to simulated data and a real-world dataset as a case study. Experimental results show that the method effectively measures the level of spatiotemporal clustering patterns among human activity events of multiple categories. The method can be applied to the analysis of large volumes of human activity events because of its computational efficiency.

A Unified Framework for the Solution of Hyperbolic PDE Systems Using High Order Direct Arbitrary-Lagrangian–Eulerian Schemes on Moving Unstructured Meshes with Topology Change

In this work, we review the family of direct Arbitrary-Lagrangian–Eulerian (ALE) finite vlume (FV) and discontinuous Galerkin (DG) schemes on moving meshes that at each time step are rearranged by explicitly allowing topology changes, in order to guarantee a robust mesh evolution even for high shear flow and very long evolution times. Two different techniques are presented: a local nonconforming approach for dealing with sliding lines, and a global regeneration of Voronoi tessellations for treating general unpredicted movements. Corresponding elements at consecutive times are connected in space-time to construct closed space-time control volumes, whose bottom and top faces may be polygons with a different number of nodes, with different neighbors, and even degenerate space-time sliver elements. Our final ALE FV-DG scheme is obtained by integrating, over these arbitrary shaped space-time control volumes, the space-time conservation formulation of the governing hyperbolic PDE system: so, we directly evolve the solution in time avoiding any remapping stage, being conservative and satisfying the GCL by construction. Arbitrary high order of accuracy in space and time is achieved through a fully discrete one-step predictor–corrector ADER approach, also integrated with well balancing techniques to further improve the accuracy and to maintain exactly even at discrete level many physical invariants of the studied system. A large set of different numerical tests has been carried out in order to check the accuracy and the robustness of our methods for both smooth and discontinuous problems, in particular in the case of vortical flows.

Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization

Recent work has dramatically reduced the gate complexity required to quantum simulate chemistry by using linear combinations of unitaries based methods to exploit structure in the plane wave basis Coulomb operator. Here, we show that one can achieve similar scaling even for arbitrary basis sets (which can be hundreds of times more compact than plane waves) by using qubitized quantum walks in a fashion that takes advantage of structure in the Coulomb operator, either by directly exploiting sparseness, or via a low rank tensor factorization. We provide circuits for several variants of our algorithm (which all improve over the scaling of prior methods) including one with O~(N3/2λ) T complexity, where N is number of orbitals and λ is the 1-norm of the chemistry Hamiltonian. We deploy our algorithms to simulate the FeMoco molecule (relevant to Nitrogen fixation) and obtain circuits requiring about seven hundred times less surface code spacetime volume than prior quantum algorithms for this system, despite us using a larger and more accurate active space.

Saving the universe with finite volume effects

Setting aside anthropic arguments, there is no reason why the universe should initially favour a net expanding phase rather than one experiencing a net contraction. However, a collapsing universe containing "normal" matter will end at a singularity in a finite time. We point out that there is a mechanism, derived from non-perturbative effects in Quantum Field Theory in a finite volume, which may provide a bias towards expansion when the spacetime volume shrinks, by dynamically violating the null energy condition, without the need for modified gravity or exotic matter. We describe a scalar field component subjected to this non-perturbative effect in a cosmological background and consider its impact on a contracting phase. We discuss how this could dynamically generate the necessary initial conditions for inflation to get started, or form part of the mechanism for a non-singular cosmological bounce.

Finite size effect on vector meson and baryon sectors in 2+1 flavor QCD at the physical point

We investigate the finite size effect on the vector meson and the baryon sectors using a subset of the "PACS10" configurations which are generated, keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. Comparing the results on (5.5 fm$)^4$ and (10.9 fm$)^4$ lattices the ground states of octet baryons , which are stable on the lattice, show no finite size effect within less than 0.5% level of statistical errors. For those of vector mesons, which are unstable on the lattice, we observe that the effective masses are well below the experimental resonance levels both on (5.5 fm$)^4$ and (10.9 fm$)^4$ lattices. For the decuplet baryon sector we have found that the time dependence of the effective mass looks quite similar to that for the vector meson sector including the $\Omega$ baryon channel. We discuss its origin due to a possible mixing with the nearby multihadron states. Since the $\Xi$ baryon mass can be determined with the smallest ambiguity among the vector meson and the baryon masses, we use it together with the pion and kaon masses as the physical inputs to determine the physical point.

The principles of duality in the light of the system economic theory

This paper shows the diversity and significance of relations of duality among different economic systems. The composition of the principles underlying the system economic theory used for the analysis of duality in the economy is investigated. The concept of the economic system is clarified and the equivalence of three basic concepts of the economic system is shown: a) as a space-time volume (“black box”); b) as a complex of elements and connections among them; c) as a tetrad, including object, project, process and environment components. In a new way, the concept of the tetrad is revealed. The actual interpretation of the interrelationships of its components, based on the mechanisms of intersystem circulation of spatial and temporal resources and the transmission of abilities from one economic system to another, is proposed. On the basis of the obtained results, the most essential aspects of duality in the theory of economic systems are considered. It is shown that the interaction of internal content and the nearest external environment of economic systems lies in the nature of the relations of duality. A new approach to modeling the structure and to functioning of the economic system, based on the description of its activities in the form of two interconnected tetrads (the first tetrad reflects the intrasystem production cycle and the second one — the external realization-reproduction cycle) is put forward. It is shown that the concept of duality in a system economy creates prerequisites for adapting the functioning of local economic systems (objects, projects, etc.) in a market, administrative and functional environments and, as a result, harmonizing the economy as a whole.

Dynamically generated inflation from non-Riemannian volume forms

We propose a simple modified gravity model without any initial matter fields in terms of several alternative non-Riemannian spacetime volume elements within the metric (second order) formalism. We show how the non-Riemannian volume-elements, when passing to the physical Einstein frame, create a canonical scalar field and produce dynamically a non-trivial inflationary-type potential for the latter with a large flat region and a stable low-lying minimum. We study the evolution of the cosmological solutions from the point of view of theory of dynamical systems. The theory predicts the spectral index n_s approx 0.96 and the tensor-to-scalar ratio r approx 0.002 for 60 e-folds, which is in accordance with the observational data. In the future Euclid and SPHEREx missions or the BICEP3 experiment are expected to provide experimental evidence to test those predictions.

High order direct Arbitrary-Lagrangian-Eulerian (ALE) PNPM schemes with WENO Adaptive-Order reconstruction on unstructured meshes

In this work we present a conservative WENO Adaptive Order (AO) reconstruction operator applied to an explicit one-step Arbitrary-Lagrangian-Eulerian (ALE) discontinuous Galerkin (DG) method. The spatial order of accuracy is improved by reconstructing higher order piecewise polynomials of degree M>N, starting from the underlying polynomial solution of degree N provided by the DG scheme. High order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor that arises from a one-step time integration procedure. As a result, space-time polynomials of order M+1 are obtained and used to perform the time evolution of the numerical solution adopting a fully explicit DG scheme.To maintain algorithm simplicity, the mesh motion is restricted to be carried out using straight lines, hence the old mesh configuration at time tn is connected with the new one at time tn+1 via space-time segments, which result in space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our algorithm falls into the category of direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where the governing PDE system is directly discretized relying on a space-time conservation formulation and which already takes into account the new grid geometry directly during the computation of the numerical fluxes. A local rezoning strategy might be used in order to locally optimize the mesh quality and avoiding the generation of invalid elements with negative determinant. The proposed approach reduces to direct ALE finite volume schemes if N=0, while explicit direct ALE DG schemes are recovered in the case of N=M.In order to stabilize the DG solution, an a priori WENO based limiting technique is employed, that makes use of the numerical solution inside the element under consideration and its neighbor cells to find a less oscillatory polynomial approximation. By using a modal basis in a reference element, the evaluation of the oscillation indicators is very easily and efficiently carried out, hence allowing higher order modes to be properly limited, while leaving the zero-th order mode untouched for ensuring conservation.Numerical convergence rates for 2≤N,M≤4 are presented as well as a wide set of benchmark test problems for hydrodynamics on moving and fixed unstructured meshes.

Toward Rate Estimation for Transient Surveys. I. Assessing Transient Detectability and Volume Sensitivity for iPTF

Abstract The past couple of decades have seen an emergence of transient detection facilities in various avenues of time-domain astronomy that have provided us with a rich data set of transients. The rates of these transients have implications in star formation, progenitor models, evolution channels, and cosmology measurements. The crucial component of any rate calculation is the detectability and spacetime volume sensitivity of a survey to a particular transient type as a function of many intrinsic and extrinsic parameters. Fully sampling that multidimensional parameter space is challenging. Instead, we present a scheme to assess the detectability of transients using supervised machine learning. The data product is a classifier that determines the detection likelihood of sources resulting from an image subtraction pipeline associated with time-domain survey telescopes, taking into consideration the intrinsic properties of the transients and the observing conditions. We apply our method to assess the spacetime volume sensitivity of type Ia supernovae (SNe Ia) in the intermediate Palomar Transient Factory (iPTF) and obtain the result, . With rate estimates in the literature, this volume sensitivity gives a count of 680–1160 SNe Ia detectable by iPTF, which is consistent with the archival data. With a view toward wider applicability of this technique we do a preliminary computation for long-duration type IIp supernovae (SNe IIp) and find . This classifier can be used for computationally fast spacetime volume sensitivity calculation of any generic transient type using their light-curve properties. Hence, it can be used as a tool to facilitate calculation of transient rates in a range of time-domain surveys, given suitable training sets.

Generalized earthquake frequency–magnitude distribution described by asymmetric Laplace mixture modelling

SUMMARYThe complete part of the earthquake frequency–magnitude distribution, above the completeness magnitude mc, is well described by the Gutenberg–Richter law. On the other hand, incomplete data does not follow any specific law, since the shape of the frequency–magnitude distribution below max(mc) is function of mc heterogeneities that depend on the seismic network spatiotemporal configuration. This paper attempts to solve this problem by presenting an asymmetric Laplace mixture model, defined as the weighted sum of Laplace (or double exponential) distribution components of constant mc, where the inverse scale parameter of the exponential function is the detection parameter κ below mc, and the Gutenberg–Richter β-value above mc. Using a variant of the Expectation-Maximization algorithm, the mixture model confirms the ontology proposed by Mignan [2012, https://doi.org/10.1029/2012JB009347], which states that the shape of the earthquake frequency–magnitude distribution shifts from angular (in log-linear space) in a homogeneous space–time volume of constant mc to rounded in a heterogeneous volume corresponding to the union of smaller homogeneous volumes. The performance of the proposed mixture model is analysed, with encouraging results obtained in simulations and in eight real earthquake catalogues that represent different seismic network spatial configurations. We find that k = κ/ln(10) ≈ 3 in most earthquake catalogues (compared to b = β/ln(10) ≈ 1), suggesting a common detection capability of different seismic networks. Although simpler algorithms may be preferred on pragmatic grounds to estimate mc and the b-value, other methods so far fail to model the angular distributions observed in homogeneous space-time volumes. Mixture modelling is a promising strategy to model the full earthquake magnitude range, hence potentially increasing seismicity data availability tenfold, since ca. 90 per cent of earthquake catalogue events are below max(mc).

A rezoning-free CESE scheme for solving the compressible Euler equations on moving unstructured meshes

We construct a space-time conservation element and solution element (CESE) scheme for solving the compressible Euler equations on moving meshes (CESE-MM) which allow an arbitrary motion for each of the mesh points. The scheme is a direct extension of a purely Eulerian CESE scheme that was previously implemented on hybrid unstructured meshes (Shen et al. (2015) [43]). It adopts a staggered mesh in space and time such that the physical variables are continuous across the interfaces of the adjacent space-time control volumes and, therefore, a Riemann solver is not required to calculate interface fluxes or the node velocities. Moreover, the staggered mesh can significantly alleviate mesh tangles so that the time step can be kept at an acceptable level without using any rezoning operation. The discretization of the integral space-time conservation law is completely based on the physical space-time control volume, thereby satisfying the physical and geometrical conservation laws. Plenty of numerical examples are carried out to validate the accuracy and robustness of the CESE-MM scheme.

Exploring the partonic phase at finite chemical potential within an extended off-shell transport approach

We extend the Parton-Hadron-String Dynamics (PHSD) transport approach in the partonic sector by explicitly calculating the total and differential partonic scattering cross sections as a function of temperature $T$ and baryon chemical potential $\mu_B$ on the basis of the effective propagators and couplings from the Dynamical QuasiParticle Model (DQPM) that is matched to reproduce the equation of state of the partonic system above the deconfinement temperature $T_c$ from lattice QCD. The ratio of shear viscosity $\eta$ over entropy density $s$, i.e. $\eta/s$, is evaluated using the collisional widths and compared to lQCD calculations for $\mu_B$ = 0 as well. We find only a very modest change of $\eta/s$ with the baryon chemical $\mu_B$. This also holds for a variety of hadronic observables from central A+A and C+Au collisions in the energy range 5 GeV $\leq \sqrt{s_{NN}} \leq$ 200 GeV when implementing the differential cross sections into the PHSD approach. We only observe small differences in the strangeness and antibaryon sector with practically no sensitivity of rapidity and $p_T$ distributions to the $\mu_B$ dependence of the partonic cross sections. Since we find only small traces of a $\mu_B$-dependence in heavy-ion observables - although the effective partonic masses and widths as well as their partonic cross sections clearly depend on $\mu_B$ - this implies that one needs a sizable partonic density and large space-time QGP volume to explore the dynamics in the partonic phase. These conditions are only fulfilled at high bombarding energies where $\mu_B$ is, however, rather low. On the other hand, when decreasing the bombarding energy and thus increasing $\mu_B$, the hadronic phase becomes dominant and accordingly, it will be difficult to extract signals from the partonic dynamics based on "bulk" observables.

Joint Dynamic Pose Image and Space Time Reversal for Human Action Recognition from Videos

Human action recognition aims to classify a given video according to which type of action it contains. Disturbance brought by clutter background and unrelated motions makes the task challenging for video frame-based methods. To solve this problem, this paper takes advantage of pose estimation to enhance the performances of video frame features. First, we present a pose feature called dynamic pose image (DPI), which describes human action as the aggregation of a sequence of joint estimation maps. Different from traditional pose features using sole joints, DPI suffers less from disturbance and provides richer information about human body shape and movements. Second, we present attention-based dynamic texture images (att-DTIs) as pose-guided video frame feature. Specifically, a video is treated as a space-time volume, and DTIs are obtained by observing the volume from different views. To alleviate the effect of disturbance on DTIs, we accumulate joint estimation maps as attention map, and extend DTIs to attention-based DTIs (att-DTIs). Finally, we fuse DPI and att-DTIs with multi-stream deep neural networks and late fusion scheme for action recognition. Experiments on NTU RGB+D, UTD-MHAD, and Penn-Action datasets show the effectiveness of DPI and att-DTIs, as well as the complementary property between them.

Holographic purification complexity

We study holographic subregion complexity, and its possible connection to purification complexity suggested recently by Ag\'on et al. In particular, we study the conjecture that subregion complexity is the purification complexity by considering holographic purifications of a holographic mixed state. We argue that these include states with any amount of coarse-graining consistent with being a purification of the mixed state in question, corresponding holographically to different choices of the cutoff surface. We find that within the complexity = volume and complexity = spacetime volume conjectures, the subregion complexity is equal to the holographic purification complexity. For complexity = action, the subregion complexity seems to provide an upper bound on the holographic purification complexity, though we show cases where this bound is not saturated. One such example is provided by black holes with a large genus behind the horizon, which were studied by Fu et al. As such, one must conclude that these offending geometries are not holographic, that CA must be modified, or else that holographic subregion complexity in CA is not dual to the purification complexity of the corresponding reduced state.

Gauss–Bonnet gravity in D = 4 without Gauss–Bonnet coupling to matter: Cosmological implications

We propose a new model of D = 4 Gauss–Bonnet gravity. To avoid the usual property of the integral over the standard D = 4 Gauss–Bonnet scalar becoming a total derivative term, we employ the formalism of metric-independent non-Riemannian spacetime volume elements which makes the D = 4 Gauss–Bonnet action term nontrivial without the need to couple it to matter fields unlike the case of ordinary D = 4 Gauss–Bonnet gravity models. The non-Riemannian volume element dynamically triggers the Gauss–Bonnet scalar to be an arbitrary integration constant M on-shell, which in turn has several interesting cosmological implications. (i) It yields specific solutions for the Hubble parameter and the Friedmann scale factor as functions of time, which are completely independent of the matter dynamics, i.e. there is no back reaction by matter on the cosmological metric. (ii) For M[Formula: see text]0, it predicts a “coasting”-like evolution immediately after the Big Bang, and it yields a late universe with dynamically produced dark energy density given through M. (iii) For the special value M = 0, we obtain exactly a linear “coasting” cosmology. (iv) For M[Formula: see text]0, we have in addition to the Big Bang also a Big Crunch with “coasting”-like evolution around both. (v) It allows for an explicit analytic solution of the pertinent Friedmann and [Formula: see text] scalar field equations of motion, while dynamically fixing uniquely the functional dependence on [Formula: see text] of the scalar potential.

Resource optimized quantum architectures for surface code implementations of magic-state distillation

Quantum computers capable of solving classically intractable problems are under construction, and intermediate-scale devices are approaching completion. Current efforts to design large-scale devices require allocating immense resources to error correction, with the majority dedicated to the production of high-fidelity ancillary states known as magic-states. Leading techniques focus on dedicating a large, contiguous region of the processor as a single “magic-state distillation factory” responsible for meeting the magic-state demands of applications.In this work we design and analyze a set of optimized factory architectural layouts that divide a single factory into spatially distributed factories located throughout the processor. We find that distributed factory architectures minimize the space-time volume overhead imposed by distillation. Additionally, we find that the number of distributed components in each optimal configuration is sensitive to application characteristics and underlying physical device error rates. More specifically, we find that the rate at which T-gates are demanded by an application has a significant impact on the optimal distillation architecture. We develop an optimization procedure that discovers the optimal number of factory distillation rounds and number of output magic states per factory, as well as an overall system architecture that interacts with the factories. This yields between a 10x and 20x resource reduction compared to commonly accepted single factory designs. Performance is analyzed across representative application classes such as quantum simulation and quantum chemistry.

Quantum strong energy inequalities

Quantum energy inequalities (QEIs) express restrictions on the extent to which weighted averages of the renormalized energy density can take negative expectation values within a quantum field theory. Here we derive, for the first time, QEIs for the effective energy density (EED) for the quantized non-minimally coupled massive scalar field. The EED is the quantity required to be non-negative in the strong energy condition (SEC), which is used as a hypothesis of the Hawking singularity theorem. Thus establishing a quantum strong energy inequality is a first step towards a singularity theorem for matter described by quantum field theory. More specifically, we derive a difference QEI, where the local average of the EED is normal-ordered relative to the one in a reference state. Furthermore, the lower bounds we derive over timelike geodesics or spacetime volumes turn out to depend on the state of interest. We analyse the state-dependence of these bounds in Minkowski spacetime for thermal (KMS) states, and show that the lower bounds grow more slowly in magnitude than the EED itself as the temperature increases. The lower bounds are therefore of lower energetic order than the EED, and qualify as nontrivial state-dependent QEIs.