Spatio-temporal Inverse Research Articles

Non-Abelian Hopf-Euler insulators

We discuss a class of three-band non-Abelian topological insulators in three dimensions that carry a single bulk Hopf index protected by spatiotemporal (PT) inversion symmetry. These phases may also host subdimensional topological invariants given by the Euler characteristic class, resulting in real Hopf-Euler insulators. Such systems naturally realize helical nodal structures in the three-dimensional Brillouin zone, providing a physical manifestation of the linking number described by the Hopf invariant. We show that, by opening a gap between the valence bands of these systems, one finds a fully-gapped “flag” phase, which displays a three-band multigap Pontryagin invariant. Unlike the previously reported PT-symmetric four-band real Hopf insulator, which hosts a Z⊕Z invariant, these phases are not unitarily equivalent to two copies of a complex two-band Hopf insulator. We show that such uncharted phases can be obtained through dimensional extension of two-dimensional Euler insulators, and that they support (i) an optical bulk integrated circular shift effect quantized by the Hopf invariant, (ii) quantum-geometric breathing in the real-space Wannier functions, and (iii) surface Euler topology on boundaries. Consequently, our findings pave the way for novel experimental realizations of real-space quantum geometry, as these systems may be directly simulated by utilizing synthetic dimensions in metamaterials or ultracold atoms. Published by the American Physical Society 2024

Refocusing of the optical branched flow on a rough curved surface

The phenomenon of branched flow has attracted researchers since its inception, with recent observations of the light branching on soap bubbles. However, previous studies have primarily focused on the flat spacetime, overlooking the effect of surface curvature on branched flows. In this paper, we explore the branched flow phenomenon of light on a rough curved surface called constant Gaussian curvature surfaces (CGCSs). Compared with flat space, a CGCS demonstrates that the first branching point advances due to the focusing effect of the positive curvature of the surface. Furthermore, unlike on flat space, optical branches on curved surfaces do not consistently become chaotic during its transmission in a random potential field. On the contrary, the “entropy” decreases at specific positions, which reveals a sink flow phenomenon following the generation of branched flows. This result highlights the time inversion characteristics of CGCSs. Lastly, we demonstrated that the anomalous entropy reduction is related to the transverse and longitudinal coherence transformations of light. We suppose these efforts would fuel further investigation of the thermodynamic evolution and spatiotemporal inversion of random caustics, as well as their future application in the information transmission of random potentials in curved spacetime.

Spatio-Temporal Inversion Using the Selection Kalman Model

Data assimilation in models representing spatio-temporal phenomena poses a challenge, particularly if the spatial histogram of the variable appears with multiple modes. The traditional Kalman model is based on a Gaussian initial distribution and Gauss-linear forward and observation models. This model is contained in the class of Gaussian distribution and is therefore analytically tractable. It is however unsuitable for representing multimodality. We define the selection Kalman model that is based on a selection-Gaussian initial distribution and Gauss-linear forward and observation models. The selection-Gaussian distribution can be seen as a generalization of the Gaussian distribution and may represent multimodality, skewness and peakedness. This selection Kalman model is contained in the class of selection-Gaussian distributions and therefore it is analytically tractable. An efficient recursive algorithm for assessing the selection Kalman model is specified. The synthetic case study of spatio-temporal inversion of an initial state, inspired by pollution monitoring, suggests that the use of the selection Kalman model offers significant improvements compared to the traditional Kalman model when reconstructing discontinuous initial states.

Fault Throw and Regional Uplift Histories From Drainage Analysis: Evolution of Southern Italy

AbstractLandscapes can record elevation changes caused by multiple tectonic processes. Here, we show how coeval histories of spatially coincident normal faulting and regional uplift can be deconvolved from river networks. We focus on Calabria, a tectonically active region incised by rivers containing knickpoints and knickzones. Marine fauna indicate that Calabria has been uplifted by >1 km since ∼0.8–1.2 Ma, which we used to calibrate parameters in a stream power erosional model. To deconvolve the local and regional uplift contributions to topography, we performed a spatiotemporal inversion of 994 fluvial longitudinal profiles. Uplift rates from fluvial inversion replicate the spatial trend of rates derived from dated Mid‐Late Pleistocene marine terraces, and the magnitude of predicted uplift rates matches the majority of marine terrace uplift rates. We used the predicted uplift history to analyze long‐term fault throw, and combined throw estimates with ratios of footwall uplift to hanging wall subsidence to isolate the nonfault related contribution to uplift. Increases in fault throw rate—which may suggest fault linkage and growth—have been identified on two major faults from fluvial inverse modeling, and total fault throw is consistent with independent estimates. The temporal evolution of nonfault related regional uplift is similar at three locations. Our results may be consistent with toroidal mantle flow generating uplift, perhaps if faulting reduces the strength of the overriding plate. In conclusion, fluvial inverse modeling can be an effective technique to quantify fault array evolution and can deconvolve different sources of uplift that are superimposed in space and time.

Inverse Cascades of Kinetic Energy as a Source of Intrinsic Variability: A Global OGCM Study

AbstractA seasonally forced 1/12° global ocean/sea ice simulation is used to characterize the spatiotemporal inverse cascade of kinetic energy (KE). Nonlinear scale interactions associated with relative vorticity advection are evaluated using cross-spectral analysis in the frequency–wavenumber domain from sea level anomaly (SLA) time series. This analysis is applied within four eddy-active midlatitude regions having large intrinsic variability spread over a wide range of scales. Over these four regions, mesoscale surface KE is shown to spontaneously cascade toward larger spatial scales—between the deformation scale and the Rhines scale—and longer time scales (possibly exceeding 10 years). Other nonlinear processes might have to be invoked to explain the longer time scales of intrinsic variability, which have a substantial surface imprint at midlatitudes. The analysis of a fully forced 1/12° hindcast shows that low-frequency and synoptic atmospheric forcing barely affects this inverse KE cascade. The inverse cascade is also at work in a 1/4° simulation, albeit with a weaker intensity, consistent with the weaker intrinsic variability found at this coarser resolution. In the midlatitude North Pacific, the spatiotemporal cascade transfers KE from high-frequency frontal Rossby waves (FRWs), probably generated by baroclinic instability, toward the lower-frequency, westward-propagating mesoscale eddy (WME) field. The WMEs provide local gradients of potential vorticity that support these short Doppler-shifted FRWs. FRWs have periods shorter than 2 months and might be subsampled by altimetric observations, perhaps explaining why the temporal inverse cascade deduced from high-resolution models and mapped altimeter products can be quite different. The nature of the nonlinear interactions between FRWs and WMEs remains unclear but might involve wave turbulence processes.

Mapping soil water dynamics and a moving wetting front by spatiotemporal inversion of electromagnetic induction data

AbstractCharacterization of the spatiotemporal distribution of soil volumetric water content (θ) is fundamental to agriculture, ecology, and earth science. Given the labor intensive and inefficient nature of determining θ, apparent electrical conductivity (ECa) measured by electromagnetic induction has been used as a proxy. A number of previous studies have employed inversion algorithms to convert ECa data to depth‐specific electrical conductivity (σ) which could then be correlated to soil θ and other soil properties. The purpose of this study was to develop a spatiotemporal inversion algorithm which accounts for the temporal continuity of ECa. The algorithm was applied to a case study where time‐lapse ECa was collected on a 350 m transect on seven different days on an alfalfa farm in the USA. Results showed that the approach was able to map the location of moving wetting front along the transect. Results also showed that the spatiotemporal inversion algorithm was more precise (RMSE = 0.0457 cm3/cm3) and less biased (ME = −0.0023 cm3/cm3) as compared with the nonspatiotemporal inversion approach (0.0483 cm3/cm3 and ME = −0.0030 cm3/cm3, respectively). In addition, the spatiotemporal inversion algorithm allows for a reduced set of ECa surveys to be used when non abrupt changes of soil water content occur with time. To apply this spatiotemporal inversion algorithm beyond low induction number condition, full solution of the EM induction phenomena can be studied in the future.

One-channel inverse filter: Spatio-temporal control of a complex wave-field from a single point

Can we make good use of the degrees of freedom of a wave-field trapped in a cavity to perform complete spatio-temporal inversion from a single emitter? To answer these questions, we used experiments conducted in the ultrasonic regime to investigate the wave-field in a water cavity where the energy was not homogeneously distributed over all of the degrees of freedom. While the time reversal from a single emitter gives poor results, we show the possibility to recover optimal spatio-temporal focusing by converting the multi-channel focusing technique of the spatio-temporal inverse filter into a single-channel method that we call the one-channel inverse filter. In particular, this method has the advantage of leaving the choice open for the duration of the time window for the inversion of the wave-field. We, thus, demonstrate that the shorter the time window, the better optimized the inversion. We believe that in addition to demonstrating the possibility of controlling the waves in a cavity, this method might have an interesting role in the improvement of solid imaging devices that are based on the exploitation of reverberations in cavities.

A passive inverse filter for Green’s function retrieval

Passive methods for the recovery of Green's functions from ambient noise require strong hypotheses, including isotropic distribution of the noise sources. Very often, this distribution is nonisotropic, which introduces bias in the Green's function reconstruction. To minimize this bias, a spatiotemporal inverse filter is proposed. The method is tested on a directive noise field computed from an experimental active seismic data set. The results indicate that the passive inverse filter allows the manipulation of the spatiotemporal degrees of freedom of a complex wave field, and it can efficiently compensate for the noise wavefield directivity.

One channel spatio-temporal inversion of acoustic wave in reverberant cavities

It has been recently shown that it was possible to optimally recover the Green functions from a complex wave field despite of a non-isotropic distribution of the noise sources. The method used is based on a particular use of the inverse filter (IF) formalism which is called the passive IF. Based on this formalism, we have investigated the possibility to control the spatio-temporal degrees of freedom in a reverberant cavity for the focusing of waves (active processes). The understanding of this phenomenon can be very useful in a lot of different applications like in acoustical imaging, seismology, or telecommunications. In the present work, the spatio-temporal focalization of ultrasounds in reverberant cavities is studied using medical arrays and water tanks. Through experiments, a complete spatio-temporal inversion is realized to synthesize optimized emitting signals. The result generalizes the focalization control over a spatial vector and during an arbitrary time window.

Spatio-temporal coding in complex media for optimum beamforming: the iterative time-reversal approach

Spatio-temporal encoding in transmit and receive modes is of major importance in the development of ultrasound imaging devices. Classically, the assumption of constant sound speed in the medium allows one to restrict the beamforming process to the application of a cylindrical time-delay law on the elements of a multiple-transducer array. Here is proposed an iterative time-reversal method capable of taking into account all the heterogeneities of the medium, concerning density, speed of sound, and absorption variations. It will be shown that this iterative focusing process converges toward a spatio-temporal inverse filter focusing, the first step of the process being a time-reversal focusing on the targeted point. This method can be seen as a calibration process and has been successfully applied to transskull focusing and intraplate echoes suppression. It is leading the way to promising applications such as high-resolution ultrasonic brain imaging and high-resolution focusing through complex reverberating media, in nondestructive testing and telecommunications. This work highlights the advantages of using spatio-temporal coding to focus through complex media. Such codes require the use of fully programmable, multichannel electronics to implement this technique in real time.

Real time inverse filter focusing through iterative time reversal

In order to achieve an optimal focusing through heterogeneous media we need to build the inverse filter of the propagation operator. Time reversal is an easy and robust way to achieve such an inverse filter in nondissipative media. However, as soon as losses appear in the medium, time reversal is not equivalent to the inverse filter anymore. Consequently, it does not produce the optimal focusing and beam degradations may appear. In such cases, we showed in previous works that the optimal focusing can be recovered by using the so-called spatiotemporal inverse filter technique. This process requires the presence of a complete set of receivers inside the medium. It allows one to reach the optimal focusing even in extreme situations such as ultrasonic focusing through human skull or audible sound focusing in strongly reverberant rooms. But, this technique is time consuming and implied fastidious numerical calculations. In this paper we propose a new way to process this inverse filter focusing technique in real time and without any calculation. The new process is based on iterative time reversal process. Contrary to the classical inverse filter technique, this iteration does not require any computation and achieves the inverse filter in an experimental way using wave propagation instead of computational power. The convergence from time reversal to inverse filter during the iterative process is theoretically explained. Finally, the feasibility of this iterative technique is experimentally demonstrated for ultrasound applications.

Sound focusing in rooms. II. The spatio-temporal inverse filter.

The potential of time reversal processing for room acoustics has been extensively investigated in the companion of this paper [J. Acoust. Soc. Am. 113(3), 1533-1543 (2003)]. In particular, a simple implementation of a loudspeaker time reversal antenna able to take advantage of the multiple reflections in reverberating rooms demonstrates its potential for audible range acoustics while improving focusing both in space and time. However, loss of information (e.g., sound absorption in walls or nonequalized bandwidths of the loudspeakers) during a time reversal experiment degrades the quality of time reversal focusing. In this paper, a more sophisticated technique called spatio-temporal inverse filtering is investigated that achieves time and space deconvolution of the propagation operator between the loudspeakers antenna and a set of microphones embedded inside the insonified volume. Theoretical and experimental comparisons between time reversal and inverse filter focusing are presented. Finally, advantages and limitations of both focusing approaches are highlighted.

Real time inverse filter focusing by iterative time reversal

In order to achieve an optimal focusing through heterogeneous media, we need to build an inverse filter of the propagation operator. Time-reversal achieves such an inverse filter in nondissipative media. However, as soon as losses appear in the medium, time-reversal is no more equivalent to an inverse filter. Consequently, it does no more produce the optimal focusing and beam degradations may appear. In such cases, previous works have shown that the optimal focusing can be recovered by using a spatiotemporal inverse filter technique. This process requires the presence of a set of receivers inside the medium but allows us to reach the optimal focusing even in extreme situations such as ultrasonic focusing through a human skull. To date, it remained time consuming and implied fastidious numerical calculations. We propose here a new way to process this inverse filtering in real time and without any calculation. The new process is based on iterative time-reversal processing. Contrary to the classical inversion, this iteration does not require any computation as it achieves the inverse filter experimentally using waves propagation instead of computational power. The feasibility of this iterative technique is theoretically and experimentally demonstrated for ultrasound applications and its potential for telecommunications is discussed.

Focusing by spatiotemporal inverse filter: Application to heterogeneous and absorbing medium

In most applications of ultrasound, a first step consists in focusing a broadband ultrasonic beam deeply inside the medium. Nevertheless, sound speed, density, or absorption heterogeneities may strongly degrade the focusing. Different techniques have been developed to correct such aberrations (time reversal, speckle brightness,...). Recently, we investigated a new broadband focusing technique, the spatiotemporal inverse filter, based on the inversion of the propagation operator relating a transducer array to a set of control points inside the medium. As this inversion is achieved both in space and time, it allows one to calculate the set of temporal signals to be emitted by each array element for an optimal focusing on a chosen control point. Potential applications have been experimentally investigated in heterogeneous and absorbing media where classical geometrical focusing is highly degraded. The strong improvement achieved by inverse filter compared to time reversal and classical focusing emphasizes the great potential of multichannel systems having the ability to apply completely different waveforms on each element. Particularly, intraplate echoes suppression in NDT, high quality focusing through a human skull, as well as hyper-resolution in reverberating media highlight its great interest in various fields such as medical imaging, nondestructive testing, room acoustics, and underwater acoustics.

Optimal focusing by spatio-temporal inverse filter. II. Experiments. Application to focusing through absorbing and reverberating media.

To focus ultrasonic waves in an unknown heterogeneous medium using a phased array, one has to calculate the optimal set of signals to be applied on the transducers of the array. (In most applications of ultrasound, medical imaging, medical therapy, nondestructive testing, the first step consists of focusing a broadband ultrasound beam deeply inside the medium to be investigated.) Focusing in a homogeneous medium simply requires to compensate for the varying focus-array elements geometrical distances. Nevertheless, heterogeneities in the medium, in terms of speed of sound, density, or absorption, may strongly degrade the focusing. Different techniques have been developed in order to correct such aberrations induced by heterogeneous media (time reversal, speckle brightness, for example). In the companion to this paper, a new broadband focusing technique was investigated: the spatio-temporal inverse filter. Experimental results obtained in various media, such as reverberating and absorbing media, are presented here. In particular, intraplate echoes suppression and high-quality focusing through a human skull, as well as hyper-resolution in a reverberating medium, will be shown. It is important to notice that all these experiments were performed with fully programmable multichannel electronics whose use is required to fully exploit the spatio-temporal technique.

Kinetic images of neuronal activity of the human brain based on the spatio-temporal MNLS inverse: a theoretical study.

Prior work proved that it is possible to find a unique solution to the problem of defining the configuration of electric current underlying observed extracranial magnetic fields, if sufficient priori knowledge of the source configuration is available. This minimum-norm least-squares (MNLS) inverse solution for a magnetic source image (MSI) is extended here to include temporal as well as spatial parameters of the underlying current pattern. This capitalizes on the temporal resolution of magnetoencephalography (MEG), which is on the order of milliseconds. Other forms of functional brain imaging are far less sensitive to the rate of change of states of the brain. Influences on the quality of the resulting MSI by measurement noise and errors in determining the image surface are characterized. A new technique for reducing noise in the inverse problem is developed by taking into consideration the spatial and time-dependence of the noise detected by the sensors. This new approach to regularization reduces the contribution from noisy measurements to the inverse calculation, and therefore improves the stability of the inverse.

Empirically derived model of the role of sleep in associative learning and recuperative processes

Neuronal firing patterns, defined as intraburst temporal relations between sequential spike intervals, were monitored extracellularly from the rostral part of the nucleus reticularis (NR) and from the centrum medianum—parafascicular complex (CM-Pf) of the thalamus in adult freely moving cats during acquisition of bar pressing behavior (BP1) for milk reward, subsequent slow wave sleep (SWS1), and contiguous rapid eye movement (REM1) sleep, and then, 16 to 48 h later, after the animal fully learned the conditioned BP behavior (BP2). The patterns were defined on the basis of relative relations between sequential spike intervals. The intervals were compared in sequential pairs, moving one interval at a time. This method, if applied to random and/or independent values, generates a novel and well-defined theoretical distribution of inequality patterns which is uniquely sensitive to the history of spike train and plastic changes at neuronal membrane. The “information” encoded in single neuronal firing patterns was quantified using two criteria: (a) the magnitude of pattern emissions with reference to the random model; and (b) the difference between pattern distribution during BP1-training/acquisition and after the animal fully acquired the BP behavior. The latter patterns, termed BP2-template, were assumed to be composed only of patterns relevant for learned behavior. Thus, other patterns observed during BP-1, SWS, and REM were classified as spurious. During BP-1 training/acquisition of conditioned behavior, in 28 out of 265 neurons studied, the firing patterns linked to and relevant for BP behavior emerged in background of spurious patterns. Subsequently, during SWS-1, the relevant patterns were selectively suppressed below chance level. Conversely, during REM-1 sleep, contiguous with SWS-1, patterns linked to acquisition of BP behavior were strongly amplified above the level observed during BP1-training episode, while the ‘spurious’ patterns were eliminated. Thus, REM-1 patterns may be regarded as amplified precursors of the BP2-template which, 16 to 48 h later, and often after additional training, emerged with the acquired conditioned BP behavior. With reference to the random model, the emission magnitudes of individual BP-1 patterns were correlated with suppressions of same patterns during subsequent SWS-1. The magnitudes of these deficits were, in turn, correlated with subsequent REM1-induced amplified emission of same patterns. These observations indicate that: (a) acquisition of operantly conditioned behavior is linked to inversions in statistical distribution of patterns during BP1, SWS1, and REM1 episodes; and (b) the inversions are not random but graded, and therefore are likely to reflect the well-known graded nature of receptor desensitization which may result from repetitive exposure to neurotransmitters and/or modulators during a motor task that requires repetitive use of the same set of neuronal assemblies and pathways over a significant period of time. The neuronal firing patterns in “control” episodes of milk drinking from a bowl (BOWL) had, on the average, no significant relationships to BP, SWS, nor REM episodes. The results provide: (a) a novel insight into the information processing based on intraburst temporal organization of spike trains, as opposed to the mean firing rate; (b) a novel concept of homeostatic behavior of neurons which is consistent with current views on the physico-chemical dynamics of neuronal membrane and its receptors; (c) the first quantifiable empirical evidence for the relationships between firing patterns, learning, SWS, and REM sleep; and (d) the results suggest a new model for learning linked to recuperative role of sleep which is based on spatio-temporal inversion of neuronal interactions and depolarization-induced recovery (DIR) of synaptic receptors that had been down regulated during waking state. This notion is compatible with receptor changes in vitro and in vivo.

How do societies and “corporate” groups delimit themselves? A puzzle common to social and medical anthropology

Classic anthropological theories define the first but neglect the second condition of social life. When they assume that the universal effect of the incest taboo is the opening of the consanguinial groups to the others, to exchange, they do not explain the closure of their sphere of reciprocity, i.e., the delimitation of the society. Hence the question: How, by which means, are stateless societies delimited or do they delimit themselves? Among the Senoufo of Ivory Coast (Nafara), one of the main acts of male initiation ceremonies--to the Poro, which is the very basis of the Senoufo's ethnic identity--is a ritual intercourse between the neophytes and their symbolic mother who has just given birth to them. This rite materializes the initiatic axiom: Senoufo men reproduce themselves by incest. In this case, the prescription of ritual incest is a means by which the society "closes" the field of reciprocity "opened" by the prohibition of actual incest. The return of the forbidden--at the heart of the institution which reproduces its identity--is the basic principle of the ritual delimitation of this society. Despite appearances, the delimitation of the so-called "corporate groups"--for example, an African lineage--is neither more "natural" nor more jural than that of the society which contains them. The limits of these groups are traced and retraced notably in the course of traditional "therapies" and by means of etiological entities which share several common, distinctive properties. (1) They cannot operate outside of the group delimited by them. (2) They are polyvalent and their effects are permutable from one group-member to another. (3) They act periodically: they have to dismantle the group periodically from the inside in order to be able to delimit it constantly from the outside. This phenomenon of spatio-temporal inversion (inside-outside; periodic-continuous), observable in any process of ritual delimitation, deserves our attention insofar as its closer analysis could lead us to rethink our present theories of ritual.