Higher-order Memory Research Articles

Memory Corrections to Markovian Langevin Dynamics.

Analysis of non-Markovian systems and memory-induced phenomena poses an everlasting challenge in the realm of physics. As a paradigmatic example, we consider a classical Brownian particle of mass M subjected to an external force and exposed to correlated thermal fluctuations. We show that the recently developed approach to this system, in which its non-Markovian dynamics given by the Generalized Langevin Equation is approximated by its memoryless counterpart but with the effective particle mass M∗<M, can be derived within the Markovian embedding technique. Using this method, we calculate the first- and the second-order memory correction to Markovian dynamics of the Brownian particle for the memory kernel represented as the Prony series. The second one lowers the effective mass of the system further and improves the precision of the approximation. Our work opens the door for the derivation of higher-order memory corrections to Markovian Langevin dynamics.

Diverse memory paradigms in Drosophila reveal diverse neural mechanisms.

In this review, we aggregated the different types of learning and memory paradigms developed in adult Drosophila and attempted to assess the similarities and differences in the neural mechanisms supporting diverse types of memory. The simplest association memory assays are conditioning paradigms (olfactory, visual, and gustatory). A great deal of work has been done on these memories, revealing hundreds of genes and neural circuits supporting this memory. Variations of conditioning assays (reversal learning, trace conditioning, latent inhibition, and extinction) also reveal interesting memory mechanisms, whereas mechanisms supporting spatial memory (thermal maze, orientation memory, and heat box) and the conditioned suppression of innate behaviors (phototaxis, negative geotaxis, anemotaxis, and locomotion) remain largely unexplored. In recent years, there has been an increased interest in multisensory and multicomponent memories (context-dependent and cross-modal memory) and higher-order memory (sensory preconditioning and second-order conditioning). Some of this work has revealed how the intricate mushroom body (MB) neural circuitry can support more complex memories. Finally, the most complex memories are arguably those involving social memory: courtship conditioning and social learning (mate-copying and egg-laying behaviors). Currently, very little is known about the mechanisms supporting social memories. Overall, the MBs are important for association memories of multiple sensory modalities and multisensory integration, whereas the central complex is important for place, orientation, and navigation memories. Interestingly, several different types of memory appear to use similar or variants of the olfactory conditioning neural circuitry, which are repurposed in different ways.

Neural field theory of adaptive effects on auditory evoked responses and mismatch negativity in multifrequency stimulus sequences.

Physiologically based neural field theory (NFT) of the corticothalamic system, including adaptation, is used to calculate the responses evoked by trains of auditory stimuli that differ in frequency. In oddball paradigms, fully distinguishable frequencies lead to different standard (common stimulus) and deviant (rare stimulus) responses; the signal obtained by subtracting the standard response from the deviant is termed the mismatch negativity (MMN). In this analysis, deviant responses are found to correspond to unadapted cortex, whereas the part of auditory cortex that processes the standard stimuli adapts over several stimulus presentations until the final standard response form is achieved. No higher-order memory processes are invoked. In multifrequency experiments, the deviant response approaches the standard one as the deviant frequency approaches that of the standard and analytic criteria for this effect to be obtained. It is shown that these criteria can also be used to understand adaptation in random tone sequences. A method of probing MMNs and adaptation in random tone sequences is suggested to makes more use of such data.

Higher-order memory guided temporal random walk for dynamic heterogeneous network embedding

Network embedding (NE) aims at learning node embeddings via structure-based sampling. However, there are complex patterns in network structure (heterogeneity, higher-order dependence, dynamics) in the real world. The existing methods suffer from high dependence and constraints on manually designed higher-order structures and loss of fine-grained temporal information. To solve the above challenges, we propose a novel higher-order memory guided temporal random walk for dynamic heterogeneous network embedding (HoMo-DyHNE). The proposed model is a two-stage architecture consisting of a meta-structure-independent random walk algorithm namely HoMo-TRW with transition vectors and higher-order memory, and a Hawkes-based featured Skip-gram (HFSG) incorporating a multivariate Hawkes point process to measure the history-current association intensity. Extensive experiments demonstrate the superior effectiveness of our proposed method.

Inefficient Recovery of Repeatedly Stimulated Memory CD8 T Cells after Polymicrobial Sepsis Induction Leads to Changes in Memory CD8 T Cell Pool Composition.

Long-lasting sepsis-induced immunoparalysis has been principally studied in primary (1°) memory CD8 T cells; however, the impact of sepsis on memory CD8 T cells with a history of repeated cognate Ag encounters is largely unknown but important in understanding the role of sepsis in shaping the pre-existing memory CD8 T cell compartment. Higher-order memory CD8 T cells are crucial in providing immunity against common pathogens that reinfect the host or are generated by repeated vaccination. In this study, we analyzed peripheral blood from septic patients and show that memory CD8 T cells with defined Ag specificity for recurring CMV infection proliferate less than bulk populations of central memory CD8 T cells. Using TCR-transgenic T cells to generate 1° and higher-order (quaternary [4°]) memory T cells within the same host, we demonstrate that the susceptibility and loss of both memory subsets are similar after sepsis induction, and sepsis diminished Ag-dependent and -independent (bystander) functions of these memory subsets equally. Both the 1° and 4° memory T cell populations proliferated in a sepsis-induced lymphopenic environment; however, due to the intrinsic differences in baseline proliferative capacity, expression of receptors (e.g., CD127/CD122), and responsiveness to homeostatic cytokines, 1° memory T cells become overrepresented over time in sepsis survivors. Finally, IL-7/anti-IL-7 mAb complex treatment early after sepsis induction preferentially rescued the proliferation and accumulation of 1° memory T cells, whereas recovery of 4° memory T cells was less pronounced. Thus, inefficient recovery of repeatedly stimulated memory cells after polymicrobial sepsis induction leads to changes in memory T cell pool composition, a notion with important implications in devising strategies to recover the number and function of pre-existing memory CD8 T cells in sepsis survivors.

Simultaneous Frequency and Amplitude Estimation for Grid Quality Monitoring: New Partitioning with Memory Based Newton-Schulz Corrections

High penetration level of renewable energy sources and introduction of controllable loads will result in significant harmonic emissions and sag and swell events in the future electricity networks. Development of the methods for high performance simultaneous estimation of the frequency and amplitude events is required for stable operation of the future electricity networks since zero crossing frequency detection method (which is widely used nowadays in industry) is not accurate enough and does not allow estimation of the amplitude events. The multiple model method which is suitable for simultaneous estimation of the frequency and amplitude is extended in this paper with introduction of a new decomposition technique based on stepwise partitioning, which allows simultaneous construction and accurate and computationally efficient inversion of the information matrix. Recursive calculations of the inverse introduce error accumulation and a new general high order memory based Newton-Schulz iteration is proposed in this paper for correction and reduction of the accumulated error. Moreover, parallel Richardson iterations which are based on partitioning method are proposed in this paper for reduction of the computational complexity. The methods are especially efficient for approximation of the signals with large number of harmonics. The approaches were tested for simultaneous estimation of the frequency and sag and swell signatures in the one-phase synchronized voltage waveform measured at the wall outlet. Simulation results show that the multiple model method provides more accurate frequency estimation in comparison to zero crossing method.In addition, the cascade multiple model method which is based on the multi-windowing technique (where the components of the signals are separated via a proper choice of the window sizes) is introduced in this paper for estimation of the significantly separated frequencies of the electrical signals. The approach was tested in the problem of frequency estimation using the measurement record from the electric vehicle with on-board charger connected to the supply voltage in the laboratory.

Nonlinear gravitational-wave memory from cusps and kinks on cosmic strings

The nonlinear memory effect is a fascinating prediction of general relativity (GR), in which oscillatory gravitational-wave (GW) signals are generically accompanied by a monotonically-increasing strain which persists in the detector long after the signal has passed. This effect is directly accessible to GW observatories, and presents a unique opportunity to test GR in the dynamical and nonlinear regime. In this article we calculate, for the first time, the nonlinear memory signal associated with GW bursts from cusps and kinks on cosmic string loops, which are an important target for current and future GW observatories. We obtain analytical waveforms for the GW memory from cusps and kinks, and use these to calculate the ‘memory of the memory’ and other higher-order memory effects. These are among the first memory observables computed for a cosmological source of GWs, with previous literature having focused almost entirely on astrophysical sources. Surprisingly, we find that the cusp GW signal diverges for sufficiently large loops, and argue that the most plausible explanation for this divergence is a breakdown in the weak-field treatment of GW emission from the cusp. This shows that previously-neglected strong gravity effects must play an important rôle near cusps, although the exact mechanism by which they cure the divergence is not currently understood. We show that one possible resolution is for these cusps to collapse to form primordial black holes (PBHs); the kink memory signal does not diverge, in agreement with the fact that kinks are not predicted to form PBHs. Finally, we investigate the prospects for detecting memory from cusps and kinks with current and future GW observatories, considering both individual memory bursts and the contribution of many such bursts to the stochastic GW background. We find that in the scenario where the cusp memory divergence is cured by PBH formation, the memory signal is strongly suppressed and is not likely to be detected. However, alternative resolutions of the cusp divergence may in principle lead to much more favourable observational prospects.

Hippocampal CA2 sharp-wave ripples reactivate and promote social memory

The consolidation of spatial memory depends on the reactivation ('replay') of hippocampal place cells that were active during recent behaviour. Such reactivation is observed during sharp-wave ripples (SWRs)-synchronous oscillatory electrical events that occur during non-rapid-eye-movement (non-REM) sleep1-8 and whose disruption impairs spatial memory3,5,6,8. Although the hippocampus also encodes a wide range of non-spatial forms of declarative memory, it is not yet known whether SWRs are necessary for such memories. Moreover, although SWRs can arise from either the CA3 or the CA2 region of the hippocampus7,9, the relative importance of SWRs from these regions for memory consolidation is unknown. Here we examine the role of SWRs during the consolidation of social memory-the ability of an animal to recognize and remember a member of the same species-focusing on CA2 because of its essential role in social memory10-12. We find that ensembles of CA2 pyramidal neurons that are active during social exploration of previously unknown conspecifics are reactivated during SWRs. Notably, disruption or enhancement of CA2 SWRs suppresses or prolongs social memory, respectively. Thus, SWR-mediated reactivation of hippocampal firing related to recent experience appears to be a general mechanism for binding spatial, temporal and sensory information into high-order memory representations, including social memory.

A crabs' high‐order brain center resolved as a mushroom body‐like structure

The hypothesis of a common origin for high-order memory centers in bilateral animals presents the question of how different brain structures, such as the vertebrate hippocampus and the arthropod mushroom bodies, are both structurally and functionally comparable. Obtaining evidence to support the hypothesis that crustaceans possess structures equivalent to the mushroom bodies that play a role in associative memories has proved challenging. Structural evidence supports that the hemiellipsoid bodies of hermit crabs, crayfish and lobsters, spiny lobsters, and shrimps are homologous to insect mushroom bodies. Although a preliminary description and functional evidence supporting such homology in true crabs (Brachyura) has recently been shown, other authors consider the identification of a possible mushroom body homolog in Brachyura as problematic. Here we present morphological and immunohistochemical data in Neohelice granulata supporting that crabs possess well-developed hemiellipsoid bodies that are resolved as mushroom bodies-like structures. Neohelice exhibits a peduncle-like tract, from which processes project into proximal and distal domains with different neuronal specializations. The proximal domains exhibit spines and en passant-like processes and are proposed here as regions mainly receiving inputs. The distal domains exhibit a "trauben"-like compartmentalized structure with bulky terminal specializations and are proposed here as output regions. In addition, we found microglomeruli-like complexes, adult neurogenesis, aminergic innervation, and elevated expression of proteins necessary for memory processes. Finally, in vivo calcium imaging suggests that, as in insect mushroom bodies, the output regions exhibit stimulus-specific activity. Our results support the shared organization of memory centers across crustaceans and insects.

Correlation in Disordered Systems

In this paper, authors consider the theoretical aspects of the dynamics of liquid metals and the issues of correlations in disordered systems. The goal is to demonstrate that in choosing variables it is necessary to bring the equation of Markov processes to an approximation in which among the selected variables there are long-range components. However, this choice should include persistent variables. In numerous studies it is shown that selection cannot be made for the initial equation of motion with dynamic variables, and memory function analysis is required. As always, it contains a high-order memory function that can quickly decrease, and finally it can be again converted by the Markov process. Ways of simplifying the equation of Markov processes are given. In this work, authors derive the connection between the Fourier transform of the autocorrelation function and the imaginary part of the dynamic susceptibility and the result of the fluctuation-dissipation theorem.

Multisensory Gains in Simple Detection Predict Global Cognition in Schoolchildren

The capacity to integrate information from different senses is central for coherent perception across the lifespan from infancy onwards. Later in life, multisensory processes are related to cognitive functions, such as speech or social communication. During learning, multisensory processes can in fact enhance subsequent recognition memory for unisensory objects. These benefits can even be predicted; adults’ recognition memory performance is shaped by earlier responses in the same task to multisensory – but not unisensory – information. Everyday environments where learning occurs, such as classrooms, are inherently multisensory in nature. Multisensory processes may therefore scaffold healthy cognitive development. Here, we provide the first evidence of a predictive relationship between multisensory benefits in simple detection and higher-level cognition that is present already in schoolchildren. Multiple regression analyses indicated that the extent to which a child (N = 68; aged 4.5–15years) exhibited multisensory benefits on a simple detection task not only predicted benefits on a continuous recognition task involving naturalistic objects (p = 0.009), even when controlling for age, but also the same relative multisensory benefit also predicted working memory scores (p = 0.023) and fluid intelligence scores (p = 0.033) as measured using age-standardised test batteries. By contrast, gains in unisensory detection did not show significant prediction of any of the above global cognition measures. Our findings show that low-level multisensory processes predict higher-order memory and cognition already during childhood, even if still subject to ongoing maturation. These results call for revision of traditional models of cognitive development (and likely also education) to account for the role of multisensory processing, while also opening exciting opportunities to facilitate early learning through multisensory programs. More generally, these data suggest that a simple detection task could provide direct insights into the integrity of global cognition in schoolchildren and could be further developed as a readily-implemented and cost-effective screening tool for neurodevelopmental disorders, particularly in cases when standard neuropsychological tests are infeasible or unavailable.

Memory built in conjunction with a stressor is privileged: Reconsolidation-resistant memories in the crab Neohelice

The dynamics of memory processes are conserved throughout evolution, a feature based on the hypothesis of a common origin of the high-order memory centers in bilateral animals. Reconsolidation is just one example. The possibility to interfere with long-term memory expression during reconsolidation has been proposed as potentially useful in clinical application to treat traumatic memories. However, several pieces of evidence in rodents show that either robust fear memories or stressful events applied before acquisition promote reconsolidation-resistant memories, i.e., memories that are resistant to the interfering effect of drugs on memory reconsolidation. Conceivably, the generation of these reconsolidation-resistant fear memories also occurs in humans. Is the induction of reconsolidation-resistant memories part of the dynamics of memory processes conserved throughout evolution? In the semiterrestrial crab Neohelice granulata, memory reconsolidation is triggered by a short reminder without reinforcement. Here, we show that an increase in the salience of the aversive stimulus augmented the memory strength; nonetheless, the protein synthesis inhibitor cycloheximide still disrupted the reconsolidation process. However, crabs stressed by a water-deprivation episode before a strong training session built up a memory that was now reconsolidation-resistant. We tested whether these reconsolidation-resistant effects can be challenged by changing parametric conditions of memory-reminder sessions; multiple memory reactivations without reinforcement were not able to trigger the labilization-reconsolidation of this resistant memory. Overall, the present findings suggest that generation of reconsolidation-resistant memories can be another part of the dynamics of memory processes conserved throughout evolution that protects privileged information from change.

Polar Codes with Higher-Order Memory

Polar Codes with Higher-Order Memory

Tracking online topics over time: understanding dynamic hashtag communities

BackgroundHashtags are widely used for communication in online media. As a condensed version of information, they characterize topics and discussions. For their analysis, we apply methods from network science and propose novel tools for tracing their dynamics in time-dependent data. The observations are characterized by bursty behaviors in the increases and decreases of hashtag usage. These features can be reproduced with a novel model of dynamic rankings.Hashtag communities in timeWe build temporal and weighted co-occurrence networks from hashtags. On static snapshots, we infer the community structure using customized methods. On temporal networks, we solve the bipartite matching problem of detected communities at subsequent timesteps by taking into account higher-order memory. This results in a matching protocol that is robust toward temporal fluctuations and instabilities of the static community detection. The proposed methodology is broadly applicable and its outcomes reveal the temporal behavior of online topics.Modeling topic-dynamicsWe consider the size of the communities in time as a proxy for online popularity dynamics. We find that the distributions of gains and losses, as well as the interevent times are fat-tailed indicating occasional, but large and sudden changes in the usage of hashtags. Inspired by typical website designs, we propose a stochastic model that incorporates a ranking with respect to a time-dependent prestige score. This causes occasional cascades of rank shift events and reproduces the observations with good agreement. This offers an explanation for the observed dynamics, based on characteristic elements of online media.

Polar Codes with Higher-Order Memory

We introduce a construction of a set of code sequences {Cn(m) : n ≥ 1, m ≥ 1} with memory order m and code length N(n). {Cn(m)} is a generalization of polar codes presented by Arikan in [1], where the encoder mapping with length N(n) is obtained recursively from the encoder mappings with lengths N(n − 1) and N(n − m), and {Cn(m)} coincides with the original polar codes when m = 1. We show that {Cn(m)} achieves the symmetric capacity I(W) of an arbitrary binary-input, discrete-output memoryless channel W for any fixed m. We also obtain an upper bound on the probability of block-decoding error Pe of {Cn(m)} and show that $${P_e} = O({2^{ - {N^\beta }}})$$ is achievable for β < 1/[1+m(ϕ − 1)], where ϕ ∈ (1, 2] is the largest real root of the polynomial F(m, ρ) = ρm − ρm − 1 − 1. The encoding and decoding complexities of {Cn(m)} decrease with increasing m, which proves the existence of new polar coding schemes that have lower complexity than Arikan’s construction.

A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches.

Velocity autocorrelation functions (VAFs) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the high order memory functions, which have a purely kinetic origin. The VAFs obtained within our method are compared with computer simulation data for the liquid Ne at different densities and the results, which follow from the Markovian approximation for the highest order kinetic kernels. It is shown that in all the thermodynamic points and at the chosen level of the hierarchy, our results agree much better with the molecular dynamic data than those of the Markovian approximation. The density dependence of the transition time, needed for the fluid to attain the hydrodynamic stage of evolution, is evaluated. The common and distinctive features of our method are discussed in their relations to the generalized collective mode theory, the mode coupling theory, and some other theoretical approaches.

Analysis of stacking disorder in ice I using pair distribution functions

Stacking-disordered materials display crystalline order in two dimensions but are disordered along the direction in which layered structural motifs are stacked. Countless examples of stacking disorder exist, ranging from close-packed metals, ice I and diamond to open-framework materials and small-molecule pharmaceuticals. In general, the presence of stacking disorder can have profound consequences for the physical and chemical properties of a material. Traditional analyses of powder diffraction data are often complicated by the presence of memory effects in the stacking sequences. Here it is shown that experimental pair distribution functions of stacking-disordered ice I can be used to determine local information on the fractions of cubic and hexagonal stacking. Ice is a particularly challenging material in this respect, since both the stacking disorder and the orientational disorder of the water molecules need to be described. Memory effects are found to contribute very little to the pair distribution functions, and consequently, the analysis of pair distribution functions is the method of choice for characterizing stacking-disordered samples with complicated and high-order memory effects. In the context of this work, the limitations of current structure-reconstruction approaches are also discussed.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

Context-dependent memory traces in the crab’s mushroom bodies: Functional support for a common origin of high-order memory centers

The hypothesis of a common origin for the high-order memory centers in bilateral animals is based on the evidence that several key features, including gene expression and neuronal network patterns, are shared across several phyla. Central to this hypothesis is the assumption that the arthropods' higher order neuropils of the forebrain [the mushroom bodies (MBs) of insects and the hemiellipsoid bodies (HBs) of crustaceans] are homologous structures. However, even though involvement in memory processes has been repeatedly demonstrated for the MBs, direct proof of such a role in HBs is lacking. Here, through neuroanatomical and immunohistochemical analysis, we identified, in the crab Neohelice granulata, HBs that resemble the calyxless MBs found in several insects. Using in vivo calcium imaging, we revealed training-dependent changes in neuronal responses of vertical and medial lobes of the HBs. These changes were stimulus-specific, and, like in the hippocampus and MBs, the changes reflected the context attribute of the memory trace, which has been envisioned as an essential feature for the HBs. The present study constitutes functional evidence in favor of a role for the HBs in memory processes, and provides key physiological evidence supporting a common origin of the arthropods' high-order memory centers.

Assessing reliable human mobility patterns from higher order memory in mobile communications.

Understanding how people move within a geographical area, e.g. a city, a country or the whole world, is fundamental in several applications, from predicting the spatio-temporal evolution of an epidemic to inferring migration patterns. Mobile phone records provide an excellent proxy of human mobility, showing that movements exhibit a high level of memory. However, the precise role of memory in widely adopted proxies of mobility, as mobile phone records, is unknown. Here we use 560 million call detail records from Senegal to show that standard Markovian approaches, including higher order ones, fail in capturing real mobility patterns and introduce spurious movements never observed in reality. We introduce an adaptive memory-driven approach to overcome such issues. At variance with Markovian models, it is able to realistically model conditional waiting times, i.e. the probability to stay in a specific area depending on individuals' historical movements. Our results demonstrate that in standard mobility models the individuals tend to diffuse faster than observed in reality, whereas the predictions of the adaptive memory approach significantly agree with observations. We show that, as a consequence, the incidence and the geographical spread of a disease could be inadequately estimated when standard approaches are used, with crucial implications on resources deployment and policy-making during an epidemic outbreak.