Linear Summation Research Articles

Operating in a Multisensory Context: Assessing the Interplay Between Multisensory Reaction Time Facilitation and Inter-sensory Task-switching Effects

Individuals respond faster to presentations of bisensory stimuli (e.g. audio-visual targets) than to presentations of either unisensory constituent in isolation (i.e. to the auditory-alone or visual-alone components of an audio-visual stimulus). This well-established multisensory speeding effect, termed the redundant signals effect (RSE), is not predicted by simple linear summation of the unisensory response time probability distributions. Rather, the speeding is typically faster than this prediction, leading researchers to ascribe the RSE to a so-called co-activation account. According to this account, multisensory neural processing occurs whereby the unisensory inputs are integrated to produce more effective sensory-motor activation. However, the typical paradigm used to test for RSE involves random sequencing of unisensory and bisensory inputs in a mixed design, raising the possibility of an alternate attention-switching account. This intermixed design requires participants to switch between sensory modalities on many task trials (e.g. from responding to a visual stimulus to an auditory stimulus). Here we show that much, if not all, of the RSE under this paradigm can be attributed to slowing of reaction times to unisensory stimuli resulting from modality switching, and is not in fact due to speeding of responses to AV stimuli. As such, the present data do not support a co-activation account, but rather suggest that switching and mixing costs akin to those observed during classic task-switching paradigms account for the observed RSE.

Overlapping but Asymmetrical Relationships Between Schizophrenia and Autism Revealed by Brain Connectivity.

Although the relationship between schizophrenia spectrum disorder (SSD) and autism spectrum disorder (ASD) has long been debated, it has not yet been fully elucidated. The authors quantified and visualized the relationship between ASD and SSD using dual classifiers that discriminate patients from healthy controls (HCs) based on resting-state functional connectivity magnetic resonance imaging. To develop a reliable SSD classifier, sophisticated machine-learning algorithms that automatically selected SSD-specific functional connections were applied to Japanese datasets from Kyoto University Hospital (N = 170) including patients with chronic-stage SSD. The generalizability of the SSD classifier was tested by 2 independent validation cohorts, and 1 cohort including first-episode schizophrenia. The specificity of the SSD classifier was tested by 2 Japanese cohorts of ASD and major depressive disorder. The weighted linear summation of the classifier's functional connections constituted the biological dimensions representing neural classification certainty for the disorders. Our previously developed ASD classifier was used as ASD dimension. Distributions of individuals with SSD, ASD, and HCs s were examined on the SSD and ASD biological dimensions. We found that the SSD and ASD populations exhibited overlapping but asymmetrical patterns in the 2 biological dimensions. That is, the SSD population showed increased classification certainty for the ASD dimension but not vice versa. Furthermore, the 2 dimensions were correlated within the ASD population but not the SSD population. In conclusion, using the 2 biological dimensions based on resting-state functional connectivity enabled us to discover the quantified relationships between SSD and ASD.

Numerical modeling of ship wave generation using Green’s functions based on linear dispersive wave theory

ABSTRACT In this study, an efficient numerical model for predicting ship waves was developed using Green’s functions. Avoiding detailed description of the complex boundary conditions around a ship, this model simply used an inversion technique for estimating the wave source induced by a ship as a function of the navigation route and adjacent measured water level fluctuations. The Green’s functions were determined as linear summations of the water level fluctuations generated from discrete points along the navigation route. At each point, a time-varying wave source was determined as a linear summation of Gaussian pulses introduced at segments along the longitudinal direction of the ship. The linear inversion was then applied for estimating the optimum combinations of the magnitudes of these Gaussian pulses. Linear dispersive wave theory was applied to compute the water level fluctuations generated by a single Gaussian pulse so that the model can reproduce the dispersive characteristics of ship waves. The developed model was tested against experimental data and showed satisfactorily predictive skills of water level fluctuations for cases not used in the inversion. The present model was also found to be robust in that the estimated best-fitted wave source was not sensitive to changes in the conditions of the measured data used for the inversion.

NetSRE: Link predictability measuring and regulating

Link prediction is an elemental issue for network-structured data mining, which has already found a wide range of applications. The organization of real-world networks usually embodies both regularities and irregularities, and the precision of link prediction algorithms coincides with the portion of a network being categorized as regular. Quantifying and controlling how well an unobserved link can be predicted is a fundamental problem in link prediction. This paper proposes a structural regularity-exploring architecture, called NetSRE, for measuring and regulating link predictability of networks. The proposed NetSRE assumes that there are consistent interaction patterns across the local subgraphs of networks and one of them can be represented by a linear summation of the others, and thus, link predictability can be characterized by the self-representation degree of network structures. Specifically, NetSRE includes (1) a low Frobenius norm pursuit-based self-representation network model for predicting the “true” underlying networks, (2) a “structural regularity” index for measuring the link predictability of networks, i.e., the inherent difficulty of link prediction independent of specific algorithms, and (3) an importance measuring method for structural role exploration of network links and a link-based structure perturbation algorithm for link predictability regulation. Experimental results on real-world networks validate the performance of our method. It is found that real-world networks have various structural regularities and link predictability can be estimated based on structure mining directly. We show that network heterogeneity provides a way to intrinsically segregate network links into qualitatively distinct groups, which have different influences on the link predictability of networks.

Green development assessment for countries along the belt and road

The construction of the green Belt and Road is an important aspect for the achievement of a green transition of the regional economy and an important aspect of the United Nations 2030 Agenda for Sustainable Development. The Chinese government has attached great importance to the green BRI, and it has successively issued the Guiding Opinions on Promoting the Green BRI and the Belt and Road Ecological and Environmental Cooperation Plan, which embodies China's firm determination and practical action to promote the green BRI. In this paper, an index system and multi-hierarchy linear summation method is proposed to evaluate the level of green development in 2015 for 49 countries along the Belt and Road. The results showed that the green development levels displayed spatial differences, varying from high to low in an easterly direction from the western region. The spatial differentiation was characterized by strong global spatial dependences and a ladder-like distribution that descends from west to east, with a centralized distribution of high-high zones and low-low zones and a dispersed distribution of low-high zones. This study also provides policy recommendations for Belt and Road countries.

Neurocomputational mechanisms underlying immoral decisions benefiting self or others.

Immoral behavior often consists of weighing transgression of a moral norm against maximizing personal profits. One important question is to understand why immoral behaviors vary based on who receives specific benefits and what are the neurocomputational mechanisms underlying such moral flexibility. Here, we used model-based functional magnetic resonance imaging to investigate how immoral behaviors change when benefiting oneself or someone else. Participants were presented with offers requiring a tradeoff between a moral cost (i.e. profiting a morally bad cause) and a benefit for either oneself or a charity. Participants were more willing to obtain ill-gotten profits for themselves than for a charity, driven by a devaluation of the moral cost when deciding for their own interests. The subjective value of an immoral offer, computed as a linear summation of the weighed monetary gain and moral cost, recruited the ventromedial prefrontal cortex (PFC) regardless of beneficiaries. Moreover, paralleling the behavioral findings, this region enhanced its functional coupling with mentalizing-related regions while deciding whether to gain morally tainted profits for oneself vs charity. Finally, individual differences in moral preference differentially modulated choice-specific signals in the dorsolateral PFC according to who benefited from the decisions. These findings provide insights for understanding the neurobiological basis of moral flexibility.

Exponential sums of squares of Fourier coefficients of cusp forms

We prove nontrivial estimates for linear sums of squares of Fourier coefficients of holomorphic and Maass cusp forms twisted by additive characters. For holomorphic forms f, we show that if $$|\alpha -a/q| \le 1/q^2$$ with $$(a,q)=1$$ , then for any $$\varepsilon >0$$ , $$\begin{aligned} \qquad \qquad \sum _{n\leqslant X}{\lambda _f(n)}^2 e(n\alpha ) \ll _{f, \varepsilon } X^{{\frac{4}{5}}+\varepsilon } \quad \text {for} \ X^{{\frac{1}{5}}} \ll q \ll X^{{\frac{4}{5}}}. \end{aligned}$$ Moreover, for any $$\varepsilon > 0,$$ there exists a set $$S \subset (0, 1)$$ with $$\mu (S)=1$$ such that for every $$\alpha \in S$$ , there exists $$X_0=X_0(\alpha )$$ such that the above inequality holds true for any $$\alpha \in S$$ and $$X \geqslant X_0(\alpha ).$$ A weaker bound for Maass cusp forms is also established.

An adaptive integral separated proportional–integral controller based strategy for particle swarm optimization

Particle swarm optimization algorithm (PSO), which updates the particle by the linear summation of the particle’s past momentum and current search direction, has demonstrated its power in many optimization applications. However, few researches have focused on the overshoot problem of PSO caused by past momentum, which may result in an oscillation search and slow convergence speed on complex optimization problems. Based on the connection between the PSO optimization process and the PID controller based control system, we first analyze the effect of the momentum in PSO, then we find that the oscillation problem relates to the gathering of the momentum term and the current search direction. Inspired by the conditional integration in automatic control, we propose an adaptive search direction learning approach for PSO, namely ISPSO (Integral Separated PI controller-based PSO). The ISPSO separates momentum term adaptively when the current search direction is consistent with historical momentum direction, and then the IS strategy will guide particles to fly to better and steady directions by eliminating the integral gathering of historical momentum. We select seven main-stream approaches as control group, and conduct experiments on benchmark CEC2013 test suite. The experimental results of ISPSO, providing the faster steady global convergence and higher solution accuracy, show a significant improvement on PSO algorithm. Compared with the results of the seven methods, the performance of ISPSO is also promising in general, especially for unimodal and composition functions. Furthermore, our results validate the generalization and effectiveness of IS strategy by the designed experiments of PSO variants with and without IS strategy, which also indicates that the IS strategy can be applied to PSO variants with any topological structures.

Generalized Beilinson Elements and Generalized Soulé Characters

AbstractThe generalized Soulé character was introduced by H. Nakamura and Z. Wojtkowiak and is a generalization of Soulé’s cyclotomic character. In this paper, we prove that certain linear sums of generalized Soulé characters essentially coincide with the image of generalized Beilinson elements in K-groups under Soulé’s higher regulator maps. This result generalizes Huber–Wildeshaus’ theorem, which is a cyclotomic field case of our results, to an arbitrary number fields.

Deterministic reconstruction and reproduction of multi-directional irregular waves based on linear summation model

Accurately reproducing multi-directional irregular waves in laboratory or numerical wave basin is crucial for in-depth study of real wave-action on marine structures. In this paper, the EEED (Equal-Energy-in-Each-Division) and PTPD (Phase-Time-Path-Difference) approaches are described, and their capability for reconstructing multi-directional irregular waves is assessed. The key difference between these two methods is the determination of the component wave directions. Theoretically and (arbitrary) numerically simulated multi-directional waves with different directional distribution width and wave steepness are reconstructed, and the latter waves are further reproduced in a numerical wave basin. The consistency between the reconstructed and the theoretical/measured waves demonstrates the approaches are acceptable. Furthermore, the variation of the quantitative error between the reconstructed and the theoretical/measured waves in the spatial domain (rr/Ls) is analyzed. This variation increases with the size of rr/Ls, but the errors are acceptable as long as this size is reasonable. The application ranges are evaluated based on a qualitative comparative analysis between the reconstructed waves and the theoretical/measured ones and the quantitative reconstruction error along rr/Ls. The PTPD approach is generally better than EEED method. The optimum relative separation for wave gauges using the PTPD approach should be smaller than 0.12Ls.

Modelling of continuously distributed target for bistatic synthetic aperture radar imaging

The point target model is widely used in the synthetic aperture radar (SAR) imaging simulation. Based on this model, the radar echo of a continuously distributed target can be expressed as the linear summation of the echo of many point targets which are known as scatters. However, the discretisation strategy is problematic. The discretisation grid must be very fine to assure convergence, thus the computation burden is heavy. Moreover, the result depends on how the target is discretised. It is shown that the SAR image generated from this model of the same target is inconsistent when using different sampling strategy. To overcome these drawbacks, a parameterised model is proposed in this study, which not only greatly reduce the amount of calculation, but also guarantee consistency of the results. Finally, the correctness of the proposed model is verified by SAR imaging results from the generated echo data.

Developmental Increase of Neocortical Presynaptic Efficacy via Maturation of Vesicle Replenishment.

The efficacy of neocortical synapses to transmit during bursts of action potentials (APs) increases during development but the underlying mechanisms are largely unclear. We investigated synaptic efficacy at synapses between layer 5 pyramidal neurons (L5PNs) during development, using paired recordings, presynaptic two-photon Ca2+ imaging, and numerical simulations. Our data confirm a developmental increase in paired-pulse ratios (PPRs). Independent of age, Ca2+ imaging revealed no AP invasion failures and linear summation of presynaptic Ca2+ transients, making differences in Ca2+ signaling an unlikely reason for developmental changes in PPR. Cumulative excitatory postsynaptic current (EPSC) amplitudes indicate that neither the size of the readily-releasable pool (RRP) nor replenishment rates were different between age groups, while the time-courses of depression differed significantly. At young synapses, EPSCs depressed rapidly to near steady-state during the first four APs, and synaptic failures (Fsyn) increased from 0 to 30%. At mature synapses this drop was significantly slower and strongly biphasic, such that near steady-state depression was reached not before 18 APs with Fsyn remaining between 0 and 5%. While young synapses reliably transmitted during pairs of APs, albeit with strong depression, mature synapses maintained near 100% transfer efficacy with significantly less depression during high-frequency bursts of APs. Our analysis indicates that at mature synapses a replenishment pool (RepP) is responsible for their high efficacy during bursting activity, while this RepP is functionally immature at young synapses. Hence, our data provide evidence that the functional maturation of a RepP underlies increasing synaptic efficacy during the development of an excitatory cortical synapse.

Analysis of Fatigue Damage Accumulation in Structural Materials under Quasi-Random Load

The spectrum of stresses at a hazardous point on bearing metal structures of mining, road-building and transporting machines, as a rule, is random by nature. Objective complexity of the fatigue process and variety of fatigue crack nucleation mechanisms are the main causes of errors in prediction of their lifespan, along with an experimentally untestable hypothesis of linear summation of damages. The method of complete stress-strain diagrams uses a representative parameter of the fatigue process, selected in accordance with the results of testing, carried out on trained thin specimens of a specific material. The summation of fatigue damages is based on experimental kinematic curves, whose intersection with a load vector is used as a criterion of fatigue failure. It is shown that the approach proposed to calculate the lifespan gives certain advantages, as far as individual properties of the material are concerned, and when it comes to describing the kinetics of the fatigue process and determining the limiting state of the material in a structure.

On q-analogues of quadratic Euler sums

In this paper we define the generalized q-analogues of Euler sums and present a new family of identities for q-analogues of Euler sums by using the method of Jackson q-integral rep- resentations of series. We then apply it to obtain a family of identities relating quadratic Euler sums to linear sums and q-polylogarithms. Furthermore, we also use certain stuffle products to evaluate several q-series with q-harmonic numbers. Some interesting new results and illustrative examples are considered. Finally, we can obtain some explicit relations for the classical Euler sums when q approaches to 1.

EVALUATIONS OF SOME QUADRATIC EULER SUMS

This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polyloga- rithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.

Effect of Viscoelastic Layer on Contact Fatigue Damage Accumulation in Rolling Friction

The cyclic rolling of an elastic sphere along a viscoelastic layer bonded to an elastic half-space is considered. For known distributions of normal and shear stresses, the internal stress state of the elastic half-space is calculated. The damage accumulation within the framework of the linear damage summation model was considered. The amplitude values of principal shear stress were calculated for various values of relative slippage and friction coefficient.

Investigation of the influence of low amplitude loads on the fatigue life of CFRP specimens with impact damage under irregular loading

The research was made to study the effect of low amplitude loads on the fatigue life of CFRP samples with impact damage in a cyclogram of irregular loading. The evaluation of the applicability of the linear summation hypothesis of damage (Palmgren’s Miner’s rule) at this level of loading was also carried out. The results have shown that in some cases correction factors need to be introduced.

An Accelerated Cue Combination Principle Accounts for Multi-cue Depth Perception

Abstract For the visual world in which we operate, the core issue is to conceptualize how its three-dimensional structure is encoded through the neural computation of multiple depth cues and their integration to a unitary depth structure. One approach to this issue is the full Bayesian model of scene understanding, but this is shown to require selection from the implausibly large number of possible scenes. An alternative approach is to propagate the implied depth structure solution for the scene through the “belief propagation” algorithm on general probability distributions. However, a more efficient model of local slant propagation is developed as an alternative.The overall depth percept must be derived from the combination of all available depth cues, but a simple linear summation rule across, say, a dozen different depth cues, would massively overestimate the perceived depth in the scene in cases where each cue alone provides a close-to-veridical depth estimate. On the other hand, a Bayesian averaging or “modified weak fusion” model for depth cue combination does not provide for the observed enhancement of perceived depth from weak depth cues. Thus, the current models do not account for the empirical properties of perceived depth from multiple depth cues.The present analysis shows that these problems can be addressed by an asymptotic, or hyperbolic Minkowski, approach to cue combination. With appropriate parameters, this first-order rule gives strong summation for a few depth cues, but the effect of an increasing number of cues beyond that remains too weak to account for the available degree of perceived depth magnitude. Finally, an accelerated asymptotic rule is proposed to match the empirical strength of perceived depth as measured, with appropriate behavior for any number of depth cues.

Cortical Interactions between Prosthetic and Natural Vision

Outer retinal degenerative diseases, such as retinitis pigmentosa (RP) and age-related macular degeneration (AMD), are among the leading causes of incurable blindness in the Western world [1]. Retinal prostheses have been shown to restore some useful vision by electrically stimulating the remaining retinal neurons [2]. In contrast to inherited retinal degenerative diseases (e.g., RP), typically leading to a complete loss of the visual field, in AMD patients the disease is localized to the macula, leaving the peripheral vision intact. Implanting a retinal prosthesis in the central macula in AMD patients [3, 4] leads to an intriguing situation where the patient's central retina is stimulated electrically, whereas the peripheral healthy retina responds to natural light stimulation. An important question is whether the visual cortex responds to these two concurrent stimuli similarly to the interaction between two adjacent natural light stimuli projected onto healthy retina. Here, we investigated the cortical interactions between prosthetic and natural vision based on visually evoked potentials (VEPs) recorded in rats implanted with photovoltaic subretinal implants. Using this model, where prosthetic and natural vision information are combined in the visual cortex, we observed striking similarities in the interactions of natural and prosthetic vision, including similar effect of background illumination, linear summation of non-patterned stimuli, and lateral inhibition with spatial patterns [5], which increased with target contrast. These results support the idea of combined prosthetic and natural vision in restoration of sight for AMD patients.

An Adaptive Multi-Target Radar Waveform Design Based on PWS Algorithm.

Due to the uncertainty of radar target prior information in actual scenes, waveform design based on radar target prior information cannot meet the requirements of detection performance and parameter estimation. Aiming at the problem of waveform design for detecting multi-target in the presence of clutter, a linear probability-weighted summation (PWS) algorithm based on multi-target impulse response is proposed and includes the radar waveform design based on mutual information (MI) and signal-to-interference ratio (SINR) criteria. In view of the traditional water-filling algorithm, the problem of multi-target is further investigated in a new way to improve the overall performance of the system. The method makes a lot of deductions by using Jensen’s inequality, to determine the algorithm objective function and energy constraint. The simulation results show that the proposed algorithm has better detection performance and more accurate target information.