This paper investigates the replication of experiments by Billock and Tsou [PNAS, 2007] using the controllability of neural fields of Amari-type modelling the cortical activity in the primary visual cortex (V1), focusing on a regular funnel pattern localised in the fovea or the peripheral visual field. The aim is to understand and model the visual phenomena observed in these experiments, emphasising their nonlinear nature. The study involves designing sensory inputs simulating the visual stimuli from Billock and Tsou's experiments. The after-images induced by these inputs are then theoretically and numerically studied to determine their capacity to replicate the experimentally observed visual effects. A key aspect of this research is investigating the effects induced by the nonlinear nature of neural responses. In particular, by highlighting the importance of both excitatory and inhibitory neurons in the emergence of certain visual phenomena, this study suggests that an interplay of both types of neuronal activities plays an essential role in visual processes, challenging the assumption that the latter is mainly driven by excitatory activities alone.
相關內容
This paper studies the fundamental limits of availability and throughput for independent and heterogeneous demands of a limited resource. Availability is the probability that the demands are below the capacity of the resource. Throughput is the expected fraction of the resource that is utilized by the demands. We offer a concentration inequality generator that gives lower bounds on feasible availability and throughput pairs with a given capacity and independent but not necessarily identical distributions of up-to-unit demands. We show that availability and throughput cannot both be poor. These bounds are analogous to tail inequalities on sums of independent random variables, but hold throughout the support of the demand distribution. This analysis gives analytically tractable bounds supporting the unit-demand characterization of Chawla, Devanur, and Lykouris (2023) and generalizes to up-to-unit demands. Our bounds also provide an approach towards improved multi-unit prophet inequalities (Hajiaghayi, Kleinberg, and Sandholm, 2007). They have applications to transaction fee mechanism design (for blockchains) where high availability limits the probability of profitable user-miner coalitions (Chung and Shi, 2023).
In this short note we formulate a stabilizer formalism in the language of noncommutative graphs. The classes of noncommutative graphs we consider are obtained via unitary representations of compact groups, and suitably chosen operators on finite-dimensional Hilbert spaces. Furthermore, in this framework, we generalize previous results in this area for determining when such noncommutative graphs have anticliques.
This study investigates the applicability of Kirchhoff migration (KM) for a fast identification of unknown objects in a real-world limited-aperture inverse scattering problem. To demonstrate the theoretical basis for the applicability including unique determination of objects, the imaging function of the KM was formulated using a uniformly convergent infinite series of Bessel functions of integer order of the first kind based on the integral equation formula for the scattered field. Numerical simulations performed using the experimental Fresnel dataset are exhibited to achieve the theoretical results.
Evaluating the Expected Information Gain (EIG) is a critical task in many areas of computational science and statistics, necessitating the approximation of nested integrals. Available techniques for this problem based on Quasi-Monte Carlo (QMC) methods have primarily focused on enhancing the efficiency of the inner integral approximation. In this work, we introduce a novel approach that extends the scope of these efforts to address inner and outer expectations simultaneously. Leveraging the principles of Owen's scrambling, we develop a randomized quasi-Monte Carlo (RQMC) method that improves the approximation of nested integrals. We also indicate how to combine this methodology with Importance Sampling to address a measure concentration arising in the inner integral. Our RQMC method capitalizes on the unique structure of nested expectations to offer a more efficient approximation mechanism. By incorporating Owen's scrambling techniques, we handle integrands exhibiting infinite variation in the Hardy-Krause (HK) sense, paving the way for theoretically sound error estimates. We derive asymptotic error bounds for the bias and variance of our estimator. In addition, we provide nearly optimal sample sizes for the inner and outer RQMC approximations, which are helpful for the actual numerical implementations. We verify the quality of our estimator through numerical experiments in the context of Bayesian optimal experimental design. Specifically, we compare the computational efficiency of our RQMC method against standard nested Monte Carlo integration across two case studies: one in thermo-mechanics and the other in pharmacokinetics. These examples highlight our approach's computational savings and enhanced applicability, showcasing the advantages of estimating the Expected Information Gain with greater efficiency and reduced computational cost.
Anthropomorphic social bots are engineered to emulate human verbal communication and generate toxic or inflammatory content across social networking services (SNSs). Bot-disseminated misinformation could subtly yet profoundly reshape societal processes by complexly interweaving factors like repeated disinformation exposure, amplified political polarization, compromised indicators of democratic health, shifted perceptions of national identity, propagation of false social norms, and manipulation of collective memory over time. However, extrapolating bots' pluripotency across hybridized, multilingual, and heterogeneous media ecologies from isolated SNS analyses remains largely unknown, underscoring the need for a comprehensive framework to characterise bots' emergent risks to civic discourse. Here we propose an interdisciplinary framework to characterise bots' pluripotency, incorporating quantification of influence, network dynamics monitoring, and interlingual feature analysis. When applied to the geopolitical discourse around the Russo-Ukrainian conflict, results from interlanguage toxicity profiling and network analysis elucidated spatiotemporal trajectories of pro-Russian and pro-Ukrainian human and bots across hybrid SNSs. Weaponized bots predominantly inhabited X, while human primarily populated Reddit in the social media warfare. This rigorous framework promises to elucidate interlingual homogeneity and heterogeneity in bots' pluripotent behaviours, revealing synergistic human-bot mechanisms underlying regimes of information manipulation, echo chamber formation, and collective memory manifestation in algorithmically structured societies.
Purpose: To develop an image space formalism of multi-layer convolutional neural networks (CNNs) for Fourier domain interpolation in MRI reconstructions and analytically estimate noise propagation during CNN inference. Theory and Methods: Nonlinear activations in the Fourier domain (also known as k-space) using complex-valued Rectifier Linear Units are expressed as elementwise multiplication with activation masks. This operation is transformed into a convolution in the image space. After network training in k-space, this approach provides an algebraic expression for the derivative of the reconstructed image with respect to the aliased coil images, which serve as the input tensors to the network in the image space. This allows the variance in the network inference to be estimated analytically and to be used to describe noise characteristics. Monte-Carlo simulations and numerical approaches based on auto-differentiation were used for validation. The framework was tested on retrospectively undersampled invivo brain images. Results: Inferences conducted in the image domain are quasi-identical to inferences in the k-space, underlined by corresponding quantitative metrics. Noise variance maps obtained from the analytical expression correspond with those obtained via Monte-Carlo simulations, as well as via an auto-differentiation approach. The noise resilience is well characterized, as in the case of classical Parallel Imaging. Komolgorov-Smirnov tests demonstrate Gaussian distributions of voxel magnitudes in variance maps obtained via Monte-Carlo simulations. Conclusion: The quasi-equivalent image space formalism for neural networks for k-space interpolation enables fast and accurate description of the noise characteristics during CNN inference, analogous to geometry-factor maps in traditional parallel imaging methods.
Modality discrepancies have perpetually posed significant challenges within the realm of Automated Audio Captioning (AAC) and across all multi-modal domains. Facilitating models in comprehending text information plays a pivotal role in establishing a seamless connection between the two modalities of text and audio. While recent research has focused on closing the gap between these two modalities through contrastive learning, it is challenging to bridge the difference between both modalities using only simple contrastive loss. This paper introduces Enhance Depth of Text Comprehension (EDTC), which enhances the model's understanding of text information from three different perspectives. First, we propose a novel fusion module, FUSER, which aims to extract shared semantic information from different audio features through feature fusion. We then introduced TRANSLATOR, a novel alignment module designed to align audio features and text features along the tensor level. Finally, the weights are updated by adding momentum to the twin structure so that the model can learn information about both modalities at the same time. The resulting method achieves state-of-the-art performance on AudioCaps datasets and demonstrates results comparable to the state-of-the-art on Clotho datasets.
The contention of this paper is that a spectral method for time-dependent PDEs is basically no more than a choice of an orthonormal basis of the underlying Hilbert space. This choice is governed by a long list of considerations: stability, speed of convergence, geometric numerical integration, fast approximation and efficient linear algebra. We subject different choices of orthonormal bases, focussing on the real line, to these considerations. While nothing is likely to improve upon a Fourier basis in the presence of periodic boundary conditions, the situation is considerably more interesting in other settings. We introduce two kinds of orthonormal bases, T-systems and W-systems, and investigate in detail their features. T-systems are designed to work with Cauchy boundary conditions, while W-systems are suited to zero Dirichlet boundary conditions.
Principal component analysis (PCA) is a longstanding and well-studied approach for dimension reduction. It rests upon the assumption that the underlying signal in the data has low rank, and thus can be well-summarized using a small number of dimensions. The output of PCA is typically represented using a scree plot, which displays the proportion of variance explained (PVE) by each principal component. While the PVE is extensively reported in routine data analyses, to the best of our knowledge the notion of inference on the PVE remains unexplored. In this paper, we consider inference on the PVE. We first introduce a new population quantity for the PVE with respect to an unknown matrix mean. Critically, our interest lies in the PVE of the sample principal components (as opposed to unobserved population principal components); thus, the population PVE that we introduce is defined conditional on the sample singular vectors. We show that it is possible to conduct inference, in the sense of confidence intervals, p-values, and point estimates, on this population quantity. Furthermore, we can conduct valid inference on the PVE of a subset of the principal components, even when the subset is selected using a data-driven approach such as the elbow rule. We demonstrate the proposed approach in simulation and in an application to a gene expression dataset.
In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used for the hidden nodes that process the underlying asset price. In addition, financial conditions, such as the absence of arbitrage, the boundaries and the asymptotic slope, are embedded into the loss function. This is one of the very first studies which discuss a methodological framework that incorporates prior financial domain knowledge into neural network architecture design and model training. The proposed model outperforms the benchmarked models with the option data on the S&P 500 index over 20 years. More importantly, the domain knowledge is satisfied empirically, showing the model is consistent with the existing financial theories and conditions related to implied volatility surface.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191