robench-2024b
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48 items • Updated
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1111222233334444λe+=λe++superscriptsubscript𝜆𝑒superscriptsubscript𝜆𝑒absent\lambda_{e}^{+}=\lambda_{e}^{++}italic_λ start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT = italic_λ start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT start_POSTSUPERSCRIPT + + end_POSTSUPERSCRIPT|λc−|=λ... | In 1D, with σ=3.2𝜎3.2\sigma=3.2italic_σ = 3.2 and ζ<σ2=1.6𝜁𝜎21.6\zeta<\frac{\sigma}{2}=1.6italic_ζ < divide start_ARG italic_σ end_ARG start_ARG 2 end_ARG = 1.6, we are able to | =γw−c(1−ρ−(σ+ζ)a+ζb).absent𝛾𝑤𝑐1𝜌𝜎𝜁𝑎𝜁𝑏\displaystyle=\gamma w-c(1-\rho-(\sigma+\zeta)a+\zeta b).= italic_γ italic_w - italic_c ( 1 - italic_ρ - ( italic_σ + italic_ζ ) italic_a + italic_ζ italic_b ) . | ODEs (3), in (γ,ζ)𝛾𝜁(\gamma,\zeta)( italic_γ , italic_ζ ) parameter space, with σ=3.2𝜎3.2\sigma=3.2italic_σ = 3.2. | and red curve (4ζ=γ24𝜁superscript𝛾24\zeta=\gamma^{2}4 italic_ζ = italic_γ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT) are tangent at (γ,ζ)=(2σ,σ/2)𝛾𝜁2𝜎𝜎2(\gamma,\zeta)=(\sqrt{2\sigma},\sigma/2)( italic_γ , italic_ζ ) = ( square-root start_ARG 2 italic_σ end_ARG , italic_σ / 2 ) and divide the parameter space i... | C |
For each network architecture tested in this study, the same procedure is used: the model is trained on the training set for 15 epochs, with an evaluation on the validation set after each epoch. Depending on the accurracy value of the model, the weights are saved after each epoch to keep the best model, which is then e... | Twelve different CNN models were used in this study, with different levels of depth and number of parameters (Table 1). The models B2 and B6 were coded from scratch and have a relatively simple architecture. The B2 model has only two convolutional layers while the B6 model is slightly deeper and more complex with six c... | All the other models are CNN models that are part of the TensorFlow Keras library (Table 1). They were developed and tested by several research groups on the Imagenet Challenge, a competition with hundreds of object categories and millions of images [25]. For instance, InceptionV3 is a model created in 2015 with a very... | The computational running time was analysed for the for B2, B6 and the more complex InceptionV3 (IV3) model, both fully re-trained (F) and with transfer learning (TL) on the PCAM dataset. The results are shown in Table 2. Note that the time corresponds to the average time observed for one epoch. We can compare the mode... | The performance of all the models on the PCAM and IDC datasets is described in Table 3 and 4. All the indicators are measured on the test sets. Most of the model show a very good performance, with AUC scores around 0.90 or above. However, when we look at the details, there are clear differences. For instance the AUC of... | A |
With this knowledge, let us construct the jump chain step by step. The first two jumps are determined easily, noting that | 𝐯(3)={8}.superscript𝐯38\displaystyle\mathbf{v}^{(3)}=\{8\}.bold_v start_POSTSUPERSCRIPT ( 3 ) end_POSTSUPERSCRIPT = { 8 } . | 𝐯(0)={0},superscript𝐯00\displaystyle\mathbf{v}^{(0)}=\{0\},bold_v start_POSTSUPERSCRIPT ( 0 ) end_POSTSUPERSCRIPT = { 0 } , | 𝐯(0)superscript𝐯0\displaystyle\mathbf{v}^{(0)}bold_v start_POSTSUPERSCRIPT ( 0 ) end_POSTSUPERSCRIPT | 𝐯(2)={5},superscript𝐯25\displaystyle\mathbf{v}^{(2)}=\{5\},bold_v start_POSTSUPERSCRIPT ( 2 ) end_POSTSUPERSCRIPT = { 5 } , | C |
(S0,I0,R0)=(θη,0,0).subscript𝑆0subscript𝐼0subscript𝑅0𝜃𝜂00\bigg{(}S_{0},I_{0},R_{0}\bigg{)}=\bigg{(}\frac{\theta}{\eta},0,0\bigg{)}.( italic_S start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_I start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_R start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) = ( divide start_ARG italic_θ... | Further, computing the reproduction number of model (2). Let y=(I,S)𝑦𝐼𝑆y=(I,S)italic_y = ( italic_I , italic_S ) and rewrite the model (2) for susceptible and infected classes as in the general form | The subsequent sections of the paper unfold as follows: Section 2: Model formulation- In this section, we meticulously detail the formulation of the model, providing a comprehensive overview of its deterministic aspects. Section 3: Dynamics of the deterministic model- we discuss the reproduction number and stability of... | By selecting a twice-differentiable function Ytsubscript𝑌𝑡Y_{t}italic_Y start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT and applying Ito’s formula to Ytsubscript𝑌𝑡Y_{t}italic_Y start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT, we can derive the stochastic basic reproduction number. Let’s set Yt=lnItsubscript𝑌𝑡subsc... | Numerical solutions of systems are invaluable in the study of epidemic models. This section presents the numerical results of our model, shedding light on how the parameters of the deterministic model (2) and the intensity of non-Gaussian noise in the stochastic model (4) impact the dynamics. We conduct numerical exper... | A |
The predominant method for computing time-varying correlation in time series data, particularly in neuroimaging studies, involves Sliding Windows (SW). This technique entails computing correlations between brain regions across various time windows (Allen et al., 2014; Hutchison et al., 2013; Shakil et al., 2016; Mokhta... | The derivation follows by simply replacing all the terms with the WFS representation. Correlation (20) is the formula we used to compute the dynamic correlation in this study. Figure 7 displays the WFS-based dynamic correlation for different bandwidths. A similar weighted correlation was proposed in Pozzi et al. (2012)... | To circumvent these limitations, we employed the Weighted Fourier Series (WFS) representation (Chung et al., 2007, 2008). This approach extends the traditional cosine Fourier transform by incorporating an additional exponential weight. This modification effectively smooths out high-frequency noise and diminishes the Gi... | However, such average is the average of the connectivity strength. Such an approach is usually sensitive to topological outliers (Chung et al., 2019a). We address the problem through the Wasserstein distance. A similar concept was proposed in the persistent homology literature through the Wasserstein barycenter (Agueh ... | The predominant method for computing time-varying correlation in time series data, particularly in neuroimaging studies, involves Sliding Windows (SW). This technique entails computing correlations between brain regions across various time windows (Allen et al., 2014; Hutchison et al., 2013; Shakil et al., 2016; Mokhta... | B |
The Stupp protocol has become standard of care for the treatment of gliomas. It consists of radiotherapy and concomitant chemotherapy with temozolomide. Precisely, radiotherapy (RT) is provided with the standard dose of 60 Gy delivered in 30 daily fractions of 2 Gy (Monday to Friday) over 6 weeks. RT planning is based ... | Firstly, we observe the tumor dynamics (first column of Figure 12), which is characterized by a strong reduction of the tumor density in the area originally occupied by the tumor mass. This shows the efficacy of the combined treatment in reducing the overall tumor volume. Moreover, we notice that, even after the restin... | The model proposed in this note is a therapy-oriented development of that considered in [7] and aligns to the approaches in [6, 8, 9, 13, 14, 15, 26]. Unlike [7, 15] we do not differentiate here between moving and proliferating cancer cells, but account for a single population of cells forming the tumor. In fact, the a... | From the mathematical viewpoint, several classes of models have been proposed during the last two decades with the aim of using modern biomedical visualization techniques to help in predicting the tumor volumes (CTV=clinical target volume, PTV=planning target volume) for therapy planning. Some of those models [27, 51] ... | In [31] we commented about the feasibility of using such multiscale models to predict tumor spread and establish CTV and PTV margins for treatment planning. Those observations still apply here - the main issue remains the relatively large number of parameters and therewith related uncertainties. However, the increasing... | C |
The brains of manatees and dugongs exhibit unique structural characteristics, as demonstrated in Fig. 5. For these species, we make similar measurements to facilitate comparative analyses. | More complex cases are illustrated in Fig. 6. For example, the American beaver’s cortex features shallow dimples [1, 20]. To manage this intricacy, one could extend the 2D method, as illustrated in Fig. 2, to a 3D measurement framework if a 3D brain image is available. The brain of the western grey kangaroo presents co... | Challenging cases: the brains of the American beaver, which has cortical dimples, and the western grey kangaroo, which features irregular sulci [1]. These examples pose challenges for measuring equivalent gyral sizes. In the case of the American beaver, it remains ambiguous whether a cortical dimple can be classified a... | Extending our analysis beyond gyrencephalic brains, Fig. 12 indicates that we can categorize mammalian brains into three primary classifications: lissencephalic, quasi-gyrencephalic, and gyrencephalic. However, this classification scheme does not accommodate the challenging cases illustrated in Fig. 6. For example, the... | Quasi-gyrencephalic brains with underdeveloped sulci. Their drawn sizes are measured as illustrated in Fig. 4 and Fig. 5 and are plotted in Fig. 12. | A |
Conventional train-test data splits may fall short of an ideal scenario, merely ensuring the exclusion of triplets (drug A, drug B, and cell line) observed in the training set from the test set. However, they do not guarantee the absence of certain drugs or cell lines in the training set. To address this limitation, we... | Conventional train-test data splits may fall short of an ideal scenario, merely ensuring the exclusion of triplets (drug A, drug B, and cell line) observed in the training set from the test set. However, they do not guarantee the absence of certain drugs or cell lines in the training set. To address this limitation, we... | Table 5: Performance evaluation of our DDoS model across various train-test split strategies: the ‘Cell Lines’ row represents the model’s performance when specific cell lines are excluded from the training set and used for testing. Similarly, the “Drug 1” row signifies the model’s evaluation when certain drugs from the... | In our study, we also conducted a calibration analysis to compare the predicted probabilities of synergy against the observed frequencies of actual synergistic outcomes. Figure 2 showcases the calibration curve derived from the results of our trained model, specifically for the ZIP synergy score. This model was trained... | In the model training process, we adopted a Stratified 5-Folds cross-validation strategy. This method ensures that the test split maintains a balanced representation of samples for each class, preserving the proportionality of class distributions in each train-test split. Additionally, 10%percent1010\%10 % of the train... | B |
Fig. S9 also functions as a sensitivity analysis of our results with respect to the technical characterization of U𝑈Uitalic_U (resp. γ𝛾\gammaitalic_γ): while decreasing U𝑈Uitalic_U (resp. γ𝛾\gammaitalic_γ) decreases the mixing, so that microphytoplankton could in fact be slightly more aggregated, the dominance inde... | One of the reasons why estimating K(r)𝐾𝑟K(r)italic_K ( italic_r ), and even more so g(r)𝑔𝑟g(r)italic_g ( italic_r ), | as g(r)=K′(r)4πr2𝑔𝑟superscript𝐾′𝑟4𝜋superscript𝑟2g(r)=\frac{K^{\prime}(r)}{4\pi r^{2}}italic_g ( italic_r ) = divide start_ARG italic_K start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_r ) end_ARG start_ARG 4 italic_π italic_r start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG. | K(r)𝐾𝑟K(r)italic_K ( italic_r ). Using its marked version, CjKij(r)subscript𝐶𝑗subscript𝐾𝑖𝑗𝑟C_{j}K_{ij}(r)italic_C start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT italic_K start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT ( italic_r ) is the average | {\partial G}{\partial r}\right)+2\lambda C= 4 italic_π ( 2 italic_D italic_r start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT divide start_ARG ∂ italic_G end_ARG start_ARG ∂ italic_r end_ARG + italic_γ italic_r start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT divide start_ARG ∂ italic_G end_ARG start_ARG ∂ italic_r end_ARG ) + 2... | A |
When these images are displayed, pixel values undergo gamma correction to recover the original statistics for human eyes to process. | What adds to the confusion is the fact that for the widely used ICA, the two objectives have indeed been proven to coincide [18]. | All nodes have similar activation probabilities, indicating an even distribution at the coarse scale across all nodes. | after the model has been trained the vast majority of the output values are either at 0 or 1, signifying that our model encoded the images using binary representation. | In the following sections, we will assume that all pixel values x𝑥xitalic_x have already been processed by dedicated IPUs, | D |
We cannot apply Fisher’s fundamental theorem for natural selection to the evolution of novel traits in polyploidy organisms. | B and C) Dependence of (B) the variance of phenotype and (C) the evolutionary rate on the number of chromosomes. | III.3 Evolutionary innovation is described by the large deviation theory and it depends on the third-order moment of chromosomes | Conversely, if the mutation rate is excessively large, then the evolution of novel traits is no longer a rare event, and thus, the large deviation theory cannot be applied. | Note that the normalized fourth-order moment kurtosis did not exhibit non-monotonic dependence on the number of chromosomes, and it was almost independent of the mutation rate (Supplementary Fig. 2). | B |
Figures 1 and 2 illustrate the Hodge decompositions of a complete graph and a non-complete graph, respectively. The MATLAB code for performing Hodge decomposition in the least squares fashion is available at | Fig. 1: Illustration of the Hodge decomposition, which decomposes the edge flow into non-loop and loop flows. These networks are then separately subjected to birth-death decomposition to obtain the topological features. | The proposed ∞\infty∞-Wasserstein distance-based test statistic exhibits robust performance on both the loop and non-loop flows. The 𝔏∞subscript𝔏\mathfrak{L}_{\infty}fraktur_L start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT distance effectively discriminated networks in both the non-loop (gradient) and loop (curl) components... | partition graphs into topologically distinct subgraphs[14, 15]. We first apply graph filtration, a technique involving the sequential removal of edges from a graph G𝐺Gitalic_G, starting with the smallest edge weight and progressing to the largest [6, 8]. We identify the birth set B(G)𝐵𝐺B(G)italic_B ( italic_G ), as... | PH quantifies multiscale topological features of data through a filtration process [8]. Hodge theory provides a unified framework combining simplicial homology and spectral geometry, offering insights into network topology [9, 10, 11]. While the Hodge Laplacian, a generalization of the graph Laplacian, offers insights ... | A |
N}}\in\mathsf{L}^{1}.roman_exp { - italic_η italic_γ ( 1 + italic_ϵ ) divide start_ARG ∑ start_POSTSUBSCRIPT italic_i = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N end_POSTSUPERSCRIPT italic_S start_POSTSUBSCRIPT italic_i - 1 end_POSTSUBSCRIPT italic_i start_POSTSUPERSCRIPT - italic_γ / italic_α end_POSTSUPERSCR... | Similarly, whenever b2≥2subscript𝑏22b_{2}\geq 2italic_b start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ≥ 2 and using Jensen’s inequality, we have | Thus, plugging these estimates and using Hölder’s inequality (p=1+ϵ𝑝1italic-ϵp=1+\epsilonitalic_p = 1 + italic_ϵ), | Plugging these into (4), Theorem 2.1 yields a general criterion for the convergence of the genealogy of AWF populations. | Plugging these into (4), Theorem 2.1 yields a general criterion for the convergence of the genealogy of AC populations. | B |
In the diagnostic task, we assessed models trained on datasets with varying degrees of heterogeneity, as indicated by the proportion factor 𝜶∈{0.05,0.1,0.3,0.5}𝜶0.050.10.30.5\bm{\alpha}\in\left\{0.05,0.1,0.3,0.5\right\}bold_italic_α ∈ { 0.05 , 0.1 , 0.3 , 0.5 } in Table 4. Our experiments aimed to validate the perfor... | The validation results for the Gleason scoring task are listed in Table 7. Compared to models trained on single-center data, the FACL model exhibited significant improvements in the Kappa score and AUC. The average Kappa across the six centers (Hebei-1, Hebe-2, PANDA-1-1, PANDA-1-2, PANDA-2-1, and PANDA-2-2) was 0.7379... | The distribution of data splits for the diagnostic task is presented in Table 4. To assess the impact of data imbalance on the model’s performance, we partitioned the dataset from four centers (DiagSet-B-1, DiagSet-B-2, PANDA-1, PANDA-2), which contains a substantial number of samples, into positive proportions denoted... | In this study, we investigated the diagnosis of prostate cancer using a two-level classification approach to differentiate between benign and malignant conditions. Furthermore, we examined the Gleason grading of prostate cancer by employing a six-level classification system based on the International Society of Urologi... | The experimental results for the diagnosis task on the validation set are presented in Table 5, demonstrating metrics such as AUC, F1, ACC, and Recall. As α𝛼\alphaitalic_α increases, the overall performance of the local center model improves due to the different proportions of categories in the diagnostic task. When α... | D |
We describe how interpolating aligned data can provide better reference processes for use in classical DSBs, paving the way to hybrid aligned/non-aligned Schrödinger bridges. | The task of modeling conformational changes starting from a given protein structure is largely unexplored, mainly due to the lack of high-quality large datasets. Here we utilize the recently proposed D3PM dataset (Peng et al., 2022) that provides protein structures before (apo) and after (holo) binding, covering variou... | In this paper, we propose a new framework to tackle the interpolation task with aligned data via diffusion Schrödinger bridges. Our central contribution is a novel algorithmic framework derived from the Schrödinger bridge theory and Doob’s hℎhitalic_h-transform. Via a combination of the two notions, we derive novel los... | In this section, we presented a proof of concept application of SBAlign for modelling conformational changes in proteins during docking. associated with the protein docking task. A combination of SBAlign for conformational change modeling, with more recent methods for rigid-protein docking (Ketata et al., 2023) can pro... | We evaluate our proposed framework on both synthetic and real data. For experiments utilizing real data, we consider two tasks where such aligned data is naturally available. The first is the task of developmental processes in single-cell biology, and the second involves protein docking. While diffusion models have bee... | D |
-\mu a}y(t-a)\,\mbox{d}a=:\int_{0}^{\infty}k(a)y_{t}(-a)\,\mbox{d}aitalic_y ( italic_t ) = italic_D caligraphic_F ( 0 ) italic_y start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT = ∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ∞ end_POSTSUPERSCRIPT italic_β ( italic_x start_POSTSUBSCRIPT italic_m end_POS... | (as indeed one can understand by using only the interpretation: it describes the linear population model corresponding to the virgin environment E=0𝐸0E=0italic_E = 0). | can be replaced by a more explicit one using the proof of Lemma 7 (i.e. using the definitions of B~~𝐵\tilde{B}over~ start_ARG italic_B end_ARG and a~~𝑎\tilde{a}over~ start_ARG italic_a end_ARG): | Our motivation to study the specific model above is to understand whether the evolution (the interpretation of x𝑥xitalic_x and u𝑢uitalic_u is explained below) of a tree population can be explained by taking into account only competition for light through a hierarchical structure affecting individual growth, assuming ... | Equation (12)12(\ref{scalar2})( ) provides the delay formulation of the model, which we are going to study here. In the delay formulation the state variable is the population birth rate history Bt:=B(t+⋅)B_{t}:=B(t+\cdot)italic_B start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT := italic_B ( italic_t + ⋅ ), instead of th... | A |
One way to increase the efficiency of greedy search procedures is by applying the, so-called, principle of coherence (Gabriel, 1969) that is used as a strategy for pruning the search space. We show that for the family of pdRCON models the twin lattice allows a more straightforward implementation of the principle of coh... | The greedy search procedure of the previous section has been implemented in the program language R, and here we describe its application to both synthetic and real-world data, including an empirical comparison with the penalized likelihood method of Ranciati and Roverato (2023). | We introduce a stepwise backward elimination procedure that exploits the twin lattice both for the computation of the meet operation and the implementation of the coherence principle. | compare it with the stepwise backward elimination procedure given in Roverato and Nguyen (2022) that does not exploit the twin lattice for the computation of the set of candidate models, and where the principle of coherence is naively implemented by only considering the submodel relationship. | We implement a stepwise backward elimination procedure with local moves on the twin lattice which satisfies the coherence principle, and we show that it is more efficient than an equivalent procedure on the model inclusion lattice. This procedure is implemented in the statistical programming language R and its behavior... | D |
To enhance performance, we perform multimodal feature integration using features extracted from the short-axis, four-chamber, and Cardiac Measurements (CM). We adopt two strategies for feature integration, namely the early and late fusion of features [6]. In early fusion, the features are fused at the input level witho... | 3) Clinical utility: Decision curve analysis indicates the diagnostic value of our pipeline, which can be used in screening high-risk patients from a large population. | Cardiac MRI scans contain high-dimensional spatial and temporal features generated throughout the cardiac cycle. The small number of samples compared to the high-dimensional features poses a challenge for machine learning classifiers. To address this issue, Multilinear Principal Component Analysis (MPCA) [11] utilizes ... | In this paper, we use three primary metrics: Area Under Curve (AUC), accuracy, and Matthew’s Correlation Coefficient (MCC), to evaluate the performance of the proposed pipeline. Decision Curve Analysis (DCA) is also conducted to demonstrate the clinical utility of our methodology. | This paper proposed a tensor learning-based pipeline for PAWP classification. We demonstrated that: 1111) tensor-based features have a diagnostic value for PAWP, 2222) the integration of CM features improved the performance of unimodal and bi-modal methods, 3333) the pipeline can be used to screen a large population, a... | C |
In parallel, the use of Transformers for multimodal fusion has gained significant attention in classification and generative tasks [70, 86, 61]. Multimodal tokens can be concatenated and fed to a regular Transformer [72, 18], a hierarchical Transformer [43], or a cross-attention Transformer [55, 46, 52]. As the number ... | Early vs. Late fusion: Early fusion methods (MCAT [10], MOTCat [87] and SurvPath) outperform all late fusion methods. We attribute this observation to the creation of a joint feature space that can model fined-grained interactions between transcriptomics and histology tokens. Overall, these findings justify the need fo... | 1. Tokenizing transcriptomics modality: Modalities based on image and text can be unequivocally tokenized into object regions and word tokens [40, 73], however, tokenizing transcriptomics in a semantically meaningful and interpretable way is challenging. As transcriptomics data is already naturally represented as a fea... | Multimodal integration is an important objective in cancer prognosis [64], as combining histology and omics data such as genomics or transcriptomics is the current clinical practice for many cancer types. The majority of these works employ late fusion mechanisms [71, 9], and mostly differ in the way modality fusion is ... | While histology provides phenotypic information about cell types and their organization into tissues, alternate modalities can provide complementary signals that may independently be linked to prognosis. For instance, bulk transcriptomics, which represents the average gene expression in a tissue, can reveal a richer gl... | C |
There are various initial conditions that we consider in this work, based on the assumption that a stationary limiting distribution for 𝐗(t)𝐗𝑡\mathbf{X}(t)bold_X ( italic_t ) exists (since θ,k>0𝜃𝑘0\theta,k>0italic_θ , italic_k > 0, this is always true for the form of 𝚯𝚯\bm{\Theta}bold_Θ expressed above, and mor... | The system can still be viewed as multivariate Ornstein-Uhlenbeck process, although 𝐒𝐒\mathbf{S}bold_S (eqs. 2 and 3) is no longer a single-element matrix but has elements on both the main and lower diagonal. | We highlight that the non-stationary covariance matrix (eq. 5b) does not depend on the initial condition 𝐗0subscript𝐗0\mathbf{X}_{0}bold_X start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and that the mean 𝐦(t)𝐦𝑡\mathbf{m}(t)bold_m ( italic_t ) is an affine transformation of the initial condition 𝐗0subscript𝐗0\mathbf{X}... | There are various initial conditions that we consider in this work, based on the assumption that a stationary limiting distribution for 𝐗(t)𝐗𝑡\mathbf{X}(t)bold_X ( italic_t ) exists (since θ,k>0𝜃𝑘0\theta,k>0italic_θ , italic_k > 0, this is always true for the form of 𝚯𝚯\bm{\Theta}bold_Θ expressed above, and mor... | The multivariate Ornstein-Uhlenbeck process conditioned on the initial condition 𝐗0subscript𝐗0\mathbf{X}_{0}bold_X start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT has exact solution [26, 27] | D |
The available MoleculeNet benchmark [9] uses SMILES for its molecular representation. After reviewing some of the molecule strings, not all are canonical. Including non-canonical SMILES is problematic as SMILES grammar is already complex; the molecules are converted to RDKit’s canonical form to reduce complexity. The n... | Fig. 3 offers a visualization of the methodology used to train the RNN. The molecules are first loaded in from a dataset from the MoleculeNet benchmark [9] and converted to SELFIES representation using the method described in Section III-A. The converted SELFIES are then processed through an embedding layer with a di... | Before training on the selected MoleculeNet datasets referenced in Section II-A, we perform an additional reduction to the dataset by setting the lower bound of 31 molecules to the SMILES string allowing for the search space to remain sufficiently complex while reducing the overall run time. The lower bound reduces the... | The available MoleculeNet benchmark [9] uses SMILES for its molecular representation. After reviewing some of the molecule strings, not all are canonical. Including non-canonical SMILES is problematic as SMILES grammar is already complex; the molecules are converted to RDKit’s canonical form to reduce complexity. The n... | Unfortunately, Vanilla RNNs suffer from memory saturation issues, so they are not always reliable. There have been many methods proposed to overcome this issue, but one of the most popular is the Gated Recurrent Unit (GRU)[17]. The basic structure of a GRU is in Fig. 2. We can mathematically describe each of the compo... | A |
Even though the CEP furnishes an intuitive explanation in the assemblage of ecological communities, counterexamples of the CEP have been found in nature. | One such example is observed in the ocean with phytoplankton, known as the paradox of the plankton [9]. | By incorporating intraspecific suppression into GCRM, we investigate the role of intraspecific suppression on consumer diversity and comprehend the paradox of the plankton. | To address the paradox within the niche theory and explain the coexistence of diverse species, we introduce intraspecific suppression as a novel mechanism, which is known for its capacity to enhance the stability of large ecological systems [15, 16]. | Even though resources are externally supplied such that resource species never go extinct, the calculated bound of coexisting consumer species cannot explain the paradox of the plankton in the generalized MCRM (GCRM). | A |
\right).over¯ start_ARG roman_T end_ARG ( italic_r ) ≤ divide start_ARG 1 end_ARG start_ARG 1 - italic_R start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_G , italic_τ ) end_ARG roman_log ( divide start_ARG 1 end_ARG start_ARG italic_r end_ARG ) . | To compare different processes, we introduce the notation y(t;G,τ,V(0))𝑦𝑡𝐺𝜏𝑉0y(t;G,\tau,V(0))italic_y ( italic_t ; italic_G , italic_τ , italic_V ( 0 ) ) for the prevalence of the static NIMFA SIS process at time t𝑡titalic_t, on the graph G𝐺Gitalic_G with effective infection rate τ𝜏\tauitalic_τ and starting i... | We start with the matrix NIMFA equation (6) and upper bound the derivative of the infection probability vector V(t)𝑉𝑡V(t)italic_V ( italic_t ) by disregarding the non-linear term. After rescaling time such that δ=1𝛿1\delta=1italic_δ = 1 we find | In this section, we explore the interplay between the timescale of the epidemic process and the timescale of the topology updating process. We assume at first that the inter-update times Tmsubscript𝑇𝑚T_{m}italic_T start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT are constant and equal to ΔtΔ𝑡\Delta{t}roman_Δ italic_t... | which are the “rescaled” NIMFA governing equations. The same method can be applied to the system (5), where an equivalent system with δ=1𝛿1\delta=1italic_δ = 1 is found. The intervals [tm−1,tm)subscript𝑡𝑚1subscript𝑡𝑚[t_{m-1},t_{m})[ italic_t start_POSTSUBSCRIPT italic_m - 1 end_POSTSUBSCRIPT , italic_t start_POSTS... | B |
(Tkj,i−Tki,j)Vk=(T11,2−T12,1)V1+(T21,2−T22,1)V2=0,subscript𝑇𝑘𝑗𝑖subscript𝑇𝑘𝑖𝑗subscript𝑉𝑘subscript𝑇112subscript𝑇121subscript𝑉1subscript𝑇212subscript𝑇221subscript𝑉20(T_{kj,i}-T_{ki,j})V_{k}=(T_{11,2}-T_{12,1})V_{1}+(T_{21,2}-T_{22,1})V_{2}=0\,,( italic_T start_POSTSUBSCRIPT italic_k italic_j , italic_... | In the full hypothesis (19) of Proposition 1, we use the standard construction of a primitive of an exact differential form in order to build the general related energy E(V)𝐸𝑉E(V)italic_E ( italic_V ): | In the first part of our account, i.e., Section III, we show that the hypothesis of these authors is a special case of a strictly more general necessary and sufficient condition (19), | This variational principle would like to translate the fact that the cerebral mechanism moves in the search and/or in the construction of equilibria with the minimum expense in the deviations from the original synaptic conductivities. | We are forced to extend the time to the full interval [0,+∞)0[0,+\infty)[ 0 , + ∞ ) because, typically, we need an infinite time to reach an equilibrium, even though in any meaningful case we see that by a trivial estimate we arrive very near to an equilibrium in a | A |
Cherry reduction involves replacing the cherry with a single vertex. Reticulated cherry reduction involves deleting the arc between the parents of the two leaves and then suppressing degree-2 vertices. | Many core features discussed in the context of networks, such as reticulations, paths, cherries, siblings, and so on, have been translated into the language of covers; a summary is given in Table 9. These translations of features have been necessary for characterising several important classes of phylogenetic network i... | By a theorem of [5, 14], for orchard networks, the order in which these are performed is not important. | A network is orchard, by definition, if and only if it can be reduced to a trivial network by cherry or reticulated cherry reductions. According to a result of [5, 14], the order of such reductions is not important. The procedures in Algorithm 4 exactly reflect the effect on the cover of these operations on the network... | Orchard networks are non-degenerate phylogenetic networks defined by the property that they can be reduced to a trivial network (a single vertex) by a series of cherry or reticulated cherry reductions [5, 14, 19]. In the present paper, we will restrict our attention to binary orchard networks. | B |
This is because the population dynamics now take place in high or infinite dimension (Hallatschek and Nelson, 2008; Barton et al., 2010; Durrett and Fan, 2016; Louvet and Véber, 2023; Etheridge et al., 2023). For example, the spatial version of (1), the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov (FKPP) equation in... | Briefly, we find that positive selection does not in general lead to (7) and (8), that very strong positive selection (relative to the sample size) leads to neutral gene genealogies with a single ancient latent mutation for the favored allele. This is described in Section 3 for scenario (i) and for the case α~∈(1,∞)~𝛼... | Some of our results for rare alleles have empirical relevance, specifically those for scenario (ii) including their robustness to time-varying population size demonstrated in Section 3.4, and those for scenario (iii) with α~<0~𝛼0\widetilde{\alpha}<0over~ start_ARG italic_α end_ARG < 0. In scenario (ii), as n𝑛nitalic_... | Here we apply the model of coalescence in a random background described by Barton et al. (2004) to prove these results (7) and (8) for rare alleles in large samples and especially to extend the analysis of latent mutations to scenarios which include selection. We investigate both the number of latent mutations and thei... | We thank Alison Etheridge for raising the question about the applicability of our limiting results to Wright-Fisher reproduction (cf. Section 2.1.1). We also thank Shamil Sunyaev, Evan Koch and Joshua Schraiber for helpful discussions, and Daniel Rickert and Kejia Geng for assistance in producing the figures. Finally, ... | D |
Table 2: Configurations of generated datasets. The generated sets are separated into subsets A, B, C, D, E, F, G, H with respect to a varying parameter. Parameters n_ase, n, w_frac and p0 are fixed to 1000, 10000, 1212\frac{1}{2}divide start_ARG 1 end_ARG start_ARG 2 end_ARG and 0.990.990.990.99 respectively. | [1.0,b]1.0𝑏[1.0,\leavevmode\nobreak\ b][ 1.0 , italic_b ], b=𝑏absentb=italic_b = 1.1, 1.2, 1.3, 1.4, 1.5 | y∼𝒩ℬ(𝓍,𝓅),𝓍∼𝒩ℬ(𝓎,1−𝓅)formulae-sequencesimilar-to𝑦𝒩ℬ𝓍𝓅similar-to𝓍𝒩ℬ𝓎1𝓅y\sim\mathpzc{NB}(x,p),\leavevmode\nobreak\ \leavevmode\nobreak\ x\sim\mathpzc% | y∼ℬ𝒾𝓃ℴ𝓂(𝓃,𝓅),𝓍∼ℬ𝒾𝓃ℴ𝓂(𝓃,1−𝓅).formulae-sequencesimilar-to𝑦ℬ𝒾𝓃ℴ𝓂𝓃𝓅similar-to𝓍ℬ𝒾𝓃ℴ𝓂𝓃1𝓅y\sim\mathpzc{Binom}(n,p),\leavevmode\nobreak\ \leavevmode\nobreak\ x\sim% | r(x,b,a)=bx+a,𝑟𝑥𝑏𝑎𝑏𝑥𝑎r(x,b,a)=bx+a,italic_r ( italic_x , italic_b , italic_a ) = italic_b italic_x + italic_a , | A |
_{1}+\dots+T_{i}\leq u<T_{1}+\dots+T_{i+1}\}}∀ italic_u ≥ 0 , italic_ζ ( italic_u ) = italic_σ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_u - ( italic_T start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT + ⋯ + italic_T start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ) ) bold_1 start_POSTSUBSCRIPT { italic_T start_POST... | often denoted by W𝑊Witalic_W (for waning) (Lavine et al., 2011; Carlsson et al., 2020). In our work, we will model the decay of immunity by | also been proposed, for instance in Hethcote et al. (1981); Cooke and Van Den Driessche (1996); Taylor and Carr (2009); Bhattacharya and Adler (2012). In such models, | complexity (Anderson and May, 1982; Farrington, 2003; Magpantay, 2017; Delmas et al., 2022). However, the bulk of this work | Acknowledgements.1Acknowledgements.1\EdefEscapeHexAcknowledgementsAcknowledgements\hyper@anchorstartAcknowledgements.1\hyper@anchorend | D |
In the present study, within the established framework of the GLV model featuring a fully connected random interaction network, we explicitly consider time-dependent species interactions and a Monod functional response, commonly used for modelling the growth of microorganisms [33]. | Moreover, theoretical models as the GLV, stand as the scaffolding upon which empirical research is built, offering a controlled setting where foundational ecological mechanisms can be disentangled. As such, they serve as a crucible for testing the robustness and generalizability of ecological theories. | Specifically, we adopt the hypothesis that these interactions can be modeled as stochastic colored noises, which we call annealed GLV (AGLV). | To make a comparison between GLV with quenched and annealed interactions, we also investigate the phase diagram for the case τ=0𝜏0\tau=0italic_τ = 0 and J(x)=x𝐽𝑥𝑥J(x)=xitalic_J ( italic_x ) = italic_x. Since δ>0𝛿0\delta>0italic_δ > 0 (see eq. (5)) and E(x)>0E𝑥0\mathrm{E}(x)>0roman_E ( italic_x ) > 0, in order f... | In this study, we have undertaken an investigation into the GLV equations with annealed disorder, incorporating finite correlation time and simple functional responses. We have determined the corresponding dynamical mean-field equations for a large number of species, which do not depend on the specific form of J(x)𝐽�... | B |
In the previous section, we considered a multistep model of RNA production and degradation, and showed that it can be mapped to an infinite-server queue A/S/∞𝐴𝑆A/S/\inftyitalic_A / italic_S / ∞, where transcription is the arrival process A𝐴Aitalic_A, RNA degradation is the service process S𝑆Sitalic_S, and the numbe... | Once we move away from renewal arrivals, there are many results potentially useful for gene expression modelling that we did not cover in detail. We first mention the BMAP/G/∞𝐵𝑀𝐴𝑃𝐺BMAP/G/\inftyitalic_B italic_M italic_A italic_P / italic_G / ∞ queue, where customers arrive in batches according to a batch Markov... | Table 1: A summary of known results for selected infinite-server queues that are relevant for stochastic gene expression modelling. The table refers to the non-stationary and stationary RNA number distributions and their corresponding moments. | It is interesting to note that the GX/G/∞superscript𝐺𝑋𝐺G^{X}/G/\inftyitalic_G start_POSTSUPERSCRIPT italic_X end_POSTSUPERSCRIPT / italic_G / ∞ queue and Ref. [71] have been the sole point of reference for most of the literature connecting stochastic gene expression to queueing theory [57, 59, 23].That is in our opi... | In this section, we review known results for six infinite-server queues made by combining the arrival and service processes described above, which are of particular importance for stochastic gene expression modelling. We focus on queues whose arrivals are described by renewal (G𝐺Gitalic_G) and Markov-modulated process... | B |
This external field is self-consistent in the sense that, at any time t≥0𝑡0t\geq 0italic_t ≥ 0, it is given by the very distribution of the state of the focal process. | The moment-mediated interactions we study allow for direct solution of self-consistent fields via a nonlinear moment equation, which is amenable to standard numerical ODE techniques. | This external field is self-consistent in the sense that, at any time t≥0𝑡0t\geq 0italic_t ≥ 0, it is given by the very distribution of the state of the focal process. | We calculate self-consistent fields by solving limiting nonlinear forward equations for the focal process. | First, the self-consistent fields 𝐫(t)𝐫𝑡\mathbf{r}(t)bold_r ( italic_t ) are calculated as in Example 4.2 by solving a D𝐷Ditalic_D-dimensional initial value problems (we reverse time such that the process starts at the tree root time τ>0𝜏0\tau>0italic_τ > 0, and ends at t=0𝑡0t=0italic_t = 0). | C |
This sequential information is crucial for understanding the folding patterns and functional motifs within the protein. | These edges play a pivotal role in encoding the protein’s tertiary structure and folding patterns, enabling us to capture the intricate spatial arrangements of amino acids within the protein’s core. | To model the diverse interactions and relationships between amino acids, we introduce different types of edges connecting the nodes. | Sequential edges are employed to connect adjacent nodes in the protein sequence, effectively representing the sequential order of amino acids and capturing the linear arrangement of the protein’s primary structure. | Additionally, we utilize spatial edges to establish connections between nodes that are in close spatial proximity within the 3D structure of the protein. | D |
{2}\,.italic_r start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = italic_N start_POSTSUBSCRIPT roman_E end_POSTSUBSCRIPT italic_σ start_POSTSUBSCRIPT roman_E end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + italic_N start_POSTSUBSCRIPT roman_I end_POSTSUBSCRIPT italic_σ start_POSTSUBSCRIPT roman_I end_POSTSUB... | the mean input μisubscript𝜇𝑖\mu_{i}italic_μ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT and input variance σi2superscriptsubscript𝜎𝑖2\sigma_{i}^{2}italic_σ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT of | with total input current Ii(t)subscript𝐼𝑖𝑡I_{i}(t)italic_I start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_t ) that consists of recurrent input | σ2superscript𝜎2\sigma^{2}italic_σ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT of the total input to each neuron while modifying the | the subthreshold dynamics of the membrane potential Visubscript𝑉𝑖V_{i}italic_V start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT of neuron | C |
Typically, asymptomatic individuals are less contagious but unaware that they have contracted the disease, whereas symptomatic individuals are more contagious but can take precautions (use of a mask, social distancing, quarantine, use of a condom, etc.) to limit the spread of the disease. | We now look at the parameter regions where one of the two infection rates is subcritical and the other one supercritical, in which case the behavior of the process is less obvious. | In particular, the characteristics of the disease and the social behavior of the population induce a variability in the rate at which the disease spreads from asymptomatic versus symptomatic individuals. | Typically, asymptomatic individuals are less contagious but unaware that they have contracted the disease, whereas symptomatic individuals are more contagious but can take precautions (use of a mask, social distancing, quarantine, use of a condom, etc.) to limit the spread of the disease. | In particular, the contact process with aging truncated at age 2 is equivalent to our epidemic model with β1<β2subscript𝛽1subscript𝛽2\beta_{1}<\beta_{2}italic_β start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT < italic_β start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT in which the asymptomatic individuals spread the disease at a slow... | B |
The conditional pose prediction task takes the encoder and decoder from the mulit-class image reconstruction task and reversed order. | Compared to the variational image reconstruction task, the inputs and ground-truth labels are no long EM images, but poses | In addition, we generated visualization of the volumes of the 1st, 5th, and 10th classes from cryoDRGN2, HetACUMN, and the groundtruth (see Figure 6). Comparing with the ground truth, it is no obvious difference for cryoDRGN2 and cryoFIRE on the first two volumes. But for the 10th class, there is some visible inconsist... | The second task is for conditional pose prediction (CPP), which exploits the same encoder-decoder as the first task but in reversed order to explore larger pose spaces. Instead of image reconstruction, it reconstructs the corresponding projection poses from randomly sampled poses with the reversed pipeline, and minimiz... | Figure 1: Architectures of the two tasks in HetACUMN. (a) the variational image reconstruction task; (b) the conditional pose prediction (CPP) task. | A |
The CPN utilized the ResNeXt backbone network [49] to extract multiscale feature maps, a regression head to generate candidate contour representations for each pixel, and a classification head to determine whether an object was present or not at these locations. A proposal sampling stage extracted a sparse list of cont... | The uncertainty-aware Listen2Student mechanism [28] was applied to incorporate unlabeled examples during training, where a teacher model generated bounding boxes as pseudo-labels to supervise the student model. The model inputs were three-channel images. For post-processing, the Vanilla NMS relying solely on the classi... | Lou et al. [30] (T2-sribdmed) first divided the images into four distinct categories based on low-level image features (e.g., intensities) in an unsupervised way. Then, class-wise cell segmentation models were trained for each category. The model employed U-Net-like architecture where ConvNeXT [29] was used as the buil... | The model inputs were three-channel images. The overall loss function was the combination of binary cross-entropy loss and mean-square error loss. The inference process relied on the sliding window strategy, a highly efficient approach for processing whole-slide images. During the merging of predictions from these smal... | Additionally, all the top three teams explored the potential of leveraging the unlabeled images to improve the segmentation performance. Specifically, T1-osilab [25] employed consistency regularization [23] to match the algorithm’s predictions on the clean and degraded unlabeled images and introduced an additional head... | A |
Our method is both a generalization of existing methods that consider higher-order phase-isostable interactions and a general framework from which to study higher-order effects. For example, a higher-order reduced model is derived using the Haken-Kelso-Bunz (HKB) equation in [36]. The higher-order terms are the lowest-... | Second, we use first order averaging, which is technically valid for small ε𝜀\varepsilonitalic_ε comparable to those used in weak coupling theory. This limitation is especially apparent in the last example, where the thalamic model is near a SNIC bifurcation and the reciprocal of the period (1/44 ms≈0.0231times44ms0.0... | Our method is both a generalization of existing methods that consider higher-order phase-isostable interactions and a general framework from which to study higher-order effects. For example, a higher-order reduced model is derived using the Haken-Kelso-Bunz (HKB) equation in [36]. The higher-order terms are the lowest-... | When a finite number of oscillators is considered, other features may be exploited, each with their own limitations. When the network exhibits symmetries, it is possible to enumerate all phase-locked states with weak or strong coupling [20], but this method is not suited to work in the case of asymmetries [23]. In netw... | Our method may aid in addressing questions of synchrony and phase-locking in general finite populations of coupled oscillators with heterogeneity where order parameters are typically used. For example, the heterogeneous systems and coupling functions considered in [1] can not exhibit synchrony and a “bounded synchroniz... | D |
)\,.- divide start_ARG italic_σ start_POSTSUPERSCRIPT italic_α end_POSTSUPERSCRIPT roman_Γ ( italic_α ) roman_cos ( divide start_ARG italic_α end_ARG start_ARG 2 end_ARG roman_arccos divide start_ARG italic_I start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT end_ARG start_ARG square-root start_ARG italic_I start_POSTSUBSCRIPT 0 ... | Equations (39) and (41) constitute the result (36) of the linear approximation for time-independent regimes in terms of physically meaningful macroscopic observables. | In this section we employ the results for firing rate (39) and mean voltage (41) to construct a self-consistent mathematical description of the macroscopic states of the population of QIFs with global synaptic coupling (9,10). Here I0=η0+Jrsubscript𝐼0subscript𝜂0𝐽𝑟I_{0}=\eta_{0}+Jritalic_I start_POSTSUBSCRIPT 0 end... | For the case of a heterogeneous population with a Cauchy distribution of η𝜂\etaitalic_η, the theoretical analytical approximation (36) [equivalently, Eqs. (39) and (41)] is examined by comparison to the ‘exact’ numerical results in Fig. 4. The analytical theory exhibits a decent accuracy even for the noise-driven regi... | In Sec. III, for the case of noninteger α𝛼\alphaitalic_α, we construct a first-order perturbation theory for the effect of noise on the characteristic function and derive macroscopic observables: population-mean voltage and firing rate. In Sec. IV, the theoretical results for macroscopic states of homogeneous populati... | A |
The code supporting the conclusions of this study is available on GitHub at https://github.com/jgornet/predictive-coding-recovers-maps. The repository contains the Malmo environment code, training scripts for both the predictive coding and autoencoding neural networks, as well as code for the analysis of predictive cod... | In the previous section, we demonstrate that the predictive coding neural network captures spatial relationships within an environment containing more internal spatial information than can be captured by an auto-encoder network that encodes image similarity. Here, we analyze the structure of the spatial code learned by... | Moreover, we study the predictive coding neural network’s representation in latent space. Each unit in the network’s latent space activates at distinct, localized regions—called place fields—with respect to physical space. At each physical location, there exists a unique combination of overlapping place fields. At two ... | All datasets supporting the findings of this study, including the latent variables for the autoencoding and predictive coding neural networks, as well as the training and validation datasets, are available on GitHub at https://github.com/jgornet/predictive-coding-recovers-maps. Researchers and readers interested in acc... | The code supporting the conclusions of this study is available on GitHub at https://github.com/jgornet/predictive-coding-recovers-maps. The repository contains the Malmo environment code, training scripts for both the predictive coding and autoencoding neural networks, as well as code for the analysis of predictive cod... | C |
We turn to more convenient and fast EEG signals and focus on the object recognition tasks, in which the semantic information is the significant gain by natural image decoding compared to visual decoding of contrast, color, etc. | Beyond the self-supervised framework, we try to demonstrate the biological plausibility by resolving the visual processing of EEG signals. | We have tried to demonstrate the feasibility and plausibility of EEG-based image decoding from three folds, zero-shot classification performance, detailed resolving of the brain activity, and model interpreting. | Motivated by these challenges, we present an EEG-based image decoding framework that employs self-supervised learning, enabling the model to achieve zero-shot generalization in object recognition tasks, further demonstrating the feasibility. | We demonstrate the feasibility of investigating natural image information from EEG signals. Extensive experiments affirm the biological plausibility, which brings a resolving of human object recognition from temporal, spatial, spectral, and semantic aspects. | B |
Here, we introduce notation defining the probability of observing a particular gene tree topology under uniform sampling. The values hw(x,y)subscriptℎ𝑤𝑥𝑦h_{w}(x,y)italic_h start_POSTSUBSCRIPT italic_w end_POSTSUBSCRIPT ( italic_x , italic_y ) each correspond to the probability of the w𝑤witalic_wth gene tree topolo... | The main theorem of this section establishes possible anomaly zones for the caterpillar tree. That is, given any choice of birth rate λ𝜆\lambdaitalic_λ and death rate μ𝜇\muitalic_μ, the caterpillar species tree with some choices of branch lengths produces a gene tree distribution where the uniformly sampled gene tree... | The main result of this section is that the species tree topology corresponds to the uniformly sampled gene tree with maximal probability. The main implication of this result is that when more independent gene trees are given, the democratic vote estimator applied to the uniform sampled gene trees obtains the species t... | In this paper, the distribution of gene trees is described further for gene trees generated under GDL. With this further information, we describe when anomaly zones can exist for gene trees generated under GDL for rooted species trees on either three or four species. As with anomalous gene trees in the multispecies coa... | If the gene trees are assumed independent of each other, then the “democratic vote” estimator finds the species tree with the highest probability by counting the number of times each branching pattern appears in the list of gene trees. As more independent gene trees are accumulated, the gene tree with the highest proba... | B |
V(L)<Λ<∞𝑉𝐿ΛV(L)<\Lambda<\inftyitalic_V ( italic_L ) < roman_Λ < ∞ so that N>N∗=exp(V(L)ϵ−1)𝑁subscript𝑁𝑉𝐿superscriptitalic-ϵ1N>N_{*}=\exp(V(L)\epsilon^{-1})italic_N > italic_N start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT = roman_exp ( italic_V ( italic_L ) italic_ϵ start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ). | If V(L)<Λ<ST|T<∞𝑉𝐿Λsubscript𝑆conditional𝑇𝑇V(L)<\Lambda<S_{T|T}<\inftyitalic_V ( italic_L ) < roman_Λ < italic_S start_POSTSUBSCRIPT italic_T | italic_T end_POSTSUBSCRIPT < ∞ then N>N∗𝑁subscript𝑁N>N_{*}italic_N > italic_N start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT and there is a sufficient number of walkers to acco... | In this regime, there is a sufficient number of walkers to accomplish the extreme rare event in finite time as ϵ→0+→italic-ϵsuperscript0\epsilon\to 0^{+}italic_ϵ → 0 start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT. | As in Regime 1, we fix the number of walkers to be N=⌊exp(ϵ−1Λ)⌋𝑁superscriptitalic-ϵ1ΛN=\lfloor\exp(\epsilon^{-1}\Lambda)\rflooritalic_N = ⌊ roman_exp ( italic_ϵ start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT roman_Λ ) ⌋ and we (i) asymptote ϵ→0+→italic-ϵsuperscript0\epsilon\to 0^{+}italic_ϵ → 0 start_POSTSUPERSCRIPT... | In this regime, increasing the number of walkers (i.e., increasing "labor") has the strongest effect on reducing the extreme first hitting time. | B |
Due to the large space of the corresponding vocabulary, the corpus need to be pre-processed using word embedding techniques before sending the sentences into the network [39]. Here we describe the main steps. | In the bottom part of the figure, we select untrained, trained-for-five-epoch, and full-trained RNN with meta predictive learning to show the performances at different training stages in generating one of the sentences in the test dataset. The correctly predicted tokens from the test sentence are highlighted, while the... | To study the network behavior, we plot the distribution of hyperparameters m𝑚mitalic_m, π𝜋\piitalic_π, ΞΞ\Xiroman_Ξ when the RNN network is trained with the MPL method, as shown in the Fig. 6. We find that the mean weight m𝑚mitalic_m for all layers is symmetrically distributed around zero, with a relatively narrow d... | Our proposed MPL achieves equal or even better performance compared with traditional methods in all three tasks, showing the advantage of ensemble predictive coding, since examples of single networks can be readily sampled from the trained distribution [28, 18]. By analyzing the distribution of hyperparameters, we are ... | The first step is to use a tokenizer tool to split the sentences into tokens and replace the useless words or characters with a special token named <<<unk>>>, indicating an unknown token. In addition, the tokens that appeared less than five times in the whole corpus will be replaced with <<<unk>>> to help the network c... | D |
We conducted an analysis of bright-field (BF) images of NE organoids formed in the neural induction medium with 2% and 8% Geltrex respectively at day 7 and day 18. The findings are presented below. | To further validate our hypothesis, we conducted a comparison between the outcomes of our research and those from a previously published peer-reviewed paper about hiSPCs derived NE organoids [5]. Theses NE organoids are generated to mimic neural tube development at early embryogenesis stage. They are defined with round... | Figure 3: (a) The average detection scores comparison between our method and the StarDist. (c) and (d) are the segmentation results from our method and the StarDist algorithm, respectively. | We conducted a comparison of the mean average precision (mAP) between the organoid detection results obtained from our method and those obtained from the open sourced StarDist method [3] in Fig. 3. Instead of training the StarDist method from scratch, we inferenced the ’2D_versatile_fluo’ model with default settings. T... | We also analyzed the morphological features of organoids among different groups in Fig, 4. Our results indicate that in the later stage of organoid formation (day 18), a higher concerntration of Geltrex leads to smaller organoid sizes, which aligns with the hypothesis that Geltrex, being a hydrogel, undergoes solidific... | C |
The starting point for the present paper is the recent article [10] just cited. In this seminal study, the author proposes a very persuasive stochastic model for brain-supervised learning | In order to understand how biological neural networks (BNNs) work, it seems natural to compare them with artificial neural networks (ANNs). Although the definition of the latter is inspired by the former, they also differ in several aspects. One of them is the way the network parameters are updated. | We review and discuss this setup in Section 2. In this model the local updating rule of the connection parameters in BNNs turns out to be a zero-order optimization procedure. More precisely, it is shown in [10] that the expected value of the iterates coincides with a modified gradient descent. However, this holds only ... | It turns out that with this modification, the updates correspond approximately to a continuous descent step along the gradient flow, see Theorem 1. This can be interpreted in the sense that it is not biologically implausible that BNNs use a kind of SGD algorithm after all, but without explicitly computing the gradient. | In simple terms, an ANN learns from data by adjusting the weights of the connections between nodes in order to minimize a loss function that measures the difference between the desired output and the actual output of the network. More specifically, the optimization step is performed using the Stochastic Gradient Descen... | B |
In conclusion, in order to narrow the gap between the promise of aqueous iontronic neuromorphic computation and its implementation, our work demonstrates the capabilities of a fluidic memristor by employing it as an artificial synapse for carrying out neuromorphic reservoir computing. Temporal signals, in the form of v... | This work is part of the D-ITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW). This work is also supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (2020... | The PNP equations form an effective theoretical framework to analyse ion transport in charged porous materials [42]. However, the complex three-dimensional geometric structure of the NCNM, with features on length scales varying from the colloidal surface-surface distance all the way up to the channel length, introduces... | The fabrication of microchannel and formation of the NCNM for the fluidic memristor is similar to previously reported methods [36, 37] and is described in the SI in detail. A master for multi-layered channels (target heights are 5 μ𝜇\muitalic_μm for shallow channel and 100 μ𝜇\muitalic_μm for deep) was created using a... | To illustrate how the results shown in Fig. 4(a) can be leveraged to classify more complex data inputs with an explanatory example, let us consider the simple single-digit numbers 0-9, represented by black and white 4×5454\times 54 × 5 pixel images. By converting a row of 4 pixels to a string of bits by letting a white... | A |
0&0&0&0&\mu_{m}\end{bmatrix}.F = [ start_ARG start_ROW start_CELL italic_β start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT divide start_ARG roman_Λ end_ARG start_ARG italic_μ end_ARG end_CELL start_CELL 0 end_CELL start_CELL 0 end_CELL start_CELL 0 end_CELL start_CELL italic_β start_POSTSUBSCRIPT italic_m end_POSTSUBSCR... | Here, the matrix FV−1superscriptFV1\textbf{FV}^{-1}FV start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT is given by | where ρ𝜌\rhoitalic_ρ represents the spectral radius of the matrix FV−1superscriptFV1\textbf{FV}^{-1}FV start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT. | ℛh=ρ(FV−1)=βhσ1+μΛμ,subscriptℛℎ𝜌superscriptFV1subscript𝛽ℎsubscript𝜎1𝜇Λ𝜇\mathcal{R}_{h}=\rho(\textbf{FV}^{-1})=\dfrac{\beta_{h}}{\sigma_{1}+\mu}\dfrac% | ℛ0=ρ(FV−1)=max{ℛh,ℛz},subscriptℛ0𝜌superscriptFV1subscriptℛℎsubscriptℛ𝑧\mathcal{R}_{0}=\rho(\textbf{FV}^{-}1)=\max\{\mathcal{R}_{h},\mathcal{R}_{z}\},caligraphic_R start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = italic_ρ ( FV start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT 1 ) = roman_max { caligraphic_R start_POSTSUBSCRIPT ... | A |
We are concerned in spiking neural networks for the BG. In 2001, based on the functional anatomy proposed by Gurney et al. GPR1 , they developed an artificial neural network for the BG GPR2 . Later, in 2006, based on the anatomical and physiological data, Humphries et al. Hump1 in the Gurney group developed a physiolo... | We are concerned in spiking neural networks for the BG. In 2001, based on the functional anatomy proposed by Gurney et al. GPR1 , they developed an artificial neural network for the BG GPR2 . Later, in 2006, based on the anatomical and physiological data, Humphries et al. Hump1 in the Gurney group developed a physiolo... | In this section, based on the spiking neural networks (SNNs) for the BG developed in previous works SPN1 ; SPN2 ; CN6 , we make refinements on the BG SNN to become satisfactory for our study. This BG SNN is based on anatomical and physiological data of the BG as follows. For the framework of the BG SNN (e.g., number of... | In this paper, we consider a spiking neural network of the BG, based on anatomical and physiological data obtained in rat-based works. | Based on the anatomical information Ana3 , the numbers of the striatal cells, the STN cells, the SNr cells, and the GP cells in the BG are chosen. | B |
[2, 31]. Rather than calculating the importance of a variable for a single model, our framework finds the importance of a variable for all models within a Rashomon set, although our framework is applicable to all of these model reliance metrics. | Figure 1 provides a demonstration of this problem: across 500 bootstrap replicates from the same data set, the Rashomon set varies wildly – ranging from ten models to over ten thousand — suggesting that we should account for its instability in any computed statistics. This instability is further highlighted when consid... | In contrast, model class reliance (MCR) methods describe how much a class of models (e.g., decision trees) relies on a variable. Fisher et al. [15] uses the Rashomon set to provide bounds on the possible range of model reliance for good models of a given class. Smith et al. [41] analytically find the range of model rel... | Several methods for measuring the MR of a model from a specific model class exist, including the variable importance measure from random forest which uses out-of-bag samples [7] and Lasso regression coefficients [20]. Lundberg et al. [28] introduce a way of measuring MR in tree ensembles using SHAP [27]. Williamson et ... | Figure 1: Statistics of Rashomon sets computed across 500 bootstrap replicates of a given dataset sampled from the Monk 3 data generation process [42]. The original dataset consisted of 124 observations, and the Rashomon set was calculated using its definition in Equation 1, with parameters specified in Section D of th... | B |
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