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(γ,Λ)𝛾Λ(\gamma,\Lambda)( italic_γ , roman_Λ ) values estimated from spiral solutions. The fact that the | 2Ω(σ+3)/32Ω𝜎332\Omega(\sigma+3)/\sqrt{3}2 roman_Ω ( italic_σ + 3 ) / square-root start_ARG 3 end_ARG | ζ<σ2γ−σ2𝜁𝜎2𝛾𝜎2\zeta<\sqrt{\frac{\sigma}{2}}\gamma-\frac{\sigma}{2}italic_ζ < square-root start_ARG divide start_ARG italic_σ end_ARG start_ARG 2 end_ARG end_ARG italic_γ - divide start_ARG italic_σ end_ARG start_ARG 2 end_ARG | 2Ω(σ+3)/32Ω𝜎332\Omega(\sigma+3)/\sqrt{3}2 roman_Ω ( italic_σ + 3 ) / square-root start_ARG 3 end_ARG plotted against σ+2ζ𝜎2𝜁\sigma+2\zetaitalic_σ + 2 italic_ζ, for results from | 23Ω(σ+3)23Ω𝜎3\frac{2}{\sqrt{3}}\Omega(\sigma+3)divide start_ARG 2 end_ARG start_ARG square-root start_ARG 3 end_ARG end_ARG roman_Ω ( italic_σ + 3 ) against σ+2ζ𝜎2𝜁\sigma+2\zetaitalic_σ + 2 italic_ζ. | A |
Breast cancer is the leading cancer type in women worldwide, with an estimated 2 million new cases and 627,000 deaths in 2018. Breast cancer staging refers to the process of describing the tumor growth or spread. Accurate staging by pathologists is an essential task that will determine the patient’s treatment and his c... | Fine tuning of the hyperparameters was done for the Inception V3 and the VGG19 models on the PCAM dataset. Two hyperparameters (Adam learning rate and batch size) were fine-tuned using the Keras Tuner with the hyperband algorithm. The performance is improved in the two models with an AUC of 0.95 for the Inception V3 mo... | Precise staging by expert pathologists of breast cancer axillary nodes, a tissue commonly used for the detection of early signs of tumor spreading, is an essential task that will determine the patient’s treatment and his chances of recovery. However, it is a difficult task that was shown to be prone to misclassificatio... | Recently, deep learning algorithms have made major advances in solving problems that have resisted the machine learning and artificial intelligence community such as speech recognition, the activity of potential drug molecules, brain circuits reconstruction and the prediction of the effects of non-coding RNA mutation o... | 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... | C |
}}\right)caligraphic_G start_POSTSUBSCRIPT ESC end_POSTSUBSCRIPT = ( caligraphic_V start_POSTSUBSCRIPT ESC end_POSTSUBSCRIPT , caligraphic_E start_POSTSUBSCRIPT ESC end_POSTSUBSCRIPT ) we take all sets of resident traits that correspond to an ESC, i.e. that have stability degree strictly bigger than α𝛼\alphaitalic_α, ... | ℰESC:=assignsubscriptℰESCabsent\displaystyle{\mathcal{E}}_{\text{ESC}}:=caligraphic_E start_POSTSUBSCRIPT ESC end_POSTSUBSCRIPT := | As vertices for the general metastability graph 𝒢ESC=(𝒱ESC,ℰESC)subscript𝒢ESCsubscript𝒱ESCsubscriptℰESC\mathcal{G}_{\text{ESC}}=\left(\mathcal{V}_{\text{ESC}},\mathcal{E}_{\text{ESC% | ESC}}(\{0\},2b)=\{4\},\quad\mathbf{v}_{\text{ESC}}(\{0\},2c)=\{4\}.bold_v start_POSTSUBSCRIPT ESC end_POSTSUBSCRIPT ( { 0 } , 2 italic_a ) = { 2 italic_a } bold_v start_POSTSUBSCRIPT ESC end_POSTSUBSCRIPT ( { 0 } , 2 italic_b ) = { 4 } , bold_v start_POSTSUBSCRIPT ESC end_POSTSUBSCRIPT ( { 0 } , 2 italic_c ) = { 4 } . | 𝒱ESC:=assignsubscript𝒱ESCabsent\displaystyle{\mathcal{V}}_{\text{ESC}}:=caligraphic_V start_POSTSUBSCRIPT ESC end_POSTSUBSCRIPT := | D |
This paper delves into the intricate dynamics of a COVID-19 epidemic model augmented with non-Gaussian noise. The exploration extends beyond the deterministic facet of the model, leading to a rigorous proof of the existence and uniqueness of a non-negative global solution for the stochastic system (4). These novel find... | From the equation (17), it is evident that ψ<ψ0𝜓subscript𝜓0\psi<\psi_{0}italic_ψ < italic_ψ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, highlighting that the stochastic approach is inherently more realistic than its deterministic counterpart. This observation underscores the significance of considering stochastic elemen... | The deterministic analysis provides a foundational understanding, while the stochastic counterpart offers a nuanced perspective, acknowledging the inherent uncertainties and fluctuations that characterize real-world epidemiological scenarios. The demonstration of the existence and uniqueness of solutions in the stochas... | 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... | Next, we aim to demonstrate that the stochastic COVID-19 model (4) possesses a unique, positive, and globally defined solution for the initial conditions (S(0),I(0))∈ℝ+2.𝑆0𝐼0superscriptsubscriptℝ2(S(0),I(0))\in\mathbb{R}_{+}^{2}.( italic_S ( 0 ) , italic_I ( 0 ) ) ∈ blackboard_R start_POSTSUBSCRIPT + end_POSTSUBSCR... | B |
\mathcal{X}_{k}).blackboard_E caligraphic_X = roman_arg roman_min start_POSTSUBSCRIPT italic_X end_POSTSUBSCRIPT ∑ start_POSTSUBSCRIPT italic_k = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT caligraphic_D ( italic_X , caligraphic_X start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ) . | Unlike the sample mean, we can have many different networks with identical topology that give the minimum. Similarly, we can define the topological variance 𝕍𝒳𝕍𝒳\mathbb{V}\mathcal{X}blackboard_V caligraphic_X as follows. | The topological variance can be interpreted as the variability of graphs from the topological mean 𝔼𝒳𝔼𝒳\mathbb{E}\mathcal{X}blackboard_E caligraphic_X. To compute the topological mean and variance, we only need to identify a network with identical topology as the topological mean or the topological variance. | The topological variance 𝕍𝒳𝕍𝒳\mathbb{V}\mathcal{X}blackboard_V caligraphic_X of networks 𝒳1,⋯,𝒳nsubscript𝒳1⋯subscript𝒳𝑛\mathcal{X}_{1},\cdots,\mathcal{X}_{n}caligraphic_X start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , ⋯ , caligraphic_X start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT is | The sum (9) does not uniquely define networks. Like the toy example in Figure 5, we can have many topologically equivalent brain networks that give the identical distance. Thus, the average of two graphs is also not uniquely defined. The situation is analogous to Fréchet mean, which frequently does not result in a uniq... | A |
We study here the effects of the various therapeutic strategies described in the experiments (C), (D) and (E) on the different system components. We denote with the index S1subscript𝑆1S_{1}italic_S start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT the solution components of experiment (C), with S2subscript𝑆2S_{2}italic_S start... | With the same choice of parameters as that employed to generate Figure 5 for experiment (A), we test the effect of the treatment plan depicted in Figure 2. The results of this experiment (C) are shown in Figure 7. The first row of Figure 7 (that also corresponds to the third row of Figure 5) represents the state of the... | Finally, in experiment (E), we analyze the effects of the treatment schedule sketched in Figure 4. Precisely, after letting the tumor grow for 24 weeks, we apply a combined treatment of radio- and chemotherapy. The former is applied 5 days per week (from Monday to Friday) for 6 weeks, at a fractionated dose of 2222 Gy ... | Comparing Figures 5 and 7, we immediately grasp the effects of the radio- and chemotherapy on the tumor population, whose density strongly decreases during treatment, while the density of the necrotic matter increases, as this component collects the effects of the therapy on tumor, ECs, and healthy tissue. The reductio... | At the end of the treatment, we let the patient rest for 10 weeks and analyze how the tumor eventually reorganizes and evolves. Figure 3 shows the specific scheme of this treatment schedule. We also prolonged the simulations by 10 more therapy-free weeks, in order to better observe a possible tumor relapse. We consider... | A |
In Fig. 7, an acoustic wave pulse is depicted as it propagates through a brain. Due to the distinct acoustic properties between cerebrospinal fluid (CSF) and brain tissue, the pulse experiences partial reflections at each boundary interface. On one hand, these reflections have the potential to amplify the damaging effe... | A head impact generates a pressure wave pulse in the CSF, which being a liquid, allows only the passage of pressure or P-waves. | Conversely, when a sulcus is oriented perpendicularly to the direction of acceleration, the density difference between the brain tissue and CSF can act as a protective mechanism, as illustrated in Fig. 10. A head impact generates a force that propagates through the brain, causing adjacent brain regions to compress. Thi... | In Fig. 7, an acoustic wave pulse is depicted as it propagates through a brain. Due to the distinct acoustic properties between cerebrospinal fluid (CSF) and brain tissue, the pulse experiences partial reflections at each boundary interface. On one hand, these reflections have the potential to amplify the damaging effe... | Sulci protecting the brain against acoustic waves: A head impact generates an acoustic wave pulse that propagates through the brain. The pulse encounters interfaces between brain tissue and CSF, leading to both reflection and refraction, thereby diminishing its energy and reducing its potential for harm. | D |
To further validate our model, we examined the top 20202020 novel synergistic predictions of drug-drug-cell line combinations (from the test set), ranked by the highest synergy probability from our DDoS model. For consistency with previous studies, we considered the top “false positives” of the Loewe dataset and invest... | We obtained the drug combination dataset from the DrugComb (Zheng et al., 2021) database222https://drugcomb.org/ (version 1.51.51.51.5). This dataset comprises an initial set of 1,432,351 samples (i.e., Drug A, Drug B, Cell Line) combination triplets. These samples are drawn from 34 distinct studies, including notable ... | To further validate our model, we examined the top 20202020 novel synergistic predictions of drug-drug-cell line combinations (from the test set), ranked by the highest synergy probability from our DDoS model. For consistency with previous studies, we considered the top “false positives” of the Loewe dataset and invest... | For further model evaluation, we generated four additional benchmark datasets, one for each of the four synergy scores (Loewe, Bliss, HSA, ZIP). These datasets differ from the reported benchmark dataset above, by including the additive triplets in their respective non-synergistic class (negative class), i.e., triplets ... | Table 6: Case studies - Top 20 “false positives” predictions of the Loewe dataset, ranked by the model probability of synergistic outcome. The number of ∗*∗ indicates how many of the HSA, ZIP, and Bliss scores support each prediction. | D |
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... | 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... | 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. | C |
4. Our model identifies luminance and color selective nodes and can be readily applied to video inputs. | These results are consistent with experimental findings showing that neurons in the early visual system exhibit | In this paper, we concentrate on representation learning, leaving the topic of inference for future studies. | This is consistent with the finding that neurons in the early visual system multiplex information about multiple stimulus properties | In summary, we abstract the complex biological early visual system using four assumptions that serve as the foundation for all studies in this paper. | D |
We denoted the distance in the phenotypic space between the local minimum and a distant point exhibiting the same fitness as d𝑑ditalic_d. | We measured the behavior at steady state by setting the fitness of cells overflowed from a region between the local and global minimum as zero. | For the fixation of different phenotypes from the local maximum, a daughter cell must display higher fitness than that observed at the local minimum in the limit of high selection pressure. | Then, the daughter cell’s phenotype must at least differ more than d𝑑ditalic_d from the mother cell’s phenotype. | We considered the probability that a phenotype of a daughter cell crosses the valley between two phenotypes at the local and global maxima on the fitness landscape. | B |
Fig. 2: Hodge decomposition on graph having 5 nodes and 6 edges. The edge flow is decomposed into gradient, curl and harmonic components. | We decomposed individual brain networks using the Hodge decomposition. In Figure 4, the Hodge decomposition applied to average female and male brain networks is displayed. We then assessed if there are topological difference between females and males in the original connectivity (edge flow). Following the test procedur... | 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... | 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. | To measure topological distance between graphs, we employ the birth-death decomposition (BDD), which | D |
\eta\gamma}{u_{N}}{i^{-{\gamma}/{\alpha}}}\right\}.blackboard_E [ roman_exp { - divide start_ARG italic_η italic_γ end_ARG start_ARG italic_u start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT end_ARG divide start_ARG 1 + italic_ϵ end_ARG start_ARG italic_ϵ end_ARG italic_i start_POSTSUPERSCRIPT - italic_γ / italic_α end_P... | in the product topology for (𝒫n)ℕsuperscriptsubscript𝒫𝑛ℕ\left(\mathscr{P}_{n}\right)^{\mathbb{N}}( script_P start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT blackboard_N end_POSTSUPERSCRIPT to a Markov chain with initial state 𝟎nsubscript0𝑛\mathbf{0}_{n}bold_0 start_POSTSUBSCRIPT italic_n end... | πi∈πsubscript𝜋𝑖𝜋\pi_{i}\in\piitalic_π start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∈ italic_π for all i∈ℕ𝑖ℕi\in\mathbb{N}italic_i ∈ blackboard_N | i) If cN→c>0→subscript𝑐𝑁𝑐0c_{N}\to c>0italic_c start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT → italic_c > 0 as N→∞→𝑁N\to\inftyitalic_N → ∞, then (Πt(N,n))t∈ℕsubscriptsubscriptsuperscriptΠ𝑁𝑛𝑡𝑡ℕ\left(\varPi^{(N,n)}_{t}\right)_{t\in\mathbb{N}}( roman_Π start_POSTSUPERSCRIPT ( italic_N , italic_n ) end_POSTSUPERSC... | Taking the product over i𝑖iitalic_i, and plugging in (5.2), we conclude, for all N∈ℕ𝑁ℕN\in\mathbb{N}italic_N ∈ blackboard_N, | D |
This research is supported in part by Science, Technology and Innovation Commission of Shenzhen Municipality (No. WDZC20200818121348001). | For the prostate cancer diagnosis task, we curated datasets from three hospitals (Hebei-1, Hebei-2, and Nanchang) and two public sources (DiagSet-B and PANDA) for training. To evaluate the effectiveness of our approach, we tested a private hospital dataset (QHD) and a public dataset (DiagSet-A). Hebei-1 and Hebei-2 rep... | The Research Ethics Committee of The Fourth Hospital of Hebei Medical University, China, approved this study. | To assess the accuracy of prostate cancer Gleason grading, we employed two private datasets (Hebei-1 and Hebei-2) and one public dataset (PANDA) for training purposes. In the evaluation phase, a private hospital dataset (Nanchang) was utilized. This allowed us to evaluate the performance and reliability of the proposed... | 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... | B |
Biological processes are determined through heterogeneous responses of single cells to external stimuli, i.e., developmental factors or drugs. Understanding and predicting the dynamics of single cells subject to a stimulus is thus crucial to enhance our understanding of health and disease and the focus of this task. | Recent developments in molecular biology, however, aim at overcoming this technological limitation. For example, Chen et al. (2022b) propose a transcriptome profiling approach that preserves cell viability. Weinreb et al. (2020) capture cell differentiation processes by clonally connecting cells and their progenitors t... | Most single-cell high-throughput technologies are destructive assays —i.e., they destroy cells upon measurement— allowing us to only measure unaligned snapshots of the evolving cell population. Recent methods address this limitation by proposing (lower-throughput) technologies that keep cells alive after transcriptome ... | To showcase SBalign’s ability to make use of such (partial) alignments when inferring cell differentiation processes, we take advantage of the genetic barcoding system developed by Weinreb et al. (2020). With a focus on fate determination in hematopoiesis, Weinreb et al. (2020) use expressed DNA barcodes to clonally tr... | Beyond, the recent use of SBs has been motivated by an important task in molecular biology: Cells change their molecular profile throughout developmental processes (Schiebinger et al., 2019; Bunne et al., 2022b) or in response to perturbations such as cancer drugs (Lotfollahi et al., 2019; Bunne et al., 2021). As most ... | B |
(but with finite maximal size M𝑀Mitalic_M) was studied in [5, 1, 2, 15], and a very general model incorporating distributed recruitment in [4]. In [18] the well-posedness of the above problem was proven by rewriting the system in terms of characteristic coordinates. | We note that the focus in [1, 2] was on numerical approximation of solutions of the hierarchical model. On the other hand, in [15] the authors derived a formal linearisation of the model and studied regularity properties of the governing linear semigroup. A characteristic equation was also deduced for the special case ... | The organisation of the paper is as follows. In Section 2 we first present the classic PDE formulation of the model. Then we present biological assumptions underlying the model and deduce a scalar nonlinear renewal equation for the population birth rate (the so called delay formulation). In Section 3 a dynamical system... | Indeed, we assume that the growth rate g𝑔gitalic_g of an individual of height x𝑥xitalic_x does not depend on x𝑥xitalic_x directly, but only indirectly, as it depends on the amount of light the individual receives per unit of time. We assume that the latter, in turn, is fully determined by the number E(x,t)𝐸𝑥𝑡E(x... | In Appendix B the more classical formulation of the model, taking the form of a first order PDE involving non-local functionals, is studied. In particular we show that the conditions guaranteeing the existence of stationary population densities (with respect to height) coincide with the conditions guaranteeing non-triv... | A |
We have considered the problem of structure learning of GGMs for paired data by focusing on the family of RCON models defined by coloured graphs named pdCGs. The main results of this paper provide insight into the structure of the model inclusion lattice of pdCGs. We have introduced an alternative representation of the... | Coloured GGMs (Højsgaard and Lauritzen, 2008) are undirected graphical models with additional symmetry restrictions in the form of equality constraints on the parameters, which are then depicted on the dependence graph of the model by colouring of edges and vertices. Equality constraints allow one to disclose symmetrie... | We have considered the problem of structure learning of GGMs for paired data by focusing on the family of RCON models defined by coloured graphs named pdCGs. The main results of this paper provide insight into the structure of the model inclusion lattice of pdCGs. We have introduced an alternative representation of the... | We recall, however, that, as explained in Sections 4 and 8.3, although penalized likelihood methods are considerably more efficient, their use is problematic when variables are not measured on comparable scales. Finally, we also remark that the range of application of our results does not restrict to pdRCON models. In ... | One way to avoid the explicit exploration of the model space is by using penalized likelihood methods, which can be applied to problems of larger dimensions. Ranciati and Roverato (2023), elaborating on previous work by Ranciati et al. (2021), introduced a graphical lasso method for learning pdRCON models; see also Li ... | C |
Table 1: Baseline characteristics of included patients. p𝑝pitalic_p values were obtained using t𝑡titalic_t-test [20]. | \times_{3}U^{(3)^{T}},m=1,2,...,M,caligraphic_Y start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT = caligraphic_X start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT × start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_U start_POSTSUPERSCRIPT ( 1 ) start_POSTSUPERSCRIPT italic_T end_POSTSUPERSCRIPT end_POSTSUPERSCRIPT × start_POST... | Our model is interpretable. The highly-weighted features were detected in the left ventricle and interventricular septum in cardiac MRI. For cardiac measurements, left atrial volume (0.778/1) contributed more than left ventricular mass (0.222/1) to the prediction. | Left Atrial Volume (ml2𝑚superscript𝑙2ml^{2}italic_m italic_l start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT) | _{2}\times P_{3}}\}{ caligraphic_Y start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , caligraphic_Y start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , . . , caligraphic_Y start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT italic_P start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT × italic_P start_POSTSUBSCRIPT 2 e... | C |
0.675¯±0.175plus-or-minus¯0.6750.175\underline{0.675}\small{\pm}0.175under¯ start_ARG 0.675 end_ARG ± 0.175 | 0.605¯±0.068plus-or-minus¯0.6050.068\underline{0.605}\small{\pm}0.068under¯ start_ARG 0.605 end_ARG ± 0.068 | 0.605¯±0.075plus-or-minus¯0.6050.075\underline{0.605}\small{\pm}0.075under¯ start_ARG 0.605 end_ARG ± 0.075 | 0.605¯±0.068plus-or-minus¯0.6050.068\underline{0.605}\small{\pm}0.068under¯ start_ARG 0.605 end_ARG ± 0.068 | 0.675¯±0.175plus-or-minus¯0.6750.175\underline{0.675}\small{\pm}0.175under¯ start_ARG 0.675 end_ARG ± 0.175 | A |
Importantly, we lay the foundation for future work to explore the properties of more general multi-compartment systems subject to external noise. For instance, study of the interaction between the external timescales (i.e., autocorrelation of the external input) and the internal timescales (i.e., progression through th... | Code used to produce the results are available on GitHub at https://github.com/ap-browning/multicompartment. | The choice to study a simplified linear stochastic model allows us to formulate the multicompartment problem as a multidimensional Gaussian process, enabling us to draw on the significant body of literature devoted to study of the statistical properties of such systems [26, 27, 28] to formulate a series of analytical e... | Multicompartment processes are ubiquitous in biology; from linear progression through the cell cycle, to phage replication in bacteria and the propagation of viruses by hijacked cellular machinery. Our analysis demonstrates that even a fundamental linear multicompartment structure provides potential advantages and bene... | Figure 4: First passage time distributions for linear multicompartment model. (a,d) Realisations of a three compartment system initiated using (a) the fixed initial condition and (d) the partially-fixed initial condition. Solutions are terminated at t=τ:X3(τ)>a:𝑡𝜏subscript𝑋3𝜏𝑎t=\tau:X_{3}(\tau)>aitalic_t = italic... | A |
Self-referencing embedded Strings (SELFIES) improve the initial idea of SMILES for usage in machine learning processes by creating a robust molecular string representation [15]. SMILES offered a simple and interpretable characterization of molecules that was able to encode the elements of molecules and their spatial fe... | Elman networks, more commonly known as vanilla recurrent neural networks (RNN), attempt to introduce the concept of a time-dependent dynamic memory [16]. The idea is to make predictions about inputs based on contextual information. Context-based predictions can be done for four input-output schemes: one-to-one, one-to-... | 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... | 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... | A |
When species share identical niches, they cannot coexist, which is known as the competitive exclusion principle (CEP). | One such example is observed in the ocean with phytoplankton, known as the paradox of the plankton [9]. | The ecological niche refers to all the environmental factors required for a species’ survival, such as resources and habitat. | Various mechanisms, such as temporal fluctuations and spatial heterogeneity, have been proposed to resolve this paradox. | To explain the biodiversity exceeding the bound that the CEP predicts, temporal environmental fluctuations, spatial heterogeneity, and other mechanisms have been proposed [9, 13, 14] and provided successful explanations. | C |
In this section, we derive lower bounds on the slowest growth V(0)=ru𝑉0𝑟𝑢V(0)=ruitalic_V ( 0 ) = italic_r italic_u and decay V(0)=u𝑉0𝑢V(0)=uitalic_V ( 0 ) = italic_u processes to compare with the upper bounds. | We have conjectured and proved upper bounds for individual graphs on T¯(r)¯T𝑟\mathrm{\overline{T}}(r)over¯ start_ARG roman_T end_ARG ( italic_r ) for decay processes in (11) and (13) and proved an upper bound for growth on connected graphs in the limit R0↓1↓subscript𝑅01R_{0}\downarrow 1italic_R start_POSTSUBSCRIPT 0... | In this work, a first step towards the analysis of the intermediate regime is presented. We define the upper-transition time T¯(r)¯T𝑟\mathrm{\overline{T}}(r)over¯ start_ARG roman_T end_ARG ( italic_r ), a threshold quantity which characterizes the border of the intermediate regime and the quenched regime, in which th... | Inequality (17) allows us to deduce a non-trivial lower bound for T¯(r)¯T𝑟\mathrm{\overline{T}}(r)over¯ start_ARG roman_T end_ARG ( italic_r ) in growth processes: | Lemma 5 (Upper bound on T¯(r)¯T𝑟\mathrm{\overline{T}}(r)over¯ start_ARG roman_T end_ARG ( italic_r ) for growth). | C |
-1}(V_{i})\right]|_{V=g(u)}\,.over˙ start_ARG italic_u end_ARG start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT = over^ start_ARG italic_X end_ARG start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_V ) | start_POSTSUBSCRIPT italic_V = italic_g ( italic_u ) end_POSTSUBSCRIPT = [ ∇ start_POSTSUBSCRIPT italic_i italic_... | By analogy with the constant matrix case, we reformulate the Jacobi function (11) and the energy function (8) starting from the new Lagrangian Φ(V)Φ𝑉\Phi(V)roman_Φ ( italic_V ) in (13). Indeed, the Jacobi function (11) is now | We observe that if we define the function ΦA(V)subscriptΦ𝐴𝑉\Phi_{A}(V)roman_Φ start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT ( italic_V ) as the dominant term of the energy: | so we recognize that it can be thought—borrowing standard arguments from analytical mechanics—also coinciding with the Jacobi function 𝒥Asubscript𝒥𝐴{\cal J}_{A}caligraphic_J start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT related to the Lagrangian ΦAsubscriptΦ𝐴\Phi_{A}roman_Φ start_POSTSUBSCRIPT italic_A end_POSTSUB... | The authors in [8, 9] extend the classical Hopfield model by devising a more general Lagrangian Φ(V)Φ𝑉\Phi(V)roman_Φ ( italic_V ) | A |
To show the forward direction, suppose that N𝑁Nitalic_N is not a tree-child network. We will show that there must be a spanning tree for N𝑁Nitalic_N that is not a support tree. If N𝑁Nitalic_N is not tree-child, then it has at least one vertex that is not visible. Let v𝑣vitalic_v be a non-visible vertex that is maxi... | An important property of tree-child networks is that all of their vertices are visible [3, Lemma 2]. A vertex v𝑣vitalic_v in a network is visible if there is a leaf x𝑥xitalic_x for which every path from the root to x𝑥xitalic_x passes through v𝑣vitalic_v. In this section, we show how visibility can be interpreted by... | Normal networks are a subclass of the tree-child networks, with the added constraint that they contain no “shortcuts” [20]. A shortcut is an edge (u,v)𝑢𝑣(u,v)( italic_u , italic_v ) for which there is an alternative directed path from u𝑢uitalic_u to v𝑣vitalic_v in the network. | Suppose N𝑁Nitalic_N has a shortcut. Then there is a vertex x𝑥xitalic_x with a non-trivial path from some vertex v𝑣vitalic_v to x𝑥xitalic_x, and there is also an edge (v,x)𝑣𝑥(v,x)( italic_v , italic_x ). The existence of a non-trivial path from v𝑣vitalic_v to x𝑥xitalic_x means that the cover has a non-trivial ba... | Let v𝑣vitalic_v be the label of the parent of S𝑆Sitalic_S. Then x𝑥xitalic_x is a child of v𝑣vitalic_v, meaning there is an edge (v,x)𝑣𝑥(v,x)( italic_v , italic_x ) in N𝑁Nitalic_N. However, the backtrack provides a non-trivial path in N𝑁Nitalic_N from v𝑣vitalic_v to x𝑥xitalic_x through S𝑆Sitalic_S. That is, N... | B |
Let T>0𝑇0T>0italic_T > 0 be the present. For comparison with our results for constant population size, we keep the same definitions of θ1subscript𝜃1\theta_{1}italic_θ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, θ2subscript𝜃2\theta_{2}italic_θ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT and α𝛼\alphaitalic_α and we set ρ(T... | Suppose we are given a sample from the selected locus at the present time t=0𝑡0t=0italic_t = 0, and that we know the allelic types of the sample but we do not know how the sample was produced. What is the genealogy of the sample? This question was answered by Barton et al. (2004), who modeled the ancestral process usi... | In this paper, we have considered a two allele model at a single genetic locus subject to recurrent mutation and selection in a large haploid population with possibly time-varying size. We assumed that a sample of size n𝑛nitalic_n was drawn uniformly from an infinite population under the diffusion approximation. By ex... | For a population with time-varying size ρ(t)N𝜌𝑡𝑁\rho(t)Nitalic_ρ ( italic_t ) italic_N at forward time t𝑡titalic_t where ρ𝜌\rhoitalic_ρ is a non-constant function, neither the Moran process nor its diffusion approximation possess a stationary distribution. However, the random background approach of Barton et al.... | Since the random background approach of Barton et al. (2004) was formulated based on the lineage dynamics of the Moran model, we begin by describing the diffusion process arising from a Moran model with time-varying population size. | D |
Remember that datasets A-G (Table 2) represent more or less “clean” data with very little noise, with an exception of E where a notion of noise is introducing by sampling success probabilities from the ℬℯ𝓉𝒶ℬℯ𝓉𝒶\mathpzc{Beta}italic_script_B italic_script_e italic_script_t italic_script_a distribution (which is st... | We rely on the automatic differentiation framework JAX (Bradbury et al., 2018) to obtain an analytical gradient of the log likelihood function 10. This, obviously, requires PMF of the model in Equation 4 to be differentiable in the first place. This condition is met if we compute G(l)𝐺𝑙G(l)italic_G ( italic_l ) stra... | Remember that datasets A-G (Table 2) represent more or less “clean” data with very little noise, with an exception of E where a notion of noise is introducing by sampling success probabilities from the ℬℯ𝓉𝒶ℬℯ𝓉𝒶\mathpzc{Beta}italic_script_B italic_script_e italic_script_t italic_script_a distribution (which is st... | MIXALIME is written in the Python programming language. We took advantage of the autodifferentiation and just-in-time compilation provided by the JAX framework and we used optimization routines present in the scipy package. For reading and processing input datasets we rely on a combination of datatable, pandas (pandas ... | To test various MIXALIME models performance, we evaluated different models and methods on the series of synthetic datasets generated by our testing framework (see Appendix I for implementation details). We generated 86 synthetic sets of varying configurations (i.e. parameters that were passed to the generator, see the ... | C |
We recall that (λ*(t),σ*(t),A*(t),C*(t))superscript𝜆𝑡superscript𝜎𝑡superscript𝐴𝑡superscript𝐶𝑡(\lambda^{*}(t),\sigma^{*}(t),A^{*}(t),C^{*}(t))( italic_λ start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT ( italic_t ) , italic_σ start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT ( italic_t ) , italic_A start_POSTSUPERSCRIPT... | σiN(t)subscriptsuperscript𝜎𝑁𝑖𝑡\sigma^{N}_{i}(t)italic_σ start_POSTSUPERSCRIPT italic_N end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_t ). We start by describing the dynamics of the epidemic in the | the McKean–Vlasov equation (4). Then, if I(t,⋅)𝐼𝑡normal-⋅I(t,\cdot)italic_I ( italic_t , ⋅ ) (resp. S(t,⋅)𝑆𝑡normal-⋅S(t,\cdot)italic_S ( italic_t , ⋅ )) is the density of A*(t)superscript𝐴𝑡A^{*}(t)italic_A start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT ( italic_t ) on the | We start by deriving the equation for I(t,⋅)𝐼𝑡⋅I(t,\cdot)italic_I ( italic_t , ⋅ ). Let us compute, | requires to study the variations of the function Fesubscript𝐹eF_{\mathrm{e}}italic_F start_POSTSUBSCRIPT roman_e end_POSTSUBSCRIPT. Let us start | C |
Second, in the white noise limit, the DMFT leads to the stochastic logistic model, a phenomenological model that proved to be consistent with several macro-ecological laws in microbial ecosystems [4, 40]. | In particular, the analytical species abundance distribution derived from the DMFT follows the Gamma distribution, a widely utilized probability distribution in macroecology [32, 1]. Again, similar truncated fat-tailed distribution has been recently shown in the chaotic phase [36] and in the strongly interacting limit ... | Facilitating species coexistence through cyclic fluctuations is a mechanism that has also been observed in the chaotic phase of the QGLV [19, 35, 36]. | In the global equilibrium phase, the biodiversity of the QGLV model is limited by the stability-diversity paradox [27, 28, 29, 17]. Moreover, the species abundance distribution (SAD), as obtained in the limit of a large number of species within the dynamical mean field theory (DMFT) or the cavity method, is a truncated... | Firstly, the introduction of annealed disorder in the GLV equations, for any finite correlation time, has exerted a substantial positive influence on the biodiversity of the system. Specifically, when the dynamics of the system converge to the stationary distribution, we observe the quasi-cycles of species populations ... | A |
Having laid out what constitute a queueing system, let us consider some examples. The simplest arrival process is a renewal process, in which the interarrival times are independent and identical random variables. Renewal processes are denoted by G𝐺Gitalic_G in Kendall’s notation, which stands for general or unspecifie... | Gene expression is a fundamental cellular process by which genetic information encoded by a gene is turned into a functional product, such as an RNA or protein molecule. Models of gene expression are typically concerned about the statistics of either RNA or protein counts as a proxy of gene activity; rarely the descrip... | Fig. 2 summarizes various stochastic processes that are related to the MAP. The simplest MAP is the Poisson process (denoted by M𝑀Mitalic_M for Markovian or memoryless), which has only one state. This process describes a gene that is always active and produces RNA at exponentially distributed intervals [Fig. 2(b)]. On... | The G/M/∞𝐺𝑀G/M/\inftyitalic_G / italic_M / ∞ queue is an infinite-server queue in which the interarrival times are independent and identically distributed random variables, customers arrive individually one by one, and the service times are exponentially distributed. It is a special case of the GX/G/∞superscript𝐺𝑋�... | Transcription—the synthesis of RNA—is typically modelled as a multistep process in which the gene switches between multiple states before it eventually produces an RNA molecule. Depending on the level of details, transitions between gene states may reflect individual biochemical events, such as binding of transcription... | A |
Ultimately, we are interested in the joint law of a finite number of focal processes within an infinite system of such mean-field interacting MTBDPs. | We prove that the empirical distribution process of the N𝑁Nitalic_N replicas converges to a deterministic probability measure-valued flow as N→∞→𝑁N\to\inftyitalic_N → ∞. | We are now prepared to prove the convergence of the empirical measure process in a system with freezing. | To this end, we establish that the process of the empirical distribution of families converges to a deterministic probability measure-valued flow. | Next, we establish the exchangeability of the finite system and demonstrate the Markovianity of the empirical measure process. | C |
One example is The CLIP (Contrastive Language-Image Pre-training) model (Radford et al.,, 2021) which is a transformer model that facilitates cross-modal understanding between images and text. | ESM2 is a protein language model that uses a transformer-based architecture and an attention mechanism to learn the interaction patterns between pairs of amino acids in the input sequence. | In addition to sequence-based approaches, graph-based representations leverage the three-dimensional (3D) structure of proteins to capture their functional properties. | It combines a ViT vision encoder, with a transformer-based language encoder to learn joint representations of images and their associated textual descriptions. | The transformer-based encoder-decoder model was first introduced by Vaswani et al., (2017) in their paper “Attention is all you need”. | C |
\right)\right]\right\}\left(\boldsymbol{1}-\boldsymbol{M}\right)^{-\mathrm{T}}\,.- bold_italic_M ) start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT { over¯ start_ARG bold_italic_D end_ARG + roman_diag [ bold_italic_Q start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( bold_italic_D = over¯ start_ARG bold_italic_D end_ARG ) ] } ... | Here 𝑫¯¯𝑫\overline{\boldsymbol{D}}over¯ start_ARG bold_italic_D end_ARG denotes the disorder-averaged noise | function Z~(𝑱)~𝑍𝑱\widetilde{Z}\left(\boldsymbol{J}\right)over~ start_ARG italic_Z end_ARG ( bold_italic_J ). Here, 𝑿~~𝑿\widetilde{\boldsymbol{X}}over~ start_ARG bold_italic_X end_ARG | together with 𝑫¯¯𝑫\overline{\boldsymbol{D}}over¯ start_ARG bold_italic_D end_ARG yields an effective noise | D}}=\left(\overline{\mathrm{CV}^{2}}\overline{\nu}\right)^{2}\boldsymbol{F}⟨ italic_δ bold_italic_C start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ⟩ start_POSTSUBSCRIPT bold_italic_W , bold_italic_D end_POSTSUBSCRIPT = ( over¯ start_ARG roman_CV start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG over¯ start_ARG italic_ν ... | A |
By monotonicity, it suffices to prove the result for β2=∞subscript𝛽2\beta_{2}=\inftyitalic_β start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = ∞ and starting from the all 2 configuration. | In this case, the infected region generated by the 2 initially at site y𝑦yitalic_y is dominated by its counterpart when starting with a single 2 at site y𝑦yitalic_y in an otherwise healthy population. | Let Tysubscript𝑇𝑦T_{y}italic_T start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT be the extinction time of the infected cluster starting at site y𝑦yitalic_y, and let τrsubscript𝜏𝑟\tau_{r}italic_τ start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT be the extinction time of the infected region generated by all the 2s initi... | For all r>0𝑟0r>0italic_r > 0, starting with a single 2 at the origin in an otherwise healthy population, and identifying ξssubscript𝜉𝑠\xi_{s}italic_ξ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT with the set of infected sites, | Assuming that d>1𝑑1d>1italic_d > 1 and starting the process with a single 1 at the origin in an otherwise healthy population, | A |
}}\|_{F}^{2}+\frac{1}{2}\|t_{i}^{\text{syn}}-t_{i}^{\text{pred}}\|_{1}\right]caligraphic_L = italic_λ start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT [ divide start_ARG 1 end_ARG start_ARG 9 end_ARG ∥ italic_R start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT syn end_POSTSUPERSCRIPT - italic_R start_P... | To address these challenges, we propose a self-supervised deep learning framework called HetACUMN based on amortized inference. By alternating the variational image reconstruction task and the conditional pose prediction task, the VAE-based architecture explicitly enforces the disentanglement of the conformation and po... | Therefore, the encoder can learn from a comprehensive pose training datasets even if the input EM image dataset is small or has highly biased | We argue that this is not an inherent drawback of amortized inference. HetACUMN is a better alternative when the data and/or computational resource is limited, which performed well on both small and large datasets. | The conditional pose prediction task takes the encoder and decoder from the mulit-class image reconstruction task and reversed order. | B |
Biomedical image data science competitions have emerged as an effective way to accelerate the development of cutting-edge algorithms. Several successful competitions have been specifically organized for microscopy image analysis, such as the cell tracking challenge (CTC) [43, 33], the Data Science Bowl (DSB) challenge ... | Figure 2: Dataset overview. a, The challenge provides a diverse microscopy image dataset that includes tissue cells, cultured cells, label-free cells, stained cells, and different microscopes (i.e., brightfield, fluorescent, phase-contrast (PC), and (Differential Interference Contrast) DIC). b, The geographical distrib... | For example, the CTC primarily concentrated on label-free images, thereby excluding stained images such as multiplexed immunofluorescent images. Similarly, the DSB challenge emphasized nucleus segmentation in fluorescent and histology images while disregarding phase-contrast and differential interference contrast image... | Fig. 2e shows four microscopy images randomly selected from each modality in the training set and testing set. In order to assess the algorithm’s generalization capabilities, all testing images were sourced from new biological experiments, including some that featured previously unseen tissues or cell types not present... | We further visualized segmentation examples of the seven algorithms to gain insights into their characteristics (Fig 4f, Extended Data Fig. 1). The top three best-performing algorithms demonstrated relatively robust results, with the best-performing algorithm (T1-osilab) displaying exceptional accuracy across diverse m... | B |
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... | In the present study, we address this gap in the literature by deriving a phase reduction method applicable to networks of (weakly or strongly attracting) coupled oscillators with arbitrary network topology beyond weak coupling, i.e., we calculate higher-order corrections to the first-order reduction methods while inco... | 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... | The most relevant reduction for the present study is the theory of weakly coupled oscillators, which allows for a general form of the vector field and coupling function so long as the coupling strength is weak [15, 26, 46, 48, 49, 47]. To be more precise, by weak coupling, we mean phase reductions that only consider ex... | 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... | C |
{2}\right)\;.× ( italic_C start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT + italic_i ∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_k start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUPERSCRIPT roman_d italic_k start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT italic_k start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT star... | It turned out to be seemingly impossible to generalize the the pseudocumulant formalism to rational fractional α=L/N𝛼𝐿𝑁\alpha=L/Nitalic_α = italic_L / italic_N via expansions of the logarithm Φ(k,t)Φ𝑘𝑡\Phi(k,t)roman_Φ ( italic_k , italic_t ) of the characteristic function in series with respect to k1/Nsuperscript... | We have addressed the problem of mathematical description of the macroscopic dynamics of populations of quadratic integrate-and-fire neurons subject to α𝛼\alphaitalic_α-stable white noises. The interest to these models are multifold: QIF is not only the normal form for the neuron models with the Class I excitability n... | In the latter equation, we can substitute expansions of all functions in series of k𝑘kitalic_k and find | Nonetheless, for α𝛼\alphaitalic_α-stable noises, one can construct expansions of Φ(k,t)Φ𝑘𝑡\Phi(k,t)roman_Φ ( italic_k , italic_t ) in series of the noise intensity σαsuperscript𝜎𝛼\sigma^{\alpha}italic_σ start_POSTSUPERSCRIPT italic_α end_POSTSUPERSCRIPT. The theoretical results derived with the latter expansion f... | C |
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... | 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 ... | 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... | 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... | 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... | D |
(B) Architecture of the EEG encoder. Temporal-spatial convolution is used with spatial modules, made with self and graph attention, to reveal spatial features of brain activity. The linear layer is used to project the feature dimension. | To address the above limitations, we introduce a self-supervised framework to decode image representations from EEG signals, focusing on object recognition. | Beyond the self-supervised framework, we try to demonstrate the biological plausibility by resolving the visual processing of EEG signals. | We propose a self-supervised framework, Natural Image Contrast EEG (NICE), to decode images from EEG signals. | In conclusion, we propose a self-supervised framework to decode natural images from EEG for object recognition. | C |
There is a natural interpretation of q(s)𝑞𝑠q(s)italic_q ( italic_s ) as the chance of success in a single trial. In the simple case with no death (i.e. μ=0𝜇0\mu=0italic_μ = 0), the value simplifies to q(s)=1−e−λs𝑞𝑠1superscript𝑒𝜆𝑠q(s)=1-e^{-\lambda s}italic_q ( italic_s ) = 1 - italic_e start_POSTSUPERSCRIPT ... | We will utilize all components of the GDL model to perform species tree estimation. As stated in the Introduction, the primary focus will be the observed numbers of copies at speciation nodes in the species tree. We review known results and provide new technical results in the Appendix. The accumulation of these result... | Before proving the Propositions, it will be useful to give an intuition behind the meaning of the results for phylogeneticists and other practitioners. Before and after the uniform sampling step, the gene tree expresses meaningful signal about the overarching species tree. Of course, if any species receives zero copies... | The specific form of Mf(τ)subscript𝑀𝑓𝜏M_{f}(\tau)italic_M start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT ( italic_τ ) is outlined in the Appendix. Unfortunately, this integral is difficult to compute analytically. However, numerical methods could be useful to characterizing the expectation of this ratio. This resul... | 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... | A |
Hence, the computation of a single extreme first hitting time requires O(NeΛ/ϵΔt)𝑂𝑁superscript𝑒Λitalic-ϵΔ𝑡O(N\frac{e^{\Lambda/\epsilon}}{\Delta t})italic_O ( italic_N divide start_ARG italic_e start_POSTSUPERSCRIPT roman_Λ / italic_ϵ end_POSTSUPERSCRIPT end_ARG start_ARG roman_Δ italic_t end_ARG ) time steps of ... | It is counter-intuitive that an extreme first passage time is highly likely to be caused by a pathway that is highly unlikely to occur in an individual walker. | Perhaps the extreme first passage time is an unlikely deviation from the typical rare event, an event that is doubly rare, in some sense. | Moreover, it is quite likely that the first passage time, because it is a rare event, is highly sensitive to discretization error. | There are many situations, particularly those involving exponential proliferation, where it is not the mean first passage time of a single event that is of interest, rather it is the first out of N𝑁Nitalic_N identical rare events to occur that is relevant [37]. | C |
A recent work demonstrated that the weight uncertainty with the form of SaS structure can be also incorporated into the transformer [45]. In addition, gated recurrent neural networks with multiplicative mechanisms were recently shown to be able to learn to implement linear self-attention [46]. Furthermore, the relation... | Grant Number 12122515 (H.H.), and Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices (No. 2022B1212010008), | 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 ... | 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... | To study the properties of this simplified language model, we plot the distribution of hyperparameters [π,m,Ξ]𝜋𝑚Ξ[\pi,m,\Xi][ italic_π , italic_m , roman_Ξ ] for the input layer, output layer, and recurrent layer, respectively. The distribution of [π,Ξ]𝜋Ξ[\pi,\Xi][ italic_π , roman_Ξ ] has the L-shape in all layers,... | A |
Organoids are self-organized 3D tissues typically derived from stem cells, exhibiting key functional, structural, and biological complexity similar to organs [1]. Their close biological resemblance makes organoid culture analysis crucial for advancing biological studies, as it aids in understanding the extent to which ... | In this paper, we utilized the SegmentAnything model in automatic organoid structure identification in microscopy images. We claim that the SegmentAnything model showed promising performance, and our post-processing efforts were also necessary to enhance the accuracy of organoid structure detection and ensure reliable ... | The first issue we encountered was that SegmentAnything sometimes misidentified the background as an object, resulting in non-zero indices for the background in the masks. Secondly, the high resolution of whole microscopy images necessitated the use of cropped patches for model fitting. However, this approach introduce... | In this study, we explore the potential of SegmentAnything [4], a foundation model trained on an extensive dataset of 11 million images encompassing diverse modalities, to automate individual organoid detection in microscopy images. Moreover, we have integrated comprehensive post-processing and analysis of morphologica... | The analysis of organoid morphology is commonly performed by capturing images of the organoids grown in multi-well plates. However, existing methods have limitations since they aggregate cell growth information over an entire well, rather than providing information about individual organoids and their constituent cells... | D |
\mathbf{Z}_{t}),\quad\mathbf{Z}_{0}=\bm{\theta}^{(k,0)},divide start_ARG italic_d bold_Z start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_ARG start_ARG italic_d italic_t end_ARG = - divide start_ARG 2 end_ARG start_ARG 3 end_ARG italic_A start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_α ∇ italic_L ( bold_Z start_P... | ∇L is bounded and Lipschitz continuous with Lipschitz constant λ.∇L is bounded and Lipschitz continuous with Lipschitz constant λ\displaystyle\mbox{$\nabla L$ is bounded and Lipschitz continuous with % | is bounded by a multiple of n−1superscript𝑛1n^{-1}italic_n start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT. | Lipschitz constant $\lambda$}.∇ italic_L is bounded and Lipschitz continuous with Lipschitz constant italic_λ . | is bounded by a multiple of n−1superscript𝑛1n^{-1}italic_n start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT and hence its square by n−2superscript𝑛2n^{-2}italic_n start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT. | A |
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... | T.M.K. conceptualized the work and developed the theory; J.K. carried out the experiments; K.K. contributed to carrying out the experiments; W.Q.B. contributed to developing the theory; C.S., J.P. and R.v.R. supervised the research. All authors discussed the results and contributed to the manuscript. | Up to this point, we treated the system in steady-state. When extending our view to the device dynamics we need to consider the time it takes for ions to accumulate into or deplete out of the channel. Utilizing our aforementioned expression for the total salt flux through the channel, we calculate the net flux γV′𝛾su... | 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... | Our memristor is inspired and supported by a comprehensive theory directly derived from the underlying physical equations of diffusive and electric continuum ion transport. We experimentally quantitatively verified the predictions of our theory on multiple occasions, amongst which the specific and surprising prediction... | A |
The first documented cases of HIV/ZIKV co-infection in Colombia and Brazil highlighted the potential interactions between these two viruses. The co-circulation of both illnesses in South America presented an important challenge for the public health authorities, as both viruses share the same transmission mechanism, wh... | Given the potential impact of HIV/ZIKV co-infection on public health, it is crucial to understand the transmission dynamics of these viruses and evaluate the effectiveness of intervention strategies. Mathematical models are useful for understanding and providing insights into public health policy decisions. To our know... | The mathematical modelling conducted in this study was used to theoretically represent the transmission dynamics of both viruses in co-infected individuals, allowing for the evaluation of different intervention scenarios. The findings of this study were particularly relevant during the 2015-2016 Zika outbreak in South ... | While this study has provided insightful information, it is crucial to recognize several limitations in its methodology. First, the mathematical modelling approach, which is essential to capture the innate complexity of viral transmission dynamics, introduces certain simplifications. These oversimplifications result fr... | In summary, this study highlighted the need for continued research on the transmission dynamics of Zika and HIV/AIDS and developing effective intervention strategies to control and prevent their spread. Future work in this field plans to incorporate compartments of women giving birth to babies with and without congenit... | B |
In this case, a BG network with parallel channels, representing different action requests, arising from the cortex, is usually considered. | Resolution of competition between the channels may be given by selection of a desired channel with the highest salience. | 𝒞dsubscript𝒞𝑑{\cal C}_{d}caligraphic_C start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT, to the case of action selection. Saliency of each channel may be given by its 𝒞dsubscript𝒞𝑑{\cal C}_{d}caligraphic_C start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT. Then, action in the channel with the highest | Saliency of a channel may be given by the firing frequency of its cortical input; the higher frequency denotes the higher saliency. | Due to more activeness of DP, the firing frequency of the SNr cells becomes much reduced to 5.5 Hz, resulting in the opened state of the BG gate to the | C |
This approach can be misleading because there may be many good models for a given dataset – a phenomenon referred to as the Rashomon effect [7, 40] — and variables that are important for one good model on a given dataset are not necessarily important for others. As such, any insights drawn from a single model need not ... | Related to our work from the stability perspective, Duncan et al. [13] developed a software package to evaluate the stability of permutation variable importance in random forest methods; we perform a similar exercise to demonstrate that current variable importance metrics computed for the Rashomon set are not stable. A... | Recently, researchers have sought to overcome the Rashomon effect by computing Rashomon sets, the set of all good (i.e., low loss) models for a given dataset [15, 12]. However, the set of all good models is not stable across reasonable perturbations (e.g., bootstrap or jackknife) of a single dataset, with stability def... | In particular, for variable X2subscript𝑋2X_{2}italic_X start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT, one interval — ranging from -0.1 to 0.33 — suggests that there exist good models that do not depend on this variable at all (0 indicates the variable is not important); on the other hand, another MCR from a bootstrapped dat... | 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 |
Our method draw insights from HVS — how humans perceive visual stimuli (forward route in Fig. 1) — to address the potential information loss during the transition from the fMRI to the visual domain (reverse route in Fig. 1). | We do that by deciphering crucial cues from fMRI recordings, thereby contributing to enhanced consistency in terms of appearance, structure, and semantics. | The qualitative results, depicted in Fig. 6, align with the numerical findings, indicating that DREAM produces more realistic outcomes that maintains consistency with the viewed images in terms of semantics, appearance, and structure, compared to the other methods. | We show through experiments that our biologically interpretable method, DREAM, outperforms state-of-the-art methods while maintaining better consistency of appearance, structure, and semantics. | This paper presents DREAM, a visual decoding method founded on principles of human perception. We design reverse pathways that mirror the forward pathways from visual stimuli to fMRI recordings. These pathways specialize in deciphering semantics, color, and depth cues from fMRI data and then use these predicted cues as... | A |
Hence, as a future work, it would be interesting to investigate consequences of degeneration of D1 SPNs and cortical pyramidal cells, in addition to | In our present striatal circuit, we considered only the D1/D2 SPNs (95 %percent\%% major population). | Within the striatum, spine projection neurons (SPNs), comprising up to 95 %percent\%% of the whole striatal population, are the only primary output neurons Str1 ; Str2 . There are two types of SPNs with D1 and D2 receptors for the DA. The DA modulates firing activity of the D1 and D2 SPNs in a different way SPN1 ; SPN2... | In the present work, we considered early stage of HD where degenerative loss of D2 SPNs occurs in the nearly normal DA level. | Next, we consider the case of phasic cortical input (10 Hz) in the phasically active state Hump1 ; CI1 ; CI2 ; CI3 ; CI4 ; CI5 ; Str2 ; CN6 ; CN14 , which is shown in Fig. 3. Population firing behavior of D1 SPNs, associated with DP (green color), is shown in their raster plot of spikes and the IPSR RD1subscript𝑅D1R_{... | A |
The spread of a new mutation in a population as a function of time can be described by the transition matrix of an appropriate Wright-Fisher model or the transition density of the approximating diffusion. Although diffusion theory leads to quite simple expressions for many important quantities, explicit and analyticall... | We combined two methods to derive an explicit and accurate time-dependent approximation for the mutant’s density in any generation n𝑛nitalic_n: a branching process approach capturing the stochastic effects and the deterministic logistic growth model. We developed this approach quite generally with the help of a slight... | In Section 3, we derive an explicit, approximate expression for the mutant frequency distribution in a finite Wright-Fisher population as a function of time. This becomes feasible by using a supercritical Galton-Watson process with a quite general offspring distribution to describe the spreading of a beneficial mutant. | The expressions (4.14) for the expected mean G¯(τ)¯𝐺𝜏\bar{G}(\tau)over¯ start_ARG italic_G end_ARG ( italic_τ ) and (4.15) for the expected variance VG(τ)subscript𝑉𝐺𝜏V_{G}(\tau)italic_V start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT ( italic_τ ) of the trait are exact within our model based on the quasi-determin... | Because it seems unfeasible to derive analytic results for the time dependence of the allele frequency for either the Wright-Fisher model or its diffusion approximation, we approximate the stochastic dynamics in the initial phase, where stochasticity is most important, by a branching process (e.g. Athreya and Ney, 1972... | A |
This paper does not raise any ethical concerns. This study does not involve human subjects, practices to data set releases, potentially harmful insights, methodologies and applications, potential conflicts of interest and sponsorship, discrimination/bias/fairness concerns, privacy and security issues, legal compliance,... | are in the form of the implicit force depending on the distance between atoms in the 3D range and the molecular structure and could involve atoms | The experimental setups for training and evaluation, as well as the hyperparameters, are described in detail in Section 4 and Appendix A, and the experiments are all conducted using public datasets. | Furthermore, we employ visual representation to depict the molecular structure of the mutagen compound containing the −NO𝑁𝑂-NO- italic_N italic_O group, as illustrated in Fig. 6. In the primary layer, hydrogen atoms (H) and oxygen atoms (O) are segregated into distinct neural atoms, regardless of the multi-hop dista... | The allocation pattern for the neural atoms at each layer, as well as the interatomic interactions suggested by the Ewald sum matrix, are visualized in Fig. 5 to 6. | B |
Here LLM’s memory was defined in terms of the conditional probability (1) through an appropriate construction of the preceding text fed to the network. This amounts to a functional definition of memory, with the LLM acting as if it were to participate in a serial memory test. | The goal of this paper is to identify and explore the features of the memory characteristics of Large Language Models and compare them to some aspects of human memory. | A very characteristic feature of human memory when memorizing lists of words is the fact that words from the beginning and from the end of the list are easier to recall, phenomena called primacy and recency effects [4] (see sample human data in Fig. 1). | The similarity of the characteristics of human biological memory to LLM’s memory can be a-priori interpreted in two ways: | Such a close similarity of the characteristics of human and LLM memory is in fact very surprising and begs explanation. | D |
By generating the data from a log-normal distribution, we construct a synthetic data set from which it should be relatively easier to reconstruct a network in comparison to real data. Real data, unlike our simulated data, may be confounded by many factors, including environmental and climate effects, variable copy numb... | To test the above theoretical problems involved in network reconstruction with paired data sets, we developed a simple algorithm for constructing synthetic data from a known “ground-truth” covariance matrix. To do this, we start with a random Power-law graph and construct a positive definite covariance matrix that matc... | In the scenario of the rabbits and piñons, there are two compositional data sets, one which measures animals and one which measures plants. These sets are “paired” with each other in the sense that each vector in one data set, representing for example the number of each animal species counted in an area, can be paired ... | To simulate paired compositional data sets, we randomly split the taxa into two groups representing two kingdoms of life before drawing synthetic reads. Then, for each exact sample, we generate two independent sets of reads as described above — one for each of the two kingdoms. This means that for each sample, we gener... | This relatively simple example demonstrates a profound problem for scientists studying the microbiome, where instead of animals and trees we are concerned with, for example, bacteria and fungi. In this setting, taxonomic information is compositional by nature[1, 2], and there exists only limited ways to compute absolut... | C |
In the United States, the large-scale vaccination campaign begins approximately 300 days after the initial outbreak, as previously mentioned. The vaccination rate, denoted by ν(t)=10−2Θ(t−300)𝜈𝑡superscript102Θ𝑡300\nu(t)=10^{-2}\Theta(t-300)italic_ν ( italic_t ) = 10 start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT r... | Similar to subsection IV.1, country 1 initiates the vaccination of its own population starting on day 300. The decision on when to share half of the vaccination rate with country 2 is left to country 1. In an extremely benevolent scenario where country 1 opts to share from the outset (on day 300), the infection rate βi... | The graph depicts the epidemic control time as a function of vaccine allocation time in both country 1 and country 2. In scenarios 1 and 2, illustrated in Fig.4(a) and Fig.4(b), and scenarios 3 and 4, shown in Fig.4(c) and Fig.4(d), respectively, the trend is examined. From the purple line in both Fig.4(a) and Fig.4(b)... | We modify the two coupled Susceptible-Infected-Recovered-Deceased (SIRD) model initially developed by J. Burton et. al.[28] to illustrate the impact of vaccination and migration on the measles outbreak within specific subpopulations in Cameroon. This model is adapted to examine the temporal progression of the COVID-19 ... | The main takeaway is that the infection rate β(t)𝛽𝑡\beta(t)italic_β ( italic_t ) observed in other countries exhibits a similar pattern and characteristics[12] as demonstrated in Fig.1(a) for the U.S.A., albeit with different functional forms and durations of sub-peaks. Subsequently, we apply the model parameters de... | D |
To showcase how harmonic persistent homology can be used in multi-omics analyses, we analyzed a set of 690690690690 breast cancer samples from the TCGA database for which both RNAseq and Methylation450 data are present. The dataset is comprised of 414414414414 Luminal-A, 141141141141 Luminal-B, and 135135135135 basal-l... | Intuitively, harmonic persistent homology establishes relationships between features or observations in the data that may lead to the discovery of hidden patterns and/or novel insights owing to the capability of TDA to analyze data at different scales. Moreover, harmonic persistent homology is naturally equipped to ana... | The clusters can be used to externally validate our findings and show how different harmonic cycles capture interactions between different subsets of data as the cycles with similar weights cluster together samples with similar descriptors. This approach can be extended to other multi-omics data, leading to a nuanced, ... | Omics studies have gained substantial importance in unraveling interactions between biomarkers that underlie complex diseases given the increasing availability of such data from across modalities due to recent technological advances [8]. These biomarkers are instrumental in clinical decision-making and drug discovery. ... | Here we utilize the fact that harmonic cycles maximize the contribution of essential simplices, and this paper is the first application of harmonic persistent homology to biological problems. We introduce a framework that uses harmonic persistent homology to extract information from multi-omics data that enables the di... | B |
In addition to the above points, please give each figure file a name which indicates the number of the figure it contains; for example, figure1.eps, figure2a.eps, etc. If the figure file contains a figure with multiple parts, for example figure 2(a) to 2(e), give it a name such as figure2a_2e.eps, and so forth. | which is the ‘master’ LATEX file that reads in all of the other ones by naming it appropriately. The ‘master’ | For a long equation which has to be split over more than one line the first line should start at the left margin, this is achieved by inserting \fl (full left) at the start of the line. The use of the alignment parameter & is not necessary unless some secondary alignment is needed. | Although it is possible to choose a font other than Computer Modern by loading external packages, this is not recommended. | by section is obtained, e.g. (2.1), (2.2), etc. Equation numbering by section is used in appendices automatically when the \appendix command is used, even if sequential numbering has been used in the rest of the article. | C |
Table 2. Prediction RMSE for annual corn yield using 10%, 20%, 50%, and 100% randomly selected training labels. | respiration (Rh), net ecosystem exchange (NEE), and crop yield for 10,335 synthetic sample locations in the United States from the years 2000-2020. All synthetic data are used for pre-training. To reduce computational load, we randomly sample 1/7 of synthetic data in the pre-training phase. We use the observational dat... | Besides the true observed yield labels, we use the physics-based Ecosys model (zhou2021quantifying, ) to simulate ecosystem autotrophic respiration (Ra), ecosystem heterotrophic | For semantic recognition, we utilize a separate language model to embed the obtained textual description and then create additional network layers (e.g., long-short term memory (LSTM)) to capture data dependencies. The use of the language model on textual descriptions enables better capturing of the nature and semantic... | where ciysuperscriptsubscript𝑐𝑖𝑦c_{i}^{y}italic_c start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_y end_POSTSUPERSCRIPT denotes the column name for the observed labels (e.g., observed water temperature), cjysuperscriptsubscript𝑐𝑗𝑦c_{j}^{y}italic_c start_POSTSUBSCRIPT italic_j end_POSTS... | B |
We define enhancer annotation as a binary classification task. Given a sequence of gene-adjacent genomic DNA that contains enhancers, a binary label indicating whether it is part of an enhancer needs to be predicted for each segment of 128bp. | Enhancers are short, noncoding segments that contribute to regulating gene expression. They can be located anywhere from a few thousand to a million bp away from their target gene and work by being brought into physical proximity to the gene’s promoter. Their annotation is a highly challenging task that requires detect... | The genome contains genes, segments that are transcribed to RNA molecules and potentially translated to proteins. Protein-coding genes are structured as introns and exons. For expression, a gene is first transcribed to a pre-mRNA molecule, and introns are removed via splicing. This combines the exons to one contiguous ... | While this task already proves to be highly challenging for current models at the given length scales, we note that biology is even more complex, with enhancers potentially being millions of bp away. | their TSS. Enhancers can be thousands of bp away from the gene. DNA is wrapped around histone proteins and densely packed as a chromosome. | A |
The BPS (Big-Small Patch)[33] method, introduced in a recent publication, utilizes a non-parametric model for the identification of spatially variable genes in 2D or 3D spatial transcriptomics data. The approach involves taking normalized spatial transcriptomics data as input. It defines big and small patches for each ... | We systematically reviewed recently developed frameworks for identifying spatially variable genes and grouped them into different categories and delved into the unique aspects of their models and underlying principles. Here, we provide a brief discussion encompassing various facets, including preprocessing steps, model... | Furthermore, model-free techniques, in many cases, do not analytically control FDR, making it challenging to establish a specific cutoff for selecting SVGs. Many methods claim to detect more SVGs than others, often undetected by alternative methods. However, the mere detection of more SVGs does not necessarily indicate... | Various methods have been developed for multiplicity correction (MC) to address this concern. Some methods analytically constrain the false discovery rate (FDR) to remain below a predetermined threshold, while others do not analytically control the FDR and simply select a user-specified number of top genes as SVGs. Res... | We have previously discussed both model-based and model-free methods for detecting SVGs. The mathematical models employed for capturing the data generation process and the innovative model-free SVG detection technique have proven valuable for uncovering significant SVGs that offer critical biological insights. However,... | D |
Early methods of molecular representation learning primarily included the topological-based approaches and physicochemical-based approaches. Topological-based methods describe molecules by analyzing the chemical bond connections between atoms in molecular structures, with the Extended Connectivity Fingerprints (ECFP) [... | The input of the Graph modality provides the model with detailed information about the molecular structure, such as the types of chemical bonds and atom types. This explicit information transfer enables the model to intuitively understand the microscopic aspects of the molecule. However, it is essential to note that in... | In recent years, the advent of Graph Neural Networks (GNNs) has brought about remarkable advancements in an array of graph-related tasks [7], subsequently inspiring their application to the learning of molecular structures. Central to the concept of a molecular structure-based GNN model is the perception of the topolog... | Early methods of molecular representation learning primarily included the topological-based approaches and physicochemical-based approaches. Topological-based methods describe molecules by analyzing the chemical bond connections between atoms in molecular structures, with the Extended Connectivity Fingerprints (ECFP) [... | Simultaneously, graph contrastive learning [10] has been applied to the field of molecular representation learning with the development of GNNs, compensating for the scarcity of labeled molecular data and significantly promoting the development of this field. Existing molecular representation learning methods based on ... | B |
While it might be expected that reduced ruggedness implies increased accessibility, we will see that this is not | Since theoretical work on models of structured fitness landscapes is largely restricted to the case of binary | understanding of evolutionary accessibility in probabilistic models of fitness landscapes. We distinguish between random | It is instructive to begin the discussion of structured landscapes with the seemingly trivial case of an | the work on structured landscapes is that ruggedness does not generally correlate with accessibility in a simple way. | A |
Does contrastive SSL prove a valid training method for extracting robust and meaningful PCG representations? | Following the above rationale, in our study we select to implement and evaluate the effectiveness of a total of 6 different augmentations, each of which is described below: | kiyasseh_clocs_2021 , implementing attention mechanisms oh_lead-agnostic_2022 or combining wavelet transformations and random | If so, which augmentations or transformations lead to such representations, proving the most effective, and which actually inhibit training? | from a single source or on low quality signals fail to generalize to previously unseen data distributions, which do not adhere to the i.i.d. assumption (i.e | C |
In this configuration, both the tumor’s origin point 𝐱→0=(x0,y0,z0)subscript→𝐱0subscript𝑥0subscript𝑦0subscript𝑧0\vec{\mathbf{x}}_{0}=(x_{0},y_{0},z_{0})over→ start_ARG bold_x end_ARG start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = ( italic_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_y start_POSTSUBSCRIPT 0 end_PO... | ODIL is a framework that addresses the challenges of solving inverse problems. It works by discretizing the PDE of the forward problem and using machine learning tools like automatic differentiation and popular deep learning optimizers (ADAM/L-BFGS) to minimize its residual while maintaining its sparse structure. | The GliODIL framework, which utilizes multi-modal data and leverages PDEs for data-driven solution regularization to capture complex dynamics yet remains tunable with limited data, significantly outperforms models strictly governed by PDEs in forecasting tumor recurrence, as well as surpassing the uniform margin approa... | In addressing the inverse problem of glioma modeling, we compare our results with those obtained from the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) method, detailed in [27, 28], which relies on numerous simulations to identify parameters that best fit the data, and the Learn-Morph-Infer (LMI) technique [... | The primary metric for evaluating the model’s efficacy is its accuracy in predicting tumor recurrence within the post-surgical radiation volume. The metric does not account for factors such as the extent of surgical resection or the impact of the radiotherapy that was administrated already to the patient. Nevertheless,... | A |
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