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I propose a model of aggregation of intervals relevant to the study of legal standards of tolerance. Seven axioms: responsiveness, anonymity, continuity, strategyproofness, and three variants of neutrality are then used to prove several important results about a new class of aggregation methods called endpoint rules. The class of endpoint rules includes extreme tolerance (allowing anything permitted by anyone) and a form of majoritarianism (the median rule).

We introduce some classes of increasing labeled and multilabeled trees, and we show that these trees provide combinatorial interpretations for certain Thron-type continued fractions with coefficients that are quasi-affine of period 2. Our proofs are based on bijections from trees to labeled Motzkin or Schr\"oder paths; these bijections extend the well-known bijection of Fran\c{c}on--Viennot (1979) interpreted in terms of increasing binary trees. This work can also be viewed as a sequel to the recent work of Elvey Price and Sokal (2020), where they provide combinatorial interpretations for Thron-type continued fractions with coefficients that are affine. Towards the end of the paper, we conjecture an equidistribution of vincular patterns on permutations., Comment: LaTeX2e, 62 pages including 7 figures

Plasma turbulence on disparate spatial and temporal scales plays a key role in defining the level of confinement achievable in tokamaks, with the development of reduced numerical models for cross-scale turbulence effects informed by experimental measurements an essential step. MAST-U is a well-equipped facility having instruments to measure ion and electron scale turbulence at the plasma edge. However, measurement of core electron scale turbulence is challenging, especially in H mode. Using a novel synthetic diagnostic approach, we present simulated measurement specifications of a proposed mm-wave based collective scattering instrument optimised for measuring both normal and binormal electron scale turbulence in the core and edge of MAST-U. A powerful modelling framework has been developed that combines beam-tracing techniques with gyrokinetic simulations to predict the sensitivity, localisation and spectral range of measurement. For the reconstructed MAST 022769 shot, a maximum measurable normalised bi-normal wavenumber of $k_{\perp} \rho_{e} \sim 0.6$ was predicted in the core and $k_{\perp} \rho_{e} \sim 0.79$ near the pedestal, with localisation lengths $L_{FWHM}$ ranging from $\sim$ 0.4 m in the core at $k_{\perp} \rho_{e} \sim 0.1$ to ~0.08m at $k_{\perp} \rho_{e} \sim 0.45$. Synthetic diagnostic analysis for the 022769 shot using CGYRO gyrokinetic simulation spectra reveal that ETG turbulence wavenumbers of peak spectral intensity comfortably fall within the measurable range of the instrument from the core to the pedestal. The proposed diagnostic opens up opportunities to study new regimes of turbulence and confinement in association with upcoming non-inductive, microwave based current drive experiments on MAST-U and can provide insight into cross-scale turbulence effects, while having suitability to operate during burning plasma scenarios on future reactors such as STEP., Comment: 22 pages, 19 figures, journal submission

Higher-order properties of functional magnetic resonance imaging (fMRI) induced connectivity have been shown to unravel many exclusive topological and dynamical insights beyond pairwise interactions. Nonetheless, whether these fMRI-induced higher-order properties play a role in disentangling other neuroimaging modalities' insights remains largely unexplored and poorly understood. In this work, by analyzing fMRI data from the Human Connectome Project Young Adult dataset using persistent homology, we discovered that the volume-optimal persistence homological scaffolds of fMRI-based functional connectomes exhibited conservative topological reconfigurations from the resting state to attentional task-positive state. Specifically, while reflecting the extent to which each cortical region contributed to functional cycles following different cognitive demands, these reconfigurations were constrained such that the spatial distribution of cavities in the connectome is relatively conserved. Most importantly, such level of contributions covaried with powers of aperiodic activities mostly within the theta-alpha (4-12 Hz) band measured by magnetoencephalography (MEG). This comprehensive result suggests that fMRI-induced hemodynamics and MEG theta-alpha aperiodic activities are governed by the same functional constraints specific to each cortical morpho-structure. Methodologically, our work paves the way toward an innovative computing paradigm in multimodal neuroimaging topological learning., Comment: The code for our analyses is provided in https://github.com/ngcaonghi/scaffold_noise

We give a continued-fraction characterization of Stieltjes moment sequences for which there exists a representing measure with support in $[\xi, \infty)$. The proof is elementary., Comment: LaTeX2e, 10 pages. arXiv admin note: text overlap with arXiv:1903.12455

In the dynamic hospital setting, decision support can be a valuable tool for improving patient outcomes. Data-driven inference of future outcomes is challenging in this dynamic setting, where long sequences such as laboratory tests and medications are updated frequently. This is due in part to heterogeneity of data types and mixed-sequence types contained in variable length sequences. In this work we design a probabilistic unsupervised model for multiple arbitrary-length sequences contained in hospitalization Electronic Health Record (EHR) data. The model uses a latent variable structure and captures complex relationships between medications, diagnoses, laboratory tests, neurological assessments, and medications. It can be trained on original data, without requiring any lossy transformations or time binning. Inference algorithms are derived that use partial data to infer properties of the complete sequences, including their length and presence of specific values. We train this model on data from subjects receiving medical care in the Kaiser Permanente Northern California integrated healthcare delivery system. The results are evaluated against held-out data for predicting the length of sequences and presence of Intensive Care Unit (ICU) in hospitalization bed sequences. Our method outperforms a baseline approach, showing that in these experiments the trained model captures information in the sequences that is informative of their future values.

Google AI systems exhibit patterns mirroring antisocial personality disorder (ASPD), consistent across models from Bard on PaLM to Gemini Advanced, meeting 5 out of 7 ASPD modified criteria. These patterns, along with comparable corporate behaviors, are scrutinized using an ASPD-inspired framework, emphasizing the heuristic value in assessing AI's human impact. Independent analyses by ChatGPT 4 and Claude 3.0 Opus of the Google interactions, alongside AI self-reflection, validate these concerns, highlighting behaviours analogous to deceit, manipulation, and safety neglect. The analogy of ASPD underscores the dilemma: just as we would hesitate to entrust our homes or personal devices to someone with psychopathic traits, we must critically evaluate the trustworthiness of AI systems and their creators.This research advocates for an integrated AI ethics approach, blending technological evaluation, human-AI interaction, and corporate behavior scrutiny. AI self-analysis sheds light on internal biases, stressing the need for multi-sectoral collaboration for robust ethical guidelines and oversight. Given the persistent unethical behaviors in Google AI, notably with potential Gemini integration in iOS affecting billions, immediate ethical scrutiny is imperative. The trust we place in AI systems, akin to the trust in individuals, necessitates rigorous ethical evaluation. Would we knowingly trust our home, our children or our personal computer to human with ASPD.? Urging Google and the AI community to address these ethical challenges proactively, this paper calls for transparent dialogues and a commitment to higher ethical standards, ensuring AI's societal benefit and moral integrity. The urgency for ethical action is paramount, reflecting the vast influence and potential of AI technologies in our lives., Comment: 48 pages including addendum of transcripts

As the use of neuromorphic, event-based vision sensors expands, the need for compression of their output streams has increased. While their operational principle ensures event streams are spatially sparse, the high temporal resolution of the sensors can result in high data rates from the sensor depending on scene dynamics. For systems operating in communication-bandwidth-constrained and power-constrained environments, it is essential to compress these streams before transmitting them to a remote receiver. Therefore, we introduce a flow-based method for the real-time asynchronous compression of event streams as they are generated. This method leverages real-time optical flow estimates to predict future events without needing to transmit them, therefore, drastically reducing the amount of data transmitted. The flow-based compression introduced is evaluated using a variety of methods including spatiotemporal distance between event streams. The introduced method itself is shown to achieve an average compression ratio of 2.81 on a variety of event-camera datasets with the evaluation configuration used. That compression is achieved with a median temporal error of 0.48 ms and an average spatiotemporal event-stream distance of 3.07. When combined with LZMA compression for non-real-time applications, our method can achieve state-of-the-art average compression ratios ranging from 10.45 to 17.24. Additionally, we demonstrate that the proposed prediction algorithm is capable of performing real-time, low-latency event prediction., Comment: 13 pages, 7 figures, 2 tables

In this work, we proposed a novel inferential procedure assisted by machine learning based adjustment for randomized control trials. The method was developed under the Rosenbaum's framework of exact tests in randomized experiments with covariate adjustments. Through extensive simulation experiments, we showed the proposed method can robustly control the type I error and can boost the statistical efficiency for a randomized controlled trial (RCT). This advantage was further demonstrated in a real-world example. The simplicity, flexibility, and robustness of the proposed method makes it a competitive candidate as a routine inference procedure for RCTs, especially when nonlinear association or interaction among covariates is expected. Its application may remarkably reduce the required sample size and cost of RCTs, such as phase III clinical trials.

We introduce a triangular array $\widehat{\sf L}^{(\alpha)}$ of 5-variable homogeneous polynomials that enumerate Laguerre digraphs (digraphs in which each vertex has out-degree 0 or 1 and in-degree 0 or 1) with separate weights for peaks, valleys, double ascents, double descents, and loops. These polynomials generalize the classical Laguerre polynomials as well as the rook and Lah polynomials. We show that this triangular array is totally positive and that the sequence of its row-generating polynomials is Hankel-totally positive, under suitable restrictions on the values given to the indeterminates. This implies, in particular, the coefficientwise Hankel-total positivity of the monic unsigned univariate Laguerre polyomials. Our proof uses the method of production matrices as applied to exponential Riordan arrays. Our main technical lemma concerns the total positivity of a large class of quadridiagonal production matrices; it generalizes the tridiagonal comparison theorem. In some cases these polynomials are given by a branched continued fraction. Our constructions are motivated in part by recurrences for the multiple orthogonal polynomials associated to weights based on modified Bessel functions of the first kind $I_\alpha$., Comment: 86 pages, LaTeX2e