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A critical problem in extreme value theory (EVT) is the estimation of parameters for the limit probability distributions. Block maxima (BM), an approach in EVT that seeks estimates of parameters of the generalized extreme value distribution (GEV), can be generalized to take into account not just the maximum realization from a given dataset, but the r largest order statistics for a given r. In this work we propose a parameter estimation method that combines the r largest order statistic (r-LOS) extension of BM with permutation bootstrapping: surrogate realizations are obtained by randomly reordering the original data set, and then r-LOS is applied to these shuffled measurements - the mean estimate computed from these surrogate realizations is the desired estimate. We used synthetic observations and real meteorological time series to verify the performance of our method; we found that the combination of r-LOS and bootstrapping resulted in estimates more accurate than when either approach was implemented separately., Comment: 16 pages, 6 figures

Driven by steady progress in generative modeling, simulation-based inference (SBI) has enabled inference over stochastic simulators. However, recent work has demonstrated that model misspecification can harm SBI's reliability. This work introduces robust posterior estimation (ROPE), a framework that overcomes model misspecification with a small real-world calibration set of ground truth parameter measurements. We formalize the misspecification gap as the solution of an optimal transport problem between learned representations of real-world and simulated observations. Assuming the prior distribution over the parameters of interest is known and well-specified, our method offers a controllable balance between calibrated uncertainty and informative inference under all possible misspecifications of the simulator. Our empirical results on four synthetic tasks and two real-world problems demonstrate that ROPE outperforms baselines and consistently returns informative and calibrated credible intervals.

In some fields of AI, machine learning and statistics, the validation of new methods and algorithms is often hindered by the scarcity of suitable real-world datasets. Researchers must often turn to simulated data, which yields limited information about the applicability of the proposed methods to real problems. As a step forward, we have constructed two devices that allow us to quickly and inexpensively produce large datasets from non-trivial but well-understood physical systems. The devices, which we call causal chambers, are computer-controlled laboratories that allow us to manipulate and measure an array of variables from these physical systems, providing a rich testbed for algorithms from a variety of fields. We illustrate potential applications through a series of case studies in fields such as causal discovery, out-of-distribution generalization, change point detection, independent component analysis, and symbolic regression. For applications to causal inference, the chambers allow us to carefully perform interventions. We also provide and empirically validate a causal model of each chamber, which can be used as ground truth for different tasks. All hardware and software is made open source, and the datasets are publicly available at causalchamber.org or through the Python package causalchamber., Comment: 40 pages, 20 figures

Automated slice classification is clinically relevant since it can be incorporated into medical image segmentation workflows as a preprocessing step that would flag slices with a higher probability of containing tumors, thereby directing physicians attention to the important slices. In this work, we train a ResNet-18 network to classify axial slices of lymphoma PET/CT images (collected from two institutions) depending on whether the slice intercepted a tumor (positive slice) in the 3D image or if the slice did not (negative slice). Various instances of the network were trained on 2D axial datasets created in different ways: (i) slice-level split and (ii) patient-level split; inputs of different types were used: (i) only PET slices and (ii) concatenated PET and CT slices; and different training strategies were employed: (i) center-aware (CAW) and (ii) center-agnostic (CAG). Model performances were compared using the area under the receiver operating characteristic curve (AUROC) and the area under the precision-recall curve (AUPRC), and various binary classification metrics. We observe and describe a performance overestimation in the case of slice-level split as compared to the patient-level split training. The model trained using patient-level split data with the network input containing only PET slices in the CAG training regime was the best performing/generalizing model on a majority of metrics. Our models were additionally more closely compared using the sensitivity metric on the positive slices from their respective test sets., Comment: 10 pages, 6 figures, 2 tables

The interaction of surfaces in relative motion in wet environments is dominated by lubrication forces, which play a pivotal role in the dynamics of microscopic systems. Here, we develop motile vesicles that exploit lubrication forces to roll on substrates. The activity of the vesicle comes from the confined rotational flow generated by a driven rotating particle encapsulated within the vesicle by droplet-microfluidics. Lubrication forces driving vesicle rolling are controlled by membrane mechanics and its tribological properties. This provides the design principles for motile vesicles that exploit frictional forces to efficiently navigate through complex environments., Comment: 6 pages, 5 figures

A characterization of the representability of neural networks is relevant to comprehend their success in artificial intelligence. This study investigate two topics on ReLU neural network expressivity and their connection with a conjecture related to the minimum depth required for representing any continuous piecewise linear (CPWL) function. The topics are the minimal depth representation of the sum and max operations, as well as the exploration of polytope neural networks. For the sum operation, we establish a sufficient condition on the minimal depth of the operands to find the minimal depth of the operation. In contrast, regarding the max operation, a comprehensive set of examples is presented, demonstrating that no sufficient conditions, depending solely on the depth of the operands, would imply a minimal depth for the operation. The study also examine the minimal depth relationship between convex CPWL functions. On polytope neural networks, we investigate basic depth properties from Minkowski sums, convex hulls, number of vertices, faces, affine transformations, and indecomposable polytopes. More significant findings include depth characterization of polygons; identification of polytopes with an increasing number of vertices, exhibiting small depth and others with arbitrary large depth; and most notably, the minimal depth of simplices, which is strictly related to the minimal depth conjecture in ReLU networks., Comment: 23 pages

The mixed-valence compound SmB6 with partially filled samarium 4f flat bands hybridizing with 5d conduction bands is a paramount example of a correlated topological heavy-fermion system. In this study we revisit the topology of SmB6 with the band theory paradigm and uncover previously overlooked aspects resulting from the formation of multiple topological gaps in the electronic structure. By invoking topological quantum chemistry (TQC) we provide a detailed classification of the strong and crystalline topological features that derive from the existence of such topological gaps. To corroborate this classification, we calculate Wilson loops and simulate the surface electronic structure using a minimal tight-binding model, allowing us to describe its surface states and confirm the crystalline topology. We finally discuss its implications for experiments.

We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model corresponds to the CDT-matrix model introduced by Benedetti and Henson [Phys. Lett. B 678, 222 (2009)]. We present exact as well as approximate results for the Gaussian averages of characters of a Hermitian matrix $A$ and $A^2$ for a given representation and establish the present limitations that prevent us to solve the model analytically. This sets the stage for the formulation of more sophisticated matter models coupled to two-dimensional CDT as dually weighted multi-matrix models providing a complementary view to the standard simplicial formulation of CDT-matter models., Comment: 48 pages, 19 figures

The challenge of answering graph queries over incomplete knowledge graphs is gaining significant attention in the machine learning community. Neuro-symbolic models have emerged as a promising approach, combining good performance with high interpretability. These models utilize trained architectures to execute atomic queries and integrate modules that mimic symbolic query operators. However, most neuro-symbolic query processors are constrained to tree-like graph pattern queries. These queries admit a bottom-up execution with constant values or anchors at the leaves and the target variable at the root. While expressive, tree-like queries fail to capture critical properties in knowledge graphs, such as the existence of multiple edges between entities or the presence of triangles. We introduce a framework for answering arbitrary graph pattern queries over incomplete knowledge graphs, encompassing both cyclic queries and tree-like queries with existentially quantified leaves. These classes of queries are vital for practical applications but are beyond the scope of most current neuro-symbolic models. Our approach employs an approximation scheme that facilitates acyclic traversals for cyclic patterns, thereby embedding additional symbolic bias into the query execution process. Our experimental evaluation demonstrates that our framework performs competitively on three datasets, effectively handling cyclic queries through our approximation strategy. Additionally, it maintains the performance of existing neuro-symbolic models on anchored tree-like queries and extends their capabilities to queries with existentially quantified variables.

We present some simple proofs of the well-known expressions for \[ \zeta(2k) = \sum_{m=1}^\infty \frac{1}{m^{2k}}, \qquad \beta(2k+1) = \sum_{m=0}^\infty \frac{(-1)^m}{(2m+1)^{2k+1}}, \] where $k = 1,2,3,\dots$, in terms of the Bernoulli and Euler polynomials. The computation is done using only the defining properties of these polynomials and employing telescoping series. The same method also yields integral formulas for $\zeta(2k+1)$ and $\beta(2k)$. In addition, the method also applies to series of type \[ \sum_{m\in\mathbb{Z}} \frac{1}{(2m-\mu)^s}, \qquad \sum_{m\in\mathbb{Z}} \frac{(-1)^m}{(2m+1-\mu)^s}, \] in this case using Apostol-Bernoulli and Apostol-Euler polynomials., Comment: 24 pages, to appear in "Orthogonal Polynomials and Special Functions: In Memory of Jos\'e Carlos Petronilho''

We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as parameter differentiation formulas for the beta incomplete function, reduction formulas of $_{3}F_{2}$ hypergeometric functions, or a definite integral which does not seem to be tabulated in the most common literature. As an application of some sums involving the digamma function, we have calculated some redution formulas for the parameter differentiation of the Mittag-Leffler function and the Wright function.