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Arbitrary, inconsistent, or faulty decision-making raises serious concerns, and preventing unfair models is an increasingly important challenge in Machine Learning. Data often reflect past discriminatory behavior, and models trained on such data may reflect bias on sensitive attributes, such as gender, race, or age. One approach to developing fair models is to preprocess the training data to remove the underlying biases while preserving the relevant information, for example, by correcting biased labels. While multiple label noise correction methods are available, the information about their behavior in identifying discrimination is very limited. In this work, we develop an empirical methodology to systematically evaluate the effectiveness of label noise correction techniques in ensuring the fairness of models trained on biased datasets. Our methodology involves manipulating the amount of label noise and can be used with fairness benchmarks but also with standard ML datasets. We apply the methodology to analyze six label noise correction methods according to several fairness metrics on standard OpenML datasets. Our results suggest that the Hybrid Label Noise Correction method achieves the best trade-off between predictive performance and fairness. Clustering-Based Correction can reduce discrimination the most, however, at the cost of lower predictive performance.

We describe a bijection between oriented cubes and adjoints of cross-polytopes. This correspondence is used to prove that the real affine cube is, up to reorientation in the same class, the unique oriented cube that is realizable. Moreover, its underlying matroid is, up to isomorphism, the unique combinatorial cube that is realizable over the reals., Comment: 23 pages, 4 figures

We introduce a family of nonnegative integer vectors - primitive vectors - defining hyperplanes of the real affine cube over $C^n:=\{-1,1\}^n$ and study their properties with respect to the rectangles of the cube. As a consequence we give a short proof that, for small dimensions ($n\leq 7$), the real affine cube can be recovered from its signed rectangles and its signed cocircuits complementary of its facets and skew-facets.

A folded disk is bistable, as it can be popped through to an inverted state with elastic energy localized in a small, highly-deformed region on the fold. Cutting out this singularity relaxes the surrounding material and leads to a loss of bistability when the hole dimensions reach a critical size. These dimensions are strongly anisotropic and feature a surprising re-entrant behavior, such that removal of additional material can re-stabilize the inverted state. A model of the surface as a wide annular developable strip is found to capture the qualitative observations in experiments and simulations. These phenomena are consequential to the mechanics and design of crumpled elastic sheets, developable surfaces, origami and kirigami, and other deployable and compliant structures., Comment: whither the singularity?

Dimensionality reduction methods are an essential tool for multidimensional data analysis, and many interesting processes can be studied as time-dependent multivariate datasets. There are, however, few studies and proposals that leverage on the concise power of expression of projections in the context of dynamic/temporal data. In this paper, we aim at providing an approach to assess projection techniques for dynamic data and understand the relationship between visual quality and stability. Our approach relies on an experimental setup that consists of existing techniques designed for time-dependent data and new variations of static methods. To support the evaluation of these techniques, we provide a collection of datasets that has a wide variety of traits that encode dynamic patterns, as well as a set of spatial and temporal stability metrics that assess the quality of the layouts. We present an evaluation of 11 methods, 10 datasets, and 12 quality metrics, and elect the best-suited methods for projecting time-dependent multivariate data, exploring the design choices and characteristics of each method. All our results are documented and made available in a public repository to allow reproducibility of results.

It is well known that an annular sheet could wrinkle as a result of axisymmetric tensile loads applied at the edges. In this system, regions under compression appear due to Poisson effect in the azimuthal direction yielding an incompatible excess in length, so that the membrane has to buckle out of the plane. Then, radial wrinkles emerge following the direction of the tensile principal stress. This so called Lam\'e configuration has been widely used as theoretical and experimental paradigms for wrinkling instabilities. In this work, we explore the consequences of changing the geometry of this model configuration by considering an elliptic hole in an infinite stretched membrane. Using the Kolosoff-Inglis solution, we analyse the stress field around the hole and identify three possible regions: taut, unidirectionally tensioned and slack regions. According to these definitions, we classify in a phase diagram the different stress states of the sheet as function of the hole eccentricity and of the applied tensions. Finally, we quantify how the tension lines vary with the geometry of the hole and discuss possible outcomes on the emerging buckled patterns.

Barlowite, Cu$_{4}$(OH)$_{6}$FBr, has attracted much attention as the parent compound of a new series of quantum spin liquid candidates, Zn$_{x}$Cu$_{4-x}$(OH)$_{6}$FBr. While it is known to undergo a magnetic phase transition to a long-range ordered state at $T_{N} = 15$ K, there is still no consensus over either its nuclear or magnetic structures. Here, we use comprehensive powder neutron diffraction studies on deuterated samples of barlowite to demonstrate that the only space group consistent with the observed nuclear and magnetic diffraction at low-temperatures is the orthorhombic $Pnma$ space group. We furthermore conclude that the magnetic intensity at $T < T_{N}$ is correctly described by the $Pn^\prime m^\prime a$ magnetic space group, which crucially allows the ferromagnetic component observed in previous single-crystal and powder magnetisation measurements. As such, the magnetic structure of barlowite resembles that of the related material clinoatacamite, Cu$_{4}$(OH)$_{6}$Cl$_{2}$, the parent compound of the well-known quantum spin liquid candidate hebertsmithite, ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$., Comment: 11 pages, 4 figures, supplemental material

We present AC and DC magnetometry, heat capacity, muon spin relaxation ($\mu$SR) and resonant inelastic X-ray scattering (RIXS) studies of the pyrochlore osmate Y$_2$Os$_2$O$_7$. We observe a non-zero effective moment governed by $\sqrt{f}\mu_{\rm{eff}} = 0.417(1)\,\mu_{\rm{B}}$ where $f$ is the fraction of Os sites which exhibit a spin, and spin freezing at temperature $T_{\rm f} \simeq 5\,$K, consistent with previous results. The field dependence of magnetisation data shows that the paramagnetic moment is most likely due to large moments $\mu_{\rm eff} \simeq 3\,\mu_{\rm B}$ on only a small fraction $f \simeq 0.02$ of Os sites. Comparison of single-ion energy level calculations with the RIXS data yields a non-magnetic $J_{\rm eff} = 0$ ground state on the Os$^{4+}$ sites. The spin-orbit interaction, Hund's coupling and trigonal distortion of OsO$_{6}$ octahedra are all important in modelling the experimentally observed spectra. We are able to rule out impurity effects, leaving disorder-related effects such as oxygen non-stoichiometry or site interchange between Os and Y ions as the most plausible explanation for the magnetic response in this material.

We give new definitions of null infinity and black hole in terms of causal boundaries, applicable to any strongly causal spacetime $(M,g)$. These are meant to extend the standard ones given in terms of conformal boundaries, and use the new definitions to prove a classic result in black hole theory for this more general context: if the null infinity is regular (i.e. well behaved in a suitable sense) and $(M,g)$ obeys the null convergence condition, then any closed trapped surface in $(M,g)$ has to be inside the black hole region. As an illustration of this general construction, we apply it to the class of generalized plane waves, where the conformal null infinity is not always well-defined. In particular, it is shown that (generalized) black hole regions do not exist in a large family of these spacetimes., Comment: 32 pages, 4 figures. Included new reference