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A surface pair $(X,C)$ is a germ of a normal surface singularity $(X,0)$ and a sum $C=\sum c_iC_i$ of curves on $X$, with $c_i\in [0,1]$. An orbifold pair has $c_i=1/n_i$, as intersecting with a small sphere gives a $3$-dimensional orbifold $(\Sigma, \gamma_i,n_i)$. There are natural notions of morphism and log cover of surface pairs. We introduce a volume $Vol(X,C)$ in $\mathbb Q_{\geq 0}$, computable from any log resolution, analogous to that in our 1990 JAMS paper when $C=0$. Denoting $\bar{C}=\sum (1-c_i)C_i$, one has $(X,C)$ log canonical iff $Vol(X,\bar{C})=0$. The main theorem (5.4-5.6) is that $Vol(X,C)$ is ``characteristic'': if $f:(X',C')\rightarrow (X,C)$ is a morphism of degree $d$, then $Vol(X',C')\geq d\cdot Vol(X,C)$, with equality if $f$ is a log cover. We prove (6.7) that $Vol(X,\sum (1/n_i)C_i)=0$ iff the associated orbifold has finite or solvable orbifold fundamental group, and these are classified. In (8.2) is proved a key case of the DCC Volumes Conjecture: The set $\{Vol(X,\sum (1/n_i)C_i)|\ X\ \text{RDP}\}$ satisfies the DCC, with minimum non-$0$ volume 1/3528., Comment: 24 pages, For 115AM Jaca Conference in June, 2023

In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables of interest are latent are largely missing. We assay the connection between invariance and causal representation learning by establishing impossibility results which show that invariance alone is insufficient to identify latent causal variables. Together with practical considerations, we use these theoretical findings to highlight the need for additional constraints in order to identify representations by exploiting invariance.

Purpose: In this work, we explore the potential and limitations of simulating gaze-contingent tunnel vision conditions using Virtual Reality (VR) with built-in eye tracking technology. This approach promises an easy and accessible way of expanding study populations and test groups for visual training, visual aids, or accessibility evaluations. However, it is crucial to assess the validity and reliability of simulating these types of visual impairments and evaluate the extend to which participants with simulated tunnel vision can represent real patients. Methods: Two age-matched participant groups were acquired: The first group (n=8 aged 20-60, average 49.1, sd 13.2) consisted of patients diagnosed with Retinitis pigmentosa (RP). The second group (n=8, aged 27-59, average 46.5, sd 10.8) consisted of visually healthy participants with simulated tunnel vision. Both groups carried out different visual tasks in a virtual environment for 30 minutes per day over the course of four weeks. Task performances as well as gaze characteristics were evaluated in both groups over the course of the study. Results: Using the "two one-sided tests for equivalence" method, the two groups were found to perform similar in all three visual tasks. Significant differences between groups were found in different aspects of their gaze behavior, though most of these aspects seem to converge over time. Conclusion: Our study evaluates the potential and limitations of using Virtual Reality technology to simulate the effects of tunnel vision within controlled virtual environments. We find that the simulation accurately represents performance of RP patients in the context of group averages, but fails to fully replicate effects on gaze behavior.

Developing and evaluating vision science methods require robust and efficient tools for assessing their performance in various real-world scenarios. This study presents a novel virtual reality (VR) simulation tool that simulates real-world optical methods while giving high experimental control to the experiment. The tool incorporates an experiment controller, to smoothly and easily handle multiple conditions, a generic eye-tracking controller, that works with most common VR eye-trackers, a configurable defocus simulator, and a generic VR questionnaire loader to assess participants' behavior in virtual reality. This VR-based simulation tool bridges the gap between theoretical and applied research on new optical methods, corrections, and therapies. It enables vision scientists to increase their research tools with a robust, realistic, and fast research environment.

This study comprehensively evaluates tuning methods for autofocal glasses using virtual reality (VR), addressing the challenge of presbyopia. With aging, presbyopia diminishes the eye's ability to focus on nearby objects, impacting the quality of life for billions. Autofocals, employing focus-tunable lenses, dynamically adjust optical power for each fixation, promising a more natural visual experience than traditional bifocal or multifocal lenses. Our research contrasts the most common tuning methods - manual, gaze-based, and vergence - within a VR setup to mimic real-world scenarios. Utilizing the XTAL VR headset equipped with eye-tracking, the study replicated autofocal scenarios, measuring performance and usability through psychophysical tasks and NASA TLX surveys. Results show varying strengths and weaknesses across methods, with gaze control excelling in precision but not necessarily comfort and manual control providing stability and predictability. The findings guide the selection of tuning methods based on task requirements and user preferences, highlighting a balance between precision and ease of use.

Doping of a Mott insulator gives rise to a wide variety of exotic emergent states, from high-temperature superconductivity to charge, spin, and orbital orders. The physics underpinning their evolution is, however, poorly understood. A major challenge is the chemical complexity associated with traditional routes to doping. Here, we study the Mott insulating CrO$_2$ layer of the delafossite PdCrO$_2$, where an intrinsic polar catastrophe provides a clean route to doping of the surface. From scanning tunnelling microscopy and angle-resolved photoemission, we find that the surface stays insulating accompanied by a short-range ordered state. From density functional theory, we demonstrate how the formation of charge disproportionation results in an insulating ground state of the surface that is disparate from the hidden Mott insulator in the bulk. We demonstrate that voltage pulses induce local modifications to this state which relax over tens of minutes, pointing to a glassy nature of the charge order., Comment: published paper and supplementary, 28 pages in total, 4 figures in the main text and 15 in the supplementary

This paper develops theory for a newly-defined bicomplex hyperbolic harmonic function with four real-dimensional inputs, in a way that generalizes the connection between real harmonic functions with two real-dimensional inputs and complex analytic functions. For example, every bicomplex hyperbolic harmonic function appears as this paper's newly-defined hyperbolic real part of a bicomplex analytic function, just as every real harmonic function with two real-dimensional inputs is the real part of a complex analytic function. In addition, this connection produces a unique (up to additive constant) and newly-defined hyperbolic harmonic conjugate function, just as every real harmonic function has a unique (up to additive constant) real harmonic conjugate. Finally, the paper determines a bicomplex Poisson kernel function that produces a corresponding integral representation for bicomplex harmonic functions, one that generalizes the complex harmonic function Poisson integral representation., Comment: 8 pages, 1 figure

We demonstrate compression and shaping of few cycle pulses from a high average power Ytterbium laser system. The pulses from a commercial 20 W, 100 kHz Yb laser system are spectrally broadened in two-stages using gas-filled, stretched hollow-core fibers and then compressed and shaped in an acousto-optic modulator-based pulse-shaper. The pulse-shaper allows for compression, characterization, and shaping all in one system, producing ~10 fs pulses with 50 uJ of energy

The task of inferring high-level causal variables from low-level observations, commonly referred to as causal representation learning, is fundamentally underconstrained. As such, recent works to address this problem focus on various assumptions that lead to identifiability of the underlying latent causal variables. A large corpus of these preceding approaches consider multi-environment data collected under different interventions on the causal model. What is common to virtually all of these works is the restrictive assumption that in each environment, only a single variable is intervened on. In this work, we relax this assumption and provide the first identifiability result for causal representation learning that allows for multiple variables to be targeted by an intervention within one environment. Our approach hinges on a general assumption on the coverage and diversity of interventions across environments, which also includes the shared assumption of single-node interventions of previous works. The main idea behind our approach is to exploit the trace that interventions leave on the variance of the ground truth causal variables and regularizing for a specific notion of sparsity with respect to this trace. In addition to and inspired by our theoretical contributions, we present a practical algorithm to learn causal representations from multi-node interventional data and provide empirical evidence that validates our identifiability results., Comment: Accepted for publication at CLeaR 2024