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Evaluating instruction following capabilities for multimodal, multi-turn dialogue is challenging. With potentially multiple instructions in the input model context, the task is time-consuming for human raters and we show LLM based judges are biased towards answers from the same model. We propose MMMT-IF, an image based multi-turn Q$\&$A evaluation set with added global instructions between questions, constraining the answer format. This challenges models to retrieve instructions dispersed across long dialogues and reason under instruction constraints. All instructions are objectively verifiable through code execution. We introduce the Programmatic Instruction Following ($\operatorname{PIF}$) metric to measure the fraction of the instructions that are correctly followed while performing a reasoning task. The $\operatorname{PIF-N-K}$ set of metrics further evaluates robustness by measuring the fraction of samples in a corpus where, for each sample, at least K out of N generated model responses achieve a $\operatorname{PIF}$ score of one. The $\operatorname{PIF}$ metric aligns with human instruction following ratings, showing 60 percent correlation. Experiments show Gemini 1.5 Pro, GPT-4o, and Claude 3.5 Sonnet, have a $\operatorname{PIF}$ metric that drops from 0.81 on average at turn 1 across the models, to 0.64 at turn 20. Across all turns, when each response is repeated 4 times ($\operatorname{PIF-4-4}$), GPT-4o and Gemini successfully follow all instructions only $11\%$ of the time. When all the instructions are also appended to the end of the model input context, the $\operatorname{PIF}$ metric improves by 22.3 points on average, showing that the challenge with the task lies not only in following the instructions, but also in retrieving the instructions spread out in the model context. We plan to open source the MMMT-IF dataset and metric computation code., Comment: 24 pages, 16 figures

The theory of composite mixtures consisting of $n$ constituents is framed within the schema provided by the notion of $n$-groupoid. The point of departure is the analysis of $n$-dimensional hypercubes and their skeletons, to each of whose edges an element (an arrow) of one of $n$ given material groupoids is assigned according to the coordinate class to which it belongs. In this way a $GL(3,{\mathbb R})$-weighted digraph is obtained. It is shown that if the double groupoid associated with each pair of constituents consists of commuting squares, the resulting $n$-groupoid is conservative. The core of this $n$-groupoid is transitive if, and only if, the mixture is materially uniform.

We study three two-stage optimization problems with a similar structure and different objectives. In the first stage of each problem, the goal is to assign input jobs of positive sizes to unsplittable bags. After this assignment is decided, the realization of the number of identical machines that will be available is revealed. Then, in the second stage, the bags are assigned to machines. The probability vector of the number of machines in the second stage is known to the algorithm as part of the input before making the decisions of the first stage. Thus, the vector of machine completion times is a random variable. The goal of the first problem is to minimize the expected value of the makespan of the second stage schedule, while the goal of the second problem is to maximize the expected value of the minimum completion time of the machines in the second stage solution. The goal of the third problem is to minimize the \ell_p norm for a fixed p>1, where the norm is applied on machines' completion times vectors. Each one of the first two problems admits a PTAS as Buchem et al. showed recently. Here we significantly improve all their results by designing an EPTAS for each one of these problems. We also design an EPTAS for \ell_p norm minimization for any p>1.

We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly perturbed half-spaces in two and three dimensions. The kernel for the double layer potential is the normal derivative of the free-space Green's function, which has a well-known analytic continuation into the complex plane as a function of both target and source locations. Here, we prove that - when the incident data are analytic and satisfy a precise asymptotic estimate - the solution to the boundary integral equation itself admits an analytic continuation into specific regions of the complex plane, and satisfies a related asymptotic estimate (this class of data includes both plane waves and the field induced by point sources). We then show that, with a carefully chosen contour deformation, the oscillatory integrals are converted to exponentially decaying integrals, effectively reducing the infinite domain to a domain of finite size. Our scheme is different from existing methods that use complex coordinate transformations, such as perfectly matched layers, or absorbing regions, such as the gradual complexification of the governing wavenumber. More precisely, in our method, we are still solving a boundary integral equation, albeit on a truncated, complexified version of the original boundary. In other words, no volumetric/domain modifications are introduced. The scheme can be extended to other boundary conditions, to open wave guides and to layered media. We illustrate the performance of the scheme with two and three dimensional examples., Comment: 27 pages, 9 figures

The set of appendices in this volume is a companion to the report "Federal Efforts Towards Investing in Innovation in Education Through the i3 Fund: A Summary of Grantmaking and Evidence-Building." The goal of the U.S. Department of Education's Investing in Innovation Fund (i3) was to build high-quality evidence about effective educational strategies and to expand implementation of these strategies. Between 2010 and 2016, i3 awarded 172 grants totaling $1.4 billion to universities, school districts, and private non-profit organizations. The i3 Fund intentionally awarded different types of grants either to develop and test new, innovative but as-yet-unproven strategies or to learn more about the circumstances under which previously tested strategies are effective. Grantees were required to fund independent evaluations that would meet high standards for quality. Appendices included in this document are: (1) Additional Details about the Investing in Innovation (i3) Fund Program; (2) Study Design and Methods; and (3) Supplemental Tables and Information on Study Findings.

Advanced Artificial Intelligence (AI) systems, specifically large language models (LLMs), have the capability to generate not just misinformation, but also deceptive explanations that can justify and propagate false information and erode trust in the truth. We examined the impact of deceptive AI generated explanations on individuals' beliefs in a pre-registered online experiment with 23,840 observations from 1,192 participants. We found that in addition to being more persuasive than accurate and honest explanations, AI-generated deceptive explanations can significantly amplify belief in false news headlines and undermine true ones as compared to AI systems that simply classify the headline incorrectly as being true/false. Moreover, our results show that personal factors such as cognitive reflection and trust in AI do not necessarily protect individuals from these effects caused by deceptive AI generated explanations. Instead, our results show that the logical validity of AI generated deceptive explanations, that is whether the explanation has a causal effect on the truthfulness of the AI's classification, plays a critical role in countering their persuasiveness - with logically invalid explanations being deemed less credible. This underscores the importance of teaching logical reasoning and critical thinking skills to identify logically invalid arguments, fostering greater resilience against advanced AI-driven misinformation.

This paper looks at the intersection of algorithmic information theory and physics, namely quantum mechanics, thermodynamics, and black holes. We discuss theorems which characterize the barrier between the quantum world and the classical realm. The notion of a ``semi-classical subspace'' is introduced. Partial signals and partial information cloning can be obtained on quantum states in semi-classical subspaces. The No Synchronization Law is detailed, which says separate and isolated physical systems evolving over time cannot have algorithmic thermodynamic entropies that are in synch. We look at future work involving the Kolmogorov complexity of black holes., Comment: arXiv admin note: text overlap with arXiv:2402.13049

The *reciprocal complement* $R(D)$ of an integral domain $D$ is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of $R(D)$ are determined when $D$ is a polynomial ring in $n\geq 2$ variables over a field. In particular, $R(D)$ is an $n$-dimensional, local, non-Noetherian, non-integrally closed, non-factorial, atomic G-domain, with infinitely many prime ideals at each height other than $0$ and $n$., Comment: 24 pages. Comments are welcome!

We present a semianalytical synthesis scheme for designing realistic printed-circuit-board- (PCB) based metagratings (MGs), capable of simultaneous beam steering and polarization conversion. These low-profile structures, comprised of sparse periodic arrangements of subwavelength polarizable particles (meta-atoms), oriented by insightful analytical models leading to fabrication-ready designs, have gained growing interest in recent years, demonstrating exceptional diffraction engineering capabilities with very high efficiencies. Herein, to facilitate cross-polarization coupling, we introduce a tilted dogbone meta-atom, going beyond the popular vertical (loaded wire) or recently proposed horizontal (dipole) configurations used in common PCB MG manifestations at microwaves, strictly susceptible to either transverse electric (TE) or transverse magnetic (TM) fields, respectively. As shown, the anisotropy introduced by the in-plane rotation of the dogbones, integrated into the MG analytical model in the form of a rotated dipole line, serves as an additional degree of freedom that can be leveraged to nonlocally manipulate the polarization and trajectory of the incident fields. Verified experimentally, the resultant semianalytical synthesis framework enables valuable physical insights, opening the door to integration of efficient anisotropic MGs in applications requiring both polarization and wavefront control, such as satellite, radar and advanced antenna systems.

Motion and deformation analysis of cardiac magnetic resonance (CMR) imaging videos is crucial for assessing myocardial strain of patients with abnormal heart functions. Recent advances in deep learning-based image registration algorithms have shown promising results in predicting motion fields from routinely acquired CMR sequences. However, their accuracy often diminishes in regions with subtle appearance change, with errors propagating over time. Advanced imaging techniques, such as displacement encoding with stimulated echoes (DENSE) CMR, offer highly accurate and reproducible motion data but require additional image acquisition, which poses challenges in busy clinical flows. In this paper, we introduce a novel Latent Motion Diffusion model (LaMoD) to predict highly accurate DENSE motions from standard CMR videos. More specifically, our method first employs an encoder from a pre-trained registration network that learns latent motion features (also considered as deformation-based shape features) from image sequences. Supervised by the ground-truth motion provided by DENSE, LaMoD then leverages a probabilistic latent diffusion model to reconstruct accurate motion from these extracted features. Experimental results demonstrate that our proposed method, LaMoD, significantly improves the accuracy of motion analysis in standard CMR images; hence improving myocardial strain analysis in clinical settings for cardiac patients. Our code will be publicly available on upon acceptance.

All strings with low mutual information with the halting sequence will have flat Kolmogorov Structure Functions, in the context of Algorithmic Statistics. Assuming the Independence Postulate, strings with non-negligible information with the halting sequence are purely mathematical constructions, and cannot be found in nature. Thus Algorithmic Statistics does not study strings in the physical world. This leads to the general thesis that two part codes require limitations as shown in the Minimum Description Length Principle. We also discuss issues with set-restricted Kolmogorov Structure Functions.

Using Kolmogorov Game Derandomization, upper bounds of the Kolmogorov complexity of deterministic winning players against deterministic environments can be proved. This paper gives improved upper bounds of the Kolmogorov complexity of such players. This paper also generalizes this result to probabilistic games. This applies to computable, lower computable, and uncomputable environments. We characterize the classic even-odds game and then generalize these results to time bounded players and also to all zero-sum repeated games. We characterize partial game derandomization. But first, we start with an illustrative example of game derandomization, taking place on the island of Crete.

Given only aggregate choice data and limited information about how menus are distributed across the population, we describe what can be inferred robustly about the distribution of preferences (or more general decision rules). We strengthen and generalize existing results on such identification and provide an alternative analytical approach to study the problem. We show further that our model and results are applicable, after suitable reinterpretation, to other contexts. One application is to the robust identification of the distribution of updating rules given only the population distribution of beliefs and limited information about heterogeneous information sources.

The brightest steady sources of radiation in the universe, active galactic nuclei (AGN), are powered by gas accretion onto a central supermassive black hole (SMBH). The large sizes and accretion rates implicated in AGN accretion disks are expected to lead to gravitational instability and fragmentation, effectively cutting off mass inflow to the SMBH. Radiative feedback from disk-embedded stars has been invoked to yield marginally stable, steady-state solutions in the outer disks. Here, we examine the consequences of this star formation with a semi-analytical model in which stellar-mass black hole (sBH) remnants in the disk provide an additional source of stabilizing radiative feedback. Assuming star formation seeds the embedded sBH population, we model the time-evolving feedback from both stars and the growing population of accreting sBHs. We find that in the outer disk, the luminosity of the sBHs quickly dominates that of their parent stars. However, because sBHs consume less gas than stars to stabilize the disk, the presence of the sBHs enhances the mass flux to the inner disk. As a result, star formation persists over the lifetime of the AGN, damped in the outer disk, but amplified in a narrow ring in the inner disk. Heating from the embedded sBHs significantly modifies the disk's temperature profile and hardens its spectral energy distribution, and direct emission from the sBHs adds a new hard X ray component, resembling a Compton reflection "hump"., Comment: 21 pages, 15 figures

We discuss general one and two-loops banana diagrams with arbitrary masses on the de Sitter spacetime by using direct methods of dS quantum field theory in the dimensional regularization approach. In the one-loop case we also compute the effective potential for an $O(N)$ model in $d=4$ dimension as an explicit function of the cosmological constant $\Lambda$, both exactly and perturbatively up to order $\Lambda$. For the two-loop case we show that the calculation is made easy thanks to a remarkable Kallen-Lehmann formula that has been in the literature for a while. We discuss the divergent cases at d=3 using a contiguity formula for generalized hypergeometric functions and we extract the dominant term at d=4 proving a general formula to deal with a divergent hypergeometric series.

We discuss general one and two-loop banana diagrams and one-loop diagrams with external lines with arbitrary masses on the anti de Sitter spacetime by using methods of AdS quantum field theory in the dimensional regularization approach. The banana diagrams explicitly computed in this paper are indeed the necessary ingredients for the evaluation of the two-loop effective potential of the Standard Model and can be used to extend the flat space results in in presence of a negative cosmological constant. In the one-loop case we also compute the effective potential for an $O(N)$ model in $d=4$ dimension as an explicit function of the cosmological constant $\Lambda$, both exactly and perturbatively up to order $\Lambda$. In the two-loop case we show the explicit calculation is possible thanks to a remarkable discrete K\"all\'en-Lehmann formula which we found and proved sometimes ago and whose domain of applicability we extend in the present paper., Comment: New introduction. Extended appendix A and new appendix B extending the Kallen-Lehmann formula generalizing our original formula and other subsequent results. Extended Section 5 including a general formula for the bubble in any background geometry. New section 6 with some comments about the relation among bulk diagrams and Witten diagrams. New section 8 including the tadpole and the sunset

In this report, we introduce the Gemini 1.5 family of models, representing the next generation of highly compute-efficient multimodal models capable of recalling and reasoning over fine-grained information from millions of tokens of context, including multiple long documents and hours of video and audio. The family includes two new models: (1) an updated Gemini 1.5 Pro, which exceeds the February version on the great majority of capabilities and benchmarks; (2) Gemini 1.5 Flash, a more lightweight variant designed for efficiency with minimal regression in quality. Gemini 1.5 models achieve near-perfect recall on long-context retrieval tasks across modalities, improve the state-of-the-art in long-document QA, long-video QA and long-context ASR, and match or surpass Gemini 1.0 Ultra's state-of-the-art performance across a broad set of benchmarks. Studying the limits of Gemini 1.5's long-context ability, we find continued improvement in next-token prediction and near-perfect retrieval (>99%) up to at least 10M tokens, a generational leap over existing models such as Claude 3.0 (200k) and GPT-4 Turbo (128k). Finally, we highlight real-world use cases, such as Gemini 1.5 collaborating with professionals on completing their tasks achieving 26 to 75% time savings across 10 different job categories, as well as surprising new capabilities of large language models at the frontier; when given a grammar manual for Kalamang, a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person who learned from the same content.

We study the inventory placement problem of splitting $Q$ units of a single item across warehouses, in advance of a downstream online matching problem that represents the dynamic fulfillment decisions of an e-commerce retailer. This is a challenging problem both in theory, because the downstream matching problem itself is computationally hard, and in practice, because the fulfillment team is constantly updating its algorithm and the placement team cannot directly evaluate how a placement decision would perform. We compare the performance of three placement procedures based on optimizing surrogate functions that have been studied and applied: Offline, Myopic, and Fluid placement. On the theory side, we show that optimizing inventory placement for the Offline surrogate leads to a $(1-(1-1/d)^d)/2$-approximation for the joint placement and fulfillment problem. We assume $d$ is an upper bound on how many warehouses can serve any demand location and that stochastic arrivals satisfy either temporal or spatial independence. The crux of our theoretical contribution is to use randomized rounding to derive a tight $(1-(1-1/d)^d)$-approximation for the integer programming problem of optimizing the Offline surrogate. We use statistical learning to show that rounding after optimizing a sample-average Offline surrogate, which is necessary due to the exponentially-sized support, does indeed have vanishing loss. On the experimental side, we extract real-world sequences of customer orders from publicly-available JD.com data and evaluate different combinations of placement and fulfillment procedures. Optimizing the Offline surrogate performs best overall, even compared to simulation procedures, corroborating our theory.

For a growing share of learners and workers in the United States, college is failing to live up to its economic mobility promise. The cost of college is rising, accompanied by mounting student debt, and many graduates are underemployed following college. Students face steep barriers to college enrollment and success, including time demands, access to housing and childcare, and transportation. These conditions have prompted many learners and workers to reconsider whether college is truly worth the expense. Higher education leaders are facing a moment of reckoning in which they must improve the economic returns of a college education. However, there is little clarity around which programs and initiatives best improve a student's earnings and employment later in their career. The dearth of information reflects, at least in part, the lack of attention and resources such programs have received from the majority of post-secondary institutions. This white paper puts "college-to-jobs" programs in focus, making the case that they should be a priority for future policy, investment, and research. It maps the field of initiatives that smooth transitions for college students to the workforce, identifying 13 "interventions" that have been deployed to improve college students' economic outcomes. The Playbook provides answers to a crucial question at a time of inflection for postsecondary education: what can we do to launch more college students onto successful career trajectories? [This report was co-published by the Project on Workforce and was funded by the Capital One Foundation.]

This paper presents a multimodal deep learning framework that utilizes advanced image techniques to improve the performance of clinical analysis heavily dependent on routinely acquired standard images. More specifically, we develop a joint learning network that for the first time leverages the accuracy and reproducibility of myocardial strains obtained from Displacement Encoding with Stimulated Echo (DENSE) to guide the analysis of cine cardiac magnetic resonance (CMR) imaging in late mechanical activation (LMA) detection. An image registration network is utilized to acquire the knowledge of cardiac motions, an important feature estimator of strain values, from standard cine CMRs. Our framework consists of two major components: (i) a DENSE-supervised strain network leveraging latent motion features learned from a registration network to predict myocardial strains; and (ii) a LMA network taking advantage of the predicted strain for effective LMA detection. Experimental results show that our proposed work substantially improves the performance of strain analysis and LMA detection from cine CMR images, aligning more closely with the achievements of DENSE.

Building high-fidelity quantum computers requires efficient methods for the characterization of gate errors that provide actionable information that may be fed back into engineering efforts. Extraction of realistic error models is also critical to accurate simulation and design of quantum circuits, including those used in quantum error correction. We provide a method for determining the parameters corresponding to decoherence in a model gateset. We demonstrate that this method is robust to SPAM and pulse area errors, and describe a simple and intuitive method for interpreting the quality and precision of the resulting error model.

Generative AI image models may inadvertently generate problematic representations of people. Past research has noted that millions of users engage daily across the world with these models and that the models, including through problematic representations of people, have the potential to compound and accelerate real-world discrimination and other harms (Bianchi et al, 2023). In this paper, we focus on addressing the generation of problematic associations between demographic groups and semantic concepts that may reflect and reinforce negative narratives embedded in social data. Building on sociological literature (Blumer, 1958) and mapping representations to model behaviors, we have developed a taxonomy to study problematic associations in image generation models. We explore the effectiveness of fine tuning at the model level as a method to address these associations, identifying a potential reduction in visual quality as a limitation of traditional fine tuning. We also propose a new methodology with twice-human-in-the-loop (T-HITL) that promises improvements in both reducing problematic associations and also maintaining visual quality. We demonstrate the effectiveness of T-HITL by providing evidence of three problematic associations addressed by T-HITL at the model level. Our contributions to scholarship are two-fold. By defining problematic associations in the context of machine learning models and generative AI, we introduce a conceptual and technical taxonomy for addressing some of these associations. Finally, we provide a method, T-HITL, that addresses these associations and simultaneously maintains visual quality of image model generations. This mitigation need not be a tradeoff, but rather an enhancement., Comment: 11 pages, 8 figures

We introduce a method to generate 3D scenes that are disentangled into their component objects. This disentanglement is unsupervised, relying only on the knowledge of a large pretrained text-to-image model. Our key insight is that objects can be discovered by finding parts of a 3D scene that, when rearranged spatially, still produce valid configurations of the same scene. Concretely, our method jointly optimizes multiple NeRFs from scratch - each representing its own object - along with a set of layouts that composite these objects into scenes. We then encourage these composited scenes to be in-distribution according to the image generator. We show that despite its simplicity, our approach successfully generates 3D scenes decomposed into individual objects, enabling new capabilities in text-to-3D content creation. For results and an interactive demo, see our project page at https://dave.ml/layoutlearning/

Polaritons are quasi-particles describing the coupling between a photon and a material excitation, which can carry large momentum and confine electromagnetic fields to small dimensions, enabling strong light-matter interactions. In the visible (VIS) to near-infrared (NIR) spectral ranges, the intraband response of metals gives rise to surface-plasmon-polaritons (SPPs), which have practically governed polaritonic response and its utilization in nanophotonics. Recently, the concept of interband-based VIS/NIR in-plane exciton polaritons has been introduced in two-dimensional materials, such as transition-metal-dichalcogenides (TMDs), thus providing an excitonic alternative to plasmonic systems. Here, we compare the properties of such in-plane exciton polaritons supported by monolayer TMDs to the equivalent configuration of SPPs supported by thin metallic films, known as the short-range-SPPs (SRSPPs). Taking into account both excitonic and plasmonic nonlocal corrections, which play a major role in large momentum modes, we find that in-plane exciton polaritons provide confinement factors that are an order of magnitude larger than those of SRSPPs, and with six times lower propagation losses. In addition, we show that unlike SPPs, in-plane exciton polaritons are coupled to the TMD's valley degree of freedom, leading to directional propagation that depends on the exciton's valley. These properties make in-plane exciton polaritons promising candidates for VIS/NIR nanophotonics and strong light-matter interaction.

An overwhelming majority of quantum (pure and mixed) states, when undertaking a POVM measurement, will result in a classical probability with no algorithmic information. Thus most quantum states produce white noise when measured. Furthermore most non-pointer states, when undergoing the decoherence process, will produce white noise. These results can be seen as consequences of the vastness of Hilbert spaces.

Recent large language models (LLMs) offer the potential to support public health monitoring by facilitating health disclosure through open-ended conversations but rarely preserve the knowledge gained about individuals across repeated interactions. Augmenting LLMs with long-term memory (LTM) presents an opportunity to improve engagement and self-disclosure, but we lack an understanding of how LTM impacts people's interaction with LLM-driven chatbots in public health interventions. We examine the case of CareCall -- an LLM-driven voice chatbot with LTM -- through the analysis of 1,252 call logs and interviews with nine users. We found that LTM enhanced health disclosure and fostered positive perceptions of the chatbot by offering familiarity. However, we also observed challenges in promoting self-disclosure through LTM, particularly around addressing chronic health conditions and privacy concerns. We discuss considerations for LTM integration in LLM-driven chatbots for public health monitoring, including carefully deciding what topics need to be remembered in light of public health goals., Comment: Accepted to ACM CHI 2024 as a full paper

Due to M\"{u}ller's theorem, the Kolmogorov complexity of a string was shown to be equal to its quantum Kolmogorov complexity. Thus there are no benefits to using quantum mechanics to compress classical information. The quantitative amount of information in classical sources is invariant to the physical model used. These consequences make this theorem arguably the most important result in the intersection of algorithmic information theory and physics. The original proof is quite extensive. This paper contains two simple proofs of this theorem. This paper also contains new bounds for quantum Kolmogorov complexity with error.

Assembling and maintaining large arrays of individually addressable atoms is a key requirement for continued scaling of neutral-atom-based quantum computers and simulators. In this work, we demonstrate a new paradigm for assembly of atomic arrays, based on a synergistic combination of optical tweezers and cavity-enhanced optical lattices, and the incremental filling of a target array from a repetitively filled reservoir. In this protocol, the tweezers provide microscopic rearrangement of atoms, while the cavity-enhanced lattices enable the creation of large numbers of optical traps with sufficient depth for rapid low-loss imaging of atoms. We apply this protocol to demonstrate near-deterministic filling (99% per-site occupancy) of 1225-site arrays of optical traps. Because the reservoir is repeatedly filled with fresh atoms, the array can be maintained in a filled state indefinitely. We anticipate that this protocol will be compatible with mid-circuit reloading of atoms into a quantum processor, which will be a key capability for running large-scale error-corrected quantum computations whose durations exceed the lifetime of a single atom in the system., Comment: 8 pages, 6 figures

We derive basic differential geometric formulae for surfaces in hyperbolic space represented as envelopes of horospheres. The dual notion of parallel hypersurfaces is also studied. The representation is applied to prove existence and regularity theorems for Weingarten surfaces in H^3, which satisfy (1-a)K = a(2-H), for an a < 0, and have a specified boundary curve at infinity. These surfaces are shown to be closely connected to conformal mappings of domains in S^2 into the unit disk and provide Riemannian interpretations for some conformal invariants associated to such mappings. This paper was originally written in 1984, before I learned to use TeX, and was typed by one of the secretaries in the Princeton Math Department. It was more or less, my first original work after my dissertation. For some reason, I was not able to get this paper published in a timely manner. The results and perspective in this paper have proved to be useful to a variety of people, some of whom asked me to render the article into TeX and post it to the arXiv. I had been seriously thinking about doing this, when Martin Bridgemen sent me a transcription of my original article into TeX. I am extremely grateful to him for the effort he has put into this project. The paper is now formatted in a more or less modern AMS-article style, but for lots of additional punctuation, a few corrections and some minor stylistic changes, the content has been largely reproduced as it originally was. Remarks about the 'state-of-the-art' in hyperbolic geometry are obviously way out of date, as there has been enormous progress in many aspects of this still rich subject., Comment: I am enormously grateful to Martin and the community of mathematicians who have let me know, over the years, that this work was of some use to them

Trapped ions for quantum information processing has been an area of intense study due to the extraordinarily high fidelity operations that have been reported experimentally. Specifically, barium trapped ions have been shown to have exceptional state-preparation and measurement (SPAM) fidelities. The $^{133}\mathrm{Ba}^+$ ($I = 1/2$) isotope in particular is a promising candidate for large-scale quantum computing experiments. However, a major pitfall with this isotope is that it is radioactive and is thus generally used in microgram quantities to satisfy safety regulations. We describe a new method for creating microgram barium chloride ($\mathrm{BaCl}_2$) ablation targets for use in trapped ion experiments and compare our procedure to previous methods. We outline two recipes for fabrication of ablation targets that increase the production of neutral atoms for isotope-selective loading of barium ions. We show that heat-treatment of the ablation targets greatly increases the consistency at which neutral atoms can be produced and we characterize the uniformity of these targets using trap-independent techniques such as energy dispersive x-ray spectroscopy (EDS) and neutral fluorescence collection. Our comparison between fabrication techniques and demonstration of consistent neutral fluorescence paves a path towards reliable loading of $^{133}\mathrm{Ba}^+$ in surface traps and opens opportunities for scalable quantum computing with this isotope.

This paper continues the analysis of the scattering problem for a network of open wave-guides started in [arXiv:2302.04353, arXiv:2310.05816]. In this part we present explicit, physically motivated radiation conditions that ensure uniqueness of the solution to the scattering problem. These conditions stem from a 2000 paper of A. Vasy on 3-body Schrodinger operators; we discuss closely related conditions from a 1994 paper of H. Isozaki. Vasy's paper also proves the existence of the limiting absorption resolvents, and that the limiting solutions satisfy the radiation conditions. The statements of these results require a calculus of pseudodifferential operators, called the 3-body scattering calculus, which is briefly introduced here. We show that the solutions to the model problem obtained in arXiv:2302.04353 satisfy these radiation conditions, which makes it possible to prove uniqueness, and therefore existence, for the system of Fredholm integral equations introduced in that paper.