Search

When studying policy interventions, researchers are often interested in two related goals: i) learning for which types of individuals the program has the largest effects (heterogeneity) and ii) understanding whether those patterns of treatment effects have predictive power across environments (generalizability). To that end, we develop a framework to learn from the data how to partition observations into groups of individual and environmental characteristics whose effects are generalizable for others - a set of generalizable archetypes. Our view is that implicit in the task of archetypal discovery is detecting those contexts where effects do not generalize and where researchers should collect more evidence before drawing inference on treatment effects. We introduce a method that jointly estimates when and how a prediction can be formed and when, instead, researchers should admit ignorance and elicit further evidence before making predictions. We provide both a decision-theoretic and Bayesian foundation of our procedure. We derive finite-sample (frequentist) regret guarantees, asymptotic theory for inference, and discuss computational properties. We illustrate the benefits of our procedure over existing alternatives that would fail to admit ignorance and force pooling across all units by re-analyzing a multifaceted program targeted towards the poor across six different countries.

We derive and simulate a mathematical model for mechanotransduction related to the Rho GTPase signalling pathway. The model addresses the bidirectional coupling between signalling processes and cell mechanics. A numerical method based on bulk-surface finite elements is proposed for the approximation of the coupled system of nonlinear reaction-diffusion equations, defined inside the cell and on the cell membrane, and the equations of elasticity. Our simulation results illustrate novel emergent features such as the strong dependence of the dynamics on cell shape, a threshold-like response to changes in substrate stiffness, and the fact that coupling mechanics and signalling can lead to the robustness of cell deformation to larger changes in substrate stiffness, ensuring mechanical homeostasis in agreement with experiments., Comment: Code available on request

Dense spin ensembles in solids present a natural platform for studying quantum many-body dynamics. Multiple-pulse coherent control can be used to manipulate the magnetic dipolar interaction between the spins to engineer their dynamics. Here, we investigate the performance of a series of well-known pulse sequences that aim to suppress inter-spin dipolar couplings. We use a combination of numerical simulations and solid-state nuclear magnetic resonance (NMR) experiments on adamantane to evaluate and compare sequence performance. We study the role of sequence parameters like inter-pulse delays and resonance offsets. Disagreements between experiments and theory are typically explained by the presence of control errors and experimental non-idealities. The simulations allow us to explore the influence of factors such as finite pulse widths, rotation errors, and phase transient errors. We also investigate the role of local disorder and establish that it is, perhaps unsurprisingly, a distinguishing factor in the decoupling efficiency of spectroscopic sequences (that preserve Hamiltonian terms proportional to $S_z$) and time-suspension sequences (which refocus all terms in the internal Hamiltonian). We discuss our findings in the context of previously known analytical results from Average Hamiltonian Theory. Finally, we explore the ability of time-suspension sequences to protect multi-spin correlations in the system., Comment: 18 pages, 16 figures, 2 tables

Social and economic networks are often multiplexed, meaning that people are connected by different types of relationships -- such as borrowing goods and giving advice. We make three contributions to the study of multiplexing. First, we document empirical multiplexing patterns in Indian village data: relationships such as socializing, advising, helping, and lending are correlated but distinct, while commonly used proxies for networks based on ethnicity and geography are nearly uncorrelated with actual relationships. Second, we examine how these layers and their overlap affect information diffusion in a field experiment. The advice network is the best predictor of diffusion, but combining layers improves predictions further. Villages with greater overlap between layers (more multiplexing) experience less overall diffusion. This leads to our third contribution: developing a model and theoretical results about diffusion in multiplex networks. Multiplexing slows the spread of simple contagions, such as diseases or basic information, but can either impede or enhance the spread of complex contagions, such as new technologies, depending on their virality. Finally, we identify differences in multiplexing by gender and connectedness. These have implications for inequality in diffusion-mediated outcomes such as access to information and adherence to norms.

This paper explores rotation estimation from the perspective of special unitary matrices. First, multiple solutions to Wahba's problem are derived through special unitary matrices, providing linear constraints on quaternion rotation parameters. Next, from these constraints, closed-form solutions to the problem are presented for minimal cases. Finally, motivated by these results, we investigate new representations for learning rotations in neural networks. Numerous experiments validate the proposed methods., Comment: 18 pages; Correction for original Wahba problem solution; added connection with Hopf fibration

Two-dimensional (2D) transition metal di-chalcogenide layers with high electrical conductivity and spin-orbit coupling (SOC) can find huge potential in spintronic devices. With limited success of 2D spin Hall material development, we demonstrate vanadium (V) substitutionally doped monolayer MoS2 (VMS) as a potential spin Hall material having tunable electrical conductivity, SOC strength, and room temperature magnetism. Systematic enhancement in the electrical conductivity is observed with the extent of V doping, where it is enhanced from ~0.3 S/m of MoS2 to ~100000 S/m upon doping to the level of 9 atomic%. Ferromagnetic resonance (FMR) based spin-pumping experiments indicate the spin transport across the junction of permalloy (Py) and VMS. Spin-torque FMR measurements demonstrate the suggesting latter's potential as a spin-orbit torque layer in 2D spintronic devices.

The observation of a Hall effect, a finite transverse voltage induced by a longitudinal current, usually requires the breaking of time-reversal symmetry, for example through the application of an external magnetic field or the presence of long range magnetic order in a sample. Recently it was suggested that under certain symmetry conditions, the presence of finite Berry curvatures in the band structure of a system with time-reversal symmetry but without inversion symmetry can give rise to a nonlinear Hall effect in the presence of a probe current. In order to observe the nonlinear Hall effect, one requires a finite component of a so-called Berry dipole along the direction of the probe current. We report here measurements of the nonlinear Hall effect in two-dimensional electron gases fabricated on the surface of KTaO$_3$ with different surface crystal orientations as a function of the probe current, a transverse electric field and back gate voltage. For all three crystal orientations, the transverse electric field modifies the nonlinear Hall effect. We discuss our results in the context of the current understanding of the nonlinear Hall effect as well as potential experimental artifacts that may give rise to the same effects.

In this paper, we study the trajectories of massive and massless particles in four dimensional static and spherically symmetric black holes in dRGT massive gravity theory via phase-plane analysis and point out several novel features. In particular, we show the existence of a static sphere, a finite radial distance outside the black holes in these theories, where a massive particle can be at rest, as seen by an asymptotic zero angular momentum observer. Topological arguments show that the stable and unstable static spheres, which come in pairs, have opposite charges. In the presence of angular momentum, we first study the behaviour of massless particles and find the presence of stable and unstable photon spheres in both neutral and charged black holes. Subsequently, we study the motion of massive test particles around these black holes, and find one pair of stable and unstable time-like circular orbits (TCOs), such that the stable and unstable TCO's are disconnected in certain regions. Computing the angular velocity $\Omega_{\text{\tiny CO}}$ of the TCOs, measured by a static observer at rest, shows the unusual nature of its monotonic increase with the radius of TCO, near the location of stable photon sphere. This confirms the existence of Aschenbach effect for spherically symmetric black holes in massive gravity, which was only found to exist in rapidly spinning black holes, with the only other exception being the rare example of gravity coupled to quasi-topological electromagnetism., Comment: 27 pages, 16 figures

For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion equation with a first-order forcing term capturing the combined effects of ambient and fire-induced wind. The fire-induced wind is introduced by way of a piecewise continuous function that ``switches'' in space. We demonstrate that, in the case of a spatially dependent wind, traveling wave solutions corresponding to fire fronts exist for a continuum of wave speeds rather than for a single unique speed. Using geometric methods, we determine the range of allowable speeds, refine this range to only those fronts which will persist in nature, and develop a selection mechanism to identify the specific wind configuration corresponding to the most stable solution. For this spectrally preferred front, we find that the wind switch occurs ahead of the fireline in a manner consistent with the physics of air entrainment. Even when the wind is not coupled to the temperature and is instead imposed as an external forcing, the conditions on the existence and stability of front solutions force the wind term in to a configuration reflective of physical reality.

Quasiparticle relaxation in pure superconductors is thought to be determined by the intrinsic inelastic scattering rate in the material. In certain applications, i.e. superconducting qubits and circuits, excess quasiparticles exist at densities far beyond the thermal equilibrium level, potentially leading to dephasing and energy loss. In order to engineer superconductors with shorter overall quasiparticle lifetimes, we consider the impact of a proximity layer on the transport of quasiparticles in a superconductor. We find that a normal metal layer can be used to significantly increase the relaxation rate of quasiparticles in a superconductor, as seen by a large reduction in the quasiparticle charge imbalance in a fully proximitized Cu/Al bilayer wire. The mechanism for this effect may be useful for preventing quasiparticle poisoning of qubits using carefully chosen proximity bilayers consisting of clean superconductors and disordered normal metals., Comment: 8 pages, 6 figures

Feature-mapping methods for topology optimization (FMTO) facilitate direct geometry extraction by leveraging high-level geometric descriptions of the designs. However, FMTO often relies solely on Boolean unions, which can restrict the design space. This work proposes an FMTO framework leveraging an expanded set of Boolean operations, namely, union, intersection, and subtraction. The optimization process entails determining the primitives and the optimal Boolean operation tree. In particular, the framework leverages a recently proposed unified Boolean operation approach. This approach presents a continuous and differentiable function that interpolates the Boolean operations, enabling gradient-based optimization. The proposed methodology is agnostic to the specific primitive parametrization and is showcased through various numerical examples., Comment: Submitted to Structural and Multidisciplinary Optimization

Multiterminal Josephson junctions (MTJJs), devices in which a normal metal is in contact with three or more superconducting leads, have been proposed as artificial analogs of topological crystals. The topological nature of MTJJs manifests as a modulation of the quasiparticle density of states (DOS) in the normal metal that may be probed by tunneling measurements. We show that one can reveal this modulation by measuring the resistance of diffusive MTJJs with normal contacts, which shows rich structure as a function of the phase differences $\{\phi_i \}$. Our approach demonstrates a simple yet powerful technique for exploring topological effects in MTJJs., Comment: 6 pages, 4 figures

We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type problems on an evolving hypersurface. Our results are new even in the setting where there is no domain evolution. The models are of particular relevance to a number of applications in cell biology. The analysis utilises $L^\infty$-estimates in the manner of De Giorgi iterations and other technical tools, all in an evolving setting. We also report on numerical simulations.

This study presents a novel physics-informed neural network (PINN) framework for modeling poroelasticity in heterogeneous media with material interfaces. The approach introduces a composite neural network (CoNN) where separate neural networks predict displacement and pressure variables for each material. While sharing identical activation functions, these networks are independently trained for all other parameters. To address challenges posed by heterogeneous material interfaces, the CoNN is integrated with the Interface-PINNs or I-PINNs framework (Sarma et al. 2024, https://dx.doi.org/10.1016/j.cma.2024.117135), allowing different activation functions across material interfaces. This ensures accurate approximation of discontinuous solution fields and gradients. Performance and accuracy of this combined architecture were evaluated against the conventional PINNs approach, a single neural network (SNN) architecture, and the eXtended PINNs (XPINNs) framework through two one-dimensional benchmark examples with discontinuous material properties. The results show that the proposed CoNN with I-PINNs architecture achieves an RMSE that is two orders of magnitude better than the conventional PINNs approach and is at least 40 times faster than the SNN framework. Compared to XPINNs, the proposed method achieves an RMSE at least one order of magnitude better and is 40% faster., Comment: 34 pages, 12 figures, 3 tables

Topology Optimization (TO) holds the promise of designing next-generation compact and efficient photonic components. However, ensuring the optimized designs comply with fabrication constraints imposed by semiconductor foundries remains a challenge. This work presents a TO framework that guarantees designs satisfy fabrication criteria, particularly minimum feature size and separation. Leveraging recent advancements in machine learning and feature mapping methods, our approach constructs components by transforming shapes from a predefined library, simplifying constraint enforcement. Specifically, we introduce a Convo-implicit Variational Autoencoder to encode the discrete shape library into a differentiable space, enabling gradient-based optimization. The efficacy of our framework is demonstrated through the design of several common photonic components., Comment: Submitted to Engineering with Computers

We consider the control of discrete-time linear dynamical systems using sparse inputs where we limit the number of active actuators at every time step. We develop an algorithm for determining a sparse actuator schedule that ensures the existence of a sparse control input sequence, following the schedule, that takes the system from any given initial state to any desired final state. Since such an actuator schedule is not unique, we look for a schedule that minimizes the energy of sparse inputs. For this, we optimize the trace of the inverse of the resulting controllability Gramian, which is an approximate measure of the average energy of the inputs. We present a greedy algorithm along with its theoretical guarantees. Finally, we empirically show that our greedy algorithm ensures the controllability of the linear system with a small number of active actuators per time step without a significant average energy expenditure compared to the fully actuated system.

The stable unit treatment value assumption states that the outcome of an individual is not affected by the treatment statuses of others, however in many real world applications, treatments can have an effect on many others beyond the immediately treated. Interference can generically be thought of as mediated through some network structure. In many empirically relevant situations however, complete network data (required to adjust for these spillover effects) are too costly or logistically infeasible to collect. Partially or indirectly observed network data (e.g., subsamples, aggregated relational data (ARD), egocentric sampling, or respondent-driven sampling) reduce the logistical and financial burden of collecting network data, but the statistical properties of treatment effect adjustments from these design strategies are only beginning to be explored. In this paper, we present a framework for the estimation and inference of treatment effect adjustments using partial network data through the lens of structural causal models. We also illustrate procedures to assign treatments using only partial network data, with the goal of either minimizing estimator variance or optimally seeding. We derive single network asymptotic results applicable to a variety of choices for an underlying graph model. We validate our approach using simulated experiments on observed graphs with applications to information diffusion in India and Malawi.

We present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs (Sarma et al.; https://dx.doi.org/10.2139/ssrn.4766623), which involves domain decomposition and assignment of different predefined activation functions to the neural networks in each subdomain across a sharp interface, while keeping all other parameters of the neural networks identical. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks. This makes the AdaI-PINNs framework fully automated without requiring preset activation functions. Comparative studies on one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs outperform I-PINNs, reducing computational costs by 2-6 times while producing similar or better accuracy., Comment: 17 pages, 8 figures, 6 tables

Josephson junctions supply the nonlinear inductance element in superconducting qubits. In the widely used transmon configuration, where the junction is shunted by a large capacitor, the low charging energy minimizes the sensitivity of the qubit to charge noise while maintaining the necessary anharmonicity to qubit states. We report here low-frequency transport measurements on small standalone junctions and identically fabricated capacitively-shunted junctions that show two distinct features normally attributed to small capacitance junctions near zero bias: reduced switching currents and prominent finite resistance associated with phase diffusion in the current-voltage characteristic. Our transport data reveals the existence of phase fluctuations in transmons arising from intrinsic junction capacitance.

Generalized large language models (LLMs) such as GPT-4 may not provide specific answers to queries formulated by materials science researchers. These models may produce a high-level outline but lack the capacity to return detailed instructions on manufacturing and material properties of novel alloys. Enhancing a smaller model with specialized domain knowledge may provide an advantage over large language models which cannot be retrained quickly enough to keep up with the rapid pace of research in metal additive manufacturing (AM). We introduce "AMGPT," a specialized LLM text generator designed for metal AM queries. The goal of AMGPT is to assist researchers and users in navigating the extensive corpus of literature in AM. Instead of training from scratch, we employ a pre-trained Llama2-7B model from Hugging Face in a Retrieval-Augmented Generation (RAG) setup, utilizing it to dynamically incorporate information from $\sim$50 AM papers and textbooks in PDF format. Mathpix is used to convert these PDF documents into TeX format, facilitating their integration into the RAG pipeline managed by LlamaIndex. Expert evaluations of this project highlight that specific embeddings from the RAG setup accelerate response times and maintain coherence in the generated text., Comment: 54 pages, 4 figures

This paper presents a new algorithm to estimate absolute camera pose given an axis of the camera's rotation matrix. Current algorithms solve the problem via algebraic solutions on limited input domains. This paper shows that the problem can be solved efficiently by finding the intersection points of a hyperbola and the unit circle. The solution can flexibly accommodate combinations of point and line features in minimal and overconstrained configurations. In addition, the two special cases of planar and minimal configurations are identified to yield simpler closed-form solutions. Extensive experiments validate the approach., Comment: Updated proof of rank bound in minimal configurations; fixed typos. 10 pages

The significant advancements in perovskite solar cell (PSC) research and development have reignited optimism for the practicality of solar energy. A deeper comprehension of the fundamental mechanisms is essential for enhancing the current solar technology. Impedance spectroscopy (IS) characterization, in conjunction with other analytical methods, stands out as the primary approach for gaining insights into the internal workings of solar cells. The continuous analysis and refinement of electrochemical spectroscopy data for PSCs have unveiled intricate operational details. Despite the ongoing improvements, the absence of a centralized repository for this information poses challenges for tracking progress effectively. This review paper aims to consolidate the physical phenomena behind the development of PSC research, aiming to establish a comprehensive knowledge base on impedance plots, equivalent circuits, and related processes.

Cellular structures found in nature exhibit remarkable properties such as high strength, high energy absorption, excellent thermal/acoustic insulation, and fluid transfusion. Many of these structures are Voronoi-like; therefore researchers have proposed Voronoi multi-scale designs for a wide variety of engineering applications. However, designing such structures can be computationally prohibitive due to the multi-scale nature of the underlying analysis and optimization. In this work, we propose the use of a neural network (NN) to carry out efficient topology optimization (TO) of multi-scale Voronoi structures. The NN is first trained using Voronoi parameters (cell site locations, thickness, orientation, and anisotropy) to predict the homogenized constitutive properties. This network is then integrated into a conventional TO framework to minimize structural compliance subject to a volume constraint. Special considerations are given for ensuring positive definiteness of the constitutive matrix and promoting macroscale connectivity. Several numerical examples are provided to showcase the proposed method., Comment: Submitted to Engineering with Computers

We study circular orbits of charged particles in spherically symmetric AdS black holes in Gauss-Bonnet gravity in arbitrary dimensions, and their limiting ISCOs (innermost stable circular orbits). The dual interpretation is in terms of certain conformal field theory (CFT) operators, whose anomalous dimensions can be extracted from the binding energy of charged probes in the bulk, in a large radius limit. The charge to mass ratio of particles in the black hole background is found to increase with the Gauss-Bonnet coupling parameter $\widetilde{\alpha}$, consistent with the Weak Gravity Conjecture (WGC) bound known for self-repulsive particles. The radius of the ISCOs decreases with $\widetilde{\alpha}$, existing until the limit set by the WGC bound., Comment: 14 pages, 2 figures

The dc current-voltage characteristics of small Josephson junctions reveal features that are not observed in larger junctions, in particular, a switch to the finite voltage state at current values much less than the expected critical current of the junction and a finite resistance in the nominally superconducting regime. Both phenomena are due to the increased sensitivity to noise associated with the small capacitance of the Josephson junction and have been extensively studied a few decades ago. Here I focus on the current bias dependence of the differential resistance of the junction at low current bias in the nominally superconducting regime, using a quantum Langevin equation approach that enables a physically transparent incorporation of the noise environment of the junction. A similar approach might be useful in modeling the sensitivity of superconducting qubits to noise in the microwave regime.

Many statistical analyses, in both observational data and randomized control trials, ask: how does the outcome of interest vary with combinations of observable covariates? How do various drug combinations affect health outcomes, or how does technology adoption depend on incentives and demographics? Our goal is to partition this factorial space into "pools" of covariate combinations where the outcome differs across the pools (but not within a pool). Existing approaches (i) search for a single "optimal" partition under assumptions about the association between covariates or (ii) sample from the entire set of possible partitions. Both these approaches ignore the reality that, especially with correlation structure in covariates, many ways to partition the covariate space may be statistically indistinguishable, despite very different implications for policy or science. We develop an alternative perspective, called Rashomon Partition Sets (RPSs). Each item in the RPS partitions the space of covariates using a tree-like geometry. RPSs incorporate all partitions that have posterior values near the maximum a posteriori partition, even if they offer substantively different explanations, and do so using a prior that makes no assumptions about associations between covariates. This prior is the $\ell_0$ prior, which we show is minimax optimal. Given the RPS we calculate the posterior of any measurable function of the feature effects vector on outcomes, conditional on being in the RPS. We also characterize approximation error relative to the entire posterior and provide bounds on the size of the RPS. Simulations demonstrate this framework allows for robust conclusions relative to conventional regularization techniques. We apply our method to three empirical settings: price effects on charitable giving, chromosomal structure (telomere length), and the introduction of microfinance.

In Linguistics, a grapheme is a written unit of a writing system corresponding to a phonological sound. In Natural Language Processing tasks, written language is analysed through two different mediums, word analysis, and character analysis. This paper focuses on a third approach, the analysis of graphemes. Graphemes have advantages over word and character analysis by being self-contained representations of phonetic sounds. Due to the nature of splitting a word into graphemes being based on complex, non-binary rules, the application of fuzzy logic would provide a suitable medium upon which to predict the number of graphemes in a word. This paper proposes the application of a Fuzzy Inference System to split words into their graphemes. This Fuzzy Inference System results in a correct prediction of the number of graphemes in a word 50.18% of the time, with 93.51% being within a margin of +- 1 from the correct classification. Given the variety in language, graphemes are tied with pronunciation and therefore can change depending on a regional accent/dialect, the +- 1 accuracy represents the impreciseness of grapheme classification when regional variances are accounted for. To give a baseline of comparison, a second method involving a recursive IPA mapping exercise using a pronunciation dictionary was developed to allow for comparisons to be made.

There has been intense recent interest in the two-dimensional electron gases (2DEGs) that form at the surfaces and interfaces of KTaO$_3$ (KTO), with the discovery of superconductivity at temperatures significantly higher than those of similar 2DEGs based on SrTiO$_3$ (STO). Like STO heterostructures, these KTO 2DEGs are formed by depositing an overlayer on top of appropriately prepared KTO surfaces. Some of these overlayers are magnetic, and the resulting 2DEGs show signatures of this magnetism, including hysteresis in the magnetoresistance (MR). Here we show that KTO 2DEGs fabricated by depositing AlO$_x$ on top of KTO also show hysteretic MR, indicative of long range magnetic order, even though the samples nominally contain no intrinsic magnetic elements. The hysteresis appears in both the transverse and longitudinal resistance in magnetic fields both perpendicular to and in the plane of the 2DEG. The hysteretic MR has different characteristic fields and shapes for surfaces of different crystal orientations, and vanishes above a few Kelvin. Density functional theory (DFT) calculations indicate that the magnetism likely arises from Ta$^{4+}$ local moments created in the presence of oxygen vacancies., Comment: 5 pages, 4 figures, supplemental materials. arXiv admin note: text overlap with arXiv:2209.10534

Network diffusion models are used to study things like disease transmission, information spread, and technology adoption. However, small amounts of mismeasurement are extremely likely in the networks constructed to operationalize these models. We show that estimates of diffusions are highly non-robust to this measurement error. First, we show that even when measurement error is vanishingly small, such that the share of missed links is close to zero, forecasts about the extent of diffusion will greatly underestimate the truth. Second, a small mismeasurement in the identity of the initial seed generates a large shift in the locations of expected diffusion path. We show that both of these results still hold when the vanishing measurement error is only local in nature. Such non-robustness in forecasting exists even under conditions where the basic reproductive number is consistently estimable. Possible solutions, such as estimating the measurement error or implementing widespread detection efforts, still face difficulties because the number of missed links are so small. Finally, we conduct Monte Carlo simulations on simulated networks, and real networks from three settings: travel data from the COVID-19 pandemic in the western US, a mobile phone marketing campaign in rural India, and in an insurance experiment in China.