cssi/SciSciGPT-SciSciNet huggingface dataset:
Quantum mechanics in non-inertial reference frames: Time-dependent rotations and loop prolongations

Abstract This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group , the generalization of the Galilei group to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of the Galilean line group that uphold the non-relativistic equivalence principle as well as representations that violate the equivalence principle. In these previous studies, the focus was on linear accelerations. In this paper, we undertake an extension of the formulation to include rotational accelerations. We show that the incorporation of rotational accelerations requires a class of loop prolongations of the Galilean line group and their unitary cocycle representations. We recover the centrifugal and Coriolis force effects from these loop representations. Loops are more general than groups in that their multiplication law need not be associative. Hence, our broad theoretical claim is that a Galilean quantum theory that holds in arbitrary non-inertial reference frames requires going beyond groups and group representations, the well-established framework for implementing symmetry transformations in quantum mechanics.
Measuring directionality in double-beta decay and neutrino interactions with kiloton-scale scintillation detectors

Large liquid-scintillator-based detectors have proven to be exceptionally effective for low energy neutrino measurements due to their good energy resolution and scalability to large volumes. The addition of directional information using Cherenkov light and fast timing would enhance the scientific reach of these detectors, especially for searches for neutrino-less double-beta decay. In this paper, we propose a technique for extracting particle direction using the difference in arrival times for Cherenkov and scintillation light, and evaluate several detector advances in timing, photodetector spectral response, and scintillator emission spectra that could be used to make direction reconstruction a reality in a kiloton-scale detector.
A Defeasible Calculus for Zetetic Agents

The study of defeasible reasoning unites epistemologists with those working in AI, in part, because both are interested in epistemic rationality. While it is traditionally thought to govern the formation and (with)holding of beliefs, epistemic rationality may also apply to the interrogative attitudes associated with our core epistemic practice of inquiry, such as wondering, investigating, and curiosity. Since generally intelligent systems should be capable of rational information-seeking behavior, AI researchers have a natural interest in the norms that govern interrogative attitudes. In this paper, we argue that these norms can be modeled via defeasible inferences to and from questions, i.e. erotetic inferences. We offer a sequent calculus that accommodates the unique features of ``erotetic defeat" and that exhibits the computational properties needed to inform the design of inquisitive systems. The calculus presented here is an improved version of the one presented in Millson (2019), extended to cover a new class of defeasible erotetic inferences.The study of defeasible reasoning unites epistemologists with those working in AI, in part, because both are interested in epistemic rationality. While it is traditionally thought to govern the formation and (with)holding of beliefs, epistemic rationality may also apply to the interrogative attitudes associated with our core epistemic practice of inquiry, such as wondering, investigating, and curiosity. Since generally intelligent systems should be capable of rational inquiry, AI researchers have a natural interest in the norms that govern interrogative attitudes. Following its recent coinage, we use the term “zetetic” to refer to the properties and norms associated with the capacity to inquire. In this paper, we argue that zetetic norms can be modeled via defeasible inferences to and from questions – a.k.a erotetic inferences – in a manner similar to the way norms of epistemic rationality are represented by defeasible inference rules. We offer a sequent calculus that accommodates the unique features of “erotetic defeat" and that exhibits the computational properties needed to inform the design of zetetic agents. The calculus presented here is an improved version of the one presented in (Millson, 2019), extended to cover a new class of defeasible erotetic inferences.
On Polar Magnetic Field Reversal and Surface Flux Transport During Solar Cycle 24

As each solar cycle progresses, remnant magnetic flux from active regions (ARs) migrates poleward to cancel the old-cycle polar field. We describe this polarity reversal process during Cycle 24 using four years (2010.33-2014.33) of line-of-sight magnetic field measurements from the Helioseismic and Magnetic Imager. The total flux associated with ARs reached maximum in the north in 2011, more than two years earlier than the south; the maximum is significantly weaker than Cycle 23. The process of polar field reversal is relatively slow, north-south asymmetric, and episodic. We estimate that the global axial dipole changed sign in 2013 October; the northern and southern polar fields (mean above 60° latitude) reversed in 2012 November and 2014 March, respectively, about 16 months apart. Notably, the poleward surges of flux in each hemisphere alternated in polarity, giving rise to multiple reversals in the north. We show that the surges of the trailing sunspot polarity tend to correspond to normal mean AR tilt, higher total AR flux, or slower mid-latitude near-surface meridional flow, while exceptions occur during low magnetic activity. In particular, the AR flux and the mid-latitude poleward flow speed exhibit a clear anti-correlation. We discuss how these features can be explained in a surface flux transport process that includes a field-dependent converging flow toward the ARs, a characteristic that may contribute to solar cycle variability.
A new bound on Hrushovski’s algorithm for computing the Galois group of a linear differential equation

The complexity of computing the Galois group of a linear differential equation is of general interest. In a recent work, Feng gave the first degree bound on Hrushovski’s algorithm for computing the...
A terminal velocity on the landscape: particle production near extra species loci in higher dimensions

We investigate particle production near extra species loci (ESL) in a higher dimensional field space and derive a speed limit in moduli space at weak coupling. This terminal velocity is set by the characteristic ESL-separation and the coupling of the extra degrees of freedom to the moduli, but it is independent of the moduli’s potential if the dimensionality of the field space is considerably larger than the dimensionality of the loci, D ≫ d. Once the terminal velocity is approached, particles are produced at a plethora of nearby ESLs, preventing a further increase in speed via their backreaction. It is possible to drive inflation at the terminal velocity, providing a generalization of trapped inflation with attractive features: we find that more than sixty e-folds of inflation for sub-Planckian excursions in field space are possible if ESLs are ubiquitous, without fine tuning of initial conditions and less tuned potentials. We construct a simple, observationally viable model with a slightly red scalar power-spectrum and suppressed gravitational waves; we comment on the presence of additional observational signatures originating from IR-cascading and individual massive particles. We also show that moduli-trapping at an ESL is suppressed for D ≫ d, hindering dynamical selection of high-symmetry vacua on the landscape based on this mechanism.
Realization of "trapped rainbow" in 1D slab waveguide with surface dispersion engineering.

We present a design of a one dimensional dielectric waveguide that can trap a broadband light pulse with different frequency component stored at different positions, effectively forming a “trapped rainbow” [Nature 450, 397 (2007)]. The spectrum of the rainbow covers the whole visible range. To do this, we first show that the dispersion of a SiO2 waveguide with a Si grating placed on top can be engineered by the design parameter of the grating. Specifically, guided modes with zero group velocity(frozen modes) can be realized. Negative Goos-Hanchen shift along the surface of the grating is responsible for such a dispersion control. The frequency of the frozen mode is tuned by changing the lateral feature parameters (period and duty cycle) of the grating. By tuning the grating feature point by point along the waveguide, a light pulse can be trapped with different frequency components frozen at different positions, so that a “rainbow” is formed. The device is expected to have extremely low ohmic loss because only dielectric materials are used. A planar geometry also promises much reduced fabrication difficulty.
Probing naked singularities in non-supersymmetric string vacua

We present a detailed analysis of non-supersymmetric spacetime varying string vacua which can lead to an exponential hierarchy between the electroweak and the gravitational scales. In particular, we identify a limit in which these vacua can be interpreted as supersymmetric vacua of F-theory. Furthermore, we study the properties of these solutions as seen by D7-brane probes and establish a non-supersymmetric analogue of the enhancon mechanism.
Distortion exponent in MIMO channels with feedback

The transmission of a Gaussian source over a blockfading multiple antenna channel in the presence of a feedback link is considered. The feedback link is assumed to be an error and delay free link of capacity 1 bit per channel use. Under the short-term power constraint, the optimal exponential behavior of the end-to-end average distortion is characterized for all source-channel bandwidth ratios. It is shown that the optimal transmission strategy is successive refinement source coding followed by progressive transmission over the channel, in which the channel block is allocated dynamically among the layers based on the channel state using the feedback link as an instantaneous automatic repeat request (ARQ) signal.
Emergence of spontaneously broken supersymmetry on an anti-D3-brane in KKLT dS vacua

The KKLT construction of de Sitter vacua includes an uplifting term coming from an anti-D3-brane. Here we show how this term can arise via spontaneous breaking of supersymmetry, based on the emergence of a nilpotent chiral supermultiplet on the world-volume of the anti-D3-brane. We establish and use the fact that both the DBI as well as the WZ term, with account of orientifolding, acquire a form of the Volkov-Akulov action. For an O3 orientifold involution of ℝ9,1 we demonstrate the cancellation between the fermionic parts of the DBI and WZ term for the D3-brane action. For the anti-D3-brane we show that the DBI action and the WZ action combine and lead to the emergence of the goldstino multiplet which is responsible for spontaneous breaking of supersymmetry. This provides a string theoretic explanation for the supersymmetric uplifting term in the KKLT effective supergravity model supplemented by a nilpotent chiral multiplet.
Bowen’s equation in the non-uniform setting

We show that Bowen’s equation, which characterizes the Hausdorff dimension of certain sets in terms of the topological pressure of an expanding conformal map, applies in greater generality than has been heretofore established. In particular, we consider an arbitrary subset Z of a compact metric space and require only that the lower Lyapunov exponents be positive on Z, together with a tempered contraction condition. Among other things, this allows us to compute the dimension spectrum for Lyapunov exponents for maps with parabolic periodic points, and to relate the Hausdorff dimension to the topological entropy for arbitrary subsets of symbolic space with the appropriate metric.
Inferring chromosome radial organization from Hi-C data

The nonrandom radial organization of eukaryotic chromosome territories (CTs) inside the nucleus plays an important role in nuclear functional compartmentalization. Increasingly, chromosome conformation capture (Hi-C) based approaches are being used to characterize the genome structure of many cell types and conditions. Computational methods to extract 3D arrangements of CTs from this type of pairwise contact data will thus increase our ability to analyze CT organization in a wider variety of biological situations. A number of full-scale polymer models have successfully reconstructed the 3D structure of chromosome territories from Hi-C. To supplement such methods, we explore alternative, direct, and less computationally intensive approaches to capture radial CT organization from Hi-C data. We show that we can infer relative chromosome ordering using PCA on a thresholded inter-chromosomal contact matrix. We simulate an ensemble of possible CT arrangements using a force-directed network layout algorithm and propose an approach to integrate additional chromosome properties into our predictions. Our CT radial organization predictions have a high correlation with microscopy imaging data for various cell nucleus geometries (lymphoblastoid, skin fibroblast, and breast epithelial cells), and we can capture previously documented changes in senescent and progeria cells. Our analysis approaches provide rapid and modular approaches to screen for alterations in CT organization across widely available Hi-C data. We demonstrate which stages of the approach can extract meaningful information, and also describe limitations of pairwise contacts alone to predict absolute 3D positions.
Rapid Driven Reset of a Qubit Readout Resonator

A promising approach for constructing networks of solid-state qubits for quantum information processing is the circuit QED architecture. In such a setup, the speed at which a qubit measurement can be turned on and off is limited by the time constant of a readout resonator. The authors demonstrate a method for populating and depopulating this resonator quickly and precisely, without prior knowledge of the qubit's state---an elegant and practical technique to help speed up a quantum computer.
A convex program for mixed linear regression with a recovery guarantee for well-separated data

We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point. These estimates can then be clustered using, for example, $k$-means. For problems with two or more mixture classes, we prove that the convex program exactly recovers all of the mixture components in the noiseless setting under technical conditions that include a well-separation assumption on the data. Under these assumptions, recovery is possible if each class has at least $d$ independent measurements. We also explore an iteratively reweighted least squares implementation of this method on real and synthetic data.
The Offset and Host Light Distributions of Long Gamma-Ray Bursts: A New View From HST Observations of Swift Bursts

[Abridged] We present the results of an extensive Hubble Space Telescope (HST) imaging study of ~100 Swift long-duration gamma-ray bursts (LGRBs) spanning 0.03 0.6 while bursts at R/R_h > 0.5 uniformly trace the light of their hosts. This indicates that the spatial correlation of LGRB locations with bright star forming regions seen in the full sample is dominated by the contribution from bursts at small offset and that LGRBs in the outer parts of galaxies show no preference for unusually bright star forming regions. We conclude that LGRBs strongly prefer the bright, inner regions of their hosts indicating that the star formation taking place there is more favorable for LGRB progenitor production. This indicates that another environmental factor beyond metallicity, such as binary interactions or IMF differences, may be operating in the central regions of LGRB hosts.
Beta-plane turbulence above monoscale topography

Using a one-layer quasi-geostrophic model, we study the effect of random monoscale topography on forced beta-plane turbulence. The forcing is a uniform steady wind stress that produces both a uniform large-scale zonal flow and smaller-scale macroturbulence characterized by standing and transient eddies. The large-scale flow is retarded by a combination of Ekman drag and the domain-averaged topographic form stress produced by the eddies. The topographic form stress typically balances most of the applied wind stress, while the Ekman drag provides all of the energy dissipation required to balance the wind work. A collection of statistically equilibrated numerical solutions delineate the main flow regimes and the dependence of the time average of on parameters such as the planetary potential vorticity (PV) gradient and the statistical properties of the topography. We obtain asymptotic scaling laws for the strength of the large-scale flow in the limiting cases of weak and strong forcing. If is significantly smaller than the topographic PV gradient, the flow consists of stagnant pools attached to pockets of closed geostrophic contours. The stagnant dead zones are bordered by jets and the flow through the domain is concentrated into a narrow channel of open geostrophic contours. In most of the domain, the flow is weak and thus the large-scale flow is an unoccupied mean. If is comparable to, or larger than, the topographic PV gradient, then all geostrophic contours are open and the flow is uniformly distributed throughout the domain. In this open-contour case, there is an ‘eddy saturation’ regime in which is insensitive to large changes in the wind stress. We show that eddy saturation requires strong transient eddies that act effectively as PV diffusion. This PV diffusion does not alter the kinetic energy of the standing eddies, but it does increase the topographic form stress by enhancing the correlation between the topographic slope and the standing-eddy pressure field. Using bounds based on the energy and enstrophy power integrals, we show that as the strength of the wind stress increases, the flow transitions from a regime in which the form stress balances most of the wind stress to a regime in which the form stress is very small and large transport ensues.
Medium modifications of charm and charmonium in high-energy heavy-ion collisions

The production of charmonia in heavy-ion collisions is investigated within a kinetic theory framework simultaneously accounting for dissociation and regeneration processes in both quark–gluon plasma (QGP) and hadron-gas phases of the reaction. In-medium modifications of open-charm states (c-quarks, D-mesons) and the survival of J/ψ mesons in the QGP are included as inferred from lattice QCD. Pertinent consequences on equilibrium charmonium abundances are evaluated and found to be especially relevant to explain the measured centrality dependence of the ψ'/ψ ratio at SPS. Predictions for recent In–In experiments, as well as comparisons to current Au–Au data from RHIC, are provided.
Understanding the group dynamics and success of teams

Complex problems often require coordinated group effort and can consume significant resources, yet our understanding of how teams form and succeed has been limited by a lack of large-scale, quantitative data. We analyse activity traces and success levels for approximately 150 000 self-organized, online team projects. While larger teams tend to be more successful, workload is highly focused across the team, with only a few members performing most work. We find that highly successful teams are significantly more focused than average teams of the same size, that their members have worked on more diverse sets of projects, and the members of highly successful teams are more likely to be core members or ‘leads’ of other teams. The relations between team success and size, focus and especially team experience cannot be explained by confounding factors such as team age, external contributions from non-team members, nor by group mechanisms such as social loafing. Taken together, these features point to organizational principles that may maximize the success of collaborative endeavours.
Aluthge Transforms of 2-Variable Weighted Shifts

We introduce two natural notions of multivariable Aluthge transforms (toral and spherical), and study their basic properties. In the case of 2-variable weighted shifts, we first prove that the toral Aluthge transform does not preserve (joint) hyponormality, in sharp contrast with the 1-variable case. Second, we identify a large class of 2-variable weighted shifts for which hyponormality is preserved under both transforms. Third, we consider whether these Aluthge transforms are norm-continuous. Fourth, we study how the Taylor and Taylor essential spectra of 2-variable weighted shifts behave under the toral and spherical Aluthge transforms; as a special case, we consider the Aluthge transforms of the Drury–Arveson 2-shift. Finally, we briefly discuss the class of spherically quasinormal 2-variable weighted shifts, which are the fixed points for the spherical Aluthge transform.
Morphing ensemble Kalman filters

A new type of ensemble filter is proposed, which combines an ensemble Kalman filter (EnKF) with the ideas of morphing and registration from image processing. This results in filters suitable for non-linear problems whose solutions exhibit moving coherent features, such as thin interfaces in wildfire modelling. The ensemble members are represented as the composition of one common state with a spatial transformation, called registration mapping, plus a residual. A fully automatic registration method is used that requires only gridded data, so the features in the model state do not need to be identified by the user. The morphing EnKF operates on a transformed state consisting of the registration mapping and the residual. Essentially, the morphing EnKF uses intermediate states obtained by morphing instead of linear combinations of the states.
A thick subcategory theorem for modules over certain ring spectra

We classify thick subcategories of the1‐categories of perfect modules over ring spectra which arise as functions on even periodic derived stacks satisfying affineness and regularity conditions. For example, we show that the thick subcategories of perfect modules over TMF are in natural bijection with the subsets of the underlying space of the moduli stack of elliptic curves which are closed under specialization. 55P43, 18E30
TESS Full Orbital Phase Curve of the WASP-18b System

We present a visible-light full orbital phase curve of the transiting planet WASP-18b measured by the TESS Mission. The phase curve includes the transit, secondary eclipse, and sinusoidal modulations across the orbital phase shaped by the planet's atmospheric characteristics and the star-planet gravitational interaction. We measure the beaming (Doppler boosting) and tidal ellipsoidal distortion phase modulations and show that the amplitudes of both agree with theoretical expectations. We find that the light from the planet's day-side hemisphere occulted during secondary eclipse, with a relative brightness of $341_{-18}^{+17}$ ppm, is dominated by thermal emission, leading to an upper limit on the geometric albedo in the TESS band of 0.048 (2$\sigma$). We also detect the phase modulation due to the planet's atmosphere longitudinal brightness distribution. We find that its maximum is well-aligned with the sub-stellar point, to within 2.9 deg (2$\sigma$). We do not detect light from the planet's night-side hemisphere, with an upper limit of 43 ppm (2$\sigma$), which is 13 % of the day-side brightness. The low albedo, lack of atmospheric phase shift, and inefficient heat distribution from the day to night hemispheres that we deduce from our analysis are consistent with theoretical expectations and similar findings for other strongly irradiated gas giant planets. This work demonstrates the potential of TESS data for studying full orbital phase curves of transiting systems. Finally, we complement our study by looking for transit timing variations (TTVs) in the TESS data and combined with previously published transit times, although we do not find a statistically significant TTV signal.
Coded Computing for Distributed Graph Analytics

Many distributed computing systems have been developed recently for implementing graph based algorithms such as PageRank over large-scale graph-structured datasets such as social networks. Performance of these systems significantly suffers from communication bottleneck as a large number of messages are exchanged among servers at each step of the computation. Motivated by graph based MapReduce, we propose a coded computing framework that leverages computation redundancy to alleviate the communication bottleneck in distributed graph processing. As a key contribution of this work, we develop a novel coding scheme that systematically injects structured redundancy in the computation phase to enable coded multicasting opportunities during message exchange between servers, reducing the communication load substantially in large-scale graph processing. For theoretical analysis, we consider random graph models, and focus on schemes in which subgraph allocation and Reduce allocation are only dependent on vertex ID while the Shuffle design varies with graph connectivity. Specifically, we prove that our proposed scheme enables an (asymptotically) inverse-linear trade-off between computation load and average communication load for two popular random graph models – Erdos-Renyi model, and power law model. Particularly, for a given computation load $r$ , (i.e. when each graph vertex is carefully stored at $r$ servers), the proposed scheme slashes the average communication load by (nearly) a multiplicative factor of $r$ . Furthermore, for the Erdos-Renyi model, we prove that our proposed scheme is optimal asymptotically as the graph size increases by providing an information-theoretic converse. To illustrate the benefits of our scheme in practice, we implement PageRank over Amazon EC2, using artificial as well as real-world datasets, demonstrating gains of up to 50.8% in comparison to the conventional PageRank implementation. Additionally, we specialize our coded scheme and extend our theoretical results to two other random graph models – random bi-partite model, and stochastic block model. Our specialized schemes asymptotically enable inverse-linear trade-offs between computation and communication loads in distributed graph processing for these popular random graph models as well. We complement the achievability results with converse bounds for both of these models.
Entropic Dynamics of Exchange Rates and Options

An Entropic Dynamics of exchange rates is laid down to model the dynamics of foreign exchange rates, FX, and European Options on FX. The main objective is to represent an alternative framework to model dynamics. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. Entropic Dynamics is an application of entropic inference, which is equipped with the entropic notion of time to model dynamics. The scale invariance is a symmetry of the dynamics of exchange rates, which is manifested in our formalism. To make the formalism manifestly invariant under this symmetry, we arrive at choosing the logarithm of the exchange rate as the proper variable to model. By taking into account the relevant information about the exchange rates, we derive the Geometric Brownian Motion, GBM, of the exchange rate, which is manifestly invariant under the scale transformation. Securities should be valued such that there is no arbitrage opportunity. To this end, we derive a risk-neutral measure to value European Options on FX. The resulting model is the celebrated Garman-Kohlhagen model.
Eliminating ensembles from equilibrium statistical physics: Maxwell’s demon, Szilard’s engine, and thermodynamics via entanglement

Abstract A system in equilibrium does not evolve — time independence is its telltale characteristic. However, in Newtonian physics the microstate of an individual system (a point in its phase space) evolves incessantly in accord with its equations of motion. Ensembles were introduced in XIX century to bridge that chasm between continuous motion of phase space points in Newtonian dynamics and stasis of thermodynamics: While states of individual classical systems inevitably evolve, a phase space distribution of such states – an ensemble – can be time-independent. I show that entanglement (e.g., with the environment) can yield a time-independent equilibrium in an individual quantum system. This allows one to eliminate ensembles – an awkward stratagem introduced to reconcile thermodynamics with Newtonian mechanics – and use an individual system interacting and therefore entangled with its heat bath to represent equilibrium and to elucidate the role of information and measurements in physics. Thus, in our quantum Universe one can practice statistical physics without ensembles — hence, in a sense, without statistics. The elimination of ensembles uses ideas that led to the recent derivation of Born’s rule from the symmetries of entanglement, and I start with a review of that derivation. I then review and discuss difficulties related to the reliance on ensembles and illustrate the need for ensembles with the classical Szilard’s engine. A similar quantum engine – a single system interacting with the thermal heat bath environment – is enough to establish thermodynamics. The role of Maxwell’s demon (which in this quantum context resembles Wigner’s friend) is also discussed.
Quantum optimization using variational algorithms on near-term quantum devices

Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.
Macdonald index and chiral algebra

For any 4d $$ \mathcal{N} $$ = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type (A 1 , A 2n ) and (A 1 , D 2n+1) where the chiral algebras are given by Virasoro and $$ \widehat{\mathfrak{su}}(2) $$ affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.
Optimal Operation of a Josephson Parametric Amplifier for Vacuum Squeezing

``Squeezed'' states of the microwave field, which allow one to beat the Heisenberg uncertainty limit for some phase values, find diverse applications in improving quantum measurements. These states can be created using a Josephson parametric amplifier (JPA) operated with a single current pump, but nonlinearities limit the available squeezing. The authors show how to choose pump-tone parameters to reduce this distortion, so that anyone with such a JPA can squeeze harder for better measurements, without needing extra hardware or a more complicated scheme.
Off-shell single-top-quark production in the Standard Model Effective Field Theory

We present a fully differential and spin-dependent t-channel single-top-quark calculation at next-to-leading order (NLO) in QCD including off-shell effects by using the complex mass scheme in the Standard Model (SM) and in the Standard Model Effective Field Theory (SMEFT). We include all relevant SMEFT operators at 1/Λ2 that contribute at NLO in QCD for a fully consistent comparison to the SM at NLO. In addition, we include chirality flipping operators that do not interfere with the SM amplitude and contribute only at 1/Λ4 with a massless b-quark. Such higher order effects are usually captured by considering anomalous right-handed Wtb and left-handed Wtb tensor couplings. Despite their formal suppression in the SMEFT, they describe an important class of models for new physics. Our calculation and analysis framework is publicly available in MCFM.
Is Flat fielding Safe for Precision CCD Astronomy

The ambitious goals of precision cosmology with wide-field optical surveys such as the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope (LSST) demand, as their foundation, precision CCD astronomy. This in turn requires an understanding of previously uncharacterized sources of systematic error in CCD sensors, many of which manifest themselves as static effective variations in pixel area. Such variation renders a critical assumption behind the traditional procedure of flat fielding--that a sensor's pixels comprise a uniform grid--invalid. In this work, we present a method to infer a curl-free model of a sensor's underlying pixel grid from flat field images, incorporating the superposition of all electrostatic sensor effects--both known and unknown--present in flat field data. We use these pixel grid models to estimate the overall impact of sensor systematics on photometry, astrometry, and PSF shape measurements in a representative sensor from the Dark Energy Camera (DECam) and a prototype LSST sensor. Applying the method to DECam data recovers known significant sensor effects for which corrections are currently being developed within DES. For an LSST prototype CCD with pixel-response non-uniformity (PRNU) of 0.4%, we find the impact of "improper" flat-fielding on these observables is negligible in nominal .7" seeing conditions. These errors scale linearly with the PRNU, so for future LSST production sensors, which may have larger PRNU, our method provides a way to assess whether pixel-level calibration beyond flat fielding will be required.
A Combined Deep Learning-Gradient Boosting Machine Framework for Fluid Intelligence Prediction

The ABCD Neurocognitive Prediction Challenge is a community driven competition asking competitors to develop algorithms to predict fluid intelligence score from T1-w MRIs. In this work, we propose a deep learning combined with gradient boosting machine framework to solve this task. We train a convolutional neural network to compress the high dimensional MRI data and learn meaningful image features by predicting the 123 continuous-valued derived data provided with each MRI. These extracted features are then used to train a gradient boosting machine that predicts the residualized fluid intelligence score. Our approach achieved mean square error (MSE) scores of 18.4374, 68.7868, and 96.1806 for the training, validation, and test set respectively.
Numerical Approximations for the Tempered Fractional Laplacian: Error Analysis and Applications

In this paper, we propose an accurate finite difference method to discretize the d-dimensional (for $$d \ge 1$$ ) tempered integral fractional Laplacian and apply it to study the tempered effects on the solution of problems arising in various applications. Compared to other existing methods, our method has higher accuracy and simpler implementation. Our numerical method has an accuracy of $${\mathcal {O}}(h^\varepsilon )$$ , for $$u \in C^{0, \,\alpha + \varepsilon } (\bar{\Omega })$$ if $$\alpha < 1$$ (or $$u \in C^{1, \,\alpha - 1 + \varepsilon } (\bar{\Omega })$$ if $$\alpha \ge 1$$ ) with $$\varepsilon > 0$$ , suggesting the minimum consistency conditions. The accuracy can be improved to $${\mathcal {O}}(h^2)$$ , for $$u \in C^{2, \,\alpha + \varepsilon } (\bar{\Omega })$$ if $$\alpha < 1$$ (or $$u \in C^{3, \,\alpha - 1 + \varepsilon } (\bar{\Omega })$$ if $$\alpha \ge 1$$ ). Numerical experiments confirm our analytical results and provide insights in solving the tempered fractional Poisson problem. It suggests that to achieve the second order of accuracy, our method only requires the solution $$u \in C^{1,1}(\bar{\Omega })$$ for any $$\alpha \in (0, 2)$$ . Moreover, if the solution of tempered fractional Poisson problems satisfies $$u \in C^{p, s}(\bar{\Omega })$$ for $$p = 0, 1$$ and $$s\in (0, 1]$$ , our method has the accuracy of $${\mathcal {O}}(h^{p+s})$$ . Since our method yields a (multilevel) Toeplitz stiffness matrix, one can design fast algorithms via the fast Fourier transform for efficient simulations. Finally, we apply it together with fast algorithms to study the tempered effects on the solutions of various tempered fractional PDEs, including the Allen–Cahn equation and Gray–Scott equations.
Pyramid diffraction in parity-time-symmetric optical lattices

Nonlinear dynamics of wave packets in two-dimensional parity-time-symmetric optical lattices near the phase transition point are analytically studied. A fourth-order equation is derived for the envelope of these wave packets. A pyramid diffraction pattern is demonstrated in both the linear and nonlinear regimes. Blow-up is also possible in the nonlinear regime for both focusing and defocusing nonlinearities.
Phonon driven transport in amorphous semiconductors: transition probabilities

Starting from Holstein’s work on small polaron hopping, the evolution equations for localized and extended states in the presence of atomic vibrations are systematically derived for an amorphous semiconductor. The transition probabilities are obtained for transitions between all combinations of localized and extended states. For any transition process involving a localized state, the activation energy is not simply the energy difference between the final and initial states; the reorganization energy of atomic configuration is also included as an important part of the activation energy (Marcus form). The activation energy for the transitions between localized states decreases with rising temperature and leads to the Meyer-Neldel rule. The predicted Meyer-Neldel temperatures are consistent with observations in several materials. The computed field-dependence of conductivity agrees with experimental data. The present work suggests that the upper temperature limit of variable range hopping is proportional to the frequency of the first peak of the phonon spectrum. We have also improved the description of the photocurrent decay at low temperatures. Analysis of the transition probability from an extended state to a localized state suggests that there exists a short-lifetime belt of extended states inside the conduction band or valence band.
Infrared Consistency and the Weak Gravity Conjecture

The weak gravity conjecture (WGC) asserts that an Abelian gauge theory coupled to gravity is inconsistent unless it contains a particle of charge q and mass m such that q≥m/m_(Pl). This criterion is obeyed by all known ultraviolet completions and is needed to evade pathologies from stable black hole remnants. In this paper, we explore the WGC from the perspective of low-energy effective field theory. Below the charged particle threshold, the effective action describes a photon and graviton interacting via higher-dimension operators. We derive infrared consistency conditions on the parameters of the effective action using i ) analyticity of light-by-light scattering, ii ) unitarity of the dynamics of an arbitrary ultraviolet completion, and iii ) absence of superluminality and causality violation in certain non-trivial backgrounds. For convenience, we begin our analysis in three spacetime dimensions, where gravity is non-dynamical but has a physical effect on photon-photon interactions. We then consider four dimensions, where propagating gravity substantially complicates all of our arguments, but bounds can still be derived. Operators in the effective action arise from two types of diagrams: those that involve electromagnetic interactions (parameterized by a charge-to-mass ratio q/m) and those that do not (parameterized by a coefficient γ). Infrared consistency implies that q/m is bounded from below for small γ.
Slow-dissipation limit of the harmonic oscillator with general power-law damping

An approximate solution is presented for simple harmonic motion in the presence of damping by a force which is a general power-law function of the velocity. The approximation is shown to be quite robust, allowing for a simple way to investigate amplitude decay in the presence of a general type of weak, nonlinear damping.
Alloying induces directionally-dependent mobility and alters migration mechanisms of faceted grain boundaries

Abstract Faceted grain boundaries exhibit unusual segregation and migration tendencies. To gain a deeper understanding of how solute atoms interact with faceted interfacial structures during migration, this study probes the migration behavior of a faceted Σ11 boundary in Cu doped with Ag atoms. The solutes are found to segregate to the facet with more free volume and strongly reduce boundary velocity in one migration direction, but not the other, due to the presence of a directionally-dependent motion mechanism that can escape solute pinning and therefore speed up migration. Hence, a new mechanism of chemically-induced anisotropy in grain boundary mobility is uncovered by these simulations.
NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis

We present a method that achieves state-of-the-art results for synthesizing novel views of complex scenes by optimizing an underlying continuous volumetric scene function using a sparse set of input views. Our algorithm represents a scene using a fully-connected (non-convolutional) deep network, whose input is a single continuous 5D coordinate (spatial location (x, y, z) and viewing direction \((\theta ,\phi )\)) and whose output is the volume density and view-dependent emitted radiance at that spatial location. We synthesize views by querying 5D coordinates along camera rays and use classic volume rendering techniques to project the output colors and densities into an image. Because volume rendering is naturally differentiable, the only input required to optimize our representation is a set of images with known camera poses. We describe how to effectively optimize neural radiance fields to render photorealistic novel views of scenes with complicated geometry and appearance, and demonstrate results that outperform prior work on neural rendering and view synthesis. View synthesis results are best viewed as videos, so we urge readers to view our supplementary video for convincing comparisons.
Taxonomy of Entrepreneurship – A Means-Oriented Approach

The growth of entrepreneurship literature spurred a discussion on the distinct characteristics of the different types of entrepreneurship, with most attention being given to market, social, and political entrepreneurship. In organizing the inquiry around these supposedly distinct types of entrepreneurship, scholars tend to focus on the goals entrepreneurs pursue: market entrepreneurs are portrayed as driven by profit, political entrepreneurs are driven by rents, and social entrepreneurs are thought to be driven by other, supposedly less venal, motivations. This paper presents the shortcomings of this ends-oriented taxonomy and offers an alternative approach for organizing inquiry, one that originates from Richard Wagner’s framework of Entangled Political Economy and his distinction between voluntary and involuntary investors. I argue that instead of focusing on the ends, the taxonomy of entrepreneurship should focus on the means, in particular, on whether the resources that support the venture were obtained through cooperation or coercion.
Statistically Model Checking PCTL Specifications on Markov Decision Processes via Reinforcement Learning

Probabilistic Computation Tree Logic (PCTL) is frequently used to formally specify control objectives such as probabilistic reachability and safety. In this work, we focus on model checking PCTL specifications statistically on Markov Decision Processes (MDPs) by sampling, e.g., checking whether there exists a feasible policy such that the probability of reaching certain goal states is greater than a threshold. We use reinforcement learning to search for such a feasible policy for PCTL specifications, and then develop a statistical model checking (SMC) method with provable guarantees on its error. Specifically, we first use upper-confidence-bound (UCB) based Q-learning to design an SMC algorithm for bounded-time PCTL specifications, and then extend this algorithm to unbounded-time specifications by identifying a proper truncation time by checking the PCTL specification and its negation at the same time. Finally, we evaluate the proposed method by case studies.
Behaviorism in Finance and Securities Law

In this Article, I take stock (as something of an outsider) of the behavioral economics movement, focusing in particular on its interaction with traditional cost-benefit analysis and its implications for agency structure. The usual strategy for such a project—a strategy that has been used by others with behavioral economics—is to marshal the existing evidence and critically assess its significance. My approach here is somewhat different. Although I describe behavioral economics and summarize the strongest criticisms of its use, the heart of the Article is inductive, and focuses on a particular context: financial and securities regulation, as recently revamped by the Dodd-Frank Act and subsequent rule making. To lay the foundation, I begin by briefly describing behavioral economics and by surveying the most significant critiques of its use. I then consider how behavioral economics has informed, or might inform, the work of the Consumer Financial Protection Bureau, SEC rule making on proxy access, and the e...
Horizontal Human Rights Law

Human rights have traditionally been seen as vertical, establishing rights for individuals and obligations for states. Recent proposals seek to reorient human rights law horizontally, imposing obligations directly on corporations and other private actors. These proposals fail to appreciate the horizontal effects of existing human rights law, and risk undermining its structure and opening the door to new restrictions on human rights.