cssi/SciSciGPT-SciSciNet huggingface dataset:
Asymptotic expansion of the heat kernel trace of Laplacians with polynomial potentials

It is well known that the asymptotic expansion of the trace of the heat kernel for Laplace operators on smooth compact Riemannian manifolds can be obtained through termwise integration of the asymptotic expansion of the on-diagonal heat kernel. The purpose of this work is to show that, in certain circumstances, termwise integration can be used to obtain the asymptotic expansion of the heat kernel trace for Laplace operators endowed with a suitable polynomial potential on unbounded domains. This is achieved by utilizing a resummed form of the asymptotic expansion of the on-diagonal heat kernel.
Recent Advances in Programmable Photonic-Assisted Ultrabroadband Radio-Frequency Arbitrary Waveform Generation

This paper reviews recent advances in photonic-assisted radio-frequency arbitrary waveform generation (RF-AWG), with emphasis on programmable ultrabroadband microwave and millimeter-wave waveforms. The key enabling components in these techniques are programmable optical pulse shaping, frequency-to-time mapping via dispersive propagation, and high-speed photodetection. The main advantages and challenges of several different photonic RF-AWG schemes are discussed. We further review some proof-of-concept demonstrations of ultrabroadband RF-AWG applications, including high-resolution ranging and ultrabroadband non-line-of-sight channel compensation. Finally, we present recent progress toward RF-AWG with increased time aperture and time-bandwidth product.
Actionable Recourse in Linear Classification

Classification models are often used to make decisions that affect humans: whether to approve a loan application, extend a job offer, or provide insurance. In such applications, individuals should have the ability to change the decision of the model. When a person is denied a loan by a credit scoring model, for example, they should be able to change the input variables of the model in a way that will guarantee approval. Otherwise, this person will be denied the loan so long as the model is deployed, and -- more importantly --will lack agency over a decision that affects their livelihood. In this paper, we propose to evaluate a linear classification model in terms of recourse, which we define as the ability of a person to change the decision of the model through actionable input variables (e.g., income vs. age or marital status). We present an integer programming toolkit to: (i) measure the feasibility and difficulty of recourse in a target population; and (ii) generate a list of actionable changes for a person to obtain a desired outcome. We discuss how our tools can inform different stakeholders by using them to audit recourse for credit scoring models built with real-world datasets. Our results illustrate how recourse can be significantly affected by common modeling practices, and motivate the need to evaluate recourse in algorithmic decision-making.
A new physical phenomenon in ultra-high energy collisions

We show that combining the published Pierre Auger Observatory measurements of the longitudinal and lateral properties of UHE atmospheric showers, points to an unforeseen change in the nature of particle interactions at ultrahigh energy. A "toy model" of UHE proton-air interactions is presented which provides the first fully consistent description of air shower observations. It demonstrates that the observed energy dependence of the depth-of-shower-maximum distribution may not indicate a transition to a heavier composition, as commonly assumed. While fundamentally phenomenological, the model is based on considerations of how the normal vacuum of QCD might be vaporized and chiral symmetry restored by the extreme energy densities produced in UHE collisions. Whatever its origin, understanding this unexpected phenomenon opens exciting directions in particle physics and may impact Early Universe cosmology. 1. PRELIMINARIES Thousands of cosmic ray air showers with energies above a few EeV (1EeV = 10 18 eV) have been observed by the Pierre Auger Observatory simultaneously in the Fluorescence and Surface Detectors (FD S at large radii and especially at large zenith angles, the SD signal is mostly due to muons from pion decay. The Auger analysis is now very mature and well- understood, so that the combined information provided by surface array and fluorescence telescope observations give an extremely powerful constraint on the primary CRs and their interactions. It has been known for some time that existing UHECR shower simulations fall short of accounting for the muon content of the ground signal, by a significant factor (3, 4). We show here that - no matter what the composition of the UHECR primaries - any presently available model based on conventional particle physics cannot simultaneously explain the totality of Auger observations on the longitudinal development and lateral shape of the showers. A model that reproduces the distribution of where in the atmosphere the showers peak, cannot explain the magnitude and zenith angle dependence of the ground signal, unless the fraction of energy carried by the hadronic shower is approximately a factor-two greater than in conventional models; as far as we can see, this requires a strong suppression in decaying 0 's at ultrahigh energies compared to predictions of standard physics.
Differentially-Private Federated Linear Bandits

The rapid proliferation of decentralized learning systems mandates the need for differentially-private cooperative learning. In this paper, we study this in context of the contextual linear bandit: we consider a collection of agents cooperating to solve a common contextual bandit, while ensuring that their communication remains private. For this problem, we devise \textsc{FedUCB}, a multiagent private algorithm for both centralized and decentralized (peer-to-peer) federated learning. We provide a rigorous technical analysis of its utility in terms of regret, improving several results in cooperative bandit learning, and provide rigorous privacy guarantees as well. Our algorithms provide competitive performance both in terms of pseudoregret bounds and empirical benchmark performance in various multi-agent settings.
RELATIVELY COHERENT SETS AS A HIERARCHICAL PARTITION METHOD

Finite time coherent sets [Froyland et al., 2010] have recently been defined by a measure-based objective function describing the degree that sets hold together, along with a Frobenius–Perron transfer operator method to produce optimally coherent sets. Here, we present an extension to generalize the concept to hierarchically define relatively coherent sets based on adjusting the finite time coherent sets to use relative measures restricted to sets which are developed iteratively and hierarchically in a tree of partitions. Several examples help clarify the meaning and expectation of the techniques, as they are the nonautonomous double gyre, the standard map, an idealized stratospheric flow, and empirical data from the Mexico Gulf during the 2010 oil spill. Also for the sake of analysis of computational complexity, we include an Appendix concerning the computational complexity of developing the Ulam–Galerkin matrix estimates of the Frobenius–Perron operator centrally used here.
Finding Extreme Subdwarfs

I develop a new technique to identify M-type extreme subdwarfs (esdMs) and demonstrate that it is substantially more efficient than previous methods. I begin by obtaining spectroscopy and improved photometry of a sample of 54 late-type halo candidates using the rNLTT reduced proper-motion (RPM) diagram. From spectroscopy, I find that four of these are esdMs, three of which were previously unknown. From the improved photometry, I show that all four lie in a narrow RPM corridor that contains only four non-esdMs. Hence, with good photometry (i.e., without spectroscopy), it appears possible to select esdM candidates with a 50% esdM yield. This is more than an order of magnitude more efficient than previous methods.
The Marginalization Paradox and the Formal Bayes' Law

It has recently been shown that the marginalization paradox (MP) can be resolved by interpreting improper inferences as probability limits. The key to the resolution is that probability limits need not satisfy the formal Bayes' law, which is used in the MP to deduce an inconsistency In this paper, I explore the differences between probability limits and the more familiar pointwise limits, which do imply the formal Bayes' law, and show how these differences underlie some key differences in the interpretation of the MP.
Relativistic Winds from Compact Gamma-Ray Sources. I. Radiative Acceleration in the Klein-Nishina Regime

We consider the radiative acceleration to relativistic bulk velocities of a cold, optically thin plasma which is exposed to an external source of γ-rays. The flow is driven by radiative momentum input to the gas, the accelerating force being due to Compton scattering in the relativistic Klein-Nishina limit. The bulk Lorentz factor of the plasma, Γ, derived as a function of distance from the radiating source, is compared with the corresponding result in the Thomson limit. Depending on the geometry and spectrum of the radiation field, we find that particles are accelerated to the asymptotic Lorentz factor at infinity much more rapidly in the relativistic regime and the radiation drag is reduced as blueshifted, aberrated photons experience a decreased relativistic cross section and scatter preferentially in the forward direction. The random energy imparted to the plasma by γ-rays can be converted into bulk motion if the hot particles execute many Larmor orbits before cooling. This "Compton afterburn" may be a supplementary source of momentum if energetic leptons are injected by pair creation but can be neglected in the case of pure Klein-Nishina scattering. Compton drag by side-scattered radiation is shown to be more important in limiting the bulk Lorentz factor than the finite inertia of the accelerating medium. The processes discussed here may be relevant to a variety of astrophysical situations where luminous compact sources of hard X-ray and γ-ray photons are observed, including active galactic nuclei, galactic black hole candidates, and γ-ray bursts.
Generating the Local Oscillator “Locally” in Continuous-Variable Quantum Key Distribution Based on Coherent Detection

Continuous-variable quantum key distribution (CV-QKD) protocols based on coherent detection have been studied extensively in both theory and experiment. In all the existing implementations of CV-QKD, both the quantum signal and the local oscillator (LO) are generated from the same laser and propagate through the insecure quantum channel. This arrangement may open security loopholes and also limit the potential applications of CV-QKD. In this paper, we propose and demonstrate a pilot-aided feedforward data recovery scheme which enables reliable coherent detection using a \locally" generated LO. Using two independent commercial laser sources and a spool of 25 km optical ber, we construct a coherent communication system. The variance of the phase noise introduced by the proposed scheme is measured to be 0:04 (rad 2 ), which is small enough to enable secure key distribution. This technology also opens the door for other quantum communication protocols, such as the recently proposed measurement-device-independent (MDI) CV-QKD where independent light sources are employed by dierent users.
INFRARED INTERFEROMETRIC OBSERVATIONS OF YOUNG STELLAR OBJECTS

We present infrared observations of four young stellar objects made using the Palomar Testbed Interferometer (PTI). For three of the sources, T Tau, MWC 147, and SU Aur, the 2.2 μm emission is resolved at the PTI's nominal fringe spacing of 4 mas, while the emission region of AB Aur is overresolved on this scale. We fit the observations with simple circumstellar material distributions and compare our data to the predictions of accretion disk models inferred from spectral energy distributions. We find that the infrared emission region is tenths of an AU in size for T Tau and SU Aur and ~1 AU for MWC 147.
Spectral imaging technologies for food safety and quality evaluations

USDA researchers in Beltsville, Maryland, have developed various spectral imaging technologies for applications in food safety and quality evaluations of agricultural commodities. We pioneered the online implementation of hyperspectral line-scan imaging technologies in a food processing environment, such as wholesomeness inspection of broiler chickens, and online safety and quality inspection of fresh produce. In addition, a macro-scale Raman chemical imaging system was developed to implement high-throughput Raman imaging using a 785-nm line-laser including a rapid line-scan system. The macro Raman imaging technologies have been used to authenticate powdered food ingredients and to detect chemical adulterants in powdered foods. The advancement of the above spectral imaging technologies is presented.
Status of head-on beam-beam compensation in RHIC

In polarized proton operation the RHIC performance is limited by the head-on beam-beam effect. To overcome this limitation two electron lenses are under commissioning. We give an overview of head-on beam-beam compensation in general and the specific design for RHIC, which is based on electron lenses. The status of installation and commissioning are presented along with plans for the future.
Gas Accretion by Star Clusters and the Formation of Ultraluminous X-Ray Sources from Cusps of Compact Remnants

Here, we show that the overabundance of ultraluminous, compact X-ray sources associated with moderately young clusters in interacting galaxies such as the Antennae and the Cartwheel can be given an alternative explanation that does not involve the presence of intermediate mass black holes (IMBHs). We argue that gas density within these systems is enhanced by the collective potential of the cluster prior to being accreted onto the individual cluster members and, as a result, the aggregate X-ray luminosity arising from the neutron star cluster members can exceed > 10{sup 39} erg s{sup -1}. Various observational tests to distinguish between IMBHs and accreting neutron star cusps are discussed.
Theory and applications of parton pseudodistributions

We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realizati...
The Effects of Latent Infection on the Dynamics of HIV

One way in which the human immunodeficiency virus (HIV-1) replicates within a host is by infecting activated CD $$4+$$ T-cells, which then produce additional copies of the virus. Even with the introduction of antiretroviral drug therapy, which has been very successful over the past decade, a large obstacle to the complete eradication of the virus is the presence of viral reservoirs in the form of latently infected CD $$4+$$ T-cells. We consider a model of HIV infection that describes T-cell and viral interactions, as well as, the production and activation of latently infected T-cells. Upon determining equilibrium states of the latent cell model, the local and global asymptotic behavior of solutions is examined, and the basic reproduction number of the system is computed to be strictly less than that of the corresponding three-component model, which omits the effects of latent infection. In particular, this implies that a wider variety of parameter values will lead to viral eradication as $$t \rightarrow \infty $$ due to the appearance of latent CD $$4+$$ T-cells. With this realization we discuss possible alternative notions for eradication and persistence of infection other than traditional dynamical tools. These results are further illustrated by a number of numerical simulations.
Composing Scalable Nonlinear Algebraic Solvers

Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may significantly improve the time to solution. We describe the basic concepts of nonlinear omposition and preconditioning and present a number of solvers applicable to nonlinear partial differential equations. We have developed a software framework in order to easily explore the possible combinations of solvers. We show that the performance gains from using composed solvers can be substantial compared with gains from standard Newton--Krylov methods.
Tensor product categorifications and the super Kazhdan-Lusztig conjecture

We give a new proof of the “super Kazhdan-Lusztig conjecture” for the Lie superalgebra gln|m(C) as formulated originally by the first author. We also prove for the first time that any integral block of category O for gln|m(C) (and also all of its parabolic analogs) possesses a graded version which is Koszul. Our approach depends crucially on an application of the uniqueness of tensor product categorifications established recently by the second two authors.
Fading Coronal Structure and the Onset of Turbulence in the Young Solar Wind

Above the top of the solar corona, the young, slow solar wind transitions from low-beta, magnetically structured flow dominated by radial structures to high-beta, less structured flow dominated by hydrodynamics. This transition, long inferred via theory, is readily apparent in the sky region close to 10deg from the Sun in processed, background-subtracted solar wind images. We present image sequences collected by the inner Heliospheric Imager instrument on board the Solar-Terrestrial Relations Observatory (STEREO/HI1) in 2008 December, covering apparent distances from approximately 4deg to 24deg from the center of the Sun and spanning this transition in the large-scale morphology of the wind. We describe the observation and novel techniques to extract evolving image structure from the images, and we use those data and techniques to present and quantify the clear textural shift in the apparent structure of the corona and solar wind in this altitude range. We demonstrate that the change in apparent texture is due both to anomalous fading of the radial striae that characterize the corona and to anomalous relative brightening of locally dense puffs of solar wind that we term "flocculae." We show that these phenomena are inconsistent with smooth radial flow, but consistent with the onset of hydrodynamic or magnetohydrodynamic instabilities leading to a turbulent cascade in the young solar wind.
PowerTransformer: Unsupervised Controllable Revision for Biased Language Correction

Unconscious biases continue to be prevalent in modern text and media, calling for algorithms that can assist writers with bias correction. For example, a female character in a story is often portrayed as passive and powerless ("_She daydreams about being a doctor_") while a man is portrayed as more proactive and powerful ("_He pursues his dream of being a doctor_"). We formulate **Controllable Debiasing**, a new revision task that aims to rewrite a given text to correct the implicit and potentially undesirable bias in character portrayals. We then introduce PowerTransformer as an approach that debiases text through the lens of connotation frames (Sap et al., 2017), which encode pragmatic knowledge of implied power dynamics with respect to verb predicates. One key challenge of our task is the lack of parallel corpora. To address this challenge, we adopt an unsupervised approach using auxiliary supervision with related tasks such as paraphrasing and self-supervision based on a reconstruction loss, building on pretrained language models. Through comprehensive experiments based on automatic and human evaluations, we demonstrate that our approach outperforms ablations and existing methods from related tasks. Furthermore, we demonstrate the use of PowerTransformer as a step toward mitigating the well-documented gender bias in character portrayal in movie scripts.
Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid

We study the problem of existence of extremizers for the L 2 to L p adjoint Fourier restriction inequalities for the hyperboloid in dimensions 3 and 4 in the case p is an even integer. We use the method developed by Foschi in [5] to show that extremizers do not exist.
Star Formation Patterns and Hierarchies

Star formation occurs in hierarchical patterns in both space and time. Galaxies form large regions on the scale of the interstellar Jeans length and these large regions apparently fragment into giant molecular clouds and cloud cores in a sequence of decreasing size and increasing density. Young stars follow this pattern, producing star complexes on the largest scales, OB associations on smaller scales, and so on down to star clusters and individual stars. Inside each scale and during the lifetime of the cloud on that scale, smaller regions come and go in a hierarchy of time. As a result, cluster positions are correlated with power law functions, and so are their ages. At the lowest level in the hierarchy, clusters are observed to form in pairs. For any hierarchy like this, the efficiency is automatically highest in the densest regions. This high efficiency promotes bound cluster formation. Also for any hierarchy, the mass function of the components is a power law with a slope of around − 2, as observed for clusters.
batman: BAsic Transit Model cAlculatioN in Python

I introduce batman, a Python package for modeling exoplanet transit and eclipse light curves. The batman package supports calculation of light curves for any radially symmetric stellar limb darkening law, using a new integration algorithm for models that cannot be quickly calculated analytically. The code uses C extension modules to speed up model calculation and is parallelized with OpenMP. For a typical light curve with 100 data points in transit, batman can calculate one million quadratic limb-darkened models in 30 s with a single 1.7 GHz Intel Core i5 processor. The same calculation takes seven minutes using the four-parameter nonlinear limb darkening model (computed to 1 ppm accuracy). Maximum truncation error for integrated models is an input parameter that can be set as low as 0.001 ppm, ensuring that the community is prepared for the precise transit light curves we anticipate measuring with upcoming facilities. The batman package is open source and publicly available at https://github.com/lkreidberg/batman.
COMPARING THE LIGHT CURVES OF SIMULATED TYPE Ia SUPERNOVAE WITH OBSERVATIONS USING DATA-DRIVEN MODELS

We propose a robust, quantitative method to compare the synthetic light curves of a Type Ia supernova (SN Ia) explosion model with a large set of observed SNe Ia, and derive a figure of merit for the explosion model's agreement with observations. The synthetic light curves are fit with the data-driven model SALT2 which returns values for stretch, color, and magnitude at peak brightness, as well as a goodness-of-fit parameter. Each fit is performed multiple times with different choices of filter bands and epoch range in order to quantify the systematic uncertainty on the fitted parameters. We use a parametric population model for the distribution of observed SN Ia parameters from large surveys, and extend it to represent red, dim, and bright outliers found in a low-redshift SN Ia data set. We discuss the potential uncertainties of this population model and find it to be reliable given the current uncertainties on cosmological parameters. Using our population model, we assign each set of fitted parameters a likelihood of being observed in nature, and a figure of merit based on this likelihood. We define a second figure of merit based on the quality of the light curve fit, and combine the two measures into an overall figure of merit for each explosion model. We compute figures of merit for a variety of one-, two-, and three-dimensional explosion models and show that our evaluation method allows meaningful inferences across a wide range of light curve quality and fitted parameters.
Mechanically induced metal-insulator transition in carbyne.

First-principles calculations for carbyne under strain predict that the Peierls transition from symmetric cumulene to broken-symmetry polyyne structure is enhanced as the material is stretched. Interpretation within a simple and instructive analytical model suggests that this behavior is valid for arbitrary 1D metals. Further, numerical calculations of the anharmonic quantum vibrational structure of carbyne show that zero-point atomic vibrations eliminate the Peierls distortion in the mechanically free chain, preserving the cumulene symmetry. The emergence and increase of Peierls dimerization under tension then implies a qualitative transition between the two forms, which our computations place around 3% strain. Thus, the competition between the zero-point vibrations and mechanical strain determines a switch in symmetry resulting in the transition from metallic state to a dielectric, with a small effective mass and a high carrier mobility. In any practical realization, it is important that the effect is a...
BPS spectrum of 5 dimensional field theories, (p,q) webs and curve counting

We study the BPS spectrum of supersymmetric 5 dimensional field theories and their representations as string webs. It is found that a state of given charges exists when it has a representation as an irreducible string web. Its spin is determined by the string web. The number of fermionic zero modes is 8g+4b, where g is the number of internal faces and b is the number of boundaries. In the lift to M theory of 4d field theories such states are described by membranes ending on the 5-brane, breaking SUSY from 8 to 4, and g becomes the genus of the membrane. Mathematically, we obtain a diagrammatic method to find the spectrum of curves on a toric complex surface, and the number of their moduli.
Reionization on Large Scales. I. A Parametric Model Constructed from Radiation-hydrodynamic Simulations

We present a new method for modeling inhomogeneous cosmic reionization on large scales. Utilizing high-resolution radiation-hydrodynamic simulations with 20483 dark matter particles, 20483 gas cells, and 17 billion adaptive rays in a L = 100 Mpc h –1 box, we show that the density and reionization redshift fields are highly correlated on large scales ( 1 Mpc h –1). This correlation can be statistically represented by a scale-dependent linear bias. We construct a parametric function for the bias, which is then used to filter any large-scale density field to derive the corresponding spatially varying reionization redshift field. The parametric model has three free parameters that can be reduced to one free parameter when we fit the two bias parameters to simulation results. We can differentiate degenerate combinations of the bias parameters by combining results for the global ionization histories and correlation length between ionized regions. Unlike previous semi-analytic models, the evolution of the reionization redshift field in our model is directly compared cell by cell against simulations and performs well in all tests. Our model maps the high-resolution, intermediate-volume radiation-hydrodynamic simulations onto lower-resolution, larger-volume N-body simulations ( 2 Gpc h –1) in order to make mock observations and theoretical predictions.
A PILOT SEARCH FOR EVIDENCE OF EXTRASOLAR EARTH-ANALOG PLATE TECTONICS

Relative to calcium, both strontium and barium are markedly enriched in Earth's continental crust compared to the basaltic crusts of other differentiated rocky bodies within the solar system. Here, we both re-examine available archived Keck spectra to place upper bounds on n(Ba)/n(Ca) and revisit published results for n(Sr)/n(Ca) in two white dwarfs that have accreted rocky planetesimals. We find that at most only a small fraction of the pollution is from crustal material that has experienced the distinctive elemental enhancements induced by Earth-analog plate tectonics. In view of the intense theoretical interest in the physical structure of extrasolar rocky planets, this search should be extended to additional targets.
Modeling Epistemological Principles for Bias Mitigation in AI Systems: An Illustration in Hiring Decisions

Artificial Intelligence (AI) has been used extensively in automatic decision making in a broad variety of scenarios, ranging from credit ratings for loans to recommendations of movies. Traditional design guidelines for AI models focus essentially on accuracy maximization, but recent work has shown that economically irrational and socially unacceptable scenarios of discrimination and unfairness are likely to arise unless these issues are explicitly addressed. This undesirable behavior has several possible sources, such as biased datasets used for training that may not be detected in black-box models. After pointing out connections between such bias of AI and the problem of induction, we focus on Popper's contributions after Hume's, which offer a logical theory of preferences. An AI model can be preferred over others on purely rational grounds after one or more attempts at refutation based on accuracy and fairness. Inspired by such epistemological principles, this paper proposes a structured approach to mitigate discrimination and unfairness caused by bias in AI systems. In the proposed computational framework, models are selected and enhanced after attempts at refutation. To illustrate our discussion, we focus on hiring decision scenarios where an AI system filters in which job applicants should go to the interview phase.
Experimental limit on an exotic parity-odd spin- and velocity-dependent interaction using an optically polarized vapor.

Exotic spin-dependent interactions between fermions have recently attracted attention in relation to theories beyond the Standard Model. The exotic interactions can be mediated by hypothetical fundamental bosons which may explain several unsolved mysteries in physics. Here we expand this area of research by probing an exotic parity-odd spin- and velocity-dependent interaction between the axial-vector electron coupling and the vector nucleon coupling for polarized electrons. This experiment utilizes a high-sensitivity atomic magnetometer, based on an optically polarized vapor that is a source of polarized electrons, and a solid-state mass containing unpolarized nucleons. The atomic magnetometer can detect an effective magnetic field induced by the exotic interaction between unpolarized nucleons and polarized electrons. We set an experimental limit on the electron-nucleon coupling $$g_{\mathrm{A}}^{\mathrm{e}}g_{\mathrm{V}}^{\mathrm{N}} \, < \, 10^{ - 30}$$ at the mediator boson mass below 10−4 eV, significantly improving the current limit by up to 17 orders of magnitude. Symmetry breaking is an important process in fundamental understanding of matter and dark matter. Here the authors discuss an experimental bound on an exotic parity odd spin- and velocity-dependent interaction between electron and nucleon by using a sensitive spin-exchange relaxation-free atomic magnetometer.
An extension of Shelah’s trichotomy theorem

Shelah (Algorithms Comb 14:420–459, 1997) develops the theory of $$\mathrm {pcf}_I(A)$$ without the assumption that $$|A|<\min (A)$$ , going so far as to get generators for every $$\lambda \in \mathrm {pcf}_I(A)$$ under some assumptions on I. Our main theorem is that we can also generalize Shelah’s trichotomy theorem to the same setting. Using this, we present a different proof of the existence of generators for $$\mathrm {pcf}_I(A)$$ which is more in line with the modern exposition. Finally, we discuss some obstacles to further generalizing the classical theory.
Randomization Tests that Condition on Non-Categorical Covariate Balance

A benefit of randomized experiments is that covariate distributions of treatment and control groups are balanced on average, resulting in simple unbiased estimators for treatment effects. However, it is possible that a particular randomization yields covariate imbalances that researchers want to address in the analysis stage through adjustment or other methods. Here we present a randomization test that conditions on covariate balance by only considering treatment assignments that are similar to the observed one in terms of covariate balance. Previous conditional randomization tests have only allowed for categorical covariates, while our randomization test allows for any type of covariate. Through extensive simulation studies, we find that our conditional randomization test is more powerful than unconditional randomization tests and other conditional tests. Furthermore, we find that our conditional randomization test is valid (1) unconditionally across levels of covariate balance, and (2) conditional on particular levels of covariate balance. Meanwhile, unconditional randomization tests are valid for (1) but not (2). Finally, we find that our conditional randomization test is similar to a randomization test that uses a model-adjusted test statistic.
Lights illuminate surfaces superluminally

When a light bulb is turned on, light moves away from it at speed c, by definition. When light from this bulb illuminates a surface, however, this illumination front is not constrained to move at speed c. A simple proof is given that this illumination front always moves faster than c. Generalized, when any compact light source itself varies, this information spreads across all of the surfaces it illuminates at speeds faster than light.
Monopole-antimonopole: interaction, scattering and creation.

The interaction of a magnetic monopoleantimonopole pair depends on their separation as well as on a second twist degree of freedom. This novel interaction leads to a non-trivial bound state solutio...
Novel aspects of the extended first law of entanglement

Using AdS/CFT an extended first law of entanglement has been previously derived for the vacuum reduced to a ball in Minkowski. The statement not only includes perturbations of the state but also of the conformal field theory (CFT), via variations of the generalized central charge. We clarify some subtleties previously overlooked and use simple arguments to generalize prior derivations to arbitrary gravity theories in the bulk as well as new regions in the boundary CFT. Our construction also applies to two-dimensional bulk theories and admits an interesting extension for a three-dimensional bulk, providing a curious result regarding the thermodynamic volume in extended black hole thermodynamics. We discuss future prospects regarding the extended first law of entanglement.
Birationality and Landau–Ginzburg Models

We introduce a new technique for approaching birationality questions that arise in the mirror symmetry of complete intersections in toric varieties. As an application we answer affirmatively and conclusively the question of Batyrev–Nill (Integer points in polyhedra—geometry, number theory, representation theory, algebra, optimization, statistics, volume 452 of Contemporary mathematics. American Mathematical Society, Providence, pp 35–66, 2008) about the birationality of Calabi–Yau families associated to multiple mirror nef-partitions. This completes the progress in this direction made by Li’s breakthrough (Li in Adv Math 299:71–107, 2016). In the process, we obtain results in the theory of Borisov’s nef-partitions (Borisov in Towards the mirror symmetry for Calabi–Yau complete intersections in Gorenstein toric Fano varieties, 1993. arXiv:alg-geom/9310001) and provide new insight into the geometric content of the multiple mirror phenomenon.
Non-commutative Hilbert Modular Symbols

In this paper we construct non-commutative Hilbert modular symbols, which are generalizations of Manin’s non-commutative modular symbol. We use a generalization of iterated path integrals to higher dimensions, which we call iterated integrals over membranes. Manin examines similarities between non-commutative modular symbol and multiple zeta values both in terms of infinite series and in terms of iterated path integrals. Here we examine similarities in the formulas for non-commutative Hilbert modular symbol and multiple Dedekind zeta values both in terms of infinite series and in terms of iterated integrals over membranes.
Modeling Quantum Gravity Effects in Inflation

Cosmological models in 1+1 dimensions are an ideal setting for investigating the quantum structure of inflationary dynamics — gravity is renormalizable, while there is room for spatial structure not present in the minisuperspace approximation. We use this fortuitous convergence to investigate the mechanism of slow-roll eternal inflation. A variant of 1+1 Liouville gravity coupled to matter is shown to model precisely the scalar sector of cosmological perturbations in 3+1 dimensions. A particular example of quintessence in 1+1d is argued on the one hand to exhibit slow-roll eternal inflation according to standard criteria; on the other hand, a field redefinition relates the model to pure de Sitter gravity coupled to a free scalar matter field with no potential. This and other examples show that the standard logic leading to slow-roll eternal inflation is not invariant under field redefinitions, thus raising concerns regarding its validity. Aspects of the quantization of Liouville gravity as a model of quantum de Sitter space are also discussed.
Matrices with restricted entries and $q$-analogues of permutations

We study the functions that count matrices of given rank over a finite field with specified positions equal to zero. We show that these matrices are $q$-analogues of permutations with certain restricted values. We obtain a simple closed formula for the number of invertible matrices with zero diagonal, a $q$-analogue of derangements, and a curious relationship between invertible skew-symmetric matrices and invertible symmetric matrices with zero diagonal. In addition, we provide recursions to enumerate matrices and symmetric matrices with zero diagonal by rank, and we frame some of our results in the context of Lie theory. Finally, we provide a brief exposition of polynomiality results for enumeration questions related to those mentioned, and give several open questions.
Canonical Traces and Directly Finite Leavitt Path Algebras

Motivated by the study of traces on graph C∗-algebras, we consider traces (additive, central maps) on Leavitt path algebras, the algebraic counterparts of graph C∗-algebras. In particular, we consider traces which vanish on nonzero graded components of a Leavitt path algebra and refer to them as canonical since they are uniquely determined by their values on the vertices. A desirable property of a \(\mathbb {C}\)-valued trace on a C∗-algebra is that the trace of an element of the positive cone is nonnegative. We adapt this property to traces on a Leavitt path algebra LK(E) with values in any involutive ring. We refer to traces with this property as positive. If a positive trace is injective on positive elements, we say that it is faithful. We characterize when a canonical, K-linear trace is positive and when it is faithful in terms of its values on the vertices. As a consequence, we obtain a bijective correspondence between the set of faithful, gauge invariant, \(\mathbb {C}\)-valued (algebra) traces on \(L_{\mathbb {C}}(E)\) of a countable graph E and the set of faithful, semifinite, lower semicontinuous, gauge invariant (operator theory) traces on the corresponding graph C∗-algebra C∗(E). With the direct finite condition (i.e xy=1 implies yx=1) for unital rings adapted to rings with local units, we characterize directly finite Leavitt path algebras as exactly those having the underlying graphs in which no cycle has an exit. Our proof involves consideration of “local” Cohn-Leavitt subalgebras of finite subgraphs. Lastly, we show that, while related, the class of locally noetherian, the class of directly finite, and the class of Leavitt path algebras which admit a faithful trace are different in general.
G-valued crystalline representations with minuscule p-adic Hodge type

We study G-valued semi-stable Galois deformation rings where G is a reductive group. We develop a theory of Kisin modules with G-structure and use this to identify the connected components of crystalline deformation rings of minuscule p-adic Hodge type with the connected components of moduli of “finite flat models with G-structure.” The main ingredients are a construction in integral p-adic Hodge theory using Liu’s theory of (φ, b G)-modules and the local models constructed by Pappas and Zhu.
Seven sphere and the exceptional nonlinear superconformal algebras

Abstract The realizations of the exceptional non-linear (quadratically generated, or W-type) N = 8 and N = 7 superconformal algebras with Spin(7) and G2 affine symmetry currents are reviewed. Both the N = 8 and N = 7 algebras admit unitary realizations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G2, with the central charges c 8 = 26 5 and c 7 = 5 , respectively. They can also be realized over the coset spaces SO(8) × U(1) SO(7) and SO(7) × U(1) G 2 for some fixed values of their central charges, respectively. The coset space SO(8) SO(7) is the seven-sphere S7, whereas the space SO(7) G 2 represents the seven-sphere with torsion. We conclude with a discussion of a novel ‘hybrid’ method developed recently that yields unitary realizations of the exceptional N = 8 and N = 7 algebras for all allowed values of their central charges.
Bloch waves and fuzzy cylinders: 1/4-BPS solutions of matrix theory

In this note, we present a broad class of 1/4-BPS solutions to matrix theory, corresponding to non-commutative cylinders of arbitrary cross-sectional profile in R8. The solutions provide a microscopic description of a general supertube configuration. Taking advantage of an analogy between a compact matrix dimension and the hamiltonian of a 1-dimensional crystal, we use a Bloch wave basis to diagonalize the transverse matrices, finding a distribution of eigenvalues which smoothly trace the profile curve as the Bloch wave number is varied.
Anisotropies in the gravitational-wave stochastic background

We consider anisotropies in the stochastic background of gravitational-waves (SBGW) arising from random fluctuations in the number of gravitational-wave sources. We first develop the general formalism which can be applied to different cosmological or astrophysical scenarios. We then apply this formalism to calculate the anisotropies of SBGW associated with the fluctuations in the number of cosmic string loops, considering both cosmic string cusps and kinks. We calculate the anisotropies as a function of angle and frequency.
Evaluation of copper, aluminum, and nickel interatomic potentials on predicting the elastic properties

Choice of appropriate force field is one of the main concerns of any atomistic simulation that needs to be seriously considered in order to yield reliable results. Since investigations on the mechanical behavior of materials at micro/nanoscale have been becoming much more widespread, it is necessary to determine an adequate potential which accurately models the interaction of the atoms for desired applications. In this framework, reliability of multiple embedded atom method based interatomic potentials for predicting the elastic properties was investigated. Assessments were carried out for different copper, aluminum, and nickel interatomic potentials at room temperature which is considered as the most applicable case. Examined force fields for the three species were taken from online repositories of National Institute of Standards and Technology, as well as the Sandia National Laboratories, the LAMMPS database. Using molecular dynamic simulations, the three independent elastic constants, C11, C12, and C44...
Spanwise effects on instabilities of compressible flow over a long rectangular cavity

The stability properties of two-dimensional (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of $$L/D=6$$ are analyzed at a free-stream Mach number of $$M_\infty =0.6$$ and depth-based Reynolds number of $$Re_D=502$$ . In this study, we closely examine the influence of three-dimensionality on the wake mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the stability characteristics of the wake mode. Using the bi-global stability analysis with the time-averaged flow as the base state, we capture the global stability properties of the wake mode at a spanwise wavenumber of $$\beta =0$$ . To uncover spanwise effects on the 2D wake mode, 3D DNS are performed with cavity width-to-depth ratio of $$W/D=1$$ and 2. We find that the 2D wake mode is not present in the 3D cavity flow with $$W/D=2$$ , in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of $$\lambda /D=0.5{-}2.0$$ to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.
Lech’s inequality for the Buchsbaum-Rim multiplicity and mixed multiplicity

We generalize an improved Lech bound, due to Huneke, Smirnov, and Validashti, for the Buchsbaum-Rim multiplicity and mixed multiplicity. We reduce the problem to the graded case and then to the polynomial ring case. There we use complete reductions, studied by Rees, to prove sharper bounds for the mixed multiplicity in low dimensions before proving the general case.
Periodic continued fractions over $S$-integers in number fields and Skolem’s $p$-adic method

We generalize the classical theory of periodic continued fractions (PCFs) over ${\mathbf Z}$ to rings ${\mathcal O}$ of $S$-integers in a number field. Let ${\mathcal B}=\{\beta, {\beta^*}\}$ be the multi-set of roots of a quadratic polynomial in ${\mathcal O}[x]$. We show that PCFs $P=[b_1,\ldots,b_N,\bar{a_1\ldots ,a_k}]$ of type $(N,k)$ potentially converging to a limit in ${\mathcal B}$ are given by ${\mathcal O}$-points on an affine variety $V:=V({\mathcal B})_{N,k}$ generically of dimension $N+k-2$. We give the equations of $V$ in terms of the continuant polynomials of Wallis and Euler. The integral points $V({\mathcal O})$ are related to writing matrices in $\textrm{SL}_2({\mathcal O})$ as products of elementary matrices. We give an algorithm to determine if a PCF converges and, if so, to compute its limit. Our standard example generalizes the PCF $\sqrt{2}=[1,\bar{2}]$ to the ${\mathbf Z}_2$-extension of ${\mathbf Q}$: $F_n={\mathbf Q}(\alpha_n)$, $\alpha_{n}:=2\cos(2\pi/2^{n+2})$, with integers ${\mathcal O}_n={\mathbf Z}[\alpha_n]$. We want to find the PCFs of $\alpha_{n+1}$ over ${\mathcal O}_{n}$ of type $(N,k)$ by finding the ${\mathcal O}_{n}$-points on $V({\mathcal B}_{n+1})_{N,k}$ for ${\mathcal B}_{n+1}:=\{\alpha_{n+1}, -\alpha_{n+1}\}$. There are three types $(N,k)=(0,3), (1,2), (2,1)$ such that the associated PCF variety $V({\mathcal B})_{N,k}$ is a curve; we analyze these curves. For generic ${\mathcal B}$, Siegel's theorem implies that each of these three $V({\mathcal B})_{N,k}({\mathcal O})$ is finite. We find all the ${\mathcal O}_n$-points on these PCF curves $V({\mathcal B}_{n+1})_{N,k}$ for $n=0,1$. When $n=1$ we make extensive use of Skolem's $p$-adic method for $p=2$, including its application to Ljunggren's equation $x^2 + 1 =2y^4$.