cssi/SciSciGPT-SciSciNet huggingface dataset:
Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs

We present exact calculations of chromatic polynomials for families of cyclic graphs consisting of linked polygons, where the polygons may be adjacent or separated by a given number of bonds. From these we calculate the (exponential of the) ground state entropy, W, for the q-state Potts model on these graphs in the limit of infinitely many vertices. A number of properties are proved concerning the continuous locus, , of nonanalyticities in W. Our results provide further evidence for a general rule concerning the maximal region in the complex q plane to which one can analytically continue from the physical interval where S0>0.
Enhancing Domain Word Embedding via Latent Semantic Imputation

We present a novel method named Latent Semantic Imputation (LSI) to transfer external knowledge into semantic space for enhancing word embedding. The method integrates graph theory to extract the latent manifold structure of the entities in the affinity space and leverages non-negative least squares with standard simplex constraints and power iteration method to derive spectral embeddings. It provides an effective and efficient approach to combining entity representations defined in different Euclidean spaces. Specifically, our approach generates and imputes reliable embedding vectors for low-frequency words in the semantic space and benefits downstream language tasks that depend on word embedding. We conduct comprehensive experiments on a carefully designed classification problem and language modeling and demonstrate the superiority of the enhanced embedding via LSI over several well-known benchmark embeddings. We also confirm the consistency of the results under different parameter settings of our method.
Kinetic Monte Carlo Simulations of the Grain-surface Back-diffusion Effect

Rate-equation models are a widely used and inexpensive tool for the simulation of interstellar chemistry under a range of physical conditions. However, their application to grain-surface chemical systems necessitates a number of simplifying assumptions, due to the requirement to treat only the total population of each species, using averaged rates, rather than treating each surface particle as an independent entity. While the outputs from rate-equation models are strictly limited to such population information, the inputs—in the form of the averaged rates that control the time-evolution of chemical populations—can be guided by the results from more exact simulation methods. Here, we examine the effects of back-diffusion, wherein particles diffusing on a surface revisit binding sites on the lattice, slowing the total reaction rate. While this effect has been studied for two-particle systems, its influence at greater surface coverage of reactants has not been explored. Results from two Monte Carlo kinetics models (one a 2D periodic lattice, the other the surface of a three-dimensionally realized grain) were used to develop a means to incorporate the grain-surface back-diffusion effect into rate-equation methods. The effects of grain size, grain morphology, and surface coverage on the magnitude of the back-diffusion effect were studied for the simple H+H reaction system. The results were fit with expressions that can be easily incorporated into astrochemical rate-equation models to accurately reproduce the effects of back-diffusion on grain-surface reaction rates. Back-diffusion reduces reaction rates by a maximum factor of around 5 for the canonical grain of ~106 surface sites, but this falls to unity at close to full surface coverage.
Non-stationary Stochastic Optimization under L_{p,q}-Variation Measures

We consider a non-stationary sequential stochastic optimization problem, in which the underlying cost functions change over time under a variation budget constraint. We propose an $L_{p,q}$-variation functional to quantify the change, which yields less variation for dynamic function sequences whose changes are constrained to short time periods or small subsets of the input domain. Under the $L_{p,q}$-variation constraint, we derive both upper and matching lower regret bounds for smooth and strongly convex function sequences, which generalize previous results in Besbes et al. (2015). { Furthermore, we provide an upper bound for general convex function sequences with noisy gradient feedback, which matches the optimal rate as $p \rightarrow \infty$. Our results reveal some surprising phenomena under this general variation functional, such as the curse of dimensionality of the function domain. The key technical novelties in our analysis include affinity lemmas that characterize the distance of the minimizers of two convex functions with bounded $L_p$ difference, and a cubic spline based construction that attains matching lower bounds.
Technical Advantages for Weak-Value Amplification: When Less Is More

``Weak-value amplification,'' an interference effect that was introduced quantum mechanically, but can also be realized using classical electromagnetic waves, uses only a small fraction of the available events to make precise measurements. How can this be? Theorists reveal that weak-value amplification achieves that by funneling all the information into a small fraction of events.
Hard probes in heavy ion collisions: current status and prospects for application of QCD evolution techniques

In the past decade the observation of cross section modification for leading hadrons, heavy flavor and two particle correlations in heavy ion collisions has provided important insights into the dynamics of parton propagation in dense strongly-interacting matter. The development of the theory of reconstructed jets and related experimental measurements have further shed light on the characteristics of in-medium parton showers. So far, experimental results from ultra-relativistic nuclear collisions at RHIC and LHC have been analyzed in the framework of parton energy loss, where the precision of the theoretical predictions cannot be systematically improved. Only recently have higher order calculations and applications of resummation and evolution to heavy ion collisions begun to emerge. Several examples of such advances are discussed in these proceedings.
The merger-driven evolution of warm infrared luminous galaxies

We present a merger-driven evolutionary model for the production of luminous (LIRGs) and ultraluminous infrared galaxies (ULIRGs) with warm infrared (IR) colours. Our results show that simulations of gas-rich major mergers including star formation, black hole growth and feedback can produce warm (U)LIRGs. We also find that while the warm evolutionary phase is associated with increased active galactic nucleus (AGN) activity, star formation alone may be sufficient to produce warm IR colours. However, the transition can be suppressed entirely – even when there is a significant AGN contribution – when we assume a single-phase interstellar medium, which maximizes the attenuation. Finally, our evolutionary models are consistent with the 25-to-60 flux density ratio versus LHX/LIR relation for local LIRGs and ULIRGs, and predict the observed scatter in IR colour at fixed LHX/LIR. Therefore, our models suggest a cautionary note in the interpretation of warm IR colours: while associated with periods of active black hole growth, they are probably produced by a complex mix of star formation and AGN activity intermediate between the cold star formation dominated phase and the birth of a bright, unobscured quasar.
Distributive laws for Lawvere theories

Lawvere Theories and monads are two related but subtly different ways of handling algebraic theories. Distributive laws give a way of combining two algebraic structures expressed as monads, so one might naturally ask whether something analogous can be done for Lawvere Theories; this question was posed to me by Jean Benabou in 2009 following my talk on iterated distributive laws for monads. In this talk I will give three ways of doing this. The first uses a generalised notion of “factorisation systems over I” [3], the second uses bimodules as in [2] and the third uses an extension of the free finite-product category 2-monad from Cat to Prof [1]. In each case Lawvere theories are reformulated as certain monads in a bicategory (as already proposed by Lack and Hyland), and distributive laws between them are then certain distributive laws in that bicategory. I will exhibit comparison functors between CAT and each of these bicategories to show that the distributive laws between the Lawvere theories correspond in a suitable way to distributive laws between their associated finitary monads. The three different but equivalent formulations then provide a framework conducive to generalisation, but also an explicit description of the composite theories arising from distributive laws.
A novel finding in pediatric leiomyosarcoma: Expanding spectrum of FGFR rearrangements in childhood cancers.

Non Rhabdomyosarcoma Soft Tissue Sarcomas (NRSTS) are rare in the pediatric age group, accounting for 1-7% of all pediatric tumors. Leiomyosarcoma, a subtype of NRSTS, is exceedingly rare in pediatric population. Due to the rarity of this condition, management is extrapolated from other common NRSTS which involves surgery, chemotherapy and radiation. Chemotherapy is not very effective in management of pediatric leiomyosarcoma and molecular information may help guide targeted therapies. We describe a patient with a FGFR1-TACC1 gene rearrangement which, based on other models, predicts for sensitivity to FGFR inhibitors.
Do we live in the center of the world

Abstract We investigate the distribution of energy density in a stationary self-reproducing inflationary universe. We show that the main fraction of the volume of the universe in a state with a given density ϱ at any given moment of time t in synchronous coordinates is concentrated near the centers of deep exponentially wide spherically symmetric holes in the density distribution.
Piezoelectricity and topological quantum phase transitions in two-dimensional spin-orbit coupled crystals with time-reversal symmetry.

Finding new physical responses that signal topological quantum phase transitions is of both theoretical and experimental importance. Here, we demonstrate that the piezoelectric response can change discontinuously across a topological quantum phase transition in two-dimensional time-reversal invariant systems with spin-orbit coupling, thus serving as a direct probe of the transition. We study all gap closing cases for all 7 plane groups that allow non-vanishing piezoelectricity, and find that any gap closing with 1 fine-tuning parameter between two gapped states changes either the Z2 invariant or the locally stable valley Chern number. The jump of the piezoelectric response is found to exist for all these transitions, and we propose the HgTe/CdTe quantum well and BaMnSb2 as two potential experimental platforms. Our work provides a general theoretical framework to classify topological quantum phase transitions, and reveals their ubiquitous relation to the piezoelectric response. The linear response and topological electronic properties of a material both depend on the underlying crystal symmetry. Here the authors study how topological phase transitions in two-dimensional materials manifest themselves in the piezoelectric response.
On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator

Extended dynamic mode decomposition (EDMD) (Williams et al. in J Nonlinear Sci 25(6):1307–1346, 2015) is an algorithm that approximates the action of the Koopman operator on an N-dimensional subspace of the space of observables by sampling at M points in the state space. Assuming that the samples are drawn either independently or ergodically from some measure $$\mu $$ , it was shown in Klus et al. (J Comput Dyn 3(1):51–79, 2016) that, in the limit as $$M\rightarrow \infty $$ , the EDMD operator $$\mathcal {K}_{N,M}$$ converges to $$\mathcal {K}_N$$ , where $$\mathcal {K}_N$$ is the $$L_2(\mu )$$ -orthogonal projection of the action of the Koopman operator on the finite-dimensional subspace of observables. We show that, as $$N \rightarrow \infty $$ , the operator $$\mathcal {K}_N$$ converges in the strong operator topology to the Koopman operator. This in particular implies convergence of the predictions of future values of a given observable over any finite time horizon, a fact important for practical applications such as forecasting, estimation and control. In addition, we show that accumulation points of the spectra of $$\mathcal {K}_N$$ correspond to the eigenvalues of the Koopman operator with the associated eigenfunctions converging weakly to an eigenfunction of the Koopman operator, provided that the weak limit of the eigenfunctions is nonzero. As a by-product, we propose an analytic version of the EDMD algorithm which, under some assumptions, allows one to construct $$\mathcal {K}_N$$ directly, without the use of sampling. Finally, under additional assumptions, we analyze convergence of $$\mathcal {K}_{N,N}$$ (i.e., $$M=N$$ ), proving convergence, along a subsequence, to weak eigenfunctions (or eigendistributions) related to the eigenmeasures of the Perron–Frobenius operator. No assumptions on the observables belonging to a finite-dimensional invariant subspace of the Koopman operator are required throughout.
The Chillingworth class is a signed stable length

Let Sg be a closed, oriented surface with genus g 3, and Sg;1 an oriented surface with genus g 3 and one boundary curve. The mapping class group of Sg , denoted Mod.Sg/, is the group of isotopy classes of orientation preserving homeomorphisms of Sg . The group Mod.Sg;1/ is defined similarly, with the added condition that the homeomorphisms act as the identity on the boundary of Sg;1 . The group Mod.Sg/ induces an action on H1.Sg;Z/, and the Torelli group Tg is the kernel of this action. The Torelli group Tg;1 is similarly defined.
Fundamental limits on communication for oblivious updates in storage networks

In distributed storage systems, storage nodes intermittently go offline for numerous reasons. On coming back online, nodes need to update their contents to reflect any modifications to the data in the interim. In this paper, we consider a setting where no information regarding modified data needs to be logged in the system. In such a setting, a ‘stale’ node needs to update its contents by downloading data from already updated nodes, while neither the stale node nor the updated nodes have any knowledge as to which data symbols are modified and what their value is. We investigate the fundamental limits on the amount of communication necessary for such an oblivious update process. We first present a generic lower bound on the amount of communication that is necessary under any storage code with a linear encoding (while allowing non-linear update protocols). This lower bound is derived under a set of extremely weak conditions, giving all updated nodes access to the entire modified data and the stale node access to the entire stale data as side information. We then present codes and update algorithms that are optimal in that they meet this lower bound. Next, we present a lower bound for an important subclass of codes, that of linear Maximum-Distance-Separable (MDS) codes. We then present an MDS code construction and an associated update algorithm that meets this lower bound. These results thus establish the capacity of oblivious updates in terms of the communication requirements under these settings.
NMR shifts for polycyclic aromatic hydrocarbons from first-principles

We present first-principles, density-functional theory calculations of the NMR chemical shifts for polycyclic aromatic hydrocarbons, starting with benzene and increasing sizes up to the one- and two-dimensional infinite limits of graphene ribbons and sheets. Our calculations are performed using a combination of the recently developed theory of orbital magnetization in solids, and a novel approach to NMR calculations where chemical shifts are obtained from the derivative of the orbital magnetization with respect to a microscopic, localized magnetic dipole. Using these methods we study on equal footing the (1)H and (13)C shifts in benzene, pyrene, coronene, in naphthalene, anthracene, naphthacene, and pentacene, and finally in graphene, graphite, and an infinite graphene ribbon. Our results show very good agreement with experiments and allow us to characterize the trends for the chemical shifts as a function of system size. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 3336-3342, 2009
DISCOVERY OF ROTATIONAL MODULATIONS IN THE PLANETARY-MASS COMPANION 2M1207b: INTERMEDIATE ROTATION PERIOD AND HETEROGENEOUS CLOUDS IN A LOW GRAVITY ATMOSPHERE

Rotational modulations of brown dwarfs have recently provided powerful constraints on the properties of ultra-cool atmospheres, including longitudinal and vertical cloud structures and cloud evolution. Furthermore, periodic light curves directly probe the rotational periods of ultra-cool objects. We present here, for thefirst time, time-resolved highprecision photometric measurements of a planetary-mass companion, 2M1207b. We observed the binary system with Hubble Space Telescope/Wide Field Camera 3 in two bands and with two spacecraft roll angles. Using point-spread function-based photometry, we reach a nearly photon-noise limited accuracy for both the primary and the secondary. While the primary is consistent with aflat light curve, the secondary shows modulations that are clearly detected in the combined light curve as well as in different subsets of the data. The amplitudes are 1.36% in the F125W and 0.78% in the F160Wfilters, respectively. Byfitting sine waves to the light curves, wefind a consistent period of 10.7 0.6 � � hr and similar phases in both bands. The J- and H-band amplitude ratio of 2M1207b is very similar to afield brown dwarf that has identical spectral type but different J‐H color. Importantly, our study also measures, for thefirst time, the rotation period for a directly imaged extra-solar planetary-mass companion.
A low-power reversible alkali atom source

An electrically controllable, solid-state, reversible device for sourcing and sinking alkali vapor is presented. When placed inside an alkali vapor cell, both an increase and decrease in the rubidium vapor density by a factor of two are demonstrated through laser absorption spectroscopy on 10–15 s time scales. The device requires low voltage (5 V), low power (<3.4 mW peak power), and low energy (<10.7 mJ per 10 s pulse). The absence of oxygen emission during operation is shown through residual gas analysis, indicating that Rb is not lost through chemical reaction but rather by ion transport through the designed channel. This device is of interest for atomic physics experiments and, in particular, for portable cold-atom systems where dynamic control of alkali vapor density can enable advances in science and technology.
Bio-inspired Multi-layer Spiking Neural Network Extracts Discriminative Features from Speech Signals

Spiking neural networks (SNNs) enable power-efficient implementations due to their sparse, spike-based coding scheme. This paper develops a bio-inspired SNN that uses unsupervised learning to extract discriminative features from speech signals, which can subsequently be used in a classifier. The architecture consists of a spiking convolutional/pooling layer followed by a fully connected spiking layer for feature discovery. The convolutional layer of leaky, integrate-and-fire (LIF) neurons represents primary acoustic features. The fully connected layer is equipped with a probabilistic spike-timing-dependent plasticity learning rule. This layer represents the discriminative features through probabilistic, LIF neurons. To assess the discriminative power of the learned features, they are used in a hidden Markov model (HMM) for spoken digit recognition. The experimental results show performance above 96% that compares favorably with popular statistical feature extraction methods. Our results provide a novel demonstration of unsupervised feature acquisition in an SNN.
Deep Learning Classification of Chest X-Ray Images

We propose a deep learning based method for classification of commonly occurring pathologies in chest X-ray images. The vast number of publicly available chest X-ray images provides the data necessary for successfully employing deep learning methodologies to reduce the misdiagnosis of thoracic diseases. We applied our method to the classification of two example pathologies, pulmonary nodules and cardiomegaly, and we compared the performance of our method to three existing methods. The results show an improvement in AUC for detection of nodules and cardiomegaly compared to the existing methods.
The Propagation of Uncertainties in Stellar Population Synthesis Modeling. II. The Challenge of Comparing Galaxy Evolution Models to Observations

Models for the formation and evolution of galaxies readily predict physical properties such as star formation rates, metal-enrichment histories, and, increasingly, gas and dust content of synthetic galaxies. Such predictions are frequently compared to the spectral energy distributions of observed galaxies via the stellar population synthesis (SPS) technique. Substantial uncertainties in SPS exist, and yet their relevance to the task of comparing galaxy evolution models to observations has received little attention. In the present work, we begin to address this issue by investigating the importance of uncertainties in stellar evolution, the initial stellar mass function (IMF), and dust and interstellar medium (ISM) properties on the translation from models to observations. We demonstrate that these uncertainties translate into substantial uncertainties in the ultraviolet, optical, and near-infrared colors of synthetic galaxies. Aspects that carry significant uncertainties include the logarithmic slope of the IMF above 1 M{sub sun}, dust attenuation law, molecular cloud disruption timescale, clumpiness of the ISM, fraction of unobscured starlight, and treatment of advanced stages of stellar evolution including blue stragglers, the horizontal branch, and the thermally pulsating asymptotic giant branch. The interpretation of the resulting uncertainties in the derived colors is highly non-trivial because many of the uncertainties aremore » likely systematic, and possibly correlated with the physical properties of galaxies. We therefore urge caution when comparing models to observations.« less
String Tension and Removal of Lattice Coarsening Effects in Monte Carlo Renormalization Group

We study the computation of the static quark potential under decimations in the Monte Carlo Renormalization Group (MCRG). Employing a multirepresentation plaquette action, we find that fine-tuning the decimation prescription so that the MCRG equilibrium self-consistency condition is satisfied produces dramatic improvement at large distances. In particular, lattice coarsening (change of effective lattice spacing on action-generated lattices after decimation) is nearly eliminated. Failure to correctly tune the decimation, on the other hand, produces large coarsening effects, of order 50% or more, consistent with those seen in previous studies. We also study rotational invariance restoration at short distances, where no particular improvement is seen for this action.
Frequency dependence of trapped flux sensitivity in SRF cavities

In this letter, we present the frequency dependence of the vortex surface resistance of bulk niobium accelerating cavities as a function of different state-of-the-art surface treatments. Higher flux surface resistance per amount of trapped magnetic field—sensitivity—is observed for higher frequencies, in agreement with our theoretical model. Higher sensitivity is observed for N-doped cavities, which possess an intermediate value of the electron mean-free-path, compared to 120 °C and EP/BCP cavities. Experimental results from our study showed that the sensitivity has a non-monotonic trend as a function of the mean-free-path, including frequencies other than 1.3 GHz, and that the vortex response to the rf field can be tuned from the pinning regime to flux-flow regime by manipulating the frequency and/or the mean-free-path of the resonator, as reported in our previous studies. The frequency dependence of the trapped flux sensitivity to the amplitude of the accelerating gradient is also highlighted.
Quasi-integrability in supersymmetric sine-Gordon models

The deformed supersymmetric sine-Gordon model, obtained through known deformation of the corresponding potential, is found to be quasi-integrable , like its non-supersymmetric counterpart, which was observed earlier. The system expectedly possesses finite number of conserved quantities, leaving-out an infinite number of non-conserved anomalous charges. The quasi-integrability of this supersymmetric model heavily rely on the boundary conditions of the potential, otherwise rendered to be completely non-integrable. Moreover, interesting additional algebraic structures appear, absent in the non-supersymmetric counterparts.
Byte Pair Encoding is Suboptimal for Language Model Pretraining

The success of pretrained transformer language models (LMs) in natural language processing has led to a wide range of pretraining setups. In particular, these models employ a variety of subword tokenization methods, most notably byte-pair encoding (BPE) (Sennrich et al., 2016; Gage, 1994), the WordPiece method (Schuster and Nakajima, 2012), and unigram language modeling (Kudo, 2018), to segment text. However, to the best of our knowledge, the literature does not contain a direct evaluation of the impact of tokenization on language model pretraining. We analyze differences between BPE and unigram LM tokenization, finding that the latter method recovers subword units that align more closely with morphology and avoids problems stemming from BPE’s greedy construction procedure. We then compare the fine-tuned task performance of identical transformer masked language models pretrained with these tokenizations. Across downstream tasks and two languages (English and Japanese), we find that the unigram LM tokenization method matches or outperforms BPE. We hope that developers of future pretrained LMs will consider adopting the unigram LM method over the more prevalent BPE.
Interplay of curvature and rigidity in shape-based models of confluent tissue

This work takes a biologically inspired model of dense disordered biological tissue and studies the structural, mechanical, and dynamical effects of embedding the model on a sphere. By focusing on the interplay between curvature and rigidity, this paper identifies a mechanism by which dividing cells can collectively rigidify or unjam by tuning the relative curvature of their domain as they grow. Outside of the biological context, this work also reflects on the nature of disordered rigidity transitions in curved space.
The B-L/electroweak hierarchy in heterotic string and M-theory

E8 × E8 heterotic string and M-theory, when compactified on a Calabi-Yau threefold admitting an SU(4) vector bundle with Wilson lines, can give rise to the exact MSSM spectrum with three right-handed neutrino chiral superields, one per family. Rank preserving Wilson lines require that the standard model group be augmented by a gauged U(1)B−L. Since there are no fields in this theory for which 3(B−L) is an even, non-zero integer, the gauged B-L symmetry must be spontaneously broken at a low scale, not too far above the electroweak scale. It is shown that in these heterotic standard models, the B-L symmetry can be broken, with a phenomenologically viable B-L/electroweak hierarchy, by at least one right-handed sneutrino acquiring a vacuum expectation value. This is explicitly demonstrated, in a specific region of parameter space, using a renormalization group analysis and soft supersymmetry breaking operators. The vacuum state is shown to be a stable, local minimum of the potential and the resultant hierarchy is explicitly presented in terms of tanβ.
Structural transitions and soft modes in frustrated DNA crystals

Relying on symmetry considerations appropriate for helical biopolymers such as DNA and filamentous actin, we argue that crystalline packings of mutually repulsive helical macromolecules fall principally into two categories: unfrustrated (hexagonal) and frustrated (rhombohedral). For both cases, we construct the Landau-Ginzburg free energy for the 2D columnar-hexagonal to 3D crystalline phase transition, including the coupling between molecular displacements along biopolymer backbone to displacements in the plane of hexagonal order. We focus on the distinct elastic properties that emerge upon crystallization of helical arrays due to this coupling. Specifically, we demonstrate that frustrated states universally exhibit a highly anisotropic in-plane elastic response, characterized by an especially soft compliance to simple-shear deformations and a comparatively large resistance to those deformations that carry the array from the low- to high-density crystalline states of DNA.
A Nonlocal Isoperimetric Problem with Dipolar Repulsion

We study a geometric variational problem for sets in the plane in which the perimeter and a regularized dipolar interaction compete under a mass constraint. In contrast to previously studied nonlocal isoperimetric problems, here the nonlocal term asymptotically localizes and contributes to the perimeter term to leading order. We establish existence of generalized minimizers for all values of the dipolar strength, mass and regularization cutoff and give conditions for existence of classical minimizers. For subcritical dipolar strengths we prove that the limiting functional is a renormalized perimeter and that for small cutoff lengths all mass-constrained minimizers are disks. For critical dipolar strength, we identify the next-order $$\Gamma $$-limit when sending the cutoff length to zero and prove that with a slight modification of the dipolar kernel there exist masses for which classical minimizers are not disks.
Estimating Error and Bias in Offline Evaluation Results

Offline evaluations of recommender systems attempt to estimate users' satisfaction with recommendations using static data from prior user interactions. These evaluations provide researchers and developers with first approximations of the likely performance of a new system and help weed out bad ideas before presenting them to users. However, offline evaluation cannot accurately assess novel, relevant recommendations, because the most novel items were previously unknown to the user, so they are missing from the historical data and cannot be judged as relevant. We present a simulation study to estimate the error that such missing data causes in commonly-used evaluation metrics in order to assess its prevalence and impact. We find that missing data in the rating or observation process causes the evaluation protocol to systematically mis-estimate metric values, and in some cases erroneously determine that a popularity-based recommender outperforms even a perfect personalized recommender. Substantial breakthroughs in recommendation quality, therefore, will be difficult to assess with existing offline techniques.
Nonlinear ultrafast fiber amplifiers beyond the gain-narrowing limit

Ultrafast lasers are becoming increasingly widespread in science and industry alike. Fiber-based ultrafast laser sources are especially attractive because of their compactness, alignment-free setups, and potentially low cost. However, confining short pulses within a fiber core leads to high intensities, which drives a host of nonlinear effects. While these phenomena and their interactions greatly complicate the design of such systems, they can also provide opportunities for engineering new capabilities. Here, we report a new fiber amplification regime distinguished by the use of a dynamically evolving gain spectrum as a degree of freedom: as a pulse experiences nonlinear spectral broadening, absorption and amplification actively reshape both the pulse and the gain spectrum itself. The dynamic co-evolution of the field and excited-state populations supports pulses that can broaden spectrally by almost two orders of magnitude and well beyond the gain bandwidth, while remaining cleanly compressible to their sub-50-fs transform limit. Theory and experiments provide evidence that a nonlinear attractor underlies the management of the nonlinearity by the gain. Further research into these mutual, pulse-inversion propagation dynamics may address open scientific questions and pave the way toward simple, compact fiber sources that produce high-energy, sub-30-fs pulses.
Photon polarizability and its effect on the dispersion of plasma waves

High-frequency photons travelling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.
Multivariate measures of concordance for copulas and their marginals

Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular,we examine the relations between the measure of concordance of an n-copula and the measures of concordance of the copula’s marginals.
Astrophysical Observations of Early Universe Phase Transitions

After a review of CMBR correlations and recent observations, a study of possible CMBR observations of the QCD early universe phase transition is discussed. A model for the QCD bubble walls gives the surface tension found in lattice calculations, and a 1+1 dimensional treatment in this model for bubble collisions shows an interior gluonic wall, a disk with the thickness of a nucleon and horizon size radius. This could lead to a similar magnetic wall, which would produce B-B type CMBR polarization correlations distinct from very early universe models. The study of magnetic fields produced in bubble collisions in MSSM models with a first order Electroweak Phase Transition is also discussed.
On the Origin of Radio Halos in Galaxy Clusters

Previously, it has been recognized that radio halos in galaxy clusters are preferentially associated with merging systems, as indicated by substructure in the X-ray images and temperature maps. Since, however, many clusters without radio halos also possess substructure, the role of mergers in the formation of radio halos has remained unclear. By using power ratios to relate gravitational potential fluctuations to substructure in X-ray images, we provide the first quantitative comparison of the dynamical states of clusters possessing radio halos. A correlation between the 1.4 GHz power (P1.4) of the radio halo (or relic) and the magnitude of the dipole power ratio (P1/P0) is discovered such that approximately P1.4 ∝ P1/P0; i.e., the strongest radio halos appear only in those clusters currently experiencing the largest departures from a virialized state. From the additional consideration of a small number of highly disturbed clusters without radio halos detected at 1.4 GHz and recalling that radio halos are more common in clusters with high X-ray luminosity (Giovannini, Tordi, & Feretti), we argue that radio halos form preferentially in massive (LX 0.5 × 1045 ergs s-1) clusters experiencing violent mergers (P1/P0 0.5 × 10-4) that have seriously disrupted the cluster core. The association of radio halos with massive, large-P1/P0, core-disrupted clusters can account for both the vital role of mergers in accelerating the relativistic particles responsible for the radio emission as well as the rare occurrence of radio halos in cluster samples.
Completely contractive projections on operator algebras

The main goal of this paper is to find operator algebra variants of certain deep results of Stormer, Friedman and Russo, Choi and Effros, Effros and Stormer, Robertson and Youngson, Youngson, and others, concerning projections on C*-algebras and their ranges. (See papers of these authors referenced in the bibliography.) In particular we investigate the `bicontractive projection problem' and related questions in the category of operator algebras. To do this, we will add the ingredient of `real positivity' from recent papers of the first author with Read.
Behavior of the maximum likelihood in quantum state tomography

Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint $\rho \geq 0$, quantum state space does not generally satisfy local asymptotic normality, meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) should not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of local asymptotic normality, metric-projected local asymptotic normality, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.
Large order fluctuations, switching, and control in complex networks.

We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of fluctuations from one ordered state to another in real and synthetic networks. The method allows us to compute the distribution of large fluctuations and the time scale associated with switching between ordered states for networks consistent with mean-field assumptions. In general, we quantify how network heterogeneity influences the scaling patterns and probabilities of fluctuations. For instance, we find that the probability of a large fluctuation near an order-disorder transition decreases exponentially with the participation ratio of a network’s principle eigenvector – measuring how many nodes effectively contribute to an ordered state. Finally, the proposed theory is used to answer how and where a network should be targeted in order to optimize the time needed to observe a switch.
On the Classification of Vertex-Transitive Structures

We consider the classification problem for several classes of countable structures which are “vertex-transitive”, meaning that the automorphism group acts transitively on the elements. (This is sometimes called homogeneous.) We show that the classification of countable vertex-transitive digraphs and partial orders are Borel complete. We identify the complexity of the classification of countable vertex-transitive linear orders. Finally we show that the classification of vertex-transitive countable tournaments is properly above $$E_0$$ in complexity.
Modeling mass independent of anisotropy

By manipulating the spherical Jeans equation, Wolf et al. (2010) show that the mass enclosed within the 3D deprojected half-light radius r1/2 can be determined with only mild assumptions about the spatial variation of the stellar velocity dispersion anisotropy as long as the projected velocity dispersion profile is fairly flat near the half-light radius, as is typically observed. They find M1/2 = 3 G−1 〈σ2los〉 r1/2 ≃ 4 G−1 〈σ2los〉 Re, where 〈σ2los〉 is the luminosity-weighted square of the line-of-sight velocity dispersion and Re is the 2D projected half-light radius. This finding can be used to show that all of the Milky Way dwarf spheroidal galaxies (MW dSphs) are consistent with having formed within a halo of mass approximately 3 × 109 M⊙, assuming a ΛCDM cosmology. In addition, the dynamical I-band mass-to-light ratio ϒI1/2 vs. M1/2 relation for dispersion-supported galaxies follows a U-shape, with a broad minimum near ϒI1/2 ≃ 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to ϒI1/2 ≃ 3,200 for ultra-faint dSphs, and a more shallow rise to ϒI1/2 ≃ 800 for galaxy cluster spheroids.
Bounded gaps between primes in short intervals

Baker, Harman, and Pintz showed that a weak form of the Prime Number Theorem holds in intervals of the form $$[x-x^{0.525},x]$$ for large x. In this paper, we extend a result of Maynard and Tao concerning small gaps between primes to intervals of this length. More precisely, we prove that for any $$\delta \in [0.525,1]$$ there exist positive integers k, d such that for sufficiently large x, the interval $$[x-x^\delta ,x]$$ contains $$\gg _{k} \frac{x^\delta }{(\log x)^k}$$ pairs of consecutive primes differing by at most d. This confirms a speculation of Maynard that results on small gaps between primes can be refined to the setting of short intervals of this length.
Limits on the Diffuse Radio and Hard X-Ray Emission of Abell 2199

The Westerbork Northern Sky Survey (WENSS) and the NRAO/VLA Sky Survey were used to determine an upper limit to the diffuse radio flux from the nearby cluster Abell 2199. For the entire cluster, this limit is less than 3.25 Jy at 327 MHz from WENSS; for the inner 15' radius, the limit is less than 168 mJy at 1.4 GHz. These limits are used to constrain the cluster magnetic field by requiring that the radio flux be consistent with the hard X-ray (HXR) flux observed by BeppoSAX, assuming that the observed HXR excess is the result of inverse Compton scattering of cosmic microwave background photons by relativistic electrons in the intracluster gas. We find that the magnetic field must be very weak (<0.073 μG) in order to avoid producing an observable radio halo. We also consider the possibility that the HXR excess is the result of nonthermal bremsstrahlung (NTB) by a population of suprathermal electrons that are being accelerated to higher energies. We find that a NTB model based on a power-law electron-momentum distribution with an exponent of μ ≈ 3.3 and containing about 5% of the number of electrons in the thermal ICM can reproduce the observed HXR flux.
The Princeton Variability Survey

The Princeton Variability Survey (PVS) is a robotic survey that makes use of readily available "off-the-shelf" type hardware products, in conjunction with a powerful set of commercial software products, in order to monitor and discover variable objects in the night sky. The main goal of the PVS has been to devise an automated telescope and data reduction system requiring only moderate technical and financial resources to assemble, which may be easily replicated by the dedicated amateur, a student group, or a professional and used to study and discover a variety of variable objects, such as stars. This paper describes the hardware and software components of the PVS device as well as observational results from the initial season of the PVS, including the discovery of a new bright variable star.
The Detectability and Characterization of the TRAPPIST-1 Exoplanet Atmospheres with JWST

The James Webb Space Telescope (JWST) will offer the first opportunity to characterize terrestrial exoplanets with sufficient precision to identify high mean molecular weight atmospheres, and TRAPPIST-1's seven known transiting Earth-sized planets are particularly favorable targets. To assist community preparations for JWST, we use simulations of plausible post-ocean-loss and habitable environments for the TRAPPIST-1 exoplanets, and test simulations of all bright object time series spectroscopy modes and all MIRI photometry filters to determine optimal observing strategies for atmospheric detection and characterization using both transmission and emission observations. We find that transmission spectroscopy with NIRSpec Prism is optimal for detecting terrestrial, CO2 containing atmospheres, potentially in fewer than 10 transits for all seven TRAPPIST-1 planets, if they lack high altitude aerosols. If the TRAPPIST-1 planets possess Venus-like H2SO4 aerosols, up to 12 times more transits may be required to detect atmospheres. We present optimal instruments and observing modes for the detection of individual molecular species in a given terrestrial atmosphere and an observational strategy for discriminating between evolutionary states. We find that water may be prohibitively difficult to detect in both Venus-like and habitable atmospheres due to its presence lower in the atmosphere where transmission spectra are less sensitive. Although the presence of biogenic O2 and O3 will be extremely challenging to detect, abiotically produced oxygen from past ocean loss may be detectable for all seven TRAPPIST-1 planets via O2-O2 collisionally-induced absorption at 1.06 and 1.27 microns, or via NIR O3 features for the outer three planets. Our results constitute a suite of hypotheses on the nature and detectability of highly-evolved terrestrial exoplanet atmospheres that may be tested with JWST.
On the energy cascade of 3-wave kinetic equations: Beyond kolmogorov-zakharov solutions

In weak turbulence theory, the Kolmogorov–Zakharov spectra is a class of time-independent solutions to the kinetic wave equations. In this paper, we construct a new class of time-dependent isotropic solutions to the decaying turbulence problems (whose solutions are energy conserved), with general initial conditions. These solutions exhibit the interesting property that the energy is cascaded from small wavenumbers to large wavenumbers. We can prove that starting with a regular initial condition whose energy at the infinity wave number $$|p|=\infty $$ is 0, as time evolves, the energy is gradually accumulated at $$\{|p|=\infty \}$$. Finally, all the energy of the system is concentrated at $$\{|p|=\infty \}$$ and the energy function becomes a Dirac function at infinity $$E\delta _{\{|p|=\infty \}}$$, where E is the total energy. The existence of this class of solutions is, in some sense, the first complete rigorous mathematical proof based on the kinetic description for the energy cascade phenomenon for waves with quadratic nonlinearities. We only represent in this paper the analysis of the statistical description of acoustic waves (and equivalently capillary waves). However, our analysis works for other cases as well.
Private Database Queries Using Quantum States with Limited Coherence Times

We describe a method for private database queries using exchange of quantum states with bits encoded in mutually incompatible bases. For technology with limited coherence time, the database vendor can announce the encoding after a suitable delay to allow the user to privately learn one of two items in the database without the ability to also definitely infer the second item. This quantum approach also allows the user to choose to learn other functions of the items, such as the exclusive-or of their bits, but not to gain more information than equivalent to learning one item, on average. This method is especially useful for items consisting of a few bits by avoiding the substantial overhead of conventional cryptographic approaches.
Empirical Priors and Posterior Concentration Rates for a Monotone Density

In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable prior concentration properties often are not satisfied. In this paper, I first develop a new prior designed specifically to satisfy an empirical version of the prior concentration property, and then I give sufficient conditions on the prior inputs such that the corresponding empirical Bayes posterior concentrates around the true monotone density at nearly the optimal minimax rate. Numerical illustrations also reveal the practical benefits of the proposed empirical Bayes approach compared to Dirichlet process mixtures.