cssi/SciSciGPT-SciSciNet huggingface dataset:
Optimal Control of the Multiphase Stefan Problem

We consider the inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary heat flux is the control, and the optimality criteria consist of the minimization of the $$L_2$$ -norm declination of the trace of the solution to the Stefan problem from the temperature measurement on the fixed right boundary. The state vector solves multiphase Stefan problem in a weak formulation, which is equivalent to Neumann problem for the quasilinear parabolic PDE with discontinuous coefficient. Full discretization through finite differences is implemented and discrete optimal control problem is introduced. We prove well-posedness in a Sobolev space framework and convergence of discrete optimal control problems to the original problem both with respect to the cost functional and control. Along the way, the convergence of the method of finite differences for the weak solution of the multiphase Stefan problem is proved. The proof is based on achieving a uniform $$L_{\infty }$$ bound, and $$W_2^{1,1}$$ -energy estimate for the discrete multiphase Stefan problem.
Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.
SUPERNOVA Ia AND GALAXY CLUSTER GAS MASS FRACTION CONSTRAINTS ON DARK ENERGY

We use the Riess et al. (2004)1 supernova Ia apparent magnitude versus redshift data and the Allen et al. (2004)2 galaxy cluster gas mass fraction versus redshift data to constrain dark energy models. These data provide complementary constraints that when combined together significantly restrict model parameters and favor slowly-evolving dark energy density models, close to the Einstein cosmological constant limit of dark energy.
Membrane paradigm realized

Are there any degrees of freedom on the black hole horizon? Using the ‘membrane paradigm’ we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need ‘real’ degrees of freedom at the horizon, which can modify Hawking’s evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outside the horizon radius. The collective behavior of these microstate solutions may give a realization of the membrane paradigm, with the fictitious membrane now replaced by real, explicit degrees of freedom.
On (2, 4) complete intersection threefolds that contain an Enriques surface

We study nodal complete intersection threefolds of type (2, 4) in $${\mathbb {P}}^5$$ which contain an Enriques surface in its Fano embedding. We completely determine Calabi–Yau birational models of a generic such threefold. These models have Hodge numbers $$h^{11}=2,h^{12}=32$$ . We also describe Calabi–Yau varieties with Hodge numbers $$(h^{11},h^{12})$$ equal to (2, 26), (23, 5) and (31, 1). The last two pairs of Hodge numbers are, to the best of our knowledge, new.
Analysis of Models for Decentralized and Collaborative AI on Blockchain

Machine learning has recently enabled large advances in artificial intelligence, but these results can be highly centralized. The large datasets required are generally proprietary; predictions are often sold on a per-query basis; and published models can quickly become out of date without effort to acquire more data and maintain them. Published proposals to provide models and data for free for certain tasks include Microsoft Research’s Decentralized and Collaborative AI on Blockchain. The framework allows participants to collaboratively build a dataset and use smart contracts to share a continuously updated model on a public blockchain. The initial proposal gave an overview of the framework omitting many details of the models used and the incentive mechanisms in real world scenarios. For example, the Self-Assessment incentive mechanism proposed in their work could have problems such as participants losing deposits and the model becoming inaccurate over time if the proper parameters are not set when the framework is configured. In this work, we evaluate the use of several models and configurations in order to propose best practices when using the Self-Assessment incentive mechanism so that models can remain accurate and well-intended participants that submit correct data have the chance to profit. We have analyzed simulations for each of three models: Perceptron, Naive Bayes, and a Nearest Centroid Classifier, with three different datasets: predicting a sport with user activity from Endomondo, sentiment analysis on movie reviews from IMDB, and determining if a news article is fake. We compare several factors for each dataset when models are hosted in smart contracts on a public blockchain: their accuracy over time, balances of a good and bad user, and transaction costs (or gas) for deploying, updating, collecting refunds, and collecting rewards. A free and open source implementation for the Ethereum blockchain of these models is provided at https://github.com/microsoft/0xDeCA10B.
On D0 brane polarization by tidal forces

Gravitational tidal forces may induce polarization of D0-branes, in analogy to the same effects arising in the context of constant background gauge fields. Such phenomena can teach us about the correspondence between smooth curved spacetime and its underlying non-commutative structure. However, unlike polarization by gauge fields, the gravitational counterpart involves concerns regarding the classical stability of the corresponding polarized states. In this work, we study this issue with respect to the solutions presented in hepth0010237 and find that they are classically unstable. The instability however appears with intricate features with all but a few decay channels being lifted. Through a detailed analysis, we then argue that these polarized states may be expected to be long-lived in a regime where the string coupling is small and the number of D0-branes is large.
A Chandra High Resolution Camera Observation of X-Ray Point Sources in M31

We present results from a 47 ks observation of the Andromeda galaxy, M31, using the High Resolution Camera of the Chandra X-Ray Observatory. We detect 142 point sources spanning 3 orders of magnitude in luminosity, from LX = 2 × 1035 to 2 × 1038 ergs s-1 in the 0.1-10 keV band. The X-ray source location accuracy is better than 1'' in the central regions of the galaxy. One source lies within 13 of SN 1885 but does not coincide with the UV absorption feature identified as the supernova remnant. However, there is an optical transient, which is likely an optical nova, at the location of the X-ray source. There is a weak source, LX ~ 4 × 1036 ergs cm2 s-1, coincident with the nucleus of M31 and 14 sources coincident with globular clusters. Our observation has very high efficiency down to luminosities of 1.5 × 1036 ergs s-1 for sources within 5' of the nucleus. Comparing with a ROSAT observation made 11 yr earlier, we find that 0.46 ± 0.26 of the sources with LX > 5 × 1036 ergs s-1 are variable. We find no evidence for X-ray pulsars in this region, indicating that the population is likely dominated by low-mass X-ray binaries. The source density radial profile follows a power-law distribution with an exponent of 1.25 ± 0.10 and is inconsistent with the optical surface brightness profile. The X-ray point-source luminosity function is well fitted by a differential broken power law with a break at a luminosity of (4.5) × 1037 ergs s-1. The luminosity function is consistent with a model of an aging population of X-ray binaries.
Non-perturbative dynamics of the operator size distribution in the Sachdev–Ye–Kitaev model

We prove non-perturbative bounds on the time evolution of the probability distribution of operator size in the q-local Sachdev–Ye–Kitaev model with N fermions for any even integer q > 2 and any positive even integer N > 2q. If the couplings in the Hamiltonian are independent and identically distributed Rademacher random variables, the infinite temperature many-body Lyapunov exponent is almost surely finite as N → ∞. In the limit q → ∞, N → ∞, and q6+δ/N → 0, the shape of the size distribution of a growing fermion, obtained by leading order perturbation calculations in 1/N and 1/q, is similar to a distribution that locally saturates our constraints. Our proof is not based on Feynman diagram resummation; instead, we note that the operator size distribution obeys a continuous time quantum walk with bounded transition rates to which we apply concentration bounds from classical probability theory.
On Normal Modes of a Warped Throat

As shown in arXiv:hep-th/0405282, the warped deformed conifold has two bosonic massless modes, a pseudoscalar and a scalar, that are dual to the phase and the modulus of the baryonic condensates in the cascading gauge theory. We reconsider the scalar mode sector, mixing fluctuations of the NS-NS 2-form and the metric, and include non-zero 4-d momentum kμ. The resulting pair of coupled equations produce a discrete spectrum of m42 = −kμ2 which is interpreted as the spectrum of JPC = 0+− glueballs in the gauge theory. Similarly, we derive the spectrum of certain pseudoscalar glueballs with JPC = 0−−, which originate from the decoupled fluctuations of the RR 2-form. We argue that each of the massive scalar or pseudoscalar modes we find belongs to a 4-d massive axial vector or vector supermultiplet. We also discuss our results in the context of a finite length throat embedded into a type IIB flux compactification.
Disordered topological insulators: a non-commutative geometry perspective

The progress in the field of topological insulators is impetuous, being sustained by a suite of exciting results on three fronts: experiment, theory and numerical simulation. Very often, the theoretical characterizations of these materials involve advanced and abstract techniques from pure mathematics, leading to complex predictions which nowadays are tested by direct experimental observations. Many of these predictions have already been confirmed. What makes these materials topological is the robustness of their key properties against smooth deformations and onset of disorder. There is quite an extensive literature discussing the properties of clean topological insulators, but the literature on disordered topological insulators is limited. This review deals with strongly disordered topological insulators and covers some recent applications of a well-established analytic theory based on the methods of non-commutative geometry and developed for the integer quantum Hall effect. Our main goal is to exemplify how this theory can be used to define topological invariants in the presence of strong disorder, other than the Chern number, and to discuss the physical properties protected by these invariants. Working with two explicit two-dimensional models, one for a Chern insulator and one for a quantum spin-Hall insulator, we first give an in-depth account of the key bulk properties of these topological insulators in the clean and disordered regimes. Extensive numerical simulations are employed here. A brisk but self-contained presentation of the non-commutative theory of the Chern number is given and a novel numerical technique to evaluate the non-commutative Chern number is presented. The non-commutative spin-Chern number is defined and the analytic theory, together with the explicit calculation of the topological invariants in the presence of strong disorder, is used to explain the key bulk properties seen in the numerical experiments presented in the first part of the review.
Resonant acoustic wave assisted spin-transfer-torque switching of nanomagnets

We report the possibility of achieving an order of magnitude reduction in the energy dissipation needed to write bits in perpendicular magnetic tunnel junctions by simulating the magnetization dynamics under a combination of resonant surface acoustic waves (r-SAWs) and spin-transfer-torque (STT). The magnetization dynamics were simulated using the Landau-Lifshitz-Gilbert equation under macrospin assumption with the inclusion of thermal noise. The resonant magnetization dynamics in the magnetostrictive nanomagnet builds over few tens of cycles of SAW application that drives the magnetization to precess in a cone with a deflection of ∼45° from the perpendicular direction. This reduces the STT current density required to switch the magnetization direction without increasing the STT application time or degrading the switching probability in the presence of room temperature thermal noise. This could lead to a pathway to achieve energy efficient switching of spin-transfer-torque random access memory whose lateral dimensions can be scaled aggressively despite using materials with low magnetostriction by employing SAW excitation to drive ferromagnetic resonance.
PROPERTIES OF AN ALTERNATE LAX DESCRIPTION OF THE KdV HIERARCHY

We study systematically the Lax description of the KdV hierarchy in terms of an operator which is the geometrical recursion operator. We formulate the Lax equation for the nth flow and construct the Hamiltonians which lead to commuting flows. In this formulation, the recursion relation between the conserved quantities follows naturally. We give a simple and compact definition of all the Hamiltonian structures of the theory which are related through a power law.
Energy-Minimizing Error-Correcting Codes

We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same size and block length. Examples of these universally optimal codes include Hamming, Golay, and Reed-Solomon codes, among many others, and this helps to explain their robustness as the channel model varies. Universal optimality of these codes is equivalent to minimality of their binomial moments, which has been proved in many cases by Ashikhmin and Barg. We highlight connections with mathematical physics and the analogy between these results and previous work by Cohn and Kumar in the continuous setting, and we develop a framework for optimizing the linear programming bounds. Furthermore, we show that if these bounds prove a code is universally optimal, then the code remains universally optimal even if one codeword is removed.
On general-relativistic hydrogen and hydrogenic ions

This paper studies how the static non-linear electromagnetic-vacuum spacetime of a point nucleus with a negative bare mass affects the self-adjointness of the general-relativistic Dirac Hamiltonian for a test electron, without and with an anomalous magnetic moment. This study interpolates between the previously studied extreme cases of a test electron in (a) the Reissner–Weyl–Nordstrom spacetime (Maxwell’s electromagnetic vacuum), which sports a very strong curvature singularity with negative infinite bare mass, and (b) the Hoffmann spacetime (Born or Born–Infeld’s electromagnetic vacuum) with vanishing bare mass, which features the mildest possible curvature singularity. The main conclusion reached is: on electrostatic spacetimes of a point nucleus with a strictly negative bare mass (which may be −∞), essential self-adjointness fails unless the radial electric field diverges sufficiently fast at the nucleus and the anomalous magnetic moment of the electron is taken into account. Thus, on the Hoffmann spacetime with a (strictly) negative bare mass, the Dirac Hamiltonian of a test electron, with or without anomalous magnetic moment, is not essentially self-adjoint. All these operators have self-adjoint extensions, though, with the usual essential spectrum (−∞, −mec2] ∪ [mec2, ∞) and an infinite discrete spectrum located in the gap (−mec2, mec2).
Deformations of circle-valued Morse functions on surfaces

Let M be a smooth connected orientable compact surface and let $ {\mathcal{F}_{{\rm cov} }}\left( {M,{S^1}} \right) $ be a space of all Morse functions f : M → S 1 without critical points on ∂M such that, for any connected component V of ∂M, the restriction f : V → S 1 is either a constant map or a covering map. The space $ {\mathcal{F}_{{\rm cov} }}\left( {M,{S^1}} \right) $ is endowed with the C ∞-topology. We present the classification of connected components of the space $ {\mathcal{F}_{{\rm cov} }}\left( {M,{S^1}} \right) $ . This result generalizes the results obtained by Matveev, Sharko, and the author for the case of Morse functions locally constant on ∂M.
INTERACTIONS OF THE MAGNETOSPHERES OF STARS AND CLOSE-IN GIANT PLANETS

Since the first discovery of an extrasolar planetary system more than a decade ago, hundreds more have been discovered. Surprisingly, many of these systems harbor Jupiter-class gas giants located close to the central star, at distances of 0.1 AU or less. Observations of chromospheric “hot spots” that rotate in phase with the planetary orbit, and elevated stellar X-ray luminosities, suggest that these close-in planets significantly affect the structure of the outer atmosphere of the star through interactions between the stellar magnetic field and the planetary magnetosphere. Here, we carry out the first detailed three-dimensional magnetohydrodynamics simulation containing the two magnetic bodies and explore the consequences of such interactions on the steady-state coronal structure. The simulations reproduce the observable features of (1) increase in the total X-ray luminosity, (2) appearance of coronal hot spots, and (3) phase shift of these spots with respect to the direction of the planet. The proximate cause of these is an increase in the density of coronal plasma in the direction of the planet, which prevents the corona from expanding and leaking away this plasma via a stellar wind. The simulations produce significant low temperature heating. By including dynamical effects, such as the planetary orbital motion, the simulation should better reproduce the observed coronal heating.
The Robot Economy: Here It Comes

Automation is not a new phenomenon, and questions about its effects have long followed its advances. More than a half-century ago, US President Lyndon B. Johnson established a national commission to examine the impact of technology on the economy, declaring that automation “can be the ally of our prosperity if we will just look ahead”. In this paper, our premise is that we are at a technological inflection point in which robots are developing the capacity to greatly increase their cognitive and physical capabilities, and thus raising questions on labor dynamics. With increasing levels of autonomy and human-robot interaction, intelligent robots could soon accomplish new human-like capabilities such as engaging into social activities. Therefore, an increase in automation and autonomy brings the question of robots directly participating in some economic activities as autonomous agents. In this paper, a technological framework describing a robot economy is outlined and the challenges it might represent in the current socio-economic scenario are pondered.
Constraints on dynamics preserving certain hyperbolic sets

We establish two results under which the topology of a hyperbolic set constrains ambient dynamics. First if a set is a compact, transitive, expanding hyperbolic attractor of codimension 1 for some diffeomorphism, then it is a union of transitive, expanding attractors (or contracting repellers) of codimension 1 for any diffeomorphism such that it is hyperbolic. Secondly, if a set is a nonwandering, locally maximal, compact hyperbolic set for a surface diffeomorphism, then it is locally maximal for any diffeomorphism for which it is hyperbolic.
Gap Probabilities for the Generalized Bessel Process: A Riemann-Hilbert Approach

We consider the gap probability for the Generalized Bessel process in the single-time and multi-time case, a determinantal process which arises as critical limiting kernel in the study of self-avoiding squared Bessel paths. We prove that such gap probabilities, i.e. the scalar and matrix Fredholm determinant of the process respectively, can be expressed in terms of determinants of suitable Its-Izergin-Korepin-Slavnov integrable kernels and therefore they can be related in a canonical way to Riemann-Hilbert problems. Moreover, such Fredholm determinants can be interpreted as isomonodromic τ-functions in the sense of Jimbo, Miwa and Ueno; in particular, in the single-time case we are able to construct an explicit Lax pair. On the other hand, in the multi-time case we explicitly define a completely new multi-time kernel and we proceed with the study of gap probabilities as in the single-time case.
Generating Narrative Text in a Switching Dynamical System

Early work on narrative modeling used explicit plans and goals to generate stories, but the language generation itself was restricted and inflexible. Modern methods use language models for more robust generation, but often lack an explicit representation of the scaffolding and dynamics that guide a coherent narrative. This paper introduces a new model that integrates explicit narrative structure with neural language models, formalizing narrative modeling as a Switching Linear Dynamical System (SLDS). A SLDS is a dynamical system in which the latent dynamics of the system (i.e. how the state vector transforms over time) is controlled by top-level discrete switching variables. The switching variables represent narrative structure (e.g., sentiment or discourse states), while the latent state vector encodes information on the current state of the narrative. This probabilistic formulation allows us to control generation, and can be learned in a semi-supervised fashion using both labeled and unlabeled data. Additionally, we derive a Gibbs sampler for our model that can “fill in” arbitrary parts of the narrative, guided by the switching variables. Our filled-in (English language) narratives outperform several baselines on both automatic and human evaluations
Hilbert C*-modules and amenable actions

We study actions of discrete groups on Hilbert C*-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a quasi-invariant probability measure which is sufficiently close to being invariant.
POLARIZATION OF THE CHARGE-EXCHANGE X-RAYS INDUCED IN THE HELIOSPHERE

We report results of a theoretical investigation of polarization of the X-ray emissions induced in charge-exchange collisions of fully stripped solar wind (SW) ions C6 + and O8 + with the heliospheric hydrogen atoms. The polarization of X-ray emissions has been computed for line-of-sight observations within the ecliptic plane as a function of SW ion velocities, including a range of velocities corresponding to the slow and fast SW, and coronal mass ejections. To determine the variability of polarization of heliospheric X-ray emissions, the polarization has been computed for solar minimum conditions with self-consistent parameters of the SW plasma and heliospheric gas and compared with the polarization calculated for an averaged solar activity. We predict the polarization of charge-exchange X-rays to be between 3% and 8%, depending on the line-of-sight geometry, SW ion velocity, and the selected emission lines.
Absolute Spacetime: The Twentieth Century Ether

All gauge theories need “somethingfixed” even as “something changes.”Underlying the implementation of these ideas all majorphysical theories make indispensable use of anelaborately designed spacetime model as the “something fixed,”i.e., absolute. This model must provide at least thefollowing sequence of structures: point set, topologicalspace, smooth manifold, geometric manifold, base forvarious bundles. The “fine structure” ofspacetime inherent in this sequence is of courseempirically unobservable directly, certainly whenquantum mechanics is taken into account. This issue isat the basis of the difficulties in quantizing generalrelativity and has been approached in many differentways. Here we review an approach taking into account thenon-Boolean properties of quantum logic when forming a spacetime model. Finally, we recall how thefundamental gauge of diffeomorphisms (the issue ofgeneral covariance vs. coordinate conditions) raiseddeep conceptual problems for Einstein in his earlydevelopment of general relativity. This is clearlyillustrated in the notorious “hole”argument. This scenario, which does not seem to bewidely known to practicing relativists, is neverthelessstill interesting in terms of its impact for fundamental gaugeissues.
Role Discovery in Networks

Roles represent node-level connectivity patterns such as star-center, star-edge nodes, near-cliques or nodes that act as bridges to different regions of the graph. Intuitively, two nodes belong to the same role if they are structurally similar. Roles have been mainly of interest to sociologists, but more recently, roles have become increasingly useful in other domains. Traditionally, the notion of roles were defined based on graph equivalences such as structural, regular, and stochastic equivalences. We briefly revisit these early notions and instead propose a more general formulation of roles based on the similarity of a feature representation (in contrast to the graph representation). This leads us to propose a taxonomy of three general classes of techniques for discovering roles that includes(i) graph-based roles, (ii) feature-based roles, and (iii) hybrid roles. We also propose a flexible framework for discovering roles using the notion of similarity on a feature-based representation. The framework consists of two fundamental components: (a) role featureconstruction and (b) role assignment using the learned feature representation. We discuss the different possibilities for discoveringfeature-based roles and the tradeoffs of the many techniques for computing them. Finally, we discuss potential applications and future directions and challenges.
The Distinction Between Thermal Nonequilibrium and Thermal Instability

For some forms of steady heating, coronal loops are in a state of thermal nonequilibrium and evolve in a manner that includes accelerated cooling, often resulting in the formation of a cold condensation. This is frequently confused with thermal instability, but the two are in fact fundamentally different. We explain the distinction and discuss situations where they may be interconnected. Large-amplitude perturbations, perhaps associated with MHD waves, likely play a role in explaining phenomena that have been attributed to thermal nonequilibrium but also seem to require cross-field communication.
Adaptive robust variable selection

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted L1-penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the L1-penalty. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size, we investigate the model selection oracle property and establish the asymptotic normality of the WR-Lasso. We show that only mild conditions on the model error distribution are needed. Our theoretical results also reveal that adaptive choice of the weight vector is essential for the WR-Lasso to enjoy these nice asymptotic properties. To make the WR-Lasso practically feasible, we propose a two-step procedure, called adaptive robust Lasso (AR-Lasso), in which the weight vector in the second step is constructed based on the L1-penalized quantile regression estimate from the first step. This two-step procedure is justified theoretically to possess the oracle property and the asymptotic normality. Numerical studies demonstrate the favorable finite-sample performance of the AR-Lasso.
unWISE tomography of Planck CMB lensing

Author(s): Krolewski, A; Ferraro, S; Schlafly, EF; White, M | Abstract: CMB lensing tomography, or the cross-correlation between CMB lensing maps and large-scale structure tracers over a well-defined redshift range, has the potential to map the amplitude and growth of structure over cosmic time, provide some of the most stringent tests of gravity, and break important degeneracies between cosmological parameters. In this work, we use the unWISE galaxy catalog to provide three samples at median redshifts z ∼ 0.6, 1.1 and 1.5, fully spanning the Dark Energy dominated era, together with the most recent Planck CMB lensing maps. We obtain a combined cross-correlation significance S/N = 79.3 over the range of scales 100 l l l 1000. We measure the redshift distribution of unWISE sources by a combination of cross-matching with the COSMOS photometric catalog and cross-correlation with BOSS galaxies and quasars and eBOSS quasars. We also show that magnification bias must be included in our analysis and perform a number of null tests. In a companion paper, we explore the derived cosmological parameters by modeling the non-linearities and propagating the redshift distribution uncertainties.
The replica limit of unitary matrix integrals

Abstract We investigate the replica trick for the microscopic spectral density, ρ s (x) , of the Euclidean QCD Dirac operator. Our starting point is the low-energy limit of the QCD partition function for n fermionic flavors (or replicas) in the sector of topological charge ν . In the domain of the smallest eigenvalues, this partition function is simply given by a U(n) unitary matrix integral. We show that the asymptotic expansion of ρ s (x) for x→∞ is obtained from the n→0 limit of this integral. The smooth contributions to this series are obtained from an expansion about the replica symmetric saddle-point, whereas the oscillatory terms follow from an expansion about a saddle-point that breaks the replica symmetry. For ν=0 we recover the small- x logarithmic singularity of the resolvent by means of the replica trick. For half integer ν , when the saddle point expansion of the U(n) integral terminates, the replica trick reproduces the exact analytical result. In all other cases only an asymptotic series that does not uniquely determine the microscopic spectral density is obtained. We argue that bosonic replicas fail to reproduce the microscopic spectral density. In all cases, the exact answer is obtained naturally by means of the supersymmetric method.
Model predictive control for transient frequency regulation of power networks

Abstract This paper introduces a control strategy to simultaneously achieve asymptotic stabilization and transient frequency regulation of power networks. The control command is generated by iteratively solving an open-loop control cost minimization problem with stability and transient frequency constraints. To deal with the non-convexity of the stability constraint, we propose a convexification strategy that uses a reference trajectory based on the system’s current state. We also employ network partitions to implement the proposed control strategy in a distributed way, where each region only requires system information from its own to execute its controller.
Sparse Deep Neural Network Exact Solutions

Deep neural networks (DNNs) have emerged as key enablers of machine learning. Applying larger DNNs to more diverse applications is an important challenge. The computations performed during DNN training and inference are dominated by operations on the weight matrices describing the DNN. As DNNs incorporate more layers and more neurons per layers, these weight matrices may be required to be sparse because of memory limitations. Sparse DNNs are one possible approach, but the underlying theory is in the early stages of development and presents a number of challenges, including determining the accuracy of inference and selecting nonzero weights for training. Associative array algebra has been developed by the big data community to combine and extend database, matrix, and graph/network concepts for use in large, sparse data problems. Applying this mathematics to DNNs simplifies the formulation of DNN mathematics and reveals that DNNs are linear over oscillating semirings. This work uses associative array DNNs to construct exact solutions and corresponding perturbation models to the rectified linear unit (ReLU) DNN equations that can be used to construct test vectors for sparse DNN implementations over various precisions. These solutions can be used for DNN verification, theoretical explorations of DNN properties, and a starting point for the challenge of sparse training.
Large Induced Acyclic and Outerplanar Subgraphs of 2-Outerplanar Graph

Albertson and Berman conjectured that every planar graph has an induced forest on half of its vertices. The best known lower bound, due to Borodin, is that every planar graph has an induced forest on two fifths of its vertices. In a related result, Chartran and Kronk, proved that the vertices of every planar graph can be partitioned into three sets, each of which induce a forest. We show tighter results for 2-outerplanar graphs. We show that every 2-outerplanar graph has an induced forest on at least half the vertices by showing that its vertices can be partitioned into two sets, each of which induces a forest. We also show that every 2-outerplanar graph has an induced outerplanar graph on at least two-thirds of its vertices.
Flexible Coaxial Ribbon Cable for High-Density Superconducting Microwave Device Arrays

Superconducting electronics often require high-density microwave interconnects capable of transporting signals between temperature stages with minimal loss, cross talk, and heat conduction. We report the design and fabrication of superconducting 53 wt% Nb-47 wt% Ti (Nb47Ti) FLexible coAXial ribbon cables (FLAX). The ten traces each consist of a ${\oslash}$ 0.076 mm NbTi inner conductor insulated with PFA ( ${ \oslash }$ 0.28 mm) and sheathed in a shared 0.025 mm thick Nb47Ti outer conductor. The cable is terminated with G3PO coaxial push-on connectors via stainless steel capillary tubing ( ${ \oslash }$ 1.6 mm, 0.13 mm thick) soldered to a coplanar wave guide transition board. The 30 cm long cable has 1 dB of loss at 8 GHz with $-$ 60 dB nearest neighbor forward cross talk. The loss is 0.5 dB more than commercially available superconducting coax likely due to impedance mismatches caused by manufacturing imperfections in the cable. The reported cross talk is 30 dB lower than previously developed laminated NbTi-on-Kapton microstrip cables. We estimate the heat load from 1 K to 90 mK to be 20 nW per trace, approximately half the computed load from the smallest commercially available superconducting coax from CryoCoax.
Jet shower evolution in medium and dijet asymmetry in Pb+Pb collisions at the LHC

We study the evolution of a partonic jet shower propagating through a quark–gluon plasma. Combining the in-medium evolutions of the leading parton and shower gluons, we compute the depletion of the energy from the jet cone by dissipation through elastic collisions with medium constituents, by scattering of shower partons to larger angles and by radiation outside the jet cone. Numerical results are presented for the nuclear modification of dijet asymmetry in Pb+Pb collisions at the large hadron collider (LHC).
Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra

The purpose of this paper is to generalize Zhu’s theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights. To recover $${SL_2(\mathbb{Z})}$$ -invariance of the characters it turns out to be necessary to consider twisted modules alongside ordinary ones. It also turns out to be necessary, in describing the space of conformal blocks in the supersymmetric case, to include certain ‘odd traces’ on modules alongside traces and supertraces. We prove that the set of supertrace functions, thus supplemented, spans a finite dimensional $${SL_2(\mathbb{Z})}$$ -invariant space. We close the paper with several examples.
Integrating temporal and spectral features of astronomical data using wavelet analysis for source classification

Temporal and spectral information extracted from a stream of photons received from astronomical sources is the foundation on which we build understanding of various objects and processes in the Universe. Typically astronomers fit a number of models separately to light curves and spectra to extract relevant features. These features are then used to classify, identify, and understand the nature of the sources. However, these feature extraction methods may not be optimally sensitive to unknown properties of light curves and spectra. One can use the raw light curves and spectra as features to train classifiers, but this typically increases the dimensionality of the problem, often by several orders of magnitude. We overcome this problem by integrating light curves and spectra to create an abstract image and using wavelet analysis to extract important features from the image. Such features incorporate both temporal and spectral properties of the astronomical data. Classification is then performed on those abstract features. In order to demonstrate this technique, we have used gamma-ray burst (GRB) data from the NASA's Swift mission to classify GRBs into high- and low-redshift groups. Reliable selection of high-redshift GRBs is of considerable interest in astrophysics and cosmology.
Influence Estimation on Social Media Networks Using Causal Inference

Estimating influence on social media networks is an important practical and theoretical problem, especially because this new medium is widely exploited as a platform for disinformation and propaganda. This paper introduces a novel approach to influence estimation on social media networks and applies it to the real-world problem of characterizing active influence operations on Twitter during the 2017 French presidential elections. The new influence estimation approach attributes impact by accounting for narrative propagation over the network using a network causal inference framework applied to data arising from graph sampling and filtering. This causal framework infers the difference in outcome as a function of exposure, in contrast to existing approaches that attribute impact to activity volume or topological features, which do not explicitly measure nor necessarily indicate actual network influence. Cramer-Rao estimation bounds are derived for parameter estimation as a step in the causal analysis, and used to achieve geometrical insight on the causal inference problem. The ability to infer high causal influence is demonstrated on real-world social media accounts that are later independently confirmed to be either directly affiliated or correlated with foreign influence operations using evidence supplied by the U.S. Congress and journalistic reports.
Renormalized reduced models for singular PDEs

We present a novel way of constructing reduced models for systems of ordinary differential equations. In particular, the approach combines the concepts of renormalization and effective field theory developed in the context of high energy physics and the Mori‐Zwanzig formalism of irreversible statistical mechanics. The reduced models we construct depend on coefficients which measure the importance of the different terms appearing in the model and need to be estimated. The proposed approach allows the estimation of these coefficients on the fly by enforcing the equality of integral quantities of the solution as computed from the original system and the reduced model. In this way we are able to construct stable reduced models of higher order than was previously possible. The method is applied to the problem of computing reduced models for ordinary differential equation systems resulting from Fourier expansions of singular (or near-singular) time-dependent partial differential equations. Results for the 1D Burgers and the 3D incompressible Euler equations are used to illustrate the construction. Under suitable assumptions, one can calculate the higher order terms by a simple and efficient recursive algorithm. Spatial discretizations or Fourier expansions of the solutions of time-dependent partial differential equations (PDEs) lead to systems of ordinary differential equations (ODEs). The most difficult case arises when the solution of a PDE becomes singular in finite time. At such instants the solution of the PDE develops activity down to the zero length scale. A brute force numerical simulation (no matter how large) of such a solution is bound to fail because the simulation has a finite resolution and thus will be unable to resolve all the length scales down to the zero scale. When the solution develops activity at a scale smaller than the smallest scale available to the simulation, the numerically computed solution becomes underresolved. This leads to a rapid deterioration of the accuracy of the simulation. The notion of propagation of activity to smaller and smaller scales depends on the physical context of the PDE. In some cases, like the 3D Euler or Navier‐Stokes
D-SLATS: Distributed Simultaneous Localization and Time Synchronization

Through the last decade, we have witnessed a surge of Internet of Things (IoT) devices, and with that a greater need to choreograph their actions across both time and space. Although these two problems, namely time synchronization and localization, share many aspects in common, they are traditionally treated separately or combined on centralized approaches that results in an inefficient use of resources, or in solutions that are not scalable in terms of the number of IoT devices. Therefore, we propose D-SLATS, a framework comprised of three different and independent algorithms to jointly solve time synchronization and localization problems in a distributed fashion. The first two algorithms are based mainly on the distributed Extended Kalman Filter (EKF) whereas the third one uses optimization techniques. No fusion center is required, and the devices only communicate with their neighbors. The proposed methods are evaluated on custom Ultra-Wideband communication Testbed and a quadrotor, representing a network of both static and mobile nodes. Our algorithms achieve up to three microseconds time synchronization accuracy and 30 cm localization error.
Fourier coefficients of the overconvergent generalized eigenform associated to a CM form

Let f be a modular form with complex multiplication. If f has critical slope, then Coleman’s classicality theorem implies that there is a p-adic overconvergent generalized Hecke eigenform with the ...
Fast semistochastic heat-bath configuration interaction

This paper presents in detail our fast semistochastic heat-bath configuration interaction (SHCI) method for solving the many-body Schrodinger equation. We identify and eliminate computational bottlenecks in both the variational and perturbative steps of the SHCI algorithm. We also describe the parallelization and the key data structures in our implementation, such as the distributed hash table. The improved SHCI algorithm enables us to include in our variational wavefunction two orders of magnitude more determinants than has been reported previously with other selected configuration interaction methods. We use our algorithm to calculate an accurate benchmark energy for the chromium dimer with the X2C relativistic Hamiltonian in the cc-pVDZ-DK basis, correlating 28 electrons in 76 spatial orbitals. Our largest calculation uses two billion Slater determinants in the variational space and semistochastically includes perturbative contributions from at least trillions of additional determinants with better than 10-5 Ha statistical uncertainty.
Analytic Prediction of Baryonic Effects from the EFT of Large Scale Structures

The large scale structures of the universe will likely be the next leading source of cosmological information. It is therefore crucial to understand their behavior. The Effective Field Theory of Large Scale Structures provides a consistent way to perturbatively predict the clustering of dark matter at large distances. The fact that baryons move distances comparable to dark matter allows us to infer that baryons at large distances can be described in a similar formalism: the backreaction of short-distance non-linearities and of star-formation physics at long distances can be encapsulated in an effective stress tensor, characterized by a few parameters. The functional form of baryonic effects can therefore be predicted. In the power spectrum the leading contribution goes as ∝ k2 P(k), with P(k) being the linear power spectrum and with the numerical prefactor depending on the details of the star-formation physics. We also perform the resummation of the contribution of the long-wavelength displacements, allowing us to consistently predict the effect of the relative motion of baryons and dark matter. We compare our predictions with simulations that contain several implementations of baryonic physics, finding percent agreement up to relatively high wavenumbers such as k 0.3 hMpc−1 or k 0.6 hMpc−1, depending on the order of the calculation. Our results open a novel way to understand baryonic effects analytically, as well as to interface with simulations.
Advective balance in pipe-formed vortex rings

Vorticity distributions in axisymmetric vortex rings produced by a piston–pipe apparatus are numerically studied over a range of Reynolds numbers, , and stroke-to-diameter ratios, . It is found that a state of advective balance, such that , is achieved within the region (called the vortex ring bubble) enclosed by the dividing streamline. Here is the ratio of azimuthal vorticity to cylindrical radius, and is the Stokes streamfunction in the frame of the ring. Some, but not all, of the dependence in the time evolution of can be captured by introducing a scaled time , where is the kinematic viscosity. When , the shape of is dominated by the linear-in- component, the coefficient of the quadratic term being an order of magnitude smaller. An important feature is that, as the dividing streamline ( ) is approached, tends to a non-zero intercept which exhibits an extra dependence. This and other features are explained by a simple toy model consisting of the one-dimensional cylindrical diffusion equation. The key ingredient in the model responsible for the extra dependence is a Robin-type boundary condition, similar to Newton’s law of cooling, that accounts for the edge layer at the dividing streamline.