cssi/SciSciGPT-SciSciNet huggingface dataset:
The Explicit Sato-Tate Conjecture and Densities Pertaining to Lehmer-Type Questions

Let f(z) = ∑∞ n=1 af (n)q n ∈ S k (Γ0(N)) be a newform with squarefree level N that does not have complex multiplication. For a prime p, define θp ∈ [0, π] to be the angle for which af (p) = 2p (k−1)/2 cos θp. Let I ⊂ [0, π] be a closed subinterval, and let dμST = 2 π sin 2 θdθ be the Sato-Tate measure of I. Assuming that the symmetric power L-functions of f satisfy certain analytic properties (all of which follow from Langlands functoriality and the Generalized Riemann Hypothesis), we prove that if x is sufficiently large, then ∣∣∣∣#{p ≤ x : θp ∈ I} − μST (I)∫ x 2 dt log t ∣∣∣∣ x log(Nkx) log x with an implied constant of 3.33. By letting I be a short interval centered at π2 and counting the primes using a smooth cutoff, we compute a lower bound for the density of positive integers n for which af (n) 6= 0. In particular, if τ is the Ramanujan tau function, then under the aforementioned hypotheses, we prove that lim x→∞ #{n ≤ x : τ(n) 6= 0} x > 1− 1.54× 10−13. We also discuss the connection between the density of positive integers n for which af (n) 6= 0 and the number of representations of n by certain positive-definite, integer-valued quadratic forms.
Binary cyclic codes that are locally repairable

Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite field to be practically significant and be tolerant to a large number of erasures. To this end, we construct new families of binary linear codes that have an optimal dimension (rate) for a given minimum distance and locality. Specifically, we construct cyclic codes that are locally repairable for locality 2 and distances 2, 6 and 10. In doing so, we discover new upper bounds on the code dimension, and prove the optimality of enabling local repair by provisioning disjoint groups of disks. Finally, we extend our construction to build codes that have multiple repair sets for each disk.
Structural, vibrational, and elastic properties of a calcium aluminosilicate glass from molecular dynamics simulations: The role of the potential

We study a calcium aluminosilicate glass of composition (SiO2)0.60(Al2O3)0.10(CaO)0.30 by means of molecular dynamics. To this end, we conduct parallel simulations, following a consistent methodology, but using three different potentials. Structural and elastic properties are analyzed and compared to available experimental data. This allows assessing the respective abilities of the potentials to produce a realistic glass. We report that, although all these potentials offer a reasonable glass structure, featuring tricluster oxygen atoms, their respective vibrational and elastic predictions differ. This allows us to draw some general conclusions about the crucial role, or otherwise, of the interaction potential in silicate systems.
The negativity contour: a quasi-local measure of entanglement for mixed states

In this paper, we study the entanglement structure of mixed states in quantum many-body systems using the $\textit{negativity contour}$, a local measure of entanglement that determines which real-space degrees of freedom in a subregion are contributing to the logarithmic negativity and with what magnitude. We construct an explicit contour function for Gaussian states using the fermionic partial-transpose. We generalize this contour function to generic many-body systems using a natural combination of derivatives of the logarithmic negativity. Though the latter negativity contour function is not strictly positive for all quantum systems, it is simple to compute and produces reasonable and interesting results. In particular, it rigorously satisfies the positivity condition for all holographic states and those obeying the quasi-particle picture. We apply this formalism to quantum field theories with a Fermi surface, contrasting the entanglement structure of Fermi liquids and holographic (hyperscale violating) non-Fermi liquids. The analysis of non-Fermi liquids show anomalous temperature dependence of the negativity depending on the dynamical critical exponent. We further compute the negativity contour following a quantum quench and discuss how this may clarify certain aspects of thermalization.
Quantum Dynamical Yang–Baxter Equation¶Over a Nonabelian Base

In this paper we consider dynamical r-matrices over a nonabelian base. There are two main results. First, corresponding to a fat reductive decomposition of a Lie algebra ?=?⊕?, we construct geometrically a non-degenerate triangular dynamical r-matrix using symplectic fibrations. Second, we prove that a triangular dynamical r-matrix \(\) naturally corresponds to a Poisson manifold ?⋆×G. A special type of quantization of this Poisson manifold, called compatible star products in this paper, yields a generalized version of the quantum dynamical Yang–Baxter equation (or Gervais–Neveu–Felder equation). As a result, the quantization problem of a general dynamical r-matrix is proposed.
The topological sliceness of $3$–strand pretzel knots

We give a complete characterization of the topological slice status of odd 3–strand pretzel knots, proving that an odd 3–strand pretzel knot is topologically slice if and only if it either is ribbon or has trivial Alexander polynomial. We also show that topologically slice even 3–strand pretzel knots, except perhaps for members of Lecuona’s exceptional family, must be ribbon. These results follow from computations of the Casson–Gordon 3–manifold signature invariants associated to the double branched covers of these knots.
Halving the cost of quantum addition

We improve the number of T gates needed to perform an n-bit adder from 8n + O(1) to 4n + O(1). We do so via a "temporary logical-AND" construction which uses four T gates to store the logical-AND of two qubits into an ancilla and zero T gates to later erase the ancilla. This construction is equivalent to one by Jones, except that our framing makes it clear that the technique is far more widely applicable than previously realized. Temporary logical-ANDs can be applied to integer arithmetic, modular arithmetic, rotation synthesis, the quantum Fourier transform, Shor's algorithm, Grover oracles, and many other circuits. Because T gates dominate the cost of quantum computation based on the surface code, and temporary logical-ANDs are widely applicable, this represents a significant reduction in projected costs of quantum computation. In addition to our n-bit adder, we present an n-bit controlled adder circuit with T-count of 8n + O(1), a temporary adder that can be computed for the same cost as the normal adder but whose result can be kept until it is later uncomputed without using T gates, and discuss some other constructions whose T-count is improved by the temporary logical-AND.
Robust topology optimization of three-dimensional photonic-crystal band-gap structures

We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc (including diamond), bcc, and simple-cubic lattices. Even without imposing the constraints of any fabrication process, the resulting optimal gaps are only slightly larger than previous hand designs, suggesting that current photonic crystals are nearly optimal in this respect. However, optimization can discover new structures, e.g. a new fcc structure with the same symmetry but slightly larger gap than the well known inverse opal, which may offer new degrees of freedom to future fabrication technologies. Furthermore, our band-gap optimization is an illustration of a computational approach to 3D dispersion engineering which is applicable to many other problems in optics, based on a novel semidefinite-program formulation for nonconvex eigenvalue optimization combined with other techniques such as a simple approach to impose symmetry constraints. We also demonstrate a technique for robust topology optimization, in which some uncertainty is included in each voxel and we optimize the worst-case gap, and we show that the resulting band gaps have increased robustness to systematic fabrication errors.
Tunneling of Atoms, Nuclei and Molecules

This is a brief review of few relevant topics on tunneling of composite particles and how the coupling to intrinsic and external degrees of freedom affects tunneling probabilities. I discuss the phenomena of resonant tunneling, different barriers seen by subsystems, damping of resonant tunneling by level bunching and continuum effects due to particle dissociation.
SMALL-TIME EXPANSIONS FOR LOCAL JUMP-DIFFUSION MODELS WITH INFINITE JUMP ACTIVITY

We consider a Markov process X, which is the solution of a stochastic dierential equation driven by a L evy process Z and an independent Wiener process W. Under some regularity conditions, including non-degeneracy of the diusive and jump components of the process as well as smoothness of the L evy density of Z outside any neighborhood of the origin, we obtain a small-time second-order polynomial expansion for the tail distribution and the transition density of the process X. Our method of proof combines a recent regularizing technique for deriving the analog small-time expansions for a L evy process with some new tail and density estimates for jump-diusion processes with small jumps based on the theory of Malliavin calculus, ow of dieomorphisms for SDEs, and time-reversibility. As an application, the leading term for out-of-the-money option prices in short maturity under a local jump-diusion model is also derived.
The free Grothendieck theorem

The main result of this article establishes the free analog of Grothendieck's Theorem on bijective polynomial mappings of $\mathbb{C}^g$. Namely, we show if $p$ is a polynomial mapping in $g$ freely non-commuting variables sending $g$-tuples of matrices (of the same size) to $g$-tuple of matrices (of the same size) that is injective, then it has a free polynomial inverse. Other results include an algorithm that tests if a free polynomial mapping $p$ has a polynomial inverse (equivalently is injective; equivalently is bijective). Further, a class of free algebraic functions, called hyporational, lying strictly between the free rational functions and the free algebraic functions are identified. They play a significant role in the proof of the main result.
Semi-automated annotation of signal events in clinical EEG data

To be effective, state of the art machine learning technology needs large amounts of annotated data. There are numerous compelling applications in healthcare that can benefit from high performance automated decision support systems provided by deep learning technology, but they lack the comprehensive data resources required to apply sophisticated machine learning models. Further, for economic reasons, it is very difficult to justify the creation of large annotated corpora for these applications. Hence, automated annotation techniques become increasingly important. In this study, we investigated the effectiveness of using an active learning algorithm to automatically annotate a large EEG corpus. The algorithm is designed to annotate six types of EEG events. Two model training schemes, namely threshold-based and volume-based, are evaluated. In the threshold-based scheme the threshold of confidence scores is optimized in the initial training iteration, whereas for the volume-based scheme only a certain amount of data is preserved after each iteration. Recognition performance is improved 2% absolute and the system is capable of automatically annotating previously unlabeled data. Given that the interpretation of clinical EEG data is an exceedingly difficult task, this study provides some evidence that the proposed method is a viable alternative to expensive manual annotation.
Effect of power losses on self-focusing of high-intensity laser beam in gases

A theoretical study of power loss from periphery of an ultrashort pulse laser beam and temporally resolved defocusing produced by laser-induced plasma are performed using paraxial approximation. Our analysis incorporates consideration of spatial distribution of the laser beam irradiance and the results show that substantial power losses (10–80%) occur from the beam periphery limiting the length of a filament. It was also shown that the generally accepted concept of self-focusing critical power is inconsistent with consideration of self-induced refraction of spatially distributed laser beam. A new criterion for self-focusing and hypothesis for multiple filamentation are proposed.
Cavity-enhanced ultrafast spectroscopy: ultrafast meets ultrasensitive

Ultrafast optical spectroscopy methods, such as transient absorption spectroscopy and 2D spectroscopy, are widely used across many disciplines. However, these techniques are typically restricted to optically thick samples, such as solids and liquid solutions. Using a frequency comb laser and optical cavities, we present a technique for performing ultrafast optical spectroscopy with high sensitivity, enabling work in dilute gas-phase molecular beams. Resonantly enhancing the probe pulses, we demonstrate transient absorption measurements with a detection limit of ΔOD=2×10−10 (1×10−9/Hz). Resonantly enhancing the pump pulses allows us to produce a high excitation fraction at a high repetition rate, so that signals can be recorded from samples with optical densities as low as OD≈10−8, or column densities <1010 molecules/cm2. To our knowledge, this represents a 5000-fold improvement of the state of the art.
Embeddings, Immersions and the Bartnik Quasi-Local Mass Conjectures

Given a Riemannian 3-ball $$({\bar{B}}, g)$$ of nonnegative scalar curvature, Bartnik conjectured that $$({\bar{B}}, g)$$ admits an asymptotically flat (AF) extension (without horizons) of the least possible ADM mass and that such a mass minimizer is an AF solution to the static vacuum Einstein equations, uniquely determined by natural geometric conditions on the boundary data of $$({\bar{B}}, g)$$ . We prove the validity of the second statement, i.e., such mass minimizers, if they exist, are indeed AF solutions of the static vacuum equations. On the other hand, we prove that the first statement is not true in general; there is a rather large class of bodies $$({\bar{B}}, g)$$ for which a minimal mass extension does not exist.
Lone Axes in Outer Space

Handel and Mosher define the axis bundle for a fully irreducible outer automorphism in "Axes in Outer Space." In this paper we give a necessary and sufficient condition for the axis bundle to consist of a unique periodic fold line. As a consequence, we give a setting, and means for identifying in this setting, when two elements of an outer automorphism group $Out(F_r)$ have conjugate powers.
Invariant measures concentrated on countable structures

Let L be a countable language. We say that a countable innite L-structure M admits an invariant measure when there is a probability measure on the space of L-structures with the same underlying set as M that is invariant under permutations of that set, and that assigns measure one to the isomorphism class of M. We show that M admits an invariant measure if and only if it has trivial denable closure, i.e., the pointwise stabilizer in Aut( M) of an arbitrary nite tuple of M xes no additional points. When M is a Frass e limit in a relational language, this amounts to requiring that the age of M have strong amalgamation. Our results give rise to new instances of structures that admit invariant measures and structures that do not.
Strange kinetics of bulk-mediated diffusion on lipid bilayers

Diffusion at solid–liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems to be deceivingly simple, recent studies showing passive superdiffusive transport suggest that diffusion on surfaces may hide rich complexities. In particular, bulk-mediated diffusion occurs when molecules are transiently released from the surface to perform three-dimensional excursions into the liquid bulk. This phenomenon bears the dichotomy where a molecule always return to the surface but the mean jump length is infinite. Such behavior is associated with a breakdown of the central limit theorem and weak ergodicity breaking. Here, we use single-particle tracking to study the statistics of bulk-mediated diffusion on a supported lipid bilayer. We find that the time-averaged mean square displacement (MSD) of individual trajectories, the archetypal measure in diffusion processes, does not converge to the ensemble MSD but it remains a random variable, even in the long observation-time limit. The distribution of time averages is shown to agree with a Levy flight model. Our results also unravel intriguing anomalies in the statistics of displacements. The time-averaged MSD is shown to depend on experimental time and investigations of fractional moments show a scaling 〈|r(t)|q〉 ∼ tqν(q) with non-linear exponents, i.e. ν(q) ≠ const. This type of behavior is termed strong anomalous diffusion and is rare among experimental observations.
FUZZY SUPERNOVA TEMPLATES. II. PARAMETER ESTIMATION

Wide-field surveys will soon be discovering Type Ia supernovae (SNe) at rates of several thousand per year. Spectroscopic follow-up can only scratch the surface for such enormous samples, so these extensive data sets will only be useful to the extent that they can be characterized by the survey photometry alone. In a companion paper we introduced the Supernova Ontology with Fuzzy Templates (SOFT) method for analyzing SNe using direct comparison to template light curves, and demonstrated its application for photometric SN classification. In this work we extend the SOFT method to derive estimates of redshift and luminosity distance for Type Ia SNe, using light curves from the Sloan Digital Sky Survey (SDSS) and Supernova Legacy Survey (SNLS) as a validation set. Redshifts determined by SOFT using light curves alone are consistent with spectroscopic redshifts, showing an rms scatter in the residuals of rms{sub z} = 0.051. SOFT can also derive simultaneous redshift and distance estimates, yielding results that are consistent with the currently favored {Lambda}CDM cosmological model. When SOFT is given spectroscopic information for SN classification and redshift priors, the rms scatter in Hubble diagram residuals is 0.18 mag for the SDSS data and 0.28 mag for the SNLS objects.more » Without access to any spectroscopic information, and even without any redshift priors from host galaxy photometry, SOFT can still measure reliable redshifts and distances, with an increase in the Hubble residuals to 0.37 mag for the combined SDSS and SNLS data set. Using Monte Carlo simulations, we predict that SOFT will be able to improve constraints on time-variable dark energy models by a factor of 2-3 with each new generation of large-scale SN surveys.« less
Rotational symmetry of self-similar solutions to the Ricci flow

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and κ-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman’s first paper.
The Fate of Scattered Planets

As gas giant planets evolve, they may scatter other planets far from their original orbits to produce hot Jupiters or rogue planets that are not gravitationally bound to any star. Here, we consider planets cast out to large orbital distances on eccentric, bound orbits through a gaseous disk. With simple numerical models, we show that super-Earths can interact with the gas through dynamical friction to settle in the remote outer regions of a planetary system. Outcomes depend on planet mass, the initial scattered orbit, and the evolution of the time-dependent disk. Efficient orbital damping by dynamical friction requires planets at least as massive as the Earth. More massive, longer-lived disks damp eccentricities more efficiently than less massive, short-lived ones. Transition disks with an expanding inner cavity can circularize orbits at larger distances than disks that experience a global (homologous) decay in surface density. Thus, orbits of remote planets may reveal the evolutionary history of their primordial gas disks. A remote planet with an orbital distance ~100 AU from the Sun is plausible and might explain correlations in the orbital parameters of several distant trans-Neptunian objects.
Implications of HERA results for very high energy cosmic ray physics

Experimental results obtained with the HERA collider and recent progress in their theoretical interpretation are reviewed. After a short introduction to HERA physics, deep inelastic scattering and photoproduction is discussed as (virtual) photon-proton scattering. It is shown that the measurement and theoretical understanding of both photoproduction as well as low- χ deep inelastic scattering are essential for obtaining reliable high energy extrapolations within hadron-hadron interaction models. Limitations of the predictive power of hadron interaction models due to the interplay of perturbative QCD and unitarity effects are discussed.
Noncommutative Momentum and Torsional Regularization

We show that in the presence of the torsion tensor $$S^k_{ij}$$ , the quantum commutation relation for the four-momentum, traced over spinor indices, is given by $$[p_i,p_j]=2i\hbar S^k_{ij}p_k$$ . In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin of fermions, this relation in a coordinate frame reduces to a commutation relation of noncommutative momentum space, $$[p_i,p_j]=i\epsilon _{ijk}Up^3 p_k$$ , where U is a constant on the order of the squared inverse of the Planck mass. We propose that this relation replaces the integration in the momentum space in Feynman diagrams with the summation over the discrete momentum eigenvalues. We derive a prescription for this summation that agrees with convergent integrals: $$\int \frac{d^4p}{(p^2+\varDelta )^s}\rightarrow 4\pi U^{s-2}\sum _{l=1}^\infty \int _0^{\pi /2} d\phi \frac{\sin ^4\phi \,n^{s-3}}{[\sin \phi +U\varDelta n]^s}$$ , where $$n=\sqrt{l(l+1)}$$ and $$\varDelta $$ does not depend on p. We show that this prescription regularizes ultraviolet-divergent integrals in loop diagrams. We extend this prescription to tensor integrals. We derive a finite, gauge-invariant vacuum polarization tensor and a finite running coupling. Including loops from all charged fermions, we find a finite value for the bare electric charge of an electron: $$\approx -1.22\,e$$ . This torsional regularization may therefore provide a realistic, physical mechanism for eliminating infinities in quantum field theory and making renormalization finite.
High-Fugacity Expansion, Lee–Yang Zeros, and Order–Disorder Transitions in Hard-Core Lattice Systems

We establish existence of order–disorder phase transitions for a class of “non-sliding” hard-core lattice particle systems on a lattice in two or more dimensions. All particles have the same shape and can be made to cover the lattice perfectly in a finite number of ways. We also show that the pressure and correlation functions have a convergent expansion in powers of the inverse of the fugacity. This implies that the Lee–Yang zeros lie in an annulus with finite positive radii.
Zero dimensional Donaldson–Thomas invariants of threefolds

Ever since the pioneer work of Donaldson and Thomas on Yang–Mills theory over Calabi–Yau threefolds [5; 13], people have been searching for their roles in the study of Calabi–Yau geometry and their relations with other branches of mathematics. The recent results and conjectures of Maulik, Nekrasov, Okounkov and Pandharipande [10; 11] that relate the invariants of the moduli of ideal sheaves of curves on a Calabi–Yau manifold to its Gromov–Witten invariants constitute major progress in this direction. This paper will address one of their conjectures on invariants associated to Hilbert scheme of points.
Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories

We apply the “weighted ensemble” (WE) simulation strategy, previously employed in the context of molecular dynamics simulations, to a series of systems-biology models that range in complexity from a one-dimensional system to a system with 354 species and 3680 reactions. WE is relatively easy to implement, does not require extensive hand-tuning of parameters, does not depend on the details of the simulation algorithm, and can facilitate the simulation of extremely rare events. For the coupled stochastic reaction systems we study, WE is able to produce accurate and efficient approximations of the joint probability distribution for all chemical species for all time t. WE is also able to efficiently extract mean first passage times for the systems, via the construction of a steady-state condition with feedback. In all cases studied here, WE results agree with independent “brute-force” calculations, but significantly enhance the precision with which rare or slow processes can be characterized. Speedups over “brute-force” in sampling rare events via the Gillespie direct Stochastic Simulation Algorithm range from ∼1012 to ∼1018 for characterizing rare states in a distribution, and ∼102 to ∼104 for finding mean first passage times.
Inside-Out Planet Formation

The compact multi-transiting planet systems discovered by Kepler challenge planet formation theories. Formation in situ from disks with radial mass surface density, Σ, profiles similar to the minimum mass solar nebula but boosted in normalization by factors ≳ 10 has been suggested. We propose that a more natural way to create these planets in the inner disk is formation sequentially from the inside-out via creation of successive gravitationally unstable rings fed from a continuous stream of small (∼cm-m size) 'pebbles', drifting inward via gas drag. Pebbles collect at the pressure maximum associated with the transition from a magnetorotational instability (MRI)-inactive ('dead zone') region to an inner MRI-active zone. A pebble ring builds up until it either becomes gravitationally unstable to form an ∼1 M {sub ⊕} planet directly or induces gradual planet formation via core accretion. The planet may undergo Type I migration into the active region, allowing a new pebble ring and planet to form behind it. Alternatively, if migration is inefficient, the planet may continue to accrete from the disk until it becomes massive enough to isolate itself from the accretion flow. A variety of densities may result depending on the relative importance of residual gas accretion asmore » the planet approaches its isolation mass. The process can repeat with a new pebble ring gathering at the new pressure maximum associated with the retreating dead-zone boundary. Our simple analytical model for this scenario of inside-out planet formation yields planetary masses, relative mass scalings with orbital radius, and minimum orbital separations consistent with those seen by Kepler. It provides an explanation of how massive planets can form with tightly packed and well-aligned system architectures, starting from typical protoplanetary disk properties.« less
Mixed Galileons and spherically symmetric solutions

It was previously found that in a certain parameter subspace of scalar–tensor theories emerging from massive gravity, the only stable field configuration created by static spherically symmetric sources was one with cosmological asymptotics. Moreover, these backgrounds were shown to be subluminal everywhere in the space; in contrast to the common belief that these theories are necessarily superluminal in the vicinity of a static source. In this work, we complete that analysis by extending it to cover the whole parameter space of these scalar–tensor theories. We find that the stability argument renders the asymptotically flat backgrounds unrealizable, forcing once again for cosmological asymptotics. In the case of pressure-less sources, these backgrounds are stable. However, they get destabilized in the presence of positive pressure, larger than a critical density. Even on the self-accelerated background, on which the scalar mode decouples from sources, in the region occupied by the source it acquires an elliptic equation of motion. Therefore, we conclude that the only parameter space which is not ruled out, by solar system measurements, is the one considered in Berezhiani et al (2013 arXiv:1302.0549), namely the one for which the scalar and tensor modes can be diagonalized via local transformations. We also reinvestigate the scale at which a perturbation theory breaks down in a general Galileon theory. We show that the Vainshtein mechanism successfully redresses the strong-coupling scale to a small one, just like in the cubic Galileon, despite the cancellations occurring in the special spherically symmetric case. We emphasize that even if these tests were performed at scales at which the perturbation theory broke down, these could not be interpreted as a lower bound for the graviton mass.
Global Supply Chains in Response to COVID-19: Adopting a Real Options Mindset

Businesses and governments may have been overconfident in their ability to react efficiently to black swan consequences. COVID-19 levied unforeseen isolation and border closings threatening the survival of global supply chains and the bankruptcy of governments and organizations alike. As a response to this challenge, our proposal takes a real options approach to mitigate supply chain disruptions by developing regional partnerships outside of densely populated areas. Its inherent novelty is twofold: (1) it anticipates survival uncertainties by securing the continued production of goods and services worldwide and (2) it recognizes a change in the relationship’s dynamic between global and regional actors.
Loop groups and twisted K-theory I

This is the first in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the “Verlinde ring” of its loop group. In this paper we set up the foundations of twisted equivariant K-groups, and more generally twisted K-theory of groupoids. We establish enough basic properties to make effective computations. We determine the twisted equivariant K-groups of a compact connected Lie group G with torsion free fundamental group. We relate this computation to the representation theory of the loop group at a level related to the twisting.
Optimality and uniqueness of the Leech lattice among lattices

We prove that the Leech lattice is the unique densest lattice in R24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in R24 can exceed the Leech lattice's density by a factor of more than 1 + 1.65 10-30, and we give a new proof that Es is the unique densest lattice in R8.
Root System Chip-Firing II: Central-Firing

Jim Propp recently proposed a labeled version of chip-firing on a line and conjectured that this process is confluent from some initial configurations. This was proved by Hopkins-McConville-Propp. We reinterpret Propp's labeled chip-firing moves in terms of root systems: a "central-firing" move consists of replacing a weight $\lambda$ by $\lambda+\alpha$ for any positive root $\alpha$ that is orthogonal to $\lambda$. We show that central-firing is always confluent from any initial weight after modding out by the Weyl group, giving a generalization of unlabeled chip-firing on a line to other types. For simply-laced root systems we describe this unlabeled chip-firing as a number game on the Dynkin diagram. We also offer a conjectural classification of when central-firing is confluent from the origin or a fundamental weight.
Topology of Entanglement Evolution of Two Qubits

The dynamics of a two-qubit system is considered with the aim of a general categorization of the different ways in which entanglement can disappear in the course of the evolution, e.g., entanglement sudden death. The dynamics is described by the function n(t), where n is the 15-dimensional polarization vector. This representation is particularly useful because the components of n are direct physical observables, there is a meaningful notion of orthogonality, and the concurrence C can be computed for any point in the space. We analyze the topology of the space S of separable states (those having C = 0), and the often lower-dimensional linear dynamical subspace D that is characteristic of a specific physical model. This allows us to give a rigorous characterization of the four possible kinds of entanglement evolution. Which evolution is realized depends on the dimensionality of D and of D∩S, the position of the asymptotic point of the evolution, and whether or not the evolution is "distance-Markovian", a notion we define. We give several examples to illustrate the general principles, and to give a method to compute critical points. We construct a model that shows all four behaviors.
Perturbative QCD at High Temperature

Recent developments of perturbation theory at finite temperature based on effective field theory methods are reviewed. These methods allow the contributions from the different scales to be separated and the perturbative series to be reorganized. The construction of the effective field theory is shown in detail for ϕ4 theory and QCD. It is applied to the evaluation of the free energy of QCD at order g5 and the calculation of the g6 term is outlined. Implications for the application of perturbative QCD to the quark–gluon plasma are also discussed.
Asymptotic Synchronization for Finite-State Sources

We extend a recent synchronization analysis of exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the proof methods are quite different, the primary results remain the same. We find that an observer’s average uncertainty in the source state vanishes exponentially fast and, as a consequence, an observer’s average uncertainty in predicting future output converges exponentially fast to the source entropy rate.
Radio emission and jets from microquasars

To some extent, all Galactic binary systems hosting a compact object are potential “microquasars”, so much as all Galactic nuclei may have been quasars, once upon a time. The necessary ingredients for a compact object of stellar mass to qualify as a microquasar seem to be: accretion, rotation, and magnetic field. The presence of a black hole may help, but is not strictly required, since neutron star X-ray binaries and dwarf novae can be powerful jet sources as well. The above issues are broadly discussed throughout this chapter, with a rather trivial question in mind: Why do we care? In other words: are jets a negligible phenomenon in terms of accretion power, or do they contribute significantly to dissipating gravitational potential energy? How do they influence their surroundings? The latter point is especially relevant in a broader context, as there is mounting evidence that outflows powered by supermassive black holes in external galaxies may play a crucial role in regulating the evolution of cosmic structures. Microquasars can also be thought of as a form of quasars for the impatient: what makes them appealing, despite their low number statistics with respect to quasars, are the fast variability timescales. In the first approximation, the physics of the jet-accretion coupling in the innermost regions should be set by the mass/size of the accretor: stellar mass objects vary by 105–108 times shorter timescales, making it possible to study variable accretion modes and related ejection phenomena over average Ph.D. timescales. At the same time, allowing for a systematic comparison between different classes of compact objects – black holes, neutron stars, and white dwarfs – microquasars hold the key to identify and characterize properties that may be unique to, e.g., the presence (or the lack) of an event horizon.
Weak Shock Propagation with Accretion. I. Self-similar Solutions and Application to Failed Supernovae

We present solutions for the self-similar propagation of a shock wave in a hydrostatic, adiabatic medium with a point mass gravitational field. In contrast to the well-known, Sedov–Taylor blast wave, these solutions apply to the case when the shock Mach number is of the order of a few, and the energy of the shocked fluid is not conserved but self-consistently modified by the binding energy of the ambient medium that is swept up by the passage of the shock. Furthermore, we show that there is one solution (for a given ambient density profile) that smoothly passes through a sonic point in the post-shock flow and results in accretion onto the central object; in analogy with the Bondi problem, we propose that these solutions are the ones that are most relevant in astrophysical environments. We apply these accreting models to failed supernovae, in which neutron star formation does not unbind the envelope, but a weak shock is still generated in the outer layers of the star from neutrino-induced mass loss. We find excellent agreement between the predictions of our self-similar, shock propagation model and numerical simulations of the collapse of a yellow supergiant; the self-similar solutions reproduce the overall scaling of the shock speed; the time- and space-dependent evolution of the velocity, density, and pressure behind the shock; and the accretion rate onto the black hole. Our results have important implications for the fallback and ejection of material in failed supernovae.
A Hilbert C*-module admitting no frames

We show that every infinite-dimensional commutative unital C∗-algebra has a Hilbert C∗-module admitting no frames. In particular, this shows that Kasparov’s stabilization theorem for countably generated Hilbert C∗-modules can not be extended to arbitrary Hilbert C∗-modules.
The Effect of Carbon Monoxide on Planetary Haze Formation

Organic haze plays a key role in many planetary processes ranging from influencing the radiation budget of an atmosphere to serving as a source of prebiotic molecules on the surface. Numerous experiments have investigated the aerosols produced by exposing mixtures of N2/CH4 to a variety of energy sources. However, many N2/CH4 atmospheres in both our solar system and extrasolar planetary systems also contain carbon monoxide (CO). We have conducted a series of atmosphere simulation experiments to investigate the effect of CO on the formation and particle size of planetary haze analogues for a range of CO mixing ratios using two different energy sources, spark discharge and UV. We find that CO strongly affects both number density and particle size of the aerosols produced in our experiments and indicates that CO may play an important, previously unexplored, role in aerosol chemistry in planetary atmospheres.
MOST DOUBLE DEGENERATE LOW-MASS WHITE DWARF BINARIES MERGE

We estimate the merger rate of double degenerate binaries containing extremely low mass (ELM) <0.3 Msun white dwarfs in the Galaxy. Such white dwarfs are detectable for timescales of 0.1 Gyr -- 1 Gyr in the ELM Survey; the binaries they reside in have gravitational wave merger times of 0.001 Gyr -- 100 Gyr. To explain the observed distribution requires that most ELM white dwarf binary progenitors detach from the common envelope phase with <1 hr orbital periods. We calculate the local space density of ELM white dwarf binaries and estimate a merger rate of 3e-3/yr over the entire disk of the Milky Way; the merger rate in the halo is 10 times smaller. The ELM white dwarf binary merger rate exceeds by a factor of 40 the formation rate of stable mass transfer AM CVn binaries, marginally exceeds the rate of underluminous supernovae, and is identical to the formation rate of R CrB stars. On this basis, we conclude that ELM white dwarf binaries can be the progenitors of all observed AM CVn and possibly underluminous supernovae, however the majority of He+CO white dwarf binaries go through unstable mass transfer and merge, e.g. into single massive ~1 Msun white dwarfs.
Dynamics of potential vorticity staircase evolution and step mergers in a reduced model of beta-plane turbulence

Author(s): Malkov, MA; Diamond, PH | Abstract: A two-field model of potential vorticity (PV) staircase structure and dynamics relevant to both beta-plane and drift-wave plasma turbulence is studied numerically and analytically. The model evolves averaged PV whose flux is both driven by and regulates, a potential enstrophy field, $\varepsilon$. The model employs a closure using a mixing length model. Its link to bistability, vital to staircase generation, is analyzed and verified by integrating the equations numerically. Long-time staircase evolution consistently manifests a pattern of meta-stable quasi-periodic configurations, lasting for hundreds of time units, yet interspersed with abrupt ($\Delta t\ll1$) mergers of adjacent steps in the staircase. The mergers occur at the staircase lattice defects where the pattern has not completely relaxed to a strictly periodic solution that can be obtained analytically. Other types of stationary solutions are solitons and kinks in the PV gradient and $\varepsilon$ - profiles. The waiting time between mergers increases strongly as the number of steps in the staircase decreases. This is because of an exponential decrease in inter-step coupling strength with growing spacing. The long-time staircase dynamics is shown numerically be determined by local interaction with adjacent steps. Mergers reveal themselves through the explosive growth of the turbulent PV-flux which, however, abruptly drops to its global constant value once the merger is completed.
Event Extraction by Answering (Almost) Natural Questions

The problem of event extraction requires detecting the event trigger and extracting its corresponding arguments. Existing work in event argument extraction typically relies heavily on entity recognition as a preprocessing/concurrent step, causing the well-known problem of error propagation. To avoid this issue, we introduce a new paradigm for event extraction by formulating it as a question answering (QA) task that extracts the event arguments in an end-to-end manner. Empirical results demonstrate that our framework outperforms prior methods substantially; in addition, it is capable of extracting event arguments for roles not seen at training time (i.e., in a zero-shot learning setting).
The First Order Correction to the Exit Distribution for Some Random Walks

We study three different random walk models on several two-dimensional lattices by Monte Carlo simulations. One is the usual nearest neighbor random walk. Another is the nearest neighbor random walk which is not allowed to backtrack. The final model is the smart kinetic walk. For all three of these models the distribution of the point where the walk exits a simply connected domain D in the plane converges weakly to harmonic measure on $$\partial D$$ as the lattice spacing $$\delta \rightarrow 0$$ . Let $$\omega (0,\cdot ;D)$$ be harmonic measure for D, and let $$\omega _\delta (0,\cdot ;D)$$ be the discrete harmonic measure for one of the random walk models. Our definition of the random walk models is unusual in that we average over the orientation of the lattice with respect to the domain. We are interested in the limit of $$(\omega _\delta (0,\cdot ;D)- \omega (0,\cdot ;D))/\delta $$ . Our Monte Carlo simulations of the three models lead to the conjecture that this limit equals $$c_{M,L} \, \rho _D(z)$$ times Lebesgue measure with respect to arc length along the boundary, where the function $$\rho _D(z)$$ depends on the domain, but not on the model or lattice, and the constant $$c_{M,L}$$ depends on the model and on the lattice, but not on the domain. So there is a form of universality for this first order correction. We also give an explicit formula for the conjectured density $$\rho _D$$ .
Tidal Evolution of the Evection Resonance/Quasi-Resonance and the Angular Momentum of the Earth-Moon System

Forming the Moon by a high-angular momentum impact may explain the Earth-Moon isotopic similarities, however, the post-impact angular momentum needs to be reduced by a factor of 2 or more to the current value (1 L_EM) after the Moon forms. Capture into the evection resonance, occurring when the lunar perigee precession period equals one year, could remove the angular momentum excess. However the appropriate angular momentum removal appears sensitive to the tidal model and chosen tidal parameters. In this work, we use a constant-time delay tidal model to explore the Moon's orbital evolution through evection. We find that exit from formal evection occurs early and that subsequently, the Moon enters a quasi-resonance regime, in which evection still regulates the lunar eccentricity even though the resonance angle is no longer librating. Although not in resonance proper, during quasi-resonance angular momentum is continuously removed from the Earth-Moon system and transferred to Earth's heliocentric orbit. The final angular momentum, set by the timing of quasi-resonance escape, is a function of the ratio of tidal strength in the Moon and Earth and the absolute rate of tidal dissipation in the Earth. We consider a physically-motivated model for tidal dissipation in the Earth as the mantle cools from a molten to a partially molten state. We find that as the mantle solidifies, increased terrestrial dissipation drives the Moon out of quasi-resonance. For post-impact systems that contain >2 L_EM, final angular momentum values after quasi-resonance escape remain significantly higher than the current Earth-Moon value.
POLYNOMIALS FOR SYMMETRIC ORBIT CLOSURES IN THE FLAG VARIETY

In [WY] we introduced polynomial representatives of cohomology classes of orbit closures in the flag variety, for the symmetric pair (GLp+q, GLp × GLq). We present analogous results for the remaining symmetric pairs of the form (GLn, K), i.e., (GLn, On) and (GL2n, Sp2n). We establish “well-definedness” of certain representatives from [Wy1]. It is also shown that the representatives have the combinatorial properties of nonnegativity and stability. Moreover, we give some extensions to equivariant K-theory.
Linking forms and stabilization of diffeomorphism groups of manifolds of dimension 4n+1

Let $n \geq 2$. We prove a homological stability theorem for the diffeomorphism groups of $(4n+1)$-dimensional manifolds, with respect to forming the connected sum with $(2n-1)$-connected, $(4n+1)$-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the diffeomorphism group of a manifold $M$, on the linking form associated to the homology groups of $M$. In particular, we construct a geometric model for the linking form using the intersections of embedded and immersed $\mathbb{Z}/k$-manifolds. In addition to our main homological stability theorem, we prove several disjunction results for the embeddings and immersions of $\mathbb{Z}/k$-manifolds that could be of independent interest.
Dark Matter Studies Entrain Nuclear Physics

Abstract We review theoretically well-motivated dark-matter candidates, and pathways to their discovery, in the light of recent results from collider physics, astrophysics, and cosmology. Taken in aggregate, these encourage broader thinking in regards to possible dark-matter candidates — dark-matter need not be made of “WIMPs”, i.e. , elementary particles with weak-scale masses and interactions. Facilities dedicated to nuclear physics are well-poised to investigate certain non-WIMP models. In parallel to this, developments in observational cosmology permit probes of the relativistic energy density at early epochs and thus provide new ways to constrain dark-matter models, provided nuclear physics inputs are sufficiently well-known. The emerging confluence of accelerator, astrophysical, and cosmological constraints permit searches for dark-matter candidates in a greater range of masses and interaction strengths than heretofore possible.
Imaging the stochastic microstructure and dynamic development of correlations in perpendicular artificial spin ice

This paper uses magneto-optical microscopy to reveal the hysteretic switching process of artificial spin ices at both the micro- and macroscale. Inter-island correlations within an array are found to be asymmetric with respect to the magnetization direction, and even though the array macrostate reproduces from one hysteresis sweep to another, its microstate is stochastic.