cssi/SciSciGPT-SciSciNet huggingface dataset:
Dependence of the quantum speed limit on system size and control complexity

We extend the work in 2017 New J. Phys. 19 103015 by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields. This bound is explicitly analyzed for a specific N-level system similar to those used to represent simple models of an atom, or the first excitation sector of a Heisenberg spin chain, both of which are of interest in quantum control for quantum computation. Specifically, it is shown that the resultant bound depends on the dimension of the system, and on the number of controls used to implement a specific target unitary operation. The value of the bound determined numerically, and an estimate of the true minimum gate time are systematically compared for a range of system dimension and number of controls; special attention is drawn to the relationship between these two variables. It is seen that the bound captures the scaling of the minimum time well for the systems studied, and quantitatively is correct in the order of magnitude.
ON AXOPLASMIC PRESSURE WAVES AND THEIR POSSIBLE ROLE IN NERVE IMPULSE PROPAGATION

It is suggested that the propagation of the action potential is accompanied by an axoplasmic pressure pulse propagating in the axoplasm along the axon length. The pressure pulse stretch-modulates voltage-gated Na+ (Nav) channels embedded in the axon membrane, causing their accelerated activation and inactivation and increasing peak channel conductance. As a result, the action potential propagates due to mechano-electrical activation of Nav channels by straggling ionic currents and the axoplasmic pressure pulse. The velocity of such propagation is higher than in the classical purely electrical Nav activation mechanism, and it may be close to the velocity of propagation of pressure pulses in the axoplasm. Extracellular Ca2+ ions influxing during the voltage spike, or Ca2+ ions released from intracellular stores, may trigger a mechanism that generates and augments the pressure pulse, thus opposing its viscous decay. The model can potentially explain a number of phenomena that are not contained within the pur...
Dark Matter that Interacts with Baryons: Density Distribution within the Earth and New Constraints on the Interaction Cross-section

For dark matter (DM) particles with masses in the 0.6 - 6 m_p range, we set stringent constraints on the interaction cross-sections for scattering with ordinary baryonic matter. These constraints follow from the recognition that such particles can be captured by - and thermalized within - the Earth, leading to a substantial accumulation and concentration of DM that interact with baryons. Here, we discuss the probability that DM intercepted by the Earth will be captured, the number of DM particles thereby accumulated over Earth's lifetime, the fraction of such particles retained in the face of evaporation, and the density distribution of such particles within the Earth. In the latter context, we note that a previous treatment of the density distribution of DM, presented by Gould and Raffelt and applied subsequently to DM in the Sun, is inconsistent with considerations of hydrostatic equilibrium. Our analysis provides an estimate of the DM particle density at Earth's surface, which may exceed 1.E+14 cm-3 for the mass range under consideration. Based upon our determination of the DM density at Earth's surface, we derive constraints on the scattering cross-sections. These constraints are placed by four considerations: (1) the lifetime of the relativistic proton beam at the Large Hadron collider (LHC); (2) the orbital decay of spacecraft in low Earth orbit (LEO); (3) the vaporization rate of cryogenic liquids in well-insulated storage dewars; and (4) the thermal conductivity of Earth's crust. As an example application of our results, we show that for the scattering cross-sections that were invoked recently in Barkana's original explanation for the anomalously deep 21 cm absorption reported by EDGES, DM particle masses in the 0.6 - 4 m_p range are ruled out.
Phase controllable Josephson junctions for cryogenic memory

Josephson junctions containing ferromagnetic layers have generated interest for application in cryogenic memory. In a junction containing both a magnetically hard fixed layer and soft free layer with carefully chosen thicknesses, the ground-state phase difference of the junction can be controllably switched between 0 and {\pi} by changing the relative orientation of the two ferromagnetic layers from antiparallel to parallel. This phase switching has been observed in junctions using Ni fixed layers and NiFe free layers. We present phase-sensitive measurements of such junctions in low-inductance symmetric SQUID loops which simplify analysis relative to our previous work. We confirm controllable 0 - {\pi} switching in junctions with 2.0 nm Ni fixed layers and 1.25 nm NiFe free layers across multiple devices and using two SQUID designs, expanding the phase diagram of known thicknesses that permit phase control.
D-branes in linear dilaton backgrounds

We construct a Dirichlet boundary state for linear dilaton backgrounds. The state is conformally invariant and satisfies Cardy's conditions. We apply this construction to two dimensional string theory.
Type Ia Supernova Intrinsic Magnitude Dispersion and the Fitting of Cosmological Parameters

I present an analysis for fitting cosmological parameters from a Hubble Diagram of a standard candle with unknown intrinsic magnitude dispersion. The dispersion is determined from the data themselves, simultaneously with the cosmological parameters. This contrasts with the strategies used to date. The advantages of the presented analysis are that it is done in a single fit (it is not iterative), it provides a statistically founded and unbiased estimate of the intrinsic dispersion, and its cosmological-parameter uncertainties account for the intrinsic dispersion uncertainty. Applied to Type Ia supernovae, my strategy provides a statistical measure to test for sub-types and assess the significance of any magnitude corrections applied to the calibrated candle. Parameter bias and differences between likelihood distributions produced by the presented and currently-used fitters are negligibly small for existing and projected supernova data sets.
Qd-tree: Learning Data Layouts for Big Data Analytics

Corporations today collect data at an unprecedented and accelerating scale, making the need to run queries on large datasets increasingly important. Technologies such as columnar block-based data organization and compression have become standard practice in most commercial database systems. However, the problem of best assigning records to data blocks on storage is still open. For example, today's systems usually partition data by arrival time into row groups, or range/hash partition the data based on selected fields. For a given workload, however, such techniques are unable to optimize for the important metric of the number of blocks accessed by a query. This metric directly relates to the I/O cost, and therefore performance, of most analytical queries. Further, they are unable to exploit additional available storage to drive this metric down further. In this paper, we propose a new framework called a query-data routing tree, or qd-tree, to address this problem, and propose two algorithms for their construction based on greedy and deep reinforcement learning techniques. Experiments over benchmark and real workloads show that a qd-tree can provide physical speedups of more than an order of magnitude compared to current blocking schemes, and can reach within 2X of the lower bound for data skipping based on selectivity, while providing complete semantic descriptions of created blocks.
Fluctuation of the Free Energy of Sherrington-Kirkpatrick Model with Curie-Weiss Interaction: The Paramagnetic Regime

We consider a spin system containing pure two spin Sherrington–Kirkpatrick Hamiltonian with Curie–Weiss interaction. The model where the spins are spherically symmetric was considered by Baik and Lee (Ann Henri Poincare 18(6):1867–1917, 2017) and Baik et al. (J Stat Phys 173(5):1484–1522, 2018) which shows a two dimensional phase transition with respect to temperature and the coupling constant. In this paper we prove a result analogous to Baik and Lee (Ann Henri Poincare 18(6):1867–1917, 2017) in the “paramagnetic regime” when the spins are i.i.d. Rademacher. We prove the free energy in this case is asymptotically Gaussian and can be approximated by a suitable linear spectral statistics. Unlike the spherical symmetric case the free energy here can not be written as a function of the eigenvalues of the corresponding interaction matrix. The method in this paper relies on a dense sub-graph conditioning technique introduced by Banerjee (J Probab 23:28, 2018). The proof of the approximation by the linear spectral statistics part is close to Banerjee and Ma (arXiv:1705.05305, 2017).
Strings on type IIB pp-wave backgrounds with interacting massive theories on the worldsheet

We consider superstring theories on pp-wave backgrounds which result in an integrable = (2,2) supersymmetric Landau-Ginzburg theory on the worldsheet. We obtain exact eigenvalues of the light-cone gauge superstring hamiltonian in the massive and interacting world-sheet theory with superpotential Z3−Z. We find the modes of the supergravity part of the string spectrum, and their space-time interpretation. Because the system is effectively at strong coupling on the worldsheet, these modes are not in one-to-one correspondence with the usual type-IIB supergravity modes in the p−→0 limit. However, the above correspondence holds in the α'→0 limit.
Optomechanics with one-dimensional gallium phosphide photonic crystal cavities

Gallium phosphide offers an attractive combination of a high refractive index (n>3 for vacuum wavelengths up to 4 μm) and a wide electronic bandgap (2.26 eV), enabling optical cavities with small mode volumes and low two-photon absorption at telecommunication wavelengths. Heating due to strongly confined light fields is therefore greatly reduced. Here, we investigate the benefits of these properties for cavity optomechanics. Utilizing a recently developed fabrication scheme based on direct wafer bonding, we realize integrated one-dimensional photonic crystal cavities made of gallium phosphide with optical quality factors as high as 1.1×105. We optimize their design to couple the optical eigenmode at ∼200 THz via radiation pressure to a co-localized mechanical mode with a frequency of 3 GHz, yielding sideband-resolved devices. The high vacuum optomechanical coupling rate (g0=2π×400 kHz) permits amplification of the mechanical mode into the so-called mechanical lasing regime with input power as low as ∼20 μW. The observation of mechanical lasing implies a multiphoton cooperativity of C>1, an important threshold for the realization of quantum state transfer protocols. Because of the reduced thermo-optic resonance shift, optomechanically induced transparency can be detected at room temperature even in non-sideband-resolved devices in addition to the normally observed optomechanically induced absorption. Considering that GaP is also piezoelectric, these results establish GaP as an attractive material for future electro–opto-mechanical systems.
Observations of CMEs and models of the eruptive corona

Current theoretical ideas on the internal structure of CMEs suggest that a flux rope is central to the CME structure, which has considerable observational support both from remote-sensing and in-situ observations. The flux-rope nature is also consistent with the post-eruption arcades with high-temperature plasmas and the charge states observed within CMEs arriving at Earth. The model involving magnetic loop expansion to explain CMEs without flux ropes is not viable because it contradicts CME kinematics and flare properties near the Sun. The flux rope is fast, it drives a shock, so the global picture of CMEs becomes complete if one includes the shock sheath to the CSHKP model.
Randomness on the lattice

Abstract In this lecture we review recent lattice QCD studies of the statistical properties of the eigenvalues of the QCD Dirac operator. We find that the fluctuations of the smallest Dirac eigenvalues are described by chiral Random Matrix Theories with the global symmetries of the QCD partition function. Deviations from chiral Random Matrix Theory beyond the Thouless energy can be understood analytically by means of partially quenched chiral perturbation theory.
A Kolmogorov Extension Theorem for POVMs

We prove a theorem about positive-operator-valued measures (POVMs) that is an analog of the Kolmogorov extension theorem, a standard theorem of probability theory. According to our theorem, if a sequence of POVMs Gn on \({\mathbb{R}}^n\) satisfies the consistency (or projectivity) condition \(G_{n+1}(A\times {\mathbb{R}}) = G_n(A)\) then there is a POVM G on the space \({\mathbb{R}}^{\mathbb{N}}\) of infinite sequences that has Gn as its marginal for the first n entries of the sequence. We also describe an application in quantum theory.
Norm Varieties and the Chain Lemma (After Markus Rost)

The goal of this paper is to present proofs of two results of Markus Rost, the Chain Lemma 1 and the Norm Principle 3. These are the steps needed to complete the published verification of the Bloch– Kato conjecture, that the norm residue maps are isomorphisms for every prime p, every n and every field k containing 1/ p.
Orbital Deflection of Comets by Directed Energy

Cometary impacts pose a long-term hazard to life on Earth. Impact mitigation techniques have been studied extensively, but they tend to focus on asteroid diversion. Typical asteroid interdiction schemes involve spacecraft physically intercepting the target, a task feasible only for targets identified decades in advance and in a narrow range of orbits—criteria unlikely to be satisfied by a threatening comet. Comets, however, are naturally perturbed from purely gravitational trajectories via solar heating of their surfaces, which activates sublimation-driven jets. Artificial heating of a comet, such as by a laser, may supplement natural heating by the Sun to purposefully manipulate its path and thereby avoid an impact. Deflection effectiveness depends on the comet's heating response, which varies dramatically depending on factors including nucleus size, orbit, and dynamical history. These factors are incorporated into a numerical orbital model to assess the effectiveness and feasibility of using high-powered laser arrays in Earth orbit and on the ground for comet deflection. Simulation results suggest that a diffraction-limited 500 m orbital or terrestrial laser array operating at 10 GW for 1% of each day over 1 yr is sufficient to fully avert the impact of a typical 500 m diameter comet with primary nongravitational parameter A_1 = 2 × 10^(−8) au day^(−2). Strategies to avoid comet fragmentation during deflection are also discussed.
Neural Bridge Sampling for Evaluating Safety-Critical Autonomous Systems

Learning-based methodologies increasingly find applications in safety-critical domains like autonomous driving and medical robotics. Due to the rare nature of dangerous events, real-world testing is prohibitively expensive and unscalable. In this work, we employ a probabilistic approach to safety evaluation in simulation, where we are concerned with computing the probability of dangerous events. We develop a novel rare-event simulation method that combines exploration, exploitation, and optimization techniques to find failure modes and estimate their rate of occurrence. We provide rigorous guarantees for the performance of our method in terms of both statistical and computational efficiency. Finally, we demonstrate the efficacy of our approach on a variety of scenarios, illustrating its usefulness as a tool for rapid sensitivity analysis and model comparison that are essential to developing and testing safety-critical autonomous systems.
Phenomenology of fermion production during axion inflation

We study the production of fermions through a derivative coupling with a pseudoscalar inflaton and the effects of the produced fermions on the scalar primordial perturbations. We present analytic results for the modification of the scalar power spectrum due to the produced fermions, and we estimate the amplitude of the non-Gaussianities in the equilateral regime. Remarkably, we find a regime where the effect of the fermions gives the dominant contribution to the scalar spectrum while the amplitude of the bispectrum is small and in agreement with observation. We also note the existence of a regime in which the backreaction of the fermions on the evolution of the zero-mode of the inflaton can lead to inflation even if the potential of the inflaton is steep and does not satisfy the slow-roll conditions.
Comparing and simplifying distinct-cluster phylogenetic networks

Phylogenetic networks are rooted acyclic directed graphs in which the leaves are identified with members of a set X of species. The cluster of a vertex is the set of leaves that are descendants of the vertex. A network is “distinct-cluster” if distinct vertices have distinct clusters. This paper focuses on the set DC(X) of distinct-cluster networks whose leaves are identified with the members of X. For a fixed X, a metric on DC(X) is defined. There is a “cluster-preserving” simplification process by which vertices or certain arcs may be removed without changing the clusters of any remaining vertices. Many of the resulting networks may be uniquely determined without regard to the order of the simplifying operations.
ACCELERATION OF PARTICLES AT THE TERMINATION SHOCK OF A RELATIVISTIC STRIPED WIND

The relativistic wind of obliquely rotating pulsars consists of toroidal stripes of opposite magnetic field polarity, separated by current sheets of hot plasma. By means of two- and three-dimensional particle-in-cell simulations, we investigate particle acceleration and magnetic field dissipation at the termination shock of a relativistic striped wind. At the shock, the flow compresses and the alternating fields annihilate by driven magnetic reconnection. Irrespective of the stripe wavelength λ or the wind magnetization σ (in the regime σ 1 of magnetically dominated flows), shock-driven reconnection transfers all the magnetic energy of alternating fields to the particles, whose average Lorentz factor increases by a factor of σ with respect to the pre-shock value. The shape of the post-shock spectrum depends primarily on the ratio λ/(rL σ), where rL is the relativistic Larmor radius in the wind. The spectrum becomes broader as the value of λ/(rL σ) increases, passing from a relativistic Maxwellian to a flat power-law tail with slope around –1.5, populated by particles accelerated by the reconnection electric field. Close to the equatorial plane of the wind, where the stripes are symmetric, the highest energy particles resulting from magnetic reconnection can escape ahead of the shock, and be injected into a Fermi-like acceleration process. In the post-shock spectrum, they populate a power-law tail with slope around –2.5, which extends beyond the flat component produced by reconnection. Our study suggests that the spectral break between the radio and the optical band in Pulsar Wind Nebulae can be a natural consequence of particle acceleration at the termination shock of striped pulsar winds.
Spin States of Zigzag-Edged Mobius Graphene Nanoribbons from First Principles

Mobius graphene nanoribbons have only one edge topologically. How the magnetic structures, previously associated with the two edges of zigzag-edged flat nanoribbons or cyclic nanorings, would change for their Mobius counterparts is an intriguing question. Using spin-polarized density functional theory, we shed light on this question. We examine spin states of zigzag-edged Mobius graphene nanoribbons with different widths and lengths. We find a triplet ground state for a Mobius cyclacene, while the corresponding two-edged cyclacene has an open-shell singlet ground state. For wider zigzag-edged Mobius graphene nanoribbons, the total magnetization of the ground state is found to increase with the ribbon length. For example, a quintet ground state is found for a zigzag-edged Mobius graphene nanoribbon. Local magnetic moments on the edge carbon atoms form domains of majority and minor spins along the edge. Spins at the domain boundaries are found to be frustrated. Our findings show that the Mobius topology (th...
Shape-dependent bounds on cell growth rates

I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like E. coli. Simple modeling immediately implies that it is the elongated profiles of such cells that allow for them to grow – as observed – at exponential rates in nutrient-rich media. Growth is strongly suppressed when nutrient capture is diffusion-limited: In three dimensions, the length is bounded by , and in lower dimensions growth is algebraic. Similar bounds are easily obtained for other cell geometries, groups of cells, etc. Fits of experimental growth curves to such bounds can be used to estimate various quantities of interest, including generalized metabolic rates.
On the consistency and confidence of distributed dynamic state estimation in wireless sensor networks

The problem of distributed dynamic state estimation in wireless sensor networks is studied. Two important properties of local estimates, namely, the consistency and confidence, are emphasized. On one hand, the consistency, which means that the approximated error covariance is lower bounded by the true unknown one, has to be guaranteed so that the estimate is not over-confident. On the other hand, since the confidence indicates the accuracy of the estimate, the estimate should be as confident as possible. We first analyze two different information fusion strategies used in the case of information sources with, respectively, uncorrelated errors and unknown but correlated errors. Then a distributed hybrid information fusion algorithm is proposed, where each agent uses the information obtained not only by itself, but also from its neighbors through communication. The proposed algorithm not only guarantees the consistency of the estimates, but also utilizes the available information sources in a more efficient manner and hence improves the confidence. Besides, the proposed algorithm is fully distributed and guarantees convergence with the sufficient condition formulated. The comparisons with existing algorithms are analytically shown.
dMelodies: A music dataset for disentanglement learning

Representation learning focused on disentangling the underlying factors of variation in given data has become an important area of research in machine learning. However, most of the studies in this area have relied on datasets from the computer vision domain and thus, have not been readily extended to music. In this paper, we present a new symbolic music dataset that will help researchers working on disentanglement problems demonstrate the efficacy of their algorithms on diverse domains. This will also provide a means for evaluating algorithms specifically designed for music. To this end, we create a dataset comprising of 2-bar monophonic melodies where each melody is the result of a unique combination of nine latent factors that span ordinal, categorical, and binary types. The dataset is large enough (≈ 1.3 million data points) to train and test deep networks for disentanglement learning. In addition, we present benchmarking experiments using popular unsupervised dis- entanglement algorithms on this dataset and compare the results with those obtained on an image-based dataset.
A Conformal Field Theory for Eternal Inflation

We study a statistical model defined by a conformally invariant distribution of overlapping spheres in arbitrary dimension d. The model arises as the asymptotic distribution of cosmic bubbles in d+1 dimensional de Sitter space, and also as the asymptotic distribution of bubble collisions with the domain wall of a fiducial ``observation bubble'' in d+2 dimensional de Sitter space. In this note we calculate the 2-, 3-, and 4-point correlation functions of exponentials of the ``bubble number operator'' analytically in d = 2. We find that these correlators are free of infrared divergences, covariant under the global conformal group, charge conserving, and transform with positive conformal dimensions that are related in a novel way to the charge. Although by themselves these operators probably do not define a full-fledged conformal field theory, one can use the partition function on a sphere to compute an approximate central charge in the 2D case. The theory in any dimension has a noninteracting limit when the nucleation rate of the bubbles in the bulk is very large. The theory in two dimensions is related to some models of continuum percolation, but it is conformal for all values of the tunneling rate.
Probability of CME Impact on Exoplanets Orbiting M Dwarfs and Solar-like Stars

Solar coronal mass ejections (CMEs) produce adverse space weather effects at Earth. Planets in the close habitable zone of magnetically active M dwarfs may experience more extreme space weather than at Earth, including frequent CME impacts leading to atmospheric erosion and leaving the surface exposed to extreme flare activity. Similar erosion may occur for hot Jupiters with close orbits around solar-like stars. We have developed a model, Forecasting a CME's Altered Trajectory (ForeCAT), which predicts a CME's deflection. We adapt ForeCAT to simulate CME deflections for the mid-type M dwarf V374 Peg and hot Jupiters with solar-type hosts. V374 Peg's strong magnetic fields can trap CMEs at the M dwarfs's Astrospheric Current Sheet, the location of the minimum in the background magnetic field. Solar-type CMEs behave similarly, but have much smaller deflections and do not get trapped at the Astrospheric Current Sheet. The probability of planetary impact decreases with increasing inclination of the planetary orbit with respect to the Astrospheric Current Sheet - 0.5 to 5 CME impacts per day for M dwarf exoplanets, 0.05 to 0.5 CME impacts per day for solar-type hot Jupiters. We determine the minimum planetary magnetic field necessary to shield a planet's atmosphere from the CME impacts. M dwarf exoplanets require values between tens and hundreds of Gauss. Hot Jupiters around a solar-type star, however, require a more reasonable <30 G. These values exceed the magnitude required to shield a planet from the stellar wind, suggesting CMEs may be the key driver of atmospheric losses.
Lifting representations of finite reductive groups: a character relation

Given a connected reductive group $\tilde{G}$ over a finite field $k$, and a semisimple $k$-automorphism $\varepsilon$ of $\tilde{G}$ of finite order, let $G$ denote the connected part of the group of $\varepsilon$-fixed points. Then there exists a lifting from packets of representations of $G(k)$ to packets for $\tilde{G}(k)$. In the case of Deligne-Lusztig representations, we show that this lifting satisfies a character relation analogous to that of Shintani.
Higher enveloping algebras

We provide spectral Lie algebras with enveloping algebras over the operad of little G –framed n –dimensional disks for any choice of dimension n and structure group G , and we describe these objects in two complementary ways. The first description is an abstract characterization by a universal mapping property, which witnesses the higher enveloping algebra as the value of a left adjoint in an adjunction. The second, a generalization of the Poincare–Birkhoff–Witt theorem, provides a concrete formula in terms of Lie algebra homology. Our construction pairs the theories of Koszul duality and Day convolution in order to lift to the world of higher algebra the fundamental combinatorics of Beilinson–Drinfeld’s theory of chiral algebras. Like that theory, ours is intimately linked to the geometry of configuration spaces and has the study of these spaces among its applications. We use it here to show that the stable homotopy types of configuration spaces are proper homotopy invariants.
Observational Predictions for Sub-Chandrasekhar Mass Explosions: Further Evidence for Multiple Progenitor Systems for Type Ia Supernovae

Author(s): Polin, A; Nugent, P; Kasen, D | Abstract: We present a numerical parameter survey of sub-Chandrasekhar mass white dwarf (WD) explosions. Carbon-oxygen WDs accreting a helium shell have the potential to explode in the sub-Chandrasekhar mass regime. Previous studies have shown how the ignition of a helium shell can either directly ignite the WD at the core-shell interface or propagate a shock wave into the the core causing a central ignition. We examine the explosions of WDs from 0.6 to 1.2 M o with helium shells of 0.01, 0.05, and 0.08 M o . Distinct observational signatures of sub-Chandrasekhar mass WD explosions are predicted for two categories of shell size. Thicker-shell models show an early time flux excess, which is caused by the presence of radioactive material in the ashes of the helium shell, and red colors due to these ashes creating significant line blanketing in the UV through the blue portion of the spectrum. Thin shell models reproduce several typical Type Ia supernova signatures. We identify a relationship between Si ii velocity and luminosity that, for the first time, identifies a subclass of observed supernovae that are consistent with these models. This subclass is further delineated by the absence of carbon in their atmospheres. We suggest that the proposed difference in the ratio of selective to total extinction between the high velocity and normal velocity Type Ia supernovae is not due to differences in the properties of the dust around these events, but is rather an artifact of applying a single extinction correction to two intrinsically different populations of supernovae.
Instanton Floer homology and the Alexander polynomial

The instanton Floer homology of a knot in the three-sphere is a vector space with a canonical mod 2 grading. It carries a distinguished endomorphism of even degree, arising from the 2–dimensional homology class represented by a Seifert surface. The Floer homology decomposes as a direct sum of the generalized eigenspaces of this endomorphism. We show that the Euler characteristics of these generalized eigenspaces are the coefficients of the Alexander polynomial of the knot. Among other applications, we deduce that instanton homology detects fibered knots.
The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-Body Evolution

We consider a 2D time-dependent quantum system of N -bosons with harmonic external confining and attractive interparticle interaction in the Gross-Pitaevskii scaling. We derive stability of matter type estimates showing that the k-th power of the energy controls the H Sobolev norm of the solution over k-particles. This estimate is new and more diffi cult for attractive interactions than repulsive interactions. For the proof, we use a version of the finite-dimensional quantum di Finetti theorem from [49]. A high particle-number averaging effect is at play in the proof, which is not needed for the corresponding estimate in the repulsive case. This a priori bound allows us to prove that the corresponding BBGKY hierarchy converges to the GP limit as was done in many previous works treating the case of repulsive interactions. As a result, we obtain that the focusing nonlinear Schrodinger equation is the mean-field limit of the 2D time-dependent quantum many-body system with attractive interatomic interaction and asymptotically factorized initial data. An assumption on the size of the L-norm of the interatomic interaction potential is needed that corresponds to the sharp constant in the 2D Gagliardo-Nirenberg inequality though the inequality is not directly relevant because we are dealing with a trace instead of a power.
Laboratory Measurements of X-Ray Emission from Highly Charged Argon Ions

Uncertainties in atomic models will introduce noticeable additional systematics in calculating the flux of weak dielectronic recombination (DR) satellite lines, affecting the detection and flux measurements of other weak spectral lines. One important example is the Ar XVII He-beta DR, which is expected to be present in emission from the hot intracluster medium (ICM) of galaxy clusters and could impact measurements of the flux of the 3.5 keV line that has been suggested as a secondary emission from a dark matter interaction. We perform a set of experiments using the Lawrence Livermore National Laboratory's electron beam ion trap (EBIT-I) and the X-Ray Spectrometer quantum calorimeter (XRS/EBIT), to test the Ar XVII He-beta DR origin of the 3.5 keV line. We measured the X-ray emission following resonant DR onto helium-like and lithium-like Argon using EBIT-I's Maxwellian simulator mode at a simulated electron temperature of Te=1.74 keV. The measured flux of the Ar XVII He-beta DR lined is too weak to account for the flux in the 3.5 keV line assuming reasonable plasma parameters. We, therefore, rule out Ar XVII He-beta DR as a significant contributor to the 3.5 keV line. A comprehensive comparison between the atomic theory and the EBIT experiment results is also provided.
The star formation histories of local group dwarf galaxies. I. Hubble space telescope/wide field planetary camera 2 observations

We present uniformly measured star formation histories (SFHs) of 40 Local Group (LG) dwarf galaxies based on color-magnitude diagram (CMD) analysis from archival Hubble Space Telescope imaging. We demonstrate that accurate SFHs can be recovered from CMDs that do not reach the oldest main sequence turn-off (MSTO), but emphasize that the oldest MSTO is critical for precisely constraining the earliest epochs of star formation. We find that: (1) the average lifetime SFHs of dwarf spheroidals (dSphs) can be approximated by an exponentially declining SFH with τ ∼ 5 Gyr; (2) lower luminosity dSphs are less likely to have extended SFHs than more luminous dSphs; (3) the average SFHs of dwarf irregulars (dIrrs), transition dwarfs, and dwarf ellipticals can be approximated by the combination of an exponentially declining SFH (τ ∼ 3-4 Gyr) for lookback ages >10-12 Gyr ago and a constant SFH thereafter; (4) the observed fraction of stellar mass formed prior to z = 2 ranges considerably (80% for galaxies with M 10{sup 7} M{sub ☉}) and is largely explained by environment; (5) the distinction between 'ultra-faint' and 'classical' dSphs is arbitrary; (6) LG dIrrs formed amore » significantly higher fraction of stellar mass prior to z = 2 than the Sloan Digital Sky Survey galaxies from Leitner and the SFHs from the abundance matching models of Behroozi et al. This may indicate higher than expected star formation efficiencies at early times in low mass galaxies. Finally, we provide all the SFHs in tabulated electronic format for use by the community.« less
Database queries and constraints via lifting problems

Previous work has demonstrated that categories are useful and expressive models for databases. In the current paper we build on that model, showing that certain queries and constraints correspond to lifting problems, as found in modern approaches to algebraic topology. In our formulation, each SPARQL graph pattern query corresponds to a category-theoretic lifting problem, whereby the set of solutions to the query is precisely the set of lifts. We interpret constraints within the same formalism, and then investigate some basic properties of queries and constraints. In particular, to any database π, we can associate a certain derived database Qry(π) of queries on π. As an application, we explain how giving users access to certain parts of Qry(π), rather than direct access to π, improves the ability to manage the impact of schema evolution.
Evanescently coupled multimode spiral spectrometer

We designed a high-resolution compact spectrometer based on an evanescently coupled multimode spiral waveguide. Interference between the modes in the waveguide forms a wavelength-dependent speckle pattern, which is used as a fingerprint to identify the input wavelength after calibration. Evanescent coupling between neighboring arms of the spiral results in a non-resonant broadband enhancement of the spectral resolution. Experimentally, we demonstrated a resolution of 0.01 nm at a wavelength of 1520 nm using a 250 μm radius spiral structure. Spectra containing 40 independent spectral channels are recovered simultaneously, and the operation bandwidth is significantly increased by applying compressive sensing to sparse spectra reconstruction. The ability to achieve such high resolution with low loss in a compact footprint is expected to have a significant impact on low-cost portable sensing and to add functionality to lab-on-a-chip systems.
The Relation between Stellar and Dynamical Surface Densities in the Central Regions of Disk Galaxies

We use the SPARC (Spitzer Photometry & Accurate Rotation Curves) database to study the relation between the central surface density of stars Sstar and dynamical mass Sdyn in 135 disk galaxies (S0 to dIrr). We find that Sdyn correlates tightly with Sstar over 4 dex. This central density relation can be described by a double power law. High surface brightness galaxies are consistent with a 1:1 relation, suggesting that they are self-gravitating and baryon dominated in the inner parts. Low surface brightness galaxies systematically deviate from the 1:1 line, indicating that the dark matter contribution progressively increases but remains tightly coupled to the stellar one. The observed scatter is small (~0.2 dex) and largely driven by observational uncertainties. The residuals show no correlations with other galaxy properties like stellar mass, size, or gas fraction.
Modeling hydrodynamics, magnetic fields, and synthetic radiographs for high-energy-density plasma flows in shock-shear targets

Three-dimensional FLASH radiation-magnetohydrodynamics (radiation-MHD) modeling is carried out to study the hydrodynamics and magnetic fields in the shock-shear derived platform. Simulations indicate that fields of tens of Tesla can be generated via the Biermann battery effect due to vortices and mix in the counterpropagating shock-induced shear layer. Synthetic proton radiography simulations using MPRAD and synthetic X-ray image simulations using SPECT3D are carried out to predict the observable features in the diagnostics. Quantifying the effects of magnetic fields in inertial confinement fusion and high-energy-density plasmas represents frontier research that has far-reaching implications in basic and applied sciences.
Design and Deployment of Photo2Building: A Cloud-based Procedural Modeling Tool as a Service

We present a Photo2Building tool to create a plausible 3D model of a building from only a single photograph. Our tool is based on a prior desktop version which, as described in this paper, is converted into a client-server model, with job queuing, web-page support, and support of concurrent usage. The reported cloud-based web-accessible tool can reconstruct a building in 40 seconds on average and costing only 0.60 USD with current pricing. This provides for an extremely scalable and possibly widespread tool for creating building models for use in urban design and planning applications. With the growing impact of rapid urbanization on weather and climate and resource availability, access to such a service is expected to help a wide variety of users such as city planners, urban meteorologists worldwide in the quest to improved prediction of urban weather and designing climate-resilient cities of the future.
Selected topics in integrable models

In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
Recurrent Neural Networks for Stochastic Control in Real-Time Bidding

Bidding in real-time auctions can be a difficult stochastic control task; especially in a very uncertain market and if underdelivery incurs strong penalties. Most current works and implementations focus on optimally delivering a campaign given a reasonable forecast of the market. Practical implementations have a feedback loop to adjust and be robust to forecasting errors, but no implementation, to the best of our knowledge, uses a model of market risk and actively anticipates market shifts. Solving such stochastic control problems in practice is actually very challenging and an approximate solution based on a Recurrent Neural Network (RNN) architecture is both effective and practical for implementation in a production environment. The RNN bidder provisions everything it needs to avoid underdelivery. It also deliberately falls short of its goal when buying the missing impressions would cost more than the penalty for not reaching it.
Understanding the Difficulty of Training Transformers

Transformers have proved effective in many NLP tasks. However, their training requires non-trivial efforts regarding carefully designing cutting-edge optimizers and learning rate schedulers (e.g., conventional SGD fails to train Transformers effectively). Our objective here is to understand __what complicates Transformer training__ from both empirical and theoretical perspectives. Our analysis reveals that unbalanced gradients are not the root cause of the instability of training. Instead, we identify an amplification effect that influences training substantially—for each layer in a multi-layer Transformer model, heavy dependency on its residual branch makes training unstable, since it amplifies small parameter perturbations (e.g., parameter updates) and results in significant disturbances in the model output. Yet we observe that a light dependency limits the model potential and leads to inferior trained models. Inspired by our analysis, we propose Admin (Adaptive model initialization) to stabilize the early stage’s training and unleash its full potential in the late stage. Extensive experiments show that Admin is more stable, converges faster, and leads to better performance
Cohomology of Spaltenstein varieties

We give a presentation for the cohomology algebra of the Spaltenstein variety of all partial flags annihilated by a fixed nilpotent matrix, generalizing the description of the cohomology algebra of the Springer fiber found by De Concini, Procesi and Tanisaki.
Gas Accretion and Angular Momentum

In this chapter, we review the role of gas accretion to the acquisition of angular momentum, both in galaxies and in their gaseous halos. We begin by discussing angular momentum in dark matter halos, with a brief review of tidal torque theory and the importance of mergers, followed by a discussion of the canonical picture of galaxy formation within this framework, where halo gas is presumed to shock-eat to the virial temperature of the halo, following the same spin distribution as the dark matter halo before cooling to the center of the halo to form a galaxy there. In the context of recent observational evidence demonstrating the presence of high angular momentum gas in galaxy halos, we review recent cosmological hydrodynamic simulations that have begun to emphasize the role of “cold flow” accretion—anisotropic gas accretion along cosmic filaments that does not shock-heat before sinking to the central galaxy. We discuss the implications of these simulations, reviewing a number of recent developments in the literature, and suggest a revision to the canonical model as it relates to the expected angular momentum content of gaseous halos around galaxies.
Bayesian Thought in Early Modern Detective Stories: Monsieur Lecoq, C. Auguste Dupin and Sherlock Holmes

This paper reviews the maxims used by three early modern fictional detectives: Monsieur Lecoq, C. Auguste Dupin and Sherlock Holmes. It find similarities between these maxims and Bayesian thought. Poe’s Dupin uses ideas very similar to Bayesian game theory. Sherlock Holmes’ statements also show thought patterns justifiable in Bayesian terms.
Boundary Between Stable and Unstable Regimes of Accretion

We investigated the boundary between stable and unstable regimes of accre- tion and its dependence on di erent parameters. Simulations were performed using a "cubed sphere" code with high grid resolution (244 grid points in the azimuthal direc- tion), which is twice as high as that used in our earlier studies. We chose a very low viscosity value, with alpha-parameter =0.02. We observed from the simulations that the boundary strongly depends on the ratio between magnetospheric radius rm (where the magnetic stress in the magnetosphere matches the matter stress in the disk) and corotation radius rcor (where the Keplerian velocity in the disk is equal to the angular velocity of the star). For a small misalignment angle of the dipole field, = 5 , accretion is unstable if rcor=rm > 1:35, and is stable otherwise. In cases of a larger misalignment angle of the dipole, = 20 , instability occurs at slightly larger values, rcor=rm > 1:41.
Proposed experiment in two-qubit linear optical photonic gates for maximal success rates

Here we propose an experiment in linear optical quantum computing (LOQC) using the framework first developed by Knill, Laflamme and Milburn. This experiment will test the ideas of the authors' previous work on imperfect LOQC gates using number-resolving photon detectors. We suggest a relatively simple physical apparatus capable of producing CZ gates with controllable fidelity less than 1 and success rates higher than the current theoretical maximum (S = 2/27) for perfect fidelity. These experimental setups are within the reach of many experimental groups and would provide an interesting experiment in photonic quantum computing.
Limit Cycles Sparked by Mutation in the Repeated Prisoner's Dilemma

We explore a replicator–mutator model of the repeated Prisoner's Dilemma involving three strategies: always cooperate (ALLC), always defect (ALLD), and tit-for-tat (TFT). The dynamics resulting from single unidirectional mutations are considered, with detailed results presented for the mutations TFT → ALLC and ALLD → ALLC. For certain combinations of parameters, given by the mutation rate μ and the complexity cost c of playing tit-for-tat, we find that the population settles into limit cycle oscillations, with the relative abundance of ALLC, ALLD, and TFT cycling periodically. Surprisingly, these oscillations can occur for unidirectional mutations between any two strategies. In each case, the limit cycles are created and destroyed by supercritical Hopf and homoclinic bifurcations, organized by a Bogdanov–Takens bifurcation. Our results suggest that stable oscillations are a robust aspect of a world of ALLC, ALLD, and costly TFT; the existence of cycles does not depend on the details of assumptions of how mutation is implemented.
Proof of Swiss Cheese Version of Deligne's Conjecture

For an associative algebra A we consider the pair "the Hochschild cochain complex C*(A,A) and the algebra A". There is a natural 2-colored operad which acts on this pair. We show that this operad is quasi-isomorphic to the singular chain operad of Voronov's Swiss Cheese operad. This statement is the Swiss Cheese version of the Deligne conjecture formulated by M. Kontsevich in arXiv:math/9904055.