cssi/SciSciGPT-SciSciNet huggingface dataset:
Nonperturbative Time Dependent Solution of a Simple Ionization Model

We present a non-perturbative solution of the Schrodinger equation $${i\psi_t(t,x)=-\psi_{xx}(t,x)-2(1 +\alpha \sin\omega t) \delta(x)\psi(t,x)}$$ , written in units in which $${\hbar=2m=1}$$ , describing the ionization of a model atom by a parametric oscillating potential. This model has been studied extensively by many authors, including us. It has surprisingly many features in common with those observed in the ionization of real atoms and emission by solids, subjected to microwave or laser radiation. Here we use new mathematical methods to go beyond previous investigations and to provide a complete and rigorous analysis of this system. We obtain the Borel-resummed transseries (multi-instanton expansion) valid for all values of α, ω, t for the wave function, ionization probability, and energy distribution of the emitted electrons, the latter not studied previously for this model. We show that for large t and small α the energy distribution has sharp peaks at energies which are multiples of ω, corresponding to photon capture. We obtain small α expansions that converge for all t, unlike those of standard perturbation theory. We expect that our analysis will serve as a basis for treating more realistic systems revealing a form of universality in different emission processes.
General theory of the plasmoid instability

A general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time. The scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of plasmoids are derived and shown to depend on the initial perturbation amplitude (w0), the characteristic rate of current sheet evolution (1/τ), and the Lundquist number (S). They are not simple power laws, and are proportional to Sατβ[ln f(S,τ,w0)]σ. The detailed dynamics of the instability is also elucidated, and shown to comprise of a period of quiescence followed by sudden growth over a short time scale.
On Positivity and Roots in Operator Algebras

In earlier papers the second author and Charles Read have introduced and studied a new notion of positivity for operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. The present paper consists of complements to some facts in the just mentioned papers, concerning this notion of positivity. For example we prove a result on the numerical range of products of the roots of commuting operators with numerical range in a sector.
Direct and Indirect Effects-An Information Theoretic Perspective.

Information theoretic (IT) approaches to quantifying causal influences have experienced some popularity in the literature, in both theoretical and applied (e.g., neuroscience and climate science) domains. While these causal measures are desirable in that they are model agnostic and can capture non-linear interactions, they are fundamentally different from common statistical notions of causal influence in that they (1) compare distributions over the effect rather than values of the effect and (2) are defined with respect to random variables representing a cause rather than specific values of a cause. We here present IT measures of direct, indirect, and total causal effects. The proposed measures are unlike existing IT techniques in that they enable measuring causal effects that are defined with respect to specific values of a cause while still offering the flexibility and general applicability of IT techniques. We provide an identifiability result and demonstrate application of the proposed measures in estimating the causal effect of the El Nino-Southern Oscillation on temperature anomalies in the North American Pacific Northwest.
Log-Scale Equidistribution of Zeros of Quantum Ergodic Eigensections

Under suitable hypotheses, a symplectic map can be quantized as a sequence of unitary operators acting on the Nth powers of a positive line bundle over a Kahler manifold. We show that if the symplectic map has sufficiently fast polynomial decay of correlations, then there exists a density one subsequence of eigensections whose masses and zeros become equidistributed in balls of logarithmically shrinking radii of lengths $$|\log N |^{-\gamma }$$ for some constant $$\gamma > 0$$ independent of N.
Heart Rate Monitoring During Different Lung Volume Phases Using Seismocardiography

Seismocardiography (SCG) is a non-invasive method that can be used for cardiac activity monitoring. This paper presents a new electrocardiogram (ECG) independent approach for estimating heart rate (HR) during low and high lung volume (LLV and HLV, respectively) phases using SCG signals. In this study, SCG, ECG, and respiratory flow rate (RFR) signals were measured simultaneously in 7 healthy subjects. The lung volume information was calculated from the RFR and was used to group the SCG events into low and high lung-volume groups. LLV and HLV SCG events were then used to estimate the subjects HR as well as the HR during LLV and HLV in 3 different postural positions, namely supine, 45 degree heads-up, and sitting. The performance of the proposed algorithm was tested against the standard ECG measurements. Results showed that the HR estimations from the SCG and ECG signals were in a good agreement (bias of 0.08 bpm). All subjects were found to have a higher HR during HLV $(\mathbf{HR}_{\mathbf{HLV}})$ compared to LLV $(\mathbf{HR}_{\mathbf{LLV}})$ at all postural positions. The $\mathbf{HR}_{\mathbf{HLV}}/\mathbf{HR}_{\mathbf{LLV}}$ ratio was $\mathbf{1.11}\pm \mathbf{0.07} \mathbf{1.08}\pm \mathbf{0.05},\ \mathbf{1.09}\pm \mathbf{0.04}$ , and $1.09\pm 0.04\ (\mathbf{mean}\pm \mathbf{SD})$ ) for supine, 45 degree-first trial, 45 degree-second trial, and sitting positions, respectively. This heart rate variability may be due, at least in part, to the well-known respiratory sinus arrhythmia. HR monitoring from SCG signals might be used in different clinical applications including wearable cardiac monitoring systems.
Improved representation of ocean heat content in energy balance models

Anomaly-diffusing energy balance models (AD-EBMs) are routinely employed to analyze and emulate the warming response of both observed and simulated Earth systems. We demonstrate a deficiency in common multi-layer as well as continuous-diffusion AD-EBM variants: They are unable to, simultaneously, properly represent surface warming and the vertical distribution of heat uptake. We show that this inability is due to the diffusion approximation. On the other hand, it is well understood that transport of water from the surface mixed layer into the ocean interior is achieved, in large part, by the process of ventilation—a process associated with outcropping isopycnals. We, therefore, start from a configuration of outcropping isopycnals and demonstrate how an AD-EBM can be modified to include the effect of ventilation on ocean uptake of anomalous radiative forcing. The resulting EBM is able to successfully represent both surface warming and the vertical distribution of heat uptake, and indeed, a simple four-layer model suffices. The simplicity of the models notwithstanding, the analysis presented and the necessity of the modification highlight the role played by processes related to the down-welling branch of global ocean circulation in shaping the vertical distribution of ocean heat uptake.
On the Use of Shot Noise for Photon Counting

Lieu et al. have recently claimed that it is possible to substantially improve the sensitivity of radio-astronomical observations. In essence, their proposal is to make use of the intensity of the photon shot noise as a measure of the photon arrival rate. Lieu et al. provide a detailed quantum-mechanical calculation of a proposed measurement scheme that uses two detectors and conclude that this scheme avoids the sensitivity degradation that is associated with photon bunching. If correct, this result could have a profound impact on radio astronomy. Here I present a detailed analysis of the sensitivity attainable using shot-noise measurement schemes that use either one or two detectors, and demonstrate that neither scheme can avoid the photon bunching penalty. I perform both semiclassical and fully quantum calculations of the sensitivity, obtaining consistent results, and provide a formal proof of the equivalence of these two approaches. These direct calculations are furthermore shown to be consistent with an indirect argument based on a correlation method that establishes an independent limit to the sensitivity of shot-noise measurement schemes. Furthermore, these calculations are directly applicable to the regime of interest identified by Lieu et al. Collectively, these results conclusively demonstrate that the photon-bunching sensitivity penalty applies to shot-noise measurement schemes just as it does to ordinary photon counting, in contradiction to the fundamental claim made by Lieu et al. The source of this contradiction is traced to a logical fallacy in their argument.
Left-orderability and cyclic branched coverings

We provide an alternative proof of a sufficient condition for the fundamental group of the nth cyclic branched cover of S along a prime knot K to be left-orderable, which is originally due to Boyer, Gordon and Watson. As an application of this sufficient condition, we show that for any .p; q/ two-bridge knot, with p 3 mod 4 , there are only finitely many cyclic branched covers whose fundamental groups are not left-orderable. This answers a question posed by Dabkowski, Przytycki and Togha.
Magnetocardiography with a modular spin-exchange relaxation-free atomic magnetometer array

We present a portable four-channel atomic magnetometer array operating in the spin-exchange relaxation-free regime. The magnetometer array has several design features intended to maximize its suitability for biomagnetic measurement, specifically foetal magnetocardiography, such as a compact modular design and fibre-coupled lasers. The modular design allows the independent positioning and orientation of each magnetometer. Using this array in a magnetically shielded room, we acquire adult magnetocadiograms. These measurements were taken with a 6-11 fT Hz(-1/2) single-channel baseline sensitivity that is consistent with the independently measured noise level of the magnetically shielded room.
Hall effect between parallel quantum wires

We study theoretically the parallel quantum wires of the experiment by Auslaender et al. (Science, 308 (2005) 88) at low electron density. It is shown that a Hall effect as observed in two- or three-dimensional electron systems develops as the wires enter the spin-incoherent regime of small spin bandwidth. This together with magnetic-field–dependent tunneling exponents clearly identifies spin incoherence in such experiments and it serves to distinguish it from disorder effects.
All-Optical Frequency Processor for Networking Applications

We propose an electro-optic approach for transparent optical networking, in which frequency channels are actively transformed into any desired mapping in a wavelength-multiplexed environment. Based on electro-optic phase modulators and Fourier-transform pulse shapers, our all-optical frequency processor (AFP) is examined numerically for the specific operations of frequency channel hopping and broadcasting, and found capable of implementing these transformations with favorable component requirements. Extending our analysis via a mutual-information–based metric for system optimization, we show how to optimize transformation performance under limited resources in a classical context, contrasting the results with those found using metrics motivated by quantum information, such as fidelity and success probability. Given its compatibility with on-chip implementation, as well as elimination of optical-to-electrical conversion in frequency channel switching, the AFP looks to offer valuable potential in silicon photonic network design, as well as the realization of high-dimensional frequency-bin gates.
The Nucleus of Comet 10P/Tempel 2 in 2013 and Consequences Regarding its Rotational State: Early Science from the Discovery Channel Telescope

We present new lightcurve measurements of Comet 10P/Tempel 2 carried out with Lowell Observatory's Discovery Channel Telescope in early 2013 when the comet was at aphelion. These data represent some of the first science obtained with this new 4.3 m facility. With Tempel 2 having been observed to exhibit a small but ongoing spin-down in its rotation period for over two decades, our primary goals at this time were two-fold. First, to determine its current rotation period and compare it to that measured shortly after its most recent perihelion passage in 2010, and second, to disentangle the spin-down from synodic effects due to the solar day and Earth's orbital motion and to determine the sense of rotation, i.e., prograde or retrograde. At our midpoint of 2013 February 24, the observed synodic period is 8.948 ± 0.001 hr, exactly matching the predicted prograde rotation solution based on 2010 results, and yields a sidereal period of the identical value due to the solar and Earth synodic components just canceling out during the interval of the 2013 observations. The retrograde solution is ruled out because the associated sidereal periods in 2010 and 2013 are quite different even though we know that extremely little outgassing, needed to produce torques, occurred in this interval. With a definitive sense of rotation, the specific amounts of spin-down to the sidereal period could be assessed. The nominal values imply that the rate of spin-down has decreased over time, consistent with the secular drop in water production since 1988. Our data also exhibited an unexpectedly small lightcurve amplitude which appears to be associated with viewing from a large, negative sub-Earth latitude, and a lightcurve shape deviating from a simple sinusoid implying a highly irregularly shaped nucleus.
Learning Latent Space Energy-Based Prior Model

We propose to learn energy-based model (EBM) in the latent space of a generator model, so that the EBM serves as a prior model that stands on the top-down network of the generator model. Both the latent space EBM and the top-down network can be learned jointly by maximum likelihood, which involves short-run MCMC sampling from both the prior and posterior distributions of the latent vector. Due to the low dimensionality of the latent space and the expressiveness of the top-down network, a simple EBM in latent space can capture regularities in the data effectively, and MCMC sampling in latent space is efficient and mixes well. We show that the learned model exhibits strong performances in terms of image and text generation and anomaly detection. The one-page code can be found in supplementary materials.
Microwave-activated conditional-phase gate for superconducting qubits

We introduce a new entangling gate between two fixed-frequency qubits statically coupled via a microwave resonator bus which combines the following desirable qualities: all-microwave control, appreciable qubit separation for reduction of crosstalk and leakage errors and the ability to function as a two-qubit conditional-phase gate. A fixed, always-on interaction is explicitly designed between higher energy (non-computational) states of two transmon qubits, and then a conditional-phase gate is ‘activated’ on the otherwise unperturbed qubit subspace via a microwave drive. We implement this microwave-activated conditional-phase gate with a fidelity from quantum process tomography of ∼ 87%.
Testing General Relativity with the Black Hole Shadow Size and Asymmetry of Sagittarius A*: Limitations from Interstellar Scattering

The Event Horizon Telescope (EHT), a global 230 GHz VLBI array, achieves an angular resolution of ${\approx} 20\,\mu{\rm as}$, sufficient to resolve the supermassive black hole Sagittarius A* (Sgr A*). This resolution may soon enable measurement of the black hole "shadow" size and asymmetry, predicted to be ${\approx}50\,\mu$as and ${\lesssim} 3\,\mu$as, respectively. Measurements that depart from these values could indicate a violation of the "no-hair theorem." However, refractive scattering by the turbulent ionized interstellar medium distorts the image of Sgr A*, affecting its apparent size and asymmetry. In this paper, we present a general analytic approach to quantify the expected image wander, distortion, and asymmetry from refractive scattering. If the turbulence in the scattering material of Sgr A* is close to Kolmogorov, we estimate the mean refractive image wander, distortion, and asymmetry to be 0.53 $\mu$as, 0.72 $\mu$as, and 0.52 $\mu$as at 230 GHz. However, alternative scattering models with flatter power spectra can yield larger values, up to 2.1 $\mu$as, 6.3 $\mu$as, and 5.0 $\mu$as, respectively. We demonstrate that these effects can be reduced by averaging images over multiple observations. For a small number of observations, the effects of scattering can be comparable to or greater than those from black hole spin, and they determine a fundamental limit for testing general relativity via images of Sgr A*.
Hurwitz monodromy and full number fields

We give conditions for the monodromy group of a Hurwitz space over the configuration space of branch points to be the full alternating or symmetric group on the degree. Specializing the resulting coverings suggests the existence of many number fields with surprisingly little ramification —for example, the existence of infinitely many Am or Sm number fields unramified away from {2,3,5}.
Decapitating the Duck: The (Non)Association of PSR B1757–24 and Supernova Remnant G5.4–1.2

We have made the first direct interferometric proper-motion measurements of the radio pulsar PSR B1757-24, which sits at the tip of the "beak" of the putative "Duck" supernova remnant. The peculiar morphology of this radio complex has been used to argue alternately that the pulsar's space motion was either surprisingly high or surprisingly low. In fact, we show that the pulsar's motion is so small that it and its associated nonthermal nebula G5.27-0.9 (the "head") are almost certainly unrelated to the much larger G5.4-1.2 (the "wings").
Rate optimal design of a wireless backhaul network using TV white space

The penetration of wireless broadband services in remote areas has primarily been limited due to the lack of economic incentives that service providers encounter in sparsely populated areas. Besides, wireless backhaul links like satellite and microwave are either expensive or require strict line of sight communication making them unattractive. TV white space channels with their desirable radio propagation characteristics can provide an excellent alternative for engineering backhaul networks in areas that lack abundant infrastructure. Specifically, TV white space channels can provide “free wireless backhaul pipes” to transport aggregated traffic from broadband sources to fiber access points. In this paper, we investigate the feasibility of multi-hop wireless backhaul in the available white space channels by using noncontiguous Orthogonal Frequency Division Multiple Access (NC-OFDMA) transmissions between fixed backhaul towers. Specifically, we consider joint power control, scheduling and routing strategies to maximize the minimum rate across broadband towers in the network. Depending on the population density and traffic demands of the location under consideration, we discuss the suitable choice of cell size for the backhaul network. Using the example of available TV white space channels in Wichita, Kansas (a small city located in central USA), we provide illustrative numerical examples for designing such wireless backhaul network.
A Graph-theoretic Method to Define any Boolean Operation on Partitions

The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theoretic method is also defined. In closing, the question is addressed of why it took so long for all Boolean operations to be defined for partitions.
Group model selection using marginal correlations: The good, the bad and the Ugly

Group model selection is the problem of determining a small subset of groups of predictors (e.g., the expression data of genes) that are responsible for majority of the variation in a response variable (e.g., the malignancy of a tumor). This paper focuses on group model selection in high-dimensional linear models, in which the number of predictors far exceeds the number of samples of the response variable. Existing works on high-dimensional group model selection either require the number of samples of the response variable to be significantly larger than the total number of predictors contributing to the response or impose restrictive statistical priors on the predictors and/or nonzero regression coefficients. This paper provides comprehensive understanding of a low-complexity approach to group model selection that avoids some of these limitations. The proposed approach, termed Group Thresholding (GroTh), is based on thresholding of marginal correlations of groups of predictors with the response variable and is reminiscent of existing thresholding-based approaches in the literature. The most important contribution of the paper in this regard is relating the performance of GroTh to a polynomial-time verifiable property of the predictors for the general case of arbitrary (random or deterministic) predictors and arbitrary nonzero regression coefficients.
Demonstration of images with negative group velocities

We report the experimental demonstration of the superluminal propagation of multi-spatial-mode images via four-wave mixing in hot atomic vapor, in which all spatial sub-regions propagate with negative group velocities. We investigate the spatial mode properties and temporal reshaping of the fast light images, and show large relative pulse peak advancements of up to 64 % of the input pulse width. The degree of temporal reshaping is quantified and increases as the relative pulse peak advancement increases. When optimized for image quality or pulse advancement, negative group velocities of up to v(g)=-c/880 and v(g)=-c/2180, respectively, are demonstrated when integrating temporally over the entire image. The present results are applicable to temporal cloaking devices that require strong manipulation of the dispersion relation, where one can envision temporally cloaking various spatial regions of an image for different durations. Additionally, the modes involved in a four-wave mixing process similar to the present experiment have been shown to exhibit quantum correlations and entanglement. The results presented here provide insight into how to tailor experimental tests of the behavior of these quantum correlations and entanglement in the superluminal regime.
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity

We revisit and prove some convexity inequalities for trace functions conjectured in this paper’s antecedent. The main functional considered is $$ \Phi_{p,q} (A_1,\, A_2, \ldots, A_m) = \left({\rm Tr}\left[\left( \, {\sum\limits_{j=1}^m A_j^p } \, \right) ^{q/p} \right] \right)^{1/q} $$ for m positive definite operators Aj. In our earlier paper, we only considered the case q = 1 and proved the concavity of Φp,1 for 0 < p ≤ 1 and the convexity for p = 2. We conjectured the convexity of Φp,1 for 1 < p < 2. Here we not only settle the unresolved case of joint convexity for 1 ≤ p ≤ 2, we are also able to include the parameter q ≥ 1 and still retain the convexity. Among other things this leads to a definition of an Lq(Lp) norm for operators when 1 ≤ p ≤ 2 and a Minkowski inequality for operators on a tensor product of three Hilbert spaces – which leads to another proof of strong subadditivity of entropy. We also prove convexity/concavity properties of some other, related functionals.
Recovery and the Data Processing Inequality for Quasi-Entropies

We prove a number of quantitative stability bounds for the cases of equality in Petz’s monotonicity theorem for quasi-relative entropies $S_{f}(\rho ||\sigma)$ defined in terms of an operator monotone decreasing functions $f$ and, in particular, the Renyi relative entropies. Included in our results are bounds in terms of the Petz recovery map, but we obtain more general results. The present treatment is entirely elementary and developed in the context of finite dimensional von Neumann algebras, where the results are already non-trivial and of interest in quantum information theory.
Computably enumerable equivalence relations

We study computably enumerable equivalence relations (ceers) on N and unravel a rich structural theory for a strong notion of reducibility among ceers.
Time-Varying Potassium in High-Resolution Spectra of the Type Ia Supernova 2014j

We present a time series of the highest resolution spectra yet published for the nearby Type Ia supernova (SN Ia) 2014J in M82. They were obtained at 11 epochs over 33 days around peak brightness with the Levy Spectrograph (resolution R ≈ 110,000) on the 2.4 m Automated Planet Finder telescope at Lick Observatory. We identify multiple Na i D and K i absorption features as well as absorption by Ca ii H&K and several of the more common diffuse interstellar bands (DIBs). We see no evolution in any component of Na i D, Ca ii, or in the DIBs, but do establish the dissipation/weakening of the two most blueshifted components of K i. We present several potential physical explanations, finding the most plausible to be photoionization of circumstellar material, and discuss the implications of our results with respect to the progenitor scenario of SN 2014J.
On global stability of financial networks

The recent financial crisis have generated renewed interests in fragilities of global financial networks among economists and regulatory authorities. In particular, a potential vulnerability of the financial networks is the "financial contagion" process in which insolvencies of individual entities propagate through the "web of dependencies" to affect the entire system. In this paper, we formalize an extension of a financial network model originally proposed by Nier et al. for scenarios such as the OTC derivatives market, define a suitable global stability measure for this model, and perform a comprehensive empirical evaluation of this stability measure over more than 700,000 combinations of networks types and parameter combinations. Based on our evaluations, we discover many interesting implications of our evaluations of this stability measure, and derive topological properties and parameters combinations that may be used to flag the network as a possible fragile network. An interactive software FIN-STAB for computing the stability is available from the website www2.cs.uic.edu/~dasgupta/financial-simulator-files
Convergence rates in periodic homogenization of systems of elasticity

This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable coefficients.
Mahler Measure and Volumes in Hyperbolic Space

The Mahler measure of the polynomials tðx m � 1Þy �ð x n � 1 Þ2 C½x; yis essen- tially the sum of volumes of a certain collection of ideal hyperbolic polyhedra in H 3 , which can be determined a priori as a function on the parameter t. We obtain a formula that generalizes some previous formulas given by Cassaigne and Maillot (Mem. Soc. Math. Fr. ðN.S.Þ 80 (2000)), and Vandervelde (J. Number Theory 100 (1) (2003), 184-202). These examples seem to be related to the ones studied by Boyd (Number Theory for the Millennium, AK Peters, Boston, 2002, pp. 127-143), and Boyd and Rodriguez Villegas (in press) for some cases of the A-polynomial of one-cusped manifolds.
Complex rotation numbers: bubbles and their intersections

The construction of complex rotation numbers, due to V. Arnold, gives rise to a fractal-like set “bubbles” related to a circle diffeomorphism. “Bubbles” is a complex analogue to Arnold tongues. This article contains a survey of the known properties of bubbles, as well as a variety of open questions. In particular, we show that bubbles can intersect and self-intersect, and provide approximate pictures of bubbles for perturbations of Mobius circle diffeomorphisms.
A good universal weight for nonconventional ergodic averages in norm

We will show that the sequence appearing in the double recurrence theorem is a good universal weight for the Furstenberg averages. That is, given a system and bounded functions , there exists a set of full-measure in that is independent of integers and and a positive integer such that, for all , for every other measure-preserving system and for each bounded and measurable function , the averages converge in .
Kinematic Signatures of Subvirial Initial Conditions in Young Clusters

Motivated by kinematic observations of young embedded clusters, this paper explores possible kinematic signatures produced by asphericity and departures from initial virial equilibrium in these systems. Specifically, the kinematic quantity that is measured and calculated in this study is the distribution of the line-of-sight velocities as a function of position along the cluster. Although clusters are found within a wide range of sizes, we focus on the regime with stellar membership N ~ 103. The gravitational potential of these young clusters is dominated by the gas, and the geometry of the gas distribution is generalized to include axisymmetric (and triaxial) forms. With this loss of symmetry, the kinematic results thus depend on viewing angle. This work also considers the stars to begin their trajectories with subvirial speeds, as indicated by observations of core motions in such clusters. Our results determine the conditions necessary for the kinematic signature to display interesting structure, i.e., a nonspherical potential, a viewing angle that is not along one of the principal axes, and subvirial starting conditions. We characterize the effects on this signature due to projection angle, initial stellar velocities, cluster elongation, and star formation efficiency. Finally, we compare our theoretical results to recent kinematic observations of the Orion Nebula Cluster; we find that the observations can be explained provided that the cluster is nonspherical, starts with subvirial initial velocities, and is not viewed along a principal axis.
Control of Large Swarms via Random Finite Set Theory

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves the control problem using model predictive control which naturally handles the challenges. This work uses information divergence to define the distance between swarm RFS and a desired distribution. A stochastic optimal control problem is formulated using a modified $L_{2}^{2}$ distance. Simulation results show that swarm densities converge to a target destination, and the RFS control formulation can vary in the number of target destinations.
Electroweak baryogenesis in the exceptional supersymmetric standard model

We study electroweak baryogenesis in the E6 inspired exceptional supersymmetric standard model (E6SSM). The relaxation coefficients driven by singlinos and the new gaugino as well as the transport equation of the Higgs supermultiplet number density in the E6SSM are calculated. Our numerical simulation shows that both CP-violating source terms from singlinos and the new gaugino can solely give rise to a correct baryon asymmetry of the Universe via the electroweak baryogenesis mechanism.
A Class of Effective Field Theory Models of Cosmic Acceleration

We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher derivative terms and exploiting the field redefinition freedom, we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found in similar theories of single-field inflation, where matter is not present. We discuss several different representations of the theory that can be obtained using the field redefinition freedom. For perturbations to the quintessence field today on subhorizon lengthscales larger than the Compton wavelength of the heavy fields, the theory is weakly coupled and natural in the sense of t'Hooft. The theory admits a regime where the perturbations become modestly nonlinear, but very strong nonlinearities lie outside its domain of validity.
Backreacted DBI magnetotransport with momentum dissipation

We examine magnetotransport in a holographic Dirac-Born-Infeld model, taking into account the effects of backreaction on the geometry. The theory we consider includes axionic scalars, introduced to break translational symmetry and generate momentum dissipation. The generic structure of the DC conductivity matrix for these theories is extremely rich, and is significantly more complex than that obtained in the probe approximation. We find new classes of black brane solutions, including geometries that exhibit Lifshitz scaling and hyperscaling violation, and examine their implications on the transport properties of the system. Depending on the choice of theory parameters, these backgrounds can lead to metallic or insulating behavior. Negative magnetoresistance is observed in a family of dynoic solutions. Some of the new backreacted geometries also support magnetic-field-induced metal-insulator transitions.
ReluDiff: differential verification of deep neural networks

As deep neural networks are increasingly being deployed in practice, their efficiency has become an important issue. While there are compression techniques for reducing the network's size, energy consumption and computational requirement, they only demonstrate empirically that there is no loss of accuracy, but lack formal guarantees of the compressed network, e.g., in the presence of adversarial examples. Existing verification techniques such as Reluplex, ReluVal, and DeepPoly provide formal guarantees, but they are designed for analyzing a single network instead of the relationship between two networks. To fill the gap, we develop a new method for differential verification of two closely related networks. Our method consists of a fast but approximate forward interval analysis pass followed by a backward pass that iteratively refines the approximation until the desired property is verified. We have two main innovations. During the forward pass, we exploit structural and behavioral similarities of the two networks to more accurately bound the difference between the output neurons of the two networks. Then in the backward pass, we leverage the gradient differences to more accurately compute the most beneficial refinement. Our experiments show that, compared to state-of-the-art verification tools, our method can achieve orders-of-magnitude speedup and prove many more properties than existing tools.
LONG-TERM EVOLUTION OF PLANET-INDUCED VORTICES IN PROTOPLANETARY DISKS

Recent observations of large-scale asymmetric features in protoplanetary disks suggest that large-scale vortices exist in such disks. Massive planets are known to be able to produce deep gaps in protoplanetary disks. The gap edges could become hydrodynamically unstable to the Rossby wave/vortex instability and form large-scale vortices. In this study we examine the long-term evolution of these vortices by carrying out high-resolution two-dimensional hydrodynamic simulations that last more than 10{sup 4} orbits (measured at the planet's orbit). We find that the disk viscosity has a strong influence on both the emergence and lifetime of vortices. In the outer disk region where asymmetric features are observed, our simulation results suggest that the disk viscous α needs to be low, ∼10{sup –5}-10{sup –4}, to sustain vortices to thousands and up to 10{sup 4} orbits in certain cases. The chance of finding a vortex feature in a disk then decreases with smaller planet orbital radius. For α ∼ 10{sup –3} or larger, even planets with masses of 5 M {sub J} will have difficulty either producing or sustaining vortices. We have also studied the effects of different disk temperatures and planet masses. We discuss the implications of our findings on current and futuremore » protoplanetary disk observations.« less
Mid-Infrared Imaging of NGC 6334 I

We present high-resolution (<05) mid-infrared Keck II images of individual sources in the central region of NGC 6334 I. We compare these images to images at a variety of other wavelengths from the near-infrared to centimeter radio continuum and speculate on the nature of the NGC 6334 I sources. We assert that the cometary shape of the ultracompact H II (UCHII) region here, NGC 6334F, is due to a champagne-like flow from a source on the edge of a molecular clump and not due to a bow shock caused by the supersonic motion of the UCHII region through the interstellar medium. The mid-infrared emission is concentrated into an arc of dust that defines the boundary between the UCHII region and the molecular clump. This dust arc contains a majority of the masers in the region. We discuss the nature of the four near-infrared sources associated with IRS I1 and suggest that one of the sources, IRS 1E, is responsible for the heating and ionizing of the UCHII region and the mid-infrared dust arc. Infrared source IRS I2, which has been thought to be a circumstellar disk associated with a linear distribution of methanol masers, is found not to be directly coincident with the masers and elongated at a much different position angle. IRS I3 is found to be a extended source of mid-infrared emission coming from a cluster of young dusty sources seen in the near-infrared.
RATIONAL POINTS ON SOME FERMAT CURVES AND SURFACES OVER FINITE FIELDS

We give an explicit description of the &#x1d53d;qi-rational points on the Fermat curve uq-1 + vq-1 + wq-1 = 0, for i ∈{1, 2, 3}. As a consequence, we observe that for any such point (u, v, w), the product uvw is a cube in &#x1d53d;qi. We also describe the &#x1d53d;q2-rational points on the Fermat surface uq-1 + vq-1 + wq-1 + xq-1 = 0, and show that the product of the coordinates of any such point is a square.
Newton-based optimization for Kullback–Leibler nonnegative tensor factorizations

Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process e.g. count data, which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton and quasi-Newton methods. We compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.
QUANTUM KALEIDOSCOPES AND BELL'S THEOREM

A quantum kaleidoscope is defined as a set of observables, or states, consisting of many different subsets that provide closely related proofs of the Bell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes prove the BKS theorem through a simple parity argument, which also doubles as a proof of Bell's nonlocality theorem if use is made of the right sort of entanglement. Three closely related kaleidoscopes are introduced and discussed in this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a 60-state kaleidoscope. The close relationship of these kaleidoscopes to a configuration of 12 points and 16 lines known as Reye's configuration is pointed out. The "rotations" needed to make each kaleidoscope yield all its apparitions are laid out. The 60-state kaleidoscope, whose underlying geometrical structure is that of ten interlinked Reyes' configurations (together with their duals), possesses a total of 1120 apparitions that provide proofs of the two Bell theorems. Some applications of these kaleidoscopes to problems in quantum tomography and quantum state estimation are discussed.
PROPER MOTIONS AND TRAJECTORIES FOR 16 EXTREME RUNAWAY AND HYPERVELOCITY STARS

We measure proper motions with the Hubble Space Telescope for 16 extreme radial velocity stars, mostly unbound B stars in the Milky Way halo. Twelve of these stars have proper motions statistically consistent with zero, and thus have radial trajectories statistically consistent with a Galactic center “hypervelocity star” origin. The trajectory of HE 0437–5439 is consistent with both Milky Way and Large Magellanic Cloud origins. A Galactic center origin is excluded at 3σ confidence for two of the lowest radial velocity stars in our sample, however. These two stars are probable disk runaways and provide evidence for ∼500 km s �1 ejections from the disk. We also measure a significant proper motion for the unbound sdO star US 708. Its 1000 km s �1 motion is in some tension with proposed supernova ejection models, but can be explained if US 708 was ejected from the stellar halo. In the future, we expect Gaia will better constrain the origin of these remarkable unbound stars.
How electronic dynamics with Pauli exclusion produces Fermi-Dirac statistics

It is important that any dynamics method approaches the correct population distribution at long times. In this paper, we derive a one-body reduced density matrix dynamics for electrons in energetic contact with a bath. We obtain a remarkable equation of motion which shows that in order to reach equilibrium properly, rates of electron transitions depend on the density matrix. Even though the bath drives the electrons towards a Boltzmann distribution, hole blocking factors in our equation of motion cause the electronic populations to relax to a Fermi-Dirac distribution. These factors are an old concept, but we show how they can be derived with a combination of time-dependent perturbation theory and the extended normal ordering of Mukherjee and Kutzelnigg for a general electronic state. The resulting non-equilibrium kinetic equations generalize the usual Redfield theory to many-electron systems, while ensuring that the orbital occupations remain between zero and one. In numerical applications of our equations, we show that relaxation rates of molecules are not constant because of the blocking effect. Other applications to model atomic chains are also presented which highlight the importance of treating both dephasing and relaxation. Finally, we show how the bath localizes the electron density matrix.
A DEEP SEARCH FOR FAINT GALAXIES ASSOCIATED WITH VERY LOW REDSHIFT C iv ABSORBERS. III. THE MASS- AND ENVIRONMENT-DEPENDENT CIRCUMGALACTIC MEDIUM

NASA from the Space Telescope Science Institute [HST-GO-11741, HST-GO-11598, HST-GO-12248, HST-AR-13894]; NASA [NAS5-26555]; Alfred P. Sloan Foundation; National Science Foundation; U.S. Department of Energy Office of Science; University of Arizona; Brazilian Participation Group; Brookhaven National Laboratory; Carnegie Mellon University; University of Florida; French Participation Group; German Participation Group; Harvard University; Instituto de Astrofisica de Canarias; Michigan State/Notre Dame/JINA Participation Group; Johns Hopkins University; Lawrence Berkeley National Laboratory; Max Planck Institute for Astrophysics; Max Planck Institute for Extraterrestrial Physics; New Mexico State University; New York University; Ohio State University; Pennsylvania State University; University of Portsmouth; Princeton University; Spanish Participation Group; University of Tokyo; University of Utah; Vanderbilt University; University of Virginia; University of Washington; Yale University
The massless Thirring model in spherical field theory

Abstract We use the massless Thirring model to demonstrate a new approach to non-perturbative fermion calculations based on the spherical field formalism. The methods we present are free from the problems of fermion doubling and difficulties associated with integrating out massless fermions. Using a non-perturbative regularization, we compute the two-point correlator and find agreement with the known analytic solution.
Generation of density perturbations by primordial magnetic fields

We study the generation and evolution of density perturbations and peculiar velocities due to primordial magnetic fields. We assume that a random magnetic field was present before recombination and follow the field’s effect on the baryon fluid starting at recombination. We find that magnetic fields generate growing density perturbations on length scales larger than the magnetic Jeans length, λB , and damped oscillations for scales smaller than λB. For small wavenumbers k (large length scales), we find the magnetic field-induced density power spectrum generally scales as k. We derive the magnetic Jeans length explicitly by including the back–reaction of the velocity field onto the magnetic field by decomposing the magnetic field into a force-free background field and perturbations about it. Depending on the strength of the magnetic field and the ultraviolet cutoff of its spectrum, structure can be generated on small or intermediate scales early in the history of the universe. For a present rms magnetic field of 10 G on intergalactic scales, we find that perturbations on galactic scales could have gone non–linear at z ≃ 6. Finally, we discuss how primordial magnetic fields affect scenarios of structure formation with non–baryonic dark matter.
Classical-quantum correspondence and Hawking radiation

A recently discovered classical-quantum correspondence (CQC) maps certain quantum problems to corresponding classical problems. We illustrate the CQC for a quantum scalar field in the gravitational background of a collapsing spherical shell. By truncating the problem to a small set of variables, we show how the CQC can yield Hawking radiation as well as the slow down of the collapse due to radiation backreaction.