cssi/SciSciGPT-SciSciNet huggingface dataset:
Obscuring Material around Seyfert Nuclei with Starbursts

The structure of obscuring matter in the environment of active galactic nuclei with associated nuclear starbursts is investigated using three-dimensional hydrodynamical simulations. Simple analytical estimates suggest that the obscuring matter with energy feedback from supernovae has a torus-like structure with a radius of several tens of parsecs and a scale height of ~10 pc. These estimates are confirmed by the fully nonlinear numerical simulations, in which the multiphase inhomogeneous interstellar matter and its interaction with the supernovae are consistently followed. The globally stable, torus-like structure is highly inhomogeneous and turbulent. To achieve the high column densities (1024 cm-2) as suggested by observations of some Seyfert 2 galaxies with nuclear starbursts, the viewing angle should be larger than about 70° from the pole-on for a 108 M☉ massive black hole. Owing to the inhomogeneous internal structure of the torus, the observed column density is sensitive to the line of sight, and it fluctuates by a factor on the order of ~100. The covering fraction for N > 1023 cm-2 is about 0.4. The average accretion rate toward R < 1 pc is ~0.4 M☉ yr-1, which is boosted to twice that in the model without the energy feedback.
Distributed Space–Time Interference Alignment With Moderately Delayed CSIT

This paper proposes an interference alignment method with distributed and delayed channel state information at the transmitter (CSIT) for a class of interference networks. The core idea of the proposed method is to align interference signals over time at the unintended receivers in a distributed manner. With the proposed method, achievable tradeoffs between the sum of degrees of freedom (sum-DoF) and feedback delay of CSI are characterized in both the X-channel and three-user interference channel to reveal the impact on how the CSI feedback delay affects the sum-DoF of the interference networks. A major implication of derived results is that distributed and moderately delayed CSIT is useful to strictly improve the sum-DoF over the case of no CSI at the transmitter in a certain class of interference networks. For a class of X-channels, the results show how to optimally use distributed and moderately delayed CSIT to yield the same sum-DoF as instantaneous and global CSIT. Furthermore, leveraging the proposed transmission method and the known outer bound results, the sum-capacity of the two-user X-channel with a particular set of channel coefficients is characterized within a constant number of bits.
Constraining globular cluster age uncertainties using the IR color-magnitude diagram

Globular Clusters (GCs) in the Milky Way are the primary laboratories for establishing the ages of the oldest stellar populations and for measuring the color-magnitude relation of stars. In infrared (IR) color-magnitude diagrams (CMDs), the stellar main sequence (MS) exhibits a "kink", due to opacity effects in M dwarfs, such that lower mass and cooler dwarfs become bluer in the IR color baseline. This diagnostic offers a new opportunity to model GC CMDs and to reduce uncertainties on cluster properties (e.g., their derived ages). In this context, we analyzed Hubble Space Telescope Wide Field Camera 3 IR archival observations of four GCs - 47Tuc, M4, NGC2808, and NGC6752 - for which the data are deep enough to fully sample the low-mass MS, reaching at least ~ 2 mag below the "kink". We derived the fiducial lines for each cluster and compared them with a grid of isochrones over a large range of parameter space, allowing age, metallicity, distance, and reddening to vary within reasonable selected ranges. The derived ages for the four clusters are respectively 11.6, 11.5, 11.2, and 12.1 Gyr and their random uncertainties are \sigma ~ 0.7 - 1.1 Gyr. Our results suggest that the near-IR MS "kink", combined with the MS turn-off, provides a valuable tool to measure GC ages and offers a promising opportunity to push the absolute age of GCs to sub-Gyr accuracy with the next generation IR telescopes such as the James Webb Space Telescope and the Wide-Field Infrared Survey Telescope.
Double Quantum Dot Floquet Gain Medium

Light-matter interactions on the level of single photons will be important in next-generation communications and electronic devices. A new experiment shows how a confined electron can repeatedly emit a microwave photon.
THE INFLUENCE OF GAS DYNAMICS ON MEASURING THE PROPERTIES OF THE BLACK HOLE IN THE CENTER OF THE MILKY WAY WITH STELLAR ORBITS AND PULSARS

Observations of stars and pulsars orbiting the black hole in the center of the Milky Way offer the potential of measuring not only the mass of the black hole but also its spin and quadrupole moment, thereby providing observational verification of the no-hair theorem. The relativistic effects that will allow us to measure these higher moments of the gravitational field, however, are very small and may be masked by drag forces that stars and pulsars experience orbiting within the hot, tenuous plasma that surrounds the black hole. The properties of this plasma at large distances from the central object have been measured using observations of the extended X-ray emission that surrounds the point source. At distances comparable to the black hole event horizon, the properties of the accretion flow have been constrained using observations of its long-wavelength emission and polarization, as well as of the size of the emitting region at 1.3 mm. I use models of the plasma density and temperature at various distances from the black hole to investigate the effect of hydrodynamic drag forces on future measurements of the higher moments of its gravitational field. I find that hydrodynamic drag does not preclude measurements of the black hole spin and quadrupole moment using high-resolution observations of stars and pulsars that orbit within a few thousand gravitational radii from its horizon.
Photon Emission from Ultrarelativistic Plasmas

The emission rate of photons from a hot, weakly coupled ultrarelativistic plasma is analyzed. Leading-log results, reflecting the sensitivity of the emission rate to scattering events with momentum transfers from gT to T, have previously been obtained. But a complete leading-order treatment requires including collinearly enhanced, inelastic processes such as bremsstrahlung. These inelastic processes receive O(1) modifications from multiple scattering during the photon emission process, which limits the coherence length of the emitted radiation (the Landau-Pomeranchuk-Migdal effect). We perform a diagrammatic analysis to identify, and sum, all leading-order contributions. We find that the leading-order photon emission rate is not sensitive to non-perturbative g2T scale dynamics. We derive an integral equation for the photon emission rate which is very similar to the result of Migdal in his original discussion of the LPM effect. The accurate solution of this integral equation for specific theories of interest will be reported in a companion paper.
HITCHIN CHARACTERS AND GEODESIC LAMINATIONS

For a closed surface $S$, the Hitchin component $\mathrm{Hit}_n (S)$ is a preferred component of the character variety consisting of group homomorphisms from the fundamental group $\pi_1(S)$ to the Lie group $\mathrm{PSL}_n (\mathbb{R})$. We construct a parametrization of the Hitchin component that is well-adapted to a geodesic lamination $\lambda$ on the surface. This is a natural extension of Thurston’s parametrization of the Teichmuller space $\mathcal{T}(S)$ by shearing coordinates associated with $\lambda$, corresponding to the case $n=2$. However, significantly new ideas are needed in this higher-dimensional case. The article concludes with a few applications.
On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm

We construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential representation are obtained using this relationship. Furthermore, it is used to find normalization constants of wave functions of quantum systems that feature energy-dependent potentials. Additionally, this relationship is used to express certain integrals involving functions that are solution of Schrodinger equations through derivatives.
Time asymmetric quantum theory – III. Decaying states and the causal Poincaré semigroup

These Gamow kets span an irreducible representation space for Poincare transformations which, similar to the Wigner representations for stable particles, are characterized by spin (angular momentum of the partial wave amplitude) and complex mass (position of the resonance pole). The Poincare transformations of the Gamow kets, as well as of the Lippmann-Schwinger plane wave scattering states, form only a semigroup of Poincare transformations into the forward light cone. Their transformation properties are derived. From these one obtains an unambiguous definition of resonance mass and width for relativistic resonances. The physical interpretation of these transformations for the Born probabilities and the problem of causality in relativistic quantum physics is discussed.
Hamiltonian Simulation by Qubitization

We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a unitary oracle $\hat{U}$ onto the state $|G\rangle$ created by another unitary oracle. Our algorithm solves this with a query complexity $\mathcal{O}\big(t+\log({1/\epsilon})\big)$ to both oracles that is optimal with respect to all parameters in both the asymptotic and non-asymptotic regime, and also with low overhead, using at most two additional ancilla qubits. This approach to Hamiltonian simulation subsumes important prior art considering Hamiltonians which are $d$-sparse or a linear combination of unitaries, leading to significant improvements in space and gate complexity, such as a quadratic speed-up for precision simulations. It also motivates useful new instances, such as where $\hat{H}$ is a density matrix. A key technical result is `qubitization', which uses the controlled version of these oracles to embed any $\hat{H}$ in an invariant $\text{SU}(2)$ subspace. A large class of operator functions of $\hat{H}$ can then be computed with optimal query complexity, of which $e^{-i\hat{H}t}$ is a special case.
Semantically Invariant Text-to-Image Generation

Image captioning has demonstrated models that are capable of generating plausible text given input images or videos. Further, recent work in image generation has shown significant improvements in image quality when text is used as a prior. Our work ties these concepts together by creating an architecture that can enable bidirectional generation of images and text. We call this network Multi-Modal Vector Representation (MMVR). Along with MMVR, we propose two improvements to the text conditioned image generation. Firstly, a n-gram metric based cost function is introduced that generalizes the caption with respect to the image. Secondly, multiple semantically similar sentences are shown to help in generating better images. Qualitative and quantitative evaluations demonstrate that MMVR improves upon existing text conditioned image generation results by over 20%, while integrating visual and text modalities.
A Solvable Model for Nonlinear Mean Field Dynamo

We formulate a solvable model that describes the generation and saturation of a mean magnetic field in a dynamo with kinetic helicity, in the limit of a large magnetic Prandtl number. This model is based on the assumption that the stochastic part of the velocity field is Gaussian and white in time (the Kazantsev-Kraichnan ensemble), while the regular part describing the back-reaction of the magnetic field is chosen by balancing the viscous and Lorentz stresses in the MHD Navier-Stokes equation. The model provides an analytical explanation for previously obtained numerical results.
The (u,v)-Calkin-Wilf forest

In this paper, we consider a refinement, due to Nathanson, of the Calkin–Wilf tree. In particular, we study the properties of such trees associated with the matrices Lu = 10u 1 and Rv = 1v0 1, where u and v are non-negative integers. We extend several known results of the original Calkin–Wilf tree, including the symmetry, numerator-denominator, and successor formulas, to this new setting. Additionally, we study the ancestry of a rational number appearing in a generalized Calkin–Wilf tree.
The Gamma-Ray Luminosity Function of Millisecond Pulsars and Implications for the GeV Excess

It has been proposed that a large population of unresolved millisecond pulsars (MSPs) could potentially account for the excess of GeV-scale gamma-rays observed from the region surrounding the Galactic Center. The viability of this scenario depends critically on the gamma-ray luminosity function of this source population, which determines how many MSPs Fermi should have already detected as resolved point sources. In this paper, we revisit the gamma-ray luminosity function of MSPs, without relying on uncertain distance measurements. Our determination, based on a comparison of models with the observed characteristics of the MSP population, suggests that Fermi should have already detected a significant number of sources associated with such a hypothesized Inner Galaxy population. We cannot rule out a scenario in which the MSPs residing near the Galactic Center are systematically less luminous than those present in the Galactic Plane or within globular clusters.
Gravitational collapse in Einstein dilaton-Gauss-Bonnet gravity

We present results from a numerical study of spherical gravitational collapse in shift symmetric Einstein dilaton Gauss-Bonnet (EdGB) gravity. This modified gravity theory has a single coupling parameter that when zero reduces to general relativity (GR) minimally coupled to a massless scalar field. We first show results from the weak EdGB coupling limit, where we obtain solutions that smoothly approach those of the Einstein-Klein-Gordon system of GR. Here, in the strong field case, though our code does not utilize horizon penetrating coordinates, we nevertheless find tentative evidence that approaching black hole formation the EdGB modifications cause the growth of scalar field "hair", consistent with known static black hole solutions in EdGB gravity. For the strong EdGB coupling regime, in a companion paper we first showed results that even in the weak field (i.e. far from black hole formation), the EdGB equations are of mixed type: evolution of the initially hyperbolic system of partial differential equations lead to formation of a region where their character changes to elliptic. Here, we present more details about this regime. In particular, we show that an effective energy density based on the Misner-Sharp mass is negative near these elliptic regions, and similarly the null convergence condition is violated then.
Ricci Flow Emerging from Rotationally Symmetric Degenerate Neckpinches

In previous work, Angenent, Isenberg, and Knopf created type-II Ricci flow neckpinch singularities. In this paper we construct solutions to Ricci flow whose initial data is the singular metric resulting from these singularities. We show in particular that the curvature decreases at the same rate at which it blew up. This is the first example of Ricci flow starting from a type-II singularity.
Large N gauge theory — Expansions and transitions

We use solvable two-dimensional gauge theories to illustrate the issues in relating large N gauge theory to string theory. We also give an introduction to recent mathematical work which allows constructing master fields for higher dimensional large N theories. We illustrate this with a new derivation of the Hopf equation governing the evolution of the spectral density in matrix quantum mechanics.
Milnor numbers of projective hypersurfaces with isolated singularities

Let V be a projective hypersurface of fixed degree and dimension which has only isolated singular points. We show that, if the sum of the Milnor numbers at the singular points of V is large, then V cannot have a point of large multiplicity, unless V is a cone. As an application, we give an affirmative answer to a conjecture of Dimca and Papadima.
On bordered theories for Khovanov homology

We describe how to formulate Khovanov's functor-valued invariant of tangles in the language of bordered Heegaard Floer homology. We then give an alternate construction of Lawrence Roberts' Type D and Type A structures in Khovanov homology, and his algebra $\mathcal{B}\Gamma_n$, in terms of Khovanov's theory of modules over the ring $H^n$. We reprove invariance and pairing properties of Roberts' bordered modules in this language. Along the way, we obtain an explicit generators-and-relations description of $H^n$ which may be of independent interest.
Computing on Masked Data to improve the security of big data

Organizations that make use of large quantities of information require the ability to store and process data from central locations so that the product can be shared or distributed across a heterogeneous group of users. However, recent events underscore the need for improving the security of data stored in such untrusted servers or databases. Advances in cryptographic techniques and database technologies provide the necessary security functionality but rely on a computational model in which the cloud is used solely for storage and retrieval. Much of big data computation and analytics make use of signal processing fundamentals for computation. As the trend of moving data storage and computation to the cloud increases, homeland security missions should understand the impact of security on key signal processing kernels such as correlation or thresholding. In this article, we propose a tool called Computing on Masked Data (CMD), which combines advances in database technologies and cryptographic tools to provide a low overhead mechanism to offload certain mathematical operations securely to the cloud. This article describes the design and development of the CMD tool.
Analytic Calculation of B4 for Hard Spheres in Even Dimensions

We exactly calculate the fourth virial coefficient for hard spheres in even dimensions for D = 4, 6, 8, 10, and 12.
Glueball mass spectrum from supergravity

We calculate the spectrum of glueball masses in non-supersymmetric Yang-Mills theory in three and four dimensions, based on a conjectured duality between supergravity and large N gauge theories. The glueball masses are obtained by solving supergravity wave equations in a black hole geometry. We find that the mass ratios are in good numerical agreement with the available lattice data. We also compute the leading (g 2 YM N)−1 corrections to the glueball masses, by taking into account stringy corrections to the supergravity action and to the black hole metric. We find that the corrections to the masses are negative and of order (g 2 YM N)−3/2 . Thus for a fixed ultraviolet cutoff the masses decrease as we decrease the 't Hooft coupling, in accordance with our expectation about the continuum limit of the gauge theories.
A TEST OF PRE-MAIN-SEQUENCE LITHIUM DEPLETION MODELS

Despite the extensive study of lithium depletion during pre-main-sequence (PMS) contraction, studies of individual stars show discrepancies between ages determined from the Hertzsprung-Russell (H-R) diagram and ages determined from lithium depletion, indicating open questions in the PMS evolutionary models. To further test these models, we present high-resolution spectra for members of the β Pictoris Moving Group (BPMG), which is young and nearby. We measure equivalent widths of the 6707.8 A Li I line in these stars and use them to determine lithium abundances. We combine the lithium abundance with the predictions of PMS evolutionary models in order to calculate a lithium depletion age for each star. We compare this age to the age predicted by the H-R diagram of the same model. We find that the evolutionary models underpredict the amount of lithium depletion for the BPMG given its nominal H-R diagram age of ~12 Myr, particularly for the mid-M stars, which have no observable Li I line. This results in systematically older ages calculated from lithium depletion isochrones than from the H-R diagram. We suggest that this discrepancy may be related to the discrepancy between measured M-dwarf radii and the smaller radii predicted by evolutionary models.
New Protocols and Negative Results for Textual Entailment Data Collection

Natural language inference (NLI) data has proven useful in benchmarking and, especially, as pretraining data for tasks requiring language understanding. However, the crowdsourcing protocol that was used to collect this data has known issues and was not explicitly optimized for either of these purposes, so it is likely far from ideal. We propose four alternative protocols, each aimed at improving either the ease with which annotators can produce sound training examples or the quality and diversity of those examples. Using these alternatives and a fifth baseline protocol, we collect and compare five new 8.5k-example training sets. In evaluations focused on transfer learning applications, our results are solidly negative, with models trained on our baseline dataset yielding good transfer performance to downstream tasks, but none of our four new methods (nor the recent ANLI) showing any improvements over that baseline. In a small silver lining, we observe that all four new protocols, especially those where annotators edit *pre-filled* text boxes, reduce previously observed issues with annotation artifacts.
Tensor recovery from noisy and multi-level quantized measurements

Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few works consider tensor recovery from quantized measurements but are restricted to binary measurements. This paper, for the first time, addresses the problem of tensor recovery from multi-level quantized measurements by leveraging the low CANDECOMP/PARAFAC (CP) rank property. We study the recovery of both general low-rank tensors and tensors that have tensor singular value decomposition (TSVD) by solving nonconvex optimization problems. We provide the theoretical upper bounds of the recovery error, which diminish to zero when the sizes of dimensions increase to infinity. We further characterize the fundamental limit of any recovery algorithm and show that our recovery error is nearly order-wise optimal. A tensor-based alternating proximal gradient descent algorithm with a convergence guarantee and a TSVD-based projected gradient descent algorithm are proposed to solve the nonconvex problems. Our recovery methods can also handle data losses and do not necessarily need the information of the quantization rule. The methods are validated on synthetic data, image datasets, and music recommender datasets.
Detecting and handling outlying trajectories in irregularly sampled functional datasets

Outlying curves often occur in functional or longitudinal datasets, and can be very influential on parameter estimators and very hard to detect visually. In this article we introduce estimators of the mean and the principal components that are resistant to, and then can be used for detection of, outlying sample trajectories. The estimators are based on reduced-rank t-models and are specifically aimed at sparse and irregularly sampled functional data. The outlier-resistance properties of the estimators and their relative efficiency for noncontaminated data are studied theoretically and by simulation. Applications to the analysis of Internet traffic data and glycated hemoglobin levels in diabetic children are presented.
Knots with unknotting number 1 and essential Conway spheres

For a knot K in S 3 , let T.K/ be the characteristic toric sub-orbifold of the orbifold .S 3 ;K/ as defined by Bonahon‐Siebenmann. If K has unknotting number one, we show that an unknotting arc for K can always be found which is disjoint from T.K/, unless either K is an EM‐knot (of Eudave-Munoz) or .S 3 ;K/ contains an EM‐tangle after cutting along T.K/. As a consequence, we describe exactly which large algebraic knots (ie, algebraic in the sense of Conway and containing an essential Conway sphere) have unknotting number one and give a practical procedure for deciding this (as well as determining an unknotting crossing). Among the knots up to 11 crossings in Conway’s table which are obviously large algebraic by virtue of their description in the Conway notation, we determine which have unknotting number one. Combined with the work of Ozsvath‐Szabo, this determines the knots with 10 or fewer crossings that have unknotting number one. We show that an alternating, large algebraic knot with unknotting number one can always be unknotted in an alternating diagram. As part of the above work, we determine the hyperbolic knots in a solid torus which admit a non-integral, toroidal Dehn surgery. Finally, we show that having unknotting number one is invariant under mutation.
Commutators in the two-weight setting

Let R be the vector of Riesz transforms on $$ \mathbb R ^{n}$$ , and let $$\mu ,\lambda \in A_p$$ be two weights on $$ \mathbb R ^{n}$$ , $$ 1< p < \infty $$ . The two-weight norm inequality for the commutator $$ ||[b, R] \;:\; L ^{p} (\mu ) \rightarrow L ^{p} (\lambda )||$$ is shown to be equivalent to the function b being in a BMO space adapted to $$ \mu $$ and $$ \lambda $$ . This is a common extension of a result of Coifman–Rochberg–Weiss in the case of both $$ \lambda $$ and $$ \mu $$ being Lebesgue measure, and Bloom in the case of dimension one.
A Bilingual Generative Transformer for Semantic Sentence Embedding

Semantic sentence embedding models encode natural language sentences into vectors, such that closeness in embedding space indicates closeness in the semantics between the sentences. Bilingual data offers a useful signal for learning such embeddings: properties shared by both sentences in a translation pair are likely semantic, while divergent properties are likely stylistic or language-specific. We propose a deep latent variable model that attempts to perform source separation on parallel sentences, isolating what they have in common in a latent semantic vector, and explaining what is left over with language-specific latent vectors. Our proposed approach differs from past work on semantic sentence encoding in two ways. First, by using a variational probabilistic framework, we introduce priors that encourage source separation, and can use our model's posterior to predict sentence embeddings for monolingual data at test time. Second, we use high-capacity transformers as both data generating distributions and inference networks -- contrasting with most past work on sentence embeddings. In experiments, our approach substantially outperforms the state-of-the-art on a standard suite of unsupervised semantic similarity evaluations. Further, we demonstrate that our approach yields the largest gains on more difficult subsets of these evaluations where simple word overlap is not a good indicator of similarity.
Are the Formation and Abundances of Metal-poor Stars the Result of Dust Dynamics?

Large dust grains can fluctuate dramatically in their local density, relative to the gas, in neutral turbulent disks. Small, high-redshift galaxies (before reionization) represent ideal environments for this process. We show via simple arguments and simulations that order-of-magnitude fluctuations are expected in local abundances of large grains (>100 A) under these conditions. This can have important consequences for star formation and stellar metal abundances in extremely metal-poor stars. Low-mass stars can form in dust-enhanced regions almost immediately after some dust forms even if the galaxy-average metallicity is too low for fragmentation to occur. We argue that the metal abundances of these "promoted" stars may contain interesting signatures as the CNO abundances (concentrated in large carbonaceous grains and ices) and Mg and Si (in large silicate grains) can be enhanced and/or fluctuate almost independently. Remarkably, the otherwise puzzling abundance patterns of some metal-poor stars can be well fit by standard IMF-averaged core-collapse SNe yields if we allow for fluctuating local dust-to-gas ratios. We also show that the observed log-normal distribution of enhancements in these species agrees with our simulations. Moreover, we confirm that Mg and Si are correlated in these stars; the abundance ratios are similar to those in local silicate grains. Meanwhile [Mg/Ca], predicted to be nearly invariant from pure SNe yields, shows very large enhancements and variations up to factors of ≳100 as expected in the dust-promoted model, preferentially in the [C/Fe]-enhanced metal-poor stars. Together, this suggests that (1) dust exists in second-generation star formation, (2) local dust-to-gas ratio fluctuations occur in protogalaxies and can be important for star formation, and (3) the light element abundances of these stars may be affected by the local chemistry of dust where they formed, rather than directly tracing nucleosynthesis from earlier populations.
Sparse endpoint estimates for Bochner–Riesz multipliers on the plane

For $$ 0< \lambda < \frac{1}{2}$$ , let $$ B _{\lambda }$$ be the Bochner–Riesz multiplier of index $$ \lambda $$ on the plane. Associated to this multiplier is the critical index $$1< p_ \lambda = \frac{4}{3+2 \lambda } < \frac{4}{3}$$ . We prove a sparse bound for $$ B _{\lambda }$$ with indices $$ (p_ \lambda , q)$$ , where $$ p_ \lambda '< q < 4$$ . This is a further quantification of the endpoint weak $$L^{p_ \lambda }$$ boundedness of $$ B _{\lambda }$$ , due to Seeger. Indeed, the sparse bound immediately implies new endpoint weighted weak type estimates for weights in $$ A_1 \cap RH _{\rho }$$ , where $$ \rho > \frac{4}{4 - 3 p _{\lambda }}$$ .
Rationality does not specialize among terminal fourfolds

We show that rationality does not specialize in flat projective families of complex fourfolds with terminal singularities. This answers a question of Totaro, who established the analogous result in all dimensions greater than 4.
THE CIRCULAR VELOCITY FUNCTION OF GROUP GALAXIES

A robust prediction of ΛCDM cosmology is the halo circular velocity function (CVF), a dynamical cousin of the halo mass function. The correspondence between theoretical and observed CVFs is uncertain, however: cluster galaxies are reported to exhibit a power-law CVF consistent with N-body simulations, but that of the field is distinctly Schechter-like, flattened compared to ΛCDM expectations at circular velocities v {sub c} ≲ 200 km s{sup –1}. Groups offer a powerful probe of the role environment plays in this discrepancy as they bridge the field and clusters. Here, we construct the CVF for a large, mass- and multiplicity-complete sample of group galaxies from the Sloan Digital Sky Survey. Using independent photometric v {sub c} estimators, we find no transition from field to ΛCDM-shaped CVF above v {sub c} = 50 km s{sup –1} as a function of group halo mass. All groups with 12.4 ≲ log M {sub halo}/M {sub ☉} ≲ 15.1 (Local Group analogs to rich clusters) display similar Schechter-like CVFs marginally suppressed at low v {sub c} compared to that of the field. Conversely, some agreement with N-body results emerges for samples saturated with late-type galaxies, with isolated late-types displaying a CVF similar in shape tomore » ΛCDM predictions. We conclude that the flattening of the low-v {sub c} slope in groups is due to their depressed late-type fractions—environment affecting the CVF only to the extent that it correlates with this quantity—and that previous cluster analyses may suffer from interloper contamination. These results serve as useful benchmarks for cosmological simulations of galaxy formation.« less
Resilient Sensor Placement for Kalman Filtering in Networked Systems: Complexity and Algorithms

Given a linear dynamical system affected by noise, we study the problem of optimally placing sensors (at design time) subject to a sensor placement budget constraint in order to minimize the trace of the steady-state error covariance of the corresponding Kalman filter. While this problem is NP-hard in general, we consider the underlying graph associated with the system dynamics matrix, and focus on the case when there is a single input at one of the nodes in the graph. We provide an optimal strategy (computed in polynomial time) to place the sensors over the network. Next, we consider the problem of attacking (i.e., removing) the placed sensors under a sensor attack budget constraint in order to maximize the trace of the steady-state error covariance of the resulting Kalman filter. Using the insights obtained for the sensor placement problem, we provide an optimal strategy (computed in polynomial time) to attack the placed sensors. Finally, we consider the scenario where a system designer places the sensors under a sensor placement budget constraint, and an adversary then attacks the placed sensors subject to a sensor attack budget constraint. The resilient sensor placement problem is to find a sensor placement strategy to minimize the trace of the steady-state error covariance of the Kalman filter corresponding to the sensors that survive the attack. We show that this problem is NP-hard, and provide a pseudopolynomial-time algorithm to solve it.
Dynamics of interacting Brownian particles: A diagrammatic formulation

We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion, we introduce a basis that consists of orthogonalized many-particle density fluctuations. We obtain an exact hierarchy of equations of motion for time-dependent correlations of orthogonalized density fluctuations. To simplify this hierarchy we neglect contributions to the vertices from higher-order cluster expansion terms. An iterative solution of the resulting equations can be represented by diagrams with three- and four-leg vertices. We analyze the structure of the diagrammatic series for the time-dependent density correlation function and obtain a diagrammatic interpretation of reducible and irreducible memory functions. The one-loop self-consistent approximation for the latter function coincides with mode-coupling approximation for Brownian systems that was derived previously using a projection operator approach.
Near-Infrared Spectroscopy of Photodissociation Regions: The Orion Bar and Orion S

We have obtained moderate-resolution (R ~ 3000) spectra of the Orion bar and Orion S regions at J (1.25 μm), H (1.64 μm), and K (2.2 μm). Toward the bar, the observations reveal a large number of H2 emission lines that, when compared to model predictions of Draine & Bertoldi, are indicative of a high-density photodissociation region (PDR) (nH = 106 cm-3, χ = 105, T0 = 1000 K) rather than of shocked material. Behind the bar and into the molecular cloud, the H2 spectrum again matches well with that predicted for a dense PDR (nH = 106 cm-3) but with a lower temperature (T0 = 500 K) and UV field strength (χ = 104). The H2 spectrum and stratification of near-IR emission lines (O I, H I, [Fe II], [Fe III], H2) near Orion S imply the presence of a dense PDR with an inclined geometry in this region (nH = 106 cm-3, χ = 105, T0 = 1500 K). The extinction measurements toward the bar (AK ~ 2.6) and Orion S (AK ~ 2.1) H2 emission regions are much larger than expected from either face-on (AK ~ 0.1) or edge-on (AK ~ 1) homogeneous PDRs, indicating that clumps may significantly affect the structure of the PDRs. In addition, we have observed the strongest ~30 near-IR He I emission lines, many of which have not been detected previously. There is good agreement between most observed and theoretical He I line ratios, while a few transitions with upper levels of n3P (particularly 43P-33S 1.2531 μm) are enhanced over strengths expected from collisional excitation. This effect is possibly due to opacity in the UV series n3P-23S. We also detect several near-IR [Fe II] and [Fe III] transitions with line ratios indicative of low densities (ne ~ 103-104 cm-3), whereas recent observations of optical [Fe II] emission imply the presence of high-density gas (ne ~ 106 cm-3). These results are consistent with a model in which high-density, partially-ionized gas is the source of the iron transitions observed in the optical, while low-density, fully-ionized material is responsible for the near-IR emission lines.
THE GAMMA CONSTRUCTION AND ASYMPTOTIC INVARIANTS OF LINE BUNDLES OVER ARBITRARY FIELDS

We extend results on asymptotic invariants of line bundles on complex projective varieties to projective varieties over arbitrary fields. To do so over imperfect fields, we prove a scheme-theoretic version of the gamma construction of Hochster and Huneke to reduce to the setting where the ground field is -regular varieties over arbitrary fields.
Covariant information theory and emergent gravity

Informational dependence between statistical or quantum subsystems can be described with Fisher information matrix or Fubini-Study metric obtained from variations/shifts of the sample/configuration...
Group leaders optimization algorithm

We present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique which is designed into a group architecture. To demonstrate the efficiency of the method, a standard suite of single and multi-dimensional optimization functions along with the energies and the geometric structures of Lennard-Jones clusters are given as well as the application of the algorithm on quantum circuit design problems. We show that as an improvement over previous methods, the algorithm scales as N 2.5 for the Lennard-Jones clusters of N-particles. In addition, an efficient circuit design is shown for a two-qubit Grover search algorithm which is a quantum algorithm providing quadratic speedup over the classical counterpart.
Integrating Low-Power Wide-Area Networks for Enhanced Scalability and Extended Coverage

Low-Power Wide-Area Networks (LPWANs) are evolving as an enabling technology for Internet-of-Things (IoT) due to their capability of communicating over long distances at very low transmission power. Existing LPWAN technologies, however, face limitations in meeting scalability and covering very wide areas which make their adoption challenging for future IoT applications, especially in infrastructure-limited rural areas. To address this limitation, in this paper, we consider achieving scalability and extended coverage by integrating multiple LPWANs. SNOW (Sensor Network Over White Spaces) , a recently proposed LPWAN architecture over the TV white spaces, has demonstrated its advantages over existing LPWANs in performance and energy-efficiency. In this paper, we propose to scale up LPWANs through a seamless integration of multiple SNOWs which enables concurrent inter-SNOW and intra-SNOW communications. We then formulate the tradeoff between scalability and inter-SNOW interference as a constrained optimization problem whose objective is to maximize scalability by managing white space spectrum sharing across multiple SNOWs. We also prove the NP-hardness of this problem. To this extent, We propose an intuitive polynomial-time heuristic algorithm for solving the scalability optimization problem which is highly efficient in practice. For the sake of theoretical bound, we also propose a simple polynomial-time $\frac {1}{2}$ -approximation algorithm for the scalability optimization problem. Hardware experiments through deployment in an area of ( $25\times 15$ )km2 as well as large scale simulations demonstrate the effectiveness of our algorithms and feasibility of achieving scalability through seamless integration of SNOWs with high reliability, low latency, and energy efficiency.
Density of states and tachyons in open and closed string theory

In this note we reexamine the possibility of constructing stable non-supersymmetric theories that exhibit an exponential density of states. For weakly coupled closed strings there is a general theorem, according to which stable theories with an exponential density of states must exhibit an almost exact cancellation of spacetime bosons and fermions (not necessarily level by level). We extend this result to open strings by showing that if the above cancellation between bosons and fermions does not occur, the open strings do not decouple from a closed string tachyon even in the NCOS scaling limit. We conclude with a brief comment on the proposed generalization of the AdS/CFT correspondence to non-supersymmetric theories.
Noether–Lefschetz Theorem with Base Locus

For an arbitrary curve (possibly reducible, non-reduced, of mixed dimension) lying on a normal surface, the general surface S of high degree containing Z is also normal but often singular. We compute the class groups of the very general such surface, thereby extending the Noether–Lefschetz theorem (the special case when Z is empty). Our method is an adaptation of Griffiths and Harris’ degeneration proof, simplified by a cohomology and base change argument. We give applications to computing Picard groups. Dedicated to Robin Hartshorne on his 70th birthday
Influence of the Coulomb interaction on the exchange coupling in granular magnets

We develop a theory of the exchange interaction between ferromagnetic (FM) metallic grains embedded into insulating matrix by taking into account the Coulomb blockade effects. For bulk ferromagnets separated by the insulating layer the exchange interaction strongly depends on the height and thickness of the tunneling barrier created by the insulator. We show that for FM grains embedded into insulating matrix the exchange coupling additionally depends on the dielectric properties of this matrix due to the Coulomb blockade effects. In particular, the FM coupling decreases with decreasing the dielectric permittivity of insulating matrix. We find that the change in the exchange interaction due to the Coulomb blockade effects can be a few tens of percent. Also, we study dependence of the intergrain exchange interaction on the grain size and other parameters of the system.
Circle homeomorphisms and shears

The space Homeo.S/ of orientation preserving homeomorphisms of the unit circle S is a classical topological group which is of interest in various fields of mathematics; see Ghys [11]. Its subgroup QS.S/ of quasisymmetric maps of S plays a fundamental role in the Teichmuller theory of Riemann surfaces; see Ahlfors [2], Bers [3] and Gardiner and Lakic [9]. In fact, the universal Teichmuller space consists of all quasisymmetric maps which fix three distinguished points on S namely it is isomorphic to Mob.S/nQS.S/, where Mob.S/ is the group of (orientation preserving) Mobius maps which preserve S [3]. The subgroup Sym.S/ of symmetric maps plays a prominent role in studying Teichmuller spaces of real dynamical systems; see Gardiner and Sullivan [10], Earle, Gardiner and Lakic [6] and Gardiner and Jiang [8].
Laser-driven collisionless shock acceleration of ions from near-critical plasmas

This paper overviews experimental and numerical results on acceleration of narrow energy spread ion beams by an electrostatic collisionless shockwave driven by 1 μm (Omega EP) and 10 μm (UCLA Neptune Laboratory) lasers in near critical density CH and He plasmas, respectively. Shock waves in CH targets produced high-energy ∼50 MeV protons (ΔE/E of ≤30%) and 314 MeV C6+ ions (ΔE/E of ≤10%). Observation of acceleration of both protons and carbon ions to similar velocities is consistent with reflection of particles off the moving potential of a shock front. For shocks driven by CO2 laser in a gas jet, ∼30 MeV peak in He ion spectrum was detected. Particle-in-cell simulations indicate that regardless of the target further control over its density profile is needed for optimization of accelerated ion beams in part of energy spread, yield and maximum kinetic energy.
An Immersive Telepresence System Using RGB-D Sensors and Head Mounted Display

We present a tele-immersive system that enables people to interact with each other in a virtual world using body gestures in addition to verbal communication. Beyond the obvious applications, including general online conversations and gaming, we hypothesize that our proposed system would be particularly beneficial to education by offering rich visual contents and interactivity. One distinct feature is the integration of egocentric pose recognition that allows participants to use their gestures to demonstrate and manipulate virtual objects simultaneously. This functionality enables the instructor to effectively and efficiently explain and illustrate complex concepts or sophisticated problems in an intuitive manner. The highly interactive and flexible environment can capture and sustain more student attention than the traditional classroom setting and, thus, delivers a compelling experience to the students. Our main focus here is to investigate possible solutions for the system design and implementation and devise strategies for fast, efficient computation suitable for visual data processing and network transmission. We describe the technique and experiments in details and provide quantitative performance results, demonstrating our system can be run comfortably and reliably for different application scenarios. Our preliminary results are promising and demonstrate the potential for more compelling directions in cyberlearning.
A path-integral approach to Bayesian inference for inverse problems using the semiclassical approximation

We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse problems of recovering continuous (in nite dimensional) coe cient functions from ordinary or partial di erential equations (ODE, PDE), a problem which is typically ill-posed. Regularization of these problems using L 2 function spaces (Tikhonov regularization) is equivalent to Bayesian probabilistic inference, using a Gaussian prior. The Bayesian interpretation of inverse problem regularization is useful since it allows one to quantify and characterize error and degree of precision in the solution of inverse problems, as well as examine assumptions made in solving the problem - namely whether the subjective choice of regularization is compatible with prior knowledge. Using path-integral formalism, Bayesian inference can be explored through various perturbative techniques, such as the semiclassical approximation, which we use in this manuscript. Perturbative path-integral approaches, while o ering alternatives to computational approaches like Markov-Chain-Monte-Carlo (MCMC), also provide natural starting points for MCMC methods that can be used to re ne approximations. In this manuscript, we illustrate a path-integral formulation for inverse problems and demonstrate it on an inverse problem in membrane biophysics as well as inverse problems in potential theories involving the Poisson equation.