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I consider the use of entanglement between two parties to enable one to authenticate her identity to another over a quantum communication channel. Exploiting the phenomenon of entanglement-catalyzed transformations between pure states gives a potentially reusable entangled identification token. In analyzing this, I consider the independently interesting problem of the best possible approximation to a given pure entangled state realizable using local actions and classical communication by parties sharing a different entangled state. | Quantum secure identification using entanglement and catalysis |
We have observed Proxima Centauri and Barnard's Star with Hubble Space Telescope Fine Guidance Sensor 3. Proxima Centauri exhibits small-amplitude, periodic photometric variations. Once several sources of systematic photometric error are corrected, we obtain 2 milli-magnitude internal photometric precision. We identify two distinct behavior modes over the past four years: higher amplitude, longer period; smaller amplitude, shorter period. Within the errors one period (P ~ 83d) is twice the other. Barnard's Star shows very weak evidence for periodicity on a timescale of approximately 130 days. If we interpret these periodic phenomena as rotational modulation of star spots, we identify three discrete spots on Proxima Cen and possibly one spot on Barnard's Star. We find that the disturbances change significantly on time scales as short as one rotation period. | Photometry of Proxima Centauri and Barnard's Star Using HST Fine Guidance Sensor 3: A Search for Periodic Variations |
We report proton temperature anisotropy variations in the inner heliosphere with Parker Solar Probe (PSP) observations. Using a linear fitting method, we derive proton temperature anisotropy with temperatures measured by the Solar Probe Cup (SPC) from the SWEAP instrument suite and magnetic field observations from the FIELDS instrument suite. The observed radial dependence of temperature variations in the fast solar wind implies stronger perpendicular heating and parallel cooling than previous results from Helios measurements made at larger radial distances. The anti-correlation between proton temperature anisotropy and parallel plasma beta is retained in fast solar wind. However, the temperature anisotropies of the slow solar wind seem to be well constrained by the mirror and parallel firehose instabilities. The perpendicular heating of the slow solar wind inside 0.24 AU may contribute to its same trend up against mirror instability thresholds as fast solar wind. These results suggest that we may see stronger anisotropy heating than expected in inner heliosphere. | Proton Temperature Anisotropy Variations in Inner Heliosphere Estimated with First Parker Solar Probe Observations |
At the location of a magnetic-field Feshbach resonance, a mixture gas of fermionic atoms and dimers of fermionic atom pairs is investigated in the unitarity limit where the absolute value of the scattering length is much larger than the mean distance between atoms. The dynamic equilibrium of the mixture gases is characterized by the minimum of the Gibbs free energy. For the fermionic atoms and dimers with divergent scattering length, it is found that the fraction of the dimers based on a very simple theory agrees with the high fraction of zero-momentum molecules observed in a recent experiment (M. W. Zwierlein et al, Phys. Rev. Lett. 92, 120403 (2004)). The dimeric gas can be also used to interpret the frequency of the radial breathing mode observed in the experiment by J. Kinast et al (Phys. Rev. Lett. 92, 150402 (2004)). | Dimers of ultracold two-component Fermi gases on magnetic-field Feshbach resonance |
In this paper, we study a close relationship between relative cluster tilting theory in extriangulated categories and tau-tilting theory in module categories. Our main results show that relative rigid objects are in bijection with $\tau$-rigid pairs, and also relative maximal rigid objects with support tau-tilting pairs under some assumptions. These results generalize their work by Adachi-Iyama-Reiten, Yang-Zhu and Fu-Geng-Liu. Finally, we introduce mutation of relative maximal rigid objects and show that any basic relative almost maximal rigid object has exactly two non-isomorphic indecomposable complements. | Relative rigid objects in extriangulated categories |
Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the \emph{data separation function}. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to $1$ in the general case of arbitrary normalized dataset consisting of $n$ samples in $d$ dimension as $n/\sqrt{d}\rightarrow 0$. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes \emph{kinetic optimal} as $n/\sqrt{d}\rightarrow 0$. We further support this theory with empirical experiments on ImageNet. | On Kinetic Optimal Probability Paths for Generative Models |
In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show that both their generating functions and two matrices determined by them satisfy certain reciprocal relations. | Reciprocity between partitions and compositions |
We associate to each stable Higgs pair $(A_0,\Phi_0)$ on a compact Riemann surface $X$ a singular limiting configuration $(A_\infty,\Phi_\infty)$, assuming that $\det \Phi$ has only simple zeroes. We then prove a desingularization theorem by constructing a family of solutions $(A_t,t\Phi_t)$ to Hitchin's equations which converge to this limiting configuration as $t \to \infty$. This provides a new proof, via gluing methods, for elements in the ends of the Higgs bundle moduli space and identifies a dense open subset of the boundary of the compactification of this moduli space. | Ends of the moduli space of Higgs bundles |
We report on observations of GRB 080503, a short gamma-ray burst with very bright extended emission (about 30 times the gamma-ray fluence of the initial spike) in conjunction with a thorough comparison to other short Swift events. In spite of the prompt-emission brightness, however, the optical counterpart is extraordinarily faint, never exceeding 25 mag in deep observations starting at ~1 hr after the BAT trigger. The optical brightness peaks at ~1 day and then falls sharply in a manner similar to the predictions of Li & Paczynski (1998) for supernova-like emission following compact-binary mergers. However, a shallow spectral index and similar evolution in X-rays inferred from Chandra observations are more consistent with an afterglow interpretation. The extreme faintness of this probable afterglow relative to the bright gamma-ray emission argues for a very low-density medium surrounding the burst (a "naked" GRB), consistent with the lack of a coincident host galaxy down to 28.5 mag in deep HST imaging. Our observations reinforce the notion that short GRBs generally occur outside regions of active star formation, but demonstrate that in some cases the luminosity of the extended prompt emission can greatly exceed that of the short spike, which may constrain theoretical interpretation of this class of events. Because most previous BAT short bursts without observed extended emission are too faint for this signature to have been detectable even if it were present at typical level, conclusions based solely on the observed presence or absence of extended emission in the existing Swift sample are premature. (abridged) | GRB 080503: Implications of a Naked Short Gamma-Ray Burst Dominated by Extended Emission |
Recent reports claiming tentative association of the massive star binary system gamma^2 Velorum (WR 11) with a high-energy gamma-ray source observed by Fermi-LAT contrast the so-far exclusive role of Eta Carinae as the hitherto only detected gamma-ray emitter in the source class of particle-accelerating colliding-wind binary systems. We aim to shed light on this claim of association by providing dedicated model predictions for the nonthermal photon emission spectrum of WR 11. We use three-dimensional magneto-hydrodynamic modeling to trace the structure and conditions of the wind-collision region of WR 11 throughout its 78.5 day orbit, including the important effect of radiative braking in the stellar winds. A transport equation is then solved in the wind-collision region to determine the population of relativistic electrons and protons which are subsequently used to compute nonthermal photon emission components. We find that - if WR 11 be indeed confirmed as the responsible object for the observed gamma-ray emission - its radiation will unavoidably be of hadronic origin owing to the strong radiation fields in the binary system which inhibit the acceleration of electrons to energies suffciently high for observable inverse Compton radiation. Different conditions in wind-collision region near the apastron and periastron configuration lead to significant variability on orbital time scales. The bulk of the hadronic gamma-ray emission originates at a 400 solar radii wide region at the apex. | MHD Models of Gamma-ray Emission in WR 11 |
We report the trapping of ultracold neutral $ \text{Rb}$ atoms and $ \text{Ba}^+ $ ions in a common optical potential in absence of any radiofrequency (RF) fields. We prepare $ \text{Ba}^+ $ at $ 370 ~ \mu K $ and demonstrate efficient sympathetic cooling by $100 ~ \mu K $ after one collision. Our approach is currently limited by the $ \text{Rb}$ density and related three-body losses, but it overcomes the fundamental limitation in RF traps set by RF-driven, micromotion-induced heating. It is applicable to a wide range of ion-atom species, and may enable novel ultracold chemistry experiments and complex many-body dynamics. | Optical Traps for sympathetic Cooling of Ions with ultracold neutral Atoms |
Following the second HST servicing mission in 1997 when the STIS instrument was installed and the capability for parallel observations was enhanced, a substantial archive of non-proprietary parallel data has been accumulating. In this paper, we discuss the use of unfiltered STIS imaging data for a project that requires deep observations along as many independent lines-of-sight as possible. We have developed a technique to determine which datasets in the archive can safely be co-added together and have developed an iterative co-addition technique which enabled us to produce 498 high-quality, deep images. The principal motivation for this work is to measure the Cosmic Shear on small angular scales and a value derived from these data will be presented in a subsequent paper. A valuable by-product of this work is a set of high quality combined fields which can be used for other projects. The data are publicly available at http://www.stecf.org/projects/shear/ | Cosmic shear from STIS Pure Parallels: I Data |
Observations of both gamma-ray bursts (GRBs) and active galactic nuclei (AGNs) point to the idea that some relativistic jets are suffocated by their environment before we observe them. In these "choked" jets, all the jet's kinetic energy is transferred into a hot and narrow cocoon of near-uniform pressure. We consider the evolution of an elongated, axisymmetric cocoon formed by a choked jet as it expands into a cold power-law ambient medium $\rho \propto R^{-\alpha}$, in the case where the shock is decelerating ($\alpha<3$). The evolution proceeds in three stages, with two breaks in behaviour: the first occurs once the outflow has doubled its initial width, and the second once it has doubled its initial height. Using the Kompaneets approximation, we derive analytical formulae for the shape of the cocoon shock, and obtain approximate expressions for the height and width of the outflow versus time in each of the three dynamical regimes. The asymptotic behaviour is different for flat ($\alpha \le 2$) and steep ($2 < \alpha < 3$) density profiles. Comparing the analytical model to numerical simulations, we find agreement to within $\sim15$ per cent out to 45 degrees from the axis, but discrepancies of a factor of 2-3 near the equator. The shape of the cocoon shock can be measured directly in AGNs, and is also expected to affect the early light from failed GRB jets. Observational constraints on the shock geometry provide a useful diagnostic of the jet properties, even long after jet activity ceases. | The propagation of choked jet outflows in power-law external media |
We present 44 and 226 GHz observations of the Galactic center within 20$"$ of Sgr A*. Millimeter continuum emission at 226 GHz is detected from eight stars that have previously been identified at near-IR and radio wavelengths. We also detect a 5.8 mJy source at 226 GHz coincident with the magnetar SGR~J1745-29 located 2.39$"$ SE of Sgr A* and identify a new 2.5$"\times1.5"$ halo of mm emission centered on Sgr A*. The X-ray emission from this halo has been detected previously and is interpreted in terms of a radiatively inefficient accretion flow. The mm halo surrounds an EW linear feature which appears to arise from Sgr A* and coincides with the diffuse X-ray emission and a minimum in the near-IR extinction. We argue that the millimeter emission is produced by synchrotron emission from relativistic electrons in equipartition with a $\sim 1.5$mG magnetic field. The origin of these is unclear but its coexistence with hot gas supports scenarios in which the gas is produced by the interaction of winds either from the fast moving S-stars, the photo-evaporation of low-mass YSO disks or by a jet-driven outflow from Sgr A*. The spatial anti-correlation of the X-ray, radio and mm emission from the halo and the low near-IR extinction provides compelling evidence for an outflow sweeping up the interstellar material, creating a dust cavity within 2$"$ of Sgr A*. Finally, the radio and mm counterparts to eight near-IR identified stars within $\sim$10\arcs\ of Sgr A* provide accurate astrometry to determine the positional shift between the peak emission at 44 and 226 GHz. | ALMA and VLA observations of emission from the environment of Sgr A* |
This work presents an initial proof of concept of how Music Emotion Recognition (MER) systems could be intentionally biased with respect to annotations of musically induced emotions in a political context. In specific, we analyze traditional Colombian music containing politically charged lyrics of two types: (1) vallenatos and social songs from the "left-wing" guerrilla Fuerzas Armadas Revolucionarias de Colombia (FARC) and (2) corridos from the "right-wing" paramilitaries Autodefensas Unidas de Colombia (AUC). We train personalized machine learning models to predict induced emotions for three users with diverse political views - we aim at identifying the songs that may induce negative emotions for a particular user, such as anger and fear. To this extent, a user's emotion judgements could be interpreted as problematizing data - subjective emotional judgments could in turn be used to influence the user in a human-centered machine learning environment. In short, highly desired "emotion regulation" applications could potentially deviate to "emotion manipulation" - the recent discredit of emotion recognition technologies might transcend ethical issues of diversity and inclusion. | Personalized musically induced emotions of not-so-popular Colombian music |
Due to selection rules, new particles are sometimes discovered/predicted to be produced in pairs. In the current search for SUSY particles this will occur if R-parity is conserved. In local relativistic field theory, there can be identical particles which are neither bosons nor fermions which are associated with higher-dimensional representations of the permutation group. Such particles will generally be pair-produced and so empirical tests are required to exclude them. A parameter-free statistical model is used to study the unusual multiplicity signatures in coherent paraboson production versus the case of ordinary bosons. | Tests for the Statistics of Pair-Produced New Particles |
We use quantum energy teleportation in the light-matter interaction as an operational means to create quantum field states that violate energy conditions and have negative local stress-energy densities. We show that the protocol is optimal in the sense that it scales in a way that saturates the quantum interest conjecture. | Engineering negative stress-energy densities with quantum energy teleportation |
We present a detailed analysis of the orbital circular motion of electrically neutral test particles on the equatorial plane of the Kerr-Newman spacetime. Many details of the motion in the cases of black hole and naked singularity sources are pointed out. We identify four different types of orbital regions, which depend on the properties of the orbital angular momentum, and define four different kinds of naked singularities, according to the values of the charge-to-mass ratio of the source. It is shown that the presence of a particular type of counter-rotating test particles is sufficient to uniquely identify naked singularities. It is pointed out that the structure of the stability regions can be used to differentiate between black holes and naked singularities. | Equatorial circular orbits of neutral test particles in the Kerr--Newman spacetime |
We prove that the spectrum of certain non-self-adjoint Schrodinger operators is unstable in the semi-classical limit. Similar results hold for a fixed operator in the high energy limit. The method involves the construction of approximate semi-classical modes of the operator by the JWKB method for energies far from the spectrum. | Semi-classical States for Non-self-adjoint Schrodinger Operators |
The Rapid and Accurate Image Super Resolution (RAISR) method of Romano, Isidoro, and Milanfar is a computationally efficient image upscaling method using a trained set of filters. We describe a generalization of RAISR, which we name Best Linear Adaptive Enhancement (BLADE). This approach is a trainable edge-adaptive filtering framework that is general, simple, computationally efficient, and useful for a wide range of problems in computational photography. We show applications to operations which may appear in a camera pipeline including denoising, demosaicing, and stylization. | BLADE: Filter Learning for General Purpose Computational Photography |
High-resolution thermal expansion measurements have been performed for exploring the mysterious "structureless transition" in (TMTTF)$_{2}$X (X = PF$_{6}$ and AsF$_{6}$), where charge ordering at $T_{CO}$ coincides with the onset of ferroelectric order. Particularly distinct lattice effects are found at $T_{CO}$ in the uniaxial expansivity along the interstack $\textbf{\textit{c*}}$-direction. We propose a scheme involving a charge modulation along the TMTTF stacks and its coupling to displacements of the counteranions X$^{-}$. These anion shifts, which lift the inversion symmetry enabling ferroelectric order to develop, determine the 3D charge pattern without ambiguity. Evidence is found for another anomaly for both materials at $T_{int}$ $\simeq$ 0.6 $\cdot$ $T_{CO}$ indicative of a phase transition related to the charge ordering. | Evidence for Lattice Effects at the Charge-Ordering Transition in (TMTTF)$_2$X |
We study creation of bi- and multipartite continuous variable entanglement in structures of coupled quantum harmonic oscillators. By adjusting the interaction strengths between nearest neighbors we show how to maximize the entanglement production between the arms in a Y-shaped structure where an initial single mode squeezed state is created in the first oscillator of the input arm. We also consider the action of the same structure as an approximate quantum cloner. For a specific time in the system dynamics the last oscillators in the output arms can be considered as imperfect copies of the initial state. By increasing the number of arms in the structure, multipartite entanglement is obtained, as well as 1 to M cloning. Finally, we are considering configurations that implement the symmetric splitting of an initial entangled state. All calculations are carried out within the framework of the rotating wave approximation in quantum optics, and our predictions could be tested with current available experimental techniques. | Manipulating quantum information by propagation |
Exact diagonalization numerical results are presented for a 32-site square cluster, with two holes propagating in an antiferromagnetic background described by the t-J model. We characterize the wave function of the lowest energy bound state found in this calculation, which has d_{x^2-y^2} symmetry. Analytical work is presented, based on a Lang-Firsov-type canonical transformation derived quasiparticle Hamiltonian, that accurately agrees with numerically determined values for the electron momentum distribution function and the pair correlation function. We interpret this agreement as strong support for the validity of this description of the hole quasiparticles. | A numerical and analytical study of two holes doped into the 2D t--J model |
We present further and more compelling evidence of the existence of E(38), a light boson that most probably couples exclusively to quarks and gluons. Observations presented in a prior paper will be rediscussed for completeness. | Material evidence of a 38 MeV boson |
We directly measure the evolution of the intergalactic Lya effective optical depth, tau_eff, over the redshift range 2<z<4.2 from a sample of 86 high-resolution, high-signal-to-noise quasar spectra obtained with the ESI and HIRES spectrographs on Keck, and with the MIKE spectrograph on Magellan. This represents an improvement over previous analyses of the Lya forest from high-resolution spectra in this redshift interval of a factor of two in the size of the data set alone. We pay particular attention to robust error estimation and extensively test for systematic effects. We find that our estimates of the quasar continuum levels in the Lya forest obtained by spline fitting are systematically biased low, with the magnitude of the bias increasing with redshift, but that this bias can be accounted for using mock spectra. The mean fractional error is <1% at z=2, 4% at z=3, and 12% at z=4. Previous measurements of tau_eff at z>~3 based on directly fitting the quasar continua in the Lya forest, which have generally neglected this effect, are therefore likely biased low. We provide estimates of the level of absorption arising from metals in the Lya forest based on both direct and statistical metal removal results in the literature, finding that this contribution is ~6-9% at z=3 and decreases monotonically with redshift. The high precision of our measurement, attaining 3% in redshift bins of width Delta z=0.2 around z=3, indicates significant departures from the best-fit power-law redshift evolution (tau_eff=0.0018(1+z)^3.92, when metals are left in), particularly near z=3.2. The observed downward departure is statistically consistent with a similar feature detected in a precision statistical measurement using Sloan Digital Sky Survey spectra by Bernardi and coworkers using an independent approach. | A Direct Precision Measurement of the Intergalactic Lyman-alpha Opacity at 2<z<4.2 |
In recent years, deep convolutional neural network (DCNN) has seen a breakthrough progress in natural image recognition because of three points: universal approximation ability via DCNN, large-scale database (such as ImageNet), and supercomputing ability powered by GPU. The remote sensing field is still lacking a large-scale benchmark compared to ImageNet and Place2. In this paper, we propose a remote sensing image classification benchmark (RSI-CB) based on massive, scalable, and diverse crowdsource data. Using crowdsource data, such as Open Street Map (OSM) data, ground objects in remote sensing images can be annotated effectively by points of interest, vector data from OSM, or other crowdsource data. The annotated images can be used in remote sensing image classification tasks. Based on this method, we construct a worldwide large-scale benchmark for remote sensing image classification. This benchmark has two sub-datasets with 256 by 256 and 128 by 128 sizes because different DCNNs require different image sizes. The former contains 6 categories with 35 subclasses of more than 24,000 images. The latter contains 6 categories with 45 subclasses of more than 36,000 images. This classification system of ground objects is defined according to the national standard of land-use classification in China and is inspired by the hierarchy mechanism of ImageNet. Finally, we conduct many experiments to compare RSI-CB with the SAT-4, SAT-6, and UC-Merced datasets on handcrafted features, such as scale-invariant feature transform, color histogram, local binary patterns, and GIST, and classical DCNN models, such as AlexNet, VGGNet, GoogLeNet, and ResNet. | RSI-CB: A Large Scale Remote Sensing Image Classification Benchmark via Crowdsource Data |
In this paper we prove the existence and uniqueness of the solution of Young differential delay equations under weaker conditions than it is known in the literature. We also prove the continuity and differentiability of the solution with respect to the initial function and give an estimate for the growth of the solution. The proofs use techniques of stopping times, Shauder-Tychonoff fixed point theorem and a Gronwall-type lemma. | Young differential delay equations driven by H\"older continuous paths |
Some enumerative aspects of the fans, called generalized associahedra, introduced by S. Fomin and A. Zelevinsky in their theory of cluster algebras are considered, in relation with a bicomplex and its two spectral sequences. A precise enumerative relation with the lattices of generalized noncrossing partitions is conjectured and some evidence is given. | Enumerative properties of generalized associahedra |
In this paper we improve the results of sec. VI of paper [M. Castagnino, Phys. Rev. D 57, 750 (1998)] by considering that the main source of entropy production are the photospheres of the stars. | Addemdum to: ''The Mathematical Structure of Quantum Superspace as a Consequence of Time Asymmetry'' |
Typical deep neural network (DNN) backdoor attacks are based on triggers embedded in inputs. Existing imperceptible triggers are computationally expensive or low in attack success. In this paper, we propose a new backdoor trigger, which is easy to generate, imperceptible, and highly effective. The new trigger is a uniformly randomly generated three-dimensional (3D) binary pattern that can be horizontally and/or vertically repeated and mirrored and superposed onto three-channel images for training a backdoored DNN model. Dispersed throughout an image, the new trigger produces weak perturbation to individual pixels, but collectively holds a strong recognizable pattern to train and activate the backdoor of the DNN. We also analytically reveal that the trigger is increasingly effective with the improving resolution of the images. Experiments are conducted using the ResNet-18 and MLP models on the MNIST, CIFAR-10, and BTSR datasets. In terms of imperceptibility, the new trigger outperforms existing triggers, such as BadNets, Trojaned NN, and Hidden Backdoor, by over an order of magnitude. The new trigger achieves an almost 100% attack success rate, only reduces the classification accuracy by less than 0.7%-2.4%, and invalidates the state-of-the-art defense techniques. | Dispersed Pixel Perturbation-based Imperceptible Backdoor Trigger for Image Classifier Models |
For a random intersection graph with a power law degree sequence having a finite mean and an infinite variance we show that the global clustering coefficient admits a tunable asymptotic distribution. | Clustering coefficient of random intersection graphs with infinite degree variance |
We propose Predict then Interpolate (PI), a simple algorithm for learning correlations that are stable across environments. The algorithm follows from the intuition that when using a classifier trained on one environment to make predictions on examples from another environment, its mistakes are informative as to which correlations are unstable. In this work, we prove that by interpolating the distributions of the correct predictions and the wrong predictions, we can uncover an oracle distribution where the unstable correlation vanishes. Since the oracle interpolation coefficients are not accessible, we use group distributionally robust optimization to minimize the worst-case risk across all such interpolations. We evaluate our method on both text classification and image classification. Empirical results demonstrate that our algorithm is able to learn robust classifiers (outperforms IRM by 23.85% on synthetic environments and 12.41% on natural environments). Our code and data are available at https://github.com/YujiaBao/Predict-then-Interpolate. | Predict then Interpolate: A Simple Algorithm to Learn Stable Classifiers |
I propose an orthogonalization procedure preserving the grading of the initial graded set of linearly independent vectors. In particular, this procedure is applicable for orthonormalization of any countable set of polynomials in several (finitely many) indeterminates. | Orthogonalization of graded sets of vectors |
We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a conservation law with a nonlocal flux. Each equation in this class generates a Lipschitz semigroup of solutions and is stable with respect to the functions and parameters defining it. Moreover, key qualitative properties such as the boundedness of the crowd density are proved. Specific models are presented and their qualitative properties are shown through numerical integrations. | A Class of Non-Local Models for Pedestrian Traffic |
We present a model for cosmological inflation based on a no-scale supergravity sector with an SU(2,1)/U(1) Kahler potential, a single modulus T and an inflaton superfield Phi described by a Wess-Zumino model with superpotential parameters (mu, lambda). This model yields a scalar spectral index n_s and a tensor-to-scalar ratio r that are compatible with the Planck measurements for values of lambda simeq mu/3M_P. For the specific choice lambda = mu/3M_P, the model is a no-scale supergravity realization of the R+R^2 Starobinsky model. | No-Scale Supergravity Realization of the Starobinsky Model of Inflation |
We use a sample of galaxy groups selected from the SDSS DR 4 with an adaptive halo-based group finder to probe how the clustering strength of groups depends on their masses and colors. In particular, we determine the relative biases of groups of different masses, as well as that of groups with the same mass but with different colors. In agreement with previous studies, we find that more massive groups are more strongly clustered, and the inferred mass dependence of the halo bias is in good agreement with predictions for the $\Lambda$CDM cosmology. Regarding the color dependence, we find that groups with red centrals are more strongly clustered than groups of the same mass but with blue centrals. Similar results are obtained when the color of a group is defined to be the total color of its member galaxies. The color dependence is more prominent in less massive groups and becomes insignificant in groups with masses $\gta 10^{14}\msunh$. We construct a mock galaxy redshift survey constructed from the large Millenium simulation that is populated with galaxies according to the semi-analytical model of Croton et al. Applying our group finder to this mock survey, and analyzing the mock data in exactly the same way as the true data, we are able to accurately recover the intrinsic mass and color dependencies of the halo bias in the model. This suggests that our group finding algorithm and our method of assigning group masses do not induce spurious mass and/or color dependencies in the group-galaxy correlation function. The semi-analytical model reveals the same color dependence of the halo bias as we find in our group catalogue. In halos with $M\sim 10^{12}\msunh$, though, the strength of the color dependence is much stronger in the model than in the data. | The clustering of SDSS galaxy groups: mass and color dependence |
In this paper, we consider the task of digitally voicing silent speech, where silently mouthed words are converted to audible speech based on electromyography (EMG) sensor measurements that capture muscle impulses. While prior work has focused on training speech synthesis models from EMG collected during vocalized speech, we are the first to train from EMG collected during silently articulated speech. We introduce a method of training on silent EMG by transferring audio targets from vocalized to silent signals. Our method greatly improves intelligibility of audio generated from silent EMG compared to a baseline that only trains with vocalized data, decreasing transcription word error rate from 64% to 4% in one data condition and 88% to 68% in another. To spur further development on this task, we share our new dataset of silent and vocalized facial EMG measurements. | Digital Voicing of Silent Speech |
In this paper, the challenges of maintaining a healthy IT operational environment have been addressed by proactively analyzing IT Service Desk tickets, customer satisfaction surveys, and social media data. A Cognitive solution goes beyond the traditional structured data analysis by deep analyses of both structured and unstructured text. The salient features of the proposed platform include language identification, translation, hierarchical extraction of the most frequently occurring topics, entities and their relationships, text summarization, sentiments, and knowledge extraction from the unstructured text using Natural Language Processing techniques. Moreover, the insights from unstructured text combined with structured data allow the development of various classification, segmentation, and time-series forecasting use-cases on the incident, problem, and change datasets. Further, the text and predictive insights together with raw data are used for visualization and exploration of actionable insights on a rich and interactive dashboard. However, it is hard not only to find these insights using traditional structured data analysis but it might also take a very long time to discover them, especially while dealing with a massive amount of unstructured data. By taking action on these insights, organizations can benefit from a significant reduction of ticket volume, reduced operational costs, and increased customer satisfaction. In various experiments, on average, upto 18-25% of yearly ticket volume has been reduced using the proposed approach. | Cognitive Computing to Optimize IT Services |
This paper discusses the overlap of the Hori-Vafa formulation of mirror symmetry with some other constructions. We focus on compact Calabi-Yau hypersurfaces \mathcal{M}_G = {G = 0} in weighted complex projective spaces. The Hori-Vafa formalism relates a family {\mathcal{M}_G \in WCP^{m-1}_{Q_1,...,Q_m}[s] | \sum_{i=1}^m Q_i = s} of such hypersurfaces to a single Landau-Ginzburg mirror theory. A technique suggested by Hori and Vafa allows the Picard-Fuchs equations satisfied by the corresponding mirror periods to be determined. Some examples in which the variety \mathcal{M}_G is crepantly resolved are considered. The resulting Picard-Fuchs equations agree with those found elsewhere working in the Batyrev-Borisov framework. When G is an invertible nondegenerate quasihomogeneous polynomial, the Chiodo-Ruan geometrical interpretation of Berglund-Huebsch-Krawitz duality can be used to associate a particular complex structure for \mathcal{M}_G with a particular Kaehler structure for the mirror \widetilde{\mathcal{M}}_G. We make this association for such G when the ambient space of \mathcal{M}_G is CP^2, CP^3, and CP^4. Finally, we probe some of the resulting mirror Kaehler structures by determining corresponding Picard-Fuchs equations. | Hori-Vafa mirror periods, Picard-Fuchs equations, and Berglund-H\"{u}bsch-Krawitz duality |
We propose a simple solution to use a single Neural Machine Translation (NMT) model to translate between multiple languages. Our solution requires no change in the model architecture from our base system but instead introduces an artificial token at the beginning of the input sentence to specify the required target language. The rest of the model, which includes encoder, decoder and attention, remains unchanged and is shared across all languages. Using a shared wordpiece vocabulary, our approach enables Multilingual NMT using a single model without any increase in parameters, which is significantly simpler than previous proposals for Multilingual NMT. Our method often improves the translation quality of all involved language pairs, even while keeping the total number of model parameters constant. On the WMT'14 benchmarks, a single multilingual model achieves comparable performance for English$\rightarrow$French and surpasses state-of-the-art results for English$\rightarrow$German. Similarly, a single multilingual model surpasses state-of-the-art results for French$\rightarrow$English and German$\rightarrow$English on WMT'14 and WMT'15 benchmarks respectively. On production corpora, multilingual models of up to twelve language pairs allow for better translation of many individual pairs. In addition to improving the translation quality of language pairs that the model was trained with, our models can also learn to perform implicit bridging between language pairs never seen explicitly during training, showing that transfer learning and zero-shot translation is possible for neural translation. Finally, we show analyses that hints at a universal interlingua representation in our models and show some interesting examples when mixing languages. | Google's Multilingual Neural Machine Translation System: Enabling Zero-Shot Translation |
Bone age assessment is a task performed daily in hospitals worldwide. This involves a clinician estimating the age of a patient from a radiograph of the non-dominant hand. Our approach to automated bone age assessment is to modularise the algorithm into the following three stages: segment and verify hand outline; segment and verify bones; use the bone outlines to construct models of age. In this paper we address the final question: given outlines of bones, can we learn how to predict the bone age of the patient? We examine two alternative approaches. Firstly, we attempt to train classifiers on individual bones to predict the bone stage categories commonly used in bone ageing. Secondly, we construct regression models to directly predict patient age. We demonstrate that models built on summary features of the bone outline perform better than those built using the one dimensional representation of the outline, and also do at least as well as other automated systems. We show that models constructed on just three bones are as accurate at predicting age as expert human assessors using the standard technique. We also demonstrate the utility of the model by quantifying the importance of ethnicity and sex on age development. Our conclusion is that the feature based system of separating the image processing from the age modelling is the best approach for automated bone ageing, since it offers flexibility and transparency and produces accurate estimates. | Predictive Modelling of Bone Age through Classification and Regression of Bone Shapes |
It is well-known that any pair of closed orientable 3-manifolds are related by a finite sequence of Dehn surgeries on knots. Furthermore Kawauchi showed that such knots can be taken to be hyperbolic. In this article, we consider the minimal length of such sequences connecting a pair of 3-manifolds, in particular, a pair of lens spaces. | Surgical distance between lens spaces |
In this paper, we study the form over the minimum spanning tree problem (MST) from which we will derive an intuitively generalized model and new methods with the upper bound of runtimes of logarithm. The new pattern we made has taken successful to better equilibrium the benefits of local and global when we employ the strategy of divide and conquer to optimize solutions on problem. Under new model, we let the course of clustering become more transparent with many details, so that the whole solution may be featured of much reasonable, flexibility, efficiency and approach to reveal or reflect the reality. There are some important methods and avenues as fruits derived from discussions or trial which can be broad usefulness in the fields of graphic analysis, data mining, k-means clustering problem and so forth. | Study Morphology of Minimum Spanning Tree Problem and Generalized Algorithms |
We determine the cone of nef divisors on the Voronoi compactification A_g^* of the moduli space A_g of principally polarized abelian varieties of dimension g for genus g=2,3. As a corollary we obtain that the spaces A_g^*(n) with level-n structure are a minimal, resp. canonical, model for g=2, n>=4, resp. n>=5 and g=3, n>=3, resp. n>=4. We give two proofs: The easy and quick one reduces the problem to \bar M_g where we can use a result of Faber. This approach cannot be generalized to higher genus g. The main point of the paper is, therefore, to give a second proof using theta functions and a result of Weissauer. This technique can be at least partially generalized to higher genus. We formulate a conjecture for the nef cone of A_g^* for all g. | Nef Divisors on Moduli Spaces of Abelian Varieties |
The authors establish a relation of the theory of varieties with degenerate Gauss maps in projective spaces with the theory of congruences and pseudocongruences of subspaces and show how these two theories can be applied to the construction of induced connections on submanifolds of projective spaces and other spaces endowed with a projective structure. | Induced connections on submanifolds in spaces with fundamental groups |
We study the complexity of Maximum Clique in intersection graphs of convex objects in the plane. On the algorithmic side, we extend the polynomial-time algorithm for unit disks [Clark '90, Raghavan and Spinrad '03] to translates of any fixed convex set. We also generalize the efficient polynomial-time approximation scheme (EPTAS) and subexponential algorithm for disks [Bonnet et al. '18, Bonamy et al. '18] to homothets of a fixed centrally symmetric convex set. The main open question on that topic is the complexity of Maximum Clique in disk graphs. It is not known whether this problem is NP-hard. We observe that, so far, all the hardness proofs for Maximum Clique in intersection graph classes $\mathcal I$ follow the same road. They show that, for every graph $G$ of a large-enough class $\mathcal C$, the complement of an even subdivision of $G$ belongs to the intersection class $\mathcal I$. Then they conclude invoking the hardness of Maximum Independent Set on the class $\mathcal C$, and the fact that the even subdivision preserves that hardness. However there is a strong evidence that this approach cannot work for disk graphs [Bonnet et al. '18]. We suggest a new approach, based on a problem that we dub Max Interval Permutation Avoidance, which we prove unlikely to have a subexponential-time approximation scheme. We transfer that hardness to Maximum Clique in intersection graphs of objects which can be either half-planes (or unit disks) or axis-parallel rectangles. That problem is not amenable to the previous approach. We hope that a scaled down (merely NP-hard) variant of Max Interval Permutation Avoidance could help making progress on the disk case, for instance by showing the NP-hardness for (convex) pseudo-disks. | Maximum Clique in Disk-Like Intersection Graphs |
We consider coupled quantum two-state systems (qubits) exposed to a global relaxation process. The global relaxation refers to the assumption that qubits are coupled to the same quantum bath with approximately equal strengths, appropriate for long-wavelength environmental fluctuations. We show that interactions do not spoil the picture of Dicke's subradiant and superradiant states where quantum interference effects lead to striking deviations from the independent relaxation picture. Remarkably, the system possess a stable entangled state and a state decaying faster than single qubit excitations. We propose a scheme how these effects can be experimentally accessed in superconducting flux qubits and, possibly, used in constructing long-lived entangled states. | Is relaxation correlated in superconducting qubits? |
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We are interested in the case of constrained minimum cut problems, where constraints include cardinality or membership requirements, which leads to NP-hard combinatorial optimization problems. Furthermore, we are interested in ambiguity issues, that is in the robustness of clustering algorithms that are based on Fiedler spectral partitioning. The above-mentioned problems are restated as matrix nearness problems for the weight matrix of the graph. A key element in the solution of these matrix nearness problems is the use of a constrained gradient system of matrix differential equations. | Graph partitioning using matrix differential equations |
The ability to understand a user's underlying needs is critical for conversational systems, especially with limited input from users in a conversation. Thus, in such a domain, Asking Clarification Questions (ACQs) to reveal users' true intent from their queries or utterances arise as an essential task. However, it is noticeable that a key limitation of the existing ACQs studies is their incomparability, from inconsistent use of data, distinct experimental setups and evaluation strategies. Therefore, in this paper, to assist the development of ACQs techniques, we comprehensively analyse the current ACQs research status, which offers a detailed comparison of publicly available datasets, and discusses the applied evaluation metrics, joined with benchmarks for multiple ACQs-related tasks. In particular, given a thorough analysis of the ACQs task, we discuss a number of corresponding research directions for the investigation of ACQs as well as the development of conversational systems. | A Survey on Asking Clarification Questions Datasets in Conversational Systems |
In this work, we aim at developing an extractive summarizer in the multi-document setting. We implement a rank based sentence selection using continuous vector representations along with key-phrases. Furthermore, we propose a model to tackle summary coherence for increasing readability. We conduct experiments on the Document Understanding Conference (DUC) 2004 datasets using ROUGE toolkit. Our experiments demonstrate that the methods bring significant improvements over the state of the art methods in terms of informativity and coherence. | Extract with Order for Coherent Multi-Document Summarization |
We study the entanglement entropy (EE) and the R\'{e}nyi entropy (RE) of multiple intervals in two-dimensional $T\overline{T}$-deformed conformal field theory (CFT) at finite temperature by field theoretic and holographic methods. First, by the replica method with the twist operators, we construct the general formula of the RE and EE up to the first order of a deformation parameter. By using our general formula, we show that the EE of multiple intervals for a holographic CFT is just a summation of the single interval case even with the small deformation. This is a non-trivial consequence from the field theory perspective, though it may be expected by the Ryu-Takayanagi formula in holography. However, the deformed RE of the two intervals is a summation of the single interval case only if the separations between the intervals are big enough. It can be understood by the tension of the cosmic branes dual to the RE. We also study the holographic EE for single and two intervals with an arbitrary cut-off radius (dual to the $T\overline{T}$ deformation) at any temperature. We confirm our holographic results agree with the field theory results with a small deformation and high temperature limit, as expected. For two intervals, there are two configurations for EE: disconnected ($s$-channel) and connected ($t$-channel) ones. We investigate the phase transition between them as we change parameters: as the deformation or temperature increases the phase transition is suppressed and the disconnected phase is more favored. | Entanglement and R\'{e}nyi Entropy of Multiple Intervals in $T\overline{T}$-Deformed CFT and Holography |
Using large $N$ arguments, we propose a scheme for calculating the two-point eigenvector correlation function for non-normal random matrices in the large $N$ limit. The setting generalizes the quaternionic extension of free probability to two-point functions. In the particular case of biunitarily invariant random matrices, we obtain a simple, general expression for the two-point eigenvector correlation function, which can be viewed as a further generalization of the single ring theorem. This construction has some striking similarities to the freeness of the second kind known for the Hermitian ensembles in large $N$. On the basis of several solved examples, we conjecture two kinds of microscopic universality of the eigenvectors - one in the bulk, and one at the rim. The form of the conjectured bulk universality agrees with the scaling limit found by Chalker and Mehlig [JT Chalker, B Mehlig, PRL, \textbf{81}, 3367 (1998)] in the case of the complex Ginibre ensemble. | Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach |
We present the GRjunction package which allows boundary surfaces and thin-shells in general relativity to be studied with a computer algebra system. Implementing the Darmois-Israel thin shell formalism requires a careful selection of definitions and algorithms to ensure that results are generated in a straight-forward way. We have used the package to correctly reproduce a wide variety of examples from the literature. We present several of these verifications as a means of demonstrating the packages capabilities. We then use GRjunction to perform a new calculation - joining two Kerr solutions with differing masses and angular momenta along a thin shell in the slow rotation limit. | Junctions and thin shells in general relativity using computer algebra I: The Darmois-Israel Formalism |
Starting from a self-dual $SU(\infty)$ Yang-Mills theory in $(2+2)$ dimensions, the Plebanski second heavenly equation is obtained after a suitable dimensional reduction. The self-dual gravitational background is the cotangent space of the internal two-dimensional Riemannian surface required in the formulation of $SU(\infty)$ Yang-Mills theory. A subsequent dimensional reduction leads to the KP equation in $(1+2)$ dimensions after the relationship from the Plebanski second heavenly function, $\Omega$, to the KP function, $u$, is obtained. Also a complexified KP equation is found when a different dimensional reduction scheme is performed . Such relationship between $\Omega$ and $u$ is based on the correspondence between the $SL(2,R)$ self-duality conditions in $(3+3)$ dimensions of Das, Khviengia, Sezgin (DKS) and the ones of $SU(\infty)$ in $(2+2)$ dimensions . The generalization to the Supersymmetric KP equation should be straightforward by extending the construction of the bosonic case to the previous Super-Plebanski equation, found by us in [1], yielding self-dual supergravity backgrounds in terms of the light-cone chiral superfield, $\Theta$, which is the supersymmetric analog of $\Omega$. The most important consequence of this Plebanski-KP correspondence is that $W$ gravity can be seen as the gauge theory of $\phi$-diffeomorphisms in the space of dimensionally-reduced $D=2+2,~SU^*(\infty)$ Yang-Mills instantons. These $\phi$ diffeomorphisms preserve a volume-three-form and are, precisely, the ones which provide the Plebanski-KP correspondence. | The KP Equation from Plebanski and $SU(\infty)$ Self-Dual Yang-Mills |
We provide Large Deviation estimates for the bridge of a $d$-dimensional general diffusion process as the conditioning time tends to $0$ and apply these results to the evaluation of the asymptotics of its exit time probabilities. We are motivated by applications to numerical simulation, especially in connection with stochastic volatility models. | Large Deviation asymptotics for the exit from a domain of the bridge of a general Diffusion |
Stirling Colgate was a remarkably imaginative physicist, an independent thinker with a wide breadth of interests and contagious enthusiasm, a born leader with enduring drive to attack fundamental problems in science. Among his many achievements, he founded the quantitative theory of stellar collapse and supernova explosions, and introduced numerical simulation into the astrophysical toolbox. He brought strong physical intuition to both theory and experiment, in the sciences of nuclear weapons, magnetic and inertial fusion, as well as astrophysics. | Biographical Memoir of Stirling Colgate |
The Reshetikhin - Turaeve approach to topological invariants of three - manifolds is generalized to quantum supergroups. A general method for constructing three - manifold invariants is developed, which requires only the study of the eigenvalues of certain central elements of the quantum supergroup in irreducible representations. To illustrate how the method works, $U_q(gl(2|1))$ at odd roots of unity is studied in detail, and the corresponding topological invariants are obtained. | Quantum supergroups and topological invariants of three - manifolds |
The capacity of the Gaussian wiretap channel model is analyzed when there are multiple antennas at the sender, intended receiver and eavesdropper. The associated channel matrices are fixed and known to all the terminals. A computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem. The converse is based on a Sato-type argument used in other broadcast settings, and the coding theorem is based on Gaussian wiretap codebooks. At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition, and independently coding across the resulting parallel channels. The associated capacity is expressed in terms of the corresponding generalized singular values. It is shown that a semi-blind "masked" multi-input multi-output (MIMO) transmission strategy that sends information along directions in which there is gain to the intended receiver, and synthetic noise along directions in which there is not, can be arbitrarily far from capacity in this regime. Necessary and sufficient conditions for the secrecy capacity to be zero are provided, which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed. The resulting scaling laws establish that to prevent secure communication, the eavesdropper needs 3 times as many antennas as the sender and intended receiver have jointly, and that the optimimum division of antennas between sender and intended receiver is in the ratio of 2:1. | Secure Transmission with Multiple Antennas II: The MIMOME Wiretap Channel |
We present a microscopic theory of cross-correlated noise processes, starting from a Hamiltonian system-reservoir description. In the proposed model, the system is nonlinearly coupled to a reservoir composed of harmonic oscillators, which in turn is driven by an external fluctuating force. We show that the resultant Langevin equation derived from the composite system (system+reservoir+external modulation) contains the essential features of cross-correlated noise processes. | Microscopic realization of cross-correlated noise processes |
Let $S_n=\frac{1}{n}X_nX_n^*$ where $X_n=\{X_{ij}\}$ is a $p\times n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)=\sqrt{p}({\mathbf {x}}_n(\mathbf {t}_1)^*(S_n+\sigma I)^{-1}{\mathbf {x}}_n(\mathbf {t}_2)-{\mathbf {x}}_n(\mathbf {t}_1)^*{\mathbf {x}}_n(\mathbf {t}_2)m_n(\sigma))$ in which $\sigma>0$ and $m_n(\sigma)=\int\frac{dF_{y_n}(x)}{x+\sigma}$ where $F_{y_n}(x)$ is the Mar\v{c}enko--Pastur law with parameter $y_n=p/n$; which converges to a positive constant as $n\to\infty$, and ${\mathbf {x}}_n(\mathbf {t}_1)$ and ${\mathbf {x}}_n(\mathbf {t}_2)$ are unit vectors in ${\Bbb{C}}^p$, having indices $\mathbf {t}_1$ and $\mathbf {t}_2$, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)$ converges weakly to a $(2m+1)$-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of $S_n$ is asymptotically close to that of a Haar-distributed unitary matrix. | Asymptotic properties of eigenmatrices of a large sample covariance matrix |
We present the detailed formalism of the extremely correlated Fermi liquid theory, developed for treating the physics of the t-J model. We start from the exact Schwinger equation of motion for the Greens function for projected electrons, and develop a systematic expansion in a parameter \lambda, relating to the double occupancy. The resulting Greens function has a canonical part arising from an effective Hamiltonian of the auxiliary electrons, and a caparison part, playing the role of a frequency dependent adaptive spectral weight. This adaptive weight balances the requirement at low \omega, of the invariance of the Fermi volume, and at high \omega, of decaying as c_0/(i \omega), with a correlation depleted c_0 <1. The effective Hamiltonian H_{eff} describing the auxiliary Fermions is given a natural interpretation with an effective interaction V_{eff} containing both the exchange J(ij), and the hopping parameters t(ij). It is made Hermitian by adding suitable terms that ultimately vanish, in the symmetrized theory developed in this paper. Simple but important shift invariances of the t-J model are noted with respect to translating its parameters uniformly. These play a crucial role in constraining the form of V_{eff} and also provide checks for further approximations. The auxiliary and physical Greens function satisfy two sum rules, and the Lagrange multipliers for these are identified. A complete set of expressions for the Greens functions to second order in \lambda is given, satisfying various invariances. A systematic iterative procedure for higher order approximations is detailed. A superconducting instability of the theory is noted at the simplest level with a high transition temperature. | Extremely Correlated Fermi Liquids: The Formalism |
We present a model for the formation of large organic molecules in dark clouds. The molecules are produced in the high density gas-phase that exists immediately after ice mantles are explosively sublimated. The explosions are initiated by the catastrophic recombination of trapped atomic hydrogen. We propose that, in molecular clouds, the processes of freeze-out onto ice mantles, accumulation of radicals, explosion and then rapid (three-body) gas-phase chemistry occurs in a cyclic fashion. This can lead to a cumulative molecular enrichment of the interstellar medium. A model of the time-dependent chemistries, based on this hypothesis, shows that significant abundances of large molecular species can be formed, although the complexity of the species is limited by the short expansion timescale in the gas, immediately following mantle explosion. We find that this mechanism may be an important source of smaller organic species, such as methanol and formaldehyde, as well as precursors to bio-molecule formation. Most significantly, we predict the gas-phase presence of these larger molecular species in quiescent molecular clouds and not just dynamically active regions, such as hot cores. As such the mechanism that we propose complements alternative methods of large molecule formation, such as those that invoke solid-state chemistry within activated ice mantles. | Episodic Explosions in Interstellar Ices |
We present a new method of estimating the distribution of sales rates of, e.g., book titles at an online bookstore, from the time evolution of ranking data found at websites of the store. The method is based on new mathematical results on an infinite particle limit of the stochastic ranking process, and is suitable for quantitative studies of the long tail structure of online retails. We give an example of a fit to the actual data obtained from Amazon.co.jp, which gives the Pareto slope parameter of the distribution of sales rates of the book titles in the store. | Mathematical analysis of long tail economy using stochastic ranking processes |
A bosonic topological order on $d$-dimensional closed space $\Sigma^d$ may have degenerate ground states. The space $\Sigma^d$ with different shapes (different metrics) form a moduli space ${\cal M}_{\Sigma^d}$. Thus the degenerate ground states on every point in the moduli space ${\cal M}_{\Sigma^d}$ form a complex vector bundle over ${\cal M}_{\Sigma^d}$. It was suggested that the collection of such vector bundles for $d$-dimensional closed spaces of all topologies completely characterizes the topological order. Using such a point of view, we propose a direct relation between two seemingly unrelated properties of 2+1-dimensional topological orders: (1) the chiral central charge $c$ that describes the many-body density of states for edge excitations (or more precisely the thermal Hall conductance of the edge), (2) the ground state degeneracy $D_g$ on closed genus $g$ surface. We show that $c D_g/2 \in \mathbb{Z},\ g\geq 3$ for bosonic topological orders. We explicitly checked the validity of this relation for over 140 simple topological orders. For fermionic topological orders, let $D_{g,\sigma}^{e}$ ($D_{g,\sigma}^{o}$) be the degeneracy with even (odd) number of fermions for genus-$g$ surface with spin structure $\sigma$. Then we have $2c D_{g,\sigma}^{e} \in \mathbb{Z}$ and $2c D_{g,\sigma}^{o} \in \mathbb{Z}$ for $g\geq 3$. | A relation between chiral central charge and ground state degeneracy in 2+1-dimensional topological orders |
This paper is devoted to some qualitative descriptions and some numerical results for ergodic Mean Field Games systems which arise, e.g., in the homogenization with a small noise limit. We shall consider either power type potentials or logarithmic type ones. In both cases, we shall establish some qualitative properties of the effective Hamiltonian $\bar H$ and of the effective drift $\bar b$. In particular we shall provide two cases where the effective system keeps/looses the Mean Field Games structure, namely where $\nabla_P \bar H(P,\alpha)$ coincides or not with $\bar b(P, \alpha)$. On the other hand, we shall provide some numerical tests validating the aforementioned qualitative properties of $\bar H$ and $\bar b$. In particular, we provide a numerical estimate of the discrepancy $\nabla_P \bar H(P,\alpha)-\bar b(P, \alpha)$. | An ergodic problem for Mean Field Games: qualitative properties and numerical simulations |
The secular evolution of disk galaxies is largely driven by resonances between the orbits of 'particles' (stars or dark matter) and the rotation of non-axisymmetric features (spiral arms or a bar). Such resonances may also explain kinematic and photometric features observed in the Milky Way and external galaxies. In simplified cases, these resonant interactions are well understood: for instance, the dynamics of a test particle trapped near a resonance of a steadily rotating bar is easily analyzed using the angle-action tools pioneered by Binney, Monari and others. However, such treatments do not address the stochasticity and messiness inherent to real galaxies - effects which have, with few exceptions, been previously explored only with complex N-body simulations. In this paper, we propose a simple kinetic equation describing the distribution function of particles near an orbital resonance with a rigidly rotating bar, allowing for diffusion of the particles' slow actions. We solve this equation for various values of the dimensionless diffusion strength $\Delta$, and then apply our theory to the calculation of bar-halo dynamical friction. For $\Delta = 0$ we recover the classic result of Tremaine & Weinberg that friction ultimately vanishes, owing to the phase-mixing of resonant orbits. However, for $\Delta > 0$ we find that diffusion suppresses phase-mixing, leading to a finite torque. Our results suggest that stochasticity - be it physical or numerical - tends to increase bar-halo friction, and that bars in cosmological simulations might experience significant artificial slowdown, even if the numerical two-body relaxation time is much longer than a Hubble time. | Galactic bar resonances with diffusion: an analytic model with implications for bar-dark matter halo dynamical friction |
The cosmological dynamics of a brane world scenario where the bulk action is taken as a generic function of the Ricci scalar is considered in a framework where the use of the $\mathbb{Z}_2$ symmetry and Israel junction conditions are relaxed. The corresponding cosmological solutions for some specific forms of $f(\mc{R})$ are obtained and shown to be in the form of exponential as well as power law for a vacuum brane space-time. It is shown that the existence of matter dominated epoch for a bulk action in the form of a power law for $\cal R$ can only be obtained in the presence of ordinary matter. Using phase space analysis, we show that the universe must start from an unstable matter dominated epoch and eventually falls into a stable accelerated expanding phase. | Cosmological dynamics of brane f(R) gravity |
Experimental observations suggest that proteins follow different pathways under different environmental conditions. We perform molecular dynamics simulations of a model of the SH3 domain over a broad range of temperatures, and identify distinct pathways in the folding transition. We determine the kinetic partition temperature --the temperature for which the SH3 domain undergoes a rapid folding transition with minimal kinetic barriers-- and observe that below this temperature the model protein may undergo a folding transition via multiple folding pathways. The folding kinetics is characterized by slow and fast pathways and the presence of only one or two intermediates. Our findings suggest the hypothesis that the SH3 domain, a protein for which only two-state folding kinetics was observed in previous experiments, may exhibit intermediates states under extreme experimental conditions, such as very low temperatures. A very recent report (Viguera et al., Proc. Natl. Acad. Sci. USA, 100:5730--5735, 2003) of an intermediate in the folding transition of the Bergerac mutant of the alpha-spectrin SH3 domain protein supports this hypothesis. | Multiple Folding Pathways of the SH3 domain |
Many research questions can be answered quickly and efficiently using data already collected for previous research. This practice is called secondary data analysis (SDA), and has gained popularity due to lower costs and improved research efficiency. In this paper we propose DFS, a file system to standardize the metadata representation of datasets, and DDU, a scalable architecture based on DFS for semi-automated metadata generation and data recommendation on the cloud. We discuss how DFS and DDU lays groundwork for automatic dataset aggregation, how it integrates with existing data wrangling and machine learning tools, and explores their implications on datasets stored in digital libraries. | DFS: A Dataset File System for Data Discovering Users |
The past decade and a half has seen the design and execution of several ground-based spectroscopic surveys, both Galactic and Extra-galactic. Additionally, new surveys are being designed that extend the boundaries of current surveys. In this context, many important considerations must be done when designing a spectrograph for the future. Among these is the determination of the optimum wavelength coverage. In this work, we present a new code for determining the wavelength ranges that provide the optimal amount of information to achieve the required science goals for a given survey. In its first mode, it utilizes a user-defined list of spectral features to compute a figure-of-merit for different spectral configurations. The second mode utilizes a set of flux-calibrated spectra, determining the spectral regions that show the largest differences among the spectra. Our algorithm is easily adaptable for any set of science requirements and any spectrograph design. We apply the algorithm to several examples, including 4MOST, showing the method yields important design constraints to the wavelength regions. | A new algorithm for optimizing the wavelength coverage for spectroscopic studies: Spectral Wavelength Optimization Code (SWOC) |
We study the deep connection between integrable models and Poisson-Lie T-duality working on a finite dimensional example constructed on SL(2,C) and its Iwasawa factors SU(2) and B. We shown the way in which Adler-Kostant-Symes theory and collective dynamics combine to solve the equivalent systems from solving the factorization problem of an exponential curve in SL(2,C). It is shown that the Toda system embraces the dynamics of the systems on SU(2) and B. | Integrable Systems and Poisson-Lie T-duality: a finite dimensional example |
Our goal is to investigate a close relative of the independent transversal problem in the class of infinite $K_n$-free graphs: we show that for any infinite $K_n$-free graph $G=(V,E)$ and $m\in \mathbb N$ there is a minimal $r=r(G,m)$ such that for any balanced $r$-colouring of the vertices of $G$ one can find an independent set which meets at least $m$ colour classes in a set of size $|V|$. Answering a conjecture of S. Thomass\'e, we express the exact value of $r(H_n,m)$ (using Ramsey-numbers for finite digraphs), where $H_n$ is Henson's countable universal homogeneous $K_n$-free graph. In turn, we deduce a new partition property of $H_n$ regarding balanced embeddings of bipartite graphs: for any finite bipartite $G$ with bipartition $A,B$, if the vertices of $H_n$ are partitioned into two infinite classes then there is an induced copy of $G$ in $H_n$ such that the images of $A$ and $B$ are contained in different classes. | Balanced independent sets in graphs omitting large cliques |
We present three Far Ultraviolet Spectroscopic Explorer (FUSE) observations of the Narrow-Line Seyfert 1 galaxy NGC4051. The most prominent features in the far-ultraviolet (FUV) spectrum are the OVI emission and absorption lines and the HI Lyman series absorption lines which are detected up to the Lyman edge. We also identify weak emission from NIII, CIII, and HeII. The CIII line shows absorption while none is detected in the NIII and HeII lines. In HI and CIII we detect two main absorption systems at outflow velocities of -50+/-30 and -240+/-40 km/s, as well as a possible third one at ~ -450 km/s. These systems are consistent in velocity with the 10 absorption systems found previously in CIV, NV, and SiIV, though the individual systems are blended together in the FUV spectrum. We estimate column densities of the two main absorption systems and find that the HI column density is lower for systems with larger outflow velocity. We detect no flux or spectral variations of NGC4051 at FUV wavelengths during three epochs spanning one year. This is consistent with the optical light curve which shows no variations between the three epochs. It is also consistent with the X-ray light curve which shows consistent flux levels at the three epochs of the FUSE observations, although the X-ray light curve shows strong variations on much shorter timescales. | Far Ultraviolet Spectroscopic Explorer Spectroscopy of Absorption and Emission Lines from the Narrow-Line Seyfert 1 Galaxy NGC 4051 |
Theoretically it has been known that breaking spin-degeneracy and effectively realizing 'spinless fermions' is a promising path to topological superconductors. Yet, topological superconductors are rare to date. Here, we propose to realize spinless fermions by splitting the spin-degeneracy in momentum space. Specifically, we identify monolayer hole-doped transition metal dichalcogenide (TMD)s as candidates for topological superconductors out of such momentum-space-split spinless fermions. Although electron-doped TMDs have recently been found superconducting, the observed superconductivity is unlikely topological due to the near spin-degeneracy. Meanwhile, hole-doped TMDs with momentum-space-split spinless fermions remain unexplored. Employing a renormalization group analysis, we propose that the unusual spin-valley locking in hole-doped TMDs together with repulsive interactions selectively favors two topological superconducting states: inter-pocket paired state with Chern number 2 and intra-pocket paired state with finite pair-momentum. A confirmation of our predictions will open up possibilities for manipulating topological superconductors on the device friendly platform of monolayer TMDs. | Topological superconductivity in monolayer transition metal dichalcogenides |
Supernova detection is a major objective of the Super-Kamiokande (SK) experiment. In the next stage of SK (SK-Gd), gadolinium (Gd) sulfate will be added to the detector, which will improve the ability of the detector to identify neutrons. A core-collapse supernova will be preceded by an increasing flux of neutrinos and anti-neutrinos, from thermal and weak nuclear processes in the star, over a timescale of hours; some of which may be detected at SK-Gd. This could provide an early warning of an imminent core-collapse supernova, hours earlier than the detection of the neutrinos from core collapse. Electron anti-neutrino detection will rely on inverse beta decay events below the usual analysis energy threshold of SK, so Gd loading is vital to reduce backgrounds while maximising detection efficiency. Assuming normal neutrino mass ordering, more than 200 events could be detected in the final 12 hours before core collapse for a 15-25 solar mass star at around 200 pc, which is representative of the nearest red supergiant to Earth, $\mathrm{\alpha}$Ori (Betelgeuse). At a statistical false alarm rate of 1 per century, detection could be up to 10 hours before core collapse, and a pre-supernova star could be detected by SK-Gd up to 600 pc away. A pre-supernova alert could be provided to the astrophysics community following gadolinium loading. | Sensitivity of Super-Kamiokande with Gadolinium to Low Energy Anti-neutrinos from Pre-supernova Emission |
We propose a construction of the Coulomb branch of a $3d\ {\mathcal N}=4$ gauge theory corresponding to a choice of a connected reductive group $G$ and a symplectic finite-dimensional reprsentation $\mathbf M$ of $G$, satisfying certain anomaly cancellation condition. This extends the construction of arXiv:1601.03586 (where it was assumed that ${\mathbf M}={\mathbf N}\oplus{\mathbf N}^*$ for some representation $\mathbf N$ of $G$). Our construction goes through certain "universal" ring object in the twisted derived Satake category of the symplectic group $Sp(2n)$. The construction of this object uses a categorical version of the Weil representation; we also compute the image of this object under the (twisted) derived Satake equivalence and show that it can be obtained from the theta-sheaf introduced by S.Lysenko on $\operatorname{Bun}_{Sp(2n)}({\mathbb P}^1)$ via certain Radon transform. We also discuss applications of our construction to a potential mathematical construction of $S$-duality for super-symmetric boundary conditions in 4-dimensional gauge theory and to (some extension of) the conjectures of D.Ben-Zvi, Y.Sakellaridis and A.Venkatesh. | Coulomb branches of noncotangent type (with appendices by Gurbir Dhillon and Theo Johnson-Freyd) |
In order to prepare the ground for evaluating classes of three-loop sum-integrals that are presently needed for thermodynamic observables, we take a fresh and systematic look on the few known cases, and review their evaluation in a unified way using coherent notation. We do this for three important cases of massless bosonic three-loop vacuum sum-integrals that have been frequently used in the literature, and aim for a streamlined exposition as compared to the original evaluations. In passing, we speculate on options for generalization of the computational techniques that have been employed. | A fresh look on three-loop sum-integrals |
Modern spectral synthesis codes need the thermally averaged free-free Gaunt factor defined over a very wide range of parameter space in order to produce an accurate prediction for the spectrum emitted by an ionized plasma. Until now no set of data exists that would meet this need in a fully satisfactory way. We have therefore undertaken to produce a table of very accurate non-relativistic Gaunt factors over a much wider range of parameters than has ever been produced before. We first produced a table of non-averaged Gaunt factors, covering the parameter space log10(epsilon_i) = -20 to +10 and log10(w) = -30 to +25. We then continued to produce a table of thermally averaged Gaunt factors covering the parameter space log10(gamma^2) = -6 to +10 and log10(u) = -16 to +13. Finally we produced a table of the frequency integrated Gaunt factor covering the parameter space log10(gamma^2) = -6 to +10. All the data presented in this paper are available online. | Accurate determination of the free-free Gaunt factor; I - non-relativistic Gaunt factors |
We apply the time-dependent variational principle of Balian-V\'en\'eroni to a system of self-interacting trapped bosons at finite temperature. The method leads to a set of coupled non-linear time dependent equations for the condensate density, the thermal cloud and the anomalous density. We solve numerically these equations in the static case for a harmonic trap. We analyze the various densities as functions of the radial distance and the temperature. We find an overall good qualitative agreement with recent experiments as well as with the results of many theoretical groups. We also discuss the behavior of the anomalous density at low temperatures owing to its importance to account for many-body effects. | Variational self-consistent theory for trapped Bose gases at finite temperature |
We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from pi, and delta, the strength of the incommensuration, are small. For free fermions, we use a continuum Dirac theory to show that there are an infinite number of bands which meet at zero energy as q approaches zero. In the limit that the ratio q/delta ---> 0, the number of states lying inside the q = 0 gap is nonzero and equal to 2 delta / pi^2. Thus the limit q ---> 0 differs from q = 0; this can be seen clearly in the behavior of the specific heat at low temperature. For interacting fermions or the XXZ spin-1/2 chain, we use bosonization to argue that similar results hold. | One-dimensional fermions with incommensurate hopping close to dimerization |
With the prevalence of LiDAR sensors in autonomous driving, 3D object tracking has received increasing attention. In a point cloud sequence, 3D object tracking aims to predict the location and orientation of an object in consecutive frames given an object template. Motivated by the success of transformers, we propose Point Tracking TRansformer (PTTR), which efficiently predicts high-quality 3D tracking results in a coarse-to-fine manner with the help of transformer operations. PTTR consists of three novel designs. 1) Instead of random sampling, we design Relation-Aware Sampling to preserve relevant points to the given template during subsampling. 2) We propose a Point Relation Transformer for effective feature aggregation and feature matching between the template and search region. 3) Based on the coarse tracking results, we employ a novel Prediction Refinement Module to obtain the final refined prediction through local feature pooling. In addition, motivated by the favorable properties of the Bird's-Eye View (BEV) of point clouds in capturing object motion, we further design a more advanced framework named PTTR++, which incorporates both the point-wise view and BEV representation to exploit their complementary effect in generating high-quality tracking results. PTTR++ substantially boosts the tracking performance on top of PTTR with low computational overhead. Extensive experiments over multiple datasets show that our proposed approaches achieve superior 3D tracking accuracy and efficiency. | Exploring Point-BEV Fusion for 3D Point Cloud Object Tracking with Transformer |
Nitrogen-vacancy (NV) centers in diamond have attracted a great deal of attention because of their possible use in information processing and electromagnetic sensing technologies. We examined theatomistic generation mechanism for the NV defect aligned in the [111] direction of C(111) substrates. We found that N is incorporated in the C bilayers during the lateral growth arising from a sequence of kink propagation along the step edge down to [-1,-1,2]. As a result, the atomic configuration with the N-atom lone-pair pointing in the [111] direction is formed, which causes preferential alignment of NVs. Our model is consistent with recent experimental data for perfect NV alignment in C(111) substrates. | Atomistic mechanism of perfect alignment of nitrogen-vacancy centers in diamond |
Deep neural networks (DNNs) have greatly contributed to the performance gains in semantic segmentation. Nevertheless, training DNNs generally requires large amounts of pixel-level labeled data, which is expensive and time-consuming to collect in practice. To mitigate the annotation burden, this paper proposes a self-ensembling generative adversarial network (SE-GAN) exploiting cross-domain data for semantic segmentation. In SE-GAN, a teacher network and a student network constitute a self-ensembling model for generating semantic segmentation maps, which together with a discriminator, forms a GAN. Despite its simplicity, we find SE-GAN can significantly boost the performance of adversarial training and enhance the stability of the model, the latter of which is a common barrier shared by most adversarial training-based methods. We theoretically analyze SE-GAN and provide an $\mathcal O(1/\sqrt{N})$ generalization bound ($N$ is the training sample size), which suggests controlling the discriminator's hypothesis complexity to enhance the generalizability. Accordingly, we choose a simple network as the discriminator. Extensive and systematic experiments in two standard settings demonstrate that the proposed method significantly outperforms current state-of-the-art approaches. The source code of our model is available online (https://github.com/YonghaoXu/SE-GAN). | Self-Ensembling GAN for Cross-Domain Semantic Segmentation |
Spin-orbit interaction provides a spin filtering effect in carbon nanotube based Cooper pair splitters that allows us to determine spin correlators directly from current measurements. The spin filtering axes are tunable by a global external magnetic field. By a bending of the nanotube the filtering axes on both sides of the Cooper pair splitter become sufficiently different that a test of entanglement of the injected Cooper pairs through the Bell inequality can be implemented. This implementation does not require noise measurements, supports imperfect splitting efficiency and disorder, and does not demand a full knowledge of the spin-orbit strength. Using a microscopic calculation we demonstrate that entanglement detection by violation of the Bell inequality is within the reach of current experimental setups. | Entanglement detection from conductance measurements in carbon nanotube Cooper pair splitters |
The subject of this thesis are various properties of quantum states that make them "non-classical" and their behaviour under unitary operations. In chapter 2 some basic concepts of quantum mechanics and quantum information are reviewed. In chapter 3 properties of quantum states analysed in the literature are identified. I chapter 4 relations between them are analysed: whether possessing of one property by a given state implies possessing another property by the same state. In chapter 5 the central notion of the thesis is introduced, namely possessing a given property in absolute vs. non-absolute way. A property is possessed by a given state in an absolute way if it is preserved under arbitrary unitary operation on this state. This will be applied notion to all properties listed in chapter 3. Two main questions asked here are as follows: Can a given property be possessed both in an absolute way and in a non-absolute way (by different classes of states)? If yes, what are necessary and sufficient conditions for a state possessing a given property in an absolute way? | Quantum correlations in composite systems under global unitary operations |
The Low Latency Fault Tolerance (LLFT) system provides fault tolerance for distributed applications, using the leader-follower replication technique. The LLFT system provides application-transparent replication, with strong replica consistency, for applications that involve multiple interacting processes or threads. The LLFT system comprises a Low Latency Messaging Protocol, a Leader-Determined Membership Protocol, and a Virtual Determinizer Framework. The Low Latency Messaging Protocol provides reliable, totally ordered message delivery by employing a direct group-to-group multicast, where the message ordering is determined by the primary replica in the group. The Leader-Determined Membership Protocol provides reconfiguration and recovery when a replica becomes faulty and when a replica joins or leaves a group, where the membership of the group is determined by the primary replica. The Virtual Determinizer Framework captures the ordering information at the primary replica and enforces the same ordering at the backup replicas for major sources of non-determinism, including multi-threading, time-related operations and socket communication. The LLFT system achieves low latency message delivery during normal operation and low latency reconfiguration and recovery when a fault occurs. | The Low Latency Fault Tolerance System |
In this article we apply a recently invented analytical real-space renormalization group formulation which is based on numerical concepts of the density matrix renormalization group. Within a rigorous mathematical framework we construct non-perturbative renormalization group transformations for the spin-1/2 XXX Heisenberg model in the finite temperature regime. The developed renormalization group scheme allows for calculating the renormalization group flow behaviour in the temperature dependent coupling constant. The constructed renormalization group transformations are applied within the ferromagnetic and the anti-ferromagnetic regime of the Heisenberg chain. The ferromagnetic fixed point is computed and compared to results derived by other techniques. | A non-perturbative real-space renormalization group scheme for the spin-1/2 XXX Heisenberg model |
We study heat kernels of Schr\"odinger operators whose kinetic terms are non-local operators built for sufficiently regular symmetric L\'evy measures with radial decreasing profiles and potentials belong to Kato class. Our setting is fairly general and novel -- it allows us to treat both heavy- and light-tailed L\'evy measures in a joint framework. We establish a certain relative-Kato bound for the corresponding semigroups and potentials. This enables us to apply a general perturbation technique to construct the heat kernels and give sharp estimates of them. Assuming that the L\'evy measure and the potential satisfy a little stronger conditions, we additionally obtain the regularity of the heat kernels. Finally, we discuss the applications to the smoothing properties of the corresponding semigroups. Our results cover many important examples of non-local operators, including fractional and quasi-relativistic Schr\"odinger operators. | Heat kernels of non-local Schr\"odinger operators with Kato potentials |
We study the (H\"older-)continuous behavior of the spectra belonging to a family of linear bounded operators $(A_t)_{t\in T}$ indexed by a topological space $T$. For the cases of self-adjoint, unitary and normal operators, a characterization of the continuity of $\Sigma:T\to \mathcal{K}(\mathbb{R}), t\mapsto \sigma(A_t),$ is proven while the distance of the spectra is measured by the Hausorff metric. If $T$ is a metric space, the H\"older-continuous behavior of $\Sigma$ is characterized for self-adjoint and unitary operators. Here we observe interesting effects, namely the rate of convergence is bisect whenever spectral gaps closes. Based on this, we provide a tool to prove the continuity of the spectra for large classes of operators. In particular, we apply this theory to generalized Schr\"odinger operators and show that the continuity of the spectra is characterized by the continuous variation of the underlying dynamical systems. Finally, we analyze the existence of periodic dynamical systems approximating a given dynamical system. This leads to periodic approximations of the corresponding Schr\"odinger operators by the previously developed theory. We prove that local symmetries of the patterns and the presence of a substitution is a sufficient criteria for periodic approximations of subshifts in $\mathbb{Z}^d$. For $d=1$, a characterization is proven for the existence of periodic approximations. For these approaches, the notion of a dictionary is further developed and defined independently of a given configuration. We prove that the set of dictionaries equipped with the local pattern topology is homeomorphic to the space of subshifts. This yields a useful tool to analyze these systems. Furthermore, it delivers the connection of the existence of periodic orbits in a subshift of finite type and the existence of periodic approximations for subshifts. | Spectral approximation of aperiodic Schr\"odinger operators |
We have used a combination of neutron resonant spin-echo and triple-axis spectroscopies to determine the energy, fine structure, and linewidth of the magnon resonance in the model spin-1/2 ladder antiferromagnet IPA-CuCl_3 at temperatures T << Delta_0 /k_B, where Delta_0 is the spin gap at T=0. In this low-temperature regime we find that the results deviate substantially from the predictions of the non-linear sigma model proposed as a description of magnon excitations in one-dimensional quantum magnets and attribute these deviations to real-space and spin-space anisotropies in the spin Hamiltonian as well as scattering of magnon excitations from a dilute density of impurities. These effects are generic to experimental realizations of one-dimensional quantum magnets. | Low Temperature Dynamics of Magnons in a Spin-1/2 Ladder Compound |
We investigate the resonant production of color octet muons in order to explore the discovery potential of the FCC-based \mu p colliders. It is shown that search potential of \mu p colliders essentially surpass potential of the LHC and would exceed that of FCC pp collider. | Resonant Production of Color Octet Muons at the Future Circular Collider Based Muon-Proton Colliders |
We present an investigation of the properties of the extended Ly$\alpha$ halo and the large-scale \ion{H}{I} absorbing structures associated with 5 high-redshift radio galaxies at z $>$ 2, using the Goodman long-slit spectrograph on the SOAR telescope, with the slit placed at large angles ($>$45$^{\circ}$) to the radio axis, to study regions that are unlikely to be illuminated by the active nucleus. Spatially extended Ly$\alpha$ emission is detected with large line widths (FWHM = 1000 -- 2500 km s$^{-1}$), which although impacted by resonant scattering, is suggestive of turbulent motion. We find a correlation between higher blueshifts and higher FWHM, which is an indication that radial motion dominates the bulk gas dynamics perpendicular to the radio axis, although we are unable to distinguish between outflow and infall scenarios due to the resonant nature of the Ly$\alpha$ line. Extended, blueshifted Ly$\alpha$ absorption is detected in the direction perpendicular to the radio axis in three radio galaxies with minimum spatial extents ranging from $\gtrsim$27 kpc to $\gtrsim$35 kpc, supporting the idea that the absorbing structure covers the entire Ly$\alpha$ halo, consistent with being part of a giant, expanding shell of gas enveloping the galaxy and its (detected) gaseous halo. | Detection of large scale Ly$\alpha$ absorbers at large angles to the radio axis of high-redshift radio galaxies using SOAR |
We introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric $q$-Whittaker functions. In particular, we show that the series part of the nonsymmetric $q$-Whittaker function is a generating function for the graded characters of generalized global Weyl modules. | Generalized Weyl modules and nonsymmetric $q$-Whittaker functions |
We introduce Bayesian QuickNAT for the automated quality control of whole-brain segmentation on MRI T1 scans. Next to the Bayesian fully convolutional neural network, we also present inherent measures of segmentation uncertainty that allow for quality control per brain structure. For estimating model uncertainty, we follow a Bayesian approach, wherein, Monte Carlo (MC) samples from the posterior distribution are generated by keeping the dropout layers active at test time. Entropy over the MC samples provides a voxel-wise model uncertainty map, whereas expectation over the MC predictions provides the final segmentation. Next to voxel-wise uncertainty, we introduce four metrics to quantify structure-wise uncertainty in segmentation for quality control. We report experiments on four out-of-sample datasets comprising of diverse age range, pathology and imaging artifacts. The proposed structure-wise uncertainty metrics are highly correlated with the Dice score estimated with manual annotation and therefore present an inherent measure of segmentation quality. In particular, the intersection over union over all the MC samples is a suitable proxy for the Dice score. In addition to quality control at scan-level, we propose to incorporate the structure-wise uncertainty as a measure of confidence to do reliable group analysis on large data repositories. We envisage that the introduced uncertainty metrics would help assess the fidelity of automated deep learning based segmentation methods for large-scale population studies, as they enable automated quality control and group analyses in processing large data repositories. | Bayesian QuickNAT: Model Uncertainty in Deep Whole-Brain Segmentation for Structure-wise Quality Control |
Auger-ionized carriers in a one-dimensional semiconductor are predicted to result in a strong band-gap renormalization. Isolated single-walled carbon nanotubes (SWCNT) under high-intensity laser irradiation exhibit strong nonlinear photoluminescence (PL) due to exciton-exciton annihilation (EEA). The presence of exciton disassociation during the rapid Auger-ionization caused by EEA would lead to a strong nonlinear absorption. By simultaneously measuring SWCNT PL and optical absorption of isolated SWCNT clusters in the PL saturation regime, we give evidence that Auger-ionized excitons do not disassociate but remain bound. | Independence of Optical Absorption on Auger Ionization in Single-Walled Carbon Nanotubes Revealed by Ultrafast e-h Photodoping |
We study the stability of five-dimensional Myers-Perry black holes with a single angular momentum under linear perturbations, and we compute the quasinormal modes (QNM's) of the black hole metric projected on the brane, using Leaver's continued fraction method. In our numerical search we do not find unstable modes. The damping time of modes having l=m=2 and l=m=1 tends to infinity as the black hole spin tends to the extremal value, showing a behaviour reminiscent of the one observed for ordinary 4-dimensional Kerr black holes. | Stability of five-dimensional rotating black holes projected on the brane |
We consider the imprints of local massive defects, such as a black hole or a massive monopole, during inflation. The massive defect breaks the background homogeneity. We consider the limit that the physical Schwarzschild radius of the defect is much smaller than the inflationary Hubble radius so a perturbative analysis is allowed. The inhomogeneities induced in scalar and gravitational wave power spectrum are calculated. We obtain the amplitudes of dipole, quadrupole and octupole anisotropies in curvature perturbation power spectrum and identify the relative configuration of the defect to CMB sphere in which large observable dipole asymmetry can be generated. We observe a curious reflection symmetry in which the configuration where the defect is inside the CMB comoving sphere has the same inhomogeneous variance as its mirror configuration where the defect is outside the CMB sphere. | Primordial inhomogeneities from massive defects during inflation |
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on several dynamical processes taking place on the network. In addition, several practical situations, such as transit in cities, can benefit by modifying a network so as to reduce the respective shortest paths. In the present work, we addressed the problem of trying to reduce the average shortest path of several theoretical and real-world complex networks by adding a given number of links according to different strategies. More specifically, we considered: placing new links between nodes with relatively low and high degrees; to enhance the degree regularity of the network; preferential attachment according to the degree; linking nodes with relatively low and high betweenness centrality; and linking nodes with relatively low/low, low/high, and high/high accessibilities. Several interesting results have been obtained, including the identification of the accessibility-based strategies as providing the largest reduction of the average shortest path length. Another interesting finding is that, for several types of networks, the degree-based methods tend to provide improvements comparable to those obtained by using the much more computationally expensive betweenness centrality measurement. | Shortest Paths in Complex Networks: Structure and Optimization |
The energy spectrum for the problem of 8-Pmmn borophene's electronic carriers under perpendicular incidence of electromagnetic waves is studied without the use of any perturbative technique. This allows to study the effects of very strong fields. To obtain the spectrum and wavefunctions, the time-dependent Dirac equation is solved by using a frame moving with the space-time cone of the wave, i.e., by transforming the equation into an ordinary differential equation in terms of the wave-phase, leading to an electron-wave quasiparticle. The limiting case of strong fields is thus analyzed.The resulting eigenfunctions obey a generalized Mathieu equation,i.e., of a classical parametric pendulum. The energy spectrum presents bands, and a gap at the Fermi energy. The gaps are due to the space-time diffraction of electrons in phase with the electromagnetic field, i.e., electrons in borophene acquire an effective mass under strong electromagnetic radiation | Metal-Insulator transition in 8-Pmmn Borophene under perpendicular incidence of electromagnetic radiation |
The paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system. The operators appearing in the system equations were fractional versions in the spectral sense of general linear operators A and B having compact resolvents and are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. The associated double-well potentials driving the phase separation process modeled by the Cahn-Hilliard system could be of a very general type that includes standard physically meaningful cases such as polynomial, logarithmic, and double obstacle nonlinearities. In the subsequent paper arXiv:1807.03218, an analysis of distributed optimal control problems was performed for such evolutionary systems, where only the differentiable case of certain polynomial and logarithmic double-well potentials could be admitted. Results concerning existence of optimizers and first-order necessary optimality conditions were derived. In the present paper, we complement these results by studying a distributed control problem for such evolutionary systems in the case of nondifferentiable nonlinearities of double obstacle type. For such nonlinearities, it is well known that the standard constraint qualifications cannot be applied to construct appropriate Lagrange multipliers. To overcome this difficulty, we follow here the so-called "deep quench" method. We first give a general convergence analysis of the deep quench approximation that includes an error estimate and then demonstrate that its use leads in the double obstacle case to appropriate first-order necessary optimality conditions in terms of a variational inequality and the associated adjoint state system. | Deep quench approximation and optimal control of general Cahn-Hilliard systems with fractional operators and double obstacle potentials |