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Inverse optimization (IO) aims to determine optimization model parameters from observed decisions. However, IO is not part of a data scientist's toolkit in practice, especially as many general-purpose machine learning packages are widely available as an alternative. When encountering IO, practitioners face the question of when, or even whether, investing in developing IO methods is worthwhile. Our paper provides a starting point toward answering these questions, focusing on the problem of imputing the objective function of a parametric convex optimization problem. We compare the predictive performance of three standard supervised machine learning (ML) algorithms (random forest, support vector regression and Gaussian process regression) to the performance of the IO model of Keshavarz, Wang, and Boyd (2011). While the IO literature focuses on the development of methods tailored to particular problem classes, our goal is to evaluate general "out-of-the-box" approaches. Our experiments demonstrate that determining whether to use an ML or IO approach requires considering (i) the training set size, (ii) the dependence of the optimization problem on external parameters, (iii) the level of confidence with regards to the correctness of the optimization prior, and (iv) the number of critical regions in the solution space. | math.OC |
The influence of dark matter particle decay on the baryon-to-photon ratio has been studied for different cosmological epochs. We consider different parameter values of dark matter particles such as mass, lifetime, the relative fraction of dark matter particles. It is shown that the modern value of the dark matter density $\Omega_{\rm CDM}=0.26$ is enough to lead to variation of the baryon-to-photon ratio up to $\Delta \eta / \eta \sim 0.01 \div 1$ for decays of the particles with masses 10 GeV $\div$ 1 TeV. However, such processes can also be accompanied by emergence of an excessive gamma ray flux. The observational data on the diffuse gamma ray background are used to making constraints on the dark matter decay models and on the maximum possible variation of the baryon-to-photon ratio $\Delta\eta/\eta\lesssim10^{-5}$. Detection of such variation of the baryon density in future cosmological experiments can serve as a powerful means of studying properties of dark matter particles. | astro-ph.CO |
Let $k$ be a field of characteristic $p>0$ not necessarily perfect. Using Berthelot's theory of arithmetic $\mathcal{D}$-modules, we construct a $p$-adic formalism of Grothendieck's six operations for realizable $k$-schemes of finite type. | math.AG |
A celebrated theorem of P.M.Cohn says that for any two division rings (not necessarily finite dimensional) over a field F, their amalgamated product over F is a domain which can be embedded in a division ring. Note that even with the two initial division rings begin finite dimensional over their centers, the resulting division ring is never finite dimensional over its center. Perhaps this led Lance Small to ask the following question. Assume $F_1$ and $F_2$ are fields with the same characteristic. Small asked whether any two division algebras $D_1/F_1$ and $D_2/F_2$ can be embedded in some third division algebra $E/F$. We start with a surprisingly straightforward counterexample, but then show that a positive solution exists for division algebras finitely generated over a common subfield which is either algebraically closed or the prime subfield. | math.RA |
In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show the convergence of the random finite element error in expectation and, when the noise is sub-Gaussian, in the Orlicz 2- norm which implies the probability that the finite element error estimates are violated decays exponentially. Numerical examples are included. | math.NA |
The $k^{\text{th}}$ power of a graph $G=(V,E)$, $G^k$, is the graph whose vertex set is $V$ and in which two distinct vertices are adjacent if and only if their distance in $G$ is at most $k$. This article proves various eigenvalue bounds for the independence number and chromatic number of $G^k$ which purely depend on the spectrum of $G$, together with a method to optimize them. Our bounds for the $k$-independence number also work for its quantum counterpart, which is not known to be a computable parameter in general, thus justifying the use of integer programming to optimize them. Some of the bounds previously known in the literature follow as a corollary of our main results. Infinite families of graphs where the bounds are sharp are presented as well. | math.CO |
Story generation and understanding -- as with all NLG/NLU tasks -- has seen a surge in neurosymbolic work. Researchers have recognized that, while large language models (LLMs) have tremendous utility, they can be augmented with symbolic means to be even better and to make up for any flaws that the neural networks might have. However, symbolic methods are extremely costly in terms of the amount of time and expertise needed to create them. In this work, we capitalize on state-of-the-art Code-LLMs, such as Codex, to bootstrap the use of symbolic methods for tracking the state of stories and aiding in story understanding. We show that our CoRRPUS system and abstracted prompting procedures can beat current state-of-the-art structured LLM techniques on pre-existing story understanding tasks (bAbI Task 2 and Re^3) with minimal hand engineering. We hope that this work can help highlight the importance of symbolic representations and specialized prompting for LLMs as these models require some guidance for performing reasoning tasks properly. | cs.CL |
The Santa Cruz Institute for Particle Physics (SCIPP) continues to be engaged in research and development towards an ILC detector. The latest efforts at SCIPP are described, including those associated with the LSTFE front-end readout ASIC, the use of charge division to obtain a longitudinal coordinate from silicon strip detectors, and the contribution of strip resistance to readout noise. | physics.ins-det |
The generating curves of rotational minimal surfaces in the de Sitter space $\s_1^3$ are characterized as solutions of a variational problem. It is proved that these curves are the critical points of the center of mass among all curves of $\s_1^2$ with prescribed endpoints and fixed length. This extends the known properties of the catenary and the catenoid in the Euclidean setting. | math.DG |
Including terrain in atmospheric models gives rise to mesh distortions near the lower boundary that can degrade accuracy and challenge the stability of transport schemes. Multidimensional transport schemes avoid splitting errors on distorted, arbitrary meshes, and method-of-lines schemes have low computational cost because they perform reconstructions at fixed points. This paper presents a multidimensional method-of-lines finite volume transport scheme, "cubicFit", which is designed to be numerically stable on arbitrary meshes. Stability conditions derived from a von Neumann stability analysis are imposed during model initialisation to obtain stability and improve accuracy in distorted regions of the mesh, and near steeply-sloping lower boundaries. Reconstruction calculations depend upon the mesh only, needing just one vector multiply per face per time-stage irrespective of the velocity field. The cubicFit scheme is evaluated using three, idealised numerical tests. The first is a variant of a standard horizontal transport test on severely distorted terrain-following meshes. The second is a new test case that assesses accuracy near the ground by transporting a tracer at the lower boundary over steep terrain on terrain-following meshes, cut-cell meshes, and new, slanted-cell meshes that do not suffer from severe time-step constraints associated with cut cells. The third, standard test deforms a tracer in a vortical flow on hexagonal-icosahedral meshes and cubed-sphere meshes. In all tests, cubicFit is stable and largely insensitive to mesh distortions, and cubicFit results are more accurate than those obtained using a multidimensional linear upwind transport scheme. The cubicFit scheme is second-order convergent regardless of mesh distortions. | math.NA |
Wavelength calibration is a routine and critical part of any spectral work-flow, but many astronomers still resort to matching detected peaks and emission lines by hand. We present RASCAL (RANSAC Assisted Spectral CALibration), a python library for automated wavelength calibration of astronomical spectrographs. RASCAL implements recent state-of-the-art methods for wavelength calibration and requires minimal input from a user. In this paper we discuss the implementation of the library and apply it to real-world calibration spectra. | astro-ph.IM |
Clifford's geometric algebra has enjoyed phenomenal development over the last 60 years by mathematicians, theoretical physicists, engineers and computer scientists in robotics, artificial intelligence and data analysis, introducing a myriad of different and often confusing notations. The geometric algebra of Euclidean 3-space, the natural generalization of both the well-known Gibbs-Heaviside vector algebra, and Hamilton's quaternions, is used here to study spheroidal domains, spheroidal-graphic projections, the Laplace equation and its Lie algebra of symmetries. The Cauchy-Kovalevska extension and the Cauchy kernel function are treated in a unified way. The concept of a quasi-monogenic family of functions is introduced and studied. | math.GM |
We update the study of the polarisation of J/psi produced in proton-proton collisions at RHIC at sqrt(s)=200 GeV using the QCD-based Colour-Singlet Model (CSM), including next-to-leading order partonic matrix elements from gluon and light quark fusion and leading-order contributions from charm-quark initiated processes. To do so, we also evaluate the corresponding cross section differential in P_T which agrees qualitatively with the measurements of PHENIX in the central and forward regions at low P_T -- for instance below 2 GeV --, while emphasising the need for Initial State Radiation (ISR) resummation. At mid P_T, we also compare the measurements from PHENIX and STAR with the same evaluation complemented with the dominant alphaS^5 contributions (NNLO*). We find a reasonable agreement with the data. Regarding the polarisation, as shown for previous studies at larger sqrt(s) and P_T, the polarisation pattern from gluon and light quark fusion in the helicity frame is drastically modified at NLO and is shown to be increasingly longitudinal. The yield from charm-gluon fusion is found to be slightly transversally polarised. Combining both these contributions with a data-driven range for the polarisation of J/psi from chi_c, we eventually provide an evaluation of the polarisation of the prompt J/psi yield which is in a good agreement with the experimental data from PHENIX both in the central and forward regions. | hep-ex;hep-ph;nucl-ex;nucl-th |
While 5G is being tested worldwide and anticipated to be rolled out gradually in 2019, researchers around the world are beginning to turn their attention to what 6G might be in 10+ years time, and there are already initiatives in various countries focusing on the research of possible 6G technologies. This article aims to extend the vision of 5G to more ambitious scenarios in a more distant future and speculates on the visionary technologies that could provide the step changes needed for enabling 6G. | cs.NI |
This paper considers a dual-hop amplify-and-forward (AF) relaying system where the relay is equipped with multiple antennas, while the source and the destination are equipped with a single antenna. Assuming that the relay is subjected to co-channel interference (CCI) and additive white Gaussian noise (AWGN) while the destination is corrupted by AWGN only, we propose three heuristic relay precoding schemes to combat the CCI, namely, 1) Maximum ratio combining/maximal ratio transmission (MRC/MRT), 2) Zero-forcing/MRT (ZF/MRT), 3) Minimum mean-square error/MRT (MMSE/MRT). We derive new exact outage expressions as well as simple high signal-to-noise ratio (SNR) outage approximations for all three schemes. Our findings suggest that both the MRC/MRT and the MMSE/MRT schemes achieve a full diversity of N, while the ZF/MRT scheme achieves a diversity order of N-M, where N is the number of relay antennas and M is the number of interferers. In addition, we show that the MMSE/MRT scheme always achieves the best outage performance, and the ZF/MRT scheme outperforms the MRC/MRT scheme in the low SNR regime, while becomes inferior to the MRC/MRT scheme in the high SNR regime. Finally, in the large N regime, we show that both the ZF/MRT and MMSE/MRT schemes are capable of completely eliminating the CCI, while perfect interference cancelation is not possible with the MRC/MRT scheme. | cs.IT;math.IT |
The very early universe provides the best arena we currently have to test quantum gravity theories. The success of the inflationary paradigm in accounting for the observed inhomogeneities in the cosmic microwave background already illustrates this point to a certain extent because the paradigm is based on quantum field theory on the curved cosmological space-times. However, this analysis excludes the Planck era because the background space-time satisfies Einstein's equations all the way back to the big bang singularity. Using techniques from loop quantum gravity, the paradigm has now been extended to a self-consistent theory from the Planck regime to the onset of inflation, covering some 11 orders of magnitude in curvature. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects, such as a modification of the consistency relation involving the scalar and tensor power spectra and a new source for non-Gaussianities. Thus, the genesis of the large scale structure of the universe can be traced back to quantum gravity fluctuations \emph{in the Planck regime}. This report provides a bird's eye view of these developments for the general relativity community. | astro-ph.CO;gr-qc;hep-th |
This paper is an exploratory analysis into fraud detection taking Enron email corpus as the case study. The paper posits conclusions like strict servitude and unquestionable faith among employees as breeding grounds for sham among higher executives. We also try to infer on the nature of communication between fraudulent employees and between non- fraudulent-fraudulent employees | cs.CL |
Unique optical properties of semiconductor nanoparticles (SN) make them very promising in the multitude of applications including lasing, light emission and photovoltaics. In many of these applications it is imperative to understand the physics of interaction of electrons in a SN with external electromagnetic fields on the quantitative level. In particular, the strength of electron-photon coupling determines such important SN parameters as the radiative lifetime and absorption cross section. This strength is often assumed to be fully encoded by the so called Kane momentum matrix element. This parameter, however, pertains to a bulk semiconductor material and, as such, is not sensitive to the quantum confinement effects in SNs. In this work we demonstrate that the quantum confinement, via the so called band mixing, can result in a significant suppression of the strength of electron interaction with electromagnetic field. Within the envelope function formalism we show how this suppression can be described by introducing an effective energy-dependent Kane momentum. Then, the effect of band mixing on the efficiencies of various photoinduced processes can be fully captured by the conventional formulae (e.g., spontaneous emission rate), once the conventional Kane momentum is substituted with the renormalized energy-dependent Kane momentum introduced in here. As an example, we evaluate the energy-dependent Kane momentum for spherical $\rm{PbSe}$ and $\rm{PbS}$ SNs (i.e., quantum dots) and show that neglecting band mixing in these systems can result in the overestimation of absorption cross sections and emission rates by a factor of $\sim$2. | cond-mat.mes-hall |
Nowadays, most business and social interactions have moved to the internet, highlighting the relevance of creating online trust. One way to obtain a measure of trust is through reputation mechanisms, which record one's past performance and interactions to generate a reputational value. We observe that numerous existing reputation mechanisms share similarities with actual social phenomena; we call such mechanisms 'social reputation mechanisms'. The aim of this paper is to discuss several social phenomena and map these to existing social reputation mechanisms in a variety of scopes. First, we focus on reputation mechanisms in the individual scope, in which everyone is responsible for their own reputation. Subjective reputational values may be communicated to different entities in the form of recommendations. Secondly, we discuss social reputation mechanisms in the acquaintances scope, where one's reputation can be tied to another through vouching or invite-only networks. Finally, we present existing social reputation mechanisms in the neighbourhood scope. In such systems, one's reputation can heavily be affected by the behaviour of others in their neighbourhood or social group. | cs.DC |
In the present paper, we generalized some notions of bounded operators to un- bounded operators on Hilbert space such as k-quasihyponormal and k-paranormal unbounded operators. Furthermore, we extend the Kaplansky theorem for normal operators to some (p; k)-quasihyponormal operators. Namely the (p; k)-quasihyponormality of the product AB and BA for two operators. | math.FA |
The occurrence of new textures of liquid crystals is an important factor in tuning their optical and photonics properties. Here, we show, both experimentally and by numerical computation, that under an electric field chitin tactoids (i.e. nematic droplets) can stretch to aspect ratios of more than 15, leading to a transition from a spindle-like to a cigar-like shape. We argue that the large extensions occur because the elastic contribution to the free energy is dominated by the anchoring. We demonstrate that the elongation involves hydrodynamic flow and is reversible, the tactoids return to their original shapes upon removing the field. | cond-mat.soft |
We investigate a general framework of multiplicative multitask feature learning which decomposes each task's model parameters into a multiplication of two components. One of the components is used across all tasks and the other component is task-specific. Several previous methods have been proposed as special cases of our framework. We study the theoretical properties of this framework when different regularization conditions are applied to the two decomposed components. We prove that this framework is mathematically equivalent to the widely used multitask feature learning methods that are based on a joint regularization of all model parameters, but with a more general form of regularizers. Further, an analytical formula is derived for the across-task component as related to the task-specific component for all these regularizers, leading to a better understanding of the shrinkage effect. Study of this framework motivates new multitask learning algorithms. We propose two new learning formulations by varying the parameters in the proposed framework. Empirical studies have revealed the relative advantages of the two new formulations by comparing with the state of the art, which provides instructive insights into the feature learning problem with multiple tasks. | cs.LG |
We propose a Topic Compositional Neural Language Model (TCNLM), a novel method designed to simultaneously capture both the global semantic meaning and the local word ordering structure in a document. The TCNLM learns the global semantic coherence of a document via a neural topic model, and the probability of each learned latent topic is further used to build a Mixture-of-Experts (MoE) language model, where each expert (corresponding to one topic) is a recurrent neural network (RNN) that accounts for learning the local structure of a word sequence. In order to train the MoE model efficiently, a matrix factorization method is applied, by extending each weight matrix of the RNN to be an ensemble of topic-dependent weight matrices. The degree to which each member of the ensemble is used is tied to the document-dependent probability of the corresponding topics. Experimental results on several corpora show that the proposed approach outperforms both a pure RNN-based model and other topic-guided language models. Further, our model yields sensible topics, and also has the capacity to generate meaningful sentences conditioned on given topics. | cs.CL;cs.LG |
Observations of quasars at redshifts z > 6 reveal that 10^9 Msol supermassive black holes (SMBHs) had already formed when the Universe was < 0.9 Gyr old. One hypothesis for the origins of these SMBHs is that they grew from the remnants of the first generation of massive stars, which formed in low-mass (~ 10^5 to 10^6 Msol) dark matter minihaloes at z > 20. This is the regime where baryonic streaming motions--the relative velocities of baryons with respect to dark matter in the early Universe--most strongly inhibit star formation by suppressing gas infall and cooling. We investigate the impact of this effect on the growth of the first SMBHs using a suite of high-fidelity, ellipsoidal-collapse Monte Carlo merger-tree simulations. We find that the suppression of seed BH formation by the streaming motions significantly reduces the number density of the most massive BHs at z > 15, but the residual effect at lower redshifts is essentially negligible. The streaming motions can reduce by a factor of few the number density of the most luminous quasars at z ~ 10-11, where such objects could be detected by the James Webb Space Telescope. We conclude, with minor theoretical caveats, that baryonic streaming motions are unlikely to pose a significant additional obstacle to the formation of the observed high-redshift quasar SMBHs. Nor do they appreciably affect the heating and reionization histories of the Universe or the merger rates of nuclear BHs in the mass and redshift ranges of interest for proposed gravitational-wave detectors. | astro-ph.CO |
We investigate the nature of the Bose glass phase of the disordered Bose-Hubbard model in $d>2$ and demonstrate the existence of a glass-like replica symmetry breaking (RSB) order parameter in terms of particle number fluctuations. Starting from a strong-coupling expansion around the atomic limit, we study the instability of the Mott insulator towards the formation of a Bose glass. We add some infinitesimal RSB, following the Parisi hierarchical approach in the most general form, and observe its flow under the momentum-shell renormalization group scheme. We find a new fixed point with one-step RSB, corresponding to the transition between the Mott insulator and a Bose glass phase with hitherto unseen RSB. The susceptibility associated to infinitesimal RSB perturbation in the Mott insulator is found to diverge at the transition with an exponent of $\gamma=1/d$. Our findings are consistent with the expectation of glassy behavior and the established breakdown of self-averaging. We discuss the possibility of measuring the glass-like order parameter in optical lattice experiments as well as in certain spin systems that are in the same universality class as the Bose-Hubbard model. | cond-mat.dis-nn |
Time series classification (TSC) is the problem of learning labels from time dependent data. One class of algorithms is derived from a bag of words approach. A window is run along a series, the subseries is shortened and discretised to form a word, then features are formed from the histogram of frequency of occurrence of words. We call this type of approach to TSC dictionary based classification. We compare four dictionary based algorithms in the context of a wider project to update the great time series classification bakeoff, a comparative study published in 2017. We experimentally characterise the algorithms in terms of predictive performance, time complexity and space complexity. We find that we can improve on the previous best in terms of accuracy, but this comes at the cost of time and space. Alternatively, the same performance can be achieved with far less cost. We review the relative merits of the four algorithms before suggesting a path to possible improvement. | cs.LG;stat.ML |
Posted price mechanisms (PPM) constitute one of the predominant practices to price goods in online marketplaces and their revenue guarantees have been a central object of study in the last decade. We consider a basic setting where the buyers' valuations are independent and identically distributed and there is a single unit on sale. It is well-known that this setting is equivalent to the so-called i.i.d. prophet inequality, for which optimal guarantees are known and evaluate to 0.745 in general (equivalent to a PPM with dynamic prices) and $1 - 1/e \approx 0.632$ in the fixed threshold case (equivalent to a fixed price PPM). In this paper we consider an additional assumption, namely, that the underlying market is very large. This is modeled by first fixing a valuation distribution F and then making the number of buyers grow large, rather than considering the worst distribution for each possible market size. In this setting Kennedy and Kertz [Ann. Probab. 1991] breaks the 0.745 fraction achievable in general with a dynamic threshold policy. We prove that this large market benefit continue to hold when using fixed price PPMs, and show that the guarantee of 0.632 actually improves to 0.712. We then move to study the case of selling k identical units and we prove that the revenue gap of the fixed price PPM approaches $1-1/\sqrt{ 2k\pi}$. As this bound is achievable without the large market assumption, we obtain the somewhat surprising result that the large market advantage vanishes as $k$ grows. | math.OC |
In quantum information and communication one looks for the non-classical features like interference and quantum correlations to harness the true power of composite systems. We show how the concept akin to interference is, in fact, intertwined in a quantitative manner to entanglement and quantum correlation. In particular, we prove that the difference in the squared visibility for a density operator before and after a complete measurement, averaged over all unitary evolutions, is directly related to the quantum correlation measure based on the measurement disturbance. For pure and mixed bipartite states the unitary average of the squared visibility is related to entanglement measure. This may constitute direct detection of entanglement and quantum correlations with quantum interference setups. Furthermore, we prove that for a fixed purity of the subsystem state, there is a complementarity relation between the linear entanglement of formation and the measurement disturbance. This brings out a quantitative difference between two kinds of quantum correlations. | math.MP;math-ph;quant-ph |
We aim to investigate the ability of simple spectral models to describe the GRB early afterglow emission. We performed a time resolved spectral analysis of a bright GRB sample detected by the Swift Burst Alert Telescope and promptly observed by the Swift X-ray Telescope,with spectroscopically measured redshift in the period April 2005 -- January 2007. The sample consists of 22 GRBs and a total of 214 spectra. We restricted our analysis to the softest spectra sub--sample which consists of 13 spectra with photon index > 3. In this sample we found that four spectra, belonging to GRB060502A, GRB060729, GRB060904B, GRB061110A prompt--afterglow transition phase, cannot be modeled neither by a single power law nor by the Band model. Instead we find that the data present high energy (> 3 keV, in the observer frame) excesses with respect to these models. We estimated the joint statistical significance of these excesses at the level of 4.3 sigma. In all four cases, the deviations can be modeled well by adding either a second power law or a blackbody component to the usual synchrotron power law spectrum. The additional power law would be explained by the emerging of the afterglow, while the blackbody could be interpreted as the photospheric emission from X-ray flares or as the shock breakout emission. In one case these models leave a 2.2 sigma excess which can be fit by a Gaussian line at the energy the highly ionized Nickel recombination. Although the data do not allow an unequivocal interpretation, the importance of this analysis consists in the fact that we show that a simple power law model or a Band model are insufficient to describe the X-ray spectra of a small homogeneous sample of GRBs at the end of their prompt phase. | astro-ph |
We present multi-epoch optical spectra of the $\gamma$-ray bright blazar 1156+295 (4C +29.45, Ton 599) obtained with the 4.3~m Lowell Discovery Telescope. During a multi-wavelength outburst in late 2017, when the $\gamma$-ray flux increased to $2.5\times 10^{-6} \; \rm phot\; cm^{-2}\; s^{-1}$ and the quasar was first detected at energies $\geq100$ GeV, the flux of the Mg II $\lambda 2798$ emission line changed, as did that of the Fe emission complex at shorter wavelengths. These emission line fluxes increased along with the highly polarized optical continuum flux, which is presumably synchrotron radiation from the relativistic jet, with a relative time delay of $\lesssim2$ weeks. This implies that the line-emitting clouds lie near the jet, which points almost directly toward the line of sight. The emission-line radiation from such clouds, which are located outside the canonical accretion-disk related broad-line region, may be a primary source of seed photons that are up-scattered to $\gamma$-ray energies by relativistic electrons in the jet. | astro-ph.GA;astro-ph.HE |
The measurement of gamma+jet events with a direct photon in coincidence with an energetic parton can provide unique insights into the propagation and fragmentation of the parton in the presence of the hot and dense medium created in heavy-ion collisions. One way to explore these effects is the study of azimuthal correlations between the direct photon and hadrons produced in the fragmentation. We present azimuthal correlations between photons with a transverse momentum of more than 10 GeV and charged hadrons with a transverse momentum of more than 2 GeV in Au+Au collisions at sqrt(s_NN) = 200 GeV that have been measured with the STAR detector at RHIC. The separation of correlations with direct photons and photons from hadronic decays will be discussed. | nucl-ex |
This paper introduces a novel quantile approach to harness the high-frequency information and improve the daily conditional quantile estimation. Specifically, we model the conditional standard deviation as a realized GARCH model and employ conditional standard deviation, realized volatility, realized quantile, and absolute overnight return as innovations in the proposed dynamic quantile models. We devise a two-step estimation procedure to estimate the conditional quantile parameters. The first step applies a quasi-maximum likelihood estimation procedure, with the realized volatility as a proxy for the volatility proxy, to estimate the conditional standard deviation parameters. The second step utilizes a quantile regression estimation procedure with the estimated conditional standard deviation in the first step. Asymptotic theory is established for the proposed estimation methods, and a simulation study is conducted to check their finite-sample performance. Finally, we apply the proposed methodology to calculate the value at risk (VaR) of 20 individual assets and compare its performance with existing competitors. | stat.ME |
The aim of this thesis is to determine classes of NP relations for which random generation and approximate counting problems admit an efficient solution. Since efficient rank implies efficient random generation, we first investigate some classes of NP relations admitting efficient ranking. On the other hand, there are situations in which efficient random generation is possible even when ranking is computationally infeasible. We introduce the notion of ambiguous description as a tool for random generation and approximate counting in such cases and show, in particular, some applications to the case of formal languages. Finally, we discuss a limit of an heuristic for combinatorial optimization problems based on the random initialization of local search algorithms showing that derandomizing such heuristic can be, in some cases, #P-hard. | cs.CC |
The paper contains two results pointing to the lack of symmetry between measure and category. Assume CH. There exists a strongly meager subset of the Cantor set that can be mapped onto the Cantor set by a uniformly continuous function. (It is well known that uniformly continuous image of a strongly null set is strongly null). A ZFC version of this result is also given. | math.LO |
I give a short review of our present understanding of new theories of the electroweak scale, with emphasis on recent progress. Plenary talk at the EPS 2007 Conference at Manchester. | hep-ph |
We show that every real nonnegative polynomial $f$ can be approximated as closely as desired by a sequence of polynomials $\{f_\epsilon\}$ that are sums of squares. Each $f_\epsilon$ has a simple et explicit form in terms of $f$ and $\epsilon$. A special representation is also obtained for convex polynomials, nonnegative on a convex semi-algebraic set. | math.AC;math.AG |
We show that local moment screening in a Kondo lattice with d-wave superconducting conduction electrons is qualitatively different from the corresponding single Kondo impurity case. Despite the conduction-electron pseudogap, Kondo-lattice screening is stable if the gap amplitude obeys $\Delta <\sqrt{\tk D}$, in contrast to the single impurity condition $\Delta <\tk$ (where $\tk$ is the Kondo temperature for $\Delta = 0$ and D is the bandwidth). Our theory explains the heavy electron behavior in the d-wave superconductor Nd_{2-x}Ce_{x}CuO_{4}. | cond-mat.str-el |
Road networks are characterised by several structural and geometric properties. Their topological structure determines partially its hierarchical arrangement, but since these are networks that are spatially situated and, therefore, spatially constrained, to fully understand the role that each road plays in the system it is fundamental to characterize the influence that geometrical properties have over the network's behaviour. In this work, we percolate the UK's road network using the relative angle between street segments as the occupation probability. We argue that road networks undergo a non-equilibrium first-order phase transition at the moment the main roads start to interconnect forming the spanning percolation cluster. The percolation process uncovers the hierarchical structure of the roads in the network, and as such, its classification. Furthermore, this technique serves to extract the set of most important roads of the network and to create a hierarchical index for each road in the system. | physics.soc-ph |
We explore a method for computing admissible heuristic evaluation functions for search problems. It utilizes pattern databases, which are precomputed tables of the exact cost of solving various subproblems of an existing problem. Unlike standard pattern database heuristics, however, we partition our problems into disjoint subproblems, so that the costs of solving the different subproblems can be added together without overestimating the cost of solving the original problem. Previously, we showed how to statically partition the sliding-tile puzzles into disjoint groups of tiles to compute an admissible heuristic, using the same partition for each state and problem instance. Here we extend the method and show that it applies to other domains as well. We also present another method for additive heuristics which we call dynamically partitioned pattern databases. Here we partition the problem into disjoint subproblems for each state of the search dynamically. We discuss the pros and cons of each of these methods and apply both methods to three different problem domains: the sliding-tile puzzles, the 4-peg Towers of Hanoi problem, and finding an optimal vertex cover of a graph. We find that in some problem domains, static partitioning is most effective, while in others dynamic partitioning is a better choice. In each of these problem domains, either statically partitioned or dynamically partitioned pattern database heuristics are the best known heuristics for the problem. | cs.AI |
Quantum optimal control problems are typically solved by gradient-based algorithms such as GRAPE, which suffer from exponential growth in storage with increasing number of qubits and linear growth in memory requirements with increasing number of time steps. Employing QOC for discrete lattices reveals that these memory requirements are a barrier for simulating large models or long time spans. We employ a nonstandard differentiable programming approach that significantly reduces the memory requirements at the cost of a reasonable amount of recomputation. The approach exploits invertibility properties of the unitary matrices to reverse the computation during back-propagation. We utilize QOC software written in the differentiable programming framework JAX that implements this approach, and demonstrate its effectiveness for lattice gauge theory. | quant-ph |
Q-balls generically exist in the supersymmetric extensions of the standard model. Taking into account the additional sources of CP violation, which are naturally accomodated by the supersymmetric models, it is shown that the Q-ball matter depends additively on individual CP phases, whereas mass per unit charge in the Q-ball depends only on the relative phases. There are regions of the parameter space where there is no stable Q-ball solution in the CP-conserving limit whereas finite CP phases induce a stable Q-ball. | hep-ph |
Numerous research recently proposed integrating Federated Learning (FL) to address the privacy concerns of using machine learning in privacy-sensitive firms. However, the standards of the available frameworks can no longer sustain the rapid advancement and hinder the integration of FL solutions, which can be prominent in advancing the field. In this paper, we propose ModularFed, a research-focused framework that addresses the complexity of FL implementations and the lack of adaptability and extendability in the available frameworks. We provide a comprehensive architecture that assists FL approaches through well-defined protocols to cover three dominant FL paradigms: adaptable workflow, datasets distribution, and third-party application support. Within this architecture, protocols are blueprints that strictly define the framework's components' design, contribute to its flexibility, and strengthen its infrastructure. Further, our protocols aim to enable modularity in FL, supporting third-party plug-and-play architecture and dynamic simulators coupled with major built-in data distributors in the field. Additionally, the framework support wrapping multiple approaches in a single environment to enable consistent replication of FL issues such as clients' deficiency, data distribution, and network latency, which entails a fair comparison of techniques outlying FL technologies. In our evaluation, we examine the applicability of our framework addressing three major FL domains, including statistical distribution and modular-based approaches for resource monitoring and client selection. | cs.DC;cs.LG |
Suppose $X$ is a torsor under an abelian variety $A$ over a number field. We show that any adelic point of $X$ that is orthogonal to the algebraic Brauer group of $X$ is orthogonal to the whole Brauer group of $X$. We also show that if there is a Brauer-Manin obstruction to the existence of rational points on $X$, then there is already an obstruction coming from the locally constant Brauer classes. These results had previously been established under the assumption that $A$ has finite Tate-Shafarevich group. Our results are unconditional. | math.NT |
We consider $\hat{sl_2}$ spaces of coinvariants with respect to two kinds of ideals of the enveloping algebra $U(sl_2\otimes\C[t])$. The first one is generated by $sl_2\otimes t^N$, and the second one is generated by $e\otimes P(t), f\otimes R(t)$ where $P(t), R(t)$ are fixed generic polynomials. (We also treat a generalization of the latter.) Using a method developed in our previous paper, we give new fermionic formulas for their Hilbert polynomials in terms of the level-restricted Kostka polynomials and $q$-multinomial symbols. As a byproduct, we obtain a fermionic formula for the fusion product of $sl_3$-modules with rectangular highest weights, generalizing a known result for symmetric (or anti-symmetric) tensors. | math.QA;math.RT |
We extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a fiberwise nondegenerate symmetric bilinear form. The Riemmanian metric and the bilinear form are used to define non-selfadjoint Laplacians acting on vector-valued smooth forms under absolute and relative boundary conditions. In the process to define the complex-valued analytic torsion, we study spectral properties associated to these generalized Laplacians. As main results, we obtain anomaly formulas for the complex-valued analytic torsion. Our reasoning takes into account that the coefficients in the heat trace asymptotic expansion associated to the boundary value problem under consideration, are locally computable. The anomaly formulas for the complex-valued Ray--Singer torsion are obtained by using the corresponding ones for the Ray--Singer metric, obtained by Bruening and Ma on manifolds with boundary, and an argument of analytic continuation. In odd dimensions, our anomaly formulas are in accord with the corresponding results of Su, without requiring the variations of the Riemannian metric and bilinear structures to be supported in the interior of the manifold. | math.DG |
We study functions on the infinite-dimensional Hamming cube $\{-1,1\}^\infty$, in particular Boolean functions into $\{-1,1\}$, generalising results on analysis of Boolean functions on $\{-1,1\}^n$ for $n\in\mathbb{N}$. The notion of noise sensitivity, first studied in arXiv:math/9811157 , is extended to this setting, and basic Fourier formulas are established. We also prove hypercontractivity estimates for these functions, and give a version of the Kahn-Kalai-Linial theorem giving a bound relating the total influence to the maximal influence. Particular attention is paid to so-called finitary functions, which are functions for which there exists an algorithm that almost surely queries only finitely many bits. Two versions of the Benjamini-Kalai-Schramm theorem characterizing noise sensitivity in terms of the sum of squared influences are given, under additional moment hypotheses on the amount of bits looked at by an algorithm. A version of the Kahn-Kalai-Linial theorem giving that the maximal influence is of order $\frac{\log(n)}{n}$ is also given, replacing $n$ with the expected number of bits looked at by an algorithm. Finally, we show that the result in arXiv:math/0504586 that revealments going to zero implies noise sensitivity also holds for finitary functions, and apply this to show noise sensitivity of a version of the voter model on sufficiently sparse graphs. | math.PR |
This summarizes the talk given at the LCWS 2019 conference in Sendai, Japan, on the progress of the WHIZARD event generator in terms of new physics features and technical improvements relevant for the physics programme of future lepton and especially linear colliders. It takes as a reference the version 2.8.2 released in October 2019, and also takes into account the development until version 2.8.3 to be released in February 2020. | hep-ex;hep-ph |
We observe how the charge-ordering (CO) temperature of Nd1/2Sr1/2MnO3 decreases with the external pressure p from 160 K at p = 0 down to 30 K at p ~ 4.5 GPa, by measuring the values p, T where the far-infrared spectral weight of the metallic phase is fully recovered. We thus determine the (p, T) phase diagram of CO in that manganite. We also find that the parameter d(lnTCO)/dp which describes this metallization from the CO phase is equal and opposite to the quantity d(lnTc)/dp which governs the metallization of the paramagnetic state at comparable Curie temperatures Tc, in similar manganites at half doping. | cond-mat.mtrl-sci;cond-mat.str-el |
Four-dimensional homogeneous static and rotating black strings in dynamical Chern-Simons modified gravity, with and without torsion, are presented. Each solution is supported by a scalar field that depends linearly on the coordinate that span the string. The solutions are locally $\mbox{AdS}_3 \times \mathbb{R}$ and they represent the continuation of the Ba\~nados-Teitelboim-Zanelli black hole. Moreover, they belong to the so-called Chern-Simons sector of the space of solutions of the theory, since the Cotton tensor contributes nontrivially to the field equations. The case with nonvanishing torsion is studied within the first-order formalism of gravity, and it considers nonminimal couplings of the scalar fields to three topological invariants: Nieh-Yan, Pontryagin and Gauss-Bonnet terms, which are studied separately. These nonminimal couplings generate torsion in vacuum, in contrast to Einstein-Cartan theory. In all cases, torsion contributes to an effective cosmological constant that, in particular cases, can be set to zero by a proper choice of the parameters. | gr-qc;hep-th |
We introduce three quantities related to orbits of non-elliptic continuous semigroups of holomorphic self-maps of the unit disc, the total speed, the orthogonal speed and the tangential speed and show how they are related and what can be inferred from those. | math.CV;math.DS |
Excited random walk is a process that has a drift to the right whenever it encounters a new vertex. The paper shows that in two dimensions it drifts to the right linearly in time. | math.PR |
We study experimentally and theoretically the Fano-shaped phonon peak at 1590 cm$^{-1}$ (0.2 eV) in the in-plane optical conductivity of pristine graphite. We show that the anomalously large spectral weight and the Fano asymmetry of the peak can be qualitatively accounted for by a charged-phonon theory. A crucial role in this context is played by the particle-hole asymmetry of the electronic $\pi$-bands. | cond-mat.mtrl-sci |
This study examines, in the framework of variational regularization methods, a multi-penalty regularization approach which builds upon the Uniform PENalty (UPEN) method, previously proposed by the authors for Nuclear Magnetic Resonance (NMR) data processing. The paper introduces two iterative methods, UpenMM and GUpenMM, formulated within the Majorization-Minimization (MM) framework. These methods are designed to identify appropriate regularization parameters and solutions for linear inverse problems utilizing multi-penalty regularization. The paper demonstrates the convergence of these methods and illustrates their potential through numerical examples in one and two-dimensional scenarios, showing the practical utility of point-wise regularization terms in solving various inverse problems. | cs.NA;math.NA |
Probabilistic inference offers a principled framework for understanding both behaviour and cortical computation. However, two basic and ubiquitous properties of cortical responses seem difficult to reconcile with probabilistic inference: neural activity displays prominent oscillations in response to constant input, and large transient changes in response to stimulus onset. Here we show that these dynamical behaviours may in fact be understood as hallmarks of the specific representation and algorithm that the cortex employs to perform probabilistic inference. We demonstrate that a particular family of probabilistic inference algorithms, Hamiltonian Monte Carlo (HMC), naturally maps onto the dynamics of excitatory-inhibitory neural networks. Specifically, we constructed a model of an excitatory-inhibitory circuit in primary visual cortex that performed HMC inference, and thus inherently gave rise to oscillations and transients. These oscillations were not mere epiphenomena but served an important functional role: speeding up inference by rapidly spanning a large volume of state space. Inference thus became an order of magnitude more efficient than in a non-oscillatory variant of the model. In addition, the network matched two specific properties of observed neural dynamics that would otherwise be difficult to account for in the context of probabilistic inference. First, the frequency of oscillations as well as the magnitude of transients increased with the contrast of the image stimulus. Second, excitation and inhibition were balanced, and inhibition lagged excitation. These results suggest a new functional role for the separation of cortical populations into excitatory and inhibitory neurons, and for the neural oscillations that emerge in such excitatory-inhibitory networks: enhancing the efficiency of cortical computations. | q-bio.NC |
We prove effective upper bounds on the global sections of nef line bundles of small generic degree over a fibered surface over a field of any characteristic. It can be viewed as a relative version of the classical Noether inequality for surfaces. As a consequence, we give a new proof of the slope inequality for fibered surface without using any stability method. The treatment is essentially different from these of Xiao, Cornalba--Harris and Moriwaki. We also study the geography problem of surfaces in positive characteristics and show that the Severi inequality is true for surfaces of general type in positive characteristic whose Albanese map is generically finite. Moreover, the geography of surfaces with Albanese fibrations is studied. | math.AG |
Using a new large-scale (~ 0.75 Gpc)^3 hydrodynamic cosmological simulation we investigate the growth rate of supermassive black holes in the early universe (z > 4.75). Remarkably, we find a clear peak in the typical Eddington ratio at black hole masses of 4-8 * 10^7 solar masses (typically found in halos of ~7 * 10^11 to 10^12 solar masses), independent of redshift and indicative that most of BH growth occurs in the cold-flow dominated regime. Black hole growth is by and large regulated by the evolution of gas density. The typical Eddington ratio at a given mass scales simply as cosmological density (1+z)^3 and the peak is caused by the competition between increased gas density available in more massive hosts, and a decrease due to strong AGN feedback that deprives the black hole of sufficient gas to fuel further rapid growth in the high mass end. In addition to evolution in the mean Eddington ratio, we show that the distribution of Eddington ratio among both mass-selected and luminosity-selected samples is approximately log-normal. We combine these findings into a single log-normal fitting formula for the distribution of Eddington ratios as a function of (M_BH,z). This formula can be used in analytic and semi analytic models for evolving black hole populations, predicting black hole masses of observed quasars, and, in conjunction with the observed distribution of Eddington ratios, can be used to constrain the black hole mass function. | astro-ph.CO |
We introduce Integrated Weak Learning, a principled framework that integrates weak supervision into the training process of machine learning models. Our approach jointly trains the end-model and a label model that aggregates multiple sources of weak supervision. We introduce a label model that can learn to aggregate weak supervision sources differently for different datapoints and takes into consideration the performance of the end-model during training. We show that our approach outperforms existing weak learning techniques across a set of 6 benchmark classification datasets. When both a small amount of labeled data and weak supervision are present the increase in performance is both consistent and large, reliably getting a 2-5 point test F1 score gain over non-integrated methods. | cs.LG |
After a short summary of the predictions of the Parton Quenching Model (PQM) for the nuclear modification factor and its centrality dependence in Au-Au collisions at RHIC, we concentrate on back-to-back jet-like correlations at high transverse momentum. We illustrate how this probe is biased by the surface effect. | hep-ph |
Conjecturally, almost all graphs are determined by their spectra. This problem has also been studied for variants such as the spectra of the Laplacian and signless Laplacian. Here we consider the problem of determining graphs with Ihara and Bartholdi zeta functions, which are also computable in polynomial time. These zeta functions are geometrically motivated, but can be viewed as certain generalizations of characteristic polynomials. After discussing some graph properties determined by zeta functions, we show that large classes of cospectral graphs can be distinguished with zeta functions and enumerate graphs distinguished by zeta functions on $\le 11$ vertices. This leads us to conjecture that almost all graphs which are not determined by their spectrum are determined by zeta functions. Along the way, we make some observations about the usual types of spectra and disprove a conjecture of Setyadi and Storm about Ihara zeta functions determining degree sequences. | math.CO |
At the fundamental level, quantum communication is ultimately limited by noise. For instance, quantum signals cannot be amplified without the introduction of noise in the amplified states. Furthermore, photon loss reduces the signal-to-noise ratio, accentuating the effect of noise. Thus, most of the efforts in quantum communications have been directed towards overcoming noise to achieve longer communication distances, larger secret key rates, or to operate in noisier environmental conditions. Here, we propose and experimentally demonstrate a platform for quantum communication based on ultrafast optical techniques. In particular, our scheme enables the experimental realization of high-rates and quantum signal filtering approaching a single spectro-temporal mode, resulting in a dramatic reduction in channel noise. By experimentally realizing a 1-ps optically induced temporal gate, we show that ultrafast time filtering can result in an improvement in noise tolerance by a factor of up to 1200 compared to a 2-ns electronic filter enabling daytime quantum key distribution or quantum communication in bright fibers. | quant-ph |
A new numerical method for the solution of the Dynamical Mean Field Theory's self-consistent equations is introduced. The method uses the Density Matrix Renormalization Group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized. | cond-mat.str-el |
Natural disasters act as a serious threat globally, requiring effective and efficient disaster management and recovery. This paper focuses on classifying natural disaster images using Convolutional Neural Networks (CNNs). Multiple CNN architectures were built and trained on a dataset containing images of earthquakes, floods, wildfires, and volcanoes. A stacked CNN ensemble approach proved to be the most effective, achieving 95% accuracy and an F1 score going up to 0.96 for individual classes. Tuning hyperparameters of individual models for optimization was critical to maximize the models' performance. The stacking of CNNs with XGBoost acting as the meta-model utilizes the strengths of the CNN and ResNet models to improve the overall accuracy of the classification. Results obtained from the models illustrated the potency of CNN-based models for automated disaster image classification. This lays the foundation for expanding these techniques to build robust systems for disaster response, damage assessment, and recovery management. | cs.CV;cs.LG |
Rain streaks significantly decrease the visibility of captured images and are also a stumbling block that restricts the performance of subsequent computer vision applications. The existing deep learning-based image deraining methods employ manually crafted networks and learn a straightforward projection from rainy images to clear images. In pursuit of better deraining performance, they focus on elaborating a more complicated architecture rather than exploiting the intrinsic properties of the positive and negative information. In this paper, we propose a contrastive learning-based image deraining method that investigates the correlation between rainy and clear images and leverages a contrastive prior to optimize the mutual information of the rainy and restored counterparts. Given the complex and varied real-world rain patterns, we develop a recursive mechanism. It involves multi-scale feature extraction and dynamic cross-level information recruitment modules. The former advances the portrayal of diverse rain patterns more precisely, while the latter can selectively compensate high-level features for shallow-level information. We term the proposed recursive dynamic multi-scale network with a contrastive prior, RDMC. Extensive experiments on synthetic benchmarks and real-world images demonstrate that the proposed RDMC delivers strong performance on the depiction of rain streaks and outperforms the state-of-the-art methods. Moreover, a practical evaluation of object detection and semantic segmentation shows the effectiveness of the proposed method. | cs.CV |
Let $G$ be a connected, simply connected, simple, complex, linear algebraic group. Let $P$ be an arbitrary parabolic subgroup of $G$. Let $X=G/P$ be the $G$-homogeneous projective space attached to this situation. Let $d\in H_2(X)$ be a degree. Let $\overline{M}_{0,3}(X,d)$ be the (coarse) moduli space of three pointed genus zero stable maps to $X$ of degree $d$. We prove under reasonable assumptions on $d$ that $\overline{M}_{0,3}(X,d)$ is quasi-homogeneous under the action of $G$. The essential assumption on $d$ is that $d$ is a minimal degree, i.e. that $d$ is a degree which is minimal with the property that $q^d$ occurs with non-zero coefficient in the quantum product $\sigma_u\star\sigma_v$ of two Schubert cycles $\sigma_u$ and $\sigma_v$, where $\star$ denotes the product in the (small) quantum cohomology ring $QH^*(X)$ attached to $X$. We prove our main result on quasi-homogeneity by constructing an explicit morphism which has a dense open $G$-orbit in $\overline{M}_{0,3}(X,d)$. To carry out the construction of this morphism, we develop a combinatorial theory of generalized cascades of orthogonal roots which is interesting in its own right. | math.AG;math.CO |
Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty. Predictive uncertainty is commonly measured by the entropy of the Bayesian model average (BMA) predictive distribution. Yet, the properness of this current measure of predictive uncertainty was recently questioned. We provide new insights regarding those limitations. Our analyses show that the current measure erroneously assumes that the BMA predictive distribution is equivalent to the predictive distribution of the true model that generated the dataset. Consequently, we introduce a theoretically grounded measure to overcome these limitations. We experimentally verify the benefits of our introduced measure of predictive uncertainty. We find that our introduced measure behaves more reasonably in controlled synthetic tasks. Moreover, our evaluations on ImageNet demonstrate that our introduced measure is advantageous in real-world applications utilizing predictive uncertainty. | cs.LG;stat.ML |
In this article, we present a solution to the problem: "Which type of linear operators can be realized by the Dirichlet-to-Neumann operator associated with the operator $-\Delta-a(z)\frac{\partial^{2}}{\partial z^2}$ on an extension problem?", which was raised in the pioneering work [Comm. Par.Diff. Equ. 32 (2007)] by Caffarelli and Silvestre. In fact, we even go a step further by replacing the negative Laplace operator $-\Delta$ on $\mathbb{R}^{d}$ by an $m$-accretive operator $A$ on a general Banach space $X$ and the Dirichlet-to-Neumann operator by the Dirichlet-to-Wentzell operator. We establish uniqueness of solutions to the extension problem in this general framework, which seems to be new in the literature and independent interest. The aim of this paper is to provide a new Phillips-Bochner type functional calculus which uses probabilistic tools from excursion theory. With our method, we are able to characterize all linear operators $\psi(A)$ among the class $CBF$ of complete Bernstein functions $\psi$, resulting in a new characterization of the famous Phillips' subordination theorem within this class $CBF$. | math.AP;math.PR |
We propose a new, two-step empirical Bayes-type of approach for neural networks. We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional parameter of interest and provides Bayesian credible sets with frequentist coverage guarantees. The approach requires fitting the neural network only once, hence it is substantially faster than Bootstrapping type approaches. We demonstrate the applicability of our method over synthetic data, observing good estimation properties and reliable uncertainty quantification. | math.ST;stat.TH |
This report describes the experimental results obtained using a proposed variational Retinex algorithm for controlled illumination correction. Two colour restoration and enhancement schemes of the algorithm are presented for drastically improved results. The algorithm modifies the reflectance image using global and local contrast enhancement approaches and gradually removes the residual illumination to yield highly pleasing results. The proposed algorithms are optimized by way of simultaneous perceptual quality metric (PQM) stabilization and entropy maximization for fully automated processing solving the problem of determination of stopping time. The usage of the HSI or HSV colour space ensures a unique solution to the optimization problem unlike in the RGB space where there is none (forcing manual selection of number of iteration. The proposed approach preserves and enhances details in both bright and dark regions of underexposed images in addition to eliminating the colour distortion, over-exposure in bright image regions, halo effect and grey-world violations observed in Retinex-based approaches. Extensive experiments indicate consistent performance as the proposed approach exploits and augments the advantages of PDE-based formulation, performing illumination correction, colour enhancement correction and restoration, contrast enhancement and noise suppression. Comparisons shows that the proposed approach surpasses most of the other conventional algorithms found in the literature. | cs.CV |
The Swift Gamma-Ray Burst Explorer, launched on 2004 November 20, is a multiwavelength, autonomous, rapid-slewing observatory for gamma-ray burst (GRB) astronomy. On 2004 December 23, during the activation phase of the mission, the Swift X-Ray Telescope (XRT) was pointed at a burst discovered earlier that day by the Swift Burst Alert Telescope. A fading, uncataloged X-ray source was discovered by the XRT and was observed over a period of about 3 hours, beginning 4.6 hours after the burst. The X-ray detection triggered a VLT observation of the optical/NIR counterpart, located about 1.1 arcseconds from the XRT position. The X-ray counterpart faded rapidly, with a power law index of -1.72 +/- 0.20. The average unabsorbed X-ray flux 4.6-7.9 hours after the burst was 6.5 x 10^{-12} erg cm^{-2} s^{-1} in the 0.5-10 keV band, for a power-law spectrum of photon index 2.02 +/- 0.13 with Galactic absorption. The NIR counterpart was observed at three epochs between 16 and 87 hours after the burst, and faded with a power-law index of -1.14 +/- 0.08 with a reddening-corrected SED power-law slope of -0.40 +/- 0.03. We find that the X-ray and NIR data are consistent with a two-component jet in a wind medium, with an early jet break in the narrow component and an underlying electron index of 1.8-2.0. | astro-ph |
This paper addresses the problem of short-term traffic prediction for signalized traffic operations management. Specifically, we focus on predicting sensor states in high-resolution (second-by-second). This contrasts with traditional traffic forecasting problems, which have focused on predicting aggregated traffic variables, typically over intervals that are no shorter than 5 minutes. Our contributions can be summarized as offering three insights: first, we show how the prediction problem can be modeled as a matrix completion problem. Second, we employ a block-coordinate descent algorithm and demonstrate that the algorithm converges in sub-linear time to a block coordinate-wise optimizer. This allows us to capitalize on the "bigness" of high-resolution data in a computationally feasible way. Third, we develop an ensemble learning (or adaptive boosting) approach to reduce the training error to within any arbitrary error threshold. The latter utilizes past days so that the boosting can be interpreted as capturing periodic patterns in the data. The performance of the proposed method is analyzed theoretically and tested empirically using both simulated data and a real-world high-resolution traffic dataset from Abu Dhabi, UAE. Our experimental results show that the proposed method outperforms other state-of-the-art algorithms. | cs.LG;math.OC |
We study the system of coupled atomic and molecular condensates within the two-mode model and beyond mean-field theory (MFT). Large amplitude atom-molecule coherent oscillations are shown to be damped by the rapid growth of fluctuations near the dynamically unstable molecular mode. This result contradicts earlier predictions about the recovery of atom-molecule oscillations in the two-mode limit. The frequency of the damped oscillation is also shown to scale as $\sqrt{N}/\log N$ with the total number of atoms $N$, rather than the expected pure $\sqrt{N}$ scaling. Using a linearized model, we obtain analytical expressions for the initial depletion of the molecular condensate in the vicinity of the instability, and show that the important effect neglected by mean field theory is an initially non-exponential `spontaneous' dissociation into the atomic vacuum. Starting with a small population in the atomic mode, the initial dissociation rate is sensitive to the exact atomic amplitudes, with the fastest (super-exponential) rate observed for the entangled state, formed by spontaneous dissociation. | cond-mat |
In this work, we propose a new class of smooth thick string-like braneworld in six dimensions. The brane exhibits a varying brane-tension and an $AdS$ asymptotic behavior. The brane-core geometry is parametrized by the Bulk cosmological constant, the brane width and by a geometrical deformation parameter. The source satisfies the dominant energy condition for the undeformed solution and has an exotic asymptotic regime for the deformed solution. This scenario provides a normalized massless Kaluza-Klein mode for the scalar, gravitational and gauge sectors. The near-brane geometry allows massive resonant modes at the brane for the $s$ state and nearby the brane for $l=1$. | gr-qc;hep-th |
We consider an optimal transport problem with backward martingale constraint. The objective function is given by the scalar product of a pseudo-Euclidean space $S$. We show that the supremum over maps equals the supremum over plans provided that the law $\nu$ of the input random variable $Y$ is atomless. An optimal map $X$ exists if $\nu$ does not charge any $c-c$ surface (the graph of a difference of convex functions) with strictly positive normal vectors in the sense of the $S$-space. The optimal map $X$ is unique if, in addition, $\nu$ does not charge $c-c$ surfaces with positive and nearly isotropic normal vectors in the $S$-space. In the latter case, the joint law of $(X,Y)$ is the unique optimal backward martingale plan. | math.PR |
We introduce a parabolic blow-up method to study the asymptotic behavior of an integral Brakke flow of planar networks (i.e. a 1-dimensional integral Brakke flow in a two dimensional region) weakly close in a space-time region to a static multiplicity 1 triple junction $J$. We show that such a network flow is regular in a smaller space-time region, in the sense that it consists of three curves coming smoothly together at a single point at 120 degree angles, staying smoothly close to $J$ and moving smoothly. Using this result and White's stratification theorem, we deduce that whenever an integral Brakke flow of networks in a space-time region ${\mathcal R}$ has no static tangent flow with density $\geq2$, there exists a closed subset $\Sigma \subset {\mathcal R}$ of parabolic Hausdorff dimension at most 1 such that the flow is classical in ${\mathcal R} \setminus \Sigma$, i.e. near every point in ${\mathcal R} \setminus \Sigma$, the flow, if non-empty, consists of either an embedded curve moving smoothly or three embedded curves meeting smoothly at a single point at 120 degree angles and moving smoothly. In particular, such a flow is classical at all times except for a closed set of times of ordinary Hausdorff dimension at most $\frac{1}{2}$. | math.AP |
Given the considerable theoretical challenges in understanding strongly coupled metals and non-Fermi liquids, it is valuable to have a framework to understand properties of metals that are universal, in the sense that they must hold in any metal. It has previously been argued that an infinite-dimensional emergent symmetry group is such a property, at least for clean, compressible metals. In this paper, we will show that such an emergent symmetry group has very strong implications for the dynamics of the metal. Specifically, we show that consideration of the hydrodynamics of the associated infinitely many emergent conserved quantities automatically recovers the collisionless Boltzmann equation that governs the dynamics of a Fermi liquid. Therefore, the hydrodynamic prediction is that in the low-temperature, collisionless regime where the emergent conservation laws hold, the dynamics and response to external fields of a general spinless metal will be identical to a Fermi liquid. We discuss some potential limitations to this general statement, including the possibility of non-hydrodynamic modes. We also report some interesting differences in the case of spinful metals. | cond-mat.str-el |
In this work we consider a class of nonlocal non-autonomous evolution equations, which generalizes the model of neuronal activity that arises in Amari (1979). Under suitable assumptions on the nonlinearity and on the parameters present in the equation, we study, in an appropriated Banach space, the assimptotic behavior of the evolution process generated by this equation. We prove results on existence, uniqueness and smoothness of the solutions and on the existence of pullback attracts for the evolution process associated to this equation. We also prove a continuous dependence of the evolution process with respect to external stimulus function present in the model. Furthermore, using the result of continuous dependence of the evolution process, we also prove the upper semicontinuity of pullback attracts with respect to stimulus function. We conclude with a small discussion about the model and about a biological interpretation of the result of continuous dependence of neuronal activity with respect to the external stimulus function. | math.DS |
We provide an algebraic classification of all supersymmetric domain wall solutions of maximal gauged supergravity in four and seven dimensions, in the presence of non-trivial scalar fields in the coset SL(8,R)/SO(8) and SL(5,R)/SO(5) respectively. These solutions satisfy first-order equations, which can be obtained using the method of Bogomol'nyi. From an eleven-dimensional point of view they correspond to various continuous distributions of M2- and M5-branes. The Christoffel-Schwarz transformation and the uniformization of the associated algebraic curves are used in order to determine the Schrodinger potential for the scalar and graviton fluctuations on the corresponding backgrounds. In many cases we explicitly solve the Schrodinger problem by employing techniques of supersymmetric quantum mechanics. The analysis is parallel to the construction of domain walls of five-dimensional gauged supergravity, with scalar fields in the coset SL(6,R)/SO(6), using algebraic curves or continuous distributions of D3-branes in ten dimensions. In seven dimensions, in particular, our classification of domain walls is complete for the full scalar sector of gauged supergravity. We also discuss some general aspects of D-dimensional gravity coupled to scalar fields in the coset SL(N,R)/SO(N). | gr-qc;hep-th |
In this article, we define the matricization of a tensor and we present some properties of the matricization. After that, we define the determinant of a tensor and we present some properties of the determinant. We define the covariance tensor and we present some properties of the covariance tensor. In a similar way, we define the correlation tensor. We define the tensor normal distribution. In a similar way, we define the tensor elliptical distributions. We prove the equivalence of the tensor elliptical distribution representations. | math.PR |
We examine the effects of a global magnetic field and outflow on radiatively inefficient accretion flow (RIAF) in the presence of magnetic resistivity. We find a self-similar solutions for the height integrated equations that govern the behavior of the flow. We use the mixing length mechanism for studying the convection parameter. We adopt a radius dependent mass accretion rate as $\dot{M}=\dot{M}_{out}{(\frac{r}{r_{out}})^{s}}$ with $s> 0$ to investigate the influence of outflow on the structure of inflow where $s$ is a constant and indication the effect of wind. Also, we have studied the radiation spectrum and temperature of CDAFs. The thermal bermsstrahlung emission as a radiation mechanism is taken into account for calculating the spectra emitted by the CDAFs. The energy that powers bremsstrahlung emission at large radii is provided by convective transport from small radii and viscous and resistivity dissipation. Our results indicate that the disc rotates slower and accretes faster, it becomes hotter and thicker for stronger wind. By increasing all component of magnetic field, the disc rotates faster and accretes slower while it becomes hotter and thicker. We show that the outflow parameter and all component of magnetic field have the same effects on the luminosity of the disc. We compare the dynamical structure of the disc in two different solutions (with and without resistivity parameter). We show that only the radial infall velocity and the surface density could changed by resistivity parameter obviously. Increasing the effect of wind increases the disc's temperature and luminosity of the disc. The effect of magnetic field is similar to the effect of wind in the disc's temperature and luminosity of the disc, but the influence of resistivity on the observational properties is not evident. | astro-ph.HE |
Atmospheric neutrinos are an important background to astrophysical neutrino searches, and are also of considerable interest in their own right. This paper points out that the contribution to conventional atmospheric $\nu_e$ of the rare semileptonic decay of $K_S$ becomes significant at high energy. Although the $K_S\rightarrow \pi e\nu$ branching ratio is very small, the short $K_S$ lifetime leads to a high critical energy, so that, for vertical showers, the inclusion of $K_S$ semileptonic decay increases the conventional $\nu_e$ flux by $\approx 30%$ at energies above 100 TeV. In this paper, we present calculations of the flux of $\nu_e$ from $K_S$. At energies above their critical energies, the $\nu_e$ fluxes from kaon decay may be simply related to the kaon semileptonic widths; this leads to a near-equality between the flux of $\nu_e$ from $K^+$, $K_L$ and $K_S$. | astro-ph.HE;hep-ph |
Training learning-based deblurring methods demands a tremendous amount of blurred and sharp image pairs. Unfortunately, existing synthetic datasets are not realistic enough, and deblurring models trained on them cannot handle real blurred images effectively. While real datasets have recently been proposed, they provide limited diversity of scenes and camera settings, and capturing real datasets for diverse settings is still challenging. To resolve this, this paper analyzes various factors that introduce differences between real and synthetic blurred images. To this end, we present RSBlur, a novel dataset with real blurred images and the corresponding sharp image sequences to enable a detailed analysis of the difference between real and synthetic blur. With the dataset, we reveal the effects of different factors in the blur generation process. Based on the analysis, we also present a novel blur synthesis pipeline to synthesize more realistic blur. We show that our synthesis pipeline can improve the deblurring performance on real blurred images. | cs.CV |
We study the excited states of $\omega$ and $\omega_3$ by comparison with the $\rho$ and $\rho_3$ families, and discuss the possibility of $X(2220)$ as $\omega$ excitation by analyzing the mass spectra and strong decay behaviors. In addition, we predict the masses and widths of $\omega(2D)$ and $\omega_3$and $\rho_3(4D)$, $\rho_3(1G)$, $\omega_3$ and $\rho_3(2G)$ and $\omega_3(3G)$ and $\rho_3(3G)$. The abundant information of their two-body strong decays predicted in this work will be helpful to further study of these $\omega$ and $\omega_3$ and $\rho$ and $\rho_3$ states in experiment and theory. | hep-ph |
We shall given a new effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent, improving our old result in T. Yamada, Colloq. Math. 103 (2005), 303--307. | math.NT |
We define three families of quivers in which the braid relations of the symmetric group $S_n$ are realized by mutations and automorphisms. A sequence of eight braid moves on a reduced word for the longest element of $S_4$ yields three trivial cluster transformations with 8, 32 and 32 mutations. For each of these cluster transformations, a unitary operator representing a single braid move in a quantum mechanical system solves the tetrahedron equation. The solutions thus obtained are constructed from the noncompact quantum dilogarithm and can be identified with the partition functions of three-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories on a squashed three-sphere. | math.MP;hep-th;math-ph |
Generic Dijkstra is a novel algorithm for finding the optimal shortest path in both wavelength-division multiplexed networks (WDM) and elastic optical networks (EON), claimed to outperform known algorithms considerably. Because of its novelty, it has not been independently implemented and verified. Its time complexity also remains unknown. In this paper, we perform run-time analysis and show that Generic Dijkstra running time grows quadratically with the number of graph vertices and logarithmically with the number of edge units. We also discover that the running time of the Generic Dijkstra algorithm in the function of network utilization is not monotonic, as peak running time is at approximately 0.25 network utilization. Additionally, we provide an independent open source implementation of Generic Dijkstra in the Python language. We confirm the correctness of the algorithm and its superior performance. In comparison to the Filtered Graphs algorithm, Generic Dijkstra is approximately 2.3 times faster in networks with 25 to 500 nodes, and in 90% of calls its computation takes less time. | cs.NI |
We determine the energy-level shift experienced by a neutral atom due the quantum electromagnetic interaction with a layered dielectric body. We use the technique of normal-mode expansion to quantize the electromagnetic field in the presence of a layered, non-dispersive and non-absorptive dielectric. We explicitly calculate the equal-time commutation relations between the electric field and vector potential operators. We show that the commutator can be expressed in terms of a generalized transverse delta-function and that this is a consequence of using the generalized Coulomb gauge to quantize the electromagnetic field. These mathematical tools turn out to be very helpful in the calculation of the energy-level shift of the atom, which can be in its ground state or excited. The results for the shift are then analysed asymptotically in various regions of the system's parameter space -- with a view to providing quick estimates of the influence of a single dielectric layer on the Casimir-Polder interaction between an atom and a dielectric half-space. We also investigate the impact of resonances between the wavelength of the atomic transition and the thickness of the top layer. | quant-ph |
We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log-transformed squared $t$-statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Simulation studies and a real data analysis are also carried out to demonstrate the advantages of our likelihood ratio test methods. | stat.ME |
Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the system qubits. To make the method more resource friendly in the noisy intermediate-scale quantum (NISQ) and early fault-tolerant era, we combine the non-Hermitian projection algorithm with multiple variational gadgets, including variational module enhancement and variational state recording, to reduce the required circuit depth and avoid the exponentially vanishing success probability for post-selections. We compare our method, the non-Hermitian-variational algorithm, with a pure variational method -- QAOA for solving the 3-SAT problem and preparing the ground state for the transverse-field Ising model. As demonstrated by numerical evidence, the non-Hermitian-variational algorithm outperforms QAOA in convergence speed with improved quantum resource efficiency. | quant-ph |
We revisit the Helmholts equation in a quarter-plane in the framework of the Riemann-Hilbert approach to linear boundary value problems suggested in late 90s by A. Fokas. We show the role of the Sommerfeld radiation condition in Fokas's scheme. | math.MP;math-ph |
We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower dimensionality, our approach aims to preserve the nonnegative components of the data that are important for classification. We identify these components from the support vectors of large-margin classifiers and derive iterative updates to preserve them in a semi-supervised version of NMF. These updates have a simple multiplicative form like their unsupervised counterparts; they are also guaranteed at each iteration to decrease their loss function---a weighted sum of I-divergences that captures the trade-off between unsupervised and supervised learning. We evaluate these updates for dimensionality reduction when they are used as a precursor to linear classification. In this role, we find that they yield much better performance than their unsupervised counterparts. We also find one unexpected benefit of the low dimensional representations discovered by our approach: often they yield more accurate classifiers than both ordinary and transductive SVMs trained in the original input space. | cs.LG |
We study the effect of film density on the uniaxial compression of thin elastic films at a liquid--fluid interface. Using a combination of experiments and theory, we show that dense films first wrinkle and then fold as the compression is increased, similarly to what has been reported when the film density is neglected. However, we highlight the changes in the shape of the fold induced by the film's own weight and extend the model of Diamant and Witten [Phys.Rev.Lett. 2011, 107, 164302, arXiv:1107.5505] to understand these changes. In particular, we suggest that it is the weight of the film that breaks the up-down symmetry apparent from previous models, but elusive experimentally. We then compress the film beyond the point of self-contact and observe a new behaviour dependent on the film density: the single fold that forms after wrinkling transitions into a closed loop after self-contact, encapsulating a cylindrical droplet of the upper fluid. The encapsulated drop either causes the loop to bend upward or to sink deeper as compression is increased, depending on the relative buoyancy of the drop-film combination. We propose a model to qualitatively explain this behaviour. Finally, we discuss the relevance of the different buckling modes predicted in previous theoretical studies and highlight the important role of surface tension in the shape of the fold that is observed from the side -- an aspect that is usually neglected in theoretical analyses. | cond-mat.soft |
The fraction of $\chi_{c1}$ and $\chi_{c2}$ decays in the prompt $J/\psi$ yield, $F_{\chi c}=\sigma_{\chi_c \to J/\psi}/\sigma_{J/\psi}$, is measured by the LHCb detector in pPb collisions at $\sqrt{s_{NN}}=8.16$ TeV. The study covers the forward ($1.5<y^*<4.0$) and backward ($-5.0<y^*<-2.5$) rapidity regions, where $y^*$ is the $J/\psi$ rapidity in the nucleon-nucleon center-of-mass system. Forward and backward rapidity samples correspond to integrated luminosities of 13.6 $\pm$ 0.3 nb$^{-1}$ and 20.8 $\pm$ 0.5 nb$^{-1}$, respectively. The result is presented as a function of the $J/\psi$ transverse momentum $p_{T,J/\psi}$ in the range 1$<p_{T, J/\psi}<20$ GeV/$c$. The $F_{\chi c}$ fraction at forward rapidity is compatible with the LHCb measurement performed in $pp$ collisions at $\sqrt{s}=7$ TeV, whereas the result at backward rapidity is 2.4 $\sigma$ larger than in the forward region for $1<p_{T, J/\psi}<3$ GeV/$c$. The increase of $F_{\chi c}$ at low $p_{T, J/\psi}$ at backward rapidity is compatible with the suppression of the $\psi$(2S) contribution to the prompt $J/\psi$ yield. The lack of in-medium dissociation of $\chi_c$ states observed in this study sets an upper limit of 180 MeV on the free energy available in these pPb collisions to dissociate or inhibit charmonium state formation. | hep-ex;nucl-ex |
A closed, orientable, splitting surface in an oriented $3$-manifold is a topologically minimal surface of index $n$ if its associated disk complex is $(n-2)$-connected but not $(n-1)$-connected. A critical surface is a topologically minimal surface of index $2$. In this paper, we use an equivalent combinatorial definition of critical surfaces to construct the first known critical bridge spheres for nontrivial links. | math.GT |
In a $\delta-$shock model, a system subject to randomly occurring shocks, the system fails when the time between two successive shocks lies below a threshold $\delta$. In this note, we study the generalization of this model where such $\delta-$shocks are accumulated and the system fails on the occurrence of $k^{th}$ such a $\delta-$shock. The probability distribution of the system failure time and the statistical characteristics are explicitly obtained. Normal approximation to the failure time distribution is proposed. | stat.AP |
The morphological stability of two-dimensional islands nucleated on a substrate during vacuum or vapour-phase atom deposition is investigated. Using simple scaling arguments, it is shown that, contrary to expectation, dendritic islands may be converted into compact ones by increasing the deposition rate, provided that the size of the critical nucleus is large enough. Implications for recent observations of Pt deposition on Pt(111) are discussed. | cond-mat.mtrl-sci;cond-mat.stat-mech |
We propose how to achieve strong photon antibunching effect in a cavity-QED system coupled with two Rydberg-Rydberg interaction atoms. Via calculating the equal time second order correlation function g(2)(0), we find that the unconventional photon blockade and the conventional photon blockade appear in the atom-driven scheme, and they are both significantly affected by the Rydberg-Rydberg interaction. We also find that under appropriate parameters, the photon antibunching and the mean photon number can be significantly enhanced by combining the conventional photon blockade and the unconventional photon blockade. In the cavity-driven scheme, the existence of the Rydberg-Rydberg interaction severely destroys the photon antibunching under the unconventional photon blockade mechanism. These results will help to guide the implementation of the single photon emitter in the Rydberg atoms-cavity system. | quant-ph |
The task of unsupervised domain adaptation is proposed to transfer the knowledge of a label-rich domain (source domain) to a label-scarce domain (target domain). Matching feature distributions between different domains is a widely applied method for the aforementioned task. However, the method does not perform well when classes in the two domains are not identical. Specifically, when the classes of the target correspond to a subset of those of the source, target samples can be incorrectly aligned with the classes that exist only in the source. This problem setting is termed as partial domain adaptation (PDA). In this study, we propose a novel method called Two Weighted Inconsistency-reduced Networks (TWINs) for PDA. We utilize two classification networks to estimate the ratio of the target samples in each class with which a classification loss is weighted to adapt the classes present in the target domain. Furthermore, to extract discriminative features for the target, we propose to minimize the divergence between domains measured by the classifiers' inconsistency on target samples. We empirically demonstrate that reducing the inconsistency between two networks is effective for PDA and that our method outperforms other existing methods with a large margin in several datasets. | cs.LG;stat.ML |
This paper is an extended summary of the talk I gave at IAU Symposium "New Horizons in Time Domain Astronomy" (Oxford, 2011). I first review the history of transients (which is intimately related to the advent of wide-field telescopic imaging; I then summarize wide field imaging projects. The motivations that led to the design of the Palomar Transient Factory (PTF) followed by a summary of the astronomical returns from PTF. I review the lessons learnt from PTF. I conclude that, during this decade, optical transient searches will continue to flourish and may even accelerate as surveys at other wavelengths -- notably radio, UV and X-ray -- come on line. As a result, I venture to suggest that specialized searches for transients will continue -- even into the LSST era. I end the article by discussing the importance of follow-up telescopes for transient object studies -- a topical issue given that in the US the Portfolio Review is under away. | astro-ph.CO;astro-ph.HE |
A coherent state representation of the expectation value of an arbitrary (but still polynomial) normal ordered quantum operator is discussed. This serves as a basis for developing a fast and easy-to-handle algorithm, based on series of Hermite polynomials, for calculating such quantities. The case of single mode field with number, coherent and squeezed states is treated in detail. Some hints on how to extend the algorithm to multimode fields are also given. | physics.optics;quant-ph |
This paper contains an analysis of short Chandra observations of 19 3C sources with redshifts between 0.3 and 0.5 not previously observed in the X-rays. This sample is part of a project to obtain Chandra data for all of the extragalactic sources in the 3C catalogue. Nuclear X-ray intensities as well as any X-ray emission associated with radio jet knots, hotspots or lobes have been measured in 3 energy bands: soft, medium and hard. Standard X-ray spectral analysis for the 4 brightest nuclei has been also performed. X-ray emission was detected for all the nuclei of the radio sources in the current sample with the exception of 3C 435A. There is one compact steep spectrum (CSS) source while all the others are FRII radio galaxies. X-ray emission from two galaxy clusters (3C 19 and 3C 320); from 6 hotspots in 4 radio galaxies (3C 16, 3C 19, 3C 268.2, 3C 313); and extended X-ray emission on kpc scales in 3C 187 and 3C 313, has been detected. | astro-ph.CO;astro-ph.HE |
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