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We study the certifiable robustness of ML classifiers on dirty datasets that could contain missing values. A test point is certifiably robust for an ML classifier if the classifier returns the same prediction for that test point, regardless of which cleaned version (among exponentially many) of the dirty dataset the classifier is trained on. In this paper, we show theoretically that for Naive Bayes Classifiers (NBC) over dirty datasets with missing values: (i) there exists an efficient polynomial time algorithm to decide whether multiple input test points are all certifiably robust over a dirty dataset; and (ii) the data poisoning attack, which aims to make all input test points certifiably non-robust by inserting missing cells to the clean dataset, is in polynomial time for single test points but NP-complete for multiple test points. Extensive experiments demonstrate that our algorithms are efficient and outperform existing baselines., Comment: 22 pages, 10 figures

Most data analytical pipelines often encounter the problem of querying inconsistent data that violate pre-determined integrity constraints. Data cleaning is an extensively studied paradigm that singles out a consistent repair of the inconsistent data. Consistent query answering (CQA) is an alternative approach to data cleaning that asks for all tuples guaranteed to be returned by a given query on all (in most cases, exponentially many) repairs of the inconsistent data. This paper identifies a class of acyclic select-project-join (SPJ) queries for which CQA can be solved via SQL rewriting with a linear time guarantee. Our rewriting method can be viewed as a generalization of Yannakakis's algorithm for acyclic joins to the inconsistent setting. We present LinCQA, a system that can output rewritings in both SQL and non-recursive Datalog rules for every query in this class. We show that LinCQA often outperforms the existing CQA systems on both synthetic and real-world workloads, and in some cases, by orders of magnitude.

The potential of frequency comb spectroscopy has aroused great interest in generating mid-infrared frequency combs in the integrated photonic setting. However, despite remarkable progress in microresonators and quantum cascade lasers, the availability of suitable mid-IR comb sources remains scarce. Here, we present a new approach for the generation of mid-IR microcombs through cascaded three-wave-mixing. By pumping a CdSiP$_2$ microresonator at 1.55 $\mu$m wavelength with a low power continuous wave laser, we generate $\chi^{(2)}$ frequency combs at 3.1 $\mu$m wavelength, with a span of about 30 nm. We observe ordinary combs states with a line spacing of the free spectral range of the resonator, and combs where the sideband numbers around the pump and half-harmonic alternate, forming staggered patterns of spectral lines. Our scheme for mid-IR microcomb generation is compatible with integrated telecom lasers. Therefore, it has the potential to be used as a simple and fully integrated mid-IR comb source, relying on only one single material.

Considering a bidirectionally pumped ring microresonator, we provide a concise derivation of the model equations allowing us to eliminate the repetition rate terms and reduce the nonlinear interaction between the counter-propagating waves to the power-dependent shifts of the resonance frequencies. We present the simulation results of the soliton control by swiping the frequency of the counter-propagating wave in the forward and backward directions and with the soliton-blockade effect either present or not. We highlight the non-reciprocity of the forward and backward scans. Furthermore, we report the soliton crystals and breathers existing in the vicinity of the blockade interval., Comment: 13 pages

We report a method to control - disrupt and restore, a regime of the unidirectional soliton generation in a bidirectionally pumped ring microresonator. This control, i.e., the soliton blockade, is achieved by tuning pump frequency of the counterrotating field. The blockade effect is correlated with the emergence of a dark-bright nonlinear resonance of the cw-states., Comment: 4 pages

There is a large body of recent work applying machine learning (ML) techniques to query optimization and query performance prediction in relational database management systems (RDBMSs). However, these works typically ignore the effect of \textit{intra-parallelism} -- a key component used to boost the performance of OLAP queries in practice -- on query performance prediction. In this paper, we take a first step towards filling this gap by studying the problem of \textit{tuning the degree of parallelism (DOP) via ML techniques} in Microsoft SQL Server, a popular commercial RDBMS that allows an individual query to execute using multiple cores. In our study, we cast the problem of DOP tuning as a {\em regression} task, and examine how several popular ML models can help with query performance prediction in a multi-core setting. We explore the design space and perform an extensive experimental study comparing different models against a list of performance metrics, testing how well they generalize in different settings: $(i)$ to queries from the same template, $(ii)$ to queries from a new template, $(iii)$ to instances of different scale, and $(iv)$ to different instances and queries. Our experimental results show that a simple featurization of the input query plan that ignores cost model estimations can accurately predict query performance, capture the speedup trend with respect to the available parallelism, as well as help with automatically choosing an optimal per-query DOP.

It was recently found that, under the action of the spin-orbit coupling (SOC) and Zeeman splitting (ZS), binary BEC with intrinsic cubic nonlinearity supports families of gap solitons, provided that the kinetic energy is negligible in comparison with the SOC and ZS terms. We demonstrate that, also under the action of SOC and ZS, a similar setting may be introduced for BEC with two components representing different atomic states, resonantly coupled by microwave radiation, while the Poisson equation accounts for the feedback of the two-component atomic wave function onto the radiation. The microwave-mediated interaction induces an effective nonlinear trapping potential, which strongly affects the purport of the linear spectrum in this system. As a result, families of both gap and embedded solitons (those overlapping with the continuous spectrum) are found, being chiefly stable. The shape of the solitons features exact or broken skew symmetry. In addition to fundamental solitons (whose shape may or may not include a node), a family of dipole solitons is constructed too, which are even more stable than their fundamental counterparts. A nontrivial stability area is identified for moving solitons in the present system, which lacks Galilean invariance. Colliding solitons merge into a single one., Comment: to be published in Physical Review A

We consider a dual-core nonlinear waveguide with the parity-time (PT) symmetry, realized in the form of equal gain and loss terms carried by the coupled cores. To expand a previously found stability region for solitons in this system, and explore possibilities for the development of dynamical control of the solitons, we introduce "management" in the form of periodic sinusoidal variation of the loss-gain (LG) coefficients, along with synchronous variation of the inter-core coupling (ICC) constant. This system, which can be realized in optics (in the temporal and spatial domains alike), features strong robustness when amplitudes of the variation of the LG and ICC coefficients keep a ratio equal to that of their constant counterparts, allowing one to find exact solutions for PT-symmetric solitons. A stability region for the solitons is identified in terms of the management amplitude and period, as well as the soliton's amplitude. In the long-period regime, the solitons evolve adiabatically, making it possible to predict their stability boundaries in an analytical form. The system keeping the Galilean invariance, collisions between moving solitons are considered too., Comment: 12 pages, 9 figures, to be published in Commun. Nonlin. Sci. Numerical Simul

Recursive query processing has experienced a recent resurgence, as a result of its use in many modern application domains, including data integration, graph analytics, security, program analysis, networking and decision making. Due to the large volumes of data being processed, several research efforts, across multiple communities, have explored how to scale up recursive queries, typically expressed in Datalog. Our experience with these tools indicated that their performance does not translate across domains (e.g., a tool design for large-scale graph analytics does not exhibit the same performance on program-analysis tasks, and vice versa). As a result, we designed and implemented a general-purpose Datalog engine, called RecStep, on top of a parallel single-node relational system. In this paper, we outline the different techniques we use in RecStep, and the contribution of each technique to overall performance. We also present results from a detailed set of experiments comparing RecStep with a number of other Datalog systems using both graph analytics and program-analysis tasks, summarizing pros and cons of existing techniques based on the analysis of our observations. We show that RecStep generally outperforms the state-of-the-art parallel Datalog engines on complex and large-scale Datalog program evaluation, by a 4-6X margin. An additional insight from our work is that we show that it is possible to build a high-performance Datalog system on top of a relational engine, an idea that has been dismissed in past work in this area.

We develop new models and algorithms for learning the temporal dynamics of the topic polytopes and related geometric objects that arise in topic model based inference. Our model is nonparametric Bayesian and the corresponding inference algorithm is able to discover new topics as the time progresses. By exploiting the connection between the modeling of topic polytope evolution, Beta-Bernoulli process and the Hungarian matching algorithm, our method is shown to be several orders of magnitude faster than existing topic modeling approaches, as demonstrated by experiments working with several million documents in under two dozens of minutes., Comment: NeurIPS 2019

We study the spontaneous symmetry breaking of dipolar Bose--Einstein condensates trapped in stacks of two-well systems, which may be effectively built as one-dimensional trapping lattices sliced by a repelling laser sheet. If the potential wells are sufficiently deep, the system is modeled by coupled discrete Gross--Pitaevskii equations with nonlocal self- and cross-interaction terms representing dipole--dipole interactions. When the dipoles are not polarized perpendicular or parallel to the lattice, the cross-interaction is asymmetric, replacing the familiar symmetric two-component solitons with a new species of cross-symmetric or -asymmetric ones. The orientation of the dipole moments and the interwell hopping rate strongly affect the shapes of the discrete two-component solitons as well as the characteristics of the cross-symmetry breaking and the associated phase transition. The sub- and super-critical types of cross-symmetry breaking can be controlled by either the hopping rate between the components or the total norm of the solitons. The effect of the interplay between the contact nonlinearity and the dipole angle on the cross-symmetry breaking is also discussed., Comment: 13 pages, 11 figures, 94 references

We present gap solitons (GSs) that can be created in free nearly two-dimensional (2D) space in dipolar spinor Bose-Einstein condensates with the spin-orbit coupling (SOC), subject to tight confinement, with size $a_{\perp }$, in the third direction. For quasi-2D patterns, with lateral sizes $l\gg a_{\perp }$, the kinetic-energy terms in the respective spinor Gross-Pitaevskii equations may be neglected in comparison with SOC. This gives rise to a bandgap in the system's spectrum, in the presence of the Zeeman splitting between the spinor components. While the present system with contact interactions does not produce 2D solitons, stable gap solitons(GSs), with vorticities $0$ and $1$ in the two components, are found, in quasi-analytical and numerical forms, under the action of dipole-dipole interaction (DDI). Namely, isotropic and anisotropic 2D GSs are obtained when the dipoles are polarized, respectively, perpendicular or parallel to the 2D plane. The GS families extend, as \textit{embedded solitons} (ESs), into spectral bands, a part of the ES branch being stable for isotropic solitons. The GSs remain stable if the competing contact interaction, with the sign opposite to that of the DDI, is included, while the addition of the contact term with the same sign destabilizes the GSs, at first replacing them by breathers, and eventually leading to destruction of the solitons. Mobility and collision of the GSs are studied too, revealing negative and positive effective masses of the isotropic and anisotropic solitons, respectively., Comment: 13 pages, 8 figures, 54 references, Physical Review A in press

We consider a dipolar Bose-Einstein condensate trapped in an array of two-well systems with an arbitrary orientations of the dipoles relative to the system's axis. The system can be built as a chain of local traps sliced into two parallel lattices by a repelling laser sheet. It is modelled by a pair of coupled discrete Gross-Pitaevskii equations, with dipole-dipole self- and cross-interactions. When the dipoles are not polarized perpendicular or parallel to the lattice, the cross-interaction is asymmetric, replacing the familiar symmetric two-component discrete solitons by two new species of cross-symmetric ones, on-site- and off-site-centered, which are strongly affected by the orientation of the dipoles and separation between the parallel lattices. A very narrow region of intermediate asymmetric discrete solitons is found at the boundary between the on- and off-site families. Two different types of solitons in the $\mathcal{PT}$%-symmetric version of the system are constructed too, and stability areas are identified for them., Comment: 13 pages, 12 figures, 72 References, Physical Review E, in press