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JSON Schemas provide useful guardrails for developers of Web APIs to guarantee that the semi-structured JSON input provided by clients matches a predefined structure. This is important both to ensure the correctness of the data received as input and also to avoid potential security issues from processing input that is not correctly validated. However, this validation process can be time-consuming and adds overhead to every request. Different keywords in the JSON Schema specification have complex interactions that may increase validation time. Since popular APIs may process thousands of requests per second and schemas change infrequently, we observe that we can resolve some of the complexity ahead of time in order to achieve faster validation. Our JSON Schema validator, Blaze, compiles complex schemas to an efficient representation in seconds to minutes, adding minimal overhead at build time. Blaze incorporates several unique optimizations to reduce the validation time by an average of approximately 10x compared existing validators on a variety of datasets. In some cases, Blaze achieves a reduction in validation time of multiple orders of magnitude compared to the next fastest valid

This article provides a pedagogical introduction to the Silver Blaze problem. This problem refers to the difficulty of reconciling to perspectives on QCD with a chemical potential. The first is the phenomenological fact that at $T=0$ QCD remains in its ground state -- the vacuum -- with all physical observables unchanged whenever the magnitude of a chemical potential is less than some critical value. The second is the fact that in functional integral treatments, the inclusion of any nonzero chemical potential changes all eigenvalues of the Dirac operator for every gauge configuration, leading to a natural expectation that the functional determinants also changes, which leads to the expectation that physical observables should be altered. The problem amounts to explaining why nothing happens below the critical chemical potential. By focusing on the eigenvalues of $γ_0$ times the Dirac operator rather than the Dirac operator itself, it is possible to show that for QCD with two flavors and identical quark masses, an isospin chemical potential with a magnitude less than $m_π$ (and no baryon chemical potential), or a baryon chemical potential of less than $\frac{3}{2} m_π$ (and no isosp

This study explores the use of synchrotron measurements as a nanometrology tool for blazed gratings. In grazing incidence geometry, one can measure both the conical diffraction and the diffuse scattering on the grating simultaneously in a single scattering pattern. The sensitivity of scattering patterns to the structure of the blazed gratings is evaluated. The diffraction component of the pattern is shown to be sensitive to the average groove profile of the gratings. Meanwhile, the diffuse scattering depends on the roughness morphology of the reflective surface of blazed gratings. These findings are supported by numerical simulations. The simulations were performed using several rigorous solvers for the Helmholtz equations, and with a perturbation theory. The analysis relies on synchrotron data, as well as data from atomic force microscopy and scanning electron microscopy. The aim of this article is to draw the attention of the optical community to the synchrotron measurements as a nanometrology tool for the modern optical elements.

Maintaining the highest quality and output of photon science in the VUV-, EUV-, soft- and tender-X-ray energy ranges requires high-quality blazed profile gratings. Currently, their availability is critical due to technological challenges and limited manufacturing resources. In this work we discuss the opportunity of an alternative method to manufacture blazed gratings by means of electron-beam lithography (EBL). We investigate the different parameters influencing the optical performance of blazed profile gratings produced by EBL and develop a robust process for the manufacturing of high-quality blazed gratings using polymethyl methacrylate (PMMA) as high resolution, positive tone resist and ion beam etching.

Software bugs require developers to exert significant effort to identify and resolve them, often consuming about one-third of their time. Bug localization, the process of pinpointing the exact source code files that need modification, is crucial in reducing this effort. Existing bug localization tools, typically reliant on deep learning techniques, face limitations in cross-project applicability and effectiveness in multi-language environments. Recent advancements with Large Language Models (LLMs) offer detailed representations for bug localization. However, they encounter challenges with limited context windows and mapping accuracy. To address these issues, we propose BLAZE, an approach that employs dynamic chunking and hard example learning. First, BLAZE dynamically segments source code to minimize continuity loss. Then, BLAZE fine-tunes a GPT-based model using challenging bug cases, in order to enhance cross-project and cross-language bug localization. To support the capability of BLAZE, we create the BEETLEBOX dataset, which comprises 26,321 bugs from 29 large and thriving open-source projects across five different programming languages (Java, C++, Python, Go, and JavaScript).

A topology optimization method is presented and applied to a blazed diffraction grating in reflection under conical incidence. This type of gratings is meant to disperse the incident light on one particular diffraction order and this property is fundamental in spectroscopy. Conventionally, a blazed metallic grating is made of a sawtooth profile designed to work with the +/-1st diffraction order in reflection. In this paper, we question this intuitive triangular pattern and look for optimal opto-geometric characteristics using topology optimization based on Finite Element modelling of Maxwell's equations. In practical contexts, the grating geometry is mono-periodic but it is enlightened by a 3D plane wave with a wavevector outside of the plane of invariance. Consequently, this study deals with the resolution of a direct and inverse problem using the Finite Element Method in this intermediate state between 2D and 3D: the so-called conical incidence. A multi-wavelength objective is used in order to obtain a broadband blazed effect. Finally, several numerical experiments are detailed. The results show that it is possible to reach a 98% diffraction efficiency on the -1st diffraction ord

Phased arrays are vital in communication systems and have received significant interest in the field of optoelectronics and photonics, enabling a wide range of applications such as LiDAR, holography, wireless communication, etc. In this work, we present a blazed grating antenna that is optimized to have upward radiation efficiency as high as 80% with a compact footprint of 3.5 μm \times 2 μm at an operational wavelength of 1.55 μm. Our numerical investigations demonstrate that this antenna in a 64 \times 64 phased array configuration is capable of producing desired far-field radiation patterns. Additionally, our antenna possesses a low side lobe level of -9.7 dB and a negligible reflection efficiency of under 1%, making it an attractive candidate for integrated optical phased arrays.

MapReduce and its variants have significantly simplified and accelerated the process of developing parallel programs. However, most MapReduce implementations focus on data-intensive tasks while many real-world tasks are compute intensive and their data can fit distributedly into the memory. For these tasks, the speed of MapReduce programs can be much slower than those hand-optimized ones. We present Blaze, a C++ library that makes it easy to develop high performance parallel programs for such compute intensive tasks. At the core of Blaze is a highly-optimized in-memory MapReduce function, which has three main improvements over conventional MapReduce implementations: eager reduction, fast serialization, and special treatment for a small fixed key range. We also offer additional conveniences that make developing parallel programs similar to developing serial programs. These improvements make Blaze an easy-to-use cluster computing library that approaches the speed of hand-optimized parallel code. We apply Blaze to some common data mining tasks, including word frequency count, PageRank, k-means, expectation maximization (Gaussian mixture model), and k-nearest neighbors. Blaze outperfor

Silicon immersion gratings and grisms enable compact, near-infrared spectrographs with high throughput. These instruments find use in ground-based efforts to characterize stellar and exoplanet atmospheres, and in space-based observatories. Our grating fabrication technique uses x-ray crystallography to orient silicon parts prior to cutting, followed by lithography and wet chemical etching to produce the blaze. This process takes advantage of the crystal structure and relative difference in etching rates between the (100) and (111) planes such that we can produce parts that have surface errors < λ/4. Previous measurements indicate that chemical etching can yield a final etched blaze that slightly differs from the orientation of the (111) plane. This difference can be corrected by the mechanical mount in the case of the immersion gratings, but doing so may compromise grating throughput due to shadowing. In the case of the grisms, failure to take the actual blaze into account will reduce the brightness of the undeviated ray. We report on multiple techniques to precisely measure the blaze of our in-house fabricated immersion gratings. The first method uses a scanning electron micros

We derive from first principles the expression for the angular/wavelength distribution of the intensity diffracted by a blazed reflective grating, according to a scalar theory of diffraction. We considered the most common case of a groove profile with rectangular apex. Our derivation correctly identifies the geometric parameters of a blazed reflective grating that determine its diffraction efficiency, and fixes an incorrect but commonly adopted expression in the literature. We compare the predictions of this scalar theory with those resulting from a rigorous vector treatment of diffraction from one-dimensional blazed reflective gratings.

Machine learning tools have illustrated their potential in many significant sectors such as healthcare and finance, to aide in deriving useful inferences. The sensitive and confidential nature of the data, in such sectors, raise natural concerns for the privacy of data. This motivated the area of Privacy-preserving Machine Learning (PPML) where privacy of the data is guaranteed. Typically, ML techniques require large computing power, which leads clients with limited infrastructure to rely on the method of Secure Outsourced Computation (SOC). In SOC setting, the computation is outsourced to a set of specialized and powerful cloud servers and the service is availed on a pay-per-use basis. In this work, we explore PPML techniques in the SOC setting for widely used ML algorithms-- Linear Regression, Logistic Regression, and Neural Networks. We propose BLAZE, a blazing fast PPML framework in the three server setting tolerating one malicious corruption over a ring (\Z{\ell}). BLAZE achieves the stronger security guarantee of fairness (all honest servers get the output whenever the corrupt server obtains the same). Leveraging an input-independent preprocessing phase, BLAZE has a fast inpu

We analyze a complex scalar field with phi-4 interaction and a chemical potential mu on the lattice. An exact flux representation of the partition sum is used which avoids the complex action problem and based on a generalized worm algorithm we can run Monte Carlo simulations at arbitrary densities. We study thermodynamical quantities as a function of the chemical potential mu for zero- and finite temperature. It is shown that at zero temperature thermodynamical observables are independent of mu up to a critical value mu_c (Silver Blaze phenomenon). In a spectroscopy calculation we cross-check that mu_c agrees with the mass m of the scalar field. The Silver Blaze region ends in a second order phase transition and we show that for low temperatures the second order phase boundary persists and separates a pseudo Silver Blaze region from a condensed phase with strong mu-dependence.

Surface-relief gratings fabricated through nanoimprint lithography (NIL) are prone to topographic distortion induced by resist shrinkage. Characterizing the impact of this effect on blazed diffraction efficiency is particularly important for applications in astrophysical spectroscopy at soft x-ray wavelengths ($λ\approx 0.5 - 5$~nm) that call for the mass-production of large-area grating replicas with sub-micron, sawtooth surface-relief profiles. A variant of NIL that lends itself well for this task is substrate-conformal imprint lithography (SCIL), which uses a flexible, composite stamp formed from a rigid master template to imprint nanoscale features in an inorganic resist that cures thermodynamically through a silica sol-gel process. While SCIL enables the production of several hundred imprints before stamp degradation and avoids many of the detriments associated with large-area imprinting in NIL, the sol-gel resist suffers shrinkage dependent on the post-imprint cure temperature. Through atomic force microscopy and diffraction-efficiency testing at beamline 6.3.2 of the Advanced Light Source, the impact of this effect on blaze response is constrained for a $\sim$160-nm-period g

We consider quantum chromodynamics (QCD) with Nc colors and Nf quark flavors at finite quark chemical potential mu_q or isospin chemical potential mu_I. We specifically address the nature of the ``Silver Blaze'' behavior in the framework of 1/Nc expansion. Starting with the QCD partition function, we implement Veneziano's Nf/Nc expansion to identify the density onset. We find the baryon mass M_B and the pion mass m_pi appearing from different order of Veneziano's expansion. We argue that the confining properties are responsible for the Silver Blaze in the region of m_pi/2 < mu_q < M_B/Nc. We point out, however, that Veneziano's expansion brings about a puzzling subtlety along the same line as the baryon problem in finite-density quenched simulations. We emphasize that the large-Nc limit can allow for the physical ordering of M_B and m_pi thanks to the similarity to the quenched approximation, while the unphysical ghost quarks contaminate the baryon sector if Nc is finite. We also discuss the ``orientifold'' large-Nc limit that does not quench quark loops.

Future soft X-ray (10 - 50 Angstrom) spectroscopy missions require higher effective areas and resolutions to perform critical science that cannot be done by instruments on current missions. An X-ray grating spectrometer employing off-plane reflection gratings would be capable of meeting these performance criteria. Off-plane gratings with blazed groove facets operated in the Littrow mounting can be used to achieve excellent throughput into orders achieving high resolutions. We have fabricated two off-plane gratings with blazed groove profiles via a technique which uses commonly available microfabrication processes, is easily scaled for mass production, and yields gratings customized for a given mission architecture. Both fabricated gratings were tested in the Littrow mounting at the Max-Planck-Institute for extraterrestrial Physics PANTER X-ray test facility to assess their performance. The line spread functions of diffracted orders were measured, and a maximum resolution of 800 $\pm$ 20 is reported. In addition, we also observe evidence of a `blaze' effect from measurements of relative efficiencies of the diffracted orders.

We study the spacetime-reduced (Eguchi-Kawai) version of large-N QCD with nonzero chemical potential. We explore a method to suppress the sign fluctuations of the Dirac determinant in the hadronic phase; the method employs a re-summation of gauge configurations that are related to each other by center transformations. We numerically test this method in two dimensions, and find that it successfully solves the silver-blaze problem. We analyze the system further, and measure its free energy F, the average phase theta of its Dirac determinant, and its chiral condensate <psi-bar-psi>. We show that F and <psi-bar-psi> are independent of mu in the hadronic phase but that, as chiral perturbation theory predicts, the quenched chiral condensate drops from its mu=0 value when mu~(pion mass)/2. Finally, we find that the distribution of theta qualitatively agrees with further, more recent, predictions from chiral perturbation theory.

We extend our previous investigation of the two-loop $Φ$-derivable approximation to finite chemical potential $μ$ and discuss Bose-Einstein condensation (BEC) in the case of a charged scalar field with $O(2)$ symmetry. We show that the approximation is renormalizable by means of counterterms which are independent of both the temperature and the chemical potential. We point out the presence of an additional skew contribution to the propagator as compared to the $μ=0$ case, which comes with its own gap equation (except at Hartree level). We solve this equation together with the field equation, and the usual longitudinal and transversal gap equations to find that the transition is second order, in agreement with recent lattice results to which we compare. We also discuss a general criterion an approximation should obey for the so-called Silver Blaze property to hold, and we show that any $Φ$-derivable approximation at finite temperature and density obeys this criterion if one chooses a UV regularization that does not cut off the Matsubara sums.