Resolution Lower Bounds for Refutation Statements

For any unsatisfiable CNF formula we give an exponential lower bound on the size of resolution refutations of a propositional statement that the formula has a resolution refutation. We describe three applications. (1) An open question in (Atserias, M\"uller 2019) asks whether a certain natural propositional encoding of the above statement is hard for Resolution. We answer by giving an exponential size lower bound. (2) We show exponential resolution size lower bounds for reflection principles, thereby improving a result in (Atserias, Bonet 2004). (3) We provide new examples of CNFs that exponentially separate Res(2) from Resolution (an exponential separation of these two proof systems was originally proved in (Segerlind, Buss, Impagliazzo 2004))

Resolution and binary decision diagrams cannot simulate each other polynomially

There are many different ways of proving formulas in proposition logic. Many of these can easily be characterized as forms of resolution. Others use so-called binary decision diagrams (BDDs). Experimental evidence suggests that BDDs and resolution based techniques are fundamentally different, in the sense that their performance can differ very much on benchmarks. In this paper we confirm these findings by mathematical proof. We provide examples that are easy for BDDS and exponentially hard for any form of resolution, and vice versa, examples that ar easy for resolution and exponentially hard for BDDs

On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers

Holographic Methods as Local Probes of the Atomic Order in Solids

In the last fifteen years several techniques based on the holographic principle have been developed for the study of the 3D local order in solids. These methods use various particles: electrons, hard x-ray photons, gamma photons, or neutrons to image the atoms. Although the practical realisation of the various imaging experiments is very different, there is a common thread; the use of inside reference points for holographic imaging. In this paper we outline the basics of atomic resolution holography using inside reference points, especially concentrating to the hard x-ray case. Further, we outline the experimental requirements and what has been practically realized in the last decade. At last we give examples of applications and future perspectives.Comment: 14 pages, 6 figure

Laboratory von H\'amos X-ray Spectroscopy for Routine Sample Characterization

High energy resolution, hard X-ray spectroscopies are powerful element selective probes of the electronic and local structure of matter, with diverse applications in chemistry, physics, biology and materials science. The routine application of these techniques is hindered by the complicated and slow access to synchrotron radiation facilities. Here we propose a new, economic, easily operated laboratory high resolution von H\'amos type X-ray spectrometer, which offers rapid transmission experiments for X-ray absorption, and is also capable of recording X-ray emission spectra. The use of a cylindrical analyzer crystal and a position sensitive detector enabled us to build a maintenance free, flexible setup with low operational costs, while delivering synchrotron grade signal to noise measurements in reasonable acquisition times. We demonstrate the proof of principle and give examples for both measurement types. Finally, tracking of a several day long chemical transformation, a case better suited for laboratory than synchrotron investigation, is also presented

X-ray ptychography on low-dimensional hard-condensed matter materials

Tailoring structural, chemical, and electronic (dis-)order in heterogeneous media is one of the transformative opportunities to enable new functionalities and sciences in energy and quantum materials. This endeavor requires elemental, chemical, and magnetic sensitivities at the nano/atomic scale in two- and three-dimensional space. Soft X-ray radiation and hard X-ray radiation provided by synchrotron facilities have emerged as standard characterization probes owing to their inherent element-specificity and high intensity. One of the most promising methods in view of sensitivity and spatial resolution is coherent diffraction imaging, namely, X-ray ptychography, which is envisioned to take on the dominance of electron imaging techniques offering with atomic resolution in the age of diffraction limited light sources. In this review, we discuss the current research examples of far-field diffraction-based X-ray ptychography on two-dimensional and three-dimensional semiconductors, ferroelectrics, and ferromagnets and their blooming future as a mainstream tool for materials sciences

Results from the solar maximum mission

The major results from SMM (Solar Max Mission) are presented as they relate to the understanding of the energy release and particle transportation processes that led to the high energy X-ray aspects of solar flares. Evidence is reviewed for a 152- to 158-day periodicity in various aspects of solar activity including the rate of occurrence of hard X-ray and gamma-ray flares. The statistical properties of over 7000 hard X-ray flares detected with the Hard X-Ray Burst Spectrometer are presented including the spectrum of peak rates and the distribution of the photo number spectrum. A flare classification scheme is used to divide flares into three different types. Type A flares have purely thermal, compact sources with very steep hard X-ray spectra. Type B flares are impulsive bursts which show double footpoints in hard X-rays, and soft-hard-soft spectral evolution. Type C flares have gradually varying hard X-ray and microwave fluxes from high altitudes and show hardening of the X-ray spectrum through the peak and on the decay. SSM data are presented for examples of Type B and Type C events. New results are presented showing coincident hard X rays, O V, and UV continuum observations in Type B events with a time resolution of 128 ms. The subsecond variations in the hard X-ray flux during 10% of the stronger events are discussed and the fastest observed variation in a time of 20 ms is presented. The properties of Type C flares are presented as determined primarily from the non-imaged hard X-ray and microwave spectral data. A model based on the association of Type C flares and coronal mass ejections is presented to explain many of the characteristics of these gradual flares

Science with Simbol-X

Simbol-X is a French-Italian mission, with a participation of German laboratories, for X-ray astronomy in the wide 0.5-80 keV band. Taking advantage of emerging technology in mirror manufacturing and spacecraft formation flying, Simbol-X will push grazing incidence imaging up to ~80 keV, providing an improvement of roughly three orders of magnitude in sensitivity and angular resolution compared to all instruments that have operated so far above 10 keV. This will open a new window in X-ray astronomy, allowing breakthrough studies on black hole physics and census and particle acceleration mechanisms. We describe briefly the main scientific goals of the Simbol-X mission, giving a few examples aimed at highlighting key issues of the Simbol-X design.Comment: Proc. of the workshop "Simbol-X: The hard X-ray universe in focus", Bologna 14-16 May, 200

Hodge structures for orbifold cohomology

We construct a polarized Hodge structure on the primitive part of Chen and Ruan's orbifold cohomology $H_{orb}^k(X)$ for projective $SL$-orbifolds $X$ satisfying a ``Hard Lefschetz Condition''. Furthermore, the total cohomology $H_{orb}^{*,*}(X)$ forms a mixed Hodge structure that is polarized by every element of the K\"ahler cone of $X$. Using results of Cattani-Kaplan-Schmid this implies the existence of an abstract polarized variation of Hodge structure on the complexified K\"ahler cone of $X$. This construction should be considered as the analogue of the abstract polarized variation of Hodge structure that can be attached to the singular cohomology of a crepant resolution of $X$, in the light of the conjectural correspondence between the (quantum) orbifold cohomology and the (quantum) cohomology of a crepant resolution.Comment: Streamlined exposition. Added examples. Final versio