Breaking the PPSZ Barrier for Unique 3-SAT

The PPSZ algorithm by Paturi, Pudl\'ak, Saks, and Zane (FOCS 1998) is the fastest known algorithm for (Promise) Unique k-SAT. We give an improved algorithm with exponentially faster bounds for Unique 3-SAT. For uniquely satisfiable 3-CNF formulas, we do the following case distinction: We call a clause critical if exactly one literal is satisfied by the unique satisfying assignment. If a formula has many critical clauses, we observe that PPSZ by itself is already faster. If there are only few clauses allover, we use an algorithm by Wahlstr\"om (ESA 2005) that is faster than PPSZ in this case. Otherwise we have a formula with few critical and many non-critical clauses. Non-critical clauses have at least two literals satisfied; we show how to exploit this to improve PPSZ.Comment: 13 pages; major revision with simplified algorithm but slightly worse constant

P-Selectivity, Immunity, and the Power of One Bit

We prove that P-sel, the class of all P-selective sets, is EXP-immune, but is not EXP/1-immune. That is, we prove that some infinite P-selective set has no infinite EXP-time subset, but we also prove that every infinite P-selective set has some infinite subset in EXP/1. Informally put, the immunity of P-sel is so fragile that it is pierced by a single bit of information. The above claims follow from broader results that we obtain about the immunity of the P-selective sets. In particular, we prove that for every recursive function f, P-sel is DTIME(f)-immune. Yet we also prove that P-sel is not \Pi_2^p/1-immune

MuPix7 - A fast monolithic HV-CMOS pixel chip for Mu3e

The MuPix7 chip is a monolithic HV-CMOS pixel chip, thinned down to 50 \mu m. It provides continuous self-triggered, non-shuttered readout at rates up to 30 Mhits/chip of 3x3 mm^2 active area and a pixel size of 103x80 \mu m^2. The hit efficiency depends on the chosen working point. Settings with a power consumption of 300 mW/cm^2 allow for a hit efficiency >99.5%. A time resolution of 14.2 ns (Gaussian sigma) is achieved. Latest results from 2016 test beam campaigns are shown.Comment: Proceedingsfor the PIXEL2016 conference, submitted to JINST A dangling reference has been removed from this version, no other change

Solving satisfiability problems by fluctuations: The dynamics of stochastic local search algorithms

Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random satisfiability problems. We find two different dynamical regimes, depending on the number of constraints per variable: For low constraintness, the problems are solved efficiently, i.e. in linear time. For higher constraintness, the solution times become exponential. We observe that the dynamical behavior is characterized by a fast equilibration and fluctuations around this equilibrium. If the algorithm runs long enough, an exponentially rare fluctuation towards a solution appears.Comment: 21 pages, 18 figures, revised version, to app. in PRE (2003

Computational Indistinguishability between Quantum States and Its Cryptographic Application

We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem, QSCDff, is to distinguish between two types of random coset states with a hidden permutation over the symmetric group of finite degree. This naturally generalizes the commonly-used distinction problem between two probability distributions in computational cryptography. As our major contribution, we show that QSCDff has three properties of cryptographic interest: (i) QSCDff has a trapdoor; (ii) the average-case hardness of QSCDff coincides with its worst-case hardness; and (iii) QSCDff is computationally at least as hard as the graph automorphism problem in the worst case. These cryptographic properties enable us to construct a quantum public-key cryptosystem, which is likely to withstand any chosen plaintext attack of a polynomial-time quantum adversary. We further discuss a generalization of QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies on similar cryptographic properties of QSCDcyc.Comment: 24 pages, 2 figures. We improved presentation, and added more detail proofs and follow-up of recent wor

Interleukin-6 gene (IL-6): a possible role in brain morphology in the healthy adult brain

Background: Cytokines such as interleukin 6 (IL-6) have been implicated in dual functions in neuropsychiatric disorders. Little is known about the genetic predisposition to neurodegenerative and neuroproliferative properties of cytokine genes. In this study the potential dual role of several IL-6 polymorphisms in brain morphology is investigated. Methodology: In a large sample of healthy individuals (N = 303), associations between genetic variants of IL-6 (rs1800795; rs1800796, rs2069833, rs2069840) and brain volume (gray matter volume) were analyzed using voxel-based morphometry (VBM). Selection of single nucleotide polymorphisms (SNPs) followed a tagging SNP approach (e.g., Stampa algorigthm), yielding a capture 97.08% of the variation in the IL-6 gene using four tagging SNPs. Principal findings/results: In a whole-brain analysis, the polymorphism rs1800795 (−174 C/G) showed a strong main effect of genotype (43 CC vs. 150 CG vs. 100 GG; x = 24, y = −10, z = −15; F(2,286) = 8.54, puncorrected = 0.0002; pAlphaSim-corrected = 0.002; cluster size k = 577) within the right hippocampus head. Homozygous carriers of the G-allele had significantly larger hippocampus gray matter volumes compared to heterozygous subjects. None of the other investigated SNPs showed a significant association with grey matter volume in whole-brain analyses. Conclusions/significance: These findings suggest a possible neuroprotective role of the G-allele of the SNP rs1800795 on hippocampal volumes. Studies on the role of this SNP in psychiatric populations and especially in those with an affected hippocampus (e.g., by maltreatment, stress) are warranted.Bernhard T Baune, Carsten Konrad, Dominik Grotegerd, Thomas Suslow, Eva Birosova, Patricia Ohrmann, Jochen Bauer, Volker Arolt, Walter Heindel, Katharina Domschke, Sonja Schöning, Astrid V Rauch, Christina Uhlmann, Harald Kugel and Udo Dannlowsk

A Search for Selectrons and Squarks at HERA

Data from electron-proton collisions at a center-of-mass energy of 300 GeV are used for a search for selectrons and squarks within the framework of the minimal supersymmetric model. The decays of selectrons and squarks into the lightest supersymmetric particle lead to final states with an electron and hadrons accompanied by large missing energy and transverse momentum. No signal is found and new bounds on the existence of these particles are derived. At 95% confidence level the excluded region extends to 65 GeV for selectron and squark masses, and to 40 GeV for the mass of the lightest supersymmetric particle.Comment: 13 pages, latex, 6 Figure

Low Q^2 Jet Production at HERA and Virtual Photon Structure

The transition between photoproduction and deep-inelastic scattering is investigated in jet production at the HERA ep collider, using data collected by the H1 experiment. Measurements of the differential inclusive jet cross-sections dsigep/dEt* and dsigmep/deta*, where Et* and eta* are the transverse energy and the pseudorapidity of the jets in the virtual photon-proton centre of mass frame, are presented for 0 < Q2 < 49 GeV2 and 0.3 < y < 0.6. The interpretation of the results in terms of the structure of the virtual photon is discussed. The data are best described by QCD calculations which include a partonic structure of the virtual photon that evolves with Q2.Comment: 20 pages, 5 Figure