Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

Since the proof of the four color theorem in 1976, computer-generated proofs have become a reality in mathematics and computer science. During the last decade, we have seen formal proofs using verified proof assistants being used to verify the validity of such proofs. In this paper, we describe a formalized theory of size-optimal sorting networks. From this formalization we extract a certified checker that successfully verifies computer-generated proofs of optimality on up to 8 inputs. The checker relies on an untrusted oracle to shortcut the search for witnesses on more than 1.6 million NP-complete subproblems.Comment: IMADA-preprint-c

Observation of quantum spin noise in a 1D light-atoms quantum interface

We observe collective quantum spin states of an ensemble of atoms in a one-dimensional light-atom interface. Strings of hundreds of cesium atoms trapped in the evanescent fiel of a tapered nanofiber are prepared in a coherent spin state, a superposition of the two clock states. A weak quantum nondemolition measurement of one projection of the collective spin is performed using a detuned probe dispersively coupled to the collective atomic observable, followed by a strong destructive measurement of the same spin projection. For the coherent spin state we achieve the value of the quantum projection noise 40 dB above the detection noise, well above the 3 dB required for reconstruction of the negative Wigner function of nonclassical states. We analyze the effects of strong spatial inhomogeneity inherent to atoms trapped and probed by the evanescent waves. We furthermore study temporal dynamics of quantum fluctuations relevant for measurement-induced spin squeezing and assess the impact of thermal atomic motion. This work paves the road towards observation of spin squeezed and entangled states and many-body interactions in 1D spin ensembles

Generation and detection of a sub-Poissonian atom number distribution in a one-dimensional optical lattice

We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance $-14$ dB below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of $\pm 8$ atoms on an ensemble of some $10^3$ atoms in a one-dimensional trap. The method is very well suited for generating collective atomic entangled or spin-squeezed states via a quantum non-demolition measurement as well as for tomography of exotic atomic states in a one-dimensional lattice

Mainstreaming prevention: Prescribing fruit and vegetables as a brief intervention in primary care

This is the author's PDF version of an article published in Public health© 2005.This articles discusses a project at the Castlefields Health Centre in Halton whereby primary care professionals issue a prescription for discounts on fruit and vegetables. The prescription is explicitly linked to the five-a-day message

An implementation of Deflate in Coq

The widely-used compression format "Deflate" is defined in RFC 1951 and is based on prefix-free codings and backreferences. There are unclear points about the way these codings are specified, and several sources for confusion in the standard. We tried to fix this problem by giving a rigorous mathematical specification, which we formalized in Coq. We produced a verified implementation in Coq which achieves competitive performance on inputs of several megabytes. In this paper we present the several parts of our implementation: a fully verified implementation of canonical prefix-free codings, which can be used in other compression formats as well, and an elegant formalism for specifying sophisticated formats, which we used to implement both a compression and decompression algorithm in Coq which we formally prove inverse to each other -- the first time this has been achieved to our knowledge. The compatibility to other Deflate implementations can be shown empirically. We furthermore discuss some of the difficulties, specifically regarding memory and runtime requirements, and our approaches to overcome them

Back-to-back correlations of high p_T hadrons in relativistic heavy ion collisions

We investigate the suppression factor and the azimuthal correlation function for high $p_T$ hadrons in central Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV by using a dynamical model in which hydrodynamics is combined with explicitly traveling jets. We study the effects of parton energy loss in a hot medium, intrinsic $k_T$ of partons in a nucleus, and $p_{\perp}$ broadening of jets on the back-to-back correlations of high $p_T$ hadrons. Parton energy loss is found to be a dominant effect on the reduction of the away-side peaks in the correlation function.Comment: 4 pages, 4 figures; version to appear in Phys. Rev. Let

Binary pattern tile set synthesis is NP-hard

In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the smallest number of tile types which will self-assemble an input pattern of $k$ colors. Of both theoretical and practical significance, $k$-PATS has been studied in a series of papers which have shown $k$-PATS to be NP-hard for $k = 60$, $k = 29$, and then $k = 11$. In this paper, we close the fundamental conjecture that 2-PATS is NP-hard, concluding this line of study. While most of our proof relies on standard mathematical proof techniques, one crucial lemma makes use of a computer-assisted proof, which is a relatively novel but increasingly utilized paradigm for deriving proofs for complex mathematical problems. This tool is especially powerful for attacking combinatorial problems, as exemplified by the proof of the four color theorem by Appel and Haken (simplified later by Robertson, Sanders, Seymour, and Thomas) or the recent important advance on the Erd\H{o}s discrepancy problem by Konev and Lisitsa using computer programs. We utilize a massively parallel algorithm and thus turn an otherwise intractable portion of our proof into a program which requires approximately a year of computation time, bringing the use of computer-assisted proofs to a new scale. We fully detail the algorithm employed by our code, and make the code freely available online

Saturation from nuclear pion dynamics

We construct an equation-of-state for nuclear matter based on the chiral Lagrangian. The relevant scales are discussed and an effective chiral power expansion scheme, which is constructed to work around the nuclear saturation density, is presented. A realistic equation-of-state is obtained by adjusting one free parameter, when the leading and subleading terms in the expansion are included. The saturation mechanism is due to correlations induced by the one-pion-exchange interaction. Furthermore, we find a substantial deviation from the Fermi-gas estimate of the quark condensate in nuclear matter already at the saturation density.Comment: revised version, with minor corrections, 13 pages, 3 Postscript figure

New developments in the genetics, pathogenesis, and therapy of IgA nephropathy

Recent years have brought notable progress in the field of IgA nephropathy. Here, we highlight important new directions and latest developments, including successful discovery of several genetic susceptibility loci, formulation of the multihit pathogenesis model, introduction of the Oxford pathology scoring system, and formalization of the Kidney Disease Improving Global Outcomes (KDIGO) consensus treatment guidelines. We focus on the latest genetic findings that confirm a strong contribution of inherited factors and explain some of the geoethnic disparities in disease susceptibility. Most IgA nephropathy susceptibility loci discovered to date encode genes involved in the maintenance of the intestinal epithelial barrier and response to mucosal pathogens. The concerted pattern of interpopulation allelic differentiation across all genetic loci parallels the disease prevalence and correlates with variation in local pathogens, suggesting that multilocus adaptation might have shaped the present-day landscape of IgA nephropathy. Importantly, the 'Intestinal Immune Network for IgA Production' emerged as one of the new targets for potential therapeutic intervention. We place these findings in the context of the multihit pathogenesis model and existing knowledge of IgA immunobiology. Lastly, we provide our perspective on the existing treatment options, discuss areas of clinical uncertainty, and outline ongoing clinical trials and translational studies.Kidney International advance online publication, 16 September 2015; doi:10.1038/ki.2015.252