Crane wheels production quality control

Quality control of crane wheels is an important part for support of crane mechanisms permanent operation. Normal functioning of logistics systems requires preventing of crane downtimes and delays. The research results of the impact of the crane wheels (710 mm diameter, 65Г steel) surface hardness on coercivity indicators are presented in this paper. Obtained research results of dependence between the coercivity indicators and the crane wheels rolling surface hardness for their use in practice are described. The influence of the crane wheels surface hardness on the coercivity indicators is researched. Research has shown the dependence of the coercive force from the regulatory crane wheels rolling surface hardness, which is received after a quenching. This research allows you to use obtained results for a quality control of the crane wheels quenching in the production process, a rapid control of the crane wheels at the expert examination

New Hardness Results for the Permanent Using Linear Optics

In 2011, Aaronson gave a striking proof, based on quantum linear optics, that the problem of computing the permanent of a matrix is #P-hard. Aaronson\u27s proof led naturally to hardness of approximation results for the permanent, and it was arguably simpler than Valiant\u27s seminal proof of the same fact in 1979. Nevertheless, it did not show #P-hardness of the permanent for any class of matrices which was not previously known. In this paper, we present a collection of new results about matrix permanents that are derived primarily via these linear optical techniques. First, we show that the problem of computing the permanent of a real orthogonal matrix is #P-hard. Much like Aaronson\u27s original proof, this implies that even a multiplicative approximation remains #P-hard to compute. The hardness result even translates to permanents of orthogonal matrices over the finite field F_{p^4} for p != 2, 3. Interestingly, this characterization is tight: in fields of characteristic 2, the permanent coincides with the determinant; in fields of characteristic 3, one can efficiently compute the permanent of an orthogonal matrix by a nontrivial result of Kogan. Finally, we use more elementary arguments to prove #P-hardness for the permanent of a positive semidefinite matrix. This result shows that certain probabilities of boson sampling experiments with thermal states are hard to compute exactly, despite the fact that they can be efficiently sampled by a classical computer

Effect of Er:YAG Laser Irradiation Combined With Fluoride Application on the Resistance of Primary and Permanent Dental Enamel to Erosion

Introduction: Erosion is an important cause of tooth mineral loss. The combined use of lasers and fluoride has been introduced as a novel modality for the prevention of enamel demineralization. This study aimed to assess the effect of Er:YAG laser combined with fluoride application on primary and permanent enamel resistance to erosion.Methods: Eighty enamel specimens of permanent (n=40) and primary (n=40) molars were prepared and randomly assigned to four groups:  C —control (no pretreatment), F—acidulated phosphate fluoride (APF) gel, ­­­­­FL—APF gel application followed by Er:YAG laser irradiation, and LF—Er:YAG laser irradiation followed by the application of APF gel . The specimens were then submitted to pH cycling using Coca-Cola (pH=2.4). Enamel micro-hardness was measured using the Vickers micro-hardness tester before pretreatment and after the erosive process. The collected data were analyzed using the Kolmogorov-Smirnov test, two-way ANOVA and repeated measures ANOVA.Results: The micro-hardness of both permanent and primary enamel significantly decreased after the erosive process (P<0.05). In the permanent enamel specimens, the greatest reduction in micro-hardness was noted in groups C and F, while the least reduction was noted in group FL. However, these differences were not statistically significant (P>0.05). In the primary enamel specimens, the greatest reduction in micro-hardness was noted in groups C and LF, while the least reduction was noted in group F. These differences were not statistically significant (P>0.05).Conclusion: Within the limitations of this study, Er:YAG laser irradiation combined with fluoride application could not prevent erosion in permanent and primary enamel during the erosive process. 

The Computational Complexity of Quantum Determinants

In this work, we study the computational complexity of quantum determinants, a $q$-deformation of matrix permanents: Given a complex number $q$ on the unit circle in the complex plane and an $n\times n$ matrix $X$, the $q$-permanent of $X$ is defined as $$\mathrm{Per}_q(X) = \sum_{\sigma\in S_n} q^{\ell(\sigma)}X_{1,\sigma(1)}\ldots X_{n,\sigma(n)},$$ where $\ell(\sigma)$ is the inversion number of permutation $\sigma$ in the symmetric group $S_n$ on $n$ elements. The function family generalizes determinant and permanent, which correspond to the cases $q=-1$ and $q=1$ respectively. For worst-case hardness, by Liouville's approximation theorem and facts from algebraic number theory, we show that for primitive $m$-th root of unity $q$ for odd prime power $m=p^k$, exactly computing $q$-permanent is $\mathsf{Mod}_p\mathsf{P}$-hard. This implies that an efficient algorithm for computing $q$-permanent results in a collapse of the polynomial hierarchy. Next, we show that computing $q$-permanent can be achieved using an oracle that approximates to within a polynomial multiplicative error and a membership oracle for a finite set of algebraic integers. From this, an efficient approximation algorithm would also imply a collapse of the polynomial hierarchy. By random self-reducibility, computing $q$-permanent remains to be hard for a wide range of distributions satisfying a property called the strong autocorrelation property. Specifically, this is proved via a reduction from $1$-permanent to $q$-permanent for $O(1/n^2)$ points $z$ on the unit circle. Since the family of permanent functions shares common algebraic structure, various techniques developed for the hardness of permanent can be generalized to $q$-permanents

Computing the partition function of the Sherrington-Kirkpatrick model is hard on average

We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In particular, we establish that unless $P= \#P$, there does not exist a polynomial-time algorithm to exactly compute the partition function on average. This is done by showing that if there exists a polynomial time algorithm, which exactly computes the partition function for inverse polynomial fraction ($1/n^{O(1)}$) of all inputs, then there is a polynomial time algorithm, which exactly computes the partition function for all inputs, with high probability, yielding $P=\#P$. The computational model that we adopt is {\em finite-precision arithmetic}, where the algorithmic inputs are truncated first to a certain level $N$ of digital precision. The ingredients of our proof include the random and downward self-reducibility of the partition function with random external field; an argument of Cai et al. \cite{cai1999hardness} for establishing the average-case hardness of computing the permanent of a matrix; a list-decoding algorithm of Sudan \cite{sudan1996maximum}, for reconstructing polynomials intersecting a given list of numbers at sufficiently many points; and near-uniformity of the log-normal distribution, modulo a large prime $p$. To the best of our knowledge, our result is the first one establishing a provable hardness of a model arising in the field of spin glasses. Furthermore, we extend our result to the same problem under a different {\em real-valued} computational model, e.g. using a Blum-Shub-Smale machine \cite{blum1988theory} operating over real-valued inputs.Comment: 31 page

Vulnerability of CMOS image sensors in megajoule class laser harsh environment

CMOS image sensors (CIS) are promising candidates as part of optical imagers for the plasma diagnostics devoted to the study of fusion by inertial confinement. However, the harsh radiative environment of Megajoule Class Lasers threatens the performances of these optical sensors. In this paper, the vulnerability of CIS to the transient and mixed pulsed radiation environment associated with such facilities is investigated during an experiment at the OMEGA facility at the Laboratory for Laser Energetics (LLE), Rochester, NY, USA. The transient and permanent effects of the 14 MeV neutron pulse on CIS are presented. The behavior of the tested CIS shows that active pixel sensors (APS) exhibit a better hardness to this harsh environment than a CCD. A first order extrapolation of the reported results to the higher level of radiation expected for Megajoule Class Laser facilities (Laser Megajoule in France or National Ignition Facility in the USA) shows that temporarily saturated pixels due to transient neutron-induced single event effects will be the major issue for the development of radiation-tolerant plasma diagnostic instruments whereas the permanent degradation of the CIS related to displacement damage or total ionizing dose effects could be reduced by applying well known mitigation techniques

Weakening Assumptions for Deterministic Subexponential Time Non-Singular Matrix Completion

In (Kabanets, Impagliazzo, 2004) it is shown how to decide the circuit polynomial identity testing problem (CPIT) in deterministic subexponential time, assuming hardness of some explicit multilinear polynomial family for arithmetical circuits. In this paper, a special case of CPIT is considered, namely low-degree non-singular matrix completion (NSMC). For this subclass of problems it is shown how to obtain the same deterministic time bound, using a weaker assumption in terms of determinantal complexity. Hardness-randomness tradeoffs will also be shown in the converse direction, in an effort to make progress on Valiant's VP versus VNP problem. To separate VP and VNP, it is known to be sufficient to prove that the determinantal complexity of the m-by-m permanent is $m^{\omega(\log m)}$. In this paper it is shown, for an appropriate notion of explicitness, that the existence of an explicit multilinear polynomial family with determinantal complexity m^{\omega(\log m)}$is equivalent to the existence of an efficiently computable generator$G_n$for multilinear NSMC with seed length$O(n^{1/\sqrt{\log n}})$. The latter is a combinatorial object that provides an efficient deterministic black-box algorithm for NSMC. ``Multilinear NSMC'' indicates that$G_n$only has to work for matrices$M(x)$of$poly(n)$size in$n$variables, for which$det(M(x))$ is a multilinear polynomial