Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Cayley-Type Conditions for Billiards within kk Quadrics in RdR^d

The notions of reflection from outside, reflection from inside and signature of a billiard trajectory within a quadric are introduced. Cayley-type conditions for periodical trajectories for the billiard in the region bounded by $k$ quadrics in $R^d$ and for the billiard ordered game within $k$ ellipsoids in $R^d$ are derived. In a limit, the condition describing periodic trajectories of billiard systems on a quadric in $R^d$ is obtained.Comment: 10 pages, some corractions are made in Section

The Dehn invariants of the Bricard octahedra

We prove that the Dehn invariants of any Bricard octahedron remain constant during the flex and that the Strong Bellows Conjecture holds true for the Steffen flexible polyhedron.Comment: 13 pages, 10 figure

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Towards concolic testing for hybrid systems

Hybrid systems exhibit both continuous and discrete behavior. Analyzing hybrid systems is known to be hard. Inspired by the idea of concolic testing (of programs), we investigate whether we can combine random sampling and symbolic execution in order to effectively verify hybrid systems. We identify a sufficient condition under which such a combination is more effective than random sampling. Furthermore, we analyze different strategies of combining random sampling and symbolic execution and propose an algorithm which allows us to dynamically switch between them so as to reduce the overall cost. Our method has been implemented as a web-based checker named HYCHECKER. HYCHECKER has been evaluated with benchmark hybrid systems and a water treatment system in order to test its effectiveness.CPCI-S(ISTP)[email protected]; [email protected]

On the Integrity of Performance Comparison for Evolutionary Multi-objective Optimisation Algorithms

This paper proposes the notion that the experimental results and performance analyses of newly developed algorithms in the field of multi-objective optimisation may not offer sufficient integrity for hypothesis testing. This is demonstrated through the multiple comparison of three implementations of the popular Non-dominated Sorting Genetic Algorithm II (NSGA-II) from well-regarded frameworks using the hypervolume indicator. The results show that of the thirty considered comparison cases, only four indicate that there was no significant difference between the performance of either implementation

Mild Hypothermia Attenuates Mitochondrial Oxidative Stress by Protecting Respiratory Enzymes and Upregulating MnSOD in a Pig Model of Cardiac Arrest

Mild hypothermia is the only effective treatment confirmed clinically to improve neurological outcomes for comatose patients with cardiac arrest. However, the underlying mechanism is not fully elucidated. In this study, our aim was to determine the effect of mild hypothermia on mitochondrial oxidative stress in the cerebral cortex. We intravascularly induced mild hypothermia (33°C), maintained this temperature for 12 h, and actively rewarmed in the inbred Chinese Wuzhishan minipigs successfully resuscitated after 8 min of untreated ventricular fibrillation. Cerebral samples were collected at 24 and 72 h following return of spontaneous circulation (ROSC). We found that mitochondrial malondialdehyde and protein carbonyl levels were significantly increased in the cerebral cortex in normothermic pigs even at 24 h after ROSC, whereas mild hypothermia attenuated this increase. Moreover, mild hypothermia attenuated the decrease in Complex I and Complex III (i.e., major sites of reactive oxygen species production) activities of the mitochondrial respiratory chain and increased antioxidant enzyme manganese superoxide dismutase (MnSOD) activity. This increase in MnSOD activity was consistent with the upregulation of nuclear factor erythroid 2-related factor 2 (Nrf2) mRNA and protein expressions, and with the increase of Nrf2 nuclear translocation in normothermic pigs at 24 and 72 h following ROSC, whereas mild hypothermia enhanced these tendencies. Thus, our findings indicate that mild hypothermia attenuates mitochondrial oxidative stress in the cerebral cortex, which may be associated with reduced impairment of mitochondrial respiratory chain enzymes, and enhancement of MnSOD activity and expression via Nrf2 activation