Constant Factor Approximation for Balanced Cut in the PIE model

We propose and study a new semi-random semi-adversarial model for Balanced Cut, a planted model with permutation-invariant random edges (PIE). Our model is much more general than planted models considered previously. Consider a set of vertices V partitioned into two clusters $L$ and $R$ of equal size. Let $G$ be an arbitrary graph on $V$ with no edges between $L$ and $R$. Let $E_{random}$ be a set of edges sampled from an arbitrary permutation-invariant distribution (a distribution that is invariant under permutation of vertices in $L$ and in $R$). Then we say that $G + E_{random}$ is a graph with permutation-invariant random edges. We present an approximation algorithm for the Balanced Cut problem that finds a balanced cut of cost $O(|E_{random}|) + n \text{polylog}(n)$ in this model. In the regime when $|E_{random}| = \Omega(n \text{polylog}(n))$, this is a constant factor approximation with respect to the cost of the planted cut.Comment: Full version of the paper at the 46th ACM Symposium on the Theory of Computing (STOC 2014). 32 page

Study of lubricant jet flow phenomena in spur gears: Out of mesh condition

The penetration depth onto the tooth flank of a jet of oil at different velocities pointed at the pitch line on the outgoing side of mesh was determined. The analysis determines the impingement depth for both the gear and the pinion. It includes the cases for speed increasers and decreasers as well as for one to one gear ratio. In some cases the jet will strike the loaded side of the teeth, and in others it will strike the unloaded side of the teeth. In nearly all cases the top land will be cooled regardless of the penetration depth, and postimpingement oil spray will usually provide adequate amounts of oil for lubrication but is marginal or inadequate for cooling

Higgs boson production in association with a jet at next-to-next-to-leading order in perturbative QCD

We report on a calculation of the cross-section for Higgs boson production in gluon fusion in association with a hadronic jet at next-to-next-to-leading order (NNLO) in perturbative QCD. The computational technique is discussed in detail. We show explicitly how to employ known soft and collinear limits of scattering amplitudes to construct subtraction terms for NNLO computations. Cancellation of singularities is demonstrated numerically for the collinearly-subtracted $gg \to H + j$ cross-section through NNLO and the finite $\sigma_{gg \to Hj}$ cross-section is computed through ${\cal O}(\alpha_s^5)$ as a function of the center-of-mass collision energy. We present numerical results for the gluon-fusion contribution to Higgs production in association with a jet at the LHC. The NNLO QCD corrections significantly reduce the residual scale dependence of the cross-section. The computational method that we describe in this paper is applicable to the calculation of NNLO QCD corrections to any other $2 \to 2$ process at a hadron colliderComment: 48 pages, 5 figure

Radiation Damage in Polarized Ammonia Solids

Solid NH3 and ND3 provide a highly polarizable, radiation resistant source of polarized protons and deuterons and have been used extensively in high luminosity experiments investigating the spin structure of the nucleon. Over the past twenty years, the UVA polarized target group has been instrumental in producing and polarizing much of the material used in these studies, and many practical considerations have been learned in this time. In this discussion, we analyze the polarization performance of the solid ammonia targets used during the recent JLab Eg4 run. Topics include the rate of polarization decay with accumulated charge, the annealing procedure for radiation damaged targets to recover polarization, and the radiation induced change in optimum microwave frequency used to polarize the sample. We also discuss the success we have had in implementing frequency modulation of the polarizing microwave frequency.Comment: 5 pages, 6 figures. XIIth International Workshop on Polarized Sources, Targets and Polarimetr

Co-cultures with stem cell-derived human sensory neurons reveal regulators of peripheral myelination

Effective bidirectional signalling between axons and Schwann cells is essential for both the development and maintenance of peripheral nerve function. We have established conditions by which human induced pluripotent stem cell-derived sensory neurons can be cultured with rat Schwann cells, and have produced for the first time long-term and stable myelinating co-cultures with human neurons. These cultures contain the specialized domains formed by axonal interaction with myelinating Schwann cells, such as clustered voltage-gated sodium channels at the node of Ranvier and Shaker-type potassium channel (Kv1.2) at the juxtaparanode. Expression of type III neuregulin-1 (TIIINRG1) in induced pluripotent stem cell-derived sensory neurons strongly enhances myelination, while conversely pharmacological blockade of the NRG1-ErbB pathway prevents myelination, providing direct evidence for the ability of this pathway to promote the myelination of human sensory axons. The β-secretase, BACE1 is a protease needed to generate active NRG1 from the full-length form. Due to the fact that it also cleaves amyloid precursor protein, BACE1 is a therapeutic target in Alzheimer’s disease, however, consistent with its role in NRG1 processing we find that BACE1 inhibition significantly impairs myelination in our co-culture system. In order to exploit co-cultures to address other clinically relevant problems, they were exposed to anti-disialosyl ganglioside antibodies, including those derived from a patient with a sensory predominant, inflammatory neuropathy with mixed axonal and demyelinating electrophysiology. The co-cultures reveal that both mouse and human disialosyl antibodies target the nodal axolemma, induce acute axonal degeneration in the presence of complement, and impair myelination. The human, neuropathy-associated IgM antibody is also shown to induce complement-independent demyelination. Myelinating co-cultures using human induced pluripotent stem cell-derived sensory neurons thus provide insights into the cellular and molecular specialization of axoglial signalling, how pharmacological agents may promote or impede such signalling and the pathogenic effects of ganglioside antibodies