An optimal (ϵ,δ)‐randomized approximation scheme for the mean of random variables with bounded relative variance

Randomized approximation algorithms for many #P‐complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a {0,1}‐matrix, and many others) reduce to creating random variables X₁,X₂,… with finite mean μ and standard deviation σ such that μ is the solution for the problem input, and the relative standard deviation |σ/μ| ≤ c for known c. Under these circumstances, it is known that the number of samples from the {X_i} needed to form an (?,δ)‐approximation that satisfies is at least . We present here an easy to implement (?,δ)‐approximation that uses samples. This achieves the same optimal running time as other estimators, but without the need for extra conditions such as bounds on third or fourth moments.     

Block low-rank single precision coarse grid solvers for extreme scale multigrid methods

Extreme scale simulation requires fast and scalable algorithms, such as multigrid methods. To achieve asymptotically optimal complexity, it is essential to employ a hierarchy of grids. The cost to solve the coarsest grid system can often be neglected in sequential computings, but cannot be ignored in massively parallel executions. In this case, the coarsest grid can be large and its efficient solution becomes a challenging task. We propose solving the coarse grid system using modern, approximate sparse direct methods and investigate the expected gains compared with traditional iterative methods. Since the coarse grid system only requires an approximate solution, we show that we can leverage block low-rank techniques, combined with the use of single precision arithmetic, to significantly reduce the computational requirements of the direct solver. In the case of extreme scale computing, the coarse grid system is too large for a sequential solution, but too small to permit massively parallel efficiency. We show that the agglomeration of the coarse grid system to a subset of processors is necessary for the sparse direct solver to achieve performance. We demonstrate the efficiency of the proposed method on a Stokes-type saddle point system solved with a monolithic Uzawa multigrid method. In particular, we show that the use of an approximate sparse direct solver for the coarse grid system can outperform that of a preconditioned minimal residual iterative method. This is demonstrated for the multigrid solution of systems of order up to $10^{11}$ degrees of freedom on a petascale supercomputer using 43,200 processes.     

Naphthoquinone–Dopamine Hybrids Inhibit α-Synuclein Aggregation,Disrupt Preformed Fibrils,and Attenuate Aggregate-Induced Toxicity

Accumulation and aggregation of the intrinsically disordered protein α-synuclein (α-Syn) into amyloid fibrils are hallmarks of a series of heterogeneous neurodegenerative disorders, known as synucleinopathies and most notably Parkinson's disease (PD). The crucial role of α-Syn aggregation in PD makes it an attractive target for the development of disease-modifying therapeutics that would inhibit α-Syn aggregation or disrupt its preformed fibrillar assemblies. To this end, we have designed and synthesized two naphthoquinone–dopamine-based hybrid small molecules, NQDA and Cl-NQDA, and demonstrated their ability to inhibit in vitro amyloid formation by α-Syn using ThT assay, CD, TEM, and Congo red birefringence. Moreover, these hybrid molecules efficiently disassembled preformed fibrils of α-Syn into nontoxic species, as evident from LUV leakage assay. NQDA and Cl-NQDA were found to have low cytotoxicity and they attenuated the toxicity induced by α-Syn towards SH-SY5Y neuroblastoma cells. NQDA was found to efficiently cross an in vitro human blood–brain barrier model. These naphthoquinone–dopamine based derivatives can be an attractive scaffold for therapeutic design towards PD.     

Ionisation and fragmentation of tetraphenyl iron (III) porphyrin chloride induced by slow multiply charged ion impact

Ionisation and ion-induced fragmentation of tetraphenyl iron (III) porphyrin chloride (FeTPPCl) molecules have been studied after slow collisions (v∼ 0.2 a.u.) with multiply charged ions (O³⁺, Ar⁸⁺). Intact molecules and large fragments are observed in charge states up to q=4. For q=1, the intact molecule is the most abundant species, in particular, when projectiles in higher charge states are used. When the internal energy of the singly charged ion is increased by the energy transfer during the collision, the singly charged system de-excites by the emission of a neutral Cl-atom, a free electron or possibly a negative Cl anion. The processes are observed as direct as well as delayed processes on a μs-time scale. For q=2 to 4 the loss of the Cl-atom and some phenyl groups becomes more likely due to the lower stability and the larger energy transfer. The charge state distribution of atomic fragments is found to be very different, in particular, when C^q+ and Cl^q+ ions are compared. In the first case mainly singly charged ions are detected, whereas in the second case ions in charge states up to q=6 are observed with high intensities. These phenomena are discussed in terms of the intramolecular charge mobility.     

A generalized exponential transform method for solving non-linear evolution equations of physical relevance

The purpose of the present paper is to introduce a new computational algebraic procedure that can easily be applied for solving non-linear partial differential equations (nPDE) especially the celebrated evolutions equations describing any time depended sequences.The crucial step needs an auxiliary variable satisfying special class of ordinary differential equations (ODE) of first order which are introduced new in this field for the first time.The validity and reliability of the method is tested by its application to some non-linear evolution equations leading to new class of solutions related with some new types of special functions.Otherwise, for practical use in science and engineering the algebraic construction of new class of solutions is of fundamental interest and moreover, the proposed approach convinced by its easiness and does not need tedious steps of evaluation and can be used without studying the whole theory.The possibility to write a symbolic software using any programming languages is given.Further, the algorithm works efficiently, is clear structured and can be used in any applications independently from the order and the non-linearity of the underlying nPDE.Therefore, the given novel algebraic method is suitable for a wider class of nPDE in order to augment the solution manifold by an alternative approach.     

Ultra-fast mass fingerprinting by high-affinity capture of peptides and proteins on derivatized poly(glycidyl methacrylate/divinylbenzene) for the analysis of serum and cell lysates

The development of support materials in mass fingerprinting is an important task required for diagnostic markers in conjunction with matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). The material-based approach, which we introduced as material-enhanced laser desorption/ionization (MELDI), focuses not only on different functionalities, but also emphasizes the morphology, i.e. porosity or particle size of the carrier material. As a result, it provides a quick and sensitive platform for effective binding of peptides and proteins out of different biofluids, e.g. serum, spinal fluid, urine or cell lysates, and to subsequently analyze them with MALDI-TOF MS. This approach includes a built-in desalting step for serum protein profiling and is sensitive enough to detect proteins and peptides down to 100 fmol/microL. Here we co-polymerized glycidyl methacrylate (GMA) with divinylbenzene (DVB) using thermal polymerization to yield a GMA/DVB polymer for further modifications. Different affinities have been created, such as immobilized metal ion affinity (IDA-Cu2+), reversed-phase (RP) and anion-exchanger (AX) chromatography. The diverse derivatizations and the dispersity of the particles created by different chemical synthetic approaches were confirmed by characteristic infrared (IR) peaks. The polymerization carried out by non-stirring yielded an average pore radius of 6.1 microm (macro-pores) that enhanced the binding capacity enormously by offering enlarged surface areas. Moreover, atomic absorption spectrometry (AAS) provided the metal content loaded on iminodiacetic acid (IDA) in the case of poly(GMA/DVB)-IDA-Cu2+. To summarize, the optimized MELDI approach is sensitive in its performance, extremely fast and can be adapted to robotic systems for routine analysis, allowing sample preparation in less than 5 min in contrast to the conventional surface-enhanced laser desorption/ionization (SELDI) methods.     

Limits on spin-independent interactions of weakly interacting massive particles with nucleons from the two-tower run of the cryogenic dark matter search

We report new results from the Cryogenic Dark Matter Search (CDMS II) at the Soudan Underground Laboratory. Two towers, each consisting of six detectors, were operated for 74.5 live days, giving spectrum-weighted exposures of 34 (12) kg d for the Ge (Si) targets after cuts, averaged over recoil energies 10-100 keV for a weakly interacting massive particle (WIMP) mass of 60 GeV/c2. A blind analysis was conducted, incorporating improved techniques for rejecting surface events. No WIMP signal exceeding expected backgrounds was observed. When combined with our previous results from Soudan, the 90% C.L. upper limit on the spin-independent WIMP-nucleon cross section is 1.6 x 10(-43) cm2 from Ge and 3 x 10(-42) cm2 from Si, for a WIMP mass of 60 GeV/c2. The combined limit from Ge (Si) is a factor of 2.5 (10) lower than our previous results and constrains predictions of supersymmetric models.     

Noncontact modal analysis of a pipe organ reed using airborne ultrasound stimulated vibrometry

The goal of this study was to excite and measure, in a noncontact manner, the vibrational modes of the reed from a reed organ pipe. To perform ultrasound stimulated excitation, the audio-range difference frequency between a pair of ultrasound beams produced a radiation force that induced vibrations. The resulting vibrational deflection shapes were measured with a scanning laser vibrometer. The resonances of any relatively small object can be studied in air using this technique. For a 36 mm x 6 mm brass reed, displacements and velocities in excess of 5 microm and 4 mm/s could be imparted at the fundamental frequency of 145 Hz. Using the same ultrasound transducer, excitation across the entire range of audio frequencies was obtained. Since the beam was focused on the reed, ultrasound stimulated excitation eliminated background effects observed during mechanical shaker excitation, such as vibrations of clamps and supports. The results obtained using single, dual and confocal ultrasound transducers in AM and two-beam modes, along with results obtained using a mechanical shaker and audio excitation using a speaker are discussed.