Fast Monotone Summation over Disjoint Sets

We study the problem of computing an ensemble of multiple sums where the summands in each sum are indexed by subsets of size $p$ of an $n$-element ground set. More precisely, the task is to compute, for each subset of size $q$ of the ground set, the sum over the values of all subsets of size $p$ that are disjoint from the subset of size $q$. We present an arithmetic circuit that, without subtraction, solves the problem using $O((n^p+n^q)\log n)$ arithmetic gates, all monotone; for constant $p$, $q$ this is within the factor $\log n$ of the optimal. The circuit design is based on viewing the summation as a "set nucleation" task and using a tree-projection approach to implement the nucleation. Applications include improved algorithms for counting heaviest $k$-paths in a weighted graph, computing permanents of rectangular matrices, and dynamic feature selection in machine learning

The effect of microwave frequency and grad B on the ECR heating

In an ECR ion source many parameters are related to the heating of the electrons. The amplitude of the electric field is one of the main factors. In addition to this, many other parameters affect the production of highly charged ions inside the ECR ion source - for example microwave frequency, the strengthand configuration of the magnetic field, plasma density, neutral density and so on. Since the ionization becomes more and more difficult when the charge state increases the ionization has to be as efficient as possible. How will the gradient of the magnetic field and the microwave frequency affect the energy of the electron? The computer code to reveal information about these parameters has been developed. The simulations have shown that more efficient heating will be achieved with higher microwave frequency and with smaller gradient of the magnetic field. Lower gradient of the magnetic field is obtained, for example, by using a larger plasma chamber. It was also noticed that the heating efficiency is more dependent on the microwave frequency at high plasma density and more dependent on the gradient of the magnetic field at low plasma density

Photoelectron Emission from Metal Surfaces Induced by VUV-emission of Filament Driven Hydrogen Arc Discharge Plasma

Photoelectron emission measurements have been performed using a filament-driven multi-cusp arc discharge volume production H^- ion source (LIISA). It has been found that photoelectron currents obtained with Al, Cu, Mo, Ta and stainless steel (SAE 304) are on the same order of magnitude. The photoelectron currents depend linearly on the discharge power. It is shown experimentally that photoelectron emission is significant only in the short wavelength range of hydrogen spectrum due to the energy dependence of the quantum efficiency. It is estimated from the measured data that the maximum photoelectron flux from plasma chamber walls is on the order of 1 A per kW of discharge power

Aivojen unenaikaiset pulsaatiot

Tiivistelmä. Työtarkoitus: Tutkielman tarkoituksena oli selvittää miten aivojen pulsaatiot eroavat toisistaan unessa ja hereillä eri taajuuskaistoilla (Todella matalat taajuudet (VLF), hengityskaista, sykekaista) mitattuna todella nopealla fMRI sekvenssillä. MREG:llä. VLF-kaista oli 0.0098–0.10 Hz, hengityskaista 0.110–0.439 Hz ja sykekaista 0.522–1.599 Hz. MREG:n näytteenottotaajuus 10 Hz on korkeampi kuin perinteisen BOLD fMRI:n (blood oxygen-level-dependent functional magnetic resonance imaging), joten tulokset antavat entistä tarkempaa tietoa aivojen unenaikaisten pulsaatioiden toiminnasta. Menetelmät: MREG datalle tehtiin aluksi perinteinen fMRI-esikäsittely, jonka jälkeen AFNI:n 3dPeriodogram komennolla saatiin FFT tehospektrit koko pään alueelle. Tämän jälkeen halutut vokselit lajiteltiin maskeilla kolmeksi ROI:ksi (region of interest), jotka olivat harmaa aine, valkoinen aine ja kaikki ventrikkelit. 4 ventrikkelin ROI saatiin etsimällä kirkkain vokseli sen alueelta ja muodostettua sen ympärille pieni ROI. Unen ja valvetilan vertailu toteutettiin työtä varten luodulla MATLAB-skriptillä, joka jakoi ROI:den datan edellä mainittuihin taajuuskaistoihin laskien keskiarvot ja keskihajonnat niiden mukaan. Tulokset: MREG:llä kerätty data tuki vahvasti aiempien tutkimusten tuloksia aivojen unenaikaisista pulsaatioista. Päälöydös oli VLF-taajuuskaistan tehospektrin selkeä unen aikainen voimistuminen kaikissa ROI:ssa verrattuna valvetilaan. Johtopäätökset: MREG:n korkeampi näytteenottotaajuus on voinut poistaa hengityselimistön ja sydämen taajuuskaistojen laskostumisen, jonka seurauksena tulokset ovat tarkempia selkäydinnesteen unenaikaisten pulsaatioiden tutkimisessa.Pulsations of brain during sleep. Abstract. Objective: The objective of this thesis was to study how physiological brain pulsations (very low frequency (VLF), respiratory, cardiac) power differ in sleep compared to wakefulness measured with ultrafast MREG (Magnetic resonance encephalography). VLF-band was 0.0098–0.1 Hz, respiratory band 0.110–0.439 Hz and cardiac band 0.522–1.599Hz. MREG has a higher 10 Hz sampling rate so the results could be more accurate compared to data collected with traditional BOLD fMRI (Blood oxygen-level-dependent functional magnetic resonance imaging). Methods: MREG data was preprocessed the way fMRI data usually is. Then AFNI’s 3dPeriodogram-command was used to generate FFT power spectrum for the whole brain. Masks were used to split the data into 3 different ROI’s (region of interest) that which were white matter, gray matter, and all ventricles. Brightest voxel was then searched from the region of 4th ventricle to generate ROI for analyzing 4th ventricle. Comparison between sleep and awake was performed by MATLAB-script that also divided the data into three frequency spectrums. The script also calculated means and standard deviations for every spectrum of every ROI. Results: MREG-data seemed to follow the results of previous studies and theories regarding pulsations of the brain during sleep. The main discovery was VLF-frequency band’s greater power spectrum during sleep in every ROI compared to awake. Conclusion: Higher sampling rate achieved by MREG prevented aliasing with respiratory and cardiac frequencies and gave more accurate results regarding CSF-pulsations during sleep

Fluctuations and scaling in creep deformation

The spatial fluctuations of deformation are studied in creep in the Andrade's power-law and the logarithmic phases, using paper samples. Measurements by the Digital Image Correlation technique show that the relative strength of the strain rate fluctuations increases with time, in both creep regimes. In the Andrade creep phase characterized by a power law decay of the strain rate $\epsilon_t \sim t^{-\theta}$, with $\theta \approx 0.7$, the fluctuations obey $\Delta \epsilon_t \sim t^{-\gamma}$, with $\gamma \approx 0.5$. The local deformation follows a data collapse appropriate for an absorbing state/depinning transition. Similar behavior is found in a crystal plasticity model, with a jamming or yielding phase transition

Primordial statistical anisotropy generated at the end of inflation

We present a new mechanism for generating primordial statistical anisotropy of curvature perturbations. We introduce a vector field which has a non-minimal kinetic term and couples with a waterfall field in hybrid inflation model. In such a system, the vector field gives fluctuations of the end of inflation and hence induces a subcomponent of curvature perturbations. Since the vector has a preferred direction, the statistical anisotropy could appear in the fluctuations. We present the explicit formula for the statistical anisotropy in the primordial power spectrum and the bispectrum of curvature perturbations. Interestingly, there is the possibility that the statistical anisotropy does not appear in the power spectrum but does appear in the bispectrum. We also find that the statistical anisotropy provides the shape dependence to the bispectrum.Comment: 9 pages, This version supersedes the JCAP version. Minor revision

Covariant conservation of energy momentum in modified gravities

An explicit proof of the vanishing of the covariant divergence of the energy-momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the curvature scalar and its couplings with a scalar field. Also the case of a function of the curvature scalar multiplying a matter Lagrangian is considered. The proof is given both in the metric and in the first-order formalism, i.e. under the Palatini variational principle. It is found that the covariant conservation of energy-momentum is built-in to the field equations. This crucial result, called the generalized Bianchi identity, can also be deduced directly from the covariance of the extended gravitational action. Furthermore, we demonstrate that in all of these cases, the freely falling world lines are determined by the field equations alone and turn out to be the geodesics associated with the metric compatible connection. The independent connection in the Palatini formulation of these generalized theories does not have a similar direct physical interpretation. However, in the conformal Einstein frame a certain bi-metricity emerges into the structure of these theories. In the light of our interpretation of the independent connection as an auxiliary variable we can also reconsider some criticisms of the Palatini formulation originally raised by Buchdahl.Comment: 8 pages. v2: more discussio