Counting solutions from finite samplings

We formulate the solution counting problem within the framework of inverse Ising problem and use fast belief propagation equations to estimate the entropy whose value provides an estimate on the true one. We test this idea on both diluted models (random 2-SAT and 3-SAT problems) and fully-connected model (binary perceptron), and show that when the constraint density is small, this estimate can be very close to the true value. The information stored by the salamander retina under the natural movie stimuli can also be estimated and our result is consistent with that obtained by Monte Carlo method. Of particular significance is sizes of other metastable states for this real neuronal network are predicted.Comment: 9 pages, 4 figures and 1 table, further discussions adde

Stability of A-150 plastic ionization chamber response over a ~30 year period

At the NIU Institute for Neutron Therapy at Fermilab, the clinical tissue-equivalent ionization chamber response is measured every treatment day using a cesium source that was configured to match readings obtained at the National Bureau of Standards. Daily measurements are performed in air using the air-to-tissue dose conversion factors given in AAPM Report no. 7. The measured exposure calibration factors have been tabulated and graphed as a function of time from 1978 to present. For A-150 plastic ionization chambers, these factors exhibit a sinusoidal variation with a period of approximately one year and amplitude of {+-} 1%. This variation, attributable to the hygroscopic nature of A-150 plastic, is correlated with the relative humidity of the facility, and is greater than the humidity corrections for gas described in the literature. Our data suggest that chamber calibration should be performed at least weekly to accommodate these variations

Exhaustive enumeration unveils clustering and freezing in random 3-SAT

We study geometrical properties of the complete set of solutions of the random 3-satisfiability problem. We show that even for moderate system sizes the number of clusters corresponds surprisingly well with the theoretic asymptotic prediction. We locate the freezing transition in the space of solutions which has been conjectured to be relevant in explaining the onset of computational hardness in random constraint satisfaction problems.Comment: 4 pages, 3 figure

Bit-Vector Model Counting using Statistical Estimation

Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms

COMMISSIONING OF THE FERMILAB ELECTRON COOLER PROTOTYPE BEAM LINE

Abstract A prototype of a 4.3-MeV electron cooling system is being assembled at Fermilab as part of the ongoing R&D program in high energy electron cooling. This electron cooler prototype will not demonstrate the actual cooling but it will allow determining if the electron beam properties are suitable for antiproton beam cooling. An electron beam is accelerated by a 5-MV Pelletron (Van de Graaff type) accelerator and transported to a prototype cooling section. The cooling will take place in a 20-m long solenoid flanked on both sides by a delivery and return beam-line -a total of 60 meters of transport channel. This paper describes the first results of commissioning this novel beam line as well as the status of the electron cooling R&D program

Electron cooling of 8-GeV antiprotons at Fermilab's Recycler: Results and operational implications

Electron cooling of 8 GeV antiprotons at Fermilab's Recycler storage ring is now routinely used in the collider operation. It requires a 0.1-0.5 A, 4.3 MeV dc electron beam and is designed to increase the longitudinal phase-space density of the circulating antiproton beam. This paper briefly describes the characteristics of the electron beam that were achieved to successfully cool antiprotons. Then, results from various cooling force measurements along with comparison to a nonmagnetized model are presented. Finally, operational aspects of the implementation of electron cooling at the Recycler are discussed, such as adjustments to the cooling rate and the influence of the electron beam on the antiproton beam lifetime

First steps towards a fast-neutron therapy planning program

<p>Abstract</p> <p>Background</p> <p>The Monte Carlo code GEANT4 was used to implement first steps towards a treatment planning program for fast-neutron therapy at the FRM II research reactor in Garching, Germany. Depth dose curves were calculated inside a water phantom using measured primary neutron and simulated primary photon spectra and compared with depth dose curves measured earlier. The calculations were performed with GEANT4 in two different ways, simulating a simple box geometry and splitting this box into millions of small voxels (this was done to validate the voxelisation procedure that was also used to voxelise the human body).</p> <p>Results</p> <p>In both cases, the dose distributions were very similar to those measured in the water phantom, up to a depth of 30 cm. In order to model the situation of patients treated at the FRM II MEDAPP therapy beamline for salivary gland tumors, a human voxel phantom was implemented in GEANT4 and irradiated with the implemented MEDAPP neutron and photon spectra. The 3D dose distribution calculated inside the head of the phantom was similar to the depth dose curves in the water phantom, with some differences that are explained by differences in elementary composition. The lateral dose distribution was studied at various depths. The calculated cumulative dose volume histograms for the voxel phantom show the exposure of organs at risk surrounding the tumor.</p> <p>Conclusions</p> <p>In order to minimize the dose to healthy tissue, a conformal treatment is necessary. This can only be accomplished with the help of an advanced treatment planning system like the one developed here. Although all calculations were done for absorbed dose only, any biological dose weighting can be implemented easily, to take into account the increased radiobiological effectiveness of neutrons compared to photons.</p

Modelling of grain boundary migration in bicrystals

A simple cellural automata model of the single grain boundary migration in bicrystals has been developed. It is based on the principle of minimization of the total grain boundary energy which is in our model proportional to the boundary area