Biased thermodynamics can explain the behaviour of smart optimization algorithms that work above the dynamical threshold

Random constraint satisfaction problems can display a very rich structure in the space of solutions, with often an ergodicity breaking -- also known as clustering or dynamical -- transition preceding the satisfiability threshold when the constraint-to-variables ratio $\alpha$ is increased. However, smart algorithms start to fail finding solutions in polynomial time at some threshold $\alpha_{\rm alg}$ which is algorithmic dependent and generally bigger than the dynamical one $\alpha_d$. The reason for this discrepancy is due to the fact that $\alpha_d$ is traditionally computed according to the uniform measure over all the solutions. Thus, while bounding the region where a uniform sampling of the solutions is easy, it cannot predict the performance of off-equilibrium processes, that are still able of finding atypical solutions even beyond $\alpha_d$. Here we show that a reconciliation between algorithmic behaviour and thermodynamic prediction is nonetheless possible at least up to some threshold $\alpha_d^{\rm opt}\geq\alpha_d$, which is defined as the maximum value of the dynamical threshold computed on all possible probability measures over the solutions. We consider a simple Monte Carlo-based optimization algorithm, which is restricted to the solution space, and we demonstrate that sampling the equilibrium distribution of a biased measure improving on $\alpha_d$ is still possible even beyond the ergodicity breaking point for the uniform measure, where other algorithms hopelessly enter the out-of-equilibrium regime. The conjecture we put forward is that many smart algorithms sample the solution space according to a biased measure: once this measure is identified, the algorithmic threshold is given by the corresponding ergodicity-breaking transition

Stochastic Gradient Descent-like relaxation is equivalent to Glauber dynamics in discrete optimization and inference problems

Is Stochastic Gradient Descent (SGD) substantially different from Glauber dynamics? This is a fundamental question at the time of understanding the most used training algorithm in the field of Machine Learning, but it received no answer until now. Here we show that in discrete optimization and inference problems, the dynamics of an SGD-like algorithm resemble very closely that of Metropolis Monte Carlo with a properly chosen temperature, which depends on the mini-batch size. This quantitative matching holds both at equilibrium and in the out-of-equilibrium regime, despite the two algorithms having fundamental differences (e.g.\ SGD does not satisfy detailed balance). Such equivalence allows us to use results about performances and limits of Monte Carlo algorithms to optimize the mini-batch size in the SGD-like algorithm and make it efficient at recovering the signal in hard inference problems.Comment: 14 pages, 5 figure

Does Pelvic Incidence Influence the Morphology of the Sacroiliac Joint?

Pelvic Incidence is defined as the angle between the perpendicular line to the upper plate of S1 at its midpoint and the line between this point and the center of bicoxofemoral line, it describes the position of femural heads in relation to sacrum. Recently some authors described a direct correlation between high values of PI and large AP pelvic axis (horizontal pelvis) and a wide pelvic ring [1]. Also the acetabular orientation is influenced by PI ; high values of PI means a more vertical acetabulum. Having regard to the relationship between PI and the main structures involved in the load transfer, to date no studies that correlate the morphology of the Sacroiliac Joint (SiJ) and PI were performed. The aim of this study is to evaluate the different morphology of the auricular surface of the sacrum comparing two groups of healthy young people with low (40°) PI. We retrospectively analysed 51 consecutive young (between 20 and 35 y.o.) people. After the evaluation of PI the sample was divided into two groups: 31 people belong to the group A (PI 40°). The following morphological parameters of the SiJ were analysed: length of long axis (LLA), length of short axis (LSA), length of oblique axis (LOA), ratio between long and short axis (RLSA), angle between axis (ABA) and surface; global shape of the joint was evaluated; two new parameters were introduced, SiJ Tilt (SiJT), defined as the angle between the vertical line and the long axis of the SiJ and SiJ Slope (SiJS), defined as the angle between the horizontal line and the short axis of the SiJ. We found a strong statistically significant correlations (p-value 0.05) between PI and RLSA, shape, ABA, SiJT and SiJS; a weaker correlations (p-value 0.10) between PI and LLA, LSA were observed; no statistically significant correlation between PI and LOA and surface were observed. The results underline that there is a strong correlation between pelvic morphology and SiJ anatomy. Further studies, about the different pattern of forces distribution among SiJ, will need to be performed to have a better knowledge that could help to understand the biomechanics and pathophysiology of normal and pathological SiJ

Massive facial edema and airway obstruction secondary to acute postoperative sialadenitis or "anesthesia mumps": a case report

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

The Large-Scale Polarization Explorer (LSPE)

The LSPE is a balloon-borne mission aimed at measuring the polarization of the Cosmic Microwave Background (CMB) at large angular scales, and in particular to constrain the curl component of CMB polarization (B-modes) produced by tensor perturbations generated during cosmic inflation, in the very early universe. Its primary target is to improve the limit on the ratio of tensor to scalar perturbations amplitudes down to r = 0.03, at 99.7% confidence. A second target is to produce wide maps of foreground polarization generated in our Galaxy by synchrotron emission and interstellar dust emission. These will be important to map Galactic magnetic fields and to study the properties of ionized gas and of diffuse interstellar dust in our Galaxy. The mission is optimized for large angular scales, with coarse angular resolution (around 1.5 degrees FWHM), and wide sky coverage (25% of the sky). The payload will fly in a circumpolar long duration balloon mission during the polar night. Using the Earth as a giant solar shield, the instrument will spin in azimuth, observing a large fraction of the northern sky. The payload will host two instruments. An array of coherent polarimeters using cryogenic HEMT amplifiers will survey the sky at 43 and 90 GHz. An array of bolometric polarimeters, using large throughput multi-mode bolometers and rotating Half Wave Plates (HWP), will survey the same sky region in three bands at 95, 145 and 245 GHz. The wide frequency coverage will allow optimal control of the polarized foregrounds, with comparable angular resolution at all frequencies.Comment: In press. Copyright 2012 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibite

Optimal Afforestation Contracts with Asymmetric Information on Private Environmental Benefits

We investigate the problem of subsidising afforestation when private information exists with respect to the level of private utility derived from the project. We develop a simple model that allows for an intelligent design of contracts when information is asymmetric. The model involves the Principal and two groups of agents (landowners): a green' group deriving high private utility from the projects and a conventional' group deriving lower utility. Afforestation projects may be produced in different environmental quality, and we distinguish between two cases, a high quality and a low quality project. We find that the optimal set of contracts under asymmetric information involves two different contracts. One in which green landowners are somewhat overcompensated for projects of high quality, and one where conventional landowners are offered contracts including lower quality projects, compared to the symmetric case, but with compensation equal to his indifference payment. It is the ability to reduce quality requirements along with subsidies offered that allows for revelation of the private information. Finally, we discus how the results obtained may be used in the implementation of incentive schemes

On Coalition Formation with Heterogeneous Agents

We propose a framework to analyze coalition formation with heterogeneous agents. Existing literature defines stability conditions that do not ensure that, once an agent decides to sign an agreement, the enlarged coalition is feasible. Defining the concepts of refraction and exchanging, we set up conditions of existence and enlargement of a coalition with heterogeneous agents. We use the concept of exchanging agents to give necessary conditions for internal stability and show that refraction is a sufficient condition for the failure of an enlargement of the coalition. With heterogeneous agents we can get a situation where a group of members of an unstable coalition does not deviate, neither within the coalition nor within the extended coalition. Hence, the possibilities of agreement are richer than in the standard analysis with homogeneous agents. Examples of industrial economics are used for illustration, and an application to climate change negotiations is discussed in more detail

Detection chain and electronic readout of the QUBIC instrument

The Q and U Bolometric Interferometer for Cosmology (QUBIC) Technical Demonstrator (TD) aiming to shows the feasibility of the combination of interferometry and bolometric detection. The electronic readout system is based on an array of 128 NbSi Transition Edge Sensors cooled at 350mK readout with 128 SQUIDs at 1K controlled and amplified by an Application Specific Integrated Circuit at 40K. This readout design allows a 128:1 Time Domain Multiplexing. We report the design and the performance of the detection chain in this paper. The technological demonstrator unwent a campaign of test in the lab. Evaluation of the QUBIC bolometers and readout electronics includes the measurement of I-V curves, time constant and the Noise Equivalent Power. Currently the mean Noise Equivalent Power is ~ 2 x 10⁻¹⁶ W/√Hz