Higher order corrections to the effective potential close to the jamming transition in the perceptron model

We analyze the perceptron model performing a Plefka-like expansion of the free energy. This model falls in the same universality class as hard spheres near jamming, allowing to get exact predictions in high dimensions for more complex systems. Our method enables to define an effective potential (or TAP free energy), namely a coarse-grained functional depending on the contact forces and the effective gaps between the particles. The derivation is performed up to the third order, with a particular emphasis on the role of third order corrections to the TAP free energy. These corrections, irrelevant in a mean-field framework in the thermodynamic limit, might instead play a fundamental role when considering finite-size effects. We also study the typical behavior of the forces and we show that two kinds of corrections can occur. The first contribution arises since the system is analyzed at a finite distance from jamming, while the second one is due to finite-size corrections. In our analysis, third order contributions vanish in the jamming limit, both for the potential and the generalized forces, in agreement with the argument proposed by Wyart and coworkers invoking isostaticity. Finally, we analyze the scalings emerging close to the jamming line, which define a crossover regime connecting the control parameters of the model to an effective temperature.Comment: 14 pages, 4 figure

Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems

We discuss a resource-competition model, which takes the MacArthur's model as a platform, to unveil interesting connections with glassy features and jamming in high dimension. This model presents two qualitatively different phases: a "shielded" phase, where a collective and self-sustained behavior emerges, and a "vulnerable" phase, where a small perturbation can destabilize the system and contribute to population extinction. We first present our perspective based on a strong similarity with continuous constraint satisfaction problems in their convex regime. Then, we discuss the stability in terms of the computation of the leading eigenvalue of the Hessian matrix of the free energy in the replica space. This computation allows us to efficiently distinguish between the two aforementioned phases and to relate high-dimensional critical ecosystems to glassy phenomena in the low-temperature regime.Comment: Updated version with references added. 6 pages, 2 figure

Dynamical Mean-Field Theory and Aging Dynamics

Dynamical Mean-Field Theory (DMFT) replaces the many-body dynamical problem with one for a single degree of freedom in a thermal bath whose features are determined self-consistently. By focusing on models with soft disordered $p$-spin interactions, we show how to incorporate the mean-field theory of aging within dynamical mean-field theory. We study cases with only one slow time-scale, corresponding statically to the one-step replica symmetry breaking (1RSB) phase, and cases with an infinite number of slow time-scales, corresponding statically to the full replica symmetry breaking (FRSB) phase. For the former, we show that the effective temperature of the slow degrees of freedom is fixed by requiring critical dynamical behavior on short time-scales, i.e. marginality. For the latter, we find that aging on an infinite number of slow time-scales is governed by a stochastic equation where the clock for dynamical evolution is fixed by the change of effective temperature, hence obtaining a dynamical derivation of the stochastic equation at the basis of the FRSB phase. Our results extend the realm of the mean-field theory of aging to all situations where DMFT holds.Comment: 28 pages, 3 figure

The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential

We present a parallel derivation of the Thouless-Anderson-Palmer (TAP) equations and of an effective potential for the negative perceptron and soft sphere models in high dimension. Both models are continuous constrained satisfaction problems with a critical jamming transition characterized by the same exponents. Our analysis reveals that a power expansion of the potential up to the second order represents a successful framework to approach the jamming line from the SAT phase (the region of the phase diagram where at least one configuration verifies all the constraints), where the ground-state energy is zero. An interesting outcome is that close to jamming the effective thermodynamic potential has a logarithmic contribution, which turns out to be dominant in a proper scaling regime. Our approach is quite general and can be directly applied to other interesting models. Finally, we study the spectrum of small harmonic fluctuations in the SAT phase recovering the typical scaling $D(\omega) \sim \omega^2$ below the cutoff frequency but a different behavior characterized by a non-trivial exponent above it.Comment: 11 pages; a few typos correcte

The combined use of corticotomy and clear aligners: a case report

OBJECTIVE:   To describe an orthodontic treatment that combines an esthetic approach (clear aligners) with surgery (alveolar corticotomy). MATERIALS AND METHODS:   A patient with moderate dental crowding and Class I skeletal and molar relationships was selected. Orthodontic records of the patient were taken. Periodontal indexes, oral health-related quality of life (OHRQoL), and treatment time were evaluated. After we reflected a full-thickness flap beyond the teeth apices, the cortical bone was exposed on the buccal aspect and a modified corticotomy procedure was performed. Interproximal corticotomy cuts were extended through the entire thickness of the cortical layer, just barely penetrating into medullary bone. Orthodontic force was applied on the teeth immediately after surgery. RESULTS:   Total treatment time was 2 months. Periodontal indexes were improved after correction of crowding. A deterioration of OHRQoL was limited to 3 days following surgery. CONCLUSION:   This case report may encourage the use, limited to selected cases, of corticotomy associated with clear aligners to treat moderate crowding

Measurement and clinical significance of biomarkers of oxidative stress in humans

Oxidative stress is the result of the imbalance between reactive oxygen species (ROS) formation and enzymatic and nonenzymatic antioxidants. Biomarkers of oxidative stress are relevant in the evaluation of the disease status and of the health-enhancing effects of antioxidants. We aim to discuss the major methodological bias of methods used for the evaluation of oxidative stress in humans. There is a lack of consensus concerning the validation, standardization, and reproducibility of methods for the measurement of the following: (1) ROS in leukocytes and platelets by flow cytometry, (2) markers based on ROS-induced modifications of lipids, DNA, and proteins, (3) enzymatic players of redox status, and (4) total antioxidant capacity of human body fluids. It has been suggested that the bias of each method could be overcome by using indexes of oxidative stress that include more than one marker. However, the choice of the markers considered in the global index should be dictated by the aim of the study and its design, as well as by the clinical relevance in the selected subjects. In conclusion, the clinical significance of biomarkers of oxidative stress in humans must come from a critical analysis of the markers that should give an overall index of redox status in particular conditions

The combined use of computer-guided, minimally invasive, flapless corticotomy and clear aligners as a novel approach to moderate crowding: a case report

The aim of this case report was to describe an innovative orthodontic treatment method that combined surgical and orthodontic techniques. The novel method was used to achieve a positive result in a case of moderate crowding by employing a computer-guided piezocision procedure followed by the use of clear aligners. A 23-year-old woman had a malocclusion with moderate crowding. Her periodontal indices, oral health-related quality of life (OHRQoL), and treatment time were evaluated. The treatment included interproximal corticotomy cuts extending through the entire thickness of the cortical layer, without a fullthickness flap reflection. This was achieved with a three-dimensionally printed surgical guide using computer-aided design and computer-aided manufacturing. Orthodontic force was applied to the teeth immediately after surgery by using clear appliances for better control of tooth movement. The total treatment time was 8 months. The periodontal indices improved after crowding correction, but the oral health impact profile showed a slight deterioration of OHRQoL during the 3 days following surgery. At the 2-year retention follow-up, the stability of treatment was excellent. The reduction in surgical time and patient discomfort, increased periodontal safety and patient acceptability, and accurate control of orthodontic movement without the risk of losing anchorage may encourage the use of this combined technique in appropriate cases

Mars Express measurements of surface albedo changes over 2004 - 2010

The pervasive Mars dust is continually transported between the surface and the atmosphere. When on the surface, dust increases the albedo of darker underlying rocks and regolith, which modifies climate energy balance and must be quantified. Remote observation of surface albedo absolute value and albedo change is however complicated by dust itself when lifted in the atmosphere. Here we present a method to calculate and map the bolometric solar hemispherical albedo of the Martian surface using the 2004 - 2010 OMEGA imaging spectrometer dataset. This method takes into account aerosols radiative transfer, surface photometry, and instrumental issues such as registration differences between visible and near-IR detectors. Resulting albedos are on average 17% higher than previous estimates for bright surfaces while similar for dark surfaces. We observed that surface albedo changes occur mostly during the storm season due to isolated events. The main variations are observed during the 2007 global dust storm and during the following year. A wide variety of change timings are detected such as dust deposited and then cleaned over a Martian year, areas modified only during successive global dust storms, and perennial changes over decades. Both similarities and differences with previous global dust storms are observed. While an optically thin layer of bright dust is involved in most changes, this coating turns out to be sufficient to mask underlying mineralogical near-IR spectral signatures. Overall, changes result from apparently erratic events; however, a cyclic evolution emerges for some (but not all) areas over long timescales

Investigation of cavitation damage of a mechanical pump impeller in high temperature potassium quarterly progress report no. 1, 7 dec. 1964 - 28 feb. 1965

Cavitation damage prediction from mixed flow centrifugal pump impeller in endurance testing in high temperature potassiu