From average case complexity to improper learning complexity

The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing lower bounds fall short of the best known algorithms. The biggest challenge in proving complexity results is to establish hardness of {\em improper learning} (a.k.a. representation independent learning).The difficulty in proving lower bounds for improper learning is that the standard reductions from $\mathbf{NP}$-hard problems do not seem to apply in this context. There is essentially only one known approach to proving lower bounds on improper learning. It was initiated in (Kearns and Valiant 89) and relies on cryptographic assumptions. We introduce a new technique for proving hardness of improper learning, based on reductions from problems that are hard on average. We put forward a (fairly strong) generalization of Feige's assumption (Feige 02) about the complexity of refuting random constraint satisfaction problems. Combining this assumption with our new technique yields far reaching implications. In particular, 1. Learning $\mathrm{DNF}$'s is hard. 2. Agnostically learning halfspaces with a constant approximation ratio is hard. 3. Learning an intersection of $\omega(1)$ halfspaces is hard.Comment: 34 page

Evolution of Indarch (EH4 Chondrite) at 1 GPa and High Temperature

The chondritic meteorites are materials that are as old as the solar system itself characterized by variations in bulk chemical and oxidation state, and have long been considered possible building blocks that accreted to form the terrestrial inner planets. Enstatite chondrites contain nearly FeO free enstatite, silicon-rich kamacite and various sulfides indicating formation under highly reducing conditions. These materials could have participated in the formation of the Earth. However, "fingerprinting" of meteoritic materials has shown that no known meteoritic class corresponds to a hypothetical bulk Earth composition in every aspect. To derive constraints on early accretion and differentiation processes and possibly resolve the debate on the formation of the Earth, it is required to study experimentally a variety of chondritic materials and investigate their melting relations and elemental partitioning behavior at variable pressure (P), temperature (T) and oxygen fugacities (fO2). Variations in fO2 can indeed change chemical features and phase equilibria dramatically. The P-T phase diagrams of peridotites and carbonaceous chondrites have been extensively studied experimentally up to pressures and temperatures corresponding to the transition zone and lower mantle. Even though partial melting experiments have been conducted at ambient pressure on the enstatite chondrite Indarch, enstatite meteorites have never been experimentally investigated at high PT. The following investigation focuses on the effect of the fO2 on the phase relations of Indarch, an EH4 chondrite

How crucial is it to account for the antecedent moisture conditions in flood forecasting? Comparison of event-based and continuous approaches on 178 catchments

This paper compares event-based and continuous hydrological modelling approaches for real-time forecasting of river flows. Both approaches are compared using a lumped hydrologic model (whose structure includes a soil moisture accounting (SMA) store and a routing store) on a data set of 178 French catchments. The main focus of this study was to investigate the actual impact of soil moisture initial conditions on the performance of flood forecasting models and the possible compensations with updating techniques. The rainfall-runoff model assimilation technique we used does not impact the SMA component of the model but only its routing part. Tests were made by running the SMA store continuously or on event basis, everything else being equal. The results show that the continuous approach remains the reference to ensure good forecasting performances. We show, however, that the possibility to assimilate the last observed flow considerably reduces the differences in performance. Last, we present a robust alternative to initialize the SMA store where continuous approaches are impossible because of data availability problems

The Evolution of the EH4 Chondrite Indarch at High Pressure and Temperature: The First Experimental Results

Chondrite groups are characterized by variations in bulk composition and oxidation state, illustrating in part heterogeneity in the early solar nebula. Planetary accretion could be explained by at least two different scenarios: the homogeneous [1] and heterogeneous accretion models [2, 3]. In particular, for the formation of the Earth, some studies (e.g. [2, 3]) assume that one component is highly reduced material comparable to enstatite chondrites, devoid of volatile elements but containing all other elements in C1 abundance ratios. To derive constraints on the understanding of early differentiation processes, studies of the silicate phase relations and their interactions with metal, at relevant P-T-fO2, are required. Melting relations and equilibrium partitioning behaviour have been studied on peridotitic and chondritic starting compositions at pressures and temperatures corresponding to the transition zone and lower mantle [4, 5, 6]. However, enstatite chondrites, which are highly reduced primitive meteorites, have not yet been studied experimentally under such conditions. Thus, multianvil experiments have been performed at 20-25 GPa and 2000-2400 C on the EH4 chondrite Indarch

Experimental Behavior of Sulfur Under Primitive Planetary Differentiation Processes, the Sulfide Formations in Enstatite Meteorites and Implications for Mercury.

Enstatite meteorites are the most reduced naturally-occuring materials of the solar system. The cubic monosulfide series with the general formula (Mg,Mn,Ca,Fe)S are common phases in these meteorite groups. The importance of such minerals, their formation, composition and textural relationships for understanding the genesis of enstatite chondrites (EC) and aubrites, has long been recognized (e.g. [1]). However, the mechanisms of formation of these sulfides is still not well constrained certainly because of possible multiple ways to produce them. We propose to simulate different models of formation in order to check their mineralogical, chemical and textural relevancies. The solubility of sulfur in silicate melts is of primary interest for planetary mantles, particularly for the Earth and Mercury. Indeed, these two planets could have formed, at least partly, from EC materials (e.g. [2, 3, 4]). The sulfur content in silicate melts depends on the melt composition but also on pressure (P), temperature (T) and oxygen fugacity fO2. Unfortunately, there is no model of general validity in a wide range of P-T-fO2-composition which describes precisely the evolution of sulfur content in silicate melts, even if the main trends are now known. The second goal of this study is to constrain the sulfur content in silicate melts under reducing conditions and different temperatures

Performance Analysis of Sidelink 5G-V2X Mode 2 through an Open-Source Simulator

The Third Generation Partnership Project (3GPP) has recently published a new set of specifications to enable advanced driving applications in fifth generation (5G) vehicle-to-everything (V2X) scenarios, with particular effort dedicated to the sidelink resource allocation in the autonomous mode, named Mode 2. In this paper, we conduct a comprehensive analysis of Mode 2 performance via an open-source system-level simulator, which implements the 5G New Radio (NR) flexible numerology and physical layer aspects together with the newly specified sidelink resource allocation modes for V2X communications and different data traffic patterns. Results collected through extensive simulation campaigns, under a wide variety of vehicle density, data transmission settings and traffic patterns, showcase the effects of the new 5G-V2X features on the sidelink resource allocation performance and provide some insights into possible ways to further improve Mode 2 performance

Nonlinear oscillator with parametric colored noise: some analytical results

The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as compared to the energy. Thus, an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out. However, the standard elimination procedure, performed earlier for a Gaussian white noise, fails when the noise is colored because of correlations between the noise and the fast angular variable. We develop here a specific averaging scheme that retains these correlations. This allows us to calculate the probability distribution function (P.D.F.) of the system and to derive the behavior of physical observables in the long time limit

3^3He Structure and Mechanisms of p3p^3He Backward Elastic Scattering

The mechanism of $p^3$He backward elastic scattering is studied. It is found that the triangle diagrams with the subprocesses $pd\to ^3$He$\pi^0$, $pd^*\to ^3$He$\pi^0$ and $p(pp)\to^3$He$\pi^+$, where $d^*$ and $pp$ denote the singlet deuteron and diproton pair in the $^1S_0$ state, respectively, dominate in the cross section at 0.3-0.8 GeV, and their contribution is comparable with that for a sequential transfer of a $np$ pair at 1-1.5 GeV. The contribution of the $d^*+pp$, estimated on the basis of the spectator mechanism of the $p(NN)\to ^3$He$\pi$ reaction, increases the $p^3$He$\to ^3$He$p$ cross section by one order of magnitude as compared to the contribution of the deuteron alone. Effects of the initial and final states interaction are taken into account.Comment: 17 pages, Latex, 4 postscript figures, expanded version, accepted by Physical Review

Toward 6G Vehicle-to-Everything Sidelink: Nonorthogonal Multiple Access in the Autonomous Mode

The cellular vehicle-to-everything (C-V2X) sidelink technology, specified in the long-term evolution (LTE) and further improved in the 5G new radio (NR) standards to facilitate direct data exchange between vehicles, will play a crucial role in revolutionizing transportation systems. However, the demand for very high reliability and ultralow latency services especially challenges the sidelink resource allocation mechanism when performed by distributed vehicles, in the so-called autonomous mode. One of the major causes of ­performance degradation is the resource allocation mechanism, which was designed for orthogonal multiple access (OMA) and can generate interference and collisions under high load conditions. In this context, here we argue in favor of the use of non-OMA (NOMA) as a game changer for the sidelink in the upcoming 6G V2X, and the purpose of this article is to provide a reference for further intriguing studies in the field. Additionally, the gain achievable over conventional allocation schemes by enabling NOMA through the use of successive interference cancelation (SIC) at the receiver is measured through realistic simulations conducted when considering the latest C-V2X specifications

Drug vaping applied to cannabis: Is "Cannavaping" a therapeutic alternative to marijuana?

Therapeutic cannabis administration is increasingly used in Western countries due to its positive role in several pathologies. Dronabinol or tetrahydrocannabinol (THC) pills, ethanolic cannabis tinctures, oromucosal sprays or table vaporizing devices are available but other cannabinoids forms can be used. Inspired by the illegal practice of dabbing of butane hashish oil (BHO), cannabinoids from cannabis were extracted with butane gas, and the resulting concentrate (BHO) was atomized with specific vaporizing devices. The efficiency of "cannavaping," defined as the "vaping" of liquid refills for e-cigarettes enriched with cannabinoids, including BHO, was studied as an alternative route of administration for therapeutic cannabinoids. The results showed that illegal cannavaping would be subjected to marginal development due to the poor solubility of BHO in commercial liquid refills (especially those with high glycerin content). This prevents the manufacture of liquid refills with high BHO concentrations adopted by most recreational users of cannabis to feel the psychoactive effects more rapidly and extensively. Conversely, "therapeutic cannavaping" could be an efficient route for cannabinoids administration because less concentrated cannabinoids-enriched liquid refills are required. However, the electronic device marketed for therapeutic cannavaping should be carefully designed to minimize potential overheating and contaminant generation