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

Sum-of-squares lower bounds for planted clique

Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size k is planted in a random G(n, 1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for k ~ sqrt(n). In this paper we study the complexity of the planted clique problem under algorithms from the Sum-of-squares hierarchy. We prove the first average case lower bound for this model: for almost all graphs in G(n,1/2), r rounds of the SOS hierarchy cannot find a planted k-clique unless k > n^{1/2r} (up to logarithmic factors). Thus, for any constant number of rounds planted cliques of size n^{o(1)} cannot be found by this powerful class of algorithms. This is shown via an integrability gap for the natural formulation of maximum clique problem on random graphs for SOS and Lasserre hierarchies, which in turn follow from degree lower bounds for the Positivestellensatz proof system. We follow the usual recipe for such proofs. First, we introduce a natural "dual certificate" (also known as a "vector-solution" or "pseudo-expectation") for the given system of polynomial equations representing the problem for every fixed input graph. Then we show that the matrix associated with this dual certificate is PSD (positive semi-definite) with high probability over the choice of the input graph.This requires the use of certain tools. One is the theory of association schemes, and in particular the eigenspaces and eigenvalues of the Johnson scheme. Another is a combinatorial method we develop to compute (via traces) norm bounds for certain random matrices whose entries are highly dependent; we hope this method will be useful elsewhere

Shape sensing of miniature snake-like robots using optical fibers

Snake like continuum robots are increasingly used for minimally invasive surgery. Most robotic devices of this sort that have been reported to date are controlled in an open loop manner. Using shape sensing to provide closed loop feedback would allow for more accurate control of the robot's position and, hence, more precise surgery. Fiber Bragg Gratings, magnetic sensors and optical reflectance sensors have all been reported for this purpose but are often limited by their cost, size, stiffness or complexity of fabrication. To address this issue, we designed, manufactured and tested a prototype two-link robot with a built-in fiber-optic shape sensor that can deliver and control the position of a CO 2 -laser fiber for soft tissue ablation. The shape sensing is based on optical reflectance, and the device (which has a 4 mm outer diameter) is fabricated using 3D printing. Here we present proof-of-concept results demonstrating successful shape sensing - i.e. measurement of the angular displacement of the upper link of the robot relative to the lower link - in real time with a mean measurement error of only 0.7°

Phonon and crystal field excitations in geometrically frustrated rare earth titanates

The phonon and crystal field excitations in several rare earth titanate pyrochlores are investigated. Magnetic measurements on single crystals of Gd2Ti2O7, Tb2Ti2O7, Dy2Ti2O7 and Ho2Ti2O7 are used for characterization, while Raman spectroscopy and terahertz time domain spectroscopy are employed to probe the excitations of the materials. The lattice excitations are found to be analogous across the compounds over the whole temperature range investigated (295-4 K). The resulting full phononic characterization of the R2Ti2O7 pyrochlore structure is then used to identify crystal field excitations observed in the materials. Several crystal field excitations have been observed in Tb2Ti2O7 in Raman spectroscopy for the first time, among which all of the previously reported excitations. The presence of additional crystal field excitations, however, suggests the presence of two inequivalent Tb3+ sites in the low temperature structure. Furthermore, the crystal field level at approximately 13 cm-1 is found to be both Raman and dipole active, indicating broken inversion symmetry in the system and thus undermining its current symmetry interpretation. In addition, evidence is found for a significant crystal field-phonon coupling in Tb2Ti2O7. These findings call for a careful reassessment of the low temperature structure of Tb2Ti2O7, which may serve to improve its theoretical understanding.Comment: 13 pages, 7 figure

Observation of the algebraic localization-delocalization transition in a 1D disordered potential with a bias force

In a one-dimensional (1D) disordered potential, quantum interferences leading to Anderson lo-calization are ubiquitous, such that all wave-functions are exponentially localized. Moreover, no phase transition toward delocalization is expected in 1D. This behavior is strongly modified in the presence of a bias force. We experimentally study this case, launching a non-interacting 39 K Bose-Einstein condensate in a 1D disordered potential induced by a far-off-resonance laser speckle, while controlling a bias force. In agreement with theoretical predictions, we observe a transition between algebraic localization and delocalization as a function of our control parameter that is the relative strength of the disorder against the bias force. We also demonstrate that the initial velocity of the wave-packet only plays a role through an effective disorder strength due to the correlation of the disorder. Adding a bias force is a quite natural way to probe the transport properties of quantum systems, a subject of broad interest that can be in particular addressed with atomic quantum gases thanks to their high degree of control and versatility [1]. For example, Bloch oscillations has been measured through the addition of a constant force to atoms in periodic potential induced by an optical lattice [2]. A force applied to a harmonic trap is equivalent to a trap displacement. The response to such a displacement permits to reveal the fluid or insulating behavior of atomic systems. In 1D interacting Bose gases, the pinning transition by an optical lattice [3] or the insulating transition in quasi-disordered optical lattice [4, 5] have been studied in this manner. More recently, transport in quantum gases is also studied in junction-type setup more analogous to condensed-matter systems: two reservoirs with different chemical potentials are connected through a constriction. For example, in a gas of fermions, the quantization of conductance through a quantum point contact [6] and the superfluid to normal transition in a disordered thin film have been observed [7]. In our work, we focus on the transport of non-interacting particles in disordered media. Without a bias force, quantum interferences between multiple paths lead to Anderson localization [8] whose signature is an exponential decay in space of single particle wave-function [9]. This phenomenon is ubiquitous in wave/quantum physics and it has been observed in many physical contexts [10] including condensed-matter [11] and ultra-cold atoms [12-14]. One-dimensional truly disordered systems are always localized [15], contrary to the 3D case where a phase transition between localized and extended single particle wave-functions takes place as a function of the disorder strength [16-18]. The localization properties of 1D disordered systems are modified in the presence of a bias force. Theoretical studies predict a transition from algebraic localization to delocalization as a function of a single control non-dimensional parameter α which is the ratio of the force to the disorder strength [19, 20]. Physically, α is the relative energy gain ∆E/E of a particle of energy E when moving over a localization length. Interestingly, in a 1D white noise disorder, this quantity is independent of E as the localization length is proportional to E. If α is small, the force does not considerably change the localization behavior of the particle while for large α its dynamics is severely affected leading to delocalization. This localization-delocalization transition is predicted in the infinite time limit for white noise disorder [20]. In a correlated disorder, as the one produced from a far-off-resonance laser speckle [21], the situation is more complicated. Speckles have no Fourier component beyond a spatial frequency 2k c. As a consequence, back-scattering and localization are not expected in the framework of Born approximation for atoms with wavevectors k > k c [12, 22]. Since localized wave-functions always have a small fraction at long distance corresponding to large energies and momenta in the presence of a bias force, we thus expect correlation-induced delocalization at infinite time. However, signatures of the algebraic localization-delocalization transition are predicted to be observable at transient times [20]. In this paper, we report on the observation of the algebraic localization-delocalization transition with cold-atoms propagating in a one dimensional disordered potential in the presence of a controlled bias force. We experimentally show that the non-dimensional parameter α is the only relevant parameter to describe the transition. We notice that the initial velocity of the quantum wave packet only plays a role through the correlation of the disordered potential, showing that the transition is in-trinsically energy independent. In the localized regime, we demonstrate an algebraic decay of the density and measure the corresponding decay exponent as a function of α. At large disorder strength, a saturation of the exp

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

Rapid Liquid Chromatography-Tandem Mass Spectrometry Analysis of Two Urinary Oxidative Stress Biomarkers: 8-oxodG and 8-isoprostane.

Human biomonitoring of oxidative stress relies on urinary effect biomarkers such as 8-oxo-7,8-dihydro-2'-deoxyguanosine (8-oxodG), and 8-iso-prostaglandin F2α (8-isoprostane); however, their levels reported for similar populations are inconsistent in the scientific literature. One of the reasons is the multitude of analytical methods with varying degrees of selectivity used to quantify these biomarkers. Single-analyte methods are often used, requiring multiple injections that increase both time and cost. We developed a rapid ultra-high-performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) method to quantify both urinary biomarkers simultaneously. A reversed-phase column using a gradient consisting of 0.1% acetic acid in water and 0.1% acetic acid in methanol/acetonitrile (70:30) was used for separation. The MS detection was by positive (8-oxodG) and negative (8-isoprostane) ion-mode by multiple reaction monitoring. Very low limit of detection (<20 pg/mL), excellent linearity (R2 > 0.999), accuracy (near 100%), and precision (CV < 10%) both for intra-day and inter-day experiments were achieved, as well as high recovery rates (>91%). Matrix effects were observed but were compensated by using internal standards. Our newly developed method is applicable for biomonitoring studies as well as large epidemiological studies investigating the effect of oxidative damage, as it requires only minimal clean up using solid phase extraction

Influence of experimental parameters on in vitro human skin permeation of Bisphenol A.

Bisphenol A (BPA) in vitro skin permeation studies have shown inconsistent results, which could be due to experimental conditions. We studied the impact of in vitro parameters on BPA skin permeation using flow-through diffusion cells with ex-vivo human skin (12 donors, 3-12 replicates). We varied skin status (viable or frozen skin) and thickness (200, 400, 800 μm), BPA concentrations (18, 250 mg/l) and vehicle volumes (10, 100 and 1000 μl/cm <sup>2</sup> ). These conditions led to a wide range of BPA absorption (2%-24% after 24 h exposure), peak permeation rates (J = 0.02-1.31 μg/cm <sup>2</sup> /h), and permeability coefficients (K <sub>p</sub> = 1.6-5.2 × 10 <sup>-3</sup> cm/h). This is the first time steady state conditions were reached for BPA aqueous solutions in vitro (1000 μl/cm <sup>2</sup> applied at concentration 250 mg/l). A reduction of the skin thickness from 800 and 400 μm to 200 μm led to a 3-fold increase of J (P < 0.05). A reduction of the vehicle volume from 1000 to 100 led to a 2-fold decrease in J (P > 0.05). Previously frozen skin led to a 3-fold increase in J compared to viable skin (P < 0.001). We found that results from published studies were consistent when adjusting J according to experimental parameters. We propose appropriate J values for different exposure scenarios to calculate BPA internal exposures for use in risk assessment

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

On the Design of Sidelink for Cellular V2X: A Literature Review and Outlook for Future

Connected and fully automated vehicles are expected to revolutionize our mobility in the near future on a global scale, by significantly improving road safety, traffic efficiency, and traveling experience. Enhanced vehicular applications, such as cooperative sensing and maneuvering or vehicle platooning, heavily rely on direct connectivity among vehicles, which is enabled by sidelink communications. In order to set the ground for the core contribution of this paper, we first analyze the main streams of the cellular-vehicle-to-everything (C-V2X) technology evolution within the Third Generation Partnership Project (3GPP), with focus on the sidelink air interface. Then, we provide a comprehensive survey of the related literature, which is classified and critically dissected, considering both the Long-Term Evolution-based solutions and the 5G New Radio-based latest advancements that promise substantial improvements in terms of latency and reliability. The wide literature review is used as a basis to finally identify further challenges and perspectives, which may shape the C-V2X sidelink developments in the next-generation vehicles beyond 5G