Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws

Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several exponential and moment inequalities, particularly those related to laws of the iterated logarithm, for self-normalized random variables including martingales. Tail probability bounds are also derived. For random variables B_t>0 and A_t, let Y_t(\lambda)=\exp{\lambda A_t-\lambda ^2B_t^2/2}. We develop inequalities for the moments of A_t/B_{t} or sup_{t\geq 0}A_t/{B_t(\log \log B_{t})^{1/2}} and variants thereof, when EY_t(\lambda )\leq 1 or when Y_t(\lambda) is a supermartingale, for all \lambda belonging to some interval. Our results are valid for a wide class of random processes including continuous martingales with A_t=M_t and B_t=\sqrt _t, and sums of conditionally symmetric variables d_i with A_t=\sum_{i=1}^td_i and B_t=\sqrt\sum_{i=1}^td_i^2. A sharp maximal inequality for conditionally symmetric random variables and for continuous local martingales with values in R^m, m\ge 1, is also established. Another development in this paper is a bounded law of the iterated logarithm for general adapted sequences that are centered at certain truncated conditional expectations and self-normalized by the square root of the sum of squares. The key ingredient in this development is a new exponential supermartingale involving \sum_{i=1}^td_i and \sum_{i=1}^td_i^2.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000039

A study on PDC drill bits quality

The quality of innovating PDC (Polycrystalline Diamond Compact) bits materials needs to be determined with accuracy by measuring cutting efficiency and wear rate, both related to the overall mechanical properties. An original approach is developed to encompass cutting efficiency and wear contribution to the overall sample quality. Therefore, a lathe-type test device was used to abrade specific samples from various manufacturers. Post-experiment analyzes are based on models establishing coupled relationships between cutting and friction stresses related to the drag bits excavation mechanism. These models are implemented in order to evaluate cutting efficiency and to estimate wear of the diamond insert. Phase analysis by XRD and finite element simulations were performed to explain the role of physicochemical parameters on the calculated quality factor values. Four main properties of PDC material were studied to explain quality results obtained in this study: cobalt content in samples that characterizes hardness/fracture toughness compromise, undesired phase as tungsten carbide weakening diamond structure, diamond grains sizes and residual stresses distribution affecting abrasion resistance

Born's rule from measurements of classical signals by threshold detectors which are properly calibrated

The very old problem of the statistical content of quantum mechanics (QM) is studied in a novel framework. The Born's rule (one of the basic postulates of QM) is derived from theory of classical random signals. We present a measurement scheme which transforms continuous signals into discrete clicks and reproduces the Born's rule. This is the sheme of threshold type detection. Calibration of detectors plays a crucial role.Comment: The problem of double clicks is resolved; hence, one can proceed in purely wave framework, i.e., the wave-partcile duality has been resolved in favor of the wave picture of prequantum realit

A Model of the Potential Distribution of Striga hermonthica in the African Continent and its Prospection under Climate Change

The genus Striga (Orobanchaceae) comprises parasitic weeds recognised as a major problem for crop production in sub-Saharan Africa. Striga hermonthica is an obligate parasite of pearl millet, sorghum and other important crops in semi-arid and arid regions of the tropics, producing millions of hectares of yield loses and a great impact on human welfare in the rural areas where it occurs. Under the present situation and the possible scenarios within the framework of climate change Striga hermonthica’s current and future distribution needs to be estimated urgently, in order to efficiently target available prevention and management strategies. Using the maximum entropy (Maxent) approach for modelling species’ distributions, our research focuses on better describe the present distribution of Striga hermonthica and to predict potential future areas where this dangerous parasite could spread in the African continent

A Novel Typing Method for Streptococcus pneumoniae Using Selected Surface Proteins

The diverse pneumococcal diseases are associated with different pneumococcal lineages, or clonal complexes. Nevertheless, intra-clonal genomic variability, which influences pathogenicity, has been reported for surface virulence factors. These factors constitute the communication interface between the pathogen and its host and their corresponding genes are subjected to strong selective pressures affecting functionality and immunogenicity. First, the presence and allelic dispersion of 97 outer protein families were screened in 19 complete pneumococcal genomes. Seventeen families were deemed variable and were then examined in 216 draft genomes. This procedure allowed the generation of binary vectors with 17 positions and the classification of strains into surfotypes. They represent the outer protein subsets with the highest inter-strain discriminative power. A total of 116 non-redundant surfotypes were identified. Those sharing a critical number of common protein features were hierarchically clustered into 18 surfogroups. Most clonal complexes with comparable epidemiological characteristics belonged to the same or similar surfogroups. However, the very large CC156 clonal complex was dispersed over several surfogroups. In order to establish a relationship between surfogroup and pathogenicity, the surfotypes of 95 clinical isolates with different serogroup/serotype combinations were analyzed. We found a significant correlation between surfogroup and type of pathogenic behavior (primary invasive, opportunistic invasive, and non-invasive). We conclude that the virulent behavior of S. pneurnoniae is related to the activity of collections of, rather than individual, surface virulence factors. Since surfotypes evolve faster than MLSTs and directly reflect virulence potential, this novel typing protocol is appropriate for the identification of emerging clones

Schroedingers equation with gauge coupling derived from a continuity equation

We consider a statistical ensemble of particles of mass m, which can be described by a probability density \rho and a probability current \vec{j} of the form \rho \nabla S/m. The continuity equation for \rho and \vec{j} implies a first differential equation for the basic variables \rho and S. We further assume that this system may be described by a linear differential equation for a complex state variable \chi. Using this assumptions and the simplest possible Ansatz \chi(\rho,S) Schroedingers equation for a particle of mass m in an external potential V(q,t) is deduced. All calculations are performed for a single spatial dimension (variable q) Using a second Ansatz \chi(\rho,S,q,t) which allows for an explict q,t-dependence of \chi, one obtains a generalized Schroedinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schroeodingers equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for an non-unique external q,t-dependence of \chi, one obtains Schroedingers equation with electromagnetic potentials \vec{A}, \phi in the familiar gauge coupling form. A possible source of the non-uniqueness is pointed out.Comment: 25 pages, no figure

Along-strike segmentation in the northern Caribbean plate boundary zone (Hispaniola sector): Tectonic implications

Highlights • Along-strike variations of tectonic framework in northeastern Caribbean margin are studied. • Shallow plate boundary structure related to the slab geometry has been defined. • First-order fault systems and its associated features have been mapped along the margin. Abstract The North American (NOAM) plate converges with the Caribbean (CARIB) plate at a rate of 20.0 ± 0.4 mm/yr. towards 254 ± 1°. Plate convergence is highly oblique (20–10°), resulting in a complex crustal boundary with along-strike segmentation, strain partitioning and microplate tectonics. We study the oblique convergence of the NOAM and CARIB plates between southeastern Cuba to northern Puerto Rico using new swath multibeam bathymetry data and 2D multi-channel seismic profiles. The combined interpretation of marine geophysical data with the seismicity and geodetic data from public databases allow us to perform a regional scale analysis of the shallower structure, the seismotectonics and the slab geometry along the plate boundary. Due to differential rollback between the NOAM oceanic crust north of Puerto Rico and the relative thicker Bahamas Carbonate Province crust north of Hispaniola a slab tear is created at 68.5°W. The northern margin of Puerto Rico records the oblique high-dip subduction and rollback of the NOAM plate below the island arc. Those processes have resulted in a forearc transpressive tectonics (without strain partitioning), controlled by the Septentrional-Oriente Fault Zone (SOFZ) and the Bunce Fault Zone (BFZ). Meanwhile, in the northern margin of Hispaniola, the collision of the Bahamas Carbonate Province results in high plate coupling with strain partitioning: SOFZ and Northern Hispaniola Deformed Belt (NHDB). In the northern Haitian margin, compression is still relevant since seismicity is mostly associated with the deformation front, whereas strike slip earthquakes are hardly anecdotal. Although in Hispaniola intermediate-depth seismicity should disappear, diffuse intermediate-depth hypocenter remains evidencing the presence of remnant NOAM subducted slab below central and western Hispaniola. Results of this study improve our understanding of the active tectonics in the NE Caribbean that it is the base for future assessment studies on seismic and tsunamigenic hazard

Taxes, Trading or Both?: An Experimental Investigation of Abatement Investment under Alternative Emissions Regulation

Emissions taxes and emissions permit trading schemes are designed to reduce greenhouse gas (GHG) emissions by providing incentives for large emitters to invest in less emissions-intensive production technologies. Whereas taxes place a fixed price on emissions, tradable permit schemes include a secondary permit market, from which allowance prices emerge after the regulation enters into force. Under a newly imposed regulation, the delay in price information contributes to uncertainty about the future cost of compliance that liable emitters will face, thereby challenging liable entities’ ability to make optimal abatement investment decisions. Using laboratory experiments, this thesis examines the effects of a policy regime that is similar to the one implemented in Australia in 2012. The regime includes a staged transition over time from a regulation-free environment, to an emissions tax and then to emissions trading. The thesis examines the effects of such a staged transition on investment decisions, the level of emissions, permit prices and trading behavior, comparing it to standard policy regimes of only an emissions tax and only emissions permit trading. The findings suggest that a regime based on a staged transition from a tax to permit trading results in lower compliance costs and higher overall allocative efficiency compared to a regime based solely on emissions trading in a market of heterogeneous producing firms