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

Remittances from Migrants: Experience of Vietnamese Households

By analyzingdatafromthethreeVietnamHouseholdLivingStandards Surveysbetween 2002 and 2006, theauthorsfoundthataverylargeproportion of Vietnamesehouseholdsreceivedremittancesduringthoseyearsandthat theseremittancesconstitutedasignificantshareofhouseholdincomes.The majorityofhouseholdsreceivedremittancesfromwithinVietnam,butforthose abletoaccessremittancesfromabroad,theamountswereverymuchlarger. In general,remittancesdoseemtoplayan �insurancerole� forthepoor, cushioninganysuddenfallsinhouseholdincomes.Thereisalsosomeevidence thatpublictransferscancrowdoutprivateremittances,buttheeffectisby no meanscomplete

Experimental Analysis of Algorithms for Coflow Scheduling

Modern data centers face new scheduling challenges in optimizing job-level performance objectives, where a significant challenge is the scheduling of highly parallel data flows with a common performance goal (e.g., the shuffle operations in MapReduce applications). Chowdhury and Stoica introduced the coflow abstraction to capture these parallel communication patterns, and Chowdhury et al. proposed effective heuristics to schedule coflows efficiently. In our previous paper, we considered the strongly NP-hard problem of minimizing the total weighted completion time of coflows with release dates, and developed the first polynomial-time scheduling algorithms with O(1)-approximation ratios. In this paper, we carry out a comprehensive experimental analysis on a Facebook trace and extensive simulated instances to evaluate the practical performance of several algorithms for coflow scheduling, including the approximation algorithms developed in our previous paper. Our experiments suggest that simple algorithms provide effective approximations of the optimal, and that the performance of our approximation algorithms is relatively robust, near optimal, and always among the best compared with the other algorithms, in both the offline and online settings.Comment: 29 pages, 8 figures, 11 table

Goal-directed actions transiently depend on dorsal hippocampus.

The role of the hippocampus in goal-directed action is currently unclear; studies investigating this issue have produced contradictory results. Here we reconcile these contradictions by demonstrating that, in rats, goal-directed action relies on the dorsal hippocampus, but only transiently, immediately after initial acquisition. Furthermore, we found that goal-directed action also depends transiently on physical context, suggesting a psychological basis for the hippocampal regulation of goal-directed action control

Toxicity of ZnO and TiO<font size=-1>₂</font> to Escherichia coli cells

published_or_final_versio

Some Thoughts About Appealing Directions for the Future of Fuzzy Theory and Technologies Along the Path Traced by Lotfi Zadeh

The quoted text is an interesting instance of a fuzzy object: it is currently known in slightly diversified forms, each rather different from the quoted one, which corresponds to the first known appearance in English of this adage

Magnetic-film atom chip with 10 μ\mum period lattices of microtraps for quantum information science with Rydberg atoms

We describe the fabrication and construction of a setup for creating lattices of magnetic microtraps for ultracold atoms on an atom chip. The lattice is defined by lithographic patterning of a permanent magnetic film. Patterned magnetic-film atom chips enable a large variety of trapping geometries over a wide range of length scales. We demonstrate an atom chip with a lattice constant of 10 $\mu$m, suitable for experiments in quantum information science employing the interaction between atoms in highly-excited Rydberg energy levels. The active trapping region contains lattice regions with square and hexagonal symmetry, with the two regions joined at an interface. A structure of macroscopic wires, cut out of a silver foil, was mounted under the atom chip in order to load ultracold $^{87}$Rb atoms into the microtraps. We demonstrate loading of atoms into the square and hexagonal lattice sections simultaneously and show resolved imaging of individual lattice sites. Magnetic-film lattices on atom chips provide a versatile platform for experiments with ultracold atoms, in particular for quantum information science and quantum simulation.Comment: 7 pages, 7 figure

In situ neutron scattering of antibody adsorption during protein A chromatography

A deeper understanding of the nanoscale and mesoscale structure of chromatographic adsorbents and the distribution of proteins within the media, is critical to a mechanistic understanding of separation processes using these materials. Characterisation of the media's architecture at this scale and protein adsorption within, is challenging using conventional techniques. In this study, we propose a novel resin characterisation technique that enables in-situ measurement of the structure of the adsorbed protein layer within the resin, under typical chromatographic conditions. A quartz flow-through cell was designed and fabricated for use with Small Angle Neutron Scattering (SANS), in order to measure the nanoscale to mesoscale structures of a silica based protein A chromatography resin during the monoclonal antibody sorption process. We were able to examine the pore-to-pore (˜133 nm) and pore size (˜63 nm) correlations of the resin and the in-plane adsorbed antibody molecules (˜ 4.2 nm) correlation at different protein loadings and washing buffers, in real time using a contrast matching approach. When 0.03 M sodium phosphate with 1 M urea and 10 % isopropanol buffer, pH 8, was introduced into the system as a wash buffer, it disrupted the system's order by causing partial unfolding of the adsorbed antibody, as evidenced by a loss of the in-plane protein correlation. This method offers new ways to investigate the nanoscale structure and ligand immobilisation within chromatography resins; and perhaps most importantly understand the in-situ behaviour of adsorbed proteins within the media under different mobile phase conditions within a sample environment replicating that of a chromatography column

Evolution of avalanche conducting states in electrorheological liquids

Charge transport in electrorheological fluids is studied experimentally under strongly nonequlibrium conditions. By injecting an electrical current into a suspension of conducting nanoparticles we are able to initiate a process of self-organization which leads, in certain cases, to formation of a stable pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such system is a complex process. It starts as an avalanche process characterized by nucleation, growth, and thermal destruction of such dissipative elements as continuous conducting chains of particles as well as electroconvective vortices. A power-law distribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of conducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum power condition and also shows a power-law distribution of the avalanche sizes.Comment: 15 pages, 6 figure

Hypermagnetic Field Effects in the Thermal Bath of Chiral Fermions

The dispersion relations for leptons in the symmetric phase of the electroweak model in the presence of a constant hypermagnetic field are investigated. The one-loop fermion self-energies are calculated in the lowest Landau level approximation and used to show that the hypermagnetic field forbids the generation of the ''effective mass'' found as a pole of the fermions' propagators at high temperature and zero fields. In the considered approximation leptons behave as massless particles propagating only along the direction of the external field. The reported results can be of interest for the cosmological implications of primordial hypermagnetic fields.Comment: 5 page