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

Development of a novel nanotechnology based artificial antigen presenting cell system for adoptive and active immunotherapy

T cells are one of the most pivotal cell types in the human adaptive immune system. They have the capacity to eradicate primary, metastatic, relapsed tumours and can ameliorate otherwise fatal viral infections. Not surprisingly therefore, the activation and expansion of T cells has become one of the main focuses for immunotherapy and immune gene therapy. However one of the problems of T cell mediated immunotherapy in terms of delivering significant clinical impact to patients, is the expansion of high numbers of functional antigen specific effector T cells. The current approaches for expanding T cells have a number of drawbacks in terms of timing, reproducibility and reliability. Many if not all the currently available systems rely on ex vivo cell manipulation, which concordantly leads to short T cell survival in vivo after infusion. In vivo artificial expansion systems would clearly circumvent this problem. Nevertheless active immunotherapy is not always the solution since sometimes in some patients, the T cells that could be potentially in- vivo expanded no longer exist because they have been deleted, killed or anergised. Therefore a flexible system should be constructed in order to performed both adoptive and/or active immunotherapy depending on the patients requirements. Currently there is no comprehensive artificial Antigen Presenting Cell system (aAPC) for both effective ex vivo and in vivo antigen specific T cell expansion. Therefore in order to address this we have constructed a novel artificial nano-sized super para magnetic antigen presenting cell system (aAPC) capable of priming and expanding antigen specific T cells ex vivo and in vivo. As defined by the NIH, nanotechnology uses nanoscale injectable, targeted and traceable devices capable of important immunological/clinical functions. This nano-system was constructed using the latest generation of immuno liposomes, approved for in vivo human use since they are non-toxic, biodegradable, avoid rapid recognition by the reticulo endothelial system, are safe in terms of size being 50 times smaller than average cells at lOOnm, have good stability and favourable pharmacokinetic behaviour for effective in vivo trafficking. We have coated these liposomes with an optimised number of MHC Class I / peptide complexes and a specific selected range of adhesion (anti LFA-1), early activation (anti CD28 and anti CD27), late activation (4-IBB) and survival receptors (anti CD40L) in the form of Fab antibody regions or monoclonal antibodies. We have made these immuno liposomes traceable since they carry fluorescent lipids and iron oxide super para magnetic nano particles or spios of 13nm size, which make them traceable in vivo using fluorescence and/or by Magnetic Resonance Imaging (MRI). The super para magnetic liposomes are also able to facilitate their own focusing to specific organs, tumour sites or body areas by applying external magnetic attraction. Production of this nano immune liposome system in a ready to use form is achievable in less than 48 hrs and viable for at least 7 days. After ex vivo stimulation with this artificial nano system using CMV pp65 as a model antigen, we have established successful expansions with high T cell numbers (55 to 200 fold) in CMV positive individuals, which are superior when compared with other systems such as peptide pulsed DCs, which are one of the standard methods currently used, coated Daudi cells, magnetic commercial beads and modified tetramers. The T cells are fully functional in terms of degranulation and production of cytokines when specifically challenged. They express predominantly effector-memory and memory phenotypes. We have demonstrated by double fluorescent staining that these liposomes activate T cells directly in an antigen specific fashion and also semi-directly by being incorporated on the surface of the natural APCs in a similar manner as exosomes. When tested in naive individuals, this nano system was also capable of accomplishing initial low levels of T cell priming without help of any adjuvants. In conclusion, we have generated an efficient artificial APC, which embodies a powerful, controllable and superior approach with enormous potential for cancer nanotechnology and T cell immunotherapy for use either in vivo or in vitro

Sharp Concentration Results for Heavy-Tailed Distributions

We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy $P(X>t) \leq {\rm e}^{- I(t)}$, where $I: \mathbb{R} \rightarrow \mathbb{R}$ is an increasing function and $I(t)/t \rightarrow \alpha \in [0, \infty)$ as $t \rightarrow \infty$. Our main theorem can not only recover some of the existing results, such as the concentration of the sum of subWeibull random variables, but it can also produce new results for the sum of random variables with heavier tails. We show that the concentration inequalities we obtain are sharp enough to offer large deviation results for the sums of independent random variables as well. Our analyses which are based on standard truncation arguments simplify, unify and generalize the existing results on the concentration and large deviation of heavy-tailed random variables.Comment: 16 page

Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame

The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski spacetime. Classical zero-point radiation and relativistic physics enter in an essential way in the derivation which is based upon the behavior of free radiation fields and the assumption that the field correlation functions contain but a single correlation time in thermal equilibrium. The work has connections with the thermal effects of acceleration found in relativistic quantum field theory.Comment: 23 page

Brownian Entanglement

We show that for two classical brownian particles there exists an analog of continuous-variable quantum entanglement: The common probability distribution of the two coordinates and the corresponding coarse-grained velocities cannot be prepared via mixing of any factorized distributions referring to the two particles in separate. This is possible for particles which interacted in the past, but do not interact in the present. Three factors are crucial for the effect: 1) separation of time-scales of coordinate and momentum which motivates the definition of coarse-grained velocities; 2) the resulting uncertainty relations between the coordinate of the brownian particle and the change of its coarse-grained velocity; 3) the fact that the coarse-grained velocity, though pertaining to a single brownian particle, is defined on a common context of two particles. The brownian entanglement is a consequence of a coarse-grained description and disappears for a finer resolution of the brownian motion. We discuss possibilities of its experimental realizations in examples of macroscopic brownian motion.Comment: 18 pages, no figure

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

Leiomyosarcoma of the breast in a patient with a 10-year-history of cyclophosphamide exposure: a case report

A 50 year old woman with a 10-year history of systemic lupus erythematosus (SLE) and intermittent low-dose cyclophosphamide therapy developed a palpable mass at the periphery of her left breast. Ultrasound guided core biopsy revealed a spindle cell neoplasm characterized on final pathology as a low grade leiomyosarcoma

An analog of Heisenberg uncertainty relation in prequantum classical field theory

Prequantum classical statistical field theory (PCSFT) is a model which provides a possibility to represent averages of quantum observables, including correlations of observables on subsystems of a composite system, as averages with respect to fluctuations of classical random fields. PCSFT is a classical model of the wave type. For example, "electron" is described by electronic field. In contrast to QM, this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of e.g. electron contains the irreducible contribution of the background field, vacuum fluctuations. In principle, the traditional QM-formalism can be considered as a special regularization procedure: subtraction of averages with respect to vacuum fluctuations. In this paper we derive a classical analog of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM. The quantum dispersion corresponds to the difference between e.g. the electron field dispersion and the dispersion of vacuum fluctuations. Classical Robertson-like inequality contains these differences. Hence, it does not imply such a rigid estimate from below for dispersions as it was done in QM

Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. Classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter -radiation interaction are illustrated in a simple relativistic classical electromagnetic example.Comment: 18 page

Bringing Earth-Abundant Plasmonic Catalysis to Light : Gram-Scale Mechanochemical Synthesis and Tuning of Activity by Dual Excitation of Antenna and Reactor Sites

The localized surface plasmon resonance (LSPR) excitation in plasmonic nanoparticles (NPs) in the visible and near-infrared ranges is currently at the forefront of improving photocatalytic performances via plasmonic photocatalysis. One bottleneck of this field is that the NPs that often display the best optical properties in the visible and near-infrared ranges are based on expensive noble metals such as silver (Ag) and gold (Au). While earth-abundant plasmonic materials have been proposed together with catalytic metals in antenna-reactor systems, their performances remain limited by their optical properties. Importantly, the synthesis of plasmonic photocatalysts remains challenging in terms of scalability while often requiring several steps, high temperatures, and special conditions. Herein, we address these challenges by developing a one-pot, gram-scale, room-temperature synthesis of earth-abundant plasmonic photocatalysts while improving their activities beyond what has been dictated by the LSPR excitation of the plasmonic component. We describe the mechanochemical synthesis of earth-abundant plasmonic photocatalysts by using MoO3 (antenna) and Au (reactor) NPs as a proof-of-concept example and demonstrate that the dual plasmonic excitation of antenna and reactor sites enables the tuning of plasmonic photocatalytic performances toward the reductive coupling of nitrobenzene to azobenzene as a model reaction. In addition to providing a pathway to the facile and gramscale synthesis of plasmonic photocatalysts, the results reported herein may open pathways to improved activities in plasmonic catalysis.Peer reviewe