On nonparametric maximum likelihood for a class of stochastic inverse problems

We establish the consistency of a nonparametric maximum likelihood estimator for a class of stochastic inverse problems. We proceed by embedding the framework into the general settings of early results of Pfanzagl related to mixtures

Semiparametric theory

In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified and unrestricted, and can often yield robust estimators that nonetheless behave similarly to those based on parametric likelihood assumptions, e.g., fast rates of convergence to normal limiting distributions. We discuss the basics of semiparametric theory, focusing on influence functions.Comment: arXiv admin note: text overlap with arXiv:1510.0474

Contrast estimation for parametric stationary determinantal point processes

We study minimum contrast estimation for parametric stationary determi-nantal point processes. These processes form a useful class of models for repulsive (or regular, or inhibitive) point patterns and are already applied in numerous statistical applications. Our main focus is on minimum contrast methods based on the Ripley's K-function or on the pair correlation function. Strong consistency and asymptotic normality of theses procedures are proved under general conditions that only concern the existence of the process and its regularity with respect to the parameters. A key ingredient of the proofs is the recently established Brillinger mixing property of stationary determinantal point processes. This work may be viewed as a complement to the study of Y. Guan and M. Sherman who establish the same kind of asymptotic properties for a large class of Cox processes, which in turn are models for clustering (or aggregation)

Information-Based Physics: An Observer-Centric Foundation

It is generally believed that physical laws, reflecting an inherent order in the universe, are ordained by nature. However, in modern physics the observer plays a central role raising questions about how an observer-centric physics can result in laws apparently worthy of a universal nature-centric physics. Over the last decade, we have found that the consistent apt quantification of algebraic and order-theoretic structures results in calculi that possess constraint equations taking the form of what are often considered to be physical laws. I review recent derivations of the formal relations among relevant variables central to special relativity, probability theory and quantum mechanics in this context by considering a problem where two observers form consistent descriptions of and make optimal inferences about a free particle that simply influences them. I show that this approach to describing such a particle based only on available information leads to the mathematics of relativistic quantum mechanics as well as a description of a free particle that reproduces many of the basic properties of a fermion. The result is an approach to foundational physics where laws derive from both consistent descriptions and optimal information-based inferences made by embedded observers.Comment: To be published in Contemporary Physics. The manuscript consists of 43 pages and 9 Figure

Redox thermodynamics of B-class dye-decolorizing peroxidases

With>5000 annotated genes dye-decolorizing peroxidases (DyPs) represent a heme b peroxidase family of broad functional diversity. Bacterial B-class DyPs are poor peroxidases of unknown physiological function. Hydrogen peroxide efficiently mediates the rapid formation of Compound I in B-class DyPs, which, however, is stable and shows modest reactivity towards organic and inorganic electron donors. To understand these characteristics, we have investigated the redox thermodynamics of the one-electron reduction of the ferric high-spin form of wild-type B-class DyP from the pathogenic bacterium Klebsiella pneumoniae (KpDyP) and the variants D143A, R232A and D143A/R232A. These distal amino acids are fully conserved in all DyPs and play important roles in Compound I formation and maintenance of the heme cavity architecture and substrate access route(s). The E°′ values of the respective redox couples Fe(III)/Fe(II) varied from −350 mV (wild-type KpDyP) to −299 mV (D143A/R232A) at pH 7.0. Variable-temperature spectroelectrochemical experiments revealed that the reduction reaction of B-class DyPs is enthalpically unfavored but entropically favored with significant differences in enthalpic and entropic contributions to E°′ between the four proteins. Molecular dynamics simulations demonstrated the impact of solvent reorganization on the entropy change during reduction reaction and revealed the dynamics and restriction of substrate access channels. Obtained data are discussed with respect to the poor peroxidase activities of B-class DyPs and compared with heme peroxidases from other (super)families as well as with chlorite dismutases, which do not react with hydrogen peroxide but share a similar fold and heme cavity architecture

Compound I formation and reactivity in dimeric chlorite dismutase – Impact of pH and the dynamics of the catalytic arginine

The heme enzyme chlorite dismutase (Cld) catalyzes the degradation of chlorite to chloride and dioxygen. Many questions about the molecular reaction mechanism of this iron protein have remained unanswered, including the electronic nature of the catalytically relevant oxoiron(IV) intermediate and its interaction with the distal, flexible, and catalytically active arginine. Here, we have investigated the dimeric Cld from Cyanothece sp. PCC7425 (CCld) and two variants having the catalytic arginine R127 (i) hydrogen-bonded to glutamine Q74 (wild-type CCld), (ii) arrested in a salt bridge with a glutamate (Q74E), or (iii) being fully flexible (Q74V). Presented stopped-flow spectroscopic studies demonstrate the initial and transient appearance of Compound I in the reaction between CCld and chlorite at pH 5.0 and 7.0 and the dominance of spectral features of an oxoiron(IV) species (418, 528, and 551 nm) during most of the chlorite degradation period at neutral and alkaline pH. Arresting the R127 in a salt bridge delays chlorite decomposition, whereas increased flexibility accelerates the reaction. The dynamics of R127 does not affect the formation of Compound I mediated by hypochlorite but has an influence on Compound I stability, which decreases rapidly with increasing pH. The decrease in activity is accompanied by the formation of protein-based amino acid radicals. Compound I is demonstrated to oxidize iodide, chlorite, and serotonin but not hypochlorite. Serotonin is able to dampen oxidative damage and inactivation of CCld at neutral and alkaline pH. Presented data are discussed with respect to the molecular mechanism of Cld and the pronounced pH dependence of chlorite degradation

Roles of distal aspartate and arginine of B-class dye-decolorizing peroxidase in heterolytic hydrogen peroxide cleavage

Dye-decolorizing peroxidases (DyPs) represent the most recently classified hydrogen peroxide dependent heme peroxidase family. Although widely distributed with more than 5000 annotated genes and hailed for their biotechnological potential detailed biochemical characterization of their reaction mechanism remains limited. Here, we present the high resolution crystal structures of wild-type B-class DyP from the pathogenic bacterium Klebsiella pneumoniae (KpDyP) (1.6 \uc5) and the variants D143A (1.3 \uc5), R232A (1.9 \uc5), and D143A/R232A (1.1 \uc5). We demonstrate the impact of elimination of the DyP-typical, distal residues Asp 143 and Arg 232 on (i) the spectral and redox properties, (ii) the kinetics of heterolytic cleavage of hydrogen peroxide, (iii) the formation of the low-spin (LS) cyanide complex as well as on (iv) the stability and reactivity of an oxoiron(IV)porphyrin \u3c0-cation radical (Compound I). Structural and functional studies reveal that the distal aspartate is responsible for deprotonation of H2O2 and for the poor oxidation capacity of Compound I. Elimination of the distal arginine promotes a collapse of the distal heme cavity including blocking of one access channel and a conformational change of the catalytic aspartate. We also provide evidence of formation of an oxoiron(IV)-type Compound II in KpDyP with absorbance maxima at 418, 527 and 553 nm. In summary, a reaction mechanism of the peroxidase cycle of B-class DyPs is proposed. Our observations challenge the idea that peroxidase activity toward conventional aromatic substrates is related to the physiological roles of B-class DyPs

Semiparametric theory and empirical processes in causal inference

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference

Quantum hypothesis testing and sufficient subalgebras

We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2- sufficient for a pair of states $\{\rho_0,\rho_1\}$ if it contains all Bayes optimal tests of $\rho_0$ against $\rho_1$. In classical statistics, this corresponds to the usual definition of sufficiency. We show this correspondence in the quantum setting for some special cases. Furthermore, we show that sufficiency is equivalent to 2 - sufficiency, if the latter is required for $\{\rho_0^{\otimes n},\rho_1^{\otimes}\}$, for all $n$.Comment: 12 page