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

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

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Infinitesimally Robust Estimation in General Smoothly Parametrized Models

We describe the shrinking neighborhood approach of Robust Statistics, which applies to general smoothly parametrized models, especially, exponential families. Equal generality is achieved by object oriented implementation of the optimally robust estimators. We evaluate the estimates on real datasets from literature by means of our R packages ROptEst and RobLox

Possible import routes of proteins into the cyanobacterial endosymbionts/plastids of Paulinella chromatophora

The rhizarian amoeba Paulinella chromatophora harbors two photosynthetically active and deeply integrated cyanobacterial endosymbionts acquired ~60 million years ago. Recent genomic analyses of P. chromatophora have revealed the loss of many essential genes from the endosymbiont’s genome, and have identified more than 30 genes that have been transferred to the host cell’s nucleus through endosymbiotic gene transfer (EGT). This indicates that, similar to classical primary plastids, Paulinella endosymbionts have evolved a transport system to import their nuclear-encoded proteins. To deduce how these proteins are transported, we searched for potential targeting signals in genes for 10 EGT-derived proteins. Our analyses indicate that five proteins carry potential signal peptides, implying they are targeted via the host endomembrane system. One sequence encodes a mitochondrial-like transit peptide, which suggests an import pathway involving a channel protein residing in the outer membrane of the endosymbiont. No N-terminal targeting signals were identified in the four other genes, but their encoded proteins could utilize non-classical targeting signals contained internally or in C-terminal regions. Several amino acids more often found in the Paulinella EGT-derived proteins than in their ancestral set (proteins still encoded in the endosymbiont genome) could constitute such signals. Characteristic features of the EGT-derived proteins are low molecular weight and nearly neutral charge, which both could be adaptations to enhance passage through the peptidoglycan wall present in the intermembrane space of the endosymbiont’s envelope. Our results suggest that Paulinella endosymbionts/plastids have evolved several different import routes, as has been shown in classical primary plastids

Identification and in vitro Analysis of the GatD/MurT Enzyme-Complex Catalyzing Lipid II Amidation in Staphylococcus aureus

The peptidoglycan of Staphylococcus aureus is characterized by a high degree of crosslinking and almost completely lacks free carboxyl groups, due to amidation of the D-glutamic acid in the stem peptide. Amidation of peptidoglycan has been proposed to play a decisive role in polymerization of cell wall building blocks, correlating with the crosslinking of neighboring peptidoglycan stem peptides. Mutants with a reduced degree of amidation are less viable and show increased susceptibility to methicillin. We identified the enzymes catalyzing the formation of D-glutamine in position 2 of the stem peptide. We provide biochemical evidence that the reaction is catalyzed by a glutamine amidotransferase-like protein and a Mur ligase homologue, encoded by SA1707 and SA1708, respectively. Both proteins, for which we propose the designation GatD and MurT, are required for amidation and appear to form a physically stable bi-enzyme complex. To investigate the reaction in vitro we purified recombinant GatD and MurT His-tag fusion proteins and their potential substrates, i.e. UDP-MurNAc-pentapeptide, as well as the membrane-bound cell wall precursors lipid I, lipid II and lipid II-Gly5. In vitro amidation occurred with all bactoprenol-bound intermediates, suggesting that in vivo lipid II and/or lipid II-Gly5 may be substrates for GatD/MurT. Inactivation of the GatD active site abolished lipid II amidation. Both, murT and gatD are organized in an operon and are essential genes of S. aureus. BLAST analysis revealed the presence of homologous transcriptional units in a number of gram-positive pathogens, e.g. Mycobacterium tuberculosis, Streptococcus pneumonia and Clostridium perfringens, all known to have a D-iso-glutamine containing PG. A less negatively charged PG reduces susceptibility towards defensins and may play a general role in innate immune signaling