A categorical foundation for Bayesian probability

Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\mu: 1 \rightarrow D$, a posterior probability $\widehat{P_H}= I \circ \mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additional measurement. The main result uses an existence theorem for regular conditional probabilities by Faden, which holds in more generality than the setting of Polish spaces. This less stringent setting then allows for non-trivial decision rules (Eilenberg--Moore algebras) on finite (as well as non finite) spaces, and also provides for a common framework for decision theory and Bayesian probability.Comment: 15 pages; revised setting to more clearly explain how to incorporate perfect measures and the Giry monad; to appear in Applied Categorical Structure

Fast cavity-enhanced atom detection with low noise and high fidelity

Cavity quantum electrodynamics describes the fundamental interactions between light and matter, and how they can be controlled by shaping the local environment. For example, optical microcavities allow high-efficiency detection and manipulation of single atoms. In this regime fluctuations of atom number are on the order of the mean number, which can lead to signal fluctuations in excess of the noise on the incident probe field. Conversely, we demonstrate that nonlinearities and multi-atom statistics can together serve to suppress the effects of atomic fluctuations when making local density measurements on clouds of cold atoms. We measure atom densities below 1 per cavity mode volume near the photon shot-noise limit. This is in direct contrast to previous experiments where fluctuations in atom number contribute significantly to the noise. Atom detection is shown to be fast and efficient, reaching fidelities in excess of 97% after 10 us and 99.9% after 30 us.Comment: 7 pages, 4 figures, 1 table; extensive changes to format and discussion according to referee comments; published in Nature Communications with open acces

First Is Best

We experience the world serially rather than simultaneously. A century of research on human and nonhuman animals has suggested that the first experience in a series of two or more is cognitively privileged. We report three experiments designed to test the effect of first position on implicit preference and choice using targets that range from individual humans and social groups to consumer goods. Experiment 1 demonstrated an implicit preference to buy goods from the first salesperson encountered and to join teams encountered first, even when the difference in encounter is mere seconds. In Experiment 2 the first of two consumer items presented in quick succession was more likely to be chosen. In Experiment 3 an alternative hypothesis that first position merely accentuates the valence of options was ruled out by demonstrating that first position enhances preference for the first even when it is evaluatively negative in meaning (a criminal). Together, these experiments demonstrate a “first is best” effect and we offer possible interpretations based on evolutionary mechanisms of this “bound” on rational behavior and suggest that automaticity of judgment may be a helpful principle in clarifying previous inconsistencies in the empirical record on the effects of order on preference and choice

Qubit-flip-induced cavity mode squeezing in the strong dispersive regime of the quantum Rabi model

Squeezed states of light are a set of nonclassical states in which the quantum fluctuations of one quadrature component are reduced below the standard quantum limit. With less noise than the best stabilised laser sources, squeezed light is a key resource in the field of quantum technologies and has already improved sensing capabilities in areas ranging from gravitational wave detection to biomedical applications. In this work we propose a novel technique for generating squeezed states of a confined light field strongly coupled to a two-level system, or qubit, in the dispersive regime. Utilising the dispersive energy shift caused by the interaction, control of the qubit state produces a time-dependent change in the frequency of the light field. An appropriately timed sequence of sudden frequency changes reduces the quantum noise fluctuations in one quadrature of the field well below the standard quantum limit. The degree of squeezing and the time of generation are directly controlled by the number of frequency shifts applied. Even in the presence of realistic noise and imperfections, our protocol promises to be capable of generating a useful degree of squeezing with present experimental capabilities

Seasonal variations in pore water and sediment geochemistry of littoral lake sediments (Asylum Lake, MI, USA)

BACKGROUND: Seasonal changes in pore water and sediment redox geochemistry have been observed in many near-surface sediments. Such changes have the potential to strongly influence trace metal distribution and thus create seasonal fluctuations in metal mobility and bioavailability. RESULTS: Seasonal trends in pore water and sediment geochemistry are assessed in the upper 50 cm of littoral kettle lake sediments. Pore waters are always redox stratified, with the least compressed redox stratification observed during fall and the most compressed redox stratification observed during summer. A 2-step sequential sediment extraction yields much more Fe in the first step, targeted at amorphous Fe(III) (hydr)oxides (AEF), then in the second step, which targets Fe(II) monosulfides. Fe extracted in the second step is relatively invariant with depth or season. In contrast, AEF decreases with sediment depth, and is seasonally variable, in agreement with changes in redox stratification inferred from pore water profiles. A 5-step Tessier extraction scheme was used to assess metal association with operationally-defined exchangeable, carbonate, iron and manganese oxide (FMO), organic/sulfide and microwave-digestible residual fractions in cores collected during winter and spring. Distribution of metals in these two seasons is similar. Co, As, Cd, and U concentrations approach detection limits. Fe, Cu and Pb are mostly associated with the organics/sulfides fraction. Cr and Zn are mostly associated with FMO. Mn is primarily associated with carbonates, and Co is nearly equally distributed between the FMO and organics/sulfide fractions. CONCLUSION: This study clearly demonstrates that near-surface lake sediment pore water redox stratification and associated solid phase geochemistry vary significantly with season. This has important ramifications for seasonal changes in the bioavailability and mobility of trace elements. Without rate measurements, it is not possible to quantify the contribution of various processes to natural organic matter degradation. However, the pore water and solid phase data suggest that iron reduction and sulfate reduction are the dominant pathways in the upper 50 cm of these sediments