Robust Bayes-Like Estimation: Rho-Bayes estimation

We consider the problem of estimating the joint distribution $P$ of $n$ independent random variables within the Bayes paradigm from a non-asymptotic point of view. Assuming that $P$ admits some density $s$ with respect to a given reference measure, we consider a density model $\overline S$ for $s$ that we endow with a prior distribution $\pi$ (with support $\overline S$) and we build a robust alternative to the classical Bayes posterior distribution which possesses similar concentration properties around $s$ whenever it belongs to the model $\overline S$. Furthermore, in density estimation, the Hellinger distance between the classical and the robust posterior distributions tends to 0, as the number of observations tends to infinity, under suitable assumptions on the model and the prior, provided that the model $\overline S$ contains the true density $s$. However, unlike what happens with the classical Bayes posterior distribution, we show that the concentration properties of this new posterior distribution are still preserved in the case of a misspecification of the model, that is when $s$ does not belong to $\overline S$ but is close enough to it with respect to the Hellinger distance.Comment: 68 page

Hydrogen Bond Dynamics in Primary Alcohols: A Femtosecond Infrared Study

Hydrogen-bonded liquids are excellent solvents, in part due to the highly dynamic character of the directional interaction associated with the hydrogen bond. Here we study the vibrational and reorientational dynamics of deuterated hydroxyl groups in various primary alcohols using polarization-resolved femtosecond infrared spectroscopy. We show that the relaxation of the OD stretch vibration is similar for ethanol and its higher homologues (∼0.9 ps), while it is appreciably faster for methanol (∼0.75 ps). The fast relaxation for methanol is attributed to strong coupling of the OD stretch vibration to the overtone of the CH₃ rocking mode. Subsequent to excited state relaxation, the dissipation of the excess energy leads to structural relaxation of the alcohol liquid structure. We show that this relaxation of the H-bonded network depends on the alkyl chain length. We find that the anisotropy of the excitation decays by both thermal diffusion from excited OD groups to nonexcited molecules and reorientational motion. The reorientation is described well by a model employing two relaxation times that increase linearly with increasing alcohol size. The short reorientation time is assigned to the partial reorientation of molecules within the alcohol cluster, while the long reorientation times can be attributed to breaking and reforming of hydrogen bonds

Experimental Access to Mode-Specific Coupling between Quantum Molecular Vibrations and Classical Bath Modes

The interaction of quantum-mechanical systems with a fluctuating thermal environment (bath) is fundamental to molecular mechanics and energy transport/dissipation. Its complete picture requires mode-specific measurements of this interaction and an understanding of its nature. Here, we present a combined experimental and theoretical study providing detailed insights into the coupling between a high-frequency vibrational two-level system and thermally excited terahertz modes. Experimentally, two-dimensional terahertz-infrared-visible spectroscopy reports directly on the coupling between quantum oscillators represented by CH3 streching vibrations in liquid dimethyl sulfoxide and distinct low-frequency modes. Theoretically, we present a mixed quantum-classical formalism of the sample response to enable the simultaneous quantum description of high-frequency oscillators and a classical description of the bath. We derive the strength and nature of interaction and find different coupling between CH3 stretch and low-frequency modes. This general approach enables quantitative and mode-specific analysis of coupled quantum and classical dynamics in complex chemical systems

Additional file 1: of Automated cell segmentation in FIJIÂŽ using the DRAQ5 nuclear dye

Additional information, methods, and macro code. (DOCX 57 kb

Quantifying Surfactant Alkyl Chain Orientation and Conformational Order from Sum Frequency Generation Spectra of CH Modes at the Surfactant–Water Interface

We combine second-order nonlinear vibrational spectroscopy and quantum-chemical calculations to quantify the molecular tilt angle and the structural variation of a decanoic acid surfactant monolayer on water. We demonstrate that there is a remarkable degree of delocalization of the vibrational modes along the backbone of the amphiphilic molecule. A simulation-based on modeled sum frequency generation (SFG) spectra offers quantitative insights into the disorder of surfactant monolayers at the water–air interface. It is shown that an average of one gauche defect in the alkyl chain suffices to give rise to the methylene stretch intensity similar in magnitude to the methyl stretch

Experimental Access to Mode-Specific Coupling between Quantum Molecular Vibrations and Classical Bath Modes

The interaction of quantum-mechanical systems with a fluctuating thermal environment (bath) is fundamental to molecular mechanics and energy transport/dissipation. Its complete picture requires mode-specific measurements of this interaction and an understanding of its nature. Here, we present a combined experimental and theoretical study providing detailed insights into the coupling between a high-frequency vibrational two-level system and thermally excited terahertz modes. Experimentally, two-dimensional terahertz-infrared-visible spectroscopy reports directly on the coupling between quantum oscillators represented by CH3 streching vibrations in liquid dimethyl sulfoxide and distinct low-frequency modes. Theoretically, we present a mixed quantum-classical formalism of the sample response to enable the simultaneous quantum description of high-frequency oscillators and a classical description of the bath. We derive the strength and nature of interaction and find different coupling between CH3 stretch and low-frequency modes. This general approach enables quantitative and mode-specific analysis of coupled quantum and classical dynamics in complex chemical systems

Background-Free Fourth-Order Sum Frequency Generation Spectroscopy

The recently developed 2D sum frequency generation spectroscopy offers new possibilities to analyze the structure and structural dynamics of interfaces in a surface-specific manner. Its implementation, however, has so far remained limited to the pump–probe geometry, with its inherent restrictions. Here we present 2D SFG experiments utilizing a novel noncollinear geometry of four incident laser pulses generating a 2D SFG response, analogous to the triangle geometry applied in bulk-sensitive 2D infrared spectroscopy. This approach allows for background-free measurements of fourth-order nonlinear signals, which is demonstrated by measuring the fourth-order material response from a GaAs (110) surface. The implementation of phase-sensitive detection and broadband excitation pulses allows for both highest possible time resolution and high spectral resolution of the pump axis of a measured 2D SFG spectrum. To reduce the noise in our spectra, we employ a referencing procedure, for which we use noncollinear pathways and individual focusing for the signal and local oscillator beams. The 2D spectra recorded from the GaAs (110) surface show nonzero responses for the real and imaginary component, pointing to contributions from resonant electronic pathways to the χ⁽⁴⁾ response

Ultrafast Two Dimensional-Infrared Spectroscopy of a Molecular Monolayer

The study of vibrational coupling and energy flow in bulk (bio)molecular systems using two-dimensional infrared spectroscopy, has dramatically broadened our ability to elucidate structures and their dynamic evolution on ultrafast timescales. For molecules at surfaces, however, these insights have been lacking. In our study, vibrational coupling in a molecular monolayer is revealed by ultrafast two-dimensional vibrational spectroscopy, with interface specificity and (sub)monolayer sensitivity. This technique provides information on vibrational coupling and energy transfer at surfaces and interfaces with subpicosecond time resolution rendering it a unique tool for the investigation of both structural and dynamical surface processes in a wide variety of disciplines

Electrolytes Change the Interfacial Water Structure but Not the Vibrational Dynamics

Heterogeneous ozone chemistry occurring on aerosols is driven by interfacial chemistry and thus affected by the surface state of aerosol particles. Therefore, the effect of electrolytes on the structure of interfacial water has been under intensive investigation. However, consequences for energy dissipation rates and mechanisms at the interface are largely unknown. Using time-resolved sum frequency generation spectroscopy, we reveal that the relaxation pathway is the same for neat water–air as for aqueous solutions of Na2SO4 and Na2CO3. We further show that similar lifetimes are extracted from all investigated systems and that these lifetimes show an excitation frequency dependent relaxation time from 0.2 ps up to 1 ps. Hence, despite static SFG on the same systems revealing that the interfacial aqueous structure changes upon adding electrolytes, the vibrational dynamics are indistinguishable for both pure water and different electrolyte solutions

Membrane-Bound Water is Energetically Decoupled from Nearby Bulk Water: An Ultrafast Surface-Specific Investigation

We report a femtosecond time-resolved study of ultrafast vibrational dynamics of membrane-bound water. The O−H stretch vibrational lifetime of water bound to a phosphatidylserine lipid monolayer is measured by employing a pump−probe scheme and using vibrational sum frequency generation (VSFG) as a surface-specific probe. We conclusively demonstrate that water molecules adjacent to a lipid layer are energetically decoupled from the bulk and therefore constitute an intrinsic part of the membrane. This contrasts starkly with recent observations by us and other groups that other types of interfacial water exchange energy efficiently with the underlying bulk