A Trigonal‐Pyramidal Erbium(III) Single‐Molecule Magnet

Given the recent advent of mononuclear single‐molecule magnets (SMMs), a rational approach based on lanthanides with axially elongated f‐electron charge cloud (prolate) has only recently received attention. We report herein a new SMM, [Li(THF)₄[Er{N(SiMe₃)₂}₃Cl]?2 THF, which exhibits slow relaxation of the magnetization under zero dc field with an effective barrier to the reversal of magnetization (ΔE_eff/k_B=63.3 K) and magnetic hysteresis up to 3 K at a magnetic field sweep rate of 34.6 Oe s^?1. This work questions the theory that oblate or prolate lanthanides must be stabilized with the appropriate ligand framework in order for SMM behavior to be favored.     

The Role of Hydrogen Bonds and Electrostatic Interactions in Enhancing Two-Photon Absorption in Green and Yellow Fluorescent Proteins

The spectral properties of fluorescent proteins (FPs) depend on the protein environment of the chromophore (CRO). A deeper understanding of the CRO – environment interactions in terms of FPs’ spectral characteristics will allow for a rational design of novel markers with desired properties. Here, we are taking a step towards achieving this important goal. With the time-dependent density functional theory (TDDFT), we calculate one- and two-photon absorption (OPA and TPA) spectra for 5 green FPs (GFPs) and 3 yellow FPs (YFPs) differing in amino acid sequence. The goal is to reveal the roles of: (i) electrostatic interactions, (ii) hydrogen-bonds (h-bonds) and (iii) h-bonds together with distant electrostatic field in absorption spectra tuning. Our results point to design hypothesis towards FPs optimised for TPA-based applications. Both h-bonds and electrostatic interactions co-operate in enhancing TPA cross-section ( ) for the transition in GFPs. Furthermore, it seems that details of h-bonds network in the CRO's vicinity influences response to CRO – environment electrostatic interactions in YFPs. We postulate that engineering FPs with more hydrophilic CRO's environment can lead to greater . We also find that removing h-bonds formed with the CRO's phenolate leads to TPA enhancement for transition to higher excited states than S₁. Particularly Y145 and T203 residues are important in this regard.     

2D H and C NMR conformational studies of thienopyridines and carboline biarylic compounds

In this paper, we report on conformational studies of biarylic compounds, as prepared through the well-known aza-Wittig methodology. The conformational studies were mainly realized by bidimensional (2D) nuclear magnetic resonance spectroscopy (NMR) and NOESY experiments. The conformational behavior showed that these biarylic compounds display an orthogonal symmetry and adopt a characteristic arrangement around the pivotal bond. Molecular modeling calculations were performed to support structure conformations.     

Stereochemistry of 1-hydroxyphosphonate-phosphate rearrangement. Retention of configuration at the phosphorus atom

1-Hydroxyphosphonate 1 in the presence of triethylamine in acetonitrile solution undergoes irreversible rearrangement to phosphate 2 and reversible retro-phospho-aldol (retro-Abramov) reaction. The X-ray structures for 1 and 2 revealed that the phosphonate-phosphate rearrangement occurs with retention of configuration at the phosphorus atom.     

On geometric convergence rate of Markov search towards the fat target

Let $f:A\to \mathbb{R}$ be a continuous function with the minimal value $f^{?}$, where $A$ is the compact metric space. Let ${\left\{X_t\right\}}_{t\in \mathbb{N}}$ be a Markov chain which represents the global optimization process on $A$. We present sufficient conditions for very strong, geometric convergence mode of the form $Ef\left(X_t\right)?f^1\le c^t?(Ef\left(X_0\right)?f^1)$, where $c\in (0,1)$ is some constant. This convergence mode is natural if the set of global minima is fat.     

Predictive tracking of an object by a pan–tilt camera of a robot

Nonlinear Dynamics - Moving-object tracking using a pan–tilt camera setup is quite a well-known task in robotics. However, the presented research addresses specific properties of the tracked...     

Dynamic job assignment: A column generation approach with an application to surgery allocation

We consider the assignment of jobs to heterogeneous agents in a dynamic system with a rolling time horizon. An example is a hospital operating theatre where the jobs are surgeries and the agents are the surgeons. The paper is presented in the context of surgery allocation and the system is characterized as follows: Patients are grouped into categories and they arrive continually following a stochastic process. Patients in each group have specific time limits within which they need treatment and if it cannot be accommodated then the patients are outsourced. The service level is the percentage of patients in each group treated within the time limit. Surgery durations are stochastic and depend on the surgeon conducting the surgeries. Each surgeon has limited time available and expected overtime is penalized by a non-decreasing convex function. We develop a column generation approach for the assignment of already arrived patients and tentative future patients to surgeons on specific days. It balances the conflicting objectives of including as many arrived patients as possible within their time limits, maximizing the service level of future patients, and minimizing the expected overtime of surgeons. A computational study is conducted with the model embedded in a rolling time horizon frame. The study indicates that the assignment of patients based on our model increases system performance in terms of service level and reduced overtime compared to a First-Come-First-Served (FCFS) policy when the arrival rates of patients are medium to high compared to the capacity of the system.     

A New Look at Molecular and Electronic Structure of Homoleptic Diiron(II,II) Complexes with N,N-Bidentate Ligands: Combined Experimental and Theoretical Study

Paddlewheel-type binuclear complexes featuring metal−metal bonding have been the subject of widespread interest due to fundamental concern in their electronic structures and potential applications. Here, we explore the molecular and electronic structures of diiron(II,II) complexes with N,N’-diarylformamidinate ligands. While a paddlewheel-type diiron(II,II) complex with N,N’-diphenylformamidinate ligands (DPhF) exhibits the centrosymmetric [Fe₂(μ-DPhF)₄] structure, a minor alteration in the ligand system, i. e., switching from phenyl to p-tolyl N-substituted formamidinate ligand (DTolF), resulted in the isolation of an unprecedented non-centrosymmetric [Fe(μ-DTolF)₃Fe(κ²-DTolF)] complex. Both complexes were characterized using single-crystal X-ray diffraction, magnetic measurements, ⁵⁷Fe Mössbauer spectroscopy, and cyclic voltammetry along with high-level ab-initio calculations. The results provide a new view on a range of factors controlling the ground-state electronic configuration and structural diversity of homoleptic diiron(II,II) complexes. Model calculations determined that the Mayer bond orders for Fe−Fe interactions are significantly lower than 1 and equal to 0.15 and 0.28 for [Fe₂(μ-DPhF)₄] and [Fe(μ-DTolF)₃Fe(κ²-DTolF)], respectively.     

Fractional Dynamics Identification via Intelligent Unpacking of the Sample Autocovariance Function by Neural Networks

Many single-particle tracking data related to the motion in crowded environments exhibit anomalous diffusion behavior. This phenomenon can be described by different theoretical models. In this paper, fractional Brownian motion (FBM) was examined as the exemplary Gaussian process with fractional dynamics. The autocovariance function (ACVF) is a function that determines completely the Gaussian process. In the case of experimental data with anomalous dynamics, the main problem is first to recognize the type of anomaly and then to reconstruct properly the physical rules governing such a phenomenon. The challenge is to identify the process from short trajectory inputs. Various approaches to address this problem can be found in the literature, e.g., theoretical properties of the sample ACVF for a given process. This method is effective; however, it does not utilize all of the information contained in the sample ACVF for a given trajectory, i.e., only values of statistics for selected lags are used for identification. An evolution of this approach is proposed in this paper, where the process is determined based on the knowledge extracted from the ACVF. The designed method is intuitive and it uses information directly available in a new fashion. Moreover, the knowledge retrieval from the sample ACVF vector is enhanced with a learning-based scheme operating on the most informative subset of available lags, which is proven to be an effective encoder of the properties inherited in complex data. Finally, the robustness of the proposed algorithm for FBM is demonstrated with the use of Monte Carlo simulations.