Imaging in turbid media using quasi-ballistic photons

We study by means of experiments and Monte Carlo simulations, the scattering of light in random media, to determine the distance up to which photons travel along almost undeviated paths within a scattering medium, and are therefore capable of casting a shadow of an opaque inclusion embedded within the medium. Such photons are isolated by polarisation discrimination wherein the plane of linear polarisation of the input light is continuously rotated and the polarisation preserving component of the emerging light is extracted by means of a Fourier transform. This technique is a software implementation of lock-in detection. We find that images may be recovered to a depth far in excess of that predicted by the diffusion theory of photon propagation. To understand our experimental results, we perform Monte Carlo simulations to model the random walk behaviour of the multiply scattered photons. We present a new definition of a diffusing photon in terms of the memory of its initial direction of propagation, which we then quantify in terms of an angular correlation function. This redefinition yields the penetration depth of the polarisation preserving photons. Based on these results, we have formulated a model to understand shadow formation in a turbid medium, the predictions of which are in good agreement with our experimental results.     

Scale invariant amplitude modulated phase-only filtering

A new synthetic discriminant-function-based amplitude modulated phase-only filtering technique is proposed for scale invariant pattern recognition. This technique has been found to yield improved correlation output when compared with the alternate techniques. The proposed technique is inherently suitable for optical implementation using the currently available spatial light modulators. Simulation results confirm the effectiveness of the proposed technique.     

Rationalizing the generation of broad spectrum antibiotics with the addition of a positive charge

Antibiotic resistance of Gram-negative bacteria is largely attributed to the low permeability of their outer membrane (OM). Recently, we disclosed the eNTRy rules, a key lesson of which is that the introduction of a primary amine enhances OM permeation in certain contexts. To understand the molecular basis for this finding, we perform an extensive set of molecular dynamics (MD) simulations and free energy calculations comparing the permeation of aminated and amine-free antibiotic derivatives through the most abundant OM porin of E. coli, OmpF. To improve sampling of conformationally flexible drugs in MD simulations, we developed a novel, Monte Carlo and graph theory based algorithm to probe more efficiently the rotational and translational degrees of freedom visited during the permeation of the antibiotic molecule through OmpF. The resulting pathways were then used for free-energy calculations, revealing a lower barrier against the permeation of the aminated compound, substantiating its greater OM permeability. Further analysis revealed that the amine facilitates permeation by enabling the antibiotic to align its dipole to the luminal electric field of the porin and form favorable electrostatic interactions with specific, highly-conserved charged residues. The importance of these interactions in permeation was further validated with experimental mutagenesis and whole cell accumulation assays. Overall, this study provides insights on the importance of the primary amine for antibiotic permeation into Gram-negative pathogens that could help the design of future antibiotics. We also offer a new computational approach for calculating free-energy of processes where relevant molecular conformations cannot be efficiently captured.

A rapid pathway sampling method combining Monte Carlo and graph theory, developed to describe permeation pathways through outer membrane porins, can distinguish between structurally similar analogs with different permeabilities.     

Interventional Fairness with Indirect Knowledge of Unobserved Protected Attributes

The deployment of machine learning (ML) systems in applications with societal impact has motivated the study of fairness for marginalized groups. Often, the protected attribute is absent from the training dataset for legal reasons. However, datasets still contain proxy attributes that capture protected information and can inject unfairness in the ML model. Some deployed systems allow auditors, decision makers, or affected users to report issues or seek recourse by flagging individual samples. In this work, we examine such systems and consider a feedback-based framework where the protected attribute is unavailable and the flagged samples are indirect knowledge. The reported samples are used as guidance to identify the proxy attributes that are causally dependent on the (unknown) protected attribute. We work under the causal interventional fairness paradigm. Without requiring the underlying structural causal model a priori, we propose an approach that performs conditional independence tests on observed data to identify such proxy attributes. We theoretically prove the optimality of our algorithm, bound its complexity, and complement it with an empirical evaluation demonstrating its efficacy on various real-world and synthetic datasets.     

Three bis‐ortho‐diynyl­arenes (BODA)

The molecule of 3,3′,4,4′‐tetrakis­(phenyl­ethynyl)­bi­phenyl, C₄₄H₂₆, is approximately planar and is located on a crystallographic inversion center. Bis­[3,4‐bis­(phenyl­ethynyl)­phenyl] ether, C₄₄H₂₆O, has mol­ecules located on twofold symmetry axes, whereas the molecule of 2,2‐bis­[3,4‐bis­(phenyl­ethynyl)­phenyl]­propane, C₄₇H₃₂, does not exhibit any molecular symmetry.     

Attaining record-high magnetic exchange,magnetic anisotropy and blocking barriers in dilanthanofullerenes

While the blocking barrier (U_eff) and blocking temperature (T_B) for “Dysprocenium” SIMs have been increased beyond liquid N₂ temperature, device fabrication of these molecules remains a challenge as low-coordinate Ln³⁺ complexes are very unstable. Encapsulating the lanthanide ion inside a cage such as a fullerene (called endohedral metallofullerene or EMF) opens up a new avenue leading to several Ln@EMF SMMs. The ab initio CASSCF calculations play a pivotal role in identifying target metal ions and suitable cages in this area. Encouraged by our earlier prediction on Ln₂@C₇₉N, which was verified by experiments, here we have undertaken a search to enhance the exchange coupling in this class of molecules beyond the highest reported value. Using DFT and ab initio calculations, we have studied a series of Gd₂@C_2n (30 ≤ 2n ≤ 80), where an antiferromagnetic J_Gd⋯Gd of −43 cm⁻¹ was found for a stable Gd₂@C₃₈-D_3h cage. This extremely large and exceptionally rare 4f⋯4f interaction results from a direct overlap of 4f orbitals due to the confinement effect. In larger cages such as Gd₂@C₆₀ and Gd₂@C₈₀, the formation of two centre-one-electron (2c-1e⁻) Gd–Gd bonds is perceived. This results in a radical formation in the fullerene cage leading to its instability. To avoid this, we have studied heterofullerenes where one of the carbon atoms is replaced by a nitrogen atom. Specifically, we have studied Ln₂@C₅₉N and Ln₂@C₇₉N, where strong delocalisation of the electron yields a mixed valence-like behaviour. This suggests a double-exchange (B) is operational, and CASSCF calculations yield a B value of 434.8 cm⁻¹ and resultant J_Gd–rad of 869.5 cm⁻¹ for the Gd₂@C₅₉N complex. These parameters are found to be two times larger than the world-record J reported for Gd₂@C₇₉N. Further ab initio calculations reveal an unprecedented U_cal of 1183 and 1501 cm⁻¹ for Dy₂@C₅₉N and Tb₂@C₅₉N, respectively. Thus, this study offers strong exchange coupling as criteria for new generation SMMs as the existing idea of enhancing the blocking barrier via crystal field modulation has reached its saturation point.

Using ab initio calculations, we have made some robust predictions towards lanthanofullerene SMMs exhibiting remarkable characteristics.     

Synthesis and studies of a trinuclear Mn(II) carboxylate complex

We report a carboxylate triangle consisting of three manganese(II) centres which is made from manganese(II) carbonate and pivalic acid. The magnetic exchange within the triangle is extremely weak, and antiferromagnetic. Several models have been used to fit the magnetic data, and the best fit uses two weak antiferromagnetic coupling constants of J(1)=-0.588 cm(-1) and J(2)=-0.855 cm(-1). Exchange interactions between the metal centres has been calculated using DFT adopting all the three possible Heisenberg models for a trinuclear system and the results are compared with experimental values. Spin density distribution is used to analyse the nature of the coupling between the metal centres. EPR spectroscopy has been used to explore the nature of the ground state. Recrystallisation of the trinuclear compound from MeCN gives a polymer, while oxidation in air leads to a known compound--an edge-sharing bitetrahedral (MnIII2MnII4) cage.     

On the advantage over a random assignment

We initiate the study of a new measure of approximation. This measure compares the performance of an approximation algorithm to the random assignment algorithm. This is a useful measure for optimization problems where the random assignment algorithm is known to give essentially the best possible polynomial time approximation. In this paper, we focus on this measure for the optimization problems Max‐Lin‐2 in which we need to maximize the number of satisfied linear equations in a system of linear equations modulo 2, and Max‐k‐Lin‐2, a special case of the above problem in which each equation has at most k variables. The main techniques we use, in our approximation algorithms and inapproximability results for this measure, are from Fourier analysis and derandomization. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Spin precession of a charged particle in a uniform magnetic field on a static space-time

We investigate the ratio of spin precession frequency to orbital frequency for a spinning charged particle confined to circular orbit in the equatorial plane of a compact object, with a uniform magnetic field, as described by the Wald and the Ernst potentials. In order to see the difference in behaviours for particles with differentg values we consider the cases of electron and proton separately.     

The Decisive Role of Spin States and Spin Coupling in Dictating Selective O2 Adsorption in Chromium(II) Metal–Organic Frameworks**

The coordinatively unsaturated chromium(II)-based Cr₃[(Cr₄Cl)₃(BTT)₈]₂ (Cr−BTT; BTT³⁻=1,3,5-benzenetristetrazolate) metal–organic framework (MOF) has been shown to exhibit exceptional selectivity towards adsorption of O₂ over N₂/H₂. Using periodic density functional theory (DFT) calculations, we attempted to decipher the origin of this puzzling selectivity. By computing and analyzing the magnetic exchange coupling, binding energies, the partial density of states (pDOS), and adsorption isotherms for the pristine and gas-bound MOFs [(Cr₄(X)₄Cl)₃(BTT)₈]³⁻ (X=O₂, N₂, and H₂), we unequivocally established the role of spin states and spin coupling in controlling the gas selectivity. The computed geometries and gas adsorption isotherms are consistent with the earlier experiments. The binding of O₂ to the MOF follows an electron-transfer mechanism resulting in a Cr^III superoxo species (O₂^.−) with a very strong antiferromagnetic coupling between the two centers, whereas N₂/H₂ are found to weakly interact with the metal center and hence only slightly perturb the associated coupling constants. Although the gas-bound and unbound MOFs have an S=0 ground state (GS), the nature of spin the configurations and the associated magnetic exchanges are dramatically different. The binding energy and the number of oxygen molecules that can favorably bind to the Cr center were found to vary with respect to the spin state, with a significant energy margin (47.6 kJ mol⁻¹). This study offers a hitherto unknown strategy of using spin state/spin couplings to control gas adsorption selectivity in MOFs.