Simulated annealing with noisy or imprecise energy measurements

The annealing algorithm (Ref. 1) is modified to allow for noisy or imprecise measurements of the energy cost function. This is important when the energy cannot be measured exactly or when it is computationally expensive to do so. Under suitable conditions on the noise/imprecision, it is shown that the modified algorithm exhibits the same convergence in probability to the globally minimum energy states as the annealing algorithm (Ref. 2). Since the annealing algorithm will typically enter and exit the minimum energy states infinitely often with probability one, the minimum energy state visited by the annealing algorithm is usually tracked. The effect of using noisy or imprecise energy measurements on tracking the minimum energy state visited by the modified algorithms is examined.The research reported here has been supported under Contracts AFOSR-85-0227, DAAG-29-84-K-0005, and DAAL-03-86-K-0171 and a Purdue Research Initiation Grant.     

On the localization of topological invariants

The approach of formal differential geometry to the topological invariants which can be localized is developed. The universal space and universal characteristic forms are constructed. They give rise to primary and secondary characteristic forms.     

Muonium states in semiconductor crystals: Quantum-chemical calculations

The electronic structure of muonium (Mu) located at the bond-centered sites of the silicon and diamond crystals is calculated by the intermediate neglect of differential overlap method. Calculations of the electronicg- and hyperfine interaction tensors of the impurity atom are performed. The results obtained are compared to the experimental properties of “anomalous” muonium Mu^*. It is shown that the properties of Mu located at the bond-centered sites of the Si and C lattices are in qualitative agreement with the observed properties of Mu^*.     

Rapid synthesis of pomalidomide-conjugates for the development of protein degrader libraries

Current methods for the preparation of heterobifunctional pomalidomide-conjugates rely on methods that are often low yielding and produce intractable byproducts. Herein we describe our strategy for the reliable and succinct preparation of pomalidomide-linkers which is essential to the formation of these conjugates. We present the preparation of 18 pomalidomide-linkers in high yield compared to current literature methods. Our findings show that secondary amines consistently afford greater yields than their primary counterparts, a trend that we were able to exploit in the synthesis of several new pomalidomide homo-dimers in enhanced yields compared to similar literature syntheses. This trend was further utilised to develop the first one-pot synthesis of JQ1-pomalidomide conjugates in yields up to 62%, providing a method that is suited to rapid preparation of conjugate libraries as is frequently required for the development of new protein degraders.

Current methods for the preparation of heterobifunctional pomalidomide-conjugates rely on methods that are often low yielding and produce intractable byproducts. Herein we describe our strategy for the succinct preparation of pomalidomide-linkers.