Gravitation, the Quantum and Bohr's Correspondence Principle

The black hole combines in some sense both thehydrogen atom and the black-bodyradiation problems of quantum gravity. Thisanalogy suggests that black-hole quantization may be thekey to a quantum theory of gravity. During the last twenty-fiveyears evidence has been mounting that black-hole surfacearea is indeed quantized, with uniformally spaced areaeigenvalues. There is, however, no general agreement on the spacing of the levels. In thisessay we use Bohr's correspondence principle to providethis missing link. We conclude that the fundamental areaunit is 4h ln 3. This is the unique spacing consistent both with the area-entropythermodynamic relation for black holes, withBoltzmann-Einstein formula in statistical physics andwith Bohr's correspondence principle.     

Time-dependent random walks and the theory of complex adaptive systems

Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are time dependent. We determine the survival probability in the presence of an absorbing boundary. For an unbiased walk, the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities. On the other hand, a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability. We use the results to reveal the underlying dynamics responsible for the phenomenon of self-segregation and clustering observed in the evolutionary minority game.     

Near-perfect correlation of the resistance components of mesoscopic samples at the quantum Hall regime

We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the nu=2 and the nu=1 quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall components of the resistance. These correlated fluctuations appear in a magnetic-field range for which the two-terminal resistance of the samples is quantized. We discuss these findings in light of edge-state transport models of the quantum Hall effect. We also show that our results lead to an ambiguity in the determination of the width of quantum Hall transitions.     

Computational modeling and in-vitro/in-silico correlation of phospholipid-based prodrugs for targeted drug delivery in inflammatory bowel disease

Targeting drugs to the inflamed intestinal tissue(s) represents a major advancement in the treatment of inflammatory bowel disease (IBD). In this work we present a powerful in-silico modeling approach to guide the molecular design of novel prodrugs targeting the enzyme PLA₂, which is overexpressed in the inflamed tissues of IBD patients. The prodrug consists of the drug moiety bound to the sn-2 position of phospholipid (PL) through a carbonic linker, aiming to allow PLA₂ to release the free drug. The linker length dictates the affinity of the PL-drug conjugate to PLA₂, and the optimal linker will enable maximal PLA₂-mediated activation. Thermodynamic integration and Weighted Histogram Analysis Method (WHAM)/Umbrella Sampling method were used to compute the changes in PLA₂ transition state binding free energy of the prodrug molecule (??G^tr) associated with decreasing/increasing linker length. The simulations revealed that 6-carbons linker is the optimal one, whereas shorter or longer linkers resulted in decreased PLA₂-mediated activation. These in-silico results were shown to be in excellent correlation with experimental in-vitro data. Overall, this modern computational approach enables optimization of the molecular design of novel prodrugs, which may allow targeting the free drug specifically to the diseased intestinal tissue of IBD patients.     

Lipschitz representations of subsets of the cube

We show that for any class of uniformly bounded functions with a reasonable combinatorial dimension, the vast majority of small subsets of the -dimensional combinatorial cube cannot be represented as a Lipschitz image of a subset of , unless the Lipschitz constant is very large. We apply this result to the case when consists of linear functionals of norm at most one on a Hilbert space.

     

Studying protein-protein interactions using peptide arrays

Screening of arrays and libraries of compounds is well-established as a high-throughput method for detecting and analyzing interactions in both biological and chemical systems. Arrays and libraries can be composed from various types of molecules, ranging from small organic compounds to DNA, proteins and peptides. The applications of libraries for detecting and characterizing biological interactions are wide and diverse, including for example epitope mapping, carbohydrate arrays, enzyme binding and protein-protein interactions. Here, we will focus on the use of peptide arrays to study protein-protein interactions. Characterization of protein-protein interactions is crucial for understanding cell functionality. Using peptides, it is possible to map the precise binding sites in such complexes. Peptide array libraries usually contain partly overlapping peptides derived from the sequence of one protein from the complex of interest. The peptides are attached to a solid support using various techniques such as SPOT-synthesis and photolithography. Then, the array is incubated with the partner protein from the complex of interest. Finally, the detection of the protein-bound peptides is carried out by using immunodetection assays. Peptide array screening is semi-quantitative, and quantitative studies with selected peptides in solution are required to validate and complement the screening results. These studies can improve our fundamental understanding of cellular processes by characterizing amino acid patterns of protein-protein interactions, which may even develop into prediction algorithms. The binding peptides can then serve as a basis for the design of drugs that inhibit or activate the target protein-protein interactions. In the current review, we will introduce the recent work on this subject performed in our and in other laboratories. We will discuss the applications, advantages and disadvantages of using peptide arrays as a tool to study protein-protein interactions.     

? 1-regularized linear regression: persistence and oracle inequalities

We study the predictive performance of ? ₁-regularized linear regression in a model-free setting, including the case where the number of covariates is substantially larger than the sample size. We introduce a new analysis method that avoids the boundedness problems that typically arise in model-free empirical minimization. Our technique provides an answer to a conjecture of Greenshtein and Ritov (Bernoulli 10(6):971–988, 2004) regarding the “persistence” rate for linear regression and allows us to prove an oracle inequality for the error of the regularized minimizer. It also demonstrates that empirical risk minimization gives optimal rates (up to log factors) of convex aggregation of a set of estimators of a regression function.     

A criterion of normality based on a single holomorphic function

Let F be a family of functions holomorphic on a domain D ⊂ ℂ Let k ≥ 2 be an integer and let h be a holomorphic function on D, all of whose zeros have multiplicity at most k −1, such that h(z) has no common zeros with any f ∈ F. Assume also that the following two conditions hold for every f ∈ F: (a) f(z) = 0 ⇒ f′(z) = h(z); and (b) f′(z) = h(z) ⇒ |f ^(k)(z)| ≤ c, where c is a constant. Then F is normal on D.