Abstract:
Trinucleotiderepeats sequences (TRS) represent a common type of genomic DNA motif whose expansion is associated with a large number of human diseases. The driving molecular mechanisms of the TRS ongoing dynamic expansion across generations and within tissues and its influence on genomic DNA functions are not well understood. Here we report results for a novel and notable collective breathing behavior of genomic DNA of tandem TRS, leading to propensity for large local DNA transient openings at physiological temperature. Our Langevin molecular dynamics (LMD) and Markov Chain Monte Carlo (MCMC) simulations demonstrate that the patterns of openings of various TRSs depend specifically on their length. The collective propensity for DNA strand separation of repeated sequences serves as a precursor for outsized intermediate bubble states independently of the G/C-content. We report that repeats have the potential to interfere with the binding of transcription factors to their consensus sequence by altered DNA breathing dynamics in proximity of the binding sites. These observations might influence ongoing attempts to use LMD and MCMC simulations for TRS–related modeling of genomic DNA functionality in elucidating the common denominators of the dynamic TRS expansion mutation with potential therapeutic applications.

This research focuses on a historic issue: the
influence of the Earl of Cromer (who served as the British Consul-General in
Egypt) on the local education system. The research reflects an
inter-disciplinary approach—education and history. Coping with the issue
was done via examination of the declared educational goals and the activities
in practice as well as the local population’s responses to the activities.
Allegedly, Cromer failed in his attempted reforms in Egyptian education. This
article attempts to examine the issue from a process-holistic approach
attributing meaning to all actions taken by Cromer in the education system. The
major leading goal of this research is the examination of the education system
in Egypt during the British occupation, when the Earl of Cromer served as the
British Consul-General from September 11, 1883 to the end of his term on May 6,
1907. Cromer is claimed to have ailed his reforms in Egyptian education, and so
this article will attempt to separate the educational goals set by the British
and Cromer and the actual practice in the field. We will also relate to the
local population’s responses to these activities.

Abstract:
The lithic assemblage of the Early Pleistocene site of Bizat Ruhama, Israel demonstrates the earliest evidence for systematic secondary knapping of flakes. The site, dated to the Matuyama chron, is one of the earliest primary context Oldowan occurrences in Eurasia. According to the experimental replication of the stone-tool production sequence, the secondary knapping of flakes was a part of a multi-stage operational sequence targeted at the production of small (<2 cm) flakes. This sequence included four stages: acquisition of chert pebbles, production of flakes, deliberate selection of flakes of specific morphologies, and their secondary knapping by free-hand or bipolar methods. The results suggest that flakes with retouch-like scars that were produced during this sequence and which commonly are interpreted as shaped tools are unintentional waste products of the small flake production. The intentional manufacture of very small flakes at Bizat Ruhama was probably an economic response to the raw material constrains. Systematic secondary knapping of flakes has not yet been reported from other Early Pleistocene sites. Systematic secondary knapping for small flake production became increasingly important only in the lithic industries of the second half of the Middle Pleistocene, almost a million years later. The results from Bizat Ruhama indicate that Oldowan stone-tool production sequence was conceptually more complex than previously suggested and offer a new perspective on the capabilities for invention and the adaptive flexibility of the Oldowan hominins.

Abstract:
The nucleation and growth of clusters in a progressively cooled vapor is studied. The chemical-potential of the vapor increases, resulting in a rapidly increasing nucleation rate. The growth of the newly created clusters depletes monomers, and counters the increase in chemical-potential. Eventually, the chemical potential reaches a maximum and begins to decrease. Shortly thereafter the nucleation of new clusters effectively ceases. Assuming a slow quench rate, asymptotic methods are used to convert the non-linear advection equation of the cluster-size distribution into a fourth-order differential equation, which is solved numerically. The distribution of cluster-sizes that emerges from this creation era of the quench process, and the total amount of clusters generated are found.

Abstract:
We present a new model of homogeneous aggregation that contains the essential physical ideas of the classical predecessors, the Becker-Doring and Lifshitz-Slyovoz models. These classical models, which give different predictions, are asymptotic limits of the new model at small and large cluster sizes (respectively). Since the new theory is valid for large and small clusters, it allows for a complete description of the nucleation process; predicting the Zeldovich nucleation rate, and the diffusion limited growth of large clusters. By retaining the physically valid ingredients from both models, we can explain the seeming incompatibilities and arbitrary choices of the classical models. We solve the equations of our new model asymptotically in the small super-saturation limit. The solution exhibits three successive `eras': nucleation, growth, and coarsening, each with its specific scales of time and cluster size. During the nucleation era, the bulk of the clusters are formed by favorable fluctuations over a free energy barrier, according to the analysis by Zeldovich. During the Growth era no new clusters are created, and the expansion of the existing ones continues. Eventually the coarsening era begins. During this competitive attrition process, smaller clusters dissolve and fuel the further growth of the larger survivors. By resolving the preceding creation and growth eras, our analysis gives explicitly the characteristic time and cluster size of the coarsening era, and a unique selection of the long time, self-similar cluster size distribution.

Abstract:
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems) then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.

Abstract:
The $L^p$-cosine transform of an even, continuous function $f\in C_e(\Sn)$ is defined by: $$H(x)=\int_{\Sn}|\ip{x}{\xi}|^pf(\xi) d\xi,\quad x\in {\R}^n.$$ It is shown that if $p$ is not an even integer then all partial derivatives of even order of $H(x)$ up to order $p+1$ (including $p+1$ if $p$ is an odd integer) exist and are continuous everywhere in ${\R}^n\backslash\{0\}$. As a result of the corresponding differentiation formula, we show that if $f$ is a positive bounded function and $p>1$ then $H^{1/p}$ is a support function of a convex body whose boundary has everywhere positive Gauss-Kronekcer curvature.

Abstract:
In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear operators. This, in turn, reveals a powerful connection between a class of optimization algorithms and the analytic theory of polynomials whereby new lower and upper bounds are derived. In particular, we present a new and natural derivation of Nesterov's well-known Accelerated Gradient Descent method by employing simple 'economic' polynomials. This rather natural interpretation of AGD contrasts with earlier ones which lacked a simple, yet solid, motivation. Lastly, whereas existing lower bounds are only valid when the dimensionality scales with the number of iterations, our lower bound holds in the natural regime where the dimensionality is fixed.

Abstract:
Let $f(j,k,n)$ denote the expected number of $j$-faces of a random $k$-section of the $n$-cube. A formula for $f(0,k,n)$ is presented, and for $j\geq 1$, a lower bound for $f(j,k,n)$ is derived, which implies a precise asymptotic formula for $f(n-m,n-l,n)$ when $1\leq l

Abstract:
Zonoids whose polars are zonoids cannot have proper faces of dimension other than $n-1$ or zero ($n\geq 3$). However, there exist non smooth zonoids whose polars are zonoids. Examples in $R^3$ and $R^4$ are given.