Abstract:
Let $E$ be a measure preserving equivalence relation, with countable equivalence classes, on a standard Borel probability space $(X,B,\mu)$. Let $([E],d_{u})$ be the the (Polish) full group endowed with the uniform metric. If $F_r = \langle s_1, \ldots, s_r \rangle$ is a free group on $r$-generators and $\alpha \in \operatorname{Hom}(F_r,[E])$ then the stabilizer of a $\mu$-random point $\alpha(F_r)_x$ is a random subgroup of $F_r$ whose distribution is conjugation invariant. Such an object is known as an "invariant random subgroup" or an IRS for short. Bowen's generic model for IRS in $F_r$ is obtained by taking $\alpha$ to be a Baire generic element in the Polish space $\operatorname{Hom}(F_r, [E])$. The "lean aperiodic model" is a similar model where one forces $\alpha(F_r)$ to have infinite orbits by imposing that $\alpha(s_1)$ be aperiodic. In this setting we show that for $r < \infty$ the generic IRS $\alpha(F_r)_x$ is of finite index in $F_r$ a.s. if and only if $E = E_0$ is the hyperfinite equivalence relation. For any ergodic equivalence relation we show that a generic IRS coming from the lean aperiodic model is co-amenable and core free. Finally, we consider the situation where $\alpha(F_r)$ is highly transitive on almost every orbit and in particular the corresponding IRS is supported on maximal subgroups. Using a result of Le-Ma\^{i}tre we show that such examples exist for any aperiodic ergodic $E$ of finite cost. For the hyperfinite equivalence relation $E_0$ we show that high transitivity is generic in the lean aperiodic model.

Abstract:
It is a well-known open problem since the 1970s whether a finitely generated perfect group can be normally generated by a single element or not. We prove that the topological version of this problem has an affirmative answer as long as we exclude infinite discrete quotients (which is probably a necessary restriction).

Abstract:
Recursive partitioning approaches producing tree-like models are a long standing staple of predictive modeling, in the last decade mostly as ``sub-learners'' within state of the art ensemble methods like Boosting and Random Forest. However, a fundamental flaw in the partitioning (or splitting) rule of commonly used tree building methods precludes them from treating different types of variables equally. This most clearly manifests in these methods' inability to properly utilize categorical variables with a large number of categories, which are ubiquitous in the new age of big data. Such variables can often be very informative, but current tree methods essentially leave us a choice of either not using them, or exposing our models to severe overfitting. We propose a conceptual framework to splitting using leave-one-out (LOO) cross validation for selecting the splitting variable, then performing a regular split (in our case, following CART's approach) for the selected variable. The most important consequence of our approach is that categorical variables with many categories can be safely used in tree building and are only chosen if they contribute to predictive power. We demonstrate in extensive simulation and real data analysis that our novel splitting approach significantly improves the performance of both single tree models and ensemble methods that utilize trees. Importantly, we design an algorithm for LOO splitting variable selection which under reasonable assumptions does not increase the overall computational complexity compared to CART for two-class classification. For regression tasks, our approach carries an increased computational burden, replacing a O(log(n)) factor in CART splitting rule search with an O(n) term.

Abstract:
We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob by using a quantum channel while Bob is performing some projective measurements. We bound the classical mutual information in terms of the Hilbert-Schmidt norm by its quantum Hilbert-Schmidt counterpart. This constitutes a Holevo-type upper bound on the classical information transmission rate via a quantum channel. The resulting inequality is rather natural and intuitive relating classical and quantum expressions using the same measure.

Abstract:
Heterogeneous network
consists of the pico cells overlaid over the macro cell coverage area in a
wireless cellular network. The pico cells are deployed to increase the capacity
of the homogeneous network by reusing the spectrum further. However, more users
will tend to be associated to the macro cell due to the fact that the transmit
power of the pico cell is low. In order to increase the number of users
associated to the pico cell, range extension techniques like biased association
are used. This will cause severe interference to cell edge users of the pico
cell from the macro cell causing degradation in throughput performance in the
cell range extension area. In this paper, interference mitigation using
receiver processing along with different scheduling techniques is proposed to
improve the throughput, average delay, and the packet delivery ratio
performance of the system. The performance comparison of the round robin,
proportional fair and modified largest weighted delay first (MLWDF) algorithm
for resource allocation using interference suppressing receiver is done, and
analyzed. It is shown that the MLWDF algorithm achieves the highest throughput
with minimum average delay of packets with the best delivery ratio.

Abstract:
In the present paper, I discuss the internal conflict that accompanies the work of fellow pedagogical supervisors in teacher training institutes. Such internal conflict is manifested in the difficulty that pedagogical supervisors face in successfully integrating the subjective (the personal) and objective (the professional) dimensions of the work of pedagogical supervision. This difficulty, I argue, challenges the possibility of formulating ideological guidelines for the tutor - student relationship, and may ultimately negatively impact the quality of the teacher education process. Below I describe the complexity of the dilemma and its pedagogical implications. Subsequently, I propose a criterion for its resolution via Dewey’s concept of ‘experience’ which I have applied in the context of my work as a pedagogical supervisor in the Primary Education Program at Contradictory Components of Teacher Training.

Abstract:
Recent results on top quark physics with the D0 experiment in pbar-p collisions at sqrt(s) = 1.8 TeV for an integrated luminosity of 125 pb**-1 are reported. The direct measurement of the top quark mass uses single lepton and dilepton events, giving the result m(top) = 172.1 +/- 7.1 GeV/c**2. The measurement of the t-tbar production cross section includes analyses from 9 top decay channels: dilepton (t-tbar --> e+mu, e+e, and mu+mu), electron and neutrino (t-tbar --> e+nu), single leptons (t-tbar --> e + jets, t-tbar --> mu + jets) with and without b tagging, and all-jets (t-tbar --> 6 jets). We measure the t-tbar production cross section to be 5.9 +/- 1.7 pb at m(top) = 172.1 GeV/c**2. Combining the D0 and the CDF measurements of the top quark mass and combining their t-tbar cross sections, in both cases taking into account error correlations, yields unofficially sigma(t-tbar) = 6.7 +/- 1.3 pb at an averaged top quark mass of m(top) = 173.8 +/- 5.2 GeV/c**2. Preliminary results on a search for charged Higgs production in top events, t --> Higgs + b, are presented.