Samplers and Extractors for Unbounded Functions

Blasiok (SODA\u2718) recently introduced the notion of a subgaussian sampler, defined as an averaging sampler for approximating the mean of functions f from {0,1}^m to the real numbers such that f(U_m) has subgaussian tails, and asked for explicit constructions. In this work, we give the first explicit constructions of subgaussian samplers (and in fact averaging samplers for the broader class of subexponential functions) that match the best known constructions of averaging samplers for [0,1]-bounded functions in the regime of parameters where the approximation error epsilon and failure probability delta are subconstant. Our constructions are established via an extension of the standard notion of randomness extractor (Nisan and Zuckerman, JCSS\u2796) where the error is measured by an arbitrary divergence rather than total variation distance, and a generalization of Zuckerman\u27s equivalence (Random Struct. Alg.\u2797) between extractors and samplers. We believe that the framework we develop, and specifically the notion of an extractor for the Kullback-Leibler (KL) divergence, are of independent interest. In particular, KL-extractors are stronger than both standard extractors and subgaussian samplers, but we show that they exist with essentially the same parameters (constructively and non-constructively) as standard extractors

Implications of δlCP∼270∘\delta^{CP}_l\sim 270^\circ and θ23≳45∘\theta_{23}\gtrsim 45^\circ for texture specific lepton mass matrices and 0νββ0\nu \beta \beta decay

We study the phenomenological consequences of recent results from atmospheric and accelerator neutrino experiments, favoring normal neutrino mass ordering $m_1 < m_2 < m_3$, a near maximal lepton Dirac CP phase $\delta_{l}\sim 270^\circ$ along with $\theta_{23}\gtrsim 45^\circ$, for possible realization of natural structure in the lepton mass matrices characterized by ${({M_{ij}})} \sim O(\sqrt {{m_i}{m_j}})$ for $i,j=1,2,3$. It is observed that deviations from parallel texture structures for $M_{l}$ and $M_{\nu}$ are essential for realizing such structures. In particular, such hierarchical neutrino mass matrices are not supportive for a vanishing neutrino mass $m_{\nu 1}\rightarrow 0$ characterized by Det$M_{\nu}\ne 0$ and predict ${m_{\nu 1}} \simeq (0.1 - 8.0)$ $meV$ , ${m_{\nu 2}} \simeq (8.0 - 13.0)$ $meV$, ${m_{\nu 3}} \simeq (47.0 - 52.0)$ $meV$, $\Sigma \simeq (56.0 - 71.0)$ $meV$ and $\left\langle {{m_{ee}}} \right\rangle \simeq (0.01 - 10.0)$ $meV$, respectively, indicating that the task of observing a $0\nu \beta \beta$ decay may be rather challenging for near future experiments.Comment: 12 pages, 10 figures, 2 table

The prognostic role of VEGF in head and neck squamous cell carcinoma

Emerging from potentially malignant disorders that in most cases will never become cancerous, head and neck squamous cell carcinoma (HNSCC) is a cancer that is extremely difficult to diagnose early. This late stage diagnosis has allowed limited improvements in overall survival (OS) as patients are prone to local recurrence, secondary primary tumors, and distant metastasis. As a result, it has become vitally important to assess the prognostic value of biological marker screening to provide an avenue for early diagnosis and identification of local recurrence or residual secondary tumor sites. Many characteristic markers such as EGFR, p16, p53 and VEGF that are constitutively mutated in HNSCC have been identified. However, the dysregulation of VEGF marks a landmark mutation that accelerates the diseases progression and spread. An angiogenic protein normally expressed in response to hypoxic conditions, VEGF allows the creation of new vasculature to remove catabolites and bestows resistance to normal cellular apoptotic signals; pathways often employed by chemotherapeutics. Therefore, early identification of VEGF poses a unique opportunity to employ aggressive therapeutic regimens in combination with precision surgical resection to eliminate the cancer before neovascualture invasion has occurred and the tumor has expanded significantly. For this reason, this review will examine the current literature available on VEGFs role in HNSCC, its value as a prognostic marker