Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space

Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations. In this logically complete and self-standing formulation, one need not choose sides--coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.Comment: LaTeX, 22 pages, 2 figure

Continuity and Stability of Partial Entropic Sums

Extensions of Fannes' inequality with partial sums of the Tsallis entropy are obtained for both the classical and quantum cases. The definition of kth partial sum under the prescribed order of terms is given. Basic properties of introduced entropic measures and some applications are discussed. The derived estimates provide a complete characterization of the continuity and stability properties in the refined scale. The results are also reformulated in terms of Uhlmann's partial fidelities.Comment: 9 pages, no figures. Some explanatory and technical improvements are made. The bibliography is extended. Detected errors and typos are correcte

Generalized entropy optimized by an arbitrary distribution

We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a great variety of distributions observed in nature, which can hardly be described by the conventional methods. As a simple example, we explicitly derive the entropy associated with the stretched exponential distribution. To include the distributions with the divergent moments (e.g., the Levy stable distributions), it is necessary to modify the definition of the expectation value.Comment: 10 pages, no figure

Relations for certain symmetric norms and anti-norms before and after partial trace

Changes of some unitarily invariant norms and anti-norms under the operation of partial trace are examined. The norms considered form a two-parametric family, including both the Ky Fan and Schatten norms as particular cases. The obtained results concern operators acting on the tensor product of two finite-dimensional Hilbert spaces. For any such operator, we obtain upper bounds on norms of its partial trace in terms of the corresponding dimensionality and norms of this operator. Similar inequalities, but in the opposite direction, are obtained for certain anti-norms of positive matrices. Through the Stinespring representation, the results are put in the context of trace-preserving completely positive maps. We also derive inequalities between the unified entropies of a composite quantum system and one of its subsystems, where traced-out dimensionality is involved as well.Comment: 11 pages, no figures. A typo error in Eq. (5.15) is corrected. Minor improvements. J. Stat. Phys. (in press

Phosphatidylinositol 3-Kinase Mediates Bronchioalveolar Stem Cell Expansion in Mouse Models of Oncogenic K-ras-Induced Lung Cancer

Background: Non-small cell lung cancer (NSCLC) is the most common cause of cancer-related death in Western countries. Developing more effective NSCLC therapeutics will require the elucidation of the genetic and biochemical bases for this disease. Bronchioalveolar stem cells (BASCs) are a putative cancer stem cell population in mouse models of oncogenic K-ras-induced lung adenocarcinoma, an histologic subtype of NSCLC. The signals activated by oncogenic K-ras that mediate BASC expansion have not been fully defined. Methodology/Principal Findings: We used genetic and pharmacologic approaches to modulate the activity of phosphatidylinositol 3-kinase (PI3K), a key mediator of oncogenic K-ras, in two genetic mouse models of lung adenocarcinoma. Oncogenic K-ras-induced BASC accumulation and tumor growth were blocked by treatment with a small molecule PI3K inhibitor and enhanced by inactivation of phosphatase and tensin homologue deleted from chromosome 10, a negative regulator of PI3K. Conclusions/Significance: We conclude that PI3K is a critical regulator of BASC expansion, supporting treatment strategies to target PI3K in NSCLC patients

Efficient Dielectrophoretic Patterning of Embryonic Stem Cells in Energy Landscapes Defined by Hydrogel Geometries

In this study, we have developed an integrated microfluidic platform for actively patterning mammalian cells, where poly(ethylene glycol) (PEG) hydrogels play two important roles as a non-fouling layer and a dielectric structure. The developed system has an embedded array of PEG microwells fabricated on a planar indium tin oxide (ITO) electrode. Due to its dielectric properties, the PEG microwells define electrical energy landscapes, effectively forming positive dielectrophoresis (DEP) traps in a low-conductivity environment. Distribution of DEP forces on a model cell was first estimated by computationally solving quasi-electrostatic Maxwell’s equations, followed by an experimental demonstration of cell and particle patterning without an external flow. Furthermore, efficient patterning of mouse embryonic stem (mES) cells was successfully achieved in combination with an external flow. With a seeding density of 107 cells/mL and a flow rate of 3 μL/min, trapping of cells in the microwells was completed in tens of seconds after initiation of the DEP operation. Captured cells subsequently formed viable and homogeneous monolayer patterns. This simple approach could provide an efficient strategy for fabricating various cell microarrays for applications such as cell-based biosensors, drug discovery, and cell microenvironment studies

BRF1 accelerates prostate tumourigenesis and perturbs immune infiltration

BRF1 is a rate-limiting factor for RNA Polymerase III-mediated transcription and is elevated in numerous cancers. Here, we report that elevated levels of BRF1 associate with poor prognosis in human prostate cancer. In vitro studies in human prostate cancer cell lines demonstrated that transient overexpression of BRF1 increased cell proliferation whereas the transient downregulation of BRF1 reduced proliferation and mediated cell cycle arrest. Consistent with our clinical observations, BRF1 overexpression in a Pten-deficient mouse (Pten BRF1 ) prostate cancer model accelerated prostate carcinogenesis and shortened survival. In Pten BRF1 tumours, immune and inflammatory processes were altered, with reduced tumoral infiltration of neutrophils and CD4 positive T cells, which can be explained by decreased levels of complement factor D (CFD) and C7 components of the complement cascade, an innate immune pathway that influences the adaptive immune response. We tested if the secretome was involved in BRF1-driven tumorigenesis. Unbiased proteomic analysis on BRF1-overexpresing PC3 cells confirmed reduced levels of CFD in the secretome, implicating the complement system in prostate carcinogenesis. We further identify that expression of C7 significantly correlates with expression of CD4 and has the potential to alter clinical outcome in human prostate cancer, where low levels of C7 associate with poorer prognosis

Tumor Spectrum, Tumor Latency and Tumor Incidence of the Pten-Deficient Mice

BACKGROUND: Pten functionally acts as a tumor suppressor gene. Lately, tissue-specific ablation of Pten gene in mice has elucidated the role of Pten in different tumor progression models. However, a temporally controlled Pten loss in all adult tissues to examine susceptibility of various tissues to Pten-deficient tumorigenesis has not been addressed yet. Our goal was to explore the genesis of Pten-deficient malignancies in multiple tissue lineages of the adult mouse. METHODS AND FINDINGS: We utilized an inducible Cre/loxP system to delete Pten exon 5 in the systemic organs of ROSA26 (R26)-CreER(T);Pten(fx/fx) mice. On reaching 45 weeks 4OHT-induced Pten loss, we found that the R26-CreER(T);Pten(fx/fx) mice developed a variety of malignancies. Overall tumor mean latency was 17 weeks in the Pten-deficient mice. Interestingly, mutant females developed malignancies more quickly at 10 approximately 11 weeks compared with a tumor latency of 21 weeks for mutant males. Lymphoma incidence (76.9% in females; 40.0% in males) was higher than the other malignancies found in the mutant mice. Mutant males developed prostate (20.0%), intestinal cancer (35.0%) and squamous cell carcinoma (10.0%), whereas the mutant females developed squamous cell carcinoma (15.4%) and endometrial cancer (46.1%) in addition to lymphomas. Furthermore, we tested the pharmacological inhibition of the PTEN downstream effectors using LY294002 on Pten-deficient prostate hyperplasia. Our data revealed that, indeed, the prostate hyperplasia resulting from the induced Pten loss was significantly suppressed by LY294002 (p = 0.007). CONCLUSIONS: Through monitoring a variety of Pten-deficient tumor formation, our results revealed that the lymphoid lineages and the epithelium of the prostate, endometrium, intestine and epidermis are highly susceptible to tumorigenesis after the Pten gene is excised. Therefore, this R26-CreER(T); Pten(fx/fx) mouse model may provide an entry point for understanding the role of Pten in the tumorigenesis of different organs and extend the search for potential therapeutic approaches to prevent Pten-deficient malignancies

Mammalian Target of Rapamycin Is a Therapeutic Target for Murine Ovarian Endometrioid Adenocarcinomas with Dysregulated Wnt/β-Catenin and PTEN

Despite the fact that epithelial ovarian cancers are the leading cause of death from gynecological cancer, very little is known about the pathophysiology of the disease. Mutations in the WNT and PI3K pathways are frequently observed in the human ovarian endometrioid adenocarcinomas (OEAs). However, the role of WNT/β-catenin and PTEN/AKT signaling in the etiology and/or progression of this disease is currently unclear. In this report we show that mice with a gain-of-function mutation in β-catenin that leads to dysregulated nuclear accumulation of β-catenin expression in the ovarian surface epithelium (OSE) cells develop indolent, undifferentiated tumors with both mesenchymal and epithelial characteristics. Combining dysregulated β-catenin with homozygous deletion of PTEN in the OSE resulted in development of significantly more aggressive tumors, which was correlated with inhibition of p53 expression and cellular senescence. Induced expression of both mTOR kinase, a master regulator of proliferation, and phosphorylation of its downstream target, S6Kinase was also observed in both the indolent and aggressive mouse tumors, as well as in human OEA with nuclear β-catenin accumulation. Ectopic allotransplants of the mouse ovarian tumor cells with a gain-of-function mutation in β-catenin and PTEN deletion developed into tumors with OEA histology, the growth of which were significantly inhibited by oral rapamycin treatment. These studies demonstrate that rapamycin might be an effective therapeutic for human ovarian endometrioid patients with dysregulated Wnt/β-catenin and Pten/PI3K signaling

Selective Deletion of PTEN in Dopamine Neurons Leads to Trophic Effects and Adaptation of Striatal Medium Spiny Projecting Neurons

The widespread distribution of the tumor suppressor PTEN in the nervous system suggests a role in a broad range of brain functions. PTEN negatively regulates the signaling pathways initiated by protein kinase B (Akt) thereby regulating signals for growth, proliferation and cell survival. Pten deletion in the mouse brain has revealed its role in controlling cell size and number. In this study, we used Cre-loxP technology to specifically inactivate Pten in dopamine (DA) neurons (Pten KO mice). The resulting mutant mice showed neuronal hypertrophy, and an increased number of dopaminergic neurons and fibers in the ventral mesencephalon. Interestingly, quantitative microdialysis studies in Pten KO mice revealed no alterations in basal DA extracellular levels or evoked DA release in the dorsal striatum, despite a significant increase in total DA tissue levels. Striatal dopamine receptor D1 (DRD1) and prodynorphin (PDyn) mRNA levels were significantly elevated in KO animals, suggesting an enhancement in neuronal activity associated with the striatonigral projection pathway, while dopamine receptor D2 (DRD2) and preproenkephalin (PPE) mRNA levels remained unchanged. In addition, PTEN inactivation protected DA neurons and significantly enhanced DA-dependent behavioral functions in KO mice after a progressive 6OHDA lesion. These results provide further evidence about the role of PTEN in the brain and suggest that manipulation of the PTEN/Akt signaling pathway during development may alter the basal state of dopaminergic neurotransmission and could provide a therapeutic strategy for the treatment of Parkinson's disease, and other neurodegenerative disorders