Mathematical Approach to Distant Correlations of Physical Observables and Its Fractal Generalisation

In this paper, the new mathematical correlation of two quantum systems that were initially allowed to interact and then separated is being formulated and analyzed. These correlations are illustrated by many examples and are also connected with fractals at a certain level. The main idea of the paper arises from the EPR paradox, the paradox of Einstein, Podolsky, and Rosen that occurs when the measurement of a physical observable performed on one system has an immediate effect on the other separate system being entangled with it. That is a physical phenomenon, especially when the particles are separated by a large distance. In this paper, we define distant correlations as the advanced method for the exact interpretation of strong connection and influence among those particles even when they are widely separated. On the given topological space (X,τ), we define a notion of τ-metric such that the set X is a τ-metric space and we prove some properties of these spaces. By using this new proposed model, we nullify the contradiction that appears in the EPR paradox. An illustrative example involving fractals is given. This innovative mathematical approach to this physical phenomenon may be attractive for future research in the field of quantum physics.</jats:p

Mathematical Approach to Distant Correlations of Physical Observables and Its Fractal Generalisation

In this paper, the new mathematical correlation of two quantum systems that were initially allowed to interact and then separated is being formulated and analyzed. These correlations are illustrated by many examples and are also connected with fractals at a certain level. The main idea of the paper arises from the EPR paradox, the paradox of Einstein, Podolsky, and Rosen that occurs when the measurement of a physical observable performed on one system has an immediate effect on the other separate system being entangled with it. That is a physical phenomenon, especially when the particles are separated by a large distance. In this paper, we define distant correlations as the advanced method for the exact interpretation of strong connection and influence among those particles even when they are widely separated. On the given topological space (X,&tau;), we define a notion of &tau;-metric such that the set X is a &tau;-metric space and we prove some properties of these spaces. By using this new proposed model, we nullify the contradiction that appears in the EPR paradox. An illustrative example involving fractals is given. This innovative mathematical approach to this physical phenomenon may be attractive for future research in the field of quantum physics

Overexpressed PKCδ Downregulates the Expression of PKCα in B16F10 Melanoma: Induction of Apoptosis by PKCδ via Ceramide Generation

In the present study, we observed a marked variation in the expression of PKCα and PKCδ isotypes in B16F10 melanoma tumor cells compared to the normal melanocytes. Interestingly, the tumor instructed expression or genetically manipulated overexpression of PKCα isotype resulted in enhanced G1 to S transition. This in turn promoted cellular proliferation by activating PLD1 expression and subsequent AKT phosphorylation, which eventually resulted in suppressed ceramide generation and apoptosis. On the other hand, B16F10 melanoma tumors preferentially blocked the expression of PKCδ isotype, which otherwise could exhibit antagonistic effects on PKCα-PLD1-AKT signaling and rendered B16F10 cells more sensitive to apoptosis via generating ceramide and subsequently triggering caspase pathway. Hence our data suggested a reciprocal PKC signaling operational in B16F10 melanoma cells, which regulates ceramide generation and provide important clues to target melanoma cancer by manipulating the PKCδ-ceramide axis

Downregulation of class II phosphoinositide 3-kinase PI3K-C2β delays cell division and potentiates the effect of docetaxel on cancer cell growth.

BACKGROUND: Alteration of signalling pathways regulating cell cycle progression is a common feature of cancer cells. Several drugs targeting distinct phases of the cell cycle have been developed but the inability of many of them to discriminate between normal and cancer cells has strongly limited their clinical potential because of their reduced efficacy at the concentrations used to limit adverse side effects. Mechanisms of resistance have also been described, further affecting their efficacy. Identification of novel targets that can potentiate the effect of these drugs or overcome drug resistance can provide a useful strategy to exploit the anti-cancer properties of these agents to their fullest. METHODS: The class II PI3K isoform PI3K-C2β was downregulated in prostate cancer PC3 cells and cervical cancer HeLa cells using selective siRNAs and the effect on cell growth was determined in the absence or presence of the microtubule-stabilizing agent/anti-cancer drug docetaxel. Mitosis progression was monitored by time-lapse microscopy. Clonogenic assays were performed to determine the ability of PC3 and HeLa cells to form colonies upon PI3K-C2β downregulation in the absence or presence of docetaxel. Cell multi-nucleation was assessed by immunofluorescence. Tumour growth in vivo was assessed using a xenograft model of PC3 cells upon PI3K-C2β downregulation and in combination with docetaxel. RESULTS: Downregulation of PI3K-C2β delays mitosis progression in PC3 and HeLa cells, resulting in reduced ability to form colonies in clonogenic assays in vitro. Compared to control cells, PC3 cells lacking PI3K-C2β form smaller and more compact colonies in vitro and they form tumours more slowly in vivo in the first weeks after cells implant. Stable and transient PI3K-C2β downregulation potentiates the effect of low concentrations of docetaxel on cancer cell growth. Combination of PI3K-C2β downregulation and docetaxel almost completely prevents colonies formation in clonogenic assays in vitro and strongly inhibits tumour growth in vivo. CONCLUSIONS: These data reveal a novel role for the class II PI3K PI3K-C2β during mitosis progression. Furthermore, data indicate that blockade of PI3K-C2β might represent a novel strategy to potentiate the effect of docetaxel on cancer cell growth.This work was supported by Prostate Cancer UK through a Project grant (grant PG13–029 to TM and MF). OC was supported by Prostate Cancer UK (grant PG13–029). IM was supported by MRC a MRC Doctoral Training Award to Barts and The London School of Medicine and Dentistry. FG is supported by Fondazione Italiana Ricerca Cancro (FIRC 19421). EH acknowledges funding from Associazione Italiana Ricerca Cancro (AIRC 21875)