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We have studied the charged BTZ black holes in noncommutative spaces arising from two independent approaches. First, by using the Seiberg-Witten map followed by a dynamic choice of gauge in the Chern-Simons gauge theory. Second, by inducing the fuzziness in the mass and charge by a Lorentzian distribution function with the width being the same as the minimal length of the associated noncommutativity. In the first approach, we have found the existence of non-static and non-stationary BTZ black holes in noncommutative spaces for the first time in the literature, while the second approach facilitates us to introduce a proper bound on the noncommutative parameter so that the corresponding black hole becomes stable and physical. We have used a contemporary tunneling formalism to study the thermodynamics of the black holes arising from both of the approaches and analyze their behavior within the context., Comment: 16 pages, 5 figures

Quantum resource theory is perhaps the most revolutionary framework that quantum physics has ever experienced. It plays vigorous roles in unifying the quantification methods of a requisite quantum effect as wells as in identifying protocols that optimize its usefulness in a given application in areas ranging from quantum information to computation. Moreover, the resource theories have transmuted radical quantum phenomena like coherence, nonclassicality and entanglement from being just intriguing to being helpful in executing realistic thoughts. A general quantum resource theoretical framework relies on the method of categorization of all possible quantum states into two sets, namely, the free set and the resource set. Associated with the set of free states there is a number of free quantum operations emerging from the natural constraints attributed to the corresponding physical system. Then, the task of quantum resource theory is to discover possible aspects arising from the restricted set of operations as resources. Along with the rapid growth of various resource theories corresponding to standard harmonic oscillator quantum optical states, significant advancement has been expedited along the same direction for generalized quantum optical states. Generalized quantum optical framework strives to bring in several prosperous contemporary ideas including nonlinearity, $\mathcal{PT}$-symmetric non-Hermitian theories, $q$-deformed bosonic systems, etc., to accomplish similar but elevated objectives of the standard quantum optics and information theories. In this article, we review the developments of nonclassical resource theories of different generalized quantum optical states and their usefulness in the context of quantum information theories., 15 pages

Squeezed states are one of the most useful quantum optical models having various applications in different areas, especially in quantum information processing. Generalized squeezed states are even more interesting since, sometimes, they provide additional degrees of freedom in the system. However, they are very difficult to construct and, therefore, people explore such states for individual setting and, thus, a generic analytical expression for generalized squeezed states is yet inadequate in the literature. In this article, we propose a method for the generalization of such states, which can be utilized to construct the squeezed states for any kind of quantum models. Our protocol works accurately for the case of the trigonometric Rosen-Morse potential, which we have considered as an example. Presumably, the scheme should also work for any other quantum mechanical model. In order to verify our results, we have studied the nonclassicality of the given system using several standard mechanisms. Among them, the Wigner function turns out to be the most challenging from the computational point of view. We, thus, also explore a generalization of the Wigner function and indicate how to compute it for a general system like the trigonometric Rosen-Morse potential with a reduced computation time., Comment: 9 pages, 3 figures

We construct a generalized version of the photon-subtracted squeezed vacuum states (PSSVS), which can be utilized to construct the same for nonlinear, deformed and any usual quantum mechanical models beyond the harmonic oscillator. We apply our general framework to trigonometric P\"oschl-Teller potential and show that our method works accurately and produces a proper nonclassical state. We analyze the nonclassicality of the state using three different approaches, namely, quadrature squeezing, photon number squeezing and Wigner function and indicate how the standard definitions of those three techniques can be generalized and utilized to examine the nonclassicality of any generalized quantum optical states including the PSSVS. We observe that the generalized PSSVS are always more nonclassical than those arising from the harmonic oscillator. Moreover, within some quantification schemes, we find that the nonclassicality of the PSSVS increases almost proportionally with the number of photons subtracted from the generalized squeezed vacuum state. Thus, generalized PSSVS may provide an additional freedom with which one can regulate the nonclassicality and obtain an appropriate nonclassical state as per requirement., Comment: 11 pages, 5 figures, Typos corrected, Few references added

We study the non-perturbative quantum corrections to a Born-Infeld black hole in a spherical cavity. These quantum corrections produce a non-trivial short distances modification to the relation between the entropy and area of this black hole. The non-perturbative quantum correction appears as an exponential term in the black hole entropy. This in turn modifies the thermodynamics of a given system, for example reduced value of the Helmholtz free energy. Moreover, the first law of black hole thermodynamics modified due to quantum corrections. We also investigate the effect of such non-perturbative corrections on the information geometry of this system. This is done using some famous information metrics., Comment: 17 pages, 15 figures. Accepted in Class. Quantum Grav

Mutations in the TP53 gene are one of the most frequent events in cancers. Certain missense mutant p53 proteins gain oncogenic functions (gain-of-functions) and drive tumorigenesis. Apart from the coding genes, a few non-coding microRNAs (miRNAs) are implicated in mediating mutant p53-driven cancer phenotypes. Here, we identified miRNAs in mutant p53R273H bearing non-small cell lung carcinoma (NSCLC) cells while using small RNA deep sequencing. Differentially regulated miRNAs were validated in the TCGA lung adenocarcinoma patients with p53 mutations and, subsequently, we identified specific miRNA signatures that are associated with lymph node metastasis and poor survival of the patients. Pathway analyses with integrated miRNA-mRNA expressions further revealed potential regulatory molecular networks in mutant p53 cancer cells. A possible contribution of putative mutant p53-regulated miRNAs in epithelial-to-mesenchymal transition (EMT) is also predicted. Most importantly, we identified a novel miRNA from the unmapped sequencing reads through a systematic computational approach. The newly identified miRNA promotes proliferation, colony-forming ability, and migration of NSCLC cells. Overall, the present study provides an altered miRNA expression profile that might be useful in biomarker discovery for non-small cell lung cancers with TP53 mutations and discovers a hitherto unknown miRNA with oncogenic potential.

Mutation in TP53 is a common genetic alteration in human cancers. Certain tumor associated p53 missense mutants acquire gain-of-function (GOF) properties and confer oncogenic phenotypes including enhanced chemoresistance. The colorectal cancers (CRC) harboring mutant p53 are generally aggressive in nature and difficult to treat. To identify a potential gene expression signature of GOF mutant p53-driven acquired chemoresistance in CRC, we performed transcriptome profiling of floxuridine (FUdR) treated SW480 cells expressing mutant p53R273H (GEO#: GSE77533). We obtained several genes differentially regulated between FUdR treated and untreated cells. Further, functional characterization and pathway analysis revealed significant enrichment of crucial biological processes and pathways upon FUdR treatment in SW480 cells. Our data suggest that in response to chemotherapeutics treatment, cancer cells with GOF mutant p53 can modulate key cellular pathways to withstand the cytotoxic effect of the drugs. The genes and pathways identified in the present study can be further validated and targeted for better chemotherapy response in colorectal cancer patients harboring mutant p53.

Almost all epithelial tumours contain cancer stem-like cells, which possess a unique property of self-renewal and differentiation. In oral cancer, several biomarkers including cell surface molecules have been exploited for the identification of this highly tumorigenic population. Implicit is the role of CD44 in defining CSCs but CD24 is not well-explored. Here we show that CD44(high)CD24(low) cells isolated from the oral cancer cell lines, not only express stem cell related genes but also exhibit Epithelial-to-Mesenchymal transition (EMT) characteristics. This CD44(high)CD24(low) population gives rise to all other cell types upon differentiation. Typical Cancer Stem Cell (CSC) phenotypes like increased colony formation, sphere forming ability, migration and invasion were also confirmed in CD44(high)CD24(low) cells. Drug transporters were found to be over-expressed in CD44(high)CD24(low) sub-population thereby contributing to elevated chemo-resistance. To validate our findings in-vivo, we determined the relative expression of CD44 and CD24 in clinical samples of OSCC patients. CD44 expression was consistently high whereas CD24 showed significantly lower expression in tumour tissues. Further, the gene expression profile of the CSC and non-CSC population unravels the molecular pathways which may contribute to stemness. We conclude that CD44(high)CD24(low) represents cancer stem-like cells in Oral Squamous Cell Carcinoma.

In this paper, we will analyze a finite temperature BIon, which is a finite temperature brane-anti-brane wormhole configuration. We will analyze the quantum fluctuations to this BIon solution using the Euclidean quantum gravity. It will be observed that these quantum fluctuations produce logarithmic corrections to the entropy of this finite temperature BIon solution. These corrections to the entropy also correct the internal energy and the specific heat for this finite temperature BIon. We will also analyze the critical points for this finite temperature BIonic system, and analyze the effects of quantum corrections on the stability of this system., 14 pages, 7 Figures, Accepted in Class. Quantum Gravity

In this paper, we show that the standard techniques that are utilized to study the classical-like properties of the pure states for Hermitian systems can be adjusted to investigate the classicality of pure states for non-Hermitian systems. The method is applied to the states of complex-valued potentials that are generated by Darboux transformations and can model both non-PT-symmetric and PT-symmetric oscillators exhibiting real spectra., MINECO project MTM2014- 57129-C2-1-P, and Junta de Castilla y León project VA057U16.

We study a protocol for constructing a squeezed atom laser for a model originating from the generalized uncertainty principle. We show that the squeezing effects arising from such systems do not require any squeezed light as an input, but the squeezing appears automatically because of the structure of the model it owns. The output atom laser beam becomes squeezed due to the nonlinear interaction between the Bose-Einstein condensate and the deformed radiation field created due to the noncommutative structure. We analyze several standard squeezing techniques based on the analytical expressions followed by a numerical analysis for further insights., Comment: 11 pages, 2 figures

It was at the dawn of the historical developments of quantum mechanics when Schrodinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as “coherent states” today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Nonclassical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superselection principles and mathematical physics. On the other hand, the compelling advancements of non-Hermitian systems and related areas have been appealing, which became popular with the seminal paper by Bender and Boettcher in 1998. The subject of non-Hermitian Hamiltonian systems possessing real eigenvalues are exploding day by day and combining with almost all other subjects rapidly, in particular, in the areas of quantum optics, lasers and condensed matter systems, where one finds ample successful experiments for the proposed theory. For this reason, the study of coherent states for non-Hermitian systems have been very important. In this article, we review the recent developments of coherent and nonclassical states for such systems and discuss their applications and usefulness in different contexts of physics. In addition, since the systems considered here originated from the broader context of the study of minimal uncertainty relations, our review is also of interest to the mathematical physics community.

In this paper, we have constructed the Feynman path integral method for non-paraxial optics. This is done by using the mathematical analogy between a non-paraxial optical system and the generalized Schr\"odinger equation deformed by the existence a minimal measurable length. Using this analogy, we investigated the consequences of a minimal length in this optical system. This path integral has been used to obtain instanton solution for such a optical systems. Moreover, the Berry phase of this optical system has been investigated. These results may disclose a new way to use the path integral approach in optics. Furthermore, as such system with an intrinsic minimal length have been studied in quantum gravity, the ultra-focused optical pluses can be used as an optical analog of quantum gravity., Comment: 12 pages, 1 figure, Accepted in EPL, Typos corrected, Few references and one figure added

The E2F family of transcription factors regulates genes involved in various aspects of the cell cycle. Beyond the well-documented role in G1/S transition, mitotic regulation by E2F has also been reported. Proper mitotic progression is monitored by the spindle assembly checkpoint (SAC). The SAC ensures bipolar separation of chromosomes and thus prevents aneuploidy. There are limited reports on the regulation of the SAC by E2F. Our previous work identified the SAC protein Cdc20 as a novel transcriptional regulator of the mitotic ubiquitin carrier protein UbcH10. However, none of the Cdc20 transcription complex proteins have any known DNA binding domain. Here we show that an E2F1-DP1 heterodimer is involved in recruitment of the Cdc20 transcription complex to the UBCH10 promoter and in transactivation of the gene. We further show that inactivation of Rb can facilitate this transactivation process. Moreover, this E2F1-mediated regulation of UbcH10 influences mitotic progression. Deregulation of this pathway results in premature anaphase, chromosomal abnormalities, and aneuploidy. We conclude that excess E2F1 due to Rb inactivation recruits the complex of Cdc20 and the anaphase-promoting complex/cyclosome (Cdc20-APC/C) to deregulate the expression of UBCH10, leading to chromosomal instability in cancer cells.

One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all such approaches. However, the identification of the appropriate passage to quantum gravity is suffering from the inadequacy of experimental techniques. It is beyond our ability to test the effects of quantum gravity thorough the available scattering experiments, as it is unattainable to probe such high energy scale at which the effects of quantum gravity appear. Here we propose an elegant alternative scheme to test such theories by detecting the deformations emerging from the noncommutative structures. Our protocol relies on the novelty of an opto-mechanical experimental setup where the information of the noncommutative oscillator is exchanged via the interaction with an optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of current technology and, thus, it could uncover a feasible route towards the realization of quantum gravitational phenomena thorough a simple table-top experiment., Comment: 7 pages, 3 figures, In press (Nuclear Physics B)

The existence of a minimal measurable length as a characteristic length in the Planck scale is one of the main features of quantum gravity and has been widely explored in the context. Various different deformations of spacetime have been employed successfully for the purpose. However, polymer quantization approach is a relatively new and dynamic field towards the quantum gravity phenomenology, which emerges from the symmetric sector of the loop quantum gravity. In this article, we extend the standard ideas of polymer quantization to find a new and tighter bound on the polymer deformation parameter. Our protocol relies on an opto-mechanical experimental setup that was originally proposed in Ref.\cite{ref:Igor} to explore some interesting phenomena by embedding the minimal length into the standard canonical commutation relation. We extend this scheme to probe the \emph{polymer length} deformed canonical commutation relation of the center of mass mode of a mechanical oscillator with a mass around the Planck scale. The method utilizes the novelty of exchanging the relevant mechanical information with a high intensity optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of the current technologies and, thus, it could uncover a decent realization of quantum gravitational phenomena thorough a simple table-top experiment., Comment: 7 pages, 1 figure, Accepted for Publication in Scientific Reports (Nature)

We study the correction of the energy spectrum of a gravitational quantum well due to the combined effect of the braneworld model with infinite extra dimensions and generalized uncertainty principle. The correction terms arise from a natural deformation of a semiclassical theory of quantum gravity governed by the Schr\"odinger-Newton equation based on a minimal length framework. The two fold correction in the energy yields new values of the spectrum, which are closer to the values obtained in the GRANIT experiment. This raises the possibility that the combined theory of the semiclassical quantum gravity and the generalized uncertainty principle may provide an intermediate theory between the semiclassical and the full theory of quantum gravity. We also prepare a schematic experimental set-up which may guide to the understanding of the phenomena in the laboratory., Comment: 12 pages, 1 figure

We have studied the effect of a non-Hermitian Bosonic bath on the dynamics of a two-level spin system. The non-Hermitian Hamiltonian of the bath is chosen such that it converges to the harmonic oscillator Hamiltonian when the non-Hermiticity is switched off. We calculate the dynamics of the spin system and found that the non-Hermiticity can have positive as well as negative effects on the coherence of the system. However, the decoherence can be completely eliminated by choosing the non-Hermiticity parameter and the phase of the system bath interaction appropriately. We have also studied the effect of this bath on the entanglement of a two-spin system when the bath is acting only on one spin., Comment: 7 pages, 1 figure

International audience; In this paper, we define the homodyne q -deformed quadrature operator and find its eigenstates in terms of the deformed Fock states. We find the quadrature representation of q -deformed Fock states in the process. Furthermore, we calculate the explicit analytical expression for the optical tomogram of the q -deformed coherent states.

In a setting of noncommutative space with minimal length we confirm the general assertion that the more nonclassical an input state for a beam splitter is, the more entangled its output state becomes. By analysing various nonclassical properties we find that the odd Schr\"odinger cat states are more nonclassical than the even Schr\"odinger cat states, hence producing more entanglement, which in turn are more nonclassical than coherent states. Both the nonclassicality and the entanglement can be enhanced by increasing the noncommutativity of the underlying space. In addition we find as a by-product some rare explicit minimum uncertainty quadrature and number squeezed states, i.e. ideal squeezed states., Comment: 15 pages, 7 figures

Coherent states are required to form a complete set of vectors in the Hilbert space by providing the resolution of identity. We study the completeness of coherent states for two different models in a noncommutative space associated with the generalised uncertainty relation by finding the resolution of unity with a positive definite weight function. The weight function, which is sometimes known as the Borel measure, is obtained through explicit analytic solutions of the Stieltjes and Hausdorff moment problem with the help of the standard techniques of the inverse Mellin transform.

We investigate certain properties of $\mathfrak{su}(N)$-valued two-dimensional soliton surfaces associated with the integrable $\mathbb{C}P^{N-1}$ sigma models constructed by the orthogonal rank-one Hermitian projectors, which are defined on the two-dimensional Riemann sphere with finite action functional. Several new properties of the projectors mapping onto one-dimensional subspaces as well as their relations with three mutually different immersion formulas, namely, the generalized Weierstrass, Sym-Tafel and Fokas-Gel'fand have been discussed in detail. Explicit connections among these three surfaces are also established by purely analytical descriptions and, it is demonstrated that the three immersion formulas actually correspond to the single surface parametrized by some specific conditions., 17 pages

We construct the photon added coherent states of a noncommutative harmonic oscillator associated to a $q$-deformed oscillator algebra. Various nonclassical properties of the corresponding system are explored, first, by studying two different types of higher order quadrature squeezing, namely the Hillery-type and the Hong--Mandel-type and, second, by testing the sub-Poissonian nature of photon statistics in higher order with the help of the correlation function and the Mandel parameter. By comparing our results with those of the usual harmonic oscillator, we notice that the quadratures and photon number distributions in noncommutative case are more squeezed for the same values of the parameters and, thus, the photon added coherent states of noncommutative harmonic oscillator may be more nonclassical in comparison to the ordinary harmonic oscillator., 13 pages, 5 figures, Accepted for publication in Phys. Rev. A

Lens epithelium-derived growth factor (LEDGF), a ubiquitously expressed nuclear protein, acts by interacting with DNA and protein and is involved in widely varying cellular functions. Despite its importance, the mechanism(s) that regulate naturally occurring LEDGF activity are unidentified. In the present study, we report that LEDGF is constitutively Sumoylated, and that the dynamical regulatory mechanism(s) (i.e. Sumoylation and deSumoylation) act as a molecular switch in modulating the DNA-binding and transcriptional activity of LEDGF with the functional consequences. Using bioinformatics analysis coupled with in vitro and in vivo Sumoylation assays, we found that lysine (K) 364 of LEDGF was Sumoylated, repressing its transcriptional activity. Conversely, mutation of K364 to arginine (R) or deSumoylation by small ubiquitin-like modifier (Sumo)-specific protease-1, a nuclear deSumoylase, enhanced the transactivation capacity of LEDGF and its cellular abundance. The enhancements were directly correlated with an increase in the DNA-binding activity and small heat shock protein transcription of LEDGF, whereas the process was reversed in cells overexpressing Sumo1. Interestingly, cells expressing Sumoylation-deficient pEGFP-K364R protein showed increased cellular survival compared to wild-type LEDGF protein. The findings provide insights into the regulation and regulatory functions of LEDGF in Sumoylation-dependent transcriptional control that may be essential for modifying the physiology of cells to maintain cellular homeostasis. These studies also provide new evidence of the important role of post-translational modification in controlling LEDGF function.

Human NEIL2, one of five oxidized base-specific DNA glycosylases, is unique in preferentially repairing oxidative damage in transcribed genes. Here we show that depletion of NEIL2 causes a 6- to 7-fold increase in spontaneous mutation frequency in the HPRT gene of the V79 Chinese hamster lung cell line. This prompted us to screen for NEIL2 variants in lung cancer patients’ genomic DNA. We identified several polymorphic variants, among which R103Q and R257L were frequently observed in lung cancer patients. We then characterized these variants biochemically, and observed a modest decrease in DNA glycosylase activity relative to the wild type (WT) only with the R257L mutant protein. However, in reconstituted repair assays containing WT NEIL2 or its R257L and R103Q variants together with other DNA base excision repair (BER) proteins (PNKP, Polβ, Lig IIIα and XRCC1) or using NEIL2-FLAG immunocomplexes, an ~ 5-fold decrease in repair was observed with the R257L variant compared to WT or R103Q NEIL2, apparently due to the R257L mutant’s lower affinity for other repair proteins, particularly Polβ. Notably, increased endogenous DNA damage was observed in NEIL2 variant (R257L)-expressing cells relative to WT cells. Taken together, our results suggest that the decreased DNA repair capacity of the R257L variant can induce mutations that lead to lung cancer development.

We generalize the Milne quantization condition to non-Hermitian systems. In the general case the underlying nonlinear Ermakov-Milne-Pinney equation needs to be replaced by a nonlinear integral differential equation. However, when the system is PT-symmetric or/and quasi/pseudo-Hermitian the equations simplify and one may employ the original energy integral to determine its quantization. We illustrate the working of the general framework with the Swanson model and two explicit examples for pairs of supersymmetric Hamiltonians. In one case both partner Hamiltonians are Hermitian and in the other a Hermitian Hamiltonian is paired by a Darboux transformation to a non-Hermitian one., 11 pages, 3 figures

We study several classical like properties of q-deformed nonlinear coherent states as well as nonclassical behaviours of q-deformed version of the Schrodinger cat states in noncommutative space. Coherent states in q-deformed space are found to be minimum uncertainty states together with the squeezed photon distributions unlike the ordinary systems, where the photon distributions are always Poissonian. Several advantages of utilising cat states in noncommutative space over the standard quantum mechanical spaces have been reported here. For instance, the q-deformed parameter has been utilised to improve the squeezing of the quadrature beyond the ordinary case. Most importantly, the parameter provides an extra degree of freedom by which we achieve both quadrature squeezed and number squeezed cat states at the same time in a single system, which is impossible to achieve from ordinary cat states., Comment: 12 pages, 5 figures

We propose a noncommutative version of the Euclidean Lie algebra $E_2$. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra., 7 pages

We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schroedinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy eigenspectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices., Comment: 17 pages, 5 figures

Expression of matrix metalloproteinase-1 (MMP-1), an interstitial collagenase, plays a major role in cellular invasion during development of gastric cancer, a leading cause of death worldwide. A single-nucleotide polymorphism (SNP) −1607 1G/2G site of the MMP-1 gene promoter has been reported to alter transcription level. While the importance’s of other SNPs in the MMP-1 promoter have not yet been studied in gastric cancer, our aim was to investigate MMP-1 gene promoter polymorphisms and gastric cancer susceptibility in eastern Indian population. A total of 145 gastric cancer patients and 145 healthy controls were genotyped for MMP-1 −1607 1G/2G (rs1799750) by PCR-restriction fragment length polymorphism (RFLP), while MMP-1 −519 A/G (rs1144393), MMP-1 −422 T/A (rs475007), MMP-1 −340 T/C (rs514921) and MMP-1 −320 T/C (rs494379) were genotyped by DNA sequencing. A positive association was found with MMP-1 −422 T/A SNP that showed significant risk for regional lymph node metastasis (P = 0.021, Odd’s ratio (OR) = 3.044, Confidence intervals (CI) = 1.187–7.807). In addition, we found a significant association with lower stomach tumor formation among gastric cancer patients for three adjacent polymorphisms near the transcriptional start sites of [MMP-1 −422 T/A (P = 0.043, OR = 2.182, CI = 1.03–4.643), MMP-1 −340 T/C (P = 0.075, OR = 1.97, CI = 0.94–4.158) and MMP-1 −320 T/C (P = 0.034, OR = 2.224, CI = 1.064–40731)]. MMP-1 level in patients’ serum was correlated with MMP-1 promoter haplotypes conferring these three SNPs to evaluate the functional importance of these polymorphisms in lower stomach tumor formation and significant correlation was observed. Furthermore, MMP-1 −519 A/G polymorphism displayed poor cellular differentiation (P = 0.024, OR = 3.8, CI = 1.69–8.56) attributing a higher risk of cancer progression. In conclusion, MMP-1 proximal promoter SNPs are associated with the risk of lower stomach tumor formation and node metastasis in eastern Indian population.

We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time-dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional canonical variables. We employ the Lewis-Riesenfeld method of invariants to construct explicit analytical solutions for the corresponding time-dependent Schroedinger equation. The eigenfunctions are expressed in terms of the solutions of variants of the nonlinear Ermakov-Pinney equation and discussed in detail for various types of background fields. We utilize the solutions to verify a generalized version of Heisenberg's uncertainty relations for which the lower bound becomes a time-dependent function of the background fields. We study the variance for various states including standard Glauber coherent states with their squeezed versions and Gaussian Klauder coherent states resembling a quasi-classical behaviour. No type of coherent states appears to be optimal in general with regard to achieving minimal uncertainties, as this feature turns out to be background field dependent., Comment: 21 pages, 6 figures

We investigate four different types of representations of deformed canonical variables leading to generalized versions of Heisenberg's uncertainty relations resulting from noncommutative spacetime structures. We demonstrate explicitly how the representations are related to each other and study three characteristically different solvable models on these spaces, the harmonic oscillator, the manifestly non-Hermitian Swanson model and an intrinsically noncommutative model with Poeschl-Teller type potential. We provide an analytical expression for the metric in terms of quantities specific to the generic solution procedure and show that when it is appropriately implemented expectation values are independent of the particular representation. A recently proposed inequivalent representation resulting from Jordan twists is shown to lead to unphysical models. We suggest an anti-PT-symmetric modification to overcome this shortcoming., 14 pages, 1 figure

The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat noncommutative space and employ it to study the eigenvalue spectrum for the harmonic oscillator on this space. The perturbative expression for the eigenenergy indicates that the model might possess an exceptional point at which the spectrum becomes complex and its PT-symmetry is spontaneously broken., 4 pages, contribution to proceedings of "Analytic and algebraic methods in physics X", Prague

We find that real and complex Bohmian quantum trajectories resulting from well-localized Klauder coherent states in the quasi-Poissonian regime possess qualitatively the same type of trajectories as those obtained from a purely classical analysis of the corresponding Hamilton-Jacobi equation. In the complex cases treated the quantum potential results to a constant, such that the agreement is exact. For the real cases we provide conjectures for analytical solutions for the trajectories as well as the corresponding quantum potentials. The overall qualitative behaviour is governed by the Mandel parameter determining the regime in which the wavefunctions evolve as soliton like structures. We demonstrate these features explicitly for the harmonic oscillator and the Poeschl-Teller potential., Comment: 20 pages, 11 figures

We provide an explicit construction for Gazeau-Klauder coherent states related to non-Hermitian Hamiltonians with discrete bounded below and nondegenerate eigenspectrum. The underlying spacetime structure is taken to be of a noncommutative type with associated uncertainty relations implying minimal lengths. The uncertainty relations for the constructed states are shown to be saturated in a Hermitian as well as a non-Hermitian setting for a perturbed harmonic oscillator. The computed value of the Mandel parameter dictates that the coherent wavepackets are assembled according to sub-Poissonian statistics. Fractional revival times, indicating the superposition of classical-like sub-wave packets are clearly identified., 14 pages, 2 figures

Lens epithelium-derived growth factor (LEDGF), a ubiquitously expressed nuclear protein, acts by interacting with DNA and protein and is involved in widely varying cellular functions. Despite its importance, the mechanism(s) that regulate naturally occurring LEDGF activity are unidentified. In the present study, we report that LEDGF is constitutively Sumoylated, and that the dynamical regulatory mechanism(s) (i.e. Sumoylation and deSumoylation) act as a molecular switch in modulating the DNA-binding and transcriptional activity of LEDGF with the functional consequences. Using bioinformatics analysis coupled with in vitro and in vivo Sumoylation assays, we found that lysine (K) 364 of LEDGF was Sumoylated, repressing its transcriptional activity. Conversely, mutation of K364 to arginine (R) or deSumoylation by small ubiquitin-like modifier (Sumo)-specific protease-1, a nuclear deSumoylase, enhanced the transactivation capacity of LEDGF and its cellular abundance. The enhancements were directly correlated with an increase in the DNA-binding activity and small heat shock protein transcription of LEDGF, whereas the process was reversed in cells overexpressing Sumo1. Interestingly, cells expressing Sumoylation-deficient pEGFP-K364R protein showed increased cellular survival compared to wild-type LEDGF protein. The findings provide insights into the regulation and regulatory functions of LEDGF in Sumoylation-dependent transcriptional control that may be essential for modifying the physiology of cells to maintain cellular homeostasis. These studies also provide new evidence of the important role of post-translational modification in controlling LEDGF function.

We investigate properties of generalized time-dependent q-deformed coherent states for a noncommutative harmonic oscillator. The states are shown to satisfy a generalized version of Heisenberg's uncertainty relations. For the initial value in time the states are demonstrated to be squeezed, i.e. the inequalities are saturated, whereas when time evolves the uncertainty product oscillates away from this value albeit still respecting the relations. For the canonical variables on a noncommutative space we verify explicitly that Ehrenfest's theorem hold at all times. We conjecture that the model exhibits revival times to infinite order. Explicit sample computations for the fractional revival times and superrevival times are presented., Comment: 9 pages, 1 figure