Mirror Inversion of Quantum States in Linear Registers

Transfer of data in linear quantum registers can be significantly simplified with pre-engineered but not dynamically controlled inter-qubit couplings. We show how to implement a mirror inversion of the state of the register in each excitation subspace with respect to the centre of the register. Our construction is especially appealing as it requires no dynamical control over individual inter-qubit interactions. If, however, individual control of the interactions is available then the mirror inversion operation can be performed on any substring of qubits in the register. In this case a sequence of mirror inversions can generate any permutation of a quantum state of the involved qubits.Comment: 4 page

On the continuous Cesàro operator in certain function spaces

“The final publication is available at Springer via http://dx.doi.org/10.1007/s11117-014-0321-5"Various properties of the (continuous) Cesàro operator C, acting on Banach and Fréchet spaces of continuous functions and L p-spaces, are investigated. For instance, the spectrum and point spectrum of C are completely determined and a study of certain dynamics of C is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of C acting in the various spaces is identified.The research of the first two authors was partially supported by the projects MTM2010-15200 and GVA Prometeo II/2013/013 (Spain). The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2015). On the continuous Cesàro operator in certain function spaces. Positivity. 19:659-679. https://doi.org/10.1007/s11117-014-0321-5S65967919Albanese, A.A.: Primary products of Banach spaces. Arch. Math. 66, 397–405 (1996)Albanese, A.A.: On subspaces of the spaces $$L^p_{\rm loc}$$ L loc p and of their strong duals. Math. Nachr. 197, 5–18 (1999)Albanese, A.A., Moscatelli, V.B.: Complemented subspaces of sums and products of copies of $$L^1 [0,1]$$ L 1 [ 0 , 1 ] . Rev. Mat. Univ. Complut. Madr. 9, 275–287 (1996)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34, 401–436 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: On mean ergodic operators. In: Curbera, G.P. (eds.) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol. 201, pp. 1–20. Birkhäuser, Basel (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: $$C_0$$ C 0 -semigroups and mean ergodic operators in a class of Fréchet spaces. J. Math. Anal. Appl. 365, 142–157 (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Bellenot, S.F., Dubinsky, E.: Fréchet spaces with nuclear Köthe quotients. Trans. Am. Math. Soc. 273, 579–594 (1982)Bonet, J., Frerick, L., Peris, A., Wengenroth, J.: Transitive and hypercyclic operators on locally convex spaces. Bull. Lond. Math. Soc. 37, 254–264 (2005)Boyd, D.W.: The spectrum of the Cesàro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)Brown, A., Halmos, P.R., Shields, A.L.: Cesàro operators. Acta Sci. Math. (Szeged) 26, 125–137 (1965)Dierolf, S., Zarnadze, D.N.: A note on strictly regular Fréchet spaces. Arch. Math. 42, 549–556 (1984)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory (2nd Printing). Wiley-Interscience, New York (1964)Galaz Fontes, F., Solís, F.J.: Iterating the Cesàro operators. Proc. Am. Math. Soc. 136, 2147–2153 (2008)Galaz Fontes, F., Ruiz-Aguilar, R.W.: Grados de ciclicidad de los operadores de Cesàro–Hardy. Misc. Mat. 57, 103–117 (2013)González, M., León-Saavedra, F.: Cyclic behaviour of the Cesàro operator on $$L_2(0,+\infty )$$ L 2 ( 0 , + ∞ ) . Proc. Am. Math. Soc. 137, 2049–2055 (2009)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear chaos. In: Universitext. Springer, London (2011)Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. In: Reprint of the 1952 Edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988)Krengel, U.: Ergodic theorems. In: De Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)Leibowitz, G.M.: Spectra of finite range Cesàro operators. Acta Sci. Math. (Szeged) 35, 27–28 (1973)Leibowitz, G.M.: The Cesàro operators and their generalizations: examples in infinite-dimensional linear analysis. Am. Math. Mon. 80, 654–661 (1973)León-Saavedra, F., Piqueras-Lerena, A., Seoane-Sepúlveda, J.B.: Orbits of Cesàro type operators. Math. Nachr. 282, 764–773 (2009)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Meise, R., Vogt, D.: Introduction to functional analysis. In: Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press; Oxford University Press, New York (1997)Metafune, G., Moscatelli, V.B.: Quojections and prequojections. In: Terzioğlu, T. (ed.) Advances in the Theory of Fréchet spaces. NATO ASI Series, vol. 287, pp. 235–254. Kluwer Academic Publishers, Dordrecht (1989)Moscatelli, V.B.: Fréchet spaces without norms and without bases. Bull. Lond. Math. Soc. 12, 63–66 (1980)Piszczek, K.: Quasi-reflexive Fréchet spaces and mean ergodicity. J. Math. Anal. Appl. 361, 224–233 (2010)Piszczek, K.: Barrelled spaces and mean ergodicity. Rev R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 104, 5–11 (2010)Yosida, K.: Functional Analysis, 6th edn. Springer, Berlin (1980

Proteomic Profiling of Colon Cancer Tissues: Discovery of New Candidate Biomarkers

Colon cancer is an aggressive tumor form with a poor prognosis. This study reports a comparative proteomic analysis performed by using two-dimensional differential in-gel electrophoresis (2D-DIGE) between 26 pooled colon cancer surgical tissues and adjacent non-tumoral tissues, to identify potential target proteins correlated with carcinogenesis. The DAVID functional classification tool revealed that most of the differentially regulated proteins, acting both intracellularly and extracellularly, concur across multiple cancer steps. The identified protein classes include proteins involved in cell proliferation, apoptosis, metabolic pathways, oxidative stress, cell motility, Ras signal transduction, and cytoskeleton. Interestingly, networks and pathways analysis showed that the identified proteins could be biologically inter-connected to the tumor-host microenvironment, including innate immune response, platelet and neutrophil degranulation, and hemostasis. Finally, transgelin (TAGL), here identified for the first time with four different protein species, collectively down-regulated in colon cancer tissues, emerged as a top-ranked biomarker for colorectal cancer (CRC). In conclusion, our findings revealed a different proteomic profiling in colon cancer tissues characterized by the deregulation of specific pathways involved in hallmarks of cancer. All of these proteins may represent promising novel colon cancer biomarkers and potential therapeutic targets, if validated in larger cohorts of patients

An overview on the N-heterocyclic carbene-catalyzed Aza-Benzoin condensation reaction

The N-heterocyclic carbene(NHCs)-catalyzed aza-benzoin condensation reaction is an efficient, single step strategy which employs easily available substrates, such as aldehydes and imines, to provide \u3b1-amino ketones. The multifunctionality and high reactivity of \u3b1-amino ketones makes these structures attractive for medicinal chemistry and as precursors of a variety of amine derivatives. The different electrophilic characteristics of aldehydes and imines ensure a high regioselective reaction. Enantiomerically-enriched \u3b1-amino ketones have been synthesized through stereoselective couplings promoted by chiral N-heterocyclic carbenes. One-pot domino procedures, including an aza-benzoin step, allow valuable complex molecules to be accessed

Large N reduction in the continuum three dimensional Yang-Mills theory

Numerical and theoretical evidence leads us to propose the following: Three dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase transition on a torus of side $l=l_c$. For $l>l_c$ the planar limit is $l$-independent, as expected of a non-interacting string theory. We expect the situation in four dimensions to be similar.Comment: 4 pages, latex file, two figures, version to appear in Phys. Rev. Let

Phenols content and 2-D electrophoresis protein pattern: a promising tool to monitor Posidonia meadows health state

<p>Abstract</p> <p>Background</p> <p>The endemic seagrass <it>Posidonia oceanica </it>(L.) Delile colonizes soft bottoms producing highly productive meadows that play a crucial role in coastal ecosystems dynamics. Human activities and natural events are responsible for a widespread meadows regression; to date the identification of "diagnostic" tools to monitor conservation status is a critical issue. In this study the feasibility of a novel tool to evaluate ecological impacts on <it>Posidonia </it>meadows has been tested. Quantification of a putative stress indicator, <it>i.e</it>. phenols content, has been coupled to 2-D electrophoretic protein analysis of rhizome samples.</p> <p>Results</p> <p>The overall expression pattern from <it>Posidonia </it>rhizome was determined using a preliminary proteomic approach, 437 protein spots were characterized by p<it>I </it>and molecular weight. We found that protein expression differs in samples belonging to sites with high or low phenols: 22 unique protein spots are peculiar of "low phenols" and 27 other spots characterize "high phenols" samples.</p> <p>Conclusion</p> <p><it>Posidonia </it>showed phenols variations within the meadow, that probably reflect the heterogeneity of environmental pressures. In addition, comparison of the 2-D electrophoresis patterns allowed to highlight qualitative protein expression differences in response to these pressures. These differences may account for changes in metabolic/physiological pathways as adaptation to stress. A combined approach, based on phenols content determination and 2-D electrophoresis protein pattern, seems a promising tool to monitor <it>Posidonia </it>meadows health state.</p

Retrospective Proteomic Screening of 100 Breast Cancer Tissues

The present investigation has been conducted on one hundred tissue fragments of breast cancer, collected and immediately cryopreserved following the surgical resection. The specimens were selected from patients with invasive ductal carcinoma of the breast, the most frequent and potentially aggressive type of mammary cancer, with the objective to increase the knowledge of breast cancer molecular markers potentially useful for clinical applications. The proteomic screening; by 2D-IPG and mass spectrometry; allowed us to identify two main classes of protein clusters: proteins expressed ubiquitously at high levels in all patients; and proteins expressed sporadically among the same patients. Within the group of ubiquitous proteins, glycolytic enzymes and proteins with anti-apoptotic activity were predominant. Among the sporadic ones, proteins involved in cell motility, molecular chaperones and proteins involved in the detoxification appeared prevalent. The data of the present study indicates that the primary tumor growth is reasonably supported by concurrent events: the inhibition of apoptosis and stimulation of cellular proliferation, and the increased expression of glycolytic enzymes with multiple functions. The second phase of the evolution of the tumor can be prematurely scheduled by the occasional presence of proteins involved in cell motility and in the defenses of the oxidative stress. We suggest that this approach on large-scale 2D-IPG proteomics of breast cancer is currently a valid tool that offers the opportunity to evaluate on the same assay the presence and recurrence of individual proteins, their isoforms and short forms, to be proposed as prognostic indicators and susceptibility to metastasis in patients operated on for invasive ductal carcinoma of the breast

A practical synthesis of 2,3-dihydro-1,5-benzothiazepines

2,3-Dihydro-1,5-benzothiazepines have been obtained through a domino process involving a Michael addition of 2-aminothiophenols to chalcones, followed by in situ cyclization. Up to 98% chemical yields have been obtained at room temperature under essentially neutral conditions by using hexafluoro-2-propanol as an efficient medium

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

Gapped ground states of quantum spin systems have been referred to in the physics literature as being `in the same phase' if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on $s \in [0,1]$, such that for each $s$, H(s) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectively. In this work, we give precise conditions under which any two gapped ground states of a given quantum spin system that 'belong to the same phase' are automorphically equivalent and show that this equivalence can be implemented as a flow generated by an $s$-dependent interaction which decays faster than any power law (in fact, almost exponentially). The flow is constructed using Hastings' 'quasi-adiabatic evolution' technique, of which we give a proof extended to infinite-dimensional Hilbert spaces. In addition, we derive a general result about the locality properties of the effect of perturbations of the dynamics for quantum systems with a quasi-local structure and prove that the flow, which we call the {\em spectral flow}, connecting the gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a result, we obtain that, in the thermodynamic limit, the spectral flow converges to a co-cycle of automorphisms of the algebra of quasi-local observables of the infinite spin system. This proves that the ground state phase structure is preserved along the curve of models $H(s), 0\leq s\leq 1$.Comment: Updated acknowledgments and new email address of S

Global regularity in ultradifferentiable classes

Se estudia la w-regularidad de soluciones de ciertos operadores que son globalmente hipoelípticos en el toro N-dimensional. Se aplican estos resultados para probar la w-regularidad global de ciertas clases de sublaplacianos. En este sentido, se extiende trabajo previo en el contexto de la clases analíticas y de Gevrey. Se dan varios ejemplos de w-hipoelipticidad local y global.The research of the authors was partially supported by MEC and FEDER Project MTM2010-15200.Albanese, AA.; Jornet Casanova, D. (2014). Global regularity in ultradifferentiable classes. Annali di Matematica Pura ed Applicata. 193(2):369-387. https://doi.org/10.1007/s10231-012-0279-5S3693871932Albanese A.A., Jornet D., Oliaro A.: Quasianalytic wave front sets for solutions of linear partial differential operators. Integr. Equ. Oper. 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