Some Applications of Simons’ Inequality

We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.

Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using l(1)-norm-based linear image reconstruction method

Traditional image reconstruction methods in rapid dynamic diffuse optical tomography employ l(2)-norm-based regularization, which is known to remove the high-frequency components in the reconstructed images and make them appear smooth. The contrast recovery in these type of methods is typically dependent on the iterative nature of method employed, where the nonlinear iterative technique is known to perform better in comparison to linear techniques (noniterative) with a caveat that nonlinear techniques are computationally complex. Assuming that there is a linear dependency of solution between successive frames resulted in a linear inverse problem. This new framework with the combination of l(1)-norm based regularization can provide better robustness to noise and provide better contrast recovery compared to conventional l(2)-based techniques. Moreover, it is shown that the proposed l(1)-based technique is computationally efficient compared to its counterpart (l(2)-based one). The proposed framework requires a reasonably close estimate of the actual solution for the initial frame, and any suboptimal estimate leads to erroneous reconstruction results for the subsequent frames.

Norm attaining operators and pseudospectrum

It is shown that if $11$, the operator $I+T$ attains its norm. A reflexive Banach space $X$ and a bounded rank one operator $T$ on $X$ are constructed such that $\|I+T\|>1$ and $I+T$ does not attain its norm.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Conversion of linear to rhombic C-4 in the gas phase: A joint experimental and theoretical study

Charge reversal (CR) and neutralization reionization (NR) experiments carried out on a 4-sector mass spectrometer demonstrate that isotopically labeled, linear C-4 anion rearranges upon collisional oxidation. The cations and neutrals formed in these experiments exhibit differing degrees of isotopic scrambling in their fragmentation patterns, indicative of (at least) partial isomerization of both states. Theoretical studies, employing the CCSD(T)/aug-cc-pVDZ//B3LYP/6-31G(d) level of theory, favor conversion to the rhombic C-4 isomer on both cationic and neutral potential-energy surfaces with the rhombic structures predicted to be slightly more stable than the linear forms in each case. The combination of experiment with theory indicates that the elusive rhombic C-4 is formed as a cation and as a neutral following charge stripping of linear C-4(-)

On the Lp-Norm Regression Models for Estimating Value-at-Risk

Analysis of risk measures associated with price series data movements and its predictions are of strategic importance in the financial markets as well as to policy makers in particular for short- and longterm planning for setting up economic growth targets. For example, oilprice risk-management focuses primarily on when and how an organization can best prevent the costly exposure to price risk. Value-at-Risk (VaR) is the commonly practised instrument to measure risk and is evaluated by analysing the negative/positive tail of the probability distributions of the returns (profit or loss). In modelling applications, least-squares estimation (LSE)-based linear regression models are often employed for modeling and analyzing correlated data. These linear models are optimal and perform relatively well under conditions such as errors following normal or approximately normal distributions, being free of large size outliers and satisfying the Gauss-Markov assumptions. However, often in practical situations, the LSE-based linear regression models fail to provide optimal results, for instance, in non-Gaussian situations especially when the errors follow distributions with fat tails and error terms possess a finite variance. This is the situation in case of risk analysis which involves analyzing tail distributions. Thus, applications of the LSE-based regression models may be questioned for appropriateness and may have limited applicability. We have carried out the risk analysis of Iranian crude oil price data based on the Lp-norm regression models and have noted that the LSE-based models do not always perform the best. We discuss results from the L1, L2 and L∞-norm based linear regression models. ACM Computing Classification System (1998): B.1.2, F.1.3, F.2.3, G.3, J.2.

An asparaginyl endopeptidase mediates in vivo protein backbone cyclization

Proteases can catalyze both peptide bond cleavage and formation, yet the hydrolysis reaction dominates in nature. This presents an interesting challenge for the biosynthesis of backbone cyclized (circular) proteins, which are encoded as part of precursor proteins and require post-translational peptide bond formation to reach their mature form. The largest family of circular proteins are the plant-produced cyclotides; extremely stable proteins with applications as bioengineering scaffolds. Little is known about the mechanism by which they are cyclized in vivo but a highly conserved Asn (occasionally Asp) residue at the C terminus of the cyclotide domain suggests that an enzyme with specificity for Asn (asparaginyl endopeptidase; AEP) is involved in the process. Nicotiana benthamiana does not endogenously produce circular proteins but when cDNA encoding the precursor of the cyclotide kalata B1 was transiently expressed in the plants they produced the cyclotide, together with linear forms not commonly observed in cyclotide-containing plants. Observation of these species over time showed that in vivo asparaginyl bond hydrolysis is necessary for cyclization. When AEP activity was suppressed, either by decreasing AEP gene expression or using a specific inhibitor, the amount of cyclic cyclotide in the plants was reduced compared with controls and was accompanied by the accumulation of extended linear species. These results suggest that an AEP is responsible for catalyzing both peptide bond cleavage and ligation of cyclotides in a single processing event.

Functional programming systems revisited

Functional Programming (FP) systems are modified and extended to form Nondeterministic Functional Programming (NFP) systems in which nondeterministic programs can be specified and both deterministic and nondeterministic programs can be verified essentially within the system. It is shown that the algebra of NFP programs has simpler laws in comparison with the algebra of FP programs. "Regular" forms are introduced to put forward a disciplined way of reasoning about programs. Finally, an alternative definition of "linear" forms is proposed for reasoning about recursively defined programs. This definition, when used to test the linearity of forms, results in simpler verification conditions than those generated by the original definition of linear forms.

New evidences on Tau-DNA interactions and relevance to neurodegeneration

Tau is mainly distributed in cytoplasm and also found to be localized in the nucleus. There is limited data on DNA binding potential of Tau.We provide novel evidence on nicking of DNA by Tau. Tau nicks the supercoiled DNA leading to open circular and linear forms. The metal ion magnesium (a co-factor for endonuclease) enhanced the Tau DNA nicking ability, while an endonuclease specific inhibitor,aurinetricarboxylic acid (ATA) inhibited the Tau DNA nicking ability Further, we also evidenced that Tau induces B-C-A mixed conformational transition in DNA and also changes DNA stability. Tau-scDNA complex is more sensitive to DNAse I digestion indicating stability changes in DNA caused by Tau. These findings indicate that Tau alters DNA helicity and integrity and also nicks the DNA. The relevance of these novel intriguing findings regarding the role Tau in neuronal dysfunction is discussed. (C) 2010 Elsevier Ltd. All rights reserved.

Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

New approaches for the diagnosis of human papillomavirus infection:relevance for clinical practice and cancer prevention

Tese de doutoramento, Biologia (Microbiologia), Universidade de Lisboa, Faculdade de Ciências, 2014

Sur la distribution des valeurs de la fonction zêta de Riemann et des fonctions L au bord de la bande critque

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Adobe Devanagari typeface

Typeface design: collaborative work commissioned by Adobe Inc. Published but unreleased. The Adobe Devanagari typefaces were commissioned from Tiro Typeworks and collaboratively designed by Tim Holloway, Fiona Ross and John Hudson, beginning in 2005. The types were officially released in 2009. The design brief was to produce a typeface for modern business communications in Hindi and other languages, to be legible both in print and on screen. Adobe Devanagari was designed to be highly readable in a range of situations including quite small sizes in spreadsheets and in continuous text setting, as well as at display sizes, where the full character of the typeface reveals itself. The construction of the letters is based on traditional penmanship but possesses less stroke contrast than many Devanagari types, in order to maintain strong, legible forms at smaller sizes. To achieve a dynamic, fluid style the design features a rounded treatment of distinguishing terminals and stroke reversals, open counters that also aid legibility at smaller sizes, and delicately flaring strokes. Together, these details reveal an original hand and provide a contemporary approach that is clean, clear and comfortable to read whether in short or long passages of text. This new approach to a traditional script is intended to counter the dominance of rigid, staccato-like effects of straight verticals and horizontals in earlier types and many existing fonts. OpenType Layout features in the fonts provide both automated and discretionary access to an extensive glyph set, enabling sophisticated typography. Many conjuncts preferred in classical literary texts and particularly in some North Indian languages are included; these literary conjuncts may be substituted by specially designed alternative linear forms and fitted half forms. The length of the ikars—ि and ी—varies automatically according to adjacent letter or conjunct width. Regional variants of characters and numerals (e.g. Marathi forms) are included as alternates. Careful attention has been given to the placements of all vowel signs and modifiers. The fonts include both proportional and tabular numerals in Indian and European styles. Extensive kerning covers several thousand possible combinations of half forms and full forms to anticipate arbitrary conjuncts in foreign loan words. _____