The orthogonal subcategory problem in homotopy theory

It is known that, in a locally presentable category, localization exists with respect to every set of morphisms, while the statement that localization with respect to every (possibly proper) class of morphisms exists in locally presentable categories is equivalent to a large-cardinal axiom from set theory. One proves similarly, on one hand, that homotopy localization exists with respect to sets of maps in every cofibrantly generated, left proper, simplicial model category M whose underlying category is locally presentable. On the other hand, as we show in this article, the existence of localization with respect to possibly proper classes of maps in a model category M satisfying the above assumptions is implied by a large-cardinal axiom called Vopënka's principle, although we do not know if the reverse implication holds. We also show that, under the same assumptions on M, every endofunctor of M that is idempotent up to homotopy is equivalent to localization with respect to some class S of maps, and if Vopënka's principle holds then S can be chosen to be a set. There are examples showing that the latter need not be true if M is not cofibrantly generated. The above assumptions on M are satisfied by simplicial sets and symmetric spectra over simplicial sets, among many other model categories.

Orthogonal systems in finite grahps

To a finite graph there corresponds a free partially commutative group: with the given graph as commutation graph. In this paper we construct an orthogonality theory for graphs and their corresponding free partially commutative groups. The theory developed here provides tools for the study of the structure of partially commutative groups, their universal theory and automorphism groups. In particular the theory is applied in this paper to the centraliser lattice of such groups.

On the zeroes of Goss polynomials

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Orthogonal higher order structure and confirmatory factor analysis of the French Wechsler Adult Intelligence Scale (WAIS-III).

According to the most widely accepted Cattell-Horn-Carroll (CHC) model of intelligence measurement, each subtest score of the Wechsler Intelligence Scale for Adults (3rd ed.; WAIS-III) should reflect both 1st- and 2nd-order factors (i.e., 4 or 5 broad abilities and 1 general factor). To disentangle the contribution of each factor, we applied a Schmid-Leiman orthogonalization transformation (SLT) to the standardization data published in the French technical manual for the WAIS-III. Results showed that the general factor accounted for 63% of the common variance and that the specific contributions of the 1st-order factors were weak (4.7%-15.9%). We also addressed this issue by using confirmatory factor analysis. Results indicated that the bifactor model (with 1st-order group and general factors) better fit the data than did the traditional higher order structure. Models based on the CHC framework were also tested. Results indicated that a higher order CHC model showed a better fit than did the classical 4-factor model; however, the WAIS bifactor structure was the most adequate. We recommend that users do not discount the Full Scale IQ when interpreting the index scores of the WAIS-III because the general factor accounts for the bulk of the common variance in the French WAIS-III. The 4 index scores cannot be considered to reflect only broad ability because they include a strong contribution of the general factor.

A sharp Remez inequality for trigonometric polynomials

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Orthogonal organic and aqueous-based washes of tissue sections to enhance protein sensitivity by MALDI imaging mass spectrometry.

Imaging mass spectrometry (IMS) is an emergent and innovative approach for measuring the composition, abundance and regioselectivity of molecules within an investigated area of fixed dimension. Although providing unprecedented molecular information compared with conventional MS techniques, enhancement of protein signature by IMS is still necessary and challenging. This paper demonstrates the combination of conventional organic washes with an optimized aqueous-based buffer for tissue section preparation before matrix-assisted laser desorption/ionization (MALDI) IMS of proteins. Based on a 500 mM ammonium formate in water-acetonitrile (9:1; v/v, 0.1% trifluororacetic acid, 0.1% Triton) solution, this buffer wash has shown to significantly enhance protein signature by profiling and IMS (~fourfold) when used after organic washes (70% EtOH followed by 90% EtOH), improving the quality and number of ion images obtained from mouse kidney and a 14-day mouse fetus whole-body tissue sections, while maintaining a similar reproducibility with conventional tissue rinsing. Even if some protein losses were observed, the data mining has demonstrated that it was primarily low abundant signals and that the number of new peaks found is greater with the described procedure. The proposed buffer has thus demonstrated to be of high efficiency for tissue section preparation providing novel and complementary information for direct on-tissue MALDI analysis compared with solely conventional organic rinsing.

Integral inequalities for algebraic and trigonometric polynomials

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Food's visually perceived fat content affects discrimination speed in an orthogonal spatial task.

Choosing what to eat is a complex activity for humans. Determining a food's pleasantness requires us to combine information about what is available at a given time with knowledge of the food's palatability, texture, fat content, and other nutritional information. It has been suggested that humans may have an implicit knowledge of a food's fat content based on its appearance; Toepel et al. (Neuroimage 44:967-974, 2009) reported visual-evoked potential modulations after participants viewed images of high-energy, high-fat food (HF), as compared to viewing low-fat food (LF). In the present study, we investigated whether there are any immediate behavioural consequences of these modulations for human performance. HF, LF, or non-food (NF) images were used to exogenously direct participants' attention to either the left or the right. Next, participants made speeded elevation discrimination responses (up vs. down) to visual targets presented either above or below the midline (and at one of three stimulus onset asynchronies: 150, 300, or 450 ms). Participants responded significantly more rapidly following the presentation of a HF image than following the presentation of either LF or NF images, despite the fact that the identity of the images was entirely task-irrelevant. Similar results were found when comparing response speeds following images of high-carbohydrate (HC) food items to low-carbohydrate (LC) food items. These results support the view that people rapidly process (i.e. within a few hundred milliseconds) the fat/carbohydrate/energy value or, perhaps more generally, the pleasantness of food. Potentially as a result of HF/HC food items being more pleasant and thus having a higher incentive value, it seems as though seeing these foods results in a response readiness, or an overall alerting effect, in the human brain.

Drift compensation of gas sensor array data by Orthogonal Signal Correction

Drift is an important issue that impairs the reliability of gas sensing systems. Sensor aging, memory effects and environmental disturbances produce shifts in sensor responses that make initial statistical models for gas or odor recognition useless after a relatively short period (typically few weeks). Frequent recalibrations are needed to preserve system accuracy. However, when recalibrations involve numerous samples they become expensive and laborious. An interesting and lower cost alternative is drift counteraction by signal processing techniques. Orthogonal Signal Correction (OSC) is proposed for drift compensation in chemical sensor arrays. The performance of OSC is also compared with Component Correction (CC). A simple classification algorithm has been employed for assessing the performance of the algorithms on a dataset composed by measurements of three analytes using an array of seventeen conductive polymer gas sensors over a ten month period.

Orthogonal protection of peptides and peptoids for cyclization by the thiol-ene reaction and conjugation

Cyclic peptides and peptoids were prepared using the thiolene Michael-type reaction. The linear precursors were provided with additional functional groups allowing for subsequent conjugation: an orthogonally protected thiol, a protected maleimide, or an alkyne. The functional group for conjugation was placed either within the cycle or in an external position. The click reactions employed for conjugation with suitably derivatized nucleoside or oligonucleotides were either cycloadditions (Diels-Alder, Cu(I)-catalyzed azide-alkyne) or the same Michael-type reaction as for cyclization.

Orthogonal protecting groups in the synthesis of tryptophanyl-hexahydropyrroloindoles

The synthesis of various polycyclic systems containing a C3aNi bond between a hexahydropyrrolo[2,3-b]indole and an indole tryptophan is described here. A series of experiments were performed to determine the best combination of five orthogonal protecting groups and the best reaction conditions for formation of said bond, which is a common feature among many recently discovered marine natural products.

Convergent Approaches for the Synthesis of the Anti-tumoral Peptide, Kahalalide F. Study of Orthogonal Protecting Groups

Kahalalide compounds are peptides that are isolated from a Hawaiian herbivorous marine species of mollusc, Elysia rufescens, and its diet, the green alga Bryopsis sp. Kahalalide F and its synthetic analogues are the most promising compounds of the Kahalalide family because they show anti-tumoral activity. Linear solid-phase syntheses of Kahalalide F have been reported. Here we describe several new improved synthetic routes based on convergent approaches with distinct orthogonal protection schemes for the preparation of Kahaladide analogues. These strategies allow a better control and characterization of the intermediates because more reactions are performed in solution. Five derivatives of Kahalalide F were synthesized using several convergent approaches.

Orthogonal protecting groups in the synthesis of tryptophanyl-hexahydropyrroloindoles

The synthesis of various polycyclic systems containing a C3a-Ni bond between a hexahydropyrrolo[2,3-b]indole and an indole tryptophan is described here. A series of experiments were performed to determine the best combination of five orthogonal protecting groups and the best reaction conditions for formation of said bond, which is a common feature among many recently discovered marine natural products.

The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive

The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the supremum norm on the polydisc $\mathbb{D}^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\mathbb{D}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant for the set of frequencies $\bigl\{ \log n: n \text{a positive integer} \le N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.