1,2-Dimethylindole-3-sulfonyl (MIS) as protecting group for the side chain of arginine

The protection of arginine (Arg) side chains is a crucial issue in peptide chemistry because of the propensity of the basic guanidinium group to produce side reactions. Currently, sulfonyl-type protecting groups, such as 2,2,5,7,8-pentamethylchroman (Pmc) and 2,2,4,6,7-pentamethyldihydrobenzofurane (Pbf), are the most widely used for this purpose. Nevertheless, Arg side chain protection remains problematic as a result of the acid stability of these two compounds. This issue is even more relevant in Arg-rich sequences, acid-sensitive peptides and large-scale syntheses. The 1,2-dimethylindole-3-sulfonyl (MIS) group is more acid-labile than Pmc and Pbf and can therefore be a better option for Arg side chain protection. In addition, MIS is compatible with tryptophan-containing peptides.

Differences based on fine motor behaviour in Parkinson's patients compared to an age matched control group in proprioceptive and visuo-proprioceptive test conditions

Personality differences based on fine motor precision performance were studied in early stage Parkinson's patients and an age-matched control group under two different test conditions: proprioceptive + visual information and proprioceptive information alone. A comparative data analysis for deviations of three measured movement types (transversal, frontal and sagittal) was done for both hands (dominant and non-dominant) with relation to personality dimensions. There were found significant differences between the two groups in decision making dimension and emotionality. After splitting the data for gender subgroups, some significant differences were found for men but not for women. The differences in fine motor task performance varied, being better in some directions for the Parkinson"s patients and worse in others. The findings may suggest that medication has both positive and negative effects on motor performance and provoke personality changes, being more pronounced in men.

p-Nitrobenzyloxycarbonyl (pNZ) as Temporary Na-Protecting Group for Mild Solid-Phase Peptide Synthesis. Avoiding Diketopiperazine and Aspartimide Formation

p-Nitrobenzyloxycarbonyl was used as temporary protecting group for the -amino function in solid-phase peptide synthesis. The corresponding derivatives are solids, easy to be synthesized, and perform well in the solid-phase mode. pNZ is removed in practical neutral conditions in the presence of catalytic amounts of acid. They are orthogonal with the most common protecting groups used in peptide chemistry. They are specially useful in combination with Fmoc chemistry to overcome those side reactions associated with the used of the piperidine such DKP and aspartiimide formation. The flexibility of pNZ can be very useful for the preparation of libraries of small organic molecules.

The unbounded dead-end depth propertie is not a group invariant

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Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

The automorphism group of a free-by-cyclic group in rank 2

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Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Growth of positive words and lower bounds of the growth rate for Thompson's group (F)p

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Computational explorations in Thompson's group F

Here we describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson's group is amenable. We also describe experiments to estimate the exponential growth rate of F and the rate of escape of symmetric random walks with respect to the standard generating set.

Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable.

When does universal peace prevail? Secession and group formation in rent seeking contests and policy conflicts

This paper analyzes secession and group formation in a general model of contest inspired by Esteban and Ray (1999). This model encompasses as special cases rent seeking contests and policy conflicts, where agents lobby over the choice of a policy in a one-dimensional policy space. We show that in both models the grand coalition is the efficient coalition structure and agents are always better off in the grand coalition than in a symmetric coalition structure. Individual agents (in the rent seeking contest) and extremists (in the policy conflict) only have an incentive to secede when they anticipate that their secession will not be followed by additional secessions. Incentives to secede are lower when agents cooperate inside groups. The grand coalition emerges as the unique subgame perfect equilibrium outcome of a sequential game of coalition formation in rent seeking contests.

A generalized assignment game

The proposed game is a natural extension of the Shapley and Shubik Assignment Game to the case where each seller owns a set of different objets instead of only one indivisible object. We propose definitions of pairwise stability and group stability that are adapted to our framework. Existence of both pairwise and group stable outcomes is proved. We study the structure of the group stable set and we finally prove that the set of group stable payoffs forms a complete lattice with one optimal group stable payoff for each side of the market.

The density of injective endomorphisms of a free group

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Organisational structure, communication and group ethics

This paper investigates experimentally how organisational decision processes affect the moral motivations of actors inside a firm that must forego profits to reduce harming a third party. In a "vertical" treatment, one insider unilaterally sets the harm-reduction strategy; the other can only accept or quit. In a "horizontal" treatment, the insiders decide by consensus. Our 2-by-2 design also controls for communication effects. In our data, communication makes vertical firms more ethical; voice appears to mitigate "responsibility-alleviation" in that subordinates with voice feel responsible for what their firms do. Vertical firms are then more ethical than the horizontal firms for which our bargaining data reveal a dynamic form of responsibility-alleviation and our chat data indicate a strong "insider-outsider" effect.