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.

Periodic orbits of the planar collision restricted 3-body problem

Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating Kepler problem can be continued into periodic orbits of the planar collision restricted 3–body problem. Additionally, we also continue to this restricted problem the so called “comets orbits”.

Maintenance of rattlesnakes in captivity / by James B. Murphy and Barry L. Armstrong.

no.3 (1978)

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.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate another agent to misrepresent his preference and, after an appropriate redistribution of their shares, each obtain a strictly preferred share. We characterize all bribe-proof rules as the class of efficient, strategy-proof, and weak replacement monotonic rules. In addition, we identify the functional form of all bribe-proof and tops-only rules.

A maximal domain of preferences for tops-only rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.

On Boas-Type Problem

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α(0 & α & 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of modulus of continuity. The aim of this paper is to obtain Boas-type theorems for generalized Lipschitz classes. To define generalized Lipschitz classes we use the concept of modulus of smoothness of fractional order.

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Percepció socioambiental del present i el futur del sector ramader a Esterri de Cardós

En aquest projecte s’ha realitzat una diagnosi socioambiental de la ramaderia en el municipi d’Esterri de Cardós, situat a la comarca del Pallars Sobirà, i que es troba dins dels límits del Parc Natural de l’Alt Pirineu. Dins del seu àmbit és un municipi peculiar degut a la quantitat de ramaders, set, i a la mitjana d’edat, que és força jove. La situació actual del sector és complicada atès el poc benefici que generen les explotacions, ja que els costos de manteniment són cada vegada més grans i els ingressos no augmenten en la mateixa proporció. És per això que des de fa uns anys els ajuts econòmics han esdevingut un factor clau per mantenir el sector. La seva continuïtat depèn de, entre altres coses, la dedicació en el sector de les generacions futures i ara per ara sembla que aquestes es decanten cada vegada més per altres tipus d’ocupacions. És per això que han de treballar totes les parts conjuntament per poder solucionar aquesta situació i que no esdevingui un problema insalvable en els pròxims anys.

The word problem distinguishes counter languages

Counter automata are more powerful versions of finite state automata where addition and subtraction operations are permitted on a set of n integer registers, called counters. We show that the word problem of Zn is accepted by a nondeterministic m-counter automaton if and only if m &= n.

On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

Comprehensive Expression Analyses of Neural Cell-Type-Specific miRNAs Identify New Determinants of the Specification and Maintenance of Neuronal Phenotypes.

MicroRNAs (miRNAs) have been shown to play important roles in both brain development and the regulation of adult neural cell functions. However, a systematic analysis of brain miRNA functions has been hindered by a lack of comprehensive information regarding the distribution of miRNAs in neuronal versus glial cells. To address this issue, we performed microarray analyses of miRNA expression in the four principal cell types of the CNS (neurons, astrocytes, oligodendrocytes, and microglia) using primary cultures from postnatal d 1 rat cortex. These analyses revealed that neural miRNA expression is highly cell-type specific, with 116 of the 351 miRNAs examined being differentially expressed fivefold or more across the four cell types. We also demonstrate that individual neuron-enriched or neuron-diminished RNAs had a significant impact on the specification of neuronal phenotype: overexpression of the neuron-enriched miRNAs miR-376a and miR-434 increased the differentiation of neural stem cells into neurons, whereas the opposite effect was observed for the glia-enriched miRNAs miR-223, miR-146a, miR-19, and miR-32. In addition, glia-enriched miRNAs were shown to inhibit aberrant glial expression of neuronal proteins and phenotypes, as exemplified by miR-146a, which inhibited neuroligin 1-dependent synaptogenesis. This study identifies new nervous system functions of specific miRNAs, reveals the global extent to which the brain may use differential miRNA expression to regulate neural cell-type-specific phenotypes, and provides an important data resource that defines the compartmentalization of brain miRNAs across different cell types.

Associations of short-term particle and noise exposures with markers of cardiovascular and respiratory health among highway maintenance workers

BACKGROUND: Highway maintenance workers are constantly and simultaneously exposed to traffic-related particle and noise emissions, and both have been linked to increased cardiovascular morbidity and mortality in population-based epidemiology studies. OBJECTIVES: We aimed to investigate short-term health effects related to particle and noise exposure. METHODS: We monitored 18 maintenance workers, during as many as five 24-hour periods from a total of 50 observation days. We measured their exposure to fine particulate matter (PM2.5), ultrafine particles, noise, and the cardiopulmonary health endpoints: blood pressure, pro-inflammatory and pro-thrombotic markers in the blood, lung function and fractional exhaled nitric oxide (FeNO) measured approximately 15 hours post-work. Heart rate variability was assessed during a sleep period approximately 10 hours post-work. RESULTS: PM2.5 exposure was significantly associated with C-reactive protein and serum amyloid A, and negatively associated with tumor necrosis factor α. None of the particle metrics were significantly associated with von Willebrand factor or tissue factor expression. PM2.5 and work noise were associated with markers of increased heart rate variability, and with increased HF and LF power. Systolic and diastolic blood pressure on the following morning were significantly associated with noise exposure after work, and non-significantly associated with PM2.5. We observed no significant associations between any of the exposures and lung function or FeNO. CONCLUSIONS: Our findings suggest that exposure to particles and noise during highway maintenance work might pose a cardiovascular health risk. Actions to reduce these exposures could lead to better health for this population of workers.