Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Foundations for contest success functions

In the literature the outcome of contests is either interpreted as win probabilities or as shares of the prize. With this in mind, we examine two approaches to contest success functions. In the first we analyze the implications of contestants' incomplete information concerning the "type" of the contest administrator. While in the case of two contestants this approach can rationalize prominent contest success functions, we show that it runs into difficulties when there are more agents. Our second approach interprets contest success functions as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular contest success functions and guidelines for the definition of new ones. Keywords: Endogenous Contests, Contest Success Function. JEL Classification: C72 (Noncooperative Games), D72 (Economic Models of Political Processes: Rent-Seeking, Elections), D74 (Conflict; Conflict Resolution; Alliances).

Nuclear receptor Rev-erb alpha (Nr1d1) functions in concert with Nr2e3 to regulate transcriptional networks in the retina.

The majority of diseases in the retina are caused by genetic mutations affecting the development and function of photoreceptor cells. The transcriptional networks directing these processes are regulated by genes such as nuclear hormone receptors. The nuclear hormone receptor gene Rev-erb alpha/Nr1d1 has been widely studied for its role in the circadian cycle and cell metabolism, however its role in the retina is unknown. In order to understand the role of Rev-erb alpha/Nr1d1 in the retina, we evaluated the effects of loss of Nr1d1 to the developing retina and its co-regulation with the photoreceptor-specific nuclear receptor gene Nr2e3 in the developing and mature retina. Knock-down of Nr1d1 expression in the developing retina results in pan-retinal spotting and reduced retinal function by electroretinogram. Our studies show that NR1D1 protein is co-expressed with NR2E3 in the outer neuroblastic layer of the developing mouse retina. In the adult retina, NR1D1 is expressed in the ganglion cell layer and is co-expressed with NR2E3 in the outer nuclear layer, within rods and cones. Several genes co-targeted by NR2E3 and NR1D1 were identified that include: Nr2c1, Recoverin, Rgr, Rarres2, Pde8a, and Nupr1. We examined the cyclic expression of Nr1d1 and Nr2e3 over a twenty-four hour period and observed that both nuclear receptors cycle in a similar manner. Taken together, these studies reveal a novel role for Nr1d1, in conjunction with its cofactor Nr2e3, in regulating transcriptional networks critical for photoreceptor development and function.

Identifying the neural correlates of executive functions in early cerebral microangiopathy: a combined VBM and DTI study.

Cerebral microangiopathy (CMA) has been associated with executive dysfunction and fronto-parietal neural network disruption. Advances in magnetic resonance imaging allow more detailed analyses of gray (e.g., voxel-based morphometry-VBM) and white matter (e.g., diffusion tensor imaging-DTI) than traditional visual rating scales. The current study investigated patients with early CMA and healthy control subjects with all three approaches. Neuropsychological assessment focused on executive functions, the cognitive domain most discussed in CMA. The DTI and age-related white matter changes rating scales revealed convergent results showing widespread white matter changes in early CMA. Correlations were found in frontal and parietal areas exclusively with speeded, but not with speed-corrected executive measures. The VBM analyses showed reduced gray matter in frontal areas. All three approaches confirmed the hypothesized fronto-parietal network disruption in early CMA. Innovative methods (DTI) converged with results from conventional methods (visual rating) while allowing greater spatial and tissue accuracy. They are thus valid additions to the analysis of neural correlates of cognitive dysfunction. We found a clear distinction between speeded and nonspeeded executive measures in relationship to imaging parameters. Cognitive slowing is related to disease severity in early CMA and therefore important for early diagnostics.

Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space H is L2(Rn), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m.

Direct binding of peptides to MHC class I molecules on living cells. Analysis at the single cell level.

To directly assess the binding of exogenous peptides to cell surface-associated MHC class I molecules at the single cell level, we examined the possibility of combining the use of biotinylated peptide derivatives with an immunofluorescence detection system based on flow cytometry. Various biotinylated derivatives of the adenovirus 5 early region 1A peptide 234-243, an antigenic peptide recognized by CTL in the context of H-2Db, were first screened in functional assays for their ability to bind efficiently to Db molecules on living cells. Suitable peptide derivatives were then tested for their ability to generate positive fluorescence signals upon addition of phycoerythrin-labeled streptavidin to peptide derivative-bearing cells. Strong fluorescent staining of Db-expressing cells was achieved after incubation with a peptide derivative containing a biotin group at the C-terminus. Competition experiments using the unmodified parental peptide as well as unrelated peptides known to bind to Kd, Kb, or Db, respectively, established that binding of the biotinylated peptide to living cells was Db-specific. By using Con A blasts derived from different H-2 congenic mouse strains, it could be shown that the biotinylated peptide bound only to Db among > 20 class I alleles tested. Moreover, binding of the biotinylated peptide to cells expressing the Dbm13 and Dbm14 mutant molecules was drastically reduced compared to Db. Binding of the biotinylated peptide to freshly isolated Db+ cells was readily detectable, allowing direct assessment of the relative amount of peptide bound to distinct lymphocyte subpopulations by three-color flow cytometry. While minor differences between peripheral T and B cells could be documented, thymocytes were found to differ widely in their peptide binding activity. In all cases, these differences correlated positively with the differential expression of Db at the cell surface. Finally, kinetic studies at different temperatures strongly suggested that the biotinylated peptide first associated with Db molecules available constitutively at the cell surface and then with newly arrived Db molecules.

Peroxisomal beta-oxidation--a metabolic pathway with multiple functions.

Fatty acid degradation in most organisms occurs primarily via the beta-oxidation cycle. In mammals, beta-oxidation occurs in both mitochondria and peroxisomes, whereas plants and most fungi harbor the beta-oxidation cycle only in the peroxisomes. Although several of the enzymes participating in this pathway in both organelles are similar, some distinct physiological roles have been uncovered. Recent advances in the structural elucidation of numerous mammalian and yeast enzymes involved in beta-oxidation have shed light on the basis of the substrate specificity for several of them. Of particular interest is the structural organization and function of the type 1 and 2 multifunctional enzyme (MFE-1 and MFE-2), two enzymes evolutionarily distant yet catalyzing the same overall enzymatic reactions but via opposite stereochemistry. New data on the physiological roles of the various enzymes participating in beta-oxidation have been gathered through the analysis of knockout mutants in plants, yeast and animals, as well as by the use of polyhydroxyalkanoate synthesis from beta-oxidation intermediates as a tool to study carbon flux through the pathway. In plants, both forward and reverse genetics performed on the model plant Arabidopsis thaliana have revealed novel roles for beta-oxidation in the germination process that is independent of the generation of carbohydrates for growth, as well as in embryo and flower development, and the generation of the phytohormone indole-3-acetic acid and the signal molecule jasmonic acid.

In vivo characterization of the circadian clock output gene usp2

Life on earth is subject to the repeated change between day and night periods. All organisms that undergo these alterations have to anticipate consequently the adaptation of their physiology and possess an endogenous periodicity of about 24 hours called circadian rhythm from the Latin circa (about) and diem (day). At the molecular level, virtually all cells of an organism possess a molecular clock which drives rhythmic gene expression and output functions. Besides altered rhythmicity in constant conditions, impaired clock function causes pathophysiological conditions such as diabetes or hypertension. These data unveil a part of the mechanisms underlying the well-described epidemiology of shift work and highlight the function of clock-driven regulatory mechanisms. The post-translational modification of proteins by the ubiquitin polypeptide is a central mechanism to regulate their stability and activity and is capital for clock function. Similarly to the majority of biological processes, it is reversible. Deubiquitylation is carried out by a wide variety of about ninety deubiquitylating enzymes and their function remains poorly understood, especially in vivo. This class of proteolytic enzymes is parted into five families including the Ubiquitin-Specific Proteases (USP), which is the most important with about sixty members. Among them, the Ubiquitin-Specific Protease 2 (Usp2) gene encodes two protein isoforms, USP2-45 and USP2-69. The first is ubiquitously expressed under the control of the circadian clock and displays all features of core clock genes or its closest outputs effectors. Additionally, Usp2-45 was also found to be induced by the mineralocorticoid hormone aldosterone and thought to participate in Na+ reabsorption and blood pressure regulation by Epithelial Na+ Channel ENaC in the kidneys. During my thesis, I aimed to characterize the role of Usp2 in vivo with respect to these two areas, by taking advantage of a total constitutive knockout mouse model. In the first project I aimed to validate the role of USP2-45 in Na+ homeostasis and blood pressure regulation by the kidneys. I found no significant alterations of diurnal Na+ homeostasis and blood pressure in these mice, indicating that Usp2 does not play a substantial role in this process. In urine analyses, we found that our Usp2-KO mice are actually hypercalciuric. In a second project, I aimed to understand the causes of this phenotype. I found that the observed hypercalciuria results essentially from intestinal hyperabsorption. These data reveal a new role for Usp2 as an output effector of the circadian clock in dietary Ca2+ metabolism in the intestine.

Does Ricardian Equivalence Hold When Expectations are not Rational?

This paper considers the Ricardian Equivalence proposition when expectations are not rational and are instead formed using adaptive learning rules. We show that Ricardian Equivalence continues to hold provided suitable additional conditions on learning dynamics are satisfied. However, new cases of failure can also emerge under learning. In particular, for Ricardian Equivalence to obtain, agents’ expectations must not depend on government’s financial variables under deficit financing.

Individual versus group strategy-proofness: when do they coincide?

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to find nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically significant domains where interesting rules satisfying individual strategy-proofness can be defined, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategy-proofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide sufficient conditions defining domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules defined on the

Analytic approximation of matrix functions in Lp

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Differentiability of functions of contractions

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Class-size Reduction Policies and the Quality of Entering Teachers

State-wide class-size reduction (CSR) policies have typically failed to produce large achievement gains. One explanation is that the introduction of such policies forces schools to hire relatively low-quality teachers. This paper uses data from an anonymous state to explore whether teacher quality suff ered from the introduction of CSR. We find that it did, but not nearly enough to explain the small achievement effects of CSR. The combined fall in achievement due to hiring lower quality teachers and more inexperienced teachers is small relative to the unrealized gains. Furthermore, between-school diff erences in the quality of incoming teachers cannot explain the poor estimated CSR performance from previous quasi-experimental treatment-control comparisons.

Immunopathology of american cutaneous leishmaniasis. Modulation of MHC class II gene products by Keratinocytes before and after glucantime therapy

Epidermal changes from 32 cutaneous and 3 mucosal American leishmaniasis (ACL) active lesions were studied for HLA-DR, -DP expression, Lanerhans cells and lymphocyte infiltration. In addition to a DR and DQ positivity at the surface of the cells of the inflammatory infiltrate, a strong reaction for DR antigens was detected on keratinocytes. Hyperplasia of Langerhans cells was present in al cutaneous lesions and epidermis was infiltrated by T lymphocytes. When healed lesions of 14 of these subjects were re-biopsied 1 to 12 months after the end of pentavalent antimonial therapy, MHC class antigens could no longer be seen on keratinocytes. Our data represrn evidence for hhe reversibility of the abnormal HLA-DR expression by keratinocytes in ACL after Glucantime therapy or spontaneous scar formation, demonstrating that this expresion is restricted to the period of active lesions. The present findings can be regarded as an indirect evidence that keratinocytes may be involved in the immunopathology of ACL.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.