Sharpened lower bounds for cut elimination

We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our new lower bounds remove the constant of proportionality, giving an exponential stack of height equal to d − O(1). The proof method is based on more efficiently expressing the Gentzen-Solovay cut formulas as low depth formulas.

Optimal asymptotic bounds for spherical designs

"Vegeu el resum a l'inici del document del fitxer adjunt"

MR spectroscopy of the human brain with enhanced signal intensity at ultrashort echo times on a clinical platform at 3T and 7T.

Recently, the spin-echo full-intensity acquired localized (SPECIAL) spectroscopy technique was proposed to unite the advantages of short TEs on the order of milliseconds (ms) with full sensitivity and applied to in vivo rat brain. In the present study, SPECIAL was adapted and optimized for use on a clinical platform at 3T and 7T by combining interleaved water suppression (WS) and outer volume saturation (OVS), optimized sequence timing, and improved shimming using FASTMAP. High-quality single voxel spectra of human brain were acquired at TEs below or equal to 6 ms on a clinical 3T and 7T system for six volunteers. Narrow linewidths (6.6 +/- 0.6 Hz at 3T and 12.1 +/- 1.0 Hz at 7T for water) and the high signal-to-noise ratio (SNR) of the artifact-free spectra enabled the quantification of a neurochemical profile consisting of 18 metabolites with Cramér-Rao lower bounds (CRLBs) below 20% at both field strengths. The enhanced sensitivity and increased spectral resolution at 7T compared to 3T allowed a two-fold reduction in scan time, an increased precision of quantification for 12 metabolites, and the additional quantification of lactate with CRLB below 20%. Improved sensitivity at 7T was also demonstrated by a 1.7-fold increase in average SNR (= peak height/root mean square [RMS]-of-noise) per unit-time.

Fair bounds based solidarity

How should scholarships be distributed among the (public) higher education students? We raise this situation as a redistribution problem. Following the approach developed in Fleurbaey (1994) and Bossert (1995), redistribution should be based on the notion of solidarity and it re-allocates resources taking into account only agents’ relevant characteristics. We also follow Luttens (2010a), who considers that compensation of relevant characteristics must be based on a lower bound on what every individual deserves. In doing so, we use the so-called fair bound (Moulin (2002)) to define an egalitarian redistribution mechanism and characterize it in terms of non-negativity, priority in lower bound and solidarity. Finally, we apply our approach to the scholarships redistribution problem. Keywords: Redistribution mechanism, Lower bounds, Scholarship, Solidarity. JEL classification: C71, D63, D71

Neurochemical profile of the mouse hypothalamus using in vivo 1H MRS at 14.1T.

The hypothalamus plays an essential role in the central nervous system of mammals by among others regulating glucose homeostasis, food intake, temperature, and to some extent blood pressure. Assessments of hypothalamic metabolism using, e.g. (1)H MRS in mouse models can provide important insights into its function. To date, direct in vivo (1)H MRS measurements of hypothalamus have not been reported. Here, we report that in vivo single voxel measurements of mouse hypothalamus are feasible using (1)H MRS at 14.1T. Localized (1)H MR spectra from hypothalamus were obtained unilaterally (2-2.2 microL, VOI) and bilaterally (4-4.4 microL) with a quality comparable to that of hippocampus (3-3.5 microL). Using LCModel, a neurochemical profile consisting of 21 metabolites was quantified for both hypothalamus and hippocampus with most of the Cramér-Rao lower bounds within 20%. Relative to the hippocampus, the hypothalamus was characterized by high gamma-aminobutryric acid and myo-inositol, and low taurine concentrations. When studying transgenic mice with no glucose transporter isoform 8 expressed, small metabolic changes were observed, yet glucose homeostasis was well maintained. We conclude that a specific neurochemical profile of mouse hypothalamus can be measured by (1)H MRS which will allow identifying and following metabolic alterations longitudinally in the hypothalamus of genetic modified models.

[Archives de la Parole]. , [The king and the margosa seed] : récit en dravidien, telugu, Province de Madras / [Sir George Grierson], éd. ; Linguistic survey of India ; [V. Krishna Rao], voix

[Traditions. Asie. Inde. Présidence de Madras [i.e. Chennai]. Ceded Districts]

[Archives de la Parole]. , [The king and the margosa seed] : récit en dravidien, telugu, Province de Madras / [Sir George Grierson], éd. ; Linguistic survey of India ; [K. Divakara Rao], voix

[Traditions. Asie. Inde. Présidence de Madras [i.e. Chennai]. Ceded Districts]

Strong minimax lower bounds for learning

Minimax lower bounds for concept learning state, for example, thatfor each sample size $n$ and learning rule $g_n$, there exists a distributionof the observation $X$ and a concept $C$ to be learnt such that the expectederror of $g_n$ is at least a constant times $V/n$, where $V$ is the VC dimensionof the concept class. However, these bounds do not tell anything about therate of decrease of the error for a {\sl fixed} distribution--concept pair.\\In this paper we investigate minimax lower bounds in such a--stronger--sense.We show that for several natural $k$--parameter concept classes, includingthe class of linear halfspaces, the class of balls, the class of polyhedrawith a certain number of faces, and a class of neural networks, for any{\sl sequence} of learning rules $\{g_n\}$, there exists a fixed distributionof $X$ and a fixed concept $C$ such that the expected error is larger thana constant times $k/n$ for {\sl infinitely many n}. We also obtain suchstrong minimax lower bounds for the tail distribution of the probabilityof error, which extend the corresponding minimax lower bounds.

Minimax lower bounds for the two-armed bandit problem

We obtain minimax lower bounds on the regret for the classicaltwo--armed bandit problem. We provide a finite--sample minimax version of the well--known log $n$ asymptotic lower bound of Lai and Robbins. Also, in contrast to the log $n$ asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable configurations of the two arms. That is, we show that for {\sl every} allocation rule and for {\sl every} $n$, there is a configuration such that the regret at time $n$ is at least 1 -- $\epsilon$ times the regret of random guessing, where $\epsilon$ is any small positive constant.

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

Nonparametric bounds on the returns to language skills

This paper applies the theoretical literature on nonparametric bounds ontreatment effects to the estimation of how limited English proficiency (LEP)affects wages and employment opportunities for Hispanic workers in theUnited States. I analyze the identifying power of several weak assumptionson treatment response and selection, and stress the interactions between LEPand education, occupation and immigration status. I show that thecombination of two weak but credible assumptions provides informative upperbounds on the returns to language skills for certain subgroups of thepopulation. Adding age at arrival as a monotone instrumental variable alsoprovides informative lower bounds.

Worst-case bounds for the logarithmic loss of predictors

We investigate on-line prediction of individual sequences. Given a class of predictors, the goal is to predict as well as the best predictor in the class, where the loss is measured by the self information (logarithmic) loss function. The excess loss (regret) is closely related to the redundancy of the associated lossless universal code. Using Shtarkov's theorem and tools from empirical process theory, we prove a general upper bound on the best possible (minimax) regret. The bound depends on certain metric properties of the class of predictors. We apply the bound to both parametric and nonparametric classes ofpredictors. Finally, we point out a suboptimal behavior of the popular Bayesian weighted average algorithm.

On bounds for network revenue management

The Network Revenue Management problem can be formulated as a stochastic dynamic programming problem (DP or the\optimal" solution V *) whose exact solution is computationally intractable. Consequently, a number of heuristics have been proposed in the literature, the most popular of which are the deterministic linear programming (DLP) model, and a simulation based method, the randomized linear programming (RLP) model. Both methods give upper bounds on the optimal solution value (DLP and PHLP respectively). These bounds are used to provide control values that can be used in practice to make accept/deny decisions for booking requests. Recently Adelman [1] and Topaloglu [18] have proposed alternate upper bounds, the affine relaxation (AR) bound and the Lagrangian relaxation (LR) bound respectively, and showed that their bounds are tighter than the DLP bound. Tight bounds are of great interest as it appears from empirical studies and practical experience that models that give tighter bounds also lead to better controls (better in the sense that they lead to more revenue). In this paper we give tightened versions of three bounds, calling themsAR (strong Affine Relaxation), sLR (strong Lagrangian Relaxation) and sPHLP (strong Perfect Hindsight LP), and show relations between them. Speciffically, we show that the sPHLP bound is tighter than sLR bound and sAR bound is tighter than the LR bound. The techniques for deriving the sLR and sPHLP bounds can potentially be applied to other instances of weakly-coupled dynamic programming.

External morphology of the adult of Dynamine postverta (Cramer) (Lepidoptera, Nymphalidae, Biblidinae) and patterns of morphological similarity among species from eight tribes of Nymphalidae

External morphology of the adult of Dynamine postverta (Cramer) (Lepidoptera, Nymphalidae, Biblidinae) and patterns of morphological similarity among species from eight tribes of Nymphalidae. The external structure of the integument of Dynamine postverta postverta (Cramer, 1779) is based on detailed morphological drawings and scanning electron microscopy. The data are compared with other species belonging to eight tribes of Nymphalidae, to assist future studies on the taxonomy and systematics of Neotropical Biblidinae.

Notes on the geographic distribution and subspecific taxonomy of Sais rosalia (Cramer) (Lepidoptera, Nymphalidae, Ithomiini), including the first records in Paraguay

Notes on the geographic distribution and subspecific taxonomy of Sais rosalia (Cramer) (Lepidoptera, Nymphalidae, Ithomiini), including the first records in Paraguay. This paper provides comments on the subspecific taxonomy and geographic distribution of Sais rosalia (Cramer, 1779) (Lepidoptera, Nymphalidae, Ithomiini), as well as an up-to-date distributional map, complemented with unpublished distributional data based on specimens deposited in the Coleção Entomológica Pe. Jesus S. Moure, Curitiba, Brazil and the Museo de Historia Natural, Lima, Peru. The following synonyms are proposed: Sais rosalia camariensis Haensch, 1905 syn. rev. as junior subjective synonym of Papilio rosalia Cramer, 1779 and Sais rosalia brasiliensis Talbot, 1928 syn. rev. as junior subjective synonym of Sais rosalia rosalinde Weymer, 1890. Additionally, the first country records of Sais rosalia in Paraguay, including the southernmost record of the species, are documented.