Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Contractions in the 2-wasserstein lenght space and thermalization of granular media

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.

On games corresponding to sequencing situations with precedence relations

In this paper we study a class of cooperative sequencing games that arise from one-machine sequencing situations in which chain precedence relations are imposed on the jobs. It is shown that these sequencing games are convex.

Quarta contribuição ao conhecimento do gênero Archytas Jaennicke, 1867: (Diptera, Tachinidae)

The author studies 5 species of Archytas Jaennicke, 1867, belonging to the "dissimilis group": A. seminigra (Wiedemann, 1830) and four species which are considered as new. The species of this group may be characterized as follow: Species of short body, exceptionally large ones. Abdomen yellowish, with a median blackish V-shapedspot. Second antennal segment with 2/3 length of third. Parafacialia with blackish hairs. Propleura pilose. Post alar wall with few hairs. The following key facilitates the identification of the species: 1. Third article of antennae, strongly convex in the anterior margin (fig. 10); posterior margin straight. Parafacialia with a facio-orbital bristle well differentiated . . . . A. arnaudi sp. n. — Third article of antennae not so convex in the anterior margin; facio-orbital bristle absent, if present not well differentiated [...] 2; 2. Parafrontalia with golden polen [...] 3; — Parafrontalia brownish to shining black with few polen . . . 4; 3. Forcipes superiores slender and sub-truncate apically (figs. 5 and 6)[...] A. seminigra; — Forcipes superiores broad apically (fig .20)[...] A, gongalvesi sp. n.; 4. First, second and third sternites yellowish [...] A. angrensis sp. n.; — All sternites brownish to black [...] A. sabroskpi sp. n.; The material studied belongs to the Instituto Oswaldo Cruz collections, where is located the types of new species.

Mixing invariants of hyperbolic 3-manifolds

Let M be a compact hyperbolic 3-manifold with incompressible boundary. Consider a complete hyperbolic metric on int(M). To each geometrically finite end of int(M) are traditionnaly associated 3 different invariants : the hyperbolic metric associated to the conformal structure at infinity, the hyperbolic metric on the boundary of the convex core and the bending measured lamination of the convex core. In this note we show how invariants of different types can be realised in the different ends.

Lymnaea Diaphana; a study of Topotypic specimens (Pulmonata: Lymnaeidae)

A description of the species Lymnaea diaphana King, 1830 is presented, on the basis of material collected at its type-locality, San Gregorio, on the north coast of the Strait of Magellan, in the Chilean province of Magallanes. It may be identified by the following characters taken together: adult shell over 10 mm in length, whorls inflated, regularly convex, separated by a well-marked suture, aperture ovate occupying about half the shell length; renal organ forming an approximately right angle with the ureter; pouch of the oviduct well noticeable high on the right ventral surface and on the right side of the nidamental gland; uterus bent to the right into an approximately right angle; body of the spermatheca projected into the pulmonary cavity and adhered to the pericardium and to the roof of the pulmonary cavity; spermiduct highly sinuous, folding dorsalward between the left half of the oviduct and the left shoulder of the nidamental gland, and then winding on ventralward to reach the prostate on the middle line; prostate voluminous, convex on the left, pushed in on the right, with a deep dorsal furrow corresponding to a fold which projects into the prostatic lumen and is more developed at the fore half of the organ; apical end of the penial sheath with about six minute protuberances corresponding to inner chambers; prepuce from about as long about twice as long as the penial sheath, with some variation beyond those limits; lateral teeth of the radula basically tricuspid, with a usually simple ectocone which may show a bifid or trifid point. A diagnosis between lymnaea diaphana and three other lymnaeids which also occur in South America and were previously studied by the author - L. columella, L. viatrix and L. rupestris - is presented.

Physa Marmorata Guilding, 1828 (Pulmonata: Physidae)

A description of Physa marmorata Guilding, 1828, based on material collected at its type-locality, the Caribbean island of Saint Vincent, is presented. The shell is thin, horn-colored, surface very glossy, diaphanous. Spire acute, elevated; protoconch distinct, rounded-conical, reddish-brown; five not shouldered, broadly convex whorls with subobsolete spiral lines and thin growth lines. Aperture elongated, 1.4-2.0 times as long as the remaining shell length, narrow obovate-lunate; upper half acute-angled,lower half oval,narrowly rounded at the base, outer lip sharp, inner lip completely closing the umbilical region; a very distinct callus on the parietal wall; columellar lip with a low ridge gradually merging into the callus. ratios: shell width/shell length = 0.44 - 0.52 (mean 0.47); spire length /shell lenght = 0.33-0.41 (mean 0.39); aperture length/shell lenght = 0.59-0.67 (mean 0.62). Oral lappets laterally mucronate, foot spatulate with deeply pigmented acuminate tail. Mantle reflection with 6-10 short triangular dentations covering nearly half the right surface of the body whorl, and 4-6 covering a part of the ventral wall. Body surface with tiny dots of greenish-yellow pigment besides melanin. Renal tube tightly folded in toa zigzag course. Ovotestis diverticula acinous, laterally pressed against each other around a collecting canal. Ovispermiduct with well-developed seminal vesicle. oviduct highly convoluted, merging into a less convoluted nidamental gland which narrows to a funnel-shaped uterus and a short vagina. Spermathecal body oblong, more or less constricted in the middle and somewhat curved; spermathecal duct uniformly narrow, a little longer than be body. About 20 prostatic diverticula, simple, bifurcate or divided into a few short branches, distalmost ones assembled into a cluster. Penis long, nearly uniformly narrow; penial canal with lateral opening about the junction of its middle and lower thirds. Penial sheath with a bulbous terminal expasion the tip of which isinserted into the caudal end of the prepuce. Prepuce shouldered, much wider than the narrow portion of the penial sheath. Penial sheath/prepuce ratio about 2.08 (1.45-2.75). The main extrinsic muscles of the penial complex are a retractor, with a branch attached to the bulb, and another to the caudal end of the penial sheath; and a protractor, with a branch attached to the shoulder of the prepuce and adjoining area of the penial sheath, and another to the caudal end of the penial sheath. Egg capsule C-shaped, with 10-30 elliptical eggs (snails 10mm long) measuring about 1.10 mm (0.90-1.32) through the long axis and surrounded by an inner and an outer lamellate membranes. Jaw a simple obtusely V-shaped plate. radula will be described separately.

Physa cubensis Pfeiffer, 1839 (Pulmonata: Physidae)

A description of Physa cubensis Pfeiffer, 1839, based on 15 speciments collected in Havana, Cuba, is presented. The shell, measuring 9.0 x 4,8mm to 12.3 x 6.4mm, is ovate-oblong, thin, diaphanous, horncolored, shining. Spire elevated, broadly conical; protoconch distinct, roundish, reddish-brown. About five moderately shouldered, roundly convex whorls, penultimate whorl expanded; spiral striation subobsolete; growth line faint on the intermediate whorls, clearly visible on the body whorl, crowded here and there. Suture well impressed. Aperture elongated 2.05 - 2.67 (mean 2.27) times as long as the remaining length of the shell, narrow obovulate-lunate; upper half acute-angled, lower half oval, narrowly rounded at the base; outer lip sharp, inner lip completely closing the umbilical region; a thick callus on the parietal wall; columellar plait well marked. Ratios: shell width/shell length - 0.52-0.61 (mean 0.55); spire length/shell length = 0.27 - 0.33 (mean 0.31); aperture length/shell length = 0.67 - 0.73 (mean 0.69). Oral lappets laterally mucronate; foot spatulate with acuminate tail. Mantle relection with 6 - 8 short triangular dentations in the right lobe (columellar side) and 4 - 6 in the left lobe (near the pneumostome). Renal tube tightly folded into a zigzag course. Ovotestis, ovispermiduct, seminal vesicle, oviduct, nidamental gland, uterus and vagina as in Physa marmorata (see Paraense, 1986, Mem. Inst. Oswaldo Cruz, 81: 459-469). Spermathecal body egg-shaped or pear-shaped; spermathecal ducta uniformly narrow with expanded base, a little longer than the body. Spermiduct, prostate and vas deferens as in P. marmorata (Paraense, loc. cit.). Penis wide proximally, narrowing gradually apicad; penial canal with subterminal outlet. Penial sheath following the width of the penis and ending up by a bulbous expansion somewhat narrower than the proximal portion. Penaial sheath/prepuce ration = 1,25 - 1,83 (mean 1.49). Prepuce much wider than the bulb of the penial shealth, moderately shouldered owing to the intromission of the bulb, and with a large gland in one side of its proximal half occupating about a third of its length. Extrinsic muscles of the penial complex as in P. marmorata. Jaw a simple obtusely V-shaped plate. Radula to be described separetely.

License prices for financially constrained firms

It is often alleged that high auction prices inhibit service deployment. We investigate this claim under the extreme case of financially constrained bidders. If demand is just slightly elastic, auctions maximize consumer surplus if consumer surplus is a convex function of quantity (a common assumption), or if consumer surplus is concave and the proportion of expenditure spent on deployment is greater than one over the elasticity of demand. The latter condition appears to be true for most of the large telecom auctions in the US and Europe. Thus, even if high auction prices inhibit service deployment, auctions appear to be optimal from the consumers' point of view.

Enrutament i control de flux en xarxes híbrides satèl·lit-terrestre

Les xarxes híbrides satèl·lit-terrestre ofereixen connectivitat a zones remotes i aïllades i permeten resoldre nombrosos problemes de comunicacions. No obstant, presenten diversos reptes, ja que realitzen la comunicació per un canal mòbil terrestre i un canal satèl·lit contigu. Un d'aquests reptes és trobar mecanismes per realitzar eficientment l'enrutament i el control de flux, de manera conjunta. L'objectiu d'aquest projecte és simular i estudiar algorismes existents que resolguin aquests problemes, així com proposar-ne de nous, mitjançant diverses tècniques d'optimització convexa. A partir de les simulacions realitzades en aquest estudi, s'han analitzat àmpliament els diversos problemes d'enrutament i control de flux, i s'han avaluat els resultats obtinguts i les prestacions dels algorismes emprats. En concret, s'han implementat de manera satisfactòria algorismes basats en el mètode de descomposició dual, el mètode de subgradient, el mètode de Newton i el mètode de la barrera logarítmica, entre d'altres, per tal de resoldre els problemes d'enrutament i control de flux plantejats.

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.

On square permutations

Severini and Mansour introduced in [4]square polygons, as graphical representations of square permutations, that is, permutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of square permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.

Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.

Exclusive Nightclubs and Lonely Hearts Columns: Nonmonotone Participation in Optional Intermediation

In many decentralised markets, the traders who benefit most from an exchange do not employ intermediaries even though they could easily afford them. At the same time, employing intermediaries is not worthwhile for traders who benefit little from trade. Together, these decisions amount to non-monotone participation choices in intermediation: only traders of middle “type” employ intermediaries, while the rest, the high and the low types, prefer to search for a trading partner directly. We provide a theoretical foundation for this, hitherto unexplained, phenomenon. We build a dynamic matching model, where a trader’s equilibrium bargaining share is a convex increasing function of her type. We also show that this is indeed a necessary condition for the existence of non-monotone equilibria.

Correlated equilibria, good and bad: an experimental study

We report results from an experiment that explores the empirical validity of correlated equilibrium, an important generalization of the Nash equilibrium concept. Specifically, we seek to understand the conditions under which subjects playing the game of Chicken will condition their behavior on private, third–party recommendations drawn from known distributions. In a “good–recommendations” treatment, the distribution we use is a correlated equilibrium with payoffs better than any symmetric payoff in the convex hull of Nash equilibrium payoff vectors. In a “bad–recommendations” treatment, the distribution is a correlated equilibrium with payoffs worse than any Nash equilibrium payoff vector. In a “Nash–recommendations” treatment, the distribution is a convex combination of Nash equilibrium outcomes (which is also a correlated equilibrium), and in a fourth “very–good–recommendations” treatment, the distribution yields high payoffs, but is not a correlated equilibrium. We compare behavior in all of these treatments to the case where subjects do not receive recommendations. We find that when recommendations are not given to subjects, behavior is very close to mixed–strategy Nash equilibrium play. When recommendations are given, behavior does differ from mixed–strategy Nash equilibrium, with the nature of the differ- ences varying according to the treatment. Our main finding is that subjects will follow third–party recommendations only if those recommendations derive from a correlated equilibrium, and further, if that correlated equilibrium is payoff–enhancing relative to the available Nash equilibria.