SAT Modulo Linear Arithmetic for Solving Polynomial

Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g., termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiability, which is more relevant in several applications as we illustrate with several examples. Nevertheless, we also present new techniques based on the analysis of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad class of problems. The power of our approach is demonstrated by means of extensive experiments comparing our prototype with state-of-the-art tools on benchmarks taken both from the academic and the industrial world.

Symmetric periodic orbits near heteroclinic loops at infinity for a class of polynomial vector fields

For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.

Organisations paysannes, confréries islamiques et structures étatiques dans le processus de transformation au Sénégal: deux études de village au Sine-Saloum

EHESS/CNRS, Programme de recherches interdisciplinaires sur le monde musulman périphérique

Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.

Integrability of a linear center perturbed by a fifth degree homogeneous polynomial

In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

Multicointegration, polynomial cointegration and I(2) cointegration with structural breaks. An application to the sustainability of the US external deficit

In this paper we model the multicointegration relation, allowing for one structural break. Since multicointegration is a particular case of polynomial or I(2) cointegration, our proposal can also be applied in these cases. The paper proposes the use of a residualbased Dickey-Fuller class of statistic that accounts for one known or unknown structural break. Finite sample performance of the proposed statistic is investigated by using Monte Carlo simulations, which reveals that the statistic shows good properties in terms of empirical size and power. We complete the study with an empirical application of the sustainability of the US external deficit. Contrary to existing evidence, the consideration of one structural break leads to conclude in favour of the sustainability of the US external deficit.

Algorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method

The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .

Radial frequency stimuli and sine-wave gratings seem to be processed by distinct contrast brain mechanisms

An assumption commonly made in the study of visual perception is that the lower the contrast threshold for a given stimulus, the more sensitive and selective will be the mechanism that processes it. On the basis of this consideration, we investigated contrast thresholds for two classes of stimuli: sine-wave gratings and radial frequency stimuli (i.e., j0 targets or stimuli modulated by spherical Bessel functions). Employing a suprathreshold summation method, we measured the selectivity of spatial and radial frequency filters using either sine-wave gratings or j0 target contrast profiles at either 1 or 4 cycles per degree of visual angle (cpd), as the test frequencies. Thus, in a forced-choice trial, observers chose between a background spatial (or radial) frequency alone and the given background stimulus plus the test frequency (1 or 4 cpd sine-wave grating or radial frequency). Contrary to our expectations, the results showed elevated thresholds (i.e., inhibition) for sine-wave gratings and decreased thresholds (i.e., summation) for radial frequencies when background and test frequencies were identical. This was true for both 1- and 4-cpd test frequencies. This finding suggests that sine-wave gratings and radial frequency stimuli are processed by different quasi-linear systems, one working at low luminance and contrast level (sine-wave gratings) and the other at high luminance and contrast levels (radial frequency stimuli). We think that this interpretation is consistent with distinct foveal only and foveal-parafoveal mechanisms involving striate and/or other higher visual areas (i.e., V2 and V4).

Differential effects of aging on spatial contrast sensitivity to linear and polar sine-wave gratings

Changes in visual function beyond high-contrast acuity are known to take place during normal aging. We determined whether sensitivity to linear sine-wave gratings and to an elementary stimulus preferentially processed in extrastriate areas could be distinctively affected by aging. We measured spatial contrast sensitivity twice for concentric polar (Bessel) and vertical linear gratings of 0.6, 2.5, 5, and 20 cycles per degree (cpd) in two age groups (20-30 and 60-70 years). All participants were free of identifiable ocular disease and had normal or corrected-to-normal visual acuity. Participants were more sensitive to Cartesian than to polar gratings in all frequencies tested, and the younger adult group was more sensitive to all stimuli tested. Significant differences between sensitivities of the two groups were found for linear (only 20 cpd; P<0.01) and polar gratings (all frequencies tested; P<0.01). The young adult group was significantly more sensitive to linear than to circular gratings in the 20 cpd frequency. The older adult group was significantly more sensitive to linear than to circular gratings in all spatial frequencies, except in the 20 cpd frequency. The results suggest that sensitivity to the two kinds of stimuli is affected differently by aging. We suggest that neural changes in the aging brain are important determinants of this difference and discuss the results according to current models of human aging.

Acute effect of alcohol intake on sine-wave Cartesian and polar contrast sensitivity functions

The aim of this study was to assess contrast sensitivity for angular frequency stimuli as well as for sine-wave gratings in adults under the effect of acute ingestion of alcohol. We measured the contrast sensitivity function (CSF) for gratings of 0.25, 1.25, 2.5, 4, 10, and 20 cycles per degree of visual angle (cpd) as well as for angular frequency stimuli of 1, 2, 4, 24, 48, and 96 cycles/360°. Twenty adults free of ocular diseases, with normal or corrected-to-normal visual acuity, and no history of alcoholism were enrolled in two experimental groups: 1) no alcohol intake (control group) and 2) alcohol ingestion (experimental group). The average concentration of alcohol in the experimental group was set to about 0.08%. We used a paradigm involving a forced-choice method. Maximum sensitivity to contrast for sine-wave gratings in the two groups occurred at 4 cpd sine-wave gratings and at 24 and 48 cycles/360° for angular frequency stimuli. Significant changes in contrast sensitivity were observed after alcohol intake compared with the control condition at spatial frequency of 4 cpd and 1, 24, and 48 cycles/360° for angular frequency stimuli. Alcohol intake seems to affect the processing of sine-wave gratings at maximum sensitivity and at the low and high frequency ends for angular frequency stimuli, both under photopic luminance conditions.

Solidae & sine fuco virtutis lineamenta quaedam exhibens

Invokaatio: Sit opelle caussa finisque Deus!

Problemata quaedam an detur certa et evidens cognitio rerum naturalium, an accidens sine subjecto existere possit, an coelum extimum sit in loco, an malum sit ens merè privatum, an anima separata operetur exhibens

Invokaatio: A.D.

Joli. de Sine muro, Concordancie excerpte de decretalibus et decretis.

Jacobins de la rue Saint-Jacques.

1.° Tractatus pacis inter Ludovicum IX. Regem Francorum, et Henricum III. Regem Angliae : anno 1259. — 2.° Tractatus pacis inter Philippum III. Regem Francorum, et Edwardum I. Regem Angliae : anno 1279. — 3.° Tractatus pacis inter eosdem Reges : anno 1286. — 4.° Quarta et ultima pax facta inter Reges : anno 1303. translata de romancio in latinum, de verbo ad verbum. — 5.° Alia concordantia, seu compositio vel pax inter Reges : anno 1303. — 6.° Pronunciatio Bonifacii, Papae, super pacibus : anno pontificatus quarto. — 7.° De remediis Aquitanorum adversùs vexationem curiae Regis Franciae. — 8.° Copia arresti contra Arnaldum de Romynhano, dati anno 1312. — 9.° Variae litterae Philippi Pulchri et Ludovici X. de rebus Anglicis. — 10.° Bulla Clementis, Papae V. approbans donationem Motae et domorum de Pessaco, factam ecclesiae Burdegalensi à nobili viro Gaillardo de Guto, germano suo, anno primo pontificatus. — 11.° Traitté de paix conclu entre les Rois Philippe et Edouard ; sans date. — 12.° Lettres de Charles IV. Roy de France et de Navarre, touchant les excès commis au lieu de Saint-Sacerdos par le Senechal de Gascogne : l'an 1324. — 13.° Traitté entre la France et l'Angleterre : en la même année. — 14.° Judicium latum apud Oleronem, anno 1287. per D. Norwicensem Episcopum, contra D. Joannem de Greilliaco, dudum Senescallum Vasconiae. — 15.° Tractatus matrimonii inter Alienoram filiam Edwardi Regis Angliae, et Alphonsum filium majorem Petri Regis Aragonum. — 16.° Litterae Petri, Regis Aragonum, de matrimonio filii sui Alphonsi cum Alienora, filia primogenita Regis Edwardi. — 17.° Joannis XXII. bulla contra Michaëlem de Cesena, Ministrum generalem ordinis Minorum : VIII. idus Junii, pontificatus anno XII. — 18.° Edwardi, Regis Anglorum, constitutiones variae ad Aquitaniam spectantes et ad Angliam. — 19.° Traitté de paix entre les Rois de France et d'Angleterre, fait en l'an 1325. — 20.° Litterae Agennensium ad Carolum IV. Regem Franciae, pro Rege Angliae, nominatim de facto Sancti-Sacerdotis, scriptae anno 1324. — 21.° Tractatus matrimonii inter Alphonsum, Regem Castellae et Legionis, et Alienoram, filiam Edwardi Regis Angliae ; item alius inter Edwardum, Regis Angliae primogenitum, et Alienoram sororem Regis Castellae : anno 1325. — 22.° Instructions données par le Roy d'Angleterre à ses Ambassadeurs allans en Espagne pour le fait dudit mariage. — 23.° Abusiones quae exercentur in regno Angliae circa beneficia ecclesiastica ; et remedia sine quibus nunquam cessare creduntur. — 24.° Clementis V. bulla de saecularisatione monasterii de sancto Aemiliano, in dioecesi Burdigalensi ; data anno pontificatus quinto. — 25.° Litterae Edwardi II. Regis Angliae, de servanda pace facta cum Carolo IV. Rege Franciae. — 26.° Ejusdem litterae quibus Edmundum, Comitem Cantiae, fratrem suum, constituit Capitaneum in Ducatu Aquitaniae. — 27.° Lettres de Charles IV. Roy de France, contre le Roy d'Angleterre, qui refusoit de luy faire les foy et hommage pour la Duché d'Aquitaine : de l'année 1324. — 28.° Litterae ejusdem Caroli IV. Regis Francorum, de eadem re ; quibus Carolo, Comiti Valesiae, patruo suo, dat potestatem puniendi rebelles Aquitaniae ; datae anno 1324. — 29.° Litterae ejusdem de salvagardia Guillelmi Galteri, Clerici, datae anno 1323. — 30.° Ejusdem litterae pro Margareta de Guouda, tutrice Pontii domini de Castellione, filii sui, datae anno 1323. — 31.° Ejusdem litterae pro Comitissa Fuxi et Vicecomitissa Bearni et Marciani, tutrice Gastonis filii sui ; datae anno 1322. — 32.° Litterae Antonini Pessaigne, Senescalli Ducatus Aquitaniae, quibus Ostencium Jordani, Clericum ac Jurisperitum, constituit suum et Regis Angliae Procuratorem ; datae anno 1318. — 33.° Litterae Almarici domini de Credonio, Senescalli Ducatus Aquitaniae, quibus Roberto de la Vertadausa, Anglico, decem libras Turonensium parvorum singulis annis solvendas concedit vice et nomine Regis Angliae ; datae anno 1322. — 34.° Divers actes entre les Rois de France et d'Angleterre, pour assurer la paix ; faits depuis l'an 1259. jusques en 1323. — 35.° Acta processus habiti in curia Romana inter capitulum ecclesiae Coventrensis et capitulum ecclesiae Lichefeldiensis de electione Episcopi, tempore Joannis XXII. — 36.° Traitté d'alliance et de confederation entre la France et l'Ecosse contre l'Angleterre ; fait en 1325. — 37.° Articuli exhibiti à Procuratore ecclesiae Lichfeldensis. — 38.° Articuli exhibiti à Procuratore ecclesiae Coventrensis. — 39.° Joannis XXII. bulla de unione Episcopatuum Corkagiensis et Clonensis, data Avenione anno pontificatus XI. — 40.° Acta processus apud eumdem Papam agitati super praebenda sancti Stephani in ecclesia Beverlacensi.

Colbertinus

1.° P. Ovidii Nasonis de remedio amoris liber. — 2.° Henrici Samariensis satyra contra fortunam : conjectae ad marginem notae. — 3.° Amphitryon carmen elegiacum. — 4.° Anonymi tractatus de algorismo, versibus hexametris. — 5.° Anonymi epistola de lamentabili statu Franciae, sub narratione poëtica. — 6.° Anonymi liber de pomo, sive de morte Aristotelis. — 7.° Constabuli, filii Lucae Medici, tractatus de differentia spiritus et animae. — 8.° Anonymi libellus de unitate et uno. — 9.° Liber facetiae, sine quo nemo potest esse benè moriginatus. — 10.° Versus de eruditione puerorum.

Colbertinus, antea Jacobi Augusti Thuani