Geometric symmetry in the quadratic Fisher discriminant operating on image pixels

This article examines the design of Quadratic Fisher Discriminants (QFDs) that operate directly on image pixels, when image ensembles are taken to comprise all rotated and reflected versions of distinct sample images. A procedure based on group theory is devised to identify and discard QFD coefficients made redundant by symmetry, for arbitrary sampling lattices. This procedure introduces the concept of a degeneracy matrix. Tensor representations are established for the square lattice point group (8-fold symmetry) and hexagonal lattice point group (12-fold symmetry). The analysis is largely applicable to the symmetrisation of any quadratic filter, and generalises to higher order polynomial (Volterra) filters. Experiments on square lattice sampled synthetic aperture radar (SAR) imagery verify that symmetrisation of QFDs can improve their generalisation and discrimination ability.Comment: Accepted for publication in IEEE Transactions on Information Theor

Weighted Average Lexicographic Values for Share Sets and Balanced Cooperative Games

Inspired by Kalai-Samet [4] and Tijs [11], weighted average lexicographic values are introduced for share sets and for cores of cooperative games using induction arguments. Continuity properties and monotonicity properties of these weighted lexicographic values are studied. For subclasses of games (convex games, simplex games, big boss games) relations are established with weighted (exact) Shapley values.Cooperative games;average lexicographic value;weighted Shapley value

Share Opportunity Sets and Cooperative Games

In many share problems there is a priori given a natural set of possible divisions to solve the sharing problem.Cooperative games related to such share sets are introduced, which may be helpful in solving share problems.Relations between properties of share sets and properties of games are investigated.The average lexicographic value for share sets and for cooperative games is studied.cooperative games;bankruptcy games;average lexicographic value;opportunity sets

Compatibilidad de pinturas de protección temporaria ("shop primers”) con esquemas anticorrosivos para carenas

Las pinturas de protección temporaria se emplean en la industria naval para mantener el acero sin oxidación durante la etapa constructiva. Dicho fondo debe ser, además, compatible con los esquemas protectores a aplicar. Se han ensayado diferentes formulaciones de "shop-primers", exponiendo paneles a la intemperie durante un lapso de 20 meses. Productos a base de cinc y de cinc-aluminio son los que han mostrado mejores condiciones de resistencia, presentando buenas propiedades anticorrosivas. Sobre estos paneles pueden aplicarse esquemas para carena, los que cumplen con las exigencias establecidas para los ensayos en balsa.The shop-primers are employed in naval shipyards to protect the steel plates against corrosion during the construction period. These primers must be also compatible with the anticorrosion systems employed subsequently. Different formulations of shop-primers were tested by accelerated exposure tests during 20 months at La Plata. Products based on zinc dust and zinc-aluminium demonstrated good exterior resistance and anticorrosion properties. Over that panels anticorrosion marine paints were applied and submitted to raft trials in Mar del Plata’s Harbour

Pinturas anticorrosivas para la protección de carenas de barcos: VII

Se ha realizado la optimización de una serie de composiciones de pinturas anticorrosivas, ensayadas con anterioridad en balsas experimentales como etapa previa a la iniciación de experiencias sobre carenas de embarcaciones. En las formulaciones se emplean cinco pigmentos anticorrosivos (minio, silicocromato básico de plomo, sulfato de plomo-aluminio y cromatos básicos de cinc de diferente solubilidad). Los mismos fueron dispersados en un barniz de resina fenólica-aceite de tung, al cual se incorporaron diferentes proporciones de caucho clorado de 20 cP. Sistemas de pinturas aplicados sobre paneles con diferente tratamiento de superficie, fueron ensayados en línea de flotación y en carena en la balsa de Puerto Belgrano.The optimizing of a series of anticorrosion paints tested previously in experimental rafts has been done. This is a new approach to this subject, before the application of that paints on ship bottoms. Five anticorrosion pigments (lead oxide, basic lead silicochromate, basic lead sulfate-aluminium and two basic zinc chromates of different solubilities) were used in the formulations. The pigments and extenders were dispersed in a binder based in a phenolic varnish where different quantities of chlorinated rubber (20 cP) had been incorporated. The paint systems were applied on plates with different surface treatment and tested in the experimental raft at Puerto Belgrano

Contribución al estudio del comportamiento de las pinturas antiincrustantes

Se ha estudiado, mediante ensayos en balsa de 18 meses de duración, el comportamiento de pinturas antiincrustantes elaboradas en base a compuestos orgánicos de estaño: TBTO, TBTF, TPTF y TBTS. Los mismos se usaron solos, asociados con óxido cuproso y con TPLA. Las pinturas se prepararon empleando caucho clorado o resinas vinílicas para la formulación de los correspondientes vehículos. Sólo tres de las pinturas preparadas exclusivamente con TBTF, TPTF o TBTS se mantienen sin fouling durante un período de 12 a 15 meses. Los mejores resultados se logran cuando estos compuestos están asociados al óxido cuproso. Lo mismo ocurre en el caso del TPLA.By means of raft tests we have studied the antifouling properties of paints prepared with TBTO, TBTF, TPTF and TBTS. That substances were employed alone or associated with cuprous oxide and TPLA. The samples were prepared with chlorinated rubber and vinyl binders. After a immersion period of 15 months, only three of the paints with TBTF, TPTF or TBTS gave good results. The best antifouling activity correspond to the organotin cornin' pounds, associated with cuprous oxide. TPLA is a good reinforcement toxic for paints based on cuprous oxide or in organotins

Bayesian functional neural operator: uncertainty quantification of parametric PDEs

LAUREA MAGISTRALEIl machine learning per il calcolo scientifico offre un'alternativa alle tecniche numeriche classiche per risolvere equazioni alle derivate parziali parametriche (EDP) tramite Neural Operators capaci di imparare mappature tra spazi funzionali. Questi modelli surrogati garantiscono un guadagno drastico in termini di costo computazionale, ma presentano inevitabili errori di approssimazione difficili da stimare a priori. Quando le loro previsioni vengono impiegate in procedure decisionali ad alto rischio, è quindi cruciale disporre di strumenti affidabili per quantificare l'incertezza associata alle predizioni. Tuttavia, le architetture stato dell'arte dei Neural Operator presentano limitazioni critiche che rendono i metodi di quantificazione dell'incertezza proibitivi: elevato numero di parametri e costo computazionale che scala sfavorevolmente con la finezza della mesh. Questo lavoro presenta il Functional Neural Operator (FunNO), un'architettura progettata per coniugare elevata espressività e leggerezza computazionale, consentendo un'applicazione efficace di algoritmi di quantificazione dell'incertezza. FunNO utilizza "layer funzionali" che estraggono coefficienti significativi dalle funzioni in input tramite trasformazioni integrali, proiettandoli su una base ottimale dello spazio di output ottenuta tramite Decomposizione Ortogonale Propria (DOP) sul train dataset. Questo schema non pone vincoli sulla regolarità del dominio e garantisce costo computazionale lineare rispetto alla finezza della mesh. Verificate le prestazioni di FunNO su problemi di flusso di Darcy e elasticità lineare (1.87% MRE con 5.584 parametri e 1.21% MRE con 2.625 parametri), introduciamo la sua versione bayesiana, B-FunNO, per la quantificazione dell'incertezza epistemica tramite Stein Variational Gradient Descent (SVGD), un metodo non parametrico che approssima la distribuzione a posteriori attraverso un insieme di particelle. I risultati dimostrano che B-FunNO consente di ottenere modelli surrogati sia veloci sia affidabili (copertura del 95,1% e 93,6% sul test dataset), aprendo la strada al loro impiego in scenari di controllo in tempo reale, ottimizzazione robusta e calcolo scientifico ad alto rischio.Scientific machine learning offers an alternative to classical numerical techniques for solving parametric partial differential equations (PDEs) through Neural Operators capable of learning mappings between functional spaces. These surrogate models guarantee dramatic gains in terms of computational cost, but present inevitable approximation errors that are difficult to estimate a priori. When their predictions are employed in high-risk decision-making procedures, it is therefore crucial to have reliable tools to quantify the uncertainty associated with predictions. However, state-of-the-art Neural Operator architectures present critical limitations that make uncertainty quantification methods prohibitive: high number of parameters and computational cost that scales unfavorably with mesh refinement. This work presents the Functional Neural Operator (FunNO), an architecture designed to combine high expressivity and computational lightness, enabling effective application of uncertainty quantification algorithms. FunNO uses 'functional layers' that extract meaningful coefficients from input functions through integral transformations, projecting them onto an optimal basis of the output space obtained through Proper Orthogonal Decomposition (POD) on the training dataset. This scheme places no constraints on domain regularity and guarantees linear computational cost with respect to number of nodes in the mesh. After verifying FunNO's performance on Darcy flow and linear elasticity problems (1.87% MRE with 5,584 parameters and 1.21% MRE with 2,625 parameters), we introduce its Bayesian version, B-FunNO, for epistemic uncertainty quantification through Stein Variational Gradient Descent (SVGD), a non-parametric method that approximates the posterior distribution through an ensemble of particles. The results demonstrate that B-FunNO enables both fast and reliable surrogate models (95.1% and 93.6% coverage on the test dataset), allowing for their deployment in real-time control scenarios, robust optimization, and high-risk scientific computing