Narrow Proofs May Be Maximally Long

We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n^Omega(w). This shows that the simple counting argument that any formula refutable in width w must have a proof in size n^O(w) is essentially tight. Moreover, our lower bound generalizes to polynomial calculus resolution (PCR) and Sherali-Adams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. Our results do not extend all the way to Lasserre, however, where the formulas we study have proofs of constant rank and size polynomial in both n and w

Narrow proofs may be maximally long

We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n(Omega(w)). This shows that the simple counting argument that any formula refutable in width w must have a proof in size n(O(w)) is essentially tight. Moreover, our lower bound generalizes to polynomial calculus resolution and Sherali-Adams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. The lower bound does not extend all the way to Lasserre, however, since we show that there the formulas we study have proofs of constant rank and size polynomial in both n and w.Peer ReviewedPostprint (author's final draft

Shape Holomorphy of the stationary Navier-Stokes Equations *

We consider the stationary Stokes and Navier-Stokes Equations for viscous, incompressible flow in parameter dependent bounded domains D T , subject to homogeneous Dirichlet (" no-slip ") boundary conditions on ∂D T. Here, D T is the image of a given fixed nominal Lipschitz domainˆDdomainˆ domainˆD ⊆ R d , d ∈ {2, 3}, under a map T : R d → R d. We establish shape holomorphy of Leray solutions which is to say, holomorphy of the map T → (ˆ u T , ˆ p T) where (ˆ u T , ˆ p T) ∈ H 1 0 (ˆ D) d ×L 2 (ˆ D) denotes the pullback of the corresponding weak solutions and T varies in W k,∞ with k ∈ {1, 2}, depending on the type of pullback. We consider in particular parametrized families {T y : y ∈ U } ⊆ W 1,∞ of domain mappings, with parameter domain U = [−1, 1] N and with affine dependence of T y on y. The presently obtained shape holomorphy implies summability results and n-term approximation rate bounds for gpc (" generalized polynomial chaos ") expansions for the corresponding parametric solution map y → (ˆ u y , ˆ p y) ∈ H 1 0 (ˆ D) d × L 2 (ˆ D)

Skeletal muscular changes in Pena-Shokeir Sequence

In 1974, PENA and SHOKEIR first described alethal syndrome consisting of facial anomalies(flat and depressed nasal tip, micro- and retro-gnathia, malformed and low-set ears, hypertelo-rism), multiple ankyloses, pulmonary hypoplasiaand camptodactyly. Since then more than 60patients with the Pena-Shokeir sequence havebeen described.In addition to the lesions mentioned above, thefollowing signs were present in most cases: Still-birth or death during delivery or within a fewdays after birth, intrauterine growth retardation,cryptorchidism, polyhydramnios, abnormal pla-centa and short umbilical cord. Familial caseshave been reported.Major congenital malformations of inner organs,however, have been diagnosed in only a fewcases.Pena-Shokeir sequence is now regarded as a he-terogeneous sequence, in which different neuro-muscular lesions may play an important patho-genetic role.In our eight patients with the characteristic find-ings of the Pena-Shokeir sequence an attemptwas made to define more clearly the nature ofskeletal muscular changes observed

Catalytic Low-Temperature Dehydration of Fructose to 5-Hydroxymethylfurfural Using Acidic Deep Eutectic Solvents and Polyoxometalate Catalysts

HMF synthesis typically requires high temperature and is carried out in aqueous solutions. In this work, the low-temperature dehydration of fructose to HMF in different deep eutectic solvents (DES) was investigated. We found a very active and selective reaction system consisting of the DES tetraethyl ammonium chloride as hydrogen bond acceptor (HBA) and levulinic acid as hydrogen bond donor (HBD) in a molar ratio of 1:2 leading to a maximum HMF yield of 68% after 120 h at 323 K. The DES still contained a low amount of water at the initial reaction, and water was also produced during the reaction. Considering the DES properties, neither the molar ratio in the DES nor the reaction temperature had a significant influence on the overall performance of the reaction system. However, the nature of the HBA as well as the acidity of the HBD play an important role for the maximum achievable HMF yield. This was validated by measured yields in a DES with different combinations of HBD (levulinic acid and lactic acid) and HBA (choline chloride and tetra-n-alkyl ammonium chlorides). Moreover, addition of vanadium containing catalysts, especially the polyoxometalate HPA-5 (H8PV5Mo7O40) leads to drastically increased reaction kinetics. Using HPA-5 and the DES tetraethyl ammonium chloride—levulinic acid we could reach a maximum HMF yield of 57% after only 5 h reaction time without decreasing the very high product selectivity

Técnicas de predicción aplicadas al mercado español de la energía eléctrica

El presente documento presenta un estudio sobre el mercado diario español de la energía eléctrica mediante técnicas de machine learning. Para este estudio se han utilizado mínimos cuadrados, Random Forest, Máquinas de soporte vectorial y Clustering. Para realizar el estudio se han probado cada una de las técnicas en tres conjuntos de datos diferentes del año 2015. Para programar los algoritmos para predecir el precio de la energía se han utilizado Matlab y Python. Se han desarrollado una serie de librerías en dichos lenguajes. Los objetivos del proyecto son el estudio de todos estos métodos y su aplicación al mercado eléctrico.This document presents a study on the Spanish daily market electricity through machine learning techniques. For this study were used least squares, Random Forest, Support Vector Machines and Clustering. To conduct the study were tested each of the techniques in three different data sets 2015. To program algorithms to predict the price of energy have been used Matlab and Python The project objectives are the study of all these methods and their application to the electricity market.Universidad de Sevilla. Grado en Ingeniería de Tecnologías Industriale

Catalytic low-temperature dehydration of fructose to 5-hydroxymethylfurfural using acidic deep eutectic solvents and polyoxometalate catalysts

HMF synthesis typically requires high temperature and is carried out in aqueous solutions. In this work, the low-temperature dehydration of fructose to HMF in different deep eutectic solvents (DES) was investigated. We found a very active and selective reaction system consisting of the DES tetraethyl ammonium chloride as hydrogen bond acceptor (HBA) and levulinic acid as hydrogen bond donor (HBD) in a molar ratio of 1:2 leading to a maximum HMF yield of 68% after 120 h at 323 K. The DES still contained a low amount of water at the initial reaction, and water was also produced during the reaction. Considering the DES properties, neither the molar ratio in the DES nor the reaction temperature had a significant influence on the overall performance of the reaction system. However, the nature of the HBA as well as the acidity of the HBD play an important role for the maximum achievable HMF yield. This was validated by measured yields in a DES with different combinations of HBD (levulinic acid and lactic acid) and HBA (choline chloride and tetra-n-alkyl ammonium chlorides). Moreover, addition of vanadium containing catalysts, especially the polyoxometalate HPA-5 (H8PV5Mo7O40) leads to drastically increased reaction kinetics. Using HPA-5 and the DES tetraethyl ammonium chloride—levulinic acid we could reach a maximum HMF yield of 57% after only 5 h reaction time without decreasing the very high product selectivity