Grassmann Integral Representation for Spanning Hyperforests

Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All these results are generalizations of Kirchhoff's matrix-tree theorem. Furthermore, we show that the class of integrals describing unrooted spanning (hyper)forests is induced by a theory with an underlying OSP(1|2) supersymmetry.Comment: 50 pages, it uses some latex macros. Accepted for publication on J. Phys.

The Phase Diagram of 1-in-3 Satisfiability Problem

We study the typical case properties of the 1-in-3 satisfiability problem, the boolean satisfaction problem where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and probability of negation of a variable in a clause. Random 1-in-3 Satisfiability and Exact 3-Cover are special cases of this ensemble. We interpolate between these cases from a region where satisfiability can be typically decided for all connectivities in polynomial time to a region where deciding satisfiability is hard, in some interval of connectivities. We derive several rigorous results in the first region, and develop the one-step--replica-symmetry-breaking cavity analysis in the second one. We discuss the prediction for the transition between the almost surely satisfiable and the almost surely unsatisfiable phase, and other structural properties of the phase diagram, in light of cavity method results.Comment: 30 pages, 12 figure

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure

Spanning Forests on Random Planar Lattices

The generating function for spanning forests on a lattice is related to the q-state Potts model in a certain q -> 0 limit, and extends the analogous notion for spanning trees, or dense self-avoiding branched polymers. Recent works have found a combinatorial perturbative equivalence also with the (quadratic action) O(n) model in the limit n -> -1, the expansion parameter t counting the number of components in the forest. We give a random-matrix formulation of this model on the ensemble of degree-k random planar lattices. For k = 3, a correspondence is found with the Kostov solution of the loop-gas problem, which arise as a reformulation of the (logarithmic action) O(n) model, at n = -2. Then, we show how to perform an expansion around the t = 0 theory. In the thermodynamic limit, at any order in t we have a finite sum of finite-dimensional Cauchy integrals. The leading contribution comes from a peculiar class of terms, for which a resummation can be performed exactly.Comment: 43 pages, Dedicated to Edouard Brezin and Giorgio Parisi, on the occasion of their special birthda

NMR Studies of the Dynamic of Palmitic Acid Complexed with Chicken Liver Basic Fatty Acid-Binding Protein and Bovine beta-Lactoglobulin

NMR Studies of the Dynamic of Palmitic Acid Complexed with Chicken Liver Basic Fatty Acid-Binding Protein and Bovine beta-Lactoglobuli

Feasibility study on the assessment of auditory sustained attention through walking motor parameters in mild cognitive impairments and healthy subjects

Dementia and other cognitive disorders affect more than 35 million people worldwide. Over the last years, cognitive training tools were used to improve the brain functioning, thus to slow down the cognitive decline. Recently, research studies have demonstrated that aerobic exercise could play an important restorative role toward cognitive impairments. Therefore, the aim of this work is to present an innovative sensorized approach which combines aerobic exercise and traditional cognitive tools for daily training

Development and testing of a new cognitive technological tool for episodic memory: A feasibility study

Cognitive Rehabilitation Therapy refers to any systemic therapy specifically designed to enhance cognitive performance. Recent studies have shown that physical exercise is beneficial for cognitive activity in patients with degenerative diseases. Therefore, the objective of the present study is to provide training for cognitive functions that take advantage of the physical activity in the execution of the task. A feasibility study concerning the application of a new bioengineering technique in cognitive rehabilitation is presented and it divided into two parts. The first one aims at developing a new cognitive tool, called SmartTapestry (ST), for motor and cognitive rehabilitation. The second part aims at understanding its technical viability and its level of sensitivity in measuring the same cognitive domains covered by the standardized tests. The hypothesis of this study is that, despite the introduction of this new variable, the proposed system has the same sensitivity of the traditional tests. The results suggest a good correlation between the two approaches and that SmartTapestry can train the same cognitive functions of traditional cognitive tasks

pH and ionic strength dependence of protein (un)folding and ligand binding to bovine beta-lactoglobulins A and B

Formation of complexes between bovine beta-lactoglobulins (BLG) and long-chain fatty acids (FAs), effect of complex formation on protein stability, and effects of pH and ionic strength on both complex formation and protein stability were investigated as a function of pH and ionic strength by electrophoretic techniques and NMR spectroscopy. The stability of BLG against unfolding is sharply affected by the pH of the medium: both A and B BLG variants are maximally stabilized against urea denaturation at acidic pH and against SDS denaturation at alkaline pH. The complexes of BLGB with oleic (OA) and palmitic acid (PA) appear more stable than the apoprotein at neutral pH whereas no differential behavior is observed in acidic and alkaline media. PA forms with BLG more stable complexes than OA. The difference between the denaturant concentration able to bring about protein unfolding in the holo versus the apo forms is larger for urea than for SDS treatment. This evidence disfavors the hypothesis of strong hydrophobic interactions being involved in complex formation. Conversely, a significant contribution to FA binding by ionic interactions is demonstrated by the effect of pH and of chloride ion concentration on the stoichiometry of FA.BLG complexes. At neutral pH in a low ionic strength buffer, one molecule of FA is bound per BLG monomer; this ratio decreases to ca. 0.5 per monomer in the presence of 200 mM NaCl. The polar heads of bound FA appear to be solvent accessible, and carboxyl resonances exhibit an NMR titration curve with an apparent pK(a) of 4.7(1)

Beta-blocker choice and exchangeability in patients with heart failure and chronic obstructive pulmonary disease: an Italian register-based cohort study

Clinical guidelines suggest that for patients with heart failure and concurrent chronic obstructive pulmonary disease (COPD), metoprolol/bisoprolol/nebivolol should be preferred over carvedilol. However, studies suggest a high proportion of carvedilol usage that remains unexplained. Therefore, we aimed to investigate the predictors of carvedilol choice in patients with heart failure and COPD that were naïve to carvedilol or metoprolol/bisoprolol/nebivolol. Caserta Local Health Unit databases (Italy) were used as data sources. Age, sex, chronic/acute comorbidities, and co-medications were included in a logistic regression model to assess predictors of carvedilol choice. Chronic comorbidities include those defined in the Elixhauser comorbidity index and all hospitalizations within two years prior to the first beta-blocker prescription. Comedications include all redeemed prescriptions within one year prior to the beta-blocker prescription. Kernel density estimations were used to assess the overlap in propensity and preference scores distributions for receiving carvedilol and thereby potential beta-blocker exchangeability. Totally, 10091 patients composed the study population; 2011 were exposed to carvedilol. The overlapping of propensity scores distributions was 57%. Accordingly, the exchangeability was not reached. Atrioventricular block (Odds Ratio, OR 8.20; 95% Confidence Interval, 95% CI 1.30–51.80), cerebrovascular thrombosis (OR 7.06; 95% CI 1.14–43.68), chronic kidney disease (OR 4.32; 95% CI 1.16–16.02), and acute heart failure (OR 1.97; 95% CI 1.28–3.03) hospitalizations were statistically significantly associated with carvedilol choice. Analogously, human insulin (OR 3.00; 95% CI 1.24–7.24), fondaparinux (OR 2.47; 95% CI 1.17–5.21) or strontium ranelate (OR 2.03; 95% CI 1.06–3.90) redeemed prescriptions. In conclusion, this study suggests the absence of beta-blockers exchangeability and a preferential choice of carvedilol in patients with heart failure, COPD and concurrent chronic kidney disease, atrioventricular block, cerebrovascular thrombosis, acute heart failure or redeeming human insulin, fondaparinux or strontium ranelate prescriptions. Therefore, it suggests that choice of prescribing carvedilol over metoprolol/bisoprolol/nebivolol is driven by differences in comorbidities and co-treatments