Bayes Complexity of Learners vs Overfitting

We introduce a new notion of complexity of functions and we show that it has the following properties: (i) it governs a PAC Bayes-like generalization bound, (ii) for neural networks it relates to natural notions of complexity of functions (such as the variation), and (iii) it explains the generalization gap between neural networks and linear schemes. While there is a large set of papers which describes bounds that have each such property in isolation, and even some that have two, as far as we know, this is a first notion that satisfies all three of them. Moreover, in contrast to previous works, our notion naturally generalizes to neural networks with several layers. Even though the computation of our complexity is nontrivial in general, an upper-bound is often easy to derive, even for higher number of layers and functions with structure, such as period functions. An upper-bound we derive allows to show a separation in the number of samples needed for good generalization between 2 and 4-layer neural networks for periodic functions

Nonlocality under Computational Assumptions

Nonlocality and its connections to entanglement are fundamental features of quantum mechanics that have found numerous applications in quantum information science. A set of correlations is said to be nonlocal if it cannot be reproduced by spacelike-separated parties sharing randomness and performing local operations. An important practical consideration is that the runtime of the parties has to be shorter than the time it takes light to travel between them. One way to model this restriction is to assume that the parties are computationally bounded. We therefore initiate the study of nonlocality under computational assumptions and derive the following results: (a) We define the set $\mathsf{NeL}$ (not-efficiently-local) as consisting of all bipartite states whose correlations arising from local measurements cannot be reproduced with shared randomness and \emph{polynomial-time} local operations. (b) Under the assumption that the Learning With Errors problem cannot be solved in \emph{quantum} polynomial-time, we show that $\mathsf{NeL}=\mathsf{ENT}$, where $\mathsf{ENT}$ is the set of \emph{all} bipartite entangled states (pure and mixed). This is in contrast to the standard notion of nonlocality where it is known that some entangled states, e.g. Werner states, are local. In essence, we show that there exist (efficient) local measurements producing correlations that cannot be reproduced through shared randomness and quantum polynomial-time computation. (c) We prove that if $\mathsf{NeL}=\mathsf{ENT}$ unconditionally, then $\mathsf{BQP}\neq\mathsf{PP}$. In other words, the ability to certify all bipartite entangled states against computationally bounded adversaries gives a non-trivial separation of complexity classes. (d) Using (c), we show that a certain natural class of 1-round delegated quantum computation protocols that are sound against $\mathsf{PP}$ provers cannot exist.Comment: 65 page

Potentiation of adipogenesis and insulinomimetic effects of novel vanadium complex (N'-[(E)-(5-bromo-2-oxophenyl)methylidene]-4-methoxybenzohydrazide)oxido(1,10-phenanthroline)vanadium(IV) in 3T3-L1 cells

Recent research on the action of vanadium compounds shows its important effect on adipogenesis processes and adipocyte function. On the basis of previous screening tests in cellular models, the novel vanadium complex (N′-[(E)-(5-bromo-2-oxophenyl)methylidene]4-methoxybenzohydrazide)oxido(1,10-phenanthroline)vanadium(IV) was selected for this study. This complex exhibits potent inhibition of tyrosine phosphatases, and differences in the degree of inhibition were observed particularly for phosphatases. A significant increase in intracellular lipid accumulation and proliferative effect on 3T3-L1 preadipocytes confirmed the ability of this complex to enhance adipogenesis. The insulinomimetic activity of the tested complex was also demonstrated in fully differentiated 3T3-L1 adipocytes, in which glucose utilization was potentiated. The obtained results support the hypothesis that vanadium complexes show promising possibilities for use as new therapeutic strategies for the treatment of type 2 diabetes

Tridentate hydrazido-hydrazones vanadium complexes : synthesis, properties and biological activity

Nine new vanadium complexes, with tridentate Schiff base ligand based on 3,5-di-tertbutyl-2-hydroxybenzaldehyde and different hydrazides, are described and characterized. The X-ray crystal structure of complex 8 shows distorted octahedral geometry of vanadium, with ONO ligand in equatorial position. The tridentate Schiff base ligand forms six membered and five-membered chelate rings at the V(V) acceptor center, with the corresponding bite angles being 82.97(9)˚ and 74.48(9)˚. The molecules are gathered by means of intermolecular OH...N hydrogen bond and layered by π...π interactions involving the pyridine and phenolate rings. Such interactions expand the structure along the crystallographic a axis. The complexes were characterized by the elemental analyses, IR, UV-Vis, EPR spectroscopy, cyclic voltammetry, thermogravimetry and magnetic susceptibility measurements. The stabilization role of co-ligands is discussed. The cytotoxicity versus HepG2 hepatocytes and inhibition of human recombinant PTP1B was studied

A comparison of the anorectic effect and safety of the alpha_{2}-adrenoceptor ligands guanfacine and yohimbine in rats with diet-induced obesity

The search for drugs with anorectic activity, acting within the adrenergic system has attracted the interest of researchers. Partial α2-adrenoceptor agonists might offer the potential for effective and safe treatment of obesity. We compared the effectiveness and safety of α2-adrenoceptor ligands in reducing body mass. We also analyzed if antagonist and partial agonists of α2-adrenoceptor--yohimbine and guanfacine--act similarly, and determined which course of action is connected with anorectic activity. We tested intrinsic activity and effect on the lipolysis of these compounds in cell cultures, evaluated their effect on meal size, body weight in Wistar rats with high-fat diet-induced obesity, and determined their effect on blood pressure, heart rate, lipid profile, spontaneous locomotor activity, core temperature and glucose, as well as glycerol and cortisol levels. Both guanfacine and yohimbine showed anorectic activity. Guanfacine was much more effective than yohimbine. Both significantly reduced the amount of intraperitoneal adipose tissue and had a beneficial effect on lipid profiles. Decreased response of α2A-adrenoceptors and partial stimulation of α2B-receptors seem to be responsible for the anorectic action of guanfacine. The stimulation of α1-adrenoceptors by guanfacine is responsible for cardiovascular side effects but may also be linked with improved anorexic effect. α1-adrenoceptor blockade is connected with the side effects of yohimbine, but it is also associated with the improvement of lipid profiles. Guanfacine has been approved by the Food and Drug Administration (FDA) to treat hypertension and conduct disorder, but as it reduces body weight, it is worth examining its effectiveness and safety in models of obesity