Abstract:
We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Function. The validity of the method is tested using Harmonic Oscillator, Morse Potential and Dikie’s Model as example, we found a good accuracy in the classical limit.

Abstract:
In the first and second parts of his masterpiece, Analytical Mechanics, dedicated to static and dynamics respectively, Lagrange (1736-1813) describes in detail the development of both branches of mechanics from a historical point of view. In this paper this important contribution of Lagrange (Lagrange, 1989) to the history of mechanics is presented and discussed in tribute to the bicentennial year of his death.

Abstract:
One of the aims most sought after by physics along the years has been to find a principle, the simplest possible, into which all natural phenomena would fit, and which would also allow the calculation of all past occurrences and principally future occurrences. Evidently, this is far from being reached and quite probably does not even exist. Nevertheless, an approximation to this ideal is always possible and the history of physics shows that some results in this direction have been achieved. Thus, the history of the principles of least action and conservation of energy presented in this paper explains the search for this ideal.

Abstract:
We prove that the family of embezzlement states defined by van Dam and Hayden [vanDamHayden2002] is universal for both quantum and classical entangled two-prover non-local games with an arbitrary number of rounds. More precisely, we show that for each $\epsilon>0$ and each strategy for a k-round two-prover non-local game which uses a bipartite shared state on 2m qubits and makes the provers win with probability $\omega$, there exists a strategy for the same game which uses an embezzlement state on $2m + 2m/\epsilon$ qubits and makes the provers win with probability $\omega-\sqrt{2\epsilon}$. Since the value of a game can be defined as the limit of the value of a maximal 2m-qubit strategy as m goes to infinity, our result implies that the classes QMIP*_{c,s}[2,k] and MIP*_{c,s}[2,k] remain invariant if we allow the provers to share only embezzlement states, for any completeness value c in [0,1] and any soundness value s < c. Finally we notice that the circuits applied by each prover may be put into a very simple universal form.

Abstract:
In a previous work we introduced slice graphs as a way to specify both infinite languages of directed acyclic graphs (DAGs) and infinite languages of partial orders. Therein we focused on the study of Hasse diagram generators, i.e., slice graphs that generate only transitive reduced DAGs, and showed that they could be used to solve several problems related to the partial order behavior of p/t-nets. In the present work we show that both slice graphs and Hasse diagram generators are worth studying on their own. First, we prove that any slice graph SG can be effectively transformed into a Hasse diagram generator HG representing the same set of partial orders. Thus from an algorithmic standpoint we introduce a method of transitive reducing infinite families of DAGs specified by slice graphs. Second, we identify the class of saturated slice graphs. By using our transitive reduction algorithm, we prove that the class of partial order languages representable by saturated slice graphs is closed under union, intersection and even under a suitable notion of complementation (cut-width complementation). Furthermore partial order languages belonging to this class can be tested for inclusion and admit canonical representatives in terms of Hasse diagram generators. As an application of our results, we give stronger forms of some results in our previous work, and establish some unknown connections between the partial order behavior of $p/t$-nets and other well known formalisms for the specification of infinite families of partial orders, such as Mazurkiewicz trace languages and message sequence chart (MSC) languages.

Abstract:
We introduce the notion of z-topological orderings for digraphs. We prove that given a digraph G on n vertices admitting a z-topological order- ing, together with such an ordering, one may count the number of subgraphs of G that at the same time satisfy a monadic second order formula {\phi} and are the union of k directed paths, in time f ({\phi}, k, z) * n^O(k*z) . Our result implies the polynomial time solvability of many natural counting problems on digraphs admitting z-topological orderings for constant values of z and k. Concerning the relationship between z-topological orderability and other digraph width measures, we observe that any digraph of directed path-width d has a z- topological ordering for z <= 2d + 1. On the other hand, there are digraphs on n vertices admitting a z-topological order for z = 2, but whose directed path-width is {\Theta}(log n). Since graphs of bounded directed path-width can have both arbitrarily large undirected tree-width and arbitrarily large clique width, our result provides for the first time a suitable way of partially trans- posing metatheorems developed in the context of the monadic second order logic of graphs of constant undirected tree-width and constant clique width to the realm of digraph width measures that are closed under taking subgraphs and whose constant levels incorporate families of graphs of arbitrarily large undirected tree-width and arbitrarily large clique width.

Abstract:
In this work we provide algorithmic solutions to five fundamental problems concerning the verification, synthesis and correction of concurrent systems that can be modeled by bounded p/t-nets. We express concurrency via partial orders and assume that behavioral specifications are given via monadic second order logic. A c-partial-order is a partial order whose Hasse diagram can be covered by c paths. For a finite set T of transitions, we let P(c,T,\phi) denote the set of all T-labelled c-partial-orders satisfying \phi. If N=(P,T) is a p/t-net we let P(N,c) denote the set of all c-partially-ordered runs of N. A (b, r)-bounded p/t-net is a b-bounded p/t-net in which each place appears repeated at most r times. We solve the following problems: 1. Verification: given an MSO formula \phi and a bounded p/t-net N determine whether P(N,c)\subseteq P(c,T,\phi), whether P(c,T,\phi)\subseteq P(N,c), or whether P(N,c)\cap P(c,T,\phi)=\emptyset. 2. Synthesis from MSO Specifications: given an MSO formula \phi, synthesize a semantically minimal (b,r)-bounded p/t-net N satisfying P(c,T,\phi)\subseteq P(N, c). 3. Semantically Safest Subsystem: given an MSO formula \phi defining a set of safe partial orders, and a b-bounded p/t-net N, possibly containing unsafe behaviors, synthesize the safest (b,r)-bounded p/t-net N' whose behavior lies in between P(N,c)\cap P(c,T,\phi) and P(N,c). 4. Behavioral Repair: given two MSO formulas \phi and \psi, and a b-bounded p/t-net N, synthesize a semantically minimal (b,r)-bounded p/t net N' whose behavior lies in between P(N,c) \cap P(c,T,\phi) and P(c,T,\psi). 5. Synthesis from Contracts: given an MSO formula \phi^yes specifying a set of good behaviors and an MSO formula \phi^no specifying a set of bad behaviors, synthesize a semantically minimal (b,r)-bounded p/t-net N such that P(c,T,\phi^yes) \subseteq P(N,c) but P(c,T,\phi^no ) \cap P(N,c)=\emptyset.

Abstract:
The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some NP-complete properties such as Hamiltonicity can be decided in polynomial time on digraphs of constant directed treewidth. Nevertheless, despite more than one decade of intensive research, the list of hard combinatorial problems that are known to be solvable in polynomial time when restricted to digraphs of constant directed treewidth has remained scarce. In this work we enrich this list by providing for the first time an algorithmic metatheorem connecting the monadic second order logic of graphs to directed treewidth. We show that most of the known positive algorithmic results for digraphs of constant directed treewidth can be reformulated in terms of our metatheorem. Additionally, we show how to use our metatheorem to provide polynomial time algorithms for two classes of combinatorial problems that have not yet been studied in the context of directed width measures. More precisely, for each fixed $k,w \in \mathbb{N}$, we show how to count in polynomial time on digraphs of directed treewidth $w$, the number of minimum spanning strong subgraphs that are the union of $k$ directed paths, and the number of maximal subgraphs that are the union of $k$ directed paths and satisfy a given minor closed property. To prove our metatheorem we devise two technical tools which we believe to be of independent interest. First, we introduce the notion of tree-zig-zag number of a digraph, a new directed width measure that is at most a constant times directed treewidth. Second, we introduce the notion of $z$-saturated tree slice language, a new formalism for the specification and manipulation of infinite sets of digraphs.

Abstract:
It has been known since long time that many NP-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results to the quantum setting. We show that given a quantum circuit $C$ with $n$ uninitialized inputs, $poly(n)$ gates and treewidth $t$, one can compute in time $(\frac{n}{\delta})^{\exp(O(t))}$ a classical witness $y\in \{0,1\}^n$ that maximizes the acceptance probability of $C$ up to a $\delta$ additive factor. In particular our algorithm runs in polynomial time if $t$ is constant and $1/poly(n) \leq \delta < 1$. For unrestricted values of $t$ this problem is known to be hard for the complexity class QCMA, a quantum generalization of NP. In contrast, we show that the same problem is already NP-hard if $t=O(\log n)$ even when $\delta$ is constant. Finally, we show that for $t=O(\log n)$ and constant $\delta$, it is QMA-hard to find a quantum witness $\ket{\varphi}$ that maximizes the acceptance probability of a quantum circuit of treewidth $t$ up to a $\delta$ additive factor.

Abstract:
As elevated triglyceride (TG) to high-density
lipoprotein cholesterol (HDL-C) ratio has been described as predictor for
cardio metabolic disease with insulin resistance (IR) in the background,
the aim was to assess the relationship between this ratio and IR in youth. Oral glucose tolerance test
was performed in 318 Brazilian students (175 girls, 11.2 ± 3.2 years,
BMI_z-score 1.2 ± 1.4 SD). Measurements: BMI, waist circumference (WC), blood
pressure (BP), lipids, insulin and high
sensitivity Creactive protein (hsCRP). Excessive weight and abdominal
obesity were defined using BMI_z-score and WC and IR by Homeostasis model assessment-insulin
resistance (HOMA-IR). TG/HDL-C
median was 2.37. There was an association between TG/ HDL-C and WC, systolic
and diastolic BP, insulin, HOMA-IR, hsCRP, (p < 0.001). Stratified TG/HDL-C
into two groups, based on a cut off point of 2.73 (Group 1: <2.73 and Group
2: ≥2.73). Ad- justing for age, gender, ethnicity TG/HDL-C was an independent
variable predicting IR (PR = 1.44; CI: 1.07 - 1.96; p = 0.018). For every 1 (cm)
in WC increased there was an addition of 0.04 of the value of TG/HDL-C and in
those with TG/HDL-C ≥ 2.73 for every 10 (cm) increase in WC there was an
improve of 4% in the ratio. In conclusion: In youth, the TG/HDL-C ratio could be a useful index for identifying
groups with IR.