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Thoughts, opinions and logging

I’M SORRY (information is out-of-date… I’m now updating it slowly).


Logging, Seminars and Talks »

[3 Nov 2015 | No Comment | 39 views]

SeminarTITLE: Multiplicity results for Schrödinger-Poisson systems

LOCATION: Department of Information Engineering, Computer Science and Mathematics – University of L’Aquila [url:01]

ABSTRACT: We discuss the core of some results about the multiplicity of solutions of Schrödinger-Poisson systems of the following type

     $$ \left\{ \begin{array}{ll} -\Delta u+u+l(x)\phi u = f(x,u)  \quad & \mbox{ in } \mathbb{R}^3,\\ -\Delta \phi = l(x)u^2\quad & \mbox{ in } \mathbb{R}^3, \end{array}\right. $$

for some classes of nonlinearities f (e.g. indefinite nonlinearity or involving the critical exponent). These systems can be seen as nonlocal equations where variational methods and critical point theory may be applied. A direct method will be shown which do not involve Palais-Smale condition or the Ekeland variational principle. Special phenomena of these systems, compared with semilinear elliptic equations, will be point out. We emphasize open questions about the extension of these systems, a numerical analysis approach based on a recent reproducing kernel Hilbert and Tikhonov regularization technique, and discuss their possible applications to superconductors and nanoscience (computational chemistry).
Joint work with L. Huang and J. Chen.


Based on some papers as: (a) Nonlin. Anal. Real World Appl. 28(2016), 1-19 (to appear); (b) Libertas Math. 34:2(2014), 91-104; (c) J. Math. Anal. Appl. 408(2013), 55-69; (d) J. Differential Equations 255(2013), 2463-2483.

Logging »

[23 Oct 2015 | No Comment | 38 views]

WaterlevelAn intense week researching on Extreme Value Analysis (EVA). Extracting relevant information from big time series of water level data. Quite interesting, learning a lot – at Institute of Cybernetics, University of Tallinn.

     Classical statistics focus on the average behavior of the stochastic process (central limit theorem). On the other hand, EVA focus on extreme and rare events (Fisher-Tippett theorem). The main distribution in EVA is the so-called The GEV cumulative distribution function is given by \begin{equation*} F(x, \theta):=\left\{\begin{array}{ll} \exp\left(-\left(1+\frac{x-L}{C}S\right)^{-1/S}\right) & \mbox{ if } S\neq0,\\ \exp\left(-\exp\left(-\frac{x-L}{C}\right)\right) & \mbox{ if } S= 0, \end{array}\right. \end{equation*} where $\theta:=(L,C,S)$ is the set of three parameters: $L$ (location), $C$ (scale), $S$ (shape). Notice that, in the statistical literature, such parameters are denoted by $\mu$, $\sigma$, $\gamma$, and, in the hydrologic literature, it is common to parametrize the above distribution using instead $\bar{\gamma}=-S$ or $\alpha=-1/S$.

Logging, Other Activities »

[20 Oct 2015 | No Comment | 30 views]

Today, we published the NIM Game in the Google Play store [url:01].

  1. About the standard NIM game

NIM01Tradicionally, the NIM game is a board game for two players with quite simple rules. Starting with any number of counters distributed in any number of piles, two players take turns to remove any number of counters from a single pile. The winner is the player who takes the last counter. In figure, a stone “Nim” probably originating from Chinese Jian Shi Zi in the 15th century.

Matematically, NIM is a subject of study in Combinatorial Game Theory, for which there is a ‘winning strategy’ and all the moves can be analysed. See for example:

  • NIM-like Games [url:02]
  • Combinatorial Game Theory [url:03]
  • The Eletronic Journal of Combinatorics – Combinatorial Games [url:04]
  • Integers: Electronic Journal of Combinatorial Number Theory [url:05]
  • Journal of Combinatorial Theory [url:06]
  1. Our NIM Game for Android

The game was developed by the group Geometrix. Besides the standard features, we added the following:

  • Three variations to the standard rules: Misére, NIM21 and Fibonacci;
  • Each game can have more than 2 players (e.g. against computer players and/or other humans) in the local multiplayer mode or in the online multiplayer mode;
  • A ‘power-up’ is available which allows a player to break the adversary winning strategy (just once), based on a harmonic oscillator equation (i.e. a second order ordinary differential equation). Graphically, the power-up is implemented as a gauge with damping, oscillating in the screen for ten seconds, where the frequency and amplitude are function of the difficulty level, the number of counters in the board, etc. The player may add or remove counters with it.
  1. Our aim in developing this game

Besides the fun and mathematical interest of the NIM game by itself, we intend to use this game as a tool to research how an anonymous player deal with a combinatorial problem. In particular, we are interested in the research issues behind the understanding of building and classifying user’s learning profiles by using techniques from deep learning, linear optimization, algebra and graph theory. For such reason, we collect basic statistics about players performance and their way of playing. If you are a player, we acknowledge your valuable collaboration to this project.

Logging »

[12 Oct 2015 | No Comment | 14 views]

Six straight hours for killing a buggy centos7 server and giving life to a host and 2 vms working nicely 🙂
What’s the relevance? NIM-server and collaborative LaTeX writting are on the way…

Logging, Opinions »

[12 Oct 2015 | No Comment | 17 views]

Reading the book Algebraic Calculi for Hybrid Systems by Peter Hofner (2009), to further increase my understanding of this topic which is far from desirable. I like his introduction to the subject, which is made in a clear and well written manner. I’m quite interested in the extension of these ideas to parallel hybrid systems.

Headline, Thoughts »

[11 Oct 2015 | One Comment | 26 views]

Motivated by the (renormalization) of some classical divergent series in String Theory, e.g.

 \sum_{n=1}^{+\infty} n = -\frac{1}{12} \:\:\mbox{ (yes, it means) } 1 + 2+ 3+ 4+5+6+\dots = -\frac{1}{12}

(see here), I start thinking on the convergence meaning of a class of divergent series, trying to make sense of them without following some of the (standard) approaches as Hardy resummation or Zeta function regularization (e.g. wikipedia). The main idea was to see if it is possible to define a class of sequences and a equivalence operation, by aggregating terms, such that their “value” is determined by some constant sequence in the same equivalent class.

In the comments of this post, you see the precise notions and a preliminary result, which is quite open for discussion…