Information-Based Physics: An Observer-Centric Foundation

It is generally believed that physical laws, reflecting an inherent order in the universe, are ordained by nature. However, in modern physics the observer plays a central role raising questions about how an observer-centric physics can result in laws apparently worthy of a universal nature-centric physics. Over the last decade, we have found that the consistent apt quantification of algebraic and order-theoretic structures results in calculi that possess constraint equations taking the form of what are often considered to be physical laws. I review recent derivations of the formal relations among relevant variables central to special relativity, probability theory and quantum mechanics in this context by considering a problem where two observers form consistent descriptions of and make optimal inferences about a free particle that simply influences them. I show that this approach to describing such a particle based only on available information leads to the mathematics of relativistic quantum mechanics as well as a description of a free particle that reproduces many of the basic properties of a fermion. The result is an approach to foundational physics where laws derive from both consistent descriptions and optimal information-based inferences made by embedded observers.Comment: To be published in Contemporary Physics. The manuscript consists of 43 pages and 9 Figure

On the π\pi and KK as qqˉq \bar q Bound States and Approximate Nambu-Goldstone Bosons

We reconsider the two different facets of $\pi$ and $K$ mesons as $q \bar q$ bound states and approximate Nambu-Goldstone bosons. We address several topics, including masses, mass splittings between $\pi$ and $\rho$ and between $K$ and $K^*$, meson wavefunctions, charge radii, and the $K-\pi$ wavefunction overlap.Comment: 15 pages, late

Run Generation Revisited: What Goes Up May or May Not Come Down

In this paper, we revisit the classic problem of run generation. Run generation is the first phase of external-memory sorting, where the objective is to scan through the data, reorder elements using a small buffer of size M , and output runs (contiguously sorted chunks of elements) that are as long as possible. We develop algorithms for minimizing the total number of runs (or equivalently, maximizing the average run length) when the runs are allowed to be sorted or reverse sorted. We study the problem in the online setting, both with and without resource augmentation, and in the offline setting. (1) We analyze alternating-up-down replacement selection (runs alternate between sorted and reverse sorted), which was studied by Knuth as far back as 1963. We show that this simple policy is asymptotically optimal. Specifically, we show that alternating-up-down replacement selection is 2-competitive and no deterministic online algorithm can perform better. (2) We give online algorithms having smaller competitive ratios with resource augmentation. Specifically, we exhibit a deterministic algorithm that, when given a buffer of size 4M , is able to match or beat any optimal algorithm having a buffer of size M . Furthermore, we present a randomized online algorithm which is 7/4-competitive when given a buffer twice that of the optimal. (3) We demonstrate that performance can also be improved with a small amount of foresight. We give an algorithm, which is 3/2-competitive, with foreknowledge of the next 3M elements of the input stream. For the extreme case where all future elements are known, we design a PTAS for computing the optimal strategy a run generation algorithm must follow. (4) Finally, we present algorithms tailored for nearly sorted inputs which are guaranteed to have optimal solutions with sufficiently long runs

Systemtherapie des kolorektalen Karzinoms

Zusammenfassung: Die medikamentöse Behandlung des kolorektalen Karzinoms hat in den letzten 10Jahren eindrückliche Fortschritte gemacht. Neben dem altbewährten 5-Fluorouracil stehen heute neue Zytostatika zur Verfügung wie Irinotecan und Oxaliplatin. Monoklonale Antikörper wie Bevacizumab und Cetuximab haben erfolgreich Eingang in aktuelle Therapiestrategien gefunden. Auf der Basis randomisierter klinischer Studien lassen sich heute rationale Therapiestrategien formulieren, wie in diesem Beitrag dargestell

An O(M(n) log n) algorithm for the Jacobi symbol

The best known algorithm to compute the Jacobi symbol of two n-bit integers runs in time O(M(n) log n), using Sch\"onhage's fast continued fraction algorithm combined with an identity due to Gauss. We give a different O(M(n) log n) algorithm based on the binary recursive gcd algorithm of Stehl\'e and Zimmermann. Our implementation - which to our knowledge is the first to run in time O(M(n) log n) - is faster than GMP's quadratic implementation for inputs larger than about 10000 decimal digits.Comment: Submitted to ANTS IX (Nancy, July 2010

Map equation for link community

Community structure exists in many real-world networks and has been reported being related to several functional properties of the networks. The conventional approach was partitioning nodes into communities, while some recent studies start partitioning links instead of nodes to find overlapping communities of nodes efficiently. We extended the map equation method, which was originally developed for node communities, to find link communities in networks. This method is tested on various kinds of networks and compared with the metadata of the networks, and the results show that our method can identify the overlapping role of nodes effectively. The advantage of this method is that the node community scheme and link community scheme can be compared quantitatively by measuring the unknown information left in the networks besides the community structure. It can be used to decide quantitatively whether or not the link community scheme should be used instead of the node community scheme. Furthermore, this method can be easily extended to the directed and weighted networks since it is based on the random walk.Comment: 9 pages,5 figure

Noncooperative algorithms in self-assembly

We show the first non-trivial positive algorithmic results (i.e. programs whose output is larger than their size), in a model of self-assembly that has so far resisted many attempts of formal analysis or programming: the planar non-cooperative variant of Winfree's abstract Tile Assembly Model. This model has been the center of several open problems and conjectures in the last fifteen years, and the first fully general results on its computational power were only proven recently (SODA 2014). These results, as well as ours, exemplify the intricate connections between computation and geometry that can occur in self-assembly. In this model, tiles can stick to an existing assembly as soon as one of their sides matches the existing assembly. This feature contrasts with the general cooperative model, where it can be required that tiles match on \emph{several} of their sides in order to bind. In order to describe our algorithms, we also introduce a generalization of regular expressions called Baggins expressions. Finally, we compare this model to other automata-theoretic models.Comment: A few bug fixes and typo correction

Revealing Relationships among Relevant Climate Variables with Information Theory

A primary objective of the NASA Earth-Sun Exploration Technology Office is to understand the observed Earth climate variability, thus enabling the determination and prediction of the climate's response to both natural and human-induced forcing. We are currently developing a suite of computational tools that will allow researchers to calculate, from data, a variety of information-theoretic quantities such as mutual information, which can be used to identify relationships among climate variables, and transfer entropy, which indicates the possibility of causal interactions. Our tools estimate these quantities along with their associated error bars, the latter of which is critical for describing the degree of uncertainty in the estimates. This work is based upon optimal binning techniques that we have developed for piecewise-constant, histogram-style models of the underlying density functions. Two useful side benefits have already been discovered. The first allows a researcher to determine whether there exist sufficient data to estimate the underlying probability density. The second permits one to determine an acceptable degree of round-off when compressing data for efficient transfer and storage. We also demonstrate how mutual information and transfer entropy can be applied so as to allow researchers not only to identify relations among climate variables, but also to characterize and quantify their possible causal interactions.Comment: 14 pages, 5 figures, Proceedings of the Earth-Sun System Technology Conference (ESTC 2005), Adelphi, M

Guessing probability distributions from small samples

We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution $p(k)$ of the elements $k$ of a population can be approximated by the frequencies $f(k)$ of a sample provided the sample is long enough so that each element $k$ occurs many times. Our method yields an approximation if this precondition does not hold. For a given $f(k)$ we recalculate the Zipf--ordered probability distribution by optimization of the parameters of a guessed distribution. We demonstrate that our method yields reliable results.Comment: 10 pages, uuencoded compressed PostScrip