Introduction to Dynamic Unary Encoding

Dynamic unary encoding takes unary encoding to the next level. Every n-bit binary string is an encoding of dynamic unary and every n-bit binary string is encodable by dynamic unary. By utilizing both forms of unary code and a single bit of parity information dynamic unary encoding partitions 2^n non-negative integers into n sets of disjoint cycles of n-bit elements. These cycles have been employed as virtual data sets, binary transforms and as a mathematical object. Characterization of both the cycles and of the cycle spectrum is given. Examples of encoding and decoding algorithms are given. Examples of other constructs utilizing the principles of dynamic unary encoding are presented. The cycle as a mathematical object is demonstrated.Comment: Seven pages of text, two pages of flow charts and two pages of data. Introduces an encoding scheme and a mathematical objec

Estuary and barrier island study

The author has identified the following significant results. Scan line distortion is apparent in ERTS-1 imagery, imparting a serrated-edge appearance to shorelines. This feature however does not hinder observation and interpretation of broad features such as shoaling areas and sediment plumes. Shoaling in the backshore areas and inlets is easily discernible in spectral bands 4 and 5. Contrast between land and water is especially striking in spectral band 7, allowing easy identification of tidal flat areas

Quantitative analysis of competition in post-transcriptional regulation reveals a novel signature in target expression variation

When small RNAs are loaded onto Argonaute proteins they can form the RNA-induced silencing complexes (RISCs), which mediate RNA interference. RISC-formation is dependent on a shared pool of Argonaute proteins and RISC loading factors, and is thus susceptible to competition among small RNAs for loading. We present a mathematical model that aims to understand how small RNA competition for the PTR resources affects target gene repression. We discuss that small RNA activity is limited by RISC-formation, RISC-degradation and the availability of Argonautes. Together, these observations explain a number of PTR saturation effects encountered experimentally. We show that different competition conditions for RISC-loading result in different signatures of PTR activity determined also by the amount of RISC-recycling taking place. In particular, we find that the small RNAs less efficient at RISC-formation, using fewer resources of the PTR pathway, can perform in the low RISC-recycling range equally well as their more effective counterparts. Additionally, we predict a novel signature of PTR in target expression levels. Under conditions of low RISC-loading efficiency and high RISC-recycling, the variation in target levels increases linearly with the target transcription rate. Furthermore, we show that RISC-recycling determines the effect that Argonaute scarcity conditions have on target expression variation. Our observations taken together offer a framework of predictions which can be used in order to infer from experimental data the particular characteristics of underlying PTR activity.Comment: 23 pages, 3 Figures, accepted for publication to the Biophysical Journa

Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity

We present some open problems and obtain some partial results for spectral optimization problems involving measure, torsional rigidity and first Dirichlet eigenvalue.Comment: 18 pages, 4 figure

On the torsion function with Robin or Dirichlet boundary conditions

For $p\in (1,+\infty)$ and $b \in (0, +\infty]$ the $p$-torsion function with Robin boundary conditions associated to an arbitrary open set \Om \subset \R^m satisfies formally the equation $-\Delta_p =1$ in \Om and $|\nabla u|^{p-2} \frac{\partial u}{\partial n} + b|u|^{p-2} u =0$ on \partial \Om. We obtain bounds of the $L^\infty$ norm of $u$ {\it only} in terms of the bottom of the spectrum (of the Robin $p$-Laplacian), $b$ and the dimension of the space in the following two extremal cases: the linear framework (corresponding to $p=2$) and arbitrary $b>0$, and the non-linear framework (corresponding to arbitrary $p>1$) and Dirichlet boundary conditions ($b=+\infty$). In the general case, $p\not=2, p \in (1, +\infty)$ and $b>0$ our bounds involve also the Lebesgue measure of \Om.Comment: 19 page

Totalitarianism and geography: L.S. Berg and the defence of an academic discipline in the age of Stalin

In considering the complex relationship between science and politics, the article focuses upon the career of the eminent Russian scholar, Lev Semenovich Berg (1876–1950), one of the leading geographers of the Stalin period. Already before the Russian Revolution, Berg had developed a naturalistic notion of landscape geography which later appeared to contradict some aspects of Marxist–Leninist ideology. Based partly upon Berg's personal archive, the article discusses the effects of the 1917 revolution, the radical changes which Stalin's cultural revolution (from the late 1920s) brought upon Soviet science, and the attacks made upon Berg and his concept of landscape geography thereafter. The ways in which Berg managed to defend his notion of geography (sometimes in surprisingly bold ways) are considered. It is argued that geography's position under Stalin was different from that of certain other disciplines in that its ideological disputes may have been regarded as of little significance by the party leaders, certainly by comparison with its practical importance, thus providing a degree of ‘freedom’ for some geographers at least analogous to that which has been described by Weiner (1999. A little corner of freedom: Russian nature protection from Stalin to Gorbachev. Berkeley: University of California Press) for conservationists. It is concluded that Berg and others successfully upheld a concept of scientific integrity and limited autonomy even under Stalinism, and that, in an era of ‘Big Science’, no modernizing state could or can afford to emasculate these things entirely

Form-factors of exponential fields in the sine-Gordon model

An integral representation for form-factors of exponential fields in the sine-Gordon model is proposed.Comment: 8 pages, harvmac.tex, added the formula (25) for two soliton form-factors at the reflectionless point