Models of genetic drift as limiting forms of the Lotka-Volterra competition model

The relationship between the Moran model and stochastic Lotka-Volterra competition (SLVC) model is explored via timescale separation arguments. For neutral systems the two are found to be equivalent at long times. For systems with selective pressure, their behavior differs. It is argued that the SLVC is preferable to the Moran model since in the SLVC population size is regulated by competition, rather than arbitrarily fixed as in the Moran model. As a consequence, ambiguities found in the Moran model associated with the introduction of more complex processes, such as selection, are avoided.Comment: 5 pages, 4 figure

It goes with the territory: Ownership across spatial boundaries.

Previous studies have shown that people are faster to process objects that they own as compared with objects that other people own. Yet object ownership is embedded within a social environment that has distinct and sometimes competing rules for interaction. Here we ask whether ownership of space can act as a filter through which we process what belongs to us. Can a sense of territory modulate the well-established benefits in information processing that owned objects enjoy? In 4 experiments participants categorized their own or another person’s objects that appeared in territories assigned either to themselves or to another. We consistently found that faster processing of self-owned than other-owned objects only emerged for objects appearing in the self-territory, with no such advantage in other territories. We propose that knowing whom spaces belong to may serve to define the space in which affordances resulting from ownership lead to facilitated processing

A perspective on the mechanism of the light-rise of the electro-oculogram

The light-rise of the electro-oculogram is believed to originate from a substance released from the rods after dark adaptation. The identity of this 'elusive' light-rise substance has not been demonstrated and therefore a new perspective on the light-rise is presented. The light-rise is caused by the depolarization of the basolateral membrane of the retinal pigment epithelium has become clearer in the last decade with the identification of calcium as the intracellular secondary messenger and the role of bestrophin as a regulator of intracellular stores of calcium and controlling the cytosolic calcium levels through L-type calcium channels. The light-rise depends upon a change from darkness to light which triggers the intracellular cascade resulting in the depolarization of the basolateral membrane. The same intracellular signalling molecules- notably calcium and inositol tri-phosphate (IP3) are strongly implicated in this cascade. Recent studies have now led to a clearer understanding of the roles and functions of the ion channels and their contribution to the light-rise with IP3 regulating the release of calcium for intracellular stores. Given that calcium and IP3 are also regulators of phagocytosis, and that the initiation of rod outer segment phagocytosis is initiated with light-onset, it may be that the light-rise is generated in response to this physiological event. Therefore, the putative light-rise substance may not be released by the rods but follows directly from IP3 release from the RPE's phospholipid membrane following the onset of light and the initiation of phagocytosis- The light rise substance, could be considered to be light itself

Kronecker\u27s Theory of Binary Bilinear Forms with Applications to Representations of Integers as Sums of Three Squares

In 1883 Leopold Kronecker published a paper containing “a few explanatory remarks” to an earlier paper of his from 1866. His work loosely connected the theory of integral binary bilinear forms to the theory of integral binary quadratic forms. In this dissertation we discover the statements within Kronecker\u27s paper and offer detailed arithmetic proofs. We begin by developing the theory of binary bilinear forms and their automorphs, providing a classification of integral binary bilinear forms up to equivalence, proper equivalence and complete equivalence. In the second chapter we introduce the class number, proper class number and complete class number as well as two refinements, which facilitate the development of a connection with binary quadratic forms. Our third chapter is devoted to deriving several class number formulas in terms of divisors of the determinant. This chapter also contains lower bounds on the class number for bilinear forms and classifies when these bounds are attained. Lastly, we use the class number formulas to rigorously develop Kronecker\u27s connection between binary bilinear forms and binary quadratic forms. We supply purely arithmetic proofs of five results stated but not proven in the original paper. We conclude by giving an application of this material to the number of representations of an integer as a sum of three squares and show the resulting formula is equivalent to the well-known result due to Gauss

The surprising lability of bis(2,2’:6’,2’’-terpyridine)- chromium(III) complexes

The complex [Cr(tpy)(O3SCF3)3] (tpy = 2,2′:6′,2′′-terpyridine) is readily made from [Cr(tpy)Cl3] and is a convenient precursor to [Cr(tpy)2][PF6]3 and to [Cr(tpy)(4′-(4-tolyl)tpy)][PF6]3 and [Cr(tpy)(5,5′′-Me2tpy)][PF6]3 (4′-(4-tolyl)tpy = 4′-(4-tolyl)-2,2′:6′,2′′-terpyridine; 5,5′′-Me2tpy = 5,5′′-dimethyl-2,2′:6′,2′′-terpyridine); these are the first examples of heteroleptic bis(tpy) chromium(III) complexes. The single crystal structures of 2{[Cr(tpy)2][PF6]3}·5MeCN, [Cr(tpy)(4′-(4-tolyl)tpy)][PF6]3·3MeCN and [Cr(tpy)(5,5′′-Me2tpy)][PF6]3·3MeCN have been determined. Each cation contains the expected octahedral {Cr(tpy)2}3+ unit; in all three structures, the need to accommodate three anions per cation and the solvent molecules prevents the formation of a grid-like array of cations that is typical of many lattices containing {M(tpy)2}2+ motifs. Three reversible electrochemical processes are observed for [Cr(tpy)(4′-(4-tolyl)tpy)][PF6]3 and [Cr(tpy)(5,5′′-Me2tpy)][PF6]3, consistent with those documented for [Cr(tpy)2]3+. At pH 6.36, aqueous solutions of [Cr(tpy)2][PF6]3 are stable for at least two months. However, contrary to the expectations of the d3 Cr3+ ion being a kinetically inert metal centre, the tpy ligands in [Cr(tpy)2]3+are labile in the presence of base; absorption and 1H NMR spectroscopies have been used to monitor the effects of adding NaOH to aqueous and CD3OD solutions, respectively, of the homo- and heteroleptic complexes. Ligand dissociation is also observed when [Bu4N]F is added to CD3OD solutions of the complexes, but in aqueous solution, [Cr(tpy)2][PF6]3 is stable in the presence of fluoride ion

Decay Modes of Unstable Strings in Plane-Wave String Field Theory

The cubic interaction vertex of light-cone string field theory in the plane-wave background has a simple effective form when considering states with only bosonic excitations. This simple effective interaction vertex is used in this paper to calculate the three string interaction matrix elements for states of arbitrary bosonic excitation and these results are used to examine certain decay modes on the mass-shell. It is shown that the matrix elements of one string to two string decays involving only bosonic excitations will vanish to all orders in 1/mu on the mass-shell when the number of excitations on the initial string is less than or equal to two, but in general will not vanish when the number of excitations is greater than two. Also, a truncated calculation of the mass-shell matrix elements for one string to three string decays of two excitation states is performed and suggests that these matrix elements do not vanish on the mass-shell. There is, however, a quantitative discrepancy between this last result and its (also non-vanishing) gauge theory prediction from the BMN correspondence.Comment: 11 pages; v2: references added; v3: normalization of interaction vertex and corresponding amplitudes changed by a factor of mu to reflect SFT normalization (must now divide by mu to compare with BMN dual gauge theory), and minor errors correcte

BMN operators and string field theory

We extract from gauge theoretical calculations the matrix elements of the SYM dilatation operator. By the BMN correspondence this should coincide with the 3-string vertex of light cone string field theory in the pp-wave background. We find a mild but important discrepancy with the SFT results. If the modified $O(g_2)$ matrix elements are used, the $O(g_2^2)$ anomalous dimensions are exactly reproduced without the need for a contact interaction in the single string sector.Comment: 11 pages; v2: references adde

Strong Evidence In Favor OF The Existence Of S-Matrix For Strings In Plane Waves

Field theories on the plane wave background are considered. We discuss that for such field theories one can only form 1+1 dimensional freely propagating wave packets. We analyze tree level four point functions of scalar field theory as well as scalars coupled to gauge fields in detail and show that these four point functions are well-behaved so that they can be interpreted as S-matrix elements for 2 particle $\to$ 2 particle scattering amplitudes. Therefore, at least classically, field theories on the plane wave background have S-matrix formulation.Comment: Latex file, 26 pages, 4 eps figures. v3: In the end of paper there is a "Note Added" as an update of the result

Complexation of lanthanides, actinides and transition metal cations with a 6-(1,2,4-triazin-3-yl)-2,2’:6’,2’’-terpyridine ligand: implications for actinide(III) /lanthanide(III) partitioning

The quadridentate N-heterocyclic ligand 6-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin-3-yl)-2,2’:6’,2’’-terpyridine (CyMe4-hemi-BTBP) has been synthesized and its interactions with Am(III), U(VI), Ln(III) and some transition metal cations have been evaluated by X-ray crystallographic analysis, Am(III)/Eu(III) solvent extraction experiments, UV absorption spectrophotometry, NMR studies and ESI-MS. Structures of the 1:1 complexes with Eu(III), Ce(III) and the linear uranyl (UO22+) ion were obtained by X-ray crystallographic analysis, and showed similar coordination behavior to related BTBP complexes. In methanol, the stability constants of the Ln(III) complexes are slightly lower than those of the analogous quadridentate bis-triazine BTBP ligands, while the stability constant for the Yb(III) complex is higher. 1H NMR titrations and ESI-MS with lanthanide nitrates showed that the ligand forms only 1:1 complexes with Eu(III), Ce(III) and Yb(III), while both 1:1 and 1:2 complexes were formed with La(III) and Y(III) in acetonitrile. A mixture of isomeric chiral 2:2 helical complexes was formed with Cu(I), with a slight preference (1.4:1) for a single directional isomer. In contrast, a 1:1 complex was observed with the larger Ag(I) ion. The ligand was unable to extract Am(III) or Eu(III) from nitric acid solutions into 1-octanol, except in the presence of a synergist at low acidity. The results show that the presence of two outer 1,2,4-triazine rings is required for the efficient extraction and separation of An(III) from Ln(III) by quadridentate N-donor ligand