Dynamical modeling of collective behavior from pigeon flight data: flock cohesion and dispersion

Several models of flocking have been promoted based on simulations with qualitatively naturalistic behavior. In this paper we provide the first direct application of computational modeling methods to infer flocking behavior from experimental field data. We show that this approach is able to infer general rules for interaction, or lack of interaction, among members of a flock or, more generally, any community. Using experimental field measurements of homing pigeons in flight we demonstrate the existence of a basic distance dependent attraction/repulsion relationship and show that this rule is sufficient to explain collective behavior observed in nature. Positional data of individuals over time are used as input data to a computational algorithm capable of building complex nonlinear functions that can represent the system behavior. Topological nearest neighbor interactions are considered to characterize the components within this model. The efficacy of this method is demonstrated with simulated noisy data generated from the classical (two dimensional) Vicsek model. When applied to experimental data from homing pigeon flights we show that the more complex three dimensional models are capable of predicting and simulating trajectories, as well as exhibiting realistic collective dynamics. The simulations of the reconstructed models are used to extract properties of the collective behavior in pigeons, and how it is affected by changing the initial conditions of the system. Our results demonstrate that this approach may be applied to construct models capable of simulating trajectories and collective dynamics using experimental field measurements of herd movement. From these models, the behavior of the individual agents (animals) may be inferred

Equivariant cohomology and analytic descriptions of ring isomorphisms

In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a $G$-manifold in terms of algebra, so that we can obtain analytic descriptions of ring isomorphisms among equivariant cohomology rings of such $G$-manifolds, and a necessary and sufficient condition that the equivariant cohomology rings of such two $G$-manifolds are isomorphic. This also leads us to analyze how many there are equivariant cohomology rings up to isomorphism for such $G$-manifolds in 2- and 3-dimensional cases.Comment: 20 pages, updated version with two references adde

Multiple solutions to a magnetic nonlinear Choquard equation

We consider the stationary nonlinear magnetic Choquard equation [(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p}) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}%] where $A\$is a real valued vector potential, $V$ is a real valued scalar potential$,$ $N\geq3$, $\alpha\in(0,N)$ and $2-(\alpha/N) <p<(2N-\alpha)/(N-2)$. \ We assume that both $A$ and $V$ are compatible with the action of some group $G$ of linear isometries of $\mathbb{R}^{N}$. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition $$u(gx)=\tau(g)u(x)\text{\ \ \ for all}g\in G,\text{}x\in\mathbb{R}^{N},$$ where $\tau:G\rightarrow\mathbb{S}^{1}$ is a given group homomorphism into the unit complex numbers.Comment: To appear on ZAM

Model category extensions of the Pirashvili-S{\l}omi\'{n}ska theorems

We describe the class of semi-stable model categories, which generalize the equivalence of finite products and coproducts in abelian and stable model categories, and use this to establish Morita equivalences among categories of functors. We provide a construction of pairs of small categories--known as conjugate pairs--whose associated categories of diagrams are Quillen equivalent in the semi-stable setting. We frame our development in the context of Morita theory, following Slominska's work on similar questions for categories of functors enriched over and taking values in R-modules.Comment: 27 pages, submitted to Journal of Homotopy and Related Structure

A new method to quantify and compare the multiple components of fitness-A study case with kelp niche partition by divergent microstage adaptations to Temperature

Point 1 Management of crops, commercialized or protected species, plagues or life-cycle evolution are subjects requiring comparisons among different demographic strategies. The simpler methods fail in relating changes in vital rates with changes in population viability whereas more complex methods lack accuracy by neglecting interactions among vital rates. Point 2 The difference between the fitness (evaluated by the population growth rate.) of two alternative demographies is decomposed into the contributions of the differences between the pair-wised vital rates and their interactions. This is achieved through a full Taylor expansion (i.e. remainder = 0) of the demographic model. The significance of each term is determined by permutation tests under the null hypothesis that all demographies come from the same pool. Point 3 An example is given with periodic demographic matrices of the microscopic haploid phase of two kelp cryptic species observed to partition their niche occupation along the Chilean coast. The method provided clear and synthetic results showing conditional differentiation of reproduction is an important driver for their differences in fitness along the latitudinal temperature gradient. But it also demonstrated that interactions among vital rates cannot be neglected as they compose a significant part of the differences between demographies. Point 4 This method allows researchers to access the effects of multiple effective changes in a life-cycle from only two experiments. Evolutionists can determine with confidence the effective causes for changes in fitness whereas population managers can determine best strategies from simpler experimental designs.CONICYT-FRENCH EMBASSADY Ph.D. gran

Modeling of Non-Small Cell Lung Cancer Volume Changes during CT-Based Image Guided Radiotherapy: Patterns Observed and Clinical Implications

Background. To characterize the lung tumor volume response during conventional and hypofractionated radiotherapy (RT) based on diagnostic quality CT images prior to each treatment fraction. Methods. Out of 26 consecutive patients who had received CT-on-rails IGRT to the lung from 2004 to 2008, 18 were selected because they had lung lesions that could be easily distinguished. The time course of the tumor volume for each patient was individually analyzed using a computer program. Results. The model fits of group L (conventional fractionation) patients were very close to experimental data, with a median Δ% (average percent difference between data and fit) of 5.1% (range 3.5–10.2%). The fits obtained in group S (hypofractionation) patients were generally good, with a median Δ% of 7.2% (range 3.7–23.9%) for the best fitting model. Four types of tumor responses were observed—Type A: “high� kill and “slow� dying rate; Type B: “high� kill and “fast� dying rate; Type C: “low� kill and “slow� dying rate; and Type D: “low� kill and “fast� dying rate. Conclusions. The models used in this study performed well in fitting the available dataset. The models provided useful insights into the possible underlying mechanisms responsible for the RT tumor volume response

Rational design of amphiphilic fluorinated peptides: evaluation of self-assembly properties and hydrogel formation

Advanced peptide-based nanomaterials composed of self-assembling peptides (SAPs) are of emerging interest in pharmaceutical and biomedical applications. The introduction of fluorine into peptides, in fact, offers unique opportunities to tune their biophysical properties and intermolecular interactions. In particular, the degree of fluorination plays a crucial role in peptide engineering as it can be used to control the characteristics of fluorine-specific interactions and, thus, peptide conformation and self-assembly. Here, we designed and explored a series of amphipathic peptides by incorporating the fluorinated amino acids (2S)-4-monofluoroethylglycine (MfeGly), (2S)-4,4-difluoroethylglycine (DfeGly) and (2S)-4,4,4-trifluoroethylglycine (TfeGly) as hydrophobic components. This approach enabled studying the impact of fluorination on secondary structure formation and peptide self-assembly on a systematic basis. We show that the interplay between polarity and hydrophobicity, both induced differentially by varying degrees of side chain fluorination, does affect peptide folding significantly. A greater degree of fluorination promotes peptide fibrillation and subsequent formation of physical hydrogels in physiological conditions. Molecular simulations revealed the key role played by electrostatically driven intra-chain and inter-chain contact pairs that are modulated by side chain fluorination and give insights into the different self-organization behaviour of selected peptides. Our study provides a systematic report about the distinct features of fluorinated oligomeric peptides with potential applications as peptide-based biomaterials

The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape

Affine modifications and affine hypersurfaces with a very transitive automorphism group

We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its geometric counterpart to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces. Here we provide certain conditions which guarantee preservation of the topology under a modification. As an application, we show that the group of biregular automorphisms of the affine hypersurface $X \subset C^{k+2}$ given by the equation $uv=p(x_1,...,x_k)$ where $p \in C[x_1,...,x_k],$ acts $m-$transitively on the smooth part reg$X$ of $X$ for any $m \in N.$ We present examples of such hypersurfaces diffeomorphic to Euclidean spaces.Comment: 39 Pages, LaTeX; a revised version with minor changes and correction