Counting the learnable functions of geometrically structured data

Cover's function counting theorem is a milestone in the theory of artificial neural networks. It provides an answer to the fundamental question of determining how many binary assignments (dichotomies) of p points in n dimensions can be linearly realized. Regrettably, it has proved hard to extend the same approach to more advanced problems than the classification of points. In particular, an emerging necessity is to find methods to deal with geometrically structured data, and specifically with non-point-like patterns. A prominent case is that of invariant recognition, whereby identification of a stimulus is insensitive to irrelevant transformations on the inputs (such as rotations or changes in perspective in an image). An object is thus represented by an extended perceptual manifold, consisting of inputs that are classified similarly. Here, we develop a function counting theory for structured data of this kind, by extending Cover's combinatorial technique, and we derive analytical expressions for the average number of dichotomies of generically correlated sets of patterns. As an application, we obtain a closed formula for the capacity of a binary classifier trained to distinguish general polytopes of any dimension. These results extend our theoretical understanding of the role of data structure in machine learning, and provide useful quantitative tools for the analysis of generalization, feature extraction, and invariant object recognition by neural networks

Hydrodynamic Synchronisation of Model Microswimmers

We define a model microswimmer with a variable cycle time, thus allowing the possibility of phase locking driven by hydrodynamic interactions between swimmers. We find that, for extensile or contractile swimmers, phase locking does occur, with the relative phase of the two swimmers being, in general, close to 0 or pi, depending on their relative position and orientation. We show that, as expected on grounds of symmetry, self T-dual swimmers, which are time-reversal covariant, do not phase-lock. We also discuss the phase behaviour of a line of tethered swimmers, or pumps. These show oscillations in their relative phases reminiscent of the metachronal waves of cilia.Comment: 17 pages, 8 figure

Stochasticity and homeostasis in the E. coli replication and division cycle

How cells correct for stochasticity to coordinate the chromosome replication and cellular division cycle is poorly understood. We used time-lapse microscopy and fluorescently labelled SeqA to determine the timing of birth, initiation, termination, and division, as well as cell size throughout the cell cycle. We found that the time between birth and initiation (B-period) compensates for stochastic variability in birth size and growth rate. The time between termination and division (D-period) also compensates for size and growth variability, invalidating the notion that replication initiation is the principal trigger for cell division. In contrast, the time between initiation and termination (C-period) did not display such compensations. Interestingly, the C-period did show small but systematic decreases for cells that spontaneously grew faster, which suggests a coupling between metabolic fluctuations and replication. An auto-regressive theoretical framework was employed to compare different possible models of sub-period control

Mixed nodule infection in Sinorhizobium meliloti-medicago sativa symbiosis suggest the presence of cheating behavior

In the symbiosis between rhizobia and legumes, host plants can forms ymbiotic root nodules with multiple rhizobial strains, potentially showing different symbiotic performances in nitrogen fixation. Here, we investigated the presence of mixed nodules, containing rhizobia with different degrees of mutualisms, and evaluate their relative fitness in the Sinorhizobium meliloti-Medicago sativa model symbiosis. We used three S. meliloti strains, the mutualist strains Rm1021 and BL225C and the non-mutualist AK83. We performed competition experiments involving both in vitro and in vivo symbiotic assays with M. sativa host plants. We show the occurrence of a high number (from 27 to 100%) of mixed nodules with no negative effect on both nitrogen fixation and plant growth. The estimation of the relative fitness as non-mutualist/mutualist ratios in single nodules shows that in some nodules the non-mutualist strain efficiently colonized root nodules along with the mutualist ones. In conclusion, we can support the hypothesis that in S. meliloti-M. sativa symbiosis mixed nodules are formed and allow non-mutualist or less-mutualist bacterial partners to be less or not sanctioned by the host plant, hence allowing a potential form of cheating behavior to be present in the nitrogen fixing symbiosis

Detection of antihydrogen annihilations with a Si-micro-strip and pure CsI detector

In 2002, the ATHENA collaboration reported the creation and detection of cold (~15 K) antihydrogen atoms [1]. The observation was based on the complete reconstruction of antihydrogen annihilations, simultaneous and spatially correlated annihilations of an antiproton and a positron. Annihilation byproducts are measured with a cylindrically symmetric detector system consisting of two layers of double sided Si-micro-strip modules that are surrounded by 16 rows of 12 pure CsI crystals (13 x 17.5 x 17 mm^3). This paper gives a brief overview of the experiment, the detector system, and event reconstruction. Reference 1. M. Amoretti et al., Nature 419, 456 (2002).Comment: 7 pages, 5 figures; Proceedings for the 8th ICATPP Conference on Astroparticle, Particle, Space Physics, Detectors and Medical Physics Applications (Como, Italy October 2003) to be published by World Scientific (style file included

First Production and Detection of Cold Antihydrogen Atoms

The ATHENA experiment recently produced the first atoms of cold antihydrogen. This paper gives a brief review of how this was achieved.Comment: Invited talk at Int. Conf. on Low Energy Antiprotons 2003 (LEAP03), to be published in NIM

The First Cold Antihydrogen

Antihydrogen, the atomic bound state of an antiproton and a positron, was produced at low energy for the first time by the ATHENA experiment, marking an important first step for precision studies of atomic antimatter. This paper describes the first production and some subsequent developments.Comment: Invitated Talk at COOL03, International Workshop on Beam Cooling and Related Topics, to be published in NIM

Fluid transport at low Reynolds number with magnetically actuated artificial cilia

By numerical modeling we investigate fluid transport in low-Reynolds-number flow achieved with a special elastic filament or artifical cilium attached to a planar surface. The filament is made of superparamagnetic particles linked together by DNA double strands. An external magnetic field induces dipolar interactions between the beads of the filament which provides a convenient way of actuating the cilium in a well-controlled manner. The filament has recently been used to successfully construct the first artificial micro-swimmer [R. Dreyfus at al., Nature 437, 862 (2005)]. In our numerical study we introduce a measure, which we call pumping performance, to quantify the fluid transport induced by the magnetically actuated cilium and identify an optimum stroke pattern of the filament. It consists of a slow transport stroke and a fast recovery stroke. Our detailed parameter study also reveals that for sufficiently large magnetic fields the artificial cilium is mainly governed by the Mason number that compares frictional to magnetic forces. Initial studies on multi-cilia systems show that the pumping performance is very sensitive to the imposed phase lag between neighboring cilia, i.e., to the details of the initiated metachronal wave.Comment: 12 pages, 10 figures. To appear in EPJE, available online at http://dx.doi.org/10.1140/epje/i2008-10388-

Producing Slow Antihydrogen for a Test of CPT Symmetry with ATHENA

The ATHENA experiment at the Antiproton Decelerator facility at CERN aims at testing CPT symmetry with antihydrogen. An overview of the experiment, together with preliminary results of development towards the production of slow antihydrogen are reported.The ATHENA experiment at the Antiproton Decelerator facility at CERN aims at testing CPT symmetry with antihydrogen. An overview of the experiment, together with preliminary results of development towards the production of slow antihydrogen are reported.The ATHENA experiment at the Antiproton Decelerator facility at CERN aims at testing CPT symmetry with antihydrogen. An overview of the experiment, together with preliminary results of development towards the production of slow antihydrogen are reported.The ATHENA experiment at the Antiproton Decelerator facility at CERN aims at testing CPT symmetry with antihydrogen. An overview of the experiment, together with preliminary results of development towards the production of slow antihydrogen are reported

Production of Slow Protonium in Vacuum

We describe how protonium, the quasi-stable antiproton-proton bound system, has been synthesized following the interaction of antiprotons with the molecular ion H$_2^+$ in a nested Penning trap environment. From a careful analysis of the spatial distributions of antiproton annihilation events in the ATHENA experiment, evidence is presented for protonium production with sub-eV kinetic energies in states around $n$ = 70, with low angular momenta. This work provides a new 2-body system for study using laser spectroscopic techniques.Comment: 9 pages with 5 figures and 1 table. Proceedings of the 4th International Conference on Trapped Charged Particles and Fundamental Physics (TCP 06), published in Hyperfine Interaction