Fast Witness Extraction Using a Decision Oracle

The gist of many (NP-)hard combinatorial problems is to decide whether a universe of $n$ elements contains a witness consisting of $k$ elements that match some prescribed pattern. For some of these problems there are known advanced algebra-based FPT algorithms which solve the decision problem but do not return the witness. We investigate techniques for turning such a YES/NO-decision oracle into an algorithm for extracting a single witness, with an objective to obtain practical scalability for large values of $n$. By relying on techniques from combinatorial group testing, we demonstrate that a witness may be extracted with $O(k\log n)$ queries to either a deterministic or a randomized set inclusion oracle with one-sided probability of error. Furthermore, we demonstrate through implementation and experiments that the algebra-based FPT algorithms are practical, in particular in the setting of the $k$-path problem. Also discussed are engineering issues such as optimizing finite field arithmetic.Comment: Journal version, 16 pages. Extended abstract presented at ESA'1

Metachronal wave and hydrodynamic interaction for deterministic switching rowers

We employ a model system, called rowers, as a generic physical framework to define the problem of the coordinated motion of cilia (the metachronal wave) as a far from equilibrium process. Rowers are active (two-state) oscillators interacting solely through forces of hydrodynamic origin. In this work, we consider the case of fully deterministic dynamics, find analytical solutions of the equation of motion in the long wavelength (continuum) limit, and investigate numerically the short wavelength limit. We prove the existence of metachronal waves below a characteristic wavelength. Such waves are unstable and become stable only if the sign of the coupling is reversed. We also find that with normal hydrodynamic interaction the metachronal pattern has the form of stable trains of traveling wave packets sustained by the onset of anti-coordinated beating of consecutive rowers.Comment: 11 pages, 7 figure

Hydrodynamic flow patterns and synchronization of beating cilia

We calculate the hydrodynamic flow field generated far from a cilium which is attached to a surface and beats periodically. In the case of two beating cilia, hydrodynamic interactions can lead to synchronization of the cilia, which are nonlinear oscillators. We present a state diagram where synchronized states occur as a function of distance of cilia and the relative orientation of their beat. Synchronized states occur with different relative phases. In addition, asynchronous solutions exist. Our work could be relevant for the synchronized motion of cilia generating hydrodynamic flows on the surface of cells.Comment: 5 pages, 4 figures, v2: minor correction

Encrypt-to-self:Securely outsourcing storage

We put forward a symmetric encryption primitive tailored towards a specific application: outsourced storage. The setting assumes a memory-bounded computing device that inflates the amount of volatile or permanent memory available to it by letting other (untrusted) devices hold encryptions of information that they return on request. For instance, web servers typically hold for each of the client connections they manage a multitude of data, ranging from user preferences to technical information like database credentials. If the amount of data per session is considerable, busy servers sooner or later run out of memory. One admissible solution to this is to let the server encrypt the session data to itself and to let the client store the ciphertext, with the agreement that the client reproduce the ciphertext in each subsequent request (e.g., via a cookie) so that the session data can be recovered when required. In this article we develop the cryptographic mechanism that should be used to achieve confidential and authentic data storage in the encrypt-to-self setting, i.e., where encryptor and decryptor coincide and constitute the only entity holding keys. We argue that standard authenticated encryption represents only a suboptimal solution for preserving confidentiality, as much as message authentication codes are suboptimal for preserving authenticity. The crucial observation is that such schemes instantaneously give up on all security promises the moment the key is compromised. In contrast, data protected with our new primitive remains fully integrity protected and unmalleable. In the course of this paper we develop a formal model for encrypt-to-self systems, show that it solves the outsourced storage problem, propose surprisingly efficient provably secure constructions, and report on our implementations

Dimensions of Maternal Parenting and Infants’ Autonomic Functioning Interactively Predict Early Internalizing Behavior Problems

Developmental pathways to childhood internalizing behavior problems are complex, with both environmental and child-level factors contributing to their emergence. The authors use data from a prospective longitudinal study (n = 206) to examine the associations between dimensions of caregiving experiences in the first year of life and anxious/depressed and withdrawn behaviors in early childhood. Additionally, the authors examine the extent to which these associations were moderated by infants’ autonomic functioning in the first year of life indexed using measures of respiratory sinus arrhythmia (RSA) and heart period (HP). Findings suggest that higher levels of maternal sensitivity in infancy are associated with fewer anxious/depressed and withdrawn behaviors at age 3 years. Negative intrusiveness was found to be positively associated with children’s anxious/depressed behaviors but not withdrawn behaviors. Further, moderation analyses suggested that the link between negative intrusive parenting during infancy and subsequent anxious/depressed behaviors is exacerbated for infants with average or low baseline HP and that positive engaging parenting during infancy was negatively related to withdrawn behaviors for infants demonstrating average to high levels baseline HP. Interestingly, RSA was not found to moderate the associations between parenting in infancy and later internalizing behavior problems suggesting that, during infancy, overall autonomic functioning may have greater implications for the development of internalizing behaviors than do parasympathetic influences alone. Implications of these findings and future directions for research are discussed

NMR study of slowly exchanging protons in yeast tRNAAsp

We have monitored the exchange of imino and amino protons by NMR after quick transfer of yeast tRNAAsp in 2H2O solvent. When the concentration of exchange-catalyzing buffer is not too high, one imino proton exchanges considerably more slowly than any other (e.g., 100 hr versus 4 hr for the second-slowest imino proton at 18°C in 15 mM Mg). This provides excellent conditions for identification, by the nuclear Overhauser effect, of the slowest exchanging proton, which we show to be the imino proton of the U-8. A-14 reverse Hoogsteen tertiary-structure base pair; other slowly exchanging protons are identified as imino protons from A.U-11 and G.ψ-13. In preliminary experiments, we find that the exchange of these protons is catalyzed by cacodylate or Tris buffer. The lifetimes of two other imino protons, ca. 10 min at 28°C, are buffer independent. Slowly exchanging amino protons have also been observed. Correlation with the exchange of the uracil-8 imino proton suggests that they may be from adenine-14

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

Generic flow profiles induced by a beating cilium

We describe a multipole expansion for the low Reynolds number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.Comment: 12 pages, 6 figures, to appear in EPJ

A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization

In a recent issue of this journal, Mordukhovich et al.\ pose and solve an interesting non-differentiable generalization of the Heron problem in the framework of modern convex analysis. In the generalized Heron problem one is given $k+1$ closed convex sets in \Real^d equipped with its Euclidean norm and asked to find the point in the last set such that the sum of the distances to the first $k$ sets is minimal. In later work the authors generalize the Heron problem even further, relax its convexity assumptions, study its theoretical properties, and pursue subgradient algorithms for solving the convex case. Here, we revisit the original problem solely from the numerical perspective. By exploiting the majorization-minimization (MM) principle of computational statistics and rudimentary techniques from differential calculus, we are able to construct a very fast algorithm for solving the Euclidean version of the generalized Heron problem.Comment: 21 pages, 3 figure