Narrow Results

Proxy Re-Encryption (PRE) is a cryptographic primitive that allows a proxy to turn an Alice’s ciphertext into a Bob’s ciphertext on the same plaintext. All of the PRE schemes are public key encryption and semantic security. Deterministic Public Key Encryption (D-PKE) provides an alternative to randomized public key encryption in various scenarios where the latter exhibits inherent drawbacks. In this paper, we construct the first multi-use unidirectional D-PRE scheme from Lattices in the auxiliary-input setting. We also prove that it is PRIV1-INDr secure in the standard model based on the LWR. Finally, an identity-based D-PRE is obtained from the basic construction.

Based on the study of the dynamics of a dissipation-modified Toda anharmonic (one-dimensional, circular) lattice ring we predict here a new form of electric conduction mediated by dissipative solitons. The electron-ion-like interaction permits the trapping of the electron by soliton excitations in the lattice, thus leading to a soliton-driven current much higher than the Drude-like (linear, Ohmic) current. Besides, as we lower the values of the externally imposed field this new form of current survives, with a field-independent value.

Assuming the quantum mechanical "tight binding" of an electron to a nonlinear lattice with Morse potential interactions we show how electric conduction can be mediated by solitons. For relatively high values of an applied electric field the current follows Ohm's law. As the field strength is lowered the current takes a finite, constant, field-independent value.

We first summarize features of free, forced and stochastic harmonic oscillations and, following an idea first proposed by Lord Rayleigh in 1883, we discuss the possibility of maintaining them in the presence of dissipation. We describe how phonons appear in a harmonic (linear) lattice and then use the Toda exponential interaction to illustrate solitonic excitations (cnoidal waves) in a one-dimensional nonlinear lattice. We discuss properties such as specific heat (at constant length/volume) and the dynamic structure factor, both over a broad range of temperature values. By considering the interacting Toda particles to be Brownian units capable of pumping energy from a surrounding heat bath taken as a reservoir we show that solitons can be excited and sustained in the presence of dissipation. Thus the original Toda lattice is converted into an active lattice using Lord Rayleigh's method. Finally, by endowing the Toda–Brownian particles with electric charge (i.e. making them positive ions) and adding free electrons to the system we study the electric currents that arise. We show that, following instability of the base linear Ohm(Drude) conduction state, the active electric Toda lattice is able to maintain a form of high-T supercurrent, whose characteristics we then discuss.

This work provides a description of the main computational tools for the study of discrete breathers. It starts with the observation of breathers through simple numerical runs, the study uses targeted initial conditions, and discrete breather impact on transient processes and thermal equilibrium. We briefly describe a set of numerical methods to obtain breathers up to machine precision. In the final part of this work we apply the discussed methods to study the competing length scales for breathers with purely anharmonic interactions — favoring superexponential localization — and long range interactions, which favor algebraic decay in space. As a result, we observe and explain the presence of three different spatial tail characteristics of the considered localized excitations.

An algebraic relational theory is being developed in order to represent biological systems. As a result, it is possible to explain, in terms of qualitative relationships, the behaviors of such systems. This paper deals with the periodic continuous responses of a new state derived from the interaction between low energies and matter. This effect was predicted by categoric developments of the algebraic relational theory.

The property of muscle movement P_m is a central functional property for the qualitative interpretations of behaviors of biological systems. In this paper, based on the example of the muscle, it is shown how relational properties can be identified by responses derived from the functional organization. At a certain level of organization, the manifestation of the property P_m is analyzed in terms of qualitative relationships between the myosin and actin fibres of muscles. A relatively pseudo complemented lattice of nine elements shows algebraic relations in connection with the interaction of the fibres. The response coming from the lattice is in correspondence with the quantitative one expressed by Hill’s equation for muscles.

It is shown how the biological reality correlates with an algebraic modification from a pseudo-Boolean structure for watering processes in normal cells up to a non-modular structure assigned to water interactions in malignant cells. A set of mathematical propositions suggests how to deviate this type of cancer process to new structures mainly maintaining those water structures resulting from the cooperativity between water molecules generated by a surface. A set of disquisitions is made: about the meaning of the change of algebra; on the dual Heyting arrow operations acting for the algebraic triggering of the cancer process; on the loss of energy in the cancer process and about the enhanced value of energy as becoming from the new structures to deviate cancer.

An interesting sequence of arrays on hierarchical hexagonal grids was employed by PYXIS Innovation Inc. for an efficient digital earth model. These arrays constitute a Cauchy sequence in terms of Hausdorff distance. In this paper, we show that the box-counting dimension for the boundary of the limit of this sequence is .