Chirality detected in Hartley’s electronic oscillator

Chirality is an elusive asymmetry important in science and technology and confined mainly to the quantum realm. This paper reports the observation of chirality in a classical (that is, not quantum) scenario, namely in stability diagrams of an autonomous electronic oscillator with a junction-gate field-effect transistor (JFET) and a tapped coil. As the number of spikes (local maxima) of stable oscillations changes along closed parameter paths, they generate two types of intricate structures. Surprisingly, such pair of structures are artful images of each other when reflected on a mirror. They are dual chiral pairs interconnecting families of stable oscillations in closed loops. Chiral pairs should not be difficult to detect experimentally. This chirality is conjectured to be a generic property of nonlinear oscillators governed by classical (that is, not quantum) equations.

A generic approach to decipher the mechanistic pathway of heterogeneous protein aggregation kinetics

Amyloid formation is a generic property of many protein/polypeptide chains.

The non-linear sewing lemma III: Stability and generic properties

Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme using a non-linear sewing lemma. In this article, we show that such solutions also solve a fixed point problem by exhibiting a suitable functional. Convergence then follows from consistency and stability, two notions that are adapted to our framework. In addition, we show that uniqueness and convergence of discrete approximations is a generic property, meaning that it holds excepted for a set of vector fields and starting points which is of Baire first category. At last, we show that Brownian flows are almost surely unique solutions to RDE associated to Lipschitz flows. The later property yields almost sure convergence of Milstein schemes.

Semantic Intelligence

Semantic intelligence is exclusive for the intelligent complex systems way of response to an ever-changing environment. Its major distinctive property is autonomous comprehension and creation of information. Another exclusive property of semantic intelligence is autonomous discrimination between true and false statements. The semantic intelligence naturally arises in the setting of concept of boundedness where it commences from highly non-trivial interplay between structural and functional properties of a complex system. The major generic property of that interplay is that it renders the relation between structural and functional properties to be non-recursive. In result, this renders the efficiency of semantic intelligence to be provided by efficiency of hierarchical self-organization of a complex system prior to the efficiency of software and to the speed of hardware.

A wave of WNT signalling balanced by secreted inhibitors controls primitive streak formation in micropattern colonies of human embryonic stem cells

Long range signalling by morphogens and their inhibitors define embryonic patterning yet quantitative data and models are rare, especially in humans. Here we use a human embryonic stem cell “gastruloid” system to model formation of the primitive streak (PS) by WNT. In the pluripotent state E-CADHERIN (E-CAD) transduces boundary forces to focus WNT signalling to colony border. Following application of WNT ligand, E-CAD mediates a wave of epithelial-to-mesenchymal (EMT) conversion analogous to PS extension in an embryo. By knocking out the secreted WNT inhibitors active in our system, we show that DKK1 alone controls the extent and duration of patterning. The NODAL inhibitor CERBERUS1 acts downstream of WNT to refine the endoderm versus mesoderm fate choice. Our EMT wave is a generic property of a bistable system with diffusion and a single quantitative model describes both the wave and our knockout data.

Semantic Intelligence

Semantic intelligence is an exclusive for the intelligent complex systems way of response to an ever-changing environment. Its major distinctive property is autonomous comprehension and creation of information. Another exclusive property of semantic intelligence is autonomous discrimination between true and false statements. The semantic intelligence naturally arises in the setting of concept of boundedness where it commences from highly non-trivial interplay between structural and functional properties of a complex system. The major generic property of that interplay is that it renders the relation between structural and functional properties to be non-recursive. In result this renders the efficiency of semantic intelligence to be provided by efficiency of hierarchical self-organization of a complex system prior to the efficiency of software and to the speed of hardware.

Separability and entanglement of two qubits density matrices using Lorentz transformations

Explicit separability of general two qubits density matrices is related to Lorentz transformations. We use the 4-dimensional form [Formula: see text] of the Hilbert–Schmidt (HS) decomposition of the density matrix. For the generic case, in which Lorentz transformations diagonalize [Formula: see text] into [Formula: see text], we give relations between the [Formula: see text] and the [Formula: see text]. In particular, we consider two cases: (a) Two qubits density matrices with one pair of linear terms in the HS decomposition. (b) Two qubits density matrices with two or three symmetric pairs of linear terms. Some of the theoretical results are demonstrated by numerical calculations. The four non-generic cases (which may be reduced to case (a) are analyzed and the non-generic property is related explicitly to Lorentz velocity [Formula: see text] which is not reachable physically.