Probability theory first reached its modern form in the work of Kolmogorov.1 Along with his famous axioms for unconditional probability, he gave a formula for calculating conditional probabilities. “If P (A) > 0, then the quotient PA(B) = P (AB) P (A) is defined to be the conditional probability of the event B under the condition A.”2 (Throughout this paper, I will use the more standard notatio...

We consider crossbar switching networks with base b (that is, constructed from b × b crossbar switches), scale k (that is, with b inputs, b outputs and b links between each consecutive pair of stages) and depth l (that is, with l stages). We assume that the crossbars are interconnected according to the spider-web pattern, whereby two diverging paths reconverge only after at least k stages. We a...

O(3, 1)L symmetry, the ground state baryons and antibaryons are assigned to the (12× 12× 12)Sym = 364-multiplet in the spin-flavor Ũ(12)SF symmetry. This multiplet includes, in addition to the ordinary 56-multiplet of the static SU(6)SF , the extra chiral 56 ′ and 70-multiplets, called “chiralons,” which are expected to exist with masses in 1 ∼ 2 GeV region. Their electro-magnetic properties, m...

Using the form of N = 2 superconformal invariants we derive the explicit relation between the bottom and top components of the correlator of four stress-tensor multiplets in N = 4 Super Yang-Mills. The result is given in terms of an eighth order differential operator acting on the function of two variables which characterises these correlators. It allows us to show a non-trivial consistency rel...

Recent studies of brain activities show that cross-frequency coupling (CFC) play an important role in memory and learning. Many measures have been proposed to investigate the CFC phenomenon, including the correlation between the amplitude envelopes of two brain waves at different frequencies - cross-frequency amplitude-amplitude coupling (AAC). In this short communication, we describe how nonst...

Jeffrey's rule has been generalized by Wagner to the case in which new evidence bounds the possible revisions of a prior probability below by a Dempsterian lower probability. Classical probability kinematics arises within this gen­ eralization as the special case in which the evidentiary focal elements of the bounding lower probability are pairwise disjoint. We discuss a twofold extension of th...

We present tree-level n-particle on-shell scattering amplitudes of various brane theories with 16 conserved supercharges. These include the world-volume theory of a probe D3-brane or D5-brane in 10D Minkowski spacetime as well as a probe M5-brane in 11D Minkowski spacetime, which describes self interactions of an abelian tensor supermultiplet with 6D (2, 0) supersymmetry. Twistor-string-like fo...

We consider here the Feynman amplitudes of renormalizable non-commutative quantum field theory models. Different representations (the parametric and the Mellin one) are presented. The latter further allows the proof of meromorphy of a amplitude in the space-time dimension.

Abstract: We use an n-dimensional projection method to calculate helicity amplitudes for photon-photon scattering up to the two-loop level, for massless particles inside the loop. We confirm the recent standard model results found by Bern et al using another calculational method. We further apply the method to N = 1 and N = 2 supersymmetric QED. As predicted by the supersymmetric Ward identity,...

We discuss what predictions can be made for one-loop superamplitudes in maximally supersymmetric Yang-Mills theory by using anomalous dual conformal symmetry. We show that the anomaly coefficient is a specific combination of two-mass hard and one-mass supercoefficients which appears in the supersymmetric on-shell recursion relations and equals the corresponding tree-level superamplitude. We dis...