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This manuscript reviews theoretical results and applications related to quadratic forms in Gaussian random variables. It summarizes definitions, canonical representations, exact and approximate distributional results, numerical inversion…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
In this paper, we derive the quadratic formula as a consequence of constructively proving the existence of standard and factored forms for general form real quadratic functions. Emphasis is put on connections to graphing of corresponding…
In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…
Participatory budgeting (PB) is a democratic process for allocating funds to projects based on the votes of members of the community. Different rules have been used to aggregate participants' votes. Past research has studied the trade-off…
In this article we discuss few new derivations of the so called Born's rule for quantum probability in the context of the pilot wave theory proposed by de Broglie in 1927.
The paper discusses the applicability of WKB and Born (small perturbations) approximations in the problem of the backscattering of quantum particles and classical waves by one-dimensional smooth potentials with amplitudes small compared to…
These proceedings summarize a newly found connection between the factorial growth of coefficients in perturbative QCD and power corrections to the perturbation series, discussed in refs. [1-4]. The improved convergence is shown for three…
We suggest and describe how to analyze new types of experiments that would test a proposed model of the quantum measurement process. That model produces the Born Rule as a corollary, and so agrees with conventional quantum predictions. The…
We study a participatory budgeting problem, where a set of strategic agents wish to split a divisible budget among different projects, by aggregating their proposals on a single division. Unfortunately, the straight-forward rule that…
We extend variational quantum optimization algorithms for Quadratic Unconstrained Binary Optimization problems to the class of Mixed Binary Optimization problems. This allows us to combine binary decision variables with continuous decision…
Newtonian and Scrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
In classical physics, probabilistic or statistical knowledge has been always related to ignorance or inaccurate subjective knowledge about an actual state of affairs. This idea has been extended to quantum mechanics through a completely…
We address a combinatorial optimization problem to determine the placement of a predefined number of sensors from multiple candidate positions, aiming to maximize information acquisition with the minimum number of sensors. Assuming that the…
Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system. It explains how the fragility of a state of a single quantum system can lead to the classical robustness of…
The absolute value squared of the probability amplitude corresponding to the overlap of an initial state with a continuum wave solution to the Schr\"odinger equation of the problem, has the physical interpretation provided by the Born rule.…
Quantum mechanics describes successfully numerous quantum phenomena both microscopic and macroscopic, such as superconductivity. But the controversies about quantum mechanics, in the old days and present day, reveal fundamental obscurity in…
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…
Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the…