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-- Our paper on energy densities in quantum mechanics was published in the Quantum Journal.  Defining a conserving energy density in quantum mechanics is challenging due to non-commutativity. To solve this problem, we start from Dirac's equation, where the relativistic covariance dictates a unique energy density with a well-defined non-relativistic limit. We uncover a new form of locally-conserving, spin-dependent, holographic energy that emerges from the rest-energy. It does not contribute to the global energy budget but is relevant locally since its density is finite in the non-relativistic limit. Once the problem is solved we address new issues and show that for Gaussian and Airy wave-packets the energy flows at a higher speed than the coordinate.

 -- The Simpson paradox is a curious and unexpected statistical phenomenon that can limit the applicability of data science. Eventually, such limitations make it a science. Here we show how to reformulate and generalize the paradox via the common cause principle, another paradigmatic notion of statistical reasoning. In simplest cases, Simpson's paradox can be resolved by using this reformulation.  

-- In this preprint, we made a new step in Doppler's metrology and explored what quantum vacuum effects can tell about the structure determination of dielectrics.  This relates to our previous paper on Rayleigh's limit.

-- The joint preprint with Lida Aleksanyan and Vardan Bardakhchyan on explaining the ultimatum game is out.  The ultimatum game is perhaps the main example of human economic behavior that consistently violates the tenets of classical rationality. So far its main explanation was based on assuming that people are fair. We offer an alternative explanation.  

-- The issue of global warming is based on the concept of mean temperature. Researchers in climate science and hydrodynamics tend to define the mean temperature via standard mathematical means; e.g. the mean arithmetic. This is incorrect since temperature is not additive and is determined for an arbitrary valid thermometer. Here we propose a definition that conforms to the laws of thermodynamics and employs the concepts of energy, entropy, and work. It results in a simple formula for the mean temperature for ideal and weakly non-ideal gases. 

-- Our joint paper with Vardan Bardakhchyan "Regret theory, Allais’ Paradox, and Savage’s omelet"  [here is preprint] will be published in the Journal of Mathematical Psychology, a special issue in honor of Peter Fishburn (we essentially use a theorem proved by Fishburn). The paper is about developing an alternative approach to the expected utility in decision theory. It shows how to solve the famous Allais' paradox rationally, and also demonstrates that the omelet example prepared by Jim Savage for illustrating the expected utility theory does contradict the expected utility, but can be solved via our regret theory approach.  

-- Our paper on Rayleigh's limit was published in Optics Letters; see here for the preprint version. Rayleigh's limit states that an electromagnetic wave with length L can be employed for seeing only sufficiently large objects because seeing (roughly) requires L<A, where A is the object's size. We tried to understand how using quantum features of light can overcome this limit; e.g. we show that using a single photon one can make L<2A in the back-scattering regime. More advantages are provided by bi-photons, but only under certain conditions. 

-- Our preprint on the common cause  principle is out. It assumes that a common (probabilistic) cause for two random variables does exist, but is unknown, and infers this cause via the generalized maximum likelihood principle.  The introduction of the preprint provides a comprehensible review of the common cause principle. 

-- Together with Andranik Khachatryan, we determined the optimal alphabet for text compression; please see here for the updated preprint and here for the published version. 

-- The basic mystery of quantum mechanics is that of identical particles. This viewpoint is argued for here. This is the published version.  

-- When you can apply the maximum entropy method as a valid inference method? Here are some partial answers within the framework of the Bayesian decision theory; here is the initial (preprint) version. 

-- Our group (please see here) got a joint grant on quantum technologies and machine learning from the government of Armenia. This is one of the biggest projects ever sponsored by Armenia in this field. 

-- My manuscript on the efficiency of wind turbines is out Physical Review Letters (see here for the preprint). It reconsiders the time-honored Betz (or Betz-Lanchester-Joukowsky) limit for this efficiency, and shows that the actual efficiency is given by altogether different expression that is similar to the Carnot efficiency for heat-engines. This analogy is far-reaching, but not complete. 

-- Our preprint on applying game-theoretic ideas to statistical physics is out. It stems from an observation (probably done by many others) that the fundamental game-theoretical notion of Pareto equilibrium just coincides with the physical Gibbsian equilibrium. This made possible to bring ideas of axiomatic barganing theory into statistical physics and solve the thermalization problem.  Here is the published version. 

-- Two page description of the quantum measurement problem and its solution. Physics, formulas, and no philosophical discussions. To my knowledge, this is the shortest description of the problem and its solution. 

-- Our group won the President Prize of Armenia for 2019.

-- I became the main local organizer for a summer school and related international conference. This is for the first time in my (scientific) life. And, I believe, the last one. 

-- Our manuscript on the work-content of classic electromagnetic field appeared in Physical Review Letters, 121, 240602 (2018). The approach allows to unify thermodynamic and electrodynamical arrows of time. 

-- Our manuscript on adaptive decision making was published in International Journal of Approximate Reasoning, 103, 270-287 (2018). It provides a probabilistic model for an agent choosing between several options. The model shows certain rudimentary forms of intelligent behavior. 

-- Lecture notes on quantum probability and quantum thermodynamics. The notes will be updated periodically. 

-- Our manuscript on understanding quantum non-locality from within quantum mechanics is published in EPL. It also shows in which specific sense locality and non-locality co-exist with each other. 

-- We continue the effort of understanding the quantum measurement problem: the  Achilles' heel of quantum theory. Now we have a clean description for the emergence of sub-ensembles and single events. The research is published in Annals of Physics 376, 324-352, 2017. Here is the free (arXiv) version. 

-- We developed a theory for vortex cooling, the notorious and somewhat controversial Ranque effect. It was published in Physical Review Fluids; here is the preprint and a short description. 

-- My first paper on classical electrodynamics (never thought I will work on this subject) addresses a problem that seems to me fundamental: how to define the energy for a particle in an electromagnetic field. It is the gauge-invariance that makes definitions of energy non-unique. Hence new principles are needed for the proper definition. One outcome of this research is that singles out the Lorenz gauge as more physical compared to others. Another outcome is that the definition of energy requires a new form of the energy-momentum tensor of the electromagnetic field. 

-- Our research on adaptive heat engines appeared in Physical Review Letters [PRL, 117, 030601 (2016)], and got selected as PRL Editors' Suggestion. Here is the pre-print of this manuscript and here is its short description. 

-- We found a relation between the dark energy (cosmological constant) and  the thermodynamic arrow of time. It is published as Physical Review E 93, 052125 (2016); see here for a free version. This paper was rather difficult to publish, we were initially rejected, had to appeal etc. The research is described by scientific press: here and also here. Also, see a report on youtube.

-- Our research on phonemes appeared in PLOS ONE. Please see  here for details. 

-- Our paper on functioning of hemoglobin was published in Scientific Reports. Please see here for a summary.

-- My paper on non-additive, imprecise probabilities in quantum mechanics appeared in New Journal of Physics. Its main point is given here.