Search

The rapid development of neutrino astronomy, which is expressed, among other things, in the emergence of new neutrino mega-projects capable of efficient registering astrophysical neutrino fluxes requires a detailed knowledge of neutrino evolution inside neutrino sources (type II supernovae, gamma-ray bursts). This evolution can be influenced by many factors, each should be accounted for by a relevant theory. In this work, we develop the theory of neutrino propagation in moving and/or polarized matter by introducing for the first time an exact spin integral of motion. This enables us to obtain the neutrino dispersion under these conditions and resolve it for most important cases. Our approach opens up the possibility to consistently classify neutrino states in moving and/or polarized medium and, as a consequence, to give a systematic description of the related physical phenomena (e.g., neutrino oscillations, neutrino electromagnetic radiation)., Comment: 4 pages, based on the presentation at the 41st International Conference on High Energy Physics (ICHEP2022 6-13 July 2022, Bologna, Italy), prepared for the ICHEP2022 proceedings

A combinatorial market consists of a set of indivisible items and a set of agents, where each agent has a valuation function that specifies for each subset of items its value for the given agent. From an optimization point of view, the goal is usually to determine a pair of pricing and allocation of the items that provides an efficient distribution of the resources, i.e., maximizes the social welfare, or is as profitable as possible for the seller, i.e., maximizes the revenue. To overcome the weaknesses of mechanisms operating with static prices, a recent line of research has concentrated on dynamic pricing schemes. In this model, agents arrive in an unspecified sequential order, and the prices can be updated between two agent-arrivals. Though the dynamic setting is capable of maximizing social welfare in various scenarios, the assumption that the agents arrive one after the other eliminates the standard concept of fairness. In this paper, we study the existence of optimal dynamic prices under fairness constraints in unit-demand markets. We propose four possible notions of envy-freeness of different strength depending on the time period over which agents compare themselves to others: the entire time horizon, only the past, only the future, or only the present. For social welfare maximization, while the first definition leads to Walrasian equilibria, we give polynomial-time algorithms that always find envy-free optimal dynamic prices in the remaining three cases. In contrast, for revenue maximization, we show that the corresponding problems are APX-hard if the ordering of the agents is fixed. On the positive side, we give polynomial-time algorithms for the setting when the seller can choose the order in which agents arrive., Comment: 19 pages, 3 figures

In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the unknot? We also show that for a link diagram of treewidth two we can test in linear time if it represents the unlink. From the algorithm, it follows that a diagram of the unknot of treewidth 2 can always be reduced to the trivial diagram with at most $n$ (un)twist and (un)poke Reidemeister moves., Comment: 19 pages, 16 figures. The first version had erroneously three subsections repeated; the updated version avoids this mistake

The status of a vertex $v$ in a connected graph is the sum of the distances from $v$ to all other vertices. The status sequence of a connected graph is the list of the statuses of all the vertices of the graph. In this paper we investigate the status sequences of trees. Particularly, we show that it is NP-complete to decide whether there exists a tree that has a given sequence of integers as its status sequence. We also present some results about trees whose status sequences are comprised of a few distinct numbers or many distinct numbers. In this direction, we provide a partial answer to a conjecture of Shang and Lin from 2011, showing that any status injective tree is unique among trees. Finally, we investigate how orbit partitions and equitable partitions relate to the status sequence.

We study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance $\delta$ from each other. We investigate the complexity of this problem in terms of the rational parameter $\delta$. The problem is polynomially solvable, if the numerator of $\delta$ is $1$ or $2$, while all other cases turn out to be NP-hard., Comment: 13 pages, 1 figure

Healthy nutrition promotions and regulations have long been regarded as a tool for increasing social welfare. One of the avenues taken in the past decade is sugar consumption regulation by introducing a sugar tax. Such a tax increases the price of extensive sugar containment in products such as soft drinks. In this article we consider a typical problem of optimal regulatory policy design, where the task is to determine the sugar tax rate maximizing the social welfare. We model the problem as a sequential game represented by the three-level mathematical program. On the upper level, the government decides upon the tax rate. On the middle level, producers decide on the product pricing. On the lower level, consumers decide upon their preferences towards the products. While the general problem is computationally intractable, the problem with a few product types is polynomially solvable, even for an arbitrary number of heterogeneous consumers. This paper presents a simple, intuitive and easily implementable framework for computing optimal sugar tax in a market with a few products. This resembles the reality as the soft drinks, for instance, are typically categorized in either regular or no-sugar drinks, e.g. Coca-Cola and Coca-Cola Zero. We illustrate the algorithm using an example based on the real data and draw conclusions for a specific local market.

The $ spin $ $ light$ $ of $ $neutrino $ ($SL\nu$) is a phenomenon of electromagnetic radiation by a massive neutrino moving in external media that is originated owing to neutrino magnetic moment. In this short paper we note on the importance of this effect in the light of its connection with the neutrino magnetic moment, recap its basic properties in dense matter and give some general criteria for its best efficiency in nature. On this basis we propose a set of possible astrophysical environments where the $SL\nu$ can be manifested in principle., Comment: 5 pages in LaTeX, Proceedings of EPS-HEP 2017 (European Physical Society conference on High Energy Physics, 5-12 July 2017, Venice, Italy)

Unit square (grid) visibility graphs (USV and USGV, resp.) are described by axis-parallel visibility between unit squares placed (on integer grid coordinates) in the plane. We investigate combinatorial properties of these graph classes and the hardness of variants of the recognition problem, i.e., the problem of representing USGV with fixed visibilities within small area and, for USV, the general recognition problem.

The ${\it {spin \ \ light \ \ of \ \ neutrino}}$ ($SL\nu$) is a new possible mechanism of electromagnetic radiation by a massive neutrino (with a nonzero magnetic moment) moving in media. Since the prediction of this mechanism, the question has been debated in a number of publications as whether the effect can be of any significance for realistic astrophysical conditions. Although this effect is strongly suppressed due to smallness of neutrino magnetic moment, for ultra-high energy neutrinos (PeV neutrinos recently observed by the IceCube collaboration, for instance) the $SL\nu$ might be of interest in the case of neutrinos propagating in dense matter. An advanced view on the $SL\nu$ in matter is given, and several astrophysical settings (a neutron star, supernova, Gamma-Ray Burst (GRB), and relic neutrino background) for which the effect can be realized are considered. Taking into account the threshold condition and also several competing processes, we determine conditions for which the $SL\nu$ mechanism is possible. We conclude that the most favorable case of the effect manifestation is provided by ultra dense matter of neutron stars and ultrahigh energy of the radiating neutrino, and note that these conditions can be met within galaxy clusters. It is also shown that due to the $SL\nu$ specific polarization properties this electromagnetic mechanism is of interest in the connection with the observed polarization of GRB emission., Comment: 21 pages, 4 figures

We consider neutrino mixing and oscillations in presence of an arbitrary constant magnetic field with nonzero transversal $B_{\perp}$ and longitudinal $B_{\parallel}$ components with respect to the direction of neutrino propagation. The electromagnetic interaction of neutrinos is determined by diagonal and transition neutrino magnetic moments that are introduced for the neutrino mass states. Explicit expressions for the effective neutrino diagonal and transition magnetic moments for the flavor basis in terms of these values for the mass states are obtained. The effective evolution Hamiltonian for the flavor neutrino and the corresponding oscillation probability are derived. The role of the longitudinal magnetic field component is examined. In particular, it is shown that: 1) $B_{\parallel}$ coupled to the corresponding magnetic moments shifts the neutrino energy, and 2) in case of nonvanishing neutrino transition magnetic moments $B_{\parallel}$ produces an additional mixing between neutrino states, both in the mass and flavor neutrino bases., Comment: 6 pages, no figures, V2: typos corrected

We study a variant of the single machine capacitated lot-sizing problem with sequence-dependent setup costs and product-dependent inventory costs. We are given a single machine and a set of products associated with a constant demand rate, maximum loading rate and holding costs per time unit. Switching production from one product to another incurs sequencing costs based on the two products. In this work, we show that by considering the high multiplicity setting and switching costs, even trivial cases of the corresponding "normal" counterparts become non-trivial in terms of size and complexity. We present solutions for one and two products., Comment: 10 pages (4 appendix), to be published in Operations Research Proceedings 2014

Compatibility of unrooted phylogenetic trees is a well studied problem in phylogenetics. It asks to determine whether for a set of k input trees there exists a larger tree (called a supertree) that contains the topologies of all k input trees. When any such supertree exists we call the instance compatible and otherwise incompatible. It is known that the problem is NP-hard and FPT, although a constructive FPT algorithm is not known. It has been shown that whenever the treewidth of an auxiliary structure known as the display graph is strictly larger than the number of input trees, the instance is incompatible. Here we show that whenever the treewidth of the display graph is at most 2, the instance is compatible. Furthermore, we give a polynomial-time algorithm to construct a supertree in this case. Finally, we demonstrate both compatible and incompatible instances that have display graphs with treewidth 3, highlighting that the treewidth of the display graph is (on its own) not sufficient to determine compatibility.

A graph G is {\xi}-nearly planar if it can be embedded in the sphere so that each of its edges is crossed at most {\xi} times. The family of {\xi}-nearly planar graphs is widely extending the notion of planarity. We introduce an alternative parameterized graph family extending the notion of planarity, the {\lambda}-flat graphs, this time defined as powers of plane graphs in regard to a novel notion of distance, the wall-by-wall distance. We show that the two parameterized graph classes are parametrically equivalent.

Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric intersection graphs GB where each body of the collection B is represented by a vertex, and two vertices of GB are adjacent if the intersection of the corresponding bodies is non-empty. For such graph classes and under natural restrictions on their maximum degree or subgraph exclusion, we prove that the relation between their treewidth and the maximum size of a grid minor is linear. These combinatorial results vastly extend the applicability of all the meta-algorithmic results of the bidimensionality theory to geometrically defined graph classes.

The spin light of neutrino is considered in the process of a neutrino radiative transition between two different mass states in presence of medium. By this study we investigate the influence of background matter on the initial and final neutrino states in the process of massive Dirac neutrino decay due to the non-zero transition magnetic moment. We derive corresponding corrections to the total width of the process over the matter density in most important for applications cases., Comment: 5 pages in LaTex, to appear in proceedings of the 9th Conference on Quantum Field Theory Under the Influence of External Conditions (Univ. of Oklahoma, Norman, OK USA, September 21-25, 2009), eds. Kim Milton and Michael Bordag (World Scientific, Singapore, 2010)

Using the exact solutions for the Dirac neutrino wave function in presence of matter we study the spin light mode in the process of neutrino transition from initial heavier to final lighter state. The spin light is emitted due to the neutrino nonzero transitional magnetic moment., Comment: to appear in the proceedings of the 21st Rencontres de Blois (France), June 21-26, 2009

Exact solution of the modified Dirac equation in rotating medium is found in polar coordinates in the limit of vanishing neutrino mass. The solution for the active left-handed particle exhibit properties similar to those peculiar for the charged particle moving in the presence of a constant magnetic field. Accordingly, the particle in the rotating matter has circle orbits with energy levels, analogous to the Landau levels in magnetic field. The relevant physical realization of the problem is motion of neutrino inside the rotating neutron star. The feature of such motion to form binding states leads to the prediction of the new mechanism for neutrino trapping. The solution found can be used for detailed description of relativistic and nearly massless neutrino dynamics in neutron stars. Results obtained further develop the "method of exact solutions" in application to particle interactions in presence of dense matter., Comment: 5 pages, in: "Particle Physics on the Eve of LHC" (Proc. of the 13th Lomonosov Conference on Elementary Particle Physics, Moscow, August 2007), ed. by A.Studenikin, p.176, World Scientific, Singapore, 2008

We derive the modified Dirac equation for an electron undergos an influence of the standard model interaction with the nuclear matter. The exact solutions for this equation and the electron energy spectrum in matter are obtained. This establishes a rather powerful method for investigation of different processes that can appear when electrons propagate in background matter. On this basis we study in detail the spin light of electron in nuclear matter, a new type of electromagnetic radiation which can be emitted by an electron moving in dense matter., Comment: 11 pages in LaTex, 4 figures, typos corrected

We further generalize the powerful method, which we have recently developed for description of the background matter influence on neutrinos, for the case of an electron moving in matter. On the basis of the modified Dirac equation for the electron, accounting for the standard model interaction with particles of the background, we predict and investigate in some detail a new mechanism of the electromagnetic radiation that is emitted by moving in matter electron due to its magnetic moment. We have termed this radiation the ``spin light of electron" in matter and predicted that this radiation can have consequences accessible for experimental observations in astrophysical and cosmological settings., Comment: 5 pages in LaTex, in: "Particle Physics at the Year of 250th Anniversary of Moscow University", ed. by A.Studenikin, World Scientific, Singapore, 2006, p. 73 (Proceedings of the 12th Lomonosov Conference on Elementary Particle Physics, August 2005, Moscow)

A short review of the properties of the spin light of neutrino ($SL\nu$) in matter, supplied with some historical notes on the discussed subject, is given. It is shown that consideration of the $SL\nu$ in matter in hep-ph/0605114 is based on erroneous calculations which ignore the fact that the energy-momentum conservation law can not be violated for this process. An attempt to rename the $SL\nu$ in matter, undertaken in hep-ph/0606262, is groundless., Comment: 6 pages, contribution to the Proceedings of the 14th International Seminar on High Energy Physics "Quarks-2006" (St.-Petersburg, Repino, May 19-25, 2006); v2: a typo corrected

The claim of preprint hep-ph/0605114 that there is "no neutrino spin light because of photon dispersion in medium" is wrong.

We consider the matter effects on neutrinos moving in background on the basis of the corresponding quantum wave equations. Both Dirac and Majorana neutrino cases are discussed. The effects for Dirac neutrino reflection and trapping as well as neutrino-antineutrino annihilation and $\nu\overline{\nu}$ pair creation in matter at the interface between two media with different densities are considered. The spin light of neutrino in matter is also discussed., Comment: 11 pages, 2 figures, in: Proceedings of the 5th International Conference on Non-Accelerator New Physics (Dubna, Russia, June 20-25, 2005). V2: typos corrected

We develop the quantum theory of the spin light of neutrino ($SL\nu$) exactly accounting for the effect of background matter. Contrary to the already performed studies of the $SL\nu$, in this paper we derive explicit and closed expressions for the $SL\nu$ rate and power and for the emitted photon energy, which are valid for an arbitrary matter density (including very high values). The spatial distribution of the radiation power and the dependence of the emitted photon energy on the direction of radiation are also studied in detail for the first time. We analyze the $SL\nu$ polarization properties and show that within a wide range of neutrino momenta and matter densities the $SL\nu$ radiation is circularly polarized. Conditions for effective $SL\nu$ photon propagation in the electron plasma are discussed. It is also shown that in dense matter the average energy of the emitted photon can reach values in the range from one third of the neutrino momentum up to one half of the neutrino energy in matter. The main features of the studied radiation are summarized, and possibilities for the $SL\nu$ production during different astrophysical and cosmology processes are discussed., Comment: 15 pages, 7 figures, in: Proceedings of Les Recontres de Physique de la Vallee d'Aoste ("Results and Perspectives in Particle Physics", March 2005, La Thuile, Italy), ed. by Mario Greco, Frascati Physics Series, Italy, 2005; modified version is accepted for publication in Phys.Lett.B

We consider propagation of a massive neutrino in matter within the quantum approach based on the two equations for the neutrino field: the first one is the Dirac-Pauli equation for a massive neutrino in an external magnetic field generalized on the inclusion of effects of the background matter; the second one is the modified Dirac equation derived directly from the neutrino-matter interaction Lagrangian. On the basis of these two equations the quantum theory of a neutrino moving in the background matter is developed (the exact solutions of these equations are found and classified over the neutrino spin states, the corresponding energy spectra are also derived). Using these solutions we study within the quantum approach the spin light of neutrino ($SL\nu$) in matter with the effect of a longitudinal magnetic field being also incorporated. In particular, the $SL\nu$ radiation rate and total power are derived. The use of the generalized Dirac-Pauli equation also enables us to consider the $SL\nu$ in matter polarized under the influence of strong magnetic field., Comment: in: "Particle Physics in Laboratory, Space and Universe", ed. by Alexander Studenikin, World Scintific Publishing Co., Singapore, 2005, pp 55-64 (Proceedings of the 11th Lomonosov Conference on Elementary Particle Physics)

We predict a new mechanism for the spin light of neutrino ($SL\nu$) that can be emitted by a neutrino moving in gravitational fields. This effect is studied on the basis of the quasiclassical equation for the neutrino spin evolution in a gravitational field. It is shown that the gravitational field of a rotating object, in the weak-field limit, can be considered as an axial vector external field which induces the neutrino spin procession. The corresponding probability of the neutrino spin oscillations in the gravitational field has been derived for the first time. The considered in this paper $SL\nu$ can be produced in the neutrino spin-flip transitions in gravitational fields. It is shown that the total power of this radiation is proportional to the neutrino gamma factor to the fourth power, and the emitted photon energy, for the case of an ultra relativistic neutrino, could span up to gamma-rays. We investigate the $SL\nu$ caused by both gravitational and electromagnetic fields, also accounting for effects of arbitrary moving and polarized matter, in various astrophysical environments. In particular, we discuss the $SL\nu$ emitted by a neutrino moving in the vicinity of a rotating neutron star, black hole surrounded by dense matter, as well as by a neutrino propagating in the relativistic jet from a quasar., Comment: 14 pages in LaTex with 1 eps figure; derivation of the neutrino spin oscillations probability in gravitational fields and several clarifying notes are added, typos corrected