arXiv subjects

Alexander Grigoriev

Publications and source records attributed to Alexander Grigoriev.

At least 19 recordsLinked to original sources

arXiv2026

Constrained graph generation: Preserving diameter and clustering coefficient simultaneously

Generating graphs subject to strict structural constraints is a fundamental computational challenge in network science. Simultaneously preserving interacting properties-such as the diameter and the clustering coefficient- is particularly demanding. Simple constructive algorithms often fail to locate vanishingly small sets of feasible graphs, while traditional Markov-chain Monte Carlo (MCMC) samplers suffer from severe ergodicity breaking. In this paper, we propose a two-step hybrid framework combining Ant Colony Optimization (ACO) and MCMC sampling. First, we design a layered ACO heuristic to perform a guided global search, effectively locating valid graphs with prescribed diameter and clustering coefficient. Second, we use these ACO-designed graphs as structurally distinct seed states for an MCMC rewiring algorithm. We evaluate this framework across a wide range of graph edge densities and varying diameter-clustering-coefficient constraint regimes. Using the spectral distance of the normalized Laplacian to quantify structural diversity of the resulting graphs, our experiments reveal a sharp contrast between the methods. Standard MCMC samplers remain rigidly trapped in an isolated subset of feasible graphs around their initial seeds. Conversely, our hybrid ACO-MCMC approach successfully bridges disconnected configuration landscapes, generating a vastly richer and structurally diverse set of valid graphs.

cs.SI↗

arXiv2026

Spin Light of neutrino in polarized matter

The Spin Light of neutrino ($SL\nu$) is an electromagnetic radiation of the neutrino magnetic moment emitted when neutrino moves in external conditions (fields or matter). The effect can be of significance in the extremely dense matter of compact astrophysical objects such as neutron stars (NS). If detected, this radiation could provide a fair opportunity to study the properties of neutrinos and the medium through which they move, since the properties of the radiation depend on both. Motivated by the possibility of the nuclear matter spin-polarization, in this paper, we study the new properties to $SL\nu$ obtained under the influence of net matter polarization. We demonstrate that the polarization can enhance or completely suppress the radiation. Also, it introduces a characteristic asymmetry into the total radiation from the compact object, which could be an observable feature dependent on the matter polarization and the magnetic field inside the stellar (if the field is connected to the stellar matter polarization). The research may have implications for the physics of NS and magnetars, bringing us closer to the possibility of studying their internal structure.

hep-ph↗

arXiv2025

On the Diameter of Arrangements of Topological Disks

Let $\mathcal{D}=\{D_0,\ldots,D_{n-1}\}$ be a set of $n$ topological disks in the plane and let $\mathcal{A} := \mathcal{A}(\mathcal{D})$ be the arrangement induced by $\mathcal{D}$. For two disks $D_i,D_j\in\mathcal{D}$, let $\Delta_{ij}$ be the number of connected components of $D_i\cap D_j$, and let $\Delta := \max_{i,j} \Delta_{ij}$. We show that the diameter of $\mathcal{G}^*$, the dual graph of $\mathcal{A}$, can be bounded as a function of $n$ and $\Delta$. Thus, any two points in the plane can be connected by a Jordan curve that crosses the disk boundaries a number of times bounded by a function of $n$ and $\Delta$. In particular, for the case of two disks, we prove that the diameter of $\mathcal{G}^*$ is at most $\max\{2,2\Delta\}$ and this bound is tight. For the general case of $n>2$ disks, we show that the diameter of $\mathcal{G}^*$ is $O(n^3 2^n \Delta)$. We achieve this by proving that the number of maximal faces in $\mathcal{A}$ -- faces whose ply is more than the ply of their neighboring faces -- is $O(n^2 2^n \Delta)$. To this end, we first show that the number of maximum faces -- faces whose ply is $n$ -- is $O(n^2\Delta)$; the latter bound, which is of independent interest, is tight in the worst case.

math.CO↗

arXiv2025

A Bayesian approach to aggregated chemical exposure assessment

Human exposure to chemicals commonly arises from multiple sources, yet traditional assessments often treat these sources in isolation, overlooking their combined impact. We introduce a Bayesian framework for aggregated chemical exposure assessment that explicitly accounts for these intertwined pathways. By integrating diverse datasets - such as consumption surveys, demographics, chemical measurements, and market presence - our approach addresses typical data challenges, including missing values, limited sample sizes, and inconsistencies, while incorporating relevant prior knowledge. Through a simulation-based strategy that reflects the full spectrum of individual exposure scenarios, we derive robust, population-level estimates of aggregated exposure. We demonstrate the value of this method using titanium dioxide, a chemical found in foods, dietary supplements, medicines, and personal care products. By capturing the complexity of real-world exposures, this comprehensive Bayesian approach provides decision-makers with more reliable probabilistic estimates to inform public health policies.

stat.AP↗

arXiv2025

Optimizing Periodic Operations for Efficient Inland Waterway Lock Management

In inland waterways, the efficient management of water lock operations impacts the level of congestion and the resulting uncertainty in inland waterway transportation. To achieve reliable and efficient traffic, schedules should be easy to understand and implement, reducing the likelihood of errors. The simplest schedules follow periodic patterns, reducing complexity and facilitating predictable management. Since vessels do not arrive in perfectly regular intervals, periodic schedules may lead to more wait time. The aim of this research is to estimate this cost by evaluating how effective these periodic schedules manage vessel traffic at water locks. The first objective is to estimate a periodic arrival pattern that closely matches a dataset of irregular vessel arrivals at a specific lock. We develop an algorithm that, given a fixed number of vessel streams, solves the problem in polynomial time. The solution then serves as input for the subsequent part, where we consider algorithms that compute operational schedules by formulating an optimisation problem with periodic arrival patterns as input, and the goal is to determine a periodic schedule that minimises the long-run average waiting time of vessels. We present a polynomial-time algorithm for the two-stream case and a pseudo-polynomial-time algorithm for the general case, along with incremental polynomial-time approximation schemes. In our numerical experiments, use AIS data to construct a periodic arrival pattern closely matching the observed data. Our experiments demonstrate that when evaluated against actual data, intuitive and straightforward policies often outperform optimal policies specifically trained on the periodic arrival pattern.

cs.DS↗

arXiv2025

A polynomial delay algorithm generating all potential maximal cliques in triconnected planar graphs

We develop a new characterization of potential maximal cliques of a triconnected planar graph and, using this characterization, give a polynomial delay algorithm generating all potential maximal cliques of a given triconnected planar graph. Combined with the dynamic programming algorithms due to Bouchitt{\'e} and Todinca, this algorithm leads to a treewidth algorithm for general planar graphs that runs in time linear in the number of potential maximal cliques and polynomial in the number of vertices.

cs.DS↗

arXiv2025

Combinatorial properties of continuous graphs: A survey of challenges, solutions and open problems

Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set, Vertex Cover, Chromatic Number and Treewidth problems on, so-called, continuous or metric graphs where every edge is represented by a unit-length continuous interval rather than by a pair of vertices. If any point of any unit-interval edge is considered as a possible member of a hitting set or a cover, the classical combinatorial problems become trickier and many open questions arise. Notably, in many real-life applications, such a continuous view of a graph is more natural than the classic combinatorial definition of a graph. The contribution of this paper is twofold: i) we survey the known results for optimization problems on continuous graphs, and ii) we create a list of open problems related to the continuous graphs.

math.CO↗

arXiv2023

Neutrino propagation in moving and polarized matter

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).

hep-ph↗

arXiv2023

Envy-free dynamic pricing schemes

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.

cs.GT↗

arXiv2020

On the status sequences of trees

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.

math.CO↗

arXiv2019

Knot Diagrams of Treewidth Two

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.

cs.DS↗

arXiv2018

Dispersing obnoxious facilities on a graph

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 $δ$ from each other. We investigate the complexity of this problem in terms of the rational parameter $δ$. The problem is polynomially solvable, if the numerator of $δ$ is $1$ or $2$, while all other cases turn out to be NP-hard.

cs.DS↗

arXiv2018

Optimal policy design for the sugar tax

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.

econ.TH↗

arXiv2018

On possible application of spin light of neutrino in astrophysics

The $ spin $ $ light$ $ of $ $neutrino $ ($SLν$) 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 $SLν$ can be manifested in principle.

hep-ph↗

arXiv2017

Combinatorial Properties and Recognition of Unit Square Visibility Graphs

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.

cs.CG↗

arXiv2017

Spin light of neutrino in astrophysical environments

The ${\it {spin \ \ light \ \ of \ \ neutrino}}$ ($SLν$) 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 $SLν$ might be of interest in the case of neutrinos propagating in dense matter. An advanced view on the $SLν$ 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 $SLν$ 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 $SLν$ specific polarization properties this electromagnetic mechanism is of interest in the connection with the observed polarization of GRB emission.

hep-ph↗

arXiv2016

Neutrino spin-flavor oscillations derived from the mass basis

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.

hep-ph↗

arXiv2015

High Multiplicity Scheduling with Switching Costs for few Products

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.

math.OC↗