arXiv subjects

A. Kostin

Publications and source records attributed to A. Kostin.

10 recordsLinked to original sources

arXiv2025

CayleyPy Growth: Efficient growth computations and hundreds of new conjectures on Cayley graphs (Brief version)

This is the third paper of the CayleyPy project applying artificial intelligence to problems in group theory. We announce the first public release of CayleyPy, an open source Python library for computations with Cayley and Schreier graphs. Compared with systems such as GAP and Sage, CayleyPy handles much larger graphs and performs several orders of magnitude faster. Using CayleyPy we obtained about 200 new conjectures on Cayley and Schreier graphs, focused on diameters and growth. For many Cayley graphs of symmetric groups Sn we observe quasi polynomial diameter formulas: a small set of quadratic or linear polynomials indexed by n mod s. We conjecture that this is a general phenomenon, giving efficient diameter computation despite the problem being NP hard. We propose a refinement of the Babai type conjecture on diameters of Sn: n^2/2 + 4n upper bounds in the undirected case, compared to previous O(n^2) bounds. We also provide explicit generator families, related to involutions in a square with whiskers pattern, conjectured to maximize the diameter; search confirms this for all n up to 15. We further conjecture an answer to a question posed by V M Glushkov in 1968 on directed Cayley graphs generated by a cyclic shift and a transposition. For nilpotent groups we conjecture an improvement of J S Ellenberg's results on upper unitriangular matrices over Z/pZ, showing linear dependence of diameter on p. Some conjectures are LLM friendly, naturally stated as sorting problems verifiable by algorithms or Python code. To benchmark path finding we created more than 10 Kaggle datasets. CayleyPy works with arbitrary permutation or matrix groups and includes over 100 predefined generators. Our growth computation code outperforms GAP and Sage up to 1000 times in speed and size.

math.CO↗

arXiv2023

TreeDQN: Sample-Efficient Off-Policy Reinforcement Learning for Combinatorial Optimization

A convenient approach to optimally solving combinatorial optimization tasks is the Branch-and-Bound method. Its branching heuristic can be learned to solve a large set of similar tasks. The promising results here are achieved by the recently appeared on-policy reinforcement learning method based on the tree Markov Decision Process. To overcome its main disadvantages, namely, very large training time and unstable training, we propose TreeDQN (Tree Deep Q-Network), a sample-efficient off-policy RL method trained by optimizing the geometric mean of expected return. To theoretically support the training procedure for our method, we prove the contraction property of the Bellman operator for the tree MDP. As a result, our method requires up to 10 times less training data and performs faster than known on-policy methods on synthetic tasks. Moreover, TreeDQN significantly outperforms the state-of-the-art techniques on a challenging practical task from the ML4CO competition.

cs.LG↗

arXiv2020

The SuperFGD Prototype Charged Particle Beam Tests

A novel scintillator detector, the SuperFGD, has been selected as the main neutrino target for an upgrade of the T2K experiment ND280 near detector. The detector design will allow nearly 4π coverage for neutrino interactions at the near detector and will provide lower energy thresholds, significantly reducing systematic errors for the experiment. The SuperFGD is made of optically-isolated scintillator cubes of size 10x10x10 mm^3, providing the required spatial and energy resolution to reduce systematic uncertainties for future T2K runs. The SuperFGD for T2K will have close to two million cubes in a 1920x560x1840 mm^3 volume. A prototype made of 24x8x48 cubes was tested at a charged particle beamline at the CERN PS facility. The SuperFGD Prototype was instrumented with readout electronics similar to the future implementation for T2K. Results on electronics and detector response are reported in this paper, along with a discussion of the 3D reconstruction capabilities of this type of detector. Several physics analyses with the prototype data are also discussed, including a study of stopping protons.

physics.ins-det↗

arXiv2018

Magnetic-field Induced Interconversion of Cooper Pairs and Density Wave States within Cuprate Composite Order

Recent studies establish that the cuprate pseudogap phase is susceptible at low temperatures to forming not only a $d$-symmetry superconducting (SC) state, but also a $d$-symmetry form factor (dFF) density wave (DW) state. The concurrent emergence of such distinct and unusual states from the pseudogap motivates theories that they are "intertwined" i.e derived from a quantum composite of dissimilar broken-symmetry orders. Some composite order theories predict that the balance between the different components can be altered, for example at superconducting vortex cores. Here, we introduce sublattice phase-resolved electronic structure imaging as a function of magnetic field and find robust dFF DW states induced at each vortex. They are predominantly unidirectional and co-oriented (nematic), exhibiting strong spatial-phase coherence. At each vortex we also detect the field-induced conversion of the SC to DW components and demonstrate that this occurs at precisely the eight momentum-space locations predicted in many composite order theories. These data provided direct microscopic evidence for the existence of composite order in the cuprates, and new indications of how the DW state becomes long-range ordered in high magnetic fields.

cond-mat.supr-con↗

arXiv2018

A fully active fine grained detector with three readout views

This paper describes a novel idea of a fine-grained fully-active plastic scintillator detector made of many optically independent $1\times1\times1~\text{cm}^3$ cubes with readout on three orthogonal projections by wavelength shifting fibers. The original purpose of this detector is to serve as an active neutrino target for the detection, measurement and identification of the final state particles down to a few tenths MeV kinetic energies. The three readout views as well as the fine granularity ensure powerful localization and measurement of the deposited energy combined with good timing properties and isotropic acceptance. The possible application as a new active target for the T2K near detector, initial simulation studies and R&D test results are reported.

physics.ins-det↗

arXiv2017

Baby MIND: A magnetized segmented neutrino detector for the WAGASCI experiment

T2K (Tokai-to-Kamioka) is a long-baseline neutrino experiment in Japan designed to study various parameters of neutrino oscillations. A near detector complex (ND280) is located 280~m downstream of the production target and measures neutrino beam parameters before any oscillations occur. ND280's measurements are used to predict the number and spectra of neutrinos in the Super-Kamiokande detector at the distance of 295~km. The difference in the target material between the far (water) and near (scintillator, hydrocarbon) detectors leads to the main non-cancelling systematic uncertainty for the oscillation analysis. In order to reduce this uncertainty a new WAter-Grid-And-SCintillator detector (WAGASCI) has been developed. A magnetized iron neutrino detector (Baby MIND) will be used to measure momentum and charge identification of the outgoing muons from charged current interactions. The Baby MIND modules are composed of magnetized iron plates and long plastic scintillator bars read out at the both ends with wavelength shifting fibers and silicon photomultipliers. The front-end electronics board has been developed to perform the readout and digitization of the signals from the scintillator bars. Detector elements were tested with cosmic rays and in the PS beam at CERN. The obtained results are presented in this paper.

physics.ins-det↗

arXiv2017

Baby MIND Experiment Construction Status

Baby MIND is a magnetized iron neutrino detector, with novel design features, and is planned to serve as a downstream magnetized muon spectrometer for the WAGASCI experiment on the T2K neutrino beam line in Japan. One of the main goals of this experiment is to reduce systematic uncertainties relevant to CP-violation searches, by measuring the neutrino contamination in the anti-neutrino beam mode of T2K. Baby MIND is currently being constructed at CERN, and is planned to be operational in Japan in October 2017.

physics.ins-det↗

arXiv2017

Baby MIND: A magnetised spectrometer for the WAGASCI experiment

The WAGASCI experiment being built at the J-PARC neutrino beam line will measure the difference in cross sections from neutrinos interacting with a water and scintillator targets, in order to constrain neutrino cross sections, essential for the T2K neutrino oscillation measurements. A prototype Magnetised Iron Neutrino Detector (MIND), called Baby MIND, is being constructed at CERN to act as a magnetic spectrometer behind the main WAGASCI target to be able to measure the charge and momentum of the outgoing muon from neutrino charged current interactions.

physics.ins-det↗

arXiv2016

Detection of a Cooper-Pair Density Wave in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$

The quantum condensate of Cooper-pairs forming a superconductor was originally conceived to be translationally invariant. In theory, however, pairs can exist with finite momentum $Q$ and thereby generate states with spatially modulating Cooper-pair density. While never observed directly in any superconductor, such a state has been created in ultra-cold $^{6}$Li gas. It is now widely hypothesized that the cuprate pseudogap phase contains such a 'pair density wave' (PDW) state. Here we use nanometer resolution scanned Josephson tunneling microscopy (SJTM) to image Cooper-pair tunneling from a $d$-wave superconducting STM tip to the condensate of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$. Condensate visualization capabilities are demonstrated directly using the Cooper-pair density variations surrounding Zn impurity atoms and at the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ crystal-supermodulation. Then, by using Fourier analysis of SJTM images, we discover the direct signature of a Cooper-pair density modulation at wavevectors $Q_{p} \approx (0.25,0)2π/ a_{0}$;$(0,0.25)2π/ a_{0}$ in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$. The amplitude of these modulations is ~5% of the homogenous condensate density and their form factor exhibits primarily $s$/$s'$-symmetry. This phenomenology is expected within Ginzburg-Landau theory when a charge density wave with $d$-symmetry form factor and wave vector $Q_{c}=Q_{p}$ coexists with a homogeneous $d$-symmetry superconductor ; it is also encompassed by several contemporary microscopic theories for the pseudogap phase.

cond-mat.supr-con↗

arXiv2013

On categorical semigroups

The structure of categorical at zero semigroups is studied from the point of view their likeness to categories.

math.GR↗